e - surface water information system - secondary...

e - Surface Water Information System - Secondary Validation

Training Manual

Copyright © 10/14/2013 by Central Water Comission. All Rights Reserved.


Table of contents

Chapter 1: Surface Water Data Processing .......................................................3Chapter 2: Different Types and Forms of Surface Water Data ..........................8Chapter 3: Primary Validation for Rainfall Data................................................18Chapter 4: Secondary Validation of Rainfall Data.............................................26Chapter 5: Correct and Complete of Rainfall Data ...........................................42Chapter 6: Compile Rainfall Data......................................................................54Chapter 7: Primary Validation for Climatic Data ..............................................61Chapter 8: Secondary Validation for Climatic Data ..........................................69Chapter 9: Analysing of Climatic Data..............................................................72Chapter 10: Primary Validation of Water Level Data........................................79Chapter 11: Secondary Validation of Water Level Data....................................86Chapter 12: Correct and Complete Water Level Data .....................................94Chapter 13:Primary Validation of Stage Data..................................................100Chapter 14: Secondary Validation of Stage Data............................................105Chapter 15: Secondary Validation of Discharge Data.....................................112Chapter 16: Compute Discharge Data ............................................................118Chapter 17: Correct and Complete Discharge Data........................................122Chapter 18: Compile Discharge Data..............................................................129Chapter 19: Analyse Discharge Data..............................................................132Chapter 20: Stage Discharge Rating Curve.....................................................143Chapter 21: Validate Rating Curve..................................................................171Chapter 22: Extrapolate Rating Curve............................................................177

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Chapter 1: Surface Water Data Processing

After entering Surface water data using eSWIS Secondary Validation tools of eSWIS is used for data processing.

Processing of hydrological data is a big process. It is carried out in a series of stages, starting with preliminary checking in the field, through receipt of raw data at Sub-divisional offices and successively higher levels of validation.

Processing and validation of hydrological data require an understanding of field practices. This includes the principles and methods of observation in the field and the hydrological variable being measured. It must never be considered as a purely statistical exercise. With knowledge of measurement techniques, typical errors can be identified. Similarly knowledge of the regime of a river will facilitate the identification of spurious data. For example for river level or flow, a long period at a constant level followed by an abrupt change to another period of static level would be identified as suspect data in a natural catchment but possibly due to dam operation in a regulated river.

1. Data validationData Validation is the process by which data is checked to ensure that the final figure stored is the best possible representation of the true value of the variable at the measurement site at a given time or in a given interval of time. Validation recognizes that values observed or measured in the field are subject to errors and that undetected errors may also arise in data entry, in computation and, (hopefully infrequently) from the mistaken ‘correction’ of good data.

Validation is carried out for three reasons:

1. To correct errors in the recorded data where ever possible, 2. To assess the reliability of a record even where it is not possible to correct errors and3. To identify the source of errors and thus to ensure that such errors are not

repeated in future.

Errors can be classified as random or systematic or spurious in nature:

Random errors are sometimes referred to as experimental errors and are equally distributed about the mean or ‘true’ value. The errors of individual readings may be large or small, e.g. the error in a staff gauge reading where the water surface is subject to wave action, but they tend to compensate with time or by taking a sufficient number of measurements.

Systematic errors is where there is a systematic difference, either positive or negative, between the measured value and the true value and the situation is not improved by increasing the number of observations. For Example, Using of wrong rain gauge measure or the effect on a water level reading of undetected slippage of a staff gauge. Hydrometric field measurements are often subject to a combination of random and systematic errors. Systematic errors are generally the more serious and are what the validation process is designed to detect and if possible to correct.

Spurious errors are sometimes distinguished from random and systematic errors as due to some abnormal external factor. An example might be an

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evaporation pan record where animals have been drinking from the pan, or a current meter gauging result using a very bent spindle. Such errors may be readily recognized but cannot so easily be statistically analyzed and the measurements must often be discarded.

Fig. 1: Classification of measurement errors

Typical errors at observation stations are as follows:

From faulty equipment, e.g. thermometer with air bubbles in column.

From malfunction of instrument, e.g. slippage of float tape in level recorder (systematic but not constant)

From improper instrument setting by observer, e.g. level recorder compared with staff gauge (systematic)

From exposure conditions, e.g. stilling well blocked so that measured level in well differs from the river (systematic)

Personal observation errors, e.g. gauge misread or value interpolated away from site (random or spurious)

Transcription error in writing the observed reading Error in field computation, e.g. current meter measurements.

Variables may be directly measured (e.g. rainfall) or they may be derived using a relationship with one or more other variables (e.g. discharge). In the latter case the error in the derived value depends both on the field measurements and on the error in the relationship which is both random and systematic, the latter being particularly important if based on a relationship extrapolated beyond the limits of observation.

As a consequence of such errors it is important not only to ensure the use of good equipment and observational procedures but also to monitor the quality of all the data received. Validation procedures must be applied in a rigorous and standardized manner.

Validation involves a process of sequential and complementary comparisons of data and includes:

For a single data series, between individual observations and pre-set physical limits

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For a single series between sequential observations to detect unacceptable rates of change and deviations from acceptable hydrological behavior most readily identified graphically.

Between two measurements of a variable at a single station, e.g. daily rainfall from a daily gauge and an accumulated total from a recording gauge

Between two or more measurements at neighboring stations, e.g. flow at two points along a river

Between measurements between different but related variables, e.g. rainfall and river flow

Improvement in computing facilities now enables such validation to be carried out whereas in the past the volume of data the time required to carry out manual validation was prohibitive.

1. Levels of validation

It is preferable to carry out the data validation as soon as the data is observed and as near to the observation station as possible. This ensures that information which may be essential to support the inferences of data validation is fresh in minds of the field staff and supervisors and that interaction between field and processing staff is possible. However, to provide full validation close to observation sites is impractical both in terms of computing equipment and staffing and a compromise must be reached which recognizes both the wide geographical spread of observation stations and the staff and equipment available. The sequence of validation steps has therefore been divided so that those steps which primarily require interaction with the observation station are carried out in close proximity (i.e. at Sub-divisional office) whereas the more complex comparisons are carried out at higher levels.

Thus, data validation can be grouped into two major categories:

(a) Primary data validation:

Primary validation is primarily involved with comparisons within a single data series and is concerned with making comparisons between observations and pre-set limits and/or statistical range of a variable or with the expected hydrological behavior of a hydrological phenomenon. However, information from a few nearby stations within a limited area may also sometimes be available and these may be used while carrying out primary validation for example with respect to daily rainfall data. eSWIS provides options to facilitate the primary validation with as little effort and ambiguity as possible.

Primary data validation highlights those data which are not within the expected range or are not hierologically consistent. These data are then revisited in the data sheets or analogue records to see if there was any error while making computations in the field or during keying-in the data. If it is found that the entered value(s) are different than the recorded ones then such entries are immediately corrected. Where such data values are found to have been correctly entered they are then flagged as doubtful with a remark against the value in the computer file indicating the reason of such a doubt.

Apart from data entry errors, suspect values are identified and flagged but not amended at the Sub-divisional level. However the flag and remarks provide a basis for further consideration of action at the time of secondary and final data validation.

(b) Secondary data validation

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Secondary data validation is done after primary validation has been carried out.

Secondary validation consists of comparisons between the same variable at two or more stations and is essentially to test the data against the expected spatial behavior of the system. Secondary validation is based on the spatial information available from a number of neighboring observation stations within a comparatively large area. The assumption, while carrying out such comparison, is that the variable under consideration has adequate spatial correlation within the distances under consideration. Such correlation must be confirmed in advance on the basis of historical records and the experience thus gained in the form of various types of statistics is utilized while validating the data. Qualitative evaluation of this relationship is not very difficult to make. For certain hydrological variables like water levels and discharges, which bear a very high degree of dependence or correlation between adjoining stations, the interrelationship, can be established with a comparatively higher level of confidence. However, for some variables which lack serial correlation and show great spatial variability (e.g. convectional rainfall), it is difficult to ascertain the behavior with the desired level of confidence. In such circumstances, it becomes very difficult, if not impossible, to detect errors.

While validating the data on the basis of a group of surrounding stations, the strategy must always be to rely on certain key stations known to be of good quality. If all the observation stations are given the status of being equally reliable then data validation will become comparatively more difficult. This is not done merely to make the data validation faster but on the understanding based on field experience that the quality of data received from certain stations will normally be expected to be better than others. This may be due to physical conditions at the station, quality of instruments or reliability of staff etc. It must always be remembered that these key or reliable stations also can report incorrect data and they do not enjoy the status of being absolutely perfect.

As for the primary data validation, for the secondary data validation the guiding factor is also that none of the test procedures must be considered as absolutely objective on their own. They must always be taken as tools to screen out certain data values which can be considered as suspect. The validity of each of these suspect values is then to be confirmed on the basis of other tests and corroborative facts perhaps based on information received from the station. It is only when it is clear that a certain value is incorrect and an alternative value provides a more reliable indication of the true value of the variable that suitable correction should be applied and the value be flagged as corrected.

If it is not possible to confidently conclude that the suspected value is incorrect then such values will be left as they have been recorded with proper flag indicating them as doubtful. All those data which have been identified as suspicious at the level of primary validation are to be validated again on the basis of additional information available from a larger surrounding area. All such data which are supported by the additional spatial information must be accepted as correct and accordingly the flags indicating them as doubtful must be removed at this stage.

2. Data in-filling (completion) and correctionRaw observed data may have missing values or sequences of values due to equipment malfunction, observer absence, etc. these gaps should, where possible, be filled to make the series complete. In addition, all values flagged as doubtful in validation must be reviewed to decide whether they should be replaced by a corrected value or whether doubt remains as to reliability but a more reliable correction is not possible and the original value then remains with a flag.

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In-filling or completion of a data series is done in a variety of ways depending on the length of the gap and the nature of the variable. The simplest case is where variables are observed with more than one instrument at the same site (e.g. daily rain gauge and recording gauge); the data from one can be used to complete the other. For single value or short gaps in a series with high serial correlation, simple linear interpolation between known values may be acceptable or values filled with reference to the graphical plot of the series. Gaps in series with a high random component and little serial correlation such as rainfall cannot be filled in this way and must be completed with reference to neighboring stations through spatial interpolation. Longer gaps will be filled through regression analysis or ultimately through rainfall runoff modeling. However, it must be emphasized here that various methods used for in-filling or correction will affect the statistics of the variable unless care is also taken with respect to its randomness. Nevertheless, it is not advisable to use completed or corrected data for the purpose of designing an observational network.

Data correction is to be done using similar procedures as used for completing the data series.

3. Data compilationCompilation refers primarily to the transformation of data observed at a certain time interval to a different interval. e.g. hourly to daily, daily to monthly, monthly to yearly. This is done by a process of aggregation. Occasionally disaggregation, for example from daily to hourly is also required.

Compilation also refers to computation of areal averages, for example catchment rainfall. Both areal averaging and aggregation are required for validation, for example in rainfall runoff comparisons, but also provide a convenient means of summarizing large data volumes.

Derived series can also be created, for example, maximum, minimum and mean in a time interval or a listing of peaks over a threshold, to which a variety of hydrological analyses may be applied.

4. Data analysisProcedures used in data validation and reporting have a wider analytical use, following are examples of available techniques:

1) Basic statistics (means standard deviations, etc.)

2) statistical tests 3) fitting of frequency distributions 4) flow duration series 5) regression analysis 6) rainfall depth-area-duration 7) rainfall intensity-frequency-duration

5. Data reporting

Periodic publication of special reports showing long term statistics of stations or special reports on unusual events may also be prepared.

This can be prepared in digital form on magnetic media thus avoiding the need to re-key the data to computer. A wide range of pdf and graphical formats is available, for example showing comparisons of current year values with long-term statistics, thematic maps of variables such as annual and seasonal rainfall, duration and frequency curves, etc. More detailed information such as stage discharge ratings can be provided to meet specific needs.

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Chapter 2: Different Types and Forms of Surface Water Data

Data can be classified in terms of hydrological variables - water level, rainfall etc. However data types may be grouped or divided in quite different ways to simplify computer processing and management. Hydrological variables can then be considered within this new framework.

Hydrological data can be classified following three major categories:

1. Space-oriented data: Space-oriented data comprise all the information related to physical characteristics of catchments, rivers, lakes and reservoirs. They also include the characteristics of observational stations and data series and various attributes associated with

2. Time oriented data: Time-oriented data comprise all the hydro-meteorological, quality and quantity data for which observations are periodically made in time at various observational stations. Time-oriented data can be equidistant, cyclic or non-equidistant in nature according to whether the observations are made at intervals which are equal, unequal but at defined intervals, or at unequal intervals. Most surface water data is equidistant or cyclic.

3. Relation oriented data: Relation-oriented data comprise information about the relationships established between two or more variables. Stage-discharge data and the calibration ratings of various instruments can also be considered under this category of relation-oriented data.

A brief description of each type of data available in HIS is presented here.

1. Space-oriented dataSpace-oriented data comprise:

a) Catchment data: physical and morphological characteristics b) River data: cross-sections, profile c) Reservoir data: elevation-area d) Station data: characteristics, history etc.

a) Catchment data: physical and morphological characteristics

The physical characteristics of the catchment, of hydrological relevance, its geographical area, the layout of the river network and topographical features. River network characteristics in terms of number, length and area for different stream orders can be associated with any catchment. Such geographical information is generally available in the form of maps from which it may be digitized, or may be derived from the remotely sensed data. Each element of the space-oriented data is referenced by its position using a co-ordinate system referred to latitude and longitude. Such geographical data can be organized in different map layers so that it is possible to use one or more such layers at any time.

b) River data: cross-sections, profile

River channel cross sections, longitudinal profiles and bed characteristics are needed for many hydrological applications. This type of data can be considered as semi-static and therefore must be obtained for each observation station at adequate intervals of time. River cross sections at gauging stations are of prime importance in interpreting stage-discharge

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data. Each cross section data set must therefore be associated with a period of applicability. Similarly, longitudinal profile data at each gauging station is to be associated with a time period.

c) Reservoir data: elevation-area

Such data based on topographic survey of a lake or reservoir might also be considered as physical or morphological data but, because of the structure of the data, are considered separately. Data are structured as a matrix of elevation and area for a lake or reservoir that is represented by an observational station. Such data are used in estimation of its capacity and evaporation corresponding to different levels. Each such matrix again has to be associated with the period of applicability.

d) Station data: characteristics, history etc.

A wide variety of information can be associated with each gauging station. This includes names and codes which are used for identification, attributes which are used to categorize and descriptive information which is used for station management or for assessing the quality of data processing.

Every observational station is given a unique station code. Other station characteristics include:

station name, type of station, administrative units (state, district and tehsil), drainage boundaries (major river basin/zone, tributary to independent river and

local river/basin), location (latitude and longitude), altitude, catchment area (for river gauging stations), reference toposheet number (w.r.t. 1:50,000 scale maps of Survey of India), agency in charge of the station, controlling offices (regional/state, circle,

division, sub-division and section office)

A record of the historical background of the station must also be maintained. Such a record must include the details of setting up of the station and of any major activity or change in its location, equipment installation or observational procedures. Special mention is made of records of the reduced level of the gauge zero for which a historical record of changes must be maintained.

2. Time-oriented data

Time series data include all those measurements which have an associated observation time, whether the measurement is of an instantaneous value (e.g. water level), an accumulative value (e.g. daily rainfall), a constant value (e.g. a gate overflow level setting), an averaged value (e.g. mean monthly discharge) or a statistic from a specified time period (e.g. daily maximum temperature, annual maximum flow). The distinction between instantaneous and accumulative values is of importance in determining whether in aggregation to another time interval, they should be averaged (e.g. flow) or accumulated (e.g. rainfall)

Time series data can be classified as follows:

a) Equidistant time series are all those measurements which are made at regular intervals of time (hourly, 3-hourly, daily) whether by manual observation, by

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abstraction of values at regular intervals from a chart, or digitally. Values may be instantaneous, accumulative or averaged. In such a series the associated time of measurement can be generated automatically by the computer and does not require entry with each entered value of the variable.

Cyclic time series are those measurements which are made at irregular intervals of time but where the irregular time sequence is repeated from day to day. An example is the observation of temperature measured twice daily at 0830 and 1730 hrs. Again, once the times of observation are specified, the associated time of measurement does not require entry with each entered value of the variable.

b) Non-equidistant time series are those measurements which are made at irregular intervals of time in which the time is not pre-specified. Such values are generally instantaneous. An example is the recording of tipping bucket rainfall where each tip of the bucket recording the occurrence of a depth (e.g. 0.5 mm) has an associated registered time. Another example is the irregular manual dipping of well level. Constant series may also be non-equidistant. Such series require entry of the time of occurrence with each entered value of the variable. In the case of digitally recorded data (e.g. tipping bucket rainfall) this entry is made by transfer from a logger file.

Hydrological variables may then be considered in their more conventional groupings of meteorological, hydrological and water quality. Within these groups the treatment of individual variables is outlined with reference to the above classification.

1. Meteorological data

Meteorological information has a variety of purposes but, with respect to hydrology, the meteorological network is primarily concerned with storage and transfer of water between the land and atmospheric portions of the hydrological cycle. Meteorological data that are strongly related to the hydrological processes are thus required in HIS. Precipitation being the primary source of fresh water is essential for most hydrological studies. The other major variable is evapo-transpiration for which data are needed for hydrological budgeting. As it is difficult to measure evapo-transpiration directly, indirect methods are generally used to estimate it. Such indirect estimation requires measurement of a range of meteorological variables which control the evaporative processes. Alternatively estimates may be made from directly measured evaporation in an evaporation pan

Meteorological and climatic variables required in the HIS are categorized and described below:

I. precipitation II. pan evaporation

III. temperature IV. air pressure V. atmospheric humidity

VI. wind speed and direction VII. sunshine VIII. derived meteorological variables

I. Precipitation data Observations on point precipitation are made regularly at a number of observational stations suitably distributed in space. Precipitation experienced throughout the project area is in the form of rainfall, and raingauges are installed for its observation. Presently there are three types of raingauges in use. They are:

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Standard or ordinary raingauges (SRG) which are read manually. The standard raingauge data is recorded once or twice a day at fixed hours at 0830 and 1730 hrs. (some agencies like CWC record at 0800 hrs and 2000 hrs.). Daily observations are taken in the morning hours. Once-daily readings are thus equidistant and accumulative; twice-daily readings are cyclic and accumulative.

Autographic or self-recording raingauges (ARG). Data from autographic raingauges is available in the form of a continuous plot from which the data are read manually and tabulated at hourly intervals corresponding to standard timings of the daily rainfall (again equidistant).

Automatic raingauges having data logger. Data from automatic raingauges is available in digital form directly through its data logger and is recorded either as rainfall at fixed interval (usually half an hour) (equidistant) or as timings for each event of rainfall of fixed quantity (usually 1 mm or 0.5 mm) (non-equidistant).

II. Pan evaporation data

Evaporation records for pans are frequently used to estimate evaporation form lakes and reservoirs and evapo-transpiration from an area. US Class A pans are employed in India for measuring pan evaporation. Evaporation pan readings are taken once (equidistant and accumulative) or twice a day (cyclic) at standard times at 0830 and 1730 hrs. Daily observations are taken in the morning hours.

III. Temperature

Temperature is primarily of interest to hydrology as a controlling variable in the evaporative processes. The temperature of air, of the soil and of water bodies is all of interest. Periodic observations of air temperature are made using thermometers whereas continuous record is obtained using thermographs. Four types of thermometers, dry bulb, wet bulb, maximum and minimum thermometers are in use. Dry-bulb thermometer is used to measure temperature of the surrounding air. Wet-bulb thermometer is used to measure the temperature of the saturated air for determining relative humidity and dew point of the surrounding air. Maximum and minimum thermometers indicate the maximum and minimum temperatures of the surrounding air achieved since the last measurement. Observations for these four temperatures are made once or twice a day at standard times at 0830 and 1730 hrs (equidistant and instantaneous for dry and wet bulb and their derivatives; equidistant and statistic for maximum and minimum temperatures). Data from the thermograph is tabulated at hourly intervals (equidistant and instantaneous).

Water temperature of a water body may be considered a water quality parameter, influencing the rate of chemical and biological activity in the water. Water temperature measured at an evaporation pan is a factor in determining evaporation.

IV. Pressure Atmospheric pressure influences the rate of evapo-transpiration and is a useful though not a critical variable in its estimation. At any point it is the weight of the air column that lies vertically above the unit area. It is usually observed using a mercury barometer for instantaneous data and can also be continuously recorded using a barograph. The observations from barometer are made daily (equidistant and instantaneous) or twice daily (cyclic) at standard times at 0830 and 1730 hrs. The thermograph record is tabulated at hourly intervals corresponding to the standard timing of the daily observations (equidistant).

V. Humidity

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Atmospheric humidity is a most important influence on evapotranspiration. Direct measurement of relative humidity is accomplished using a hygrograph. Indirect estimation of relative humidity is accomplished using dry and wet bulb temperature records. The estimated humidity from the dry and wet bulb temperatures are obtained daily (equidistant and instantaneous) or twice daily at standard times at 0830 and 1730 hrs. The continuous record obtained from the hygrograph is tabulated at hourly intervals.

VI. Wind speed and direction

Wind speed and direction is of importance while estimating the evapo-transpiration. Wind speed and wind direction is measured using anemometer and wind vane respectively. Observations are made daily or twice daily at standard times at 0830 and 1730 hrs. Wind speed measurements may be instantaneous or, if wind run over a time interval is observed, then it is accumulative. Wind direction may influence measured evaporation totals if the surrounding environment in terms of wetness differs in different directions It is not normally used in calculations but if required, it can be recorded on a 16-point scale.

VII. Sunshine duration

The duration of sunshine is a useful variable in estimation of evapotranspiration. The instrument commonly employed for observation of sunshine duration is the Campbell Stokes sunshine recorder. The lengths of burnt traces on the sunshine card indicate the sunshine duration. Sunshine duration data is tabulated for each hourly duration in the day and is considered as of equidistant and accumulative nature.

VIII. Derived meteorological quantities

Several meteorological quantities are only estimated from other directly measured meteorological variables. Such quantities are relative humidity, dew point temperature, estimated lake or reservoir evaporation and evapo-transpiration. Some are manually-derived before entry to computer whilst others (e.g. evapotranspiration) are computed using HIS software from other variables previously entered.

2. Hydrological data

Quantitative records of time series of level (stage) and flow in surface water bodies constitute the bulk of hydrological data. Direct measurement of water level data is made using a variety of equipment. Measurement of flows is comparatively difficult to accomplish and is therefore estimated indirectly by using the stage-discharge relationship. However, intermittent measurements of flow are made for the establishment of the stage-discharge relationship (held as relation-oriented data). A brief description of time series hydrological data in the HIS is given below.

Water level data Water level is observed in three ways:

from staff gauges from autographic water level (chart) recorders from digital type water level recorders.

From the staff gauges the observations are generally made once in a day in lean season (equidistant and instantaneous) and at multiple times a day (equidistant or cyclic and instantaneous) during flood. For a flashy river staff gauges may even be read at hourly intervals during the flood season. However, standard timings are generally followed for the observations during the day by different agencies.

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An autographic (chart) type of water level recorder on the other hand gives a continuous record of water level in time from which levels must be extracted manually, usually at an hourly interval, before entry to the computer.

Digital data from a digital water level recorder can either be at equal intervals of time, usually at quarter or half hour interval, or can be reported only for those instants when there is a change in water level which is more than a pre-set amount (non-equidistant and instantaneous). Such a non-equidistant record can be converted to an equidistant record by interpolation.

Derived hydrological quantities

As mentioned above the direct observation of discharge is made only for the purpose of establishing the stage-discharge relationship. Once the relationship is established, the same can be used to transform observed stages into a derived time series of discharge.

Water Quality data

Water quality parameters can rarely be measured continuously and are therefore based on sampling which may be at regular intervals (equidistant) or more often at irregular intervals (non-equidistant) and the recorded values represent the state of the water at a particular time (instantaneous). More important water quality parameters or those which change more rapidly with time are measured with greater frequency than those which are conservative in character.

Water quality analysis is carried out for certain field parameters at the observation station. Many analyses require more sophisticated equipment and are therefore determined at a divisional laboratory where they are entered.

Water quality parameters take many forms and there is a wide range of measurement techniques and units used. The following groups may be distinguished:

I. organic matter II. dissolved oxygen

III. major and minor ions IV. toxic metals and organic compounds V. nutrients

VI. biological properties

I. Organic matter This is important for the health of a water body because the decomposition of organic matter draws upon the oxygen resources in the water and may render it unsuitable for aquatic life. Common parameters to characterize it are: BOD (biochemical oxygen demand), COD (chemical oxygen demand) and volatile solids. The widely-used BOD test measures the oxygen equivalence of organic matter and is the most important parameter in assessing pollution by organic matter.

II. Dissolved oxygen Similarly direct measurement of dissolved oxygen is an important indication of the health of the water. Absence of DO or a low level indicates pollution by organic matter. It is recorded as a percentage of saturation.

III. Major and minor ions Natural waters contain a variety of salts in solution originating from rain or soil and rock with which they have been in contact. Analysis is most frequently carried out and recorded for major cations, calcium (Ca++), magnesium (Mg++), sodium (N+) and potassium (K+) and associated anions include sulphate (SO4

=), bicarbonate (HCO3-) and chloride (Cl-) and

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reported as concentration (mg/l). Aggregate salts are derived as total dissolved solids (TDS) (mg/l).

IV. Toxic metals and organic compounds

Toxic metals and other elements may exist naturally in waters but may be seriously increased through man’s activity, including copper (Cu), chromium (Cr), mercury (Hg), lead (Pb), Nickel (Ni), Cadmium (Cd) and arsenic (As). Toxic organic substances will also be sampled and recorded but infrequently and at few sites as they require advanced instrumentation.

V. Nutrients Nutrient elements such as P and K may be enhanced by agricultural and industrial activity. An excess may lead to deteriorating water quality and regular sampling is carried out.

VI. Biological properties

Surface water polluted by domestic wastewater may contain a variety of pathogenic organisms including viruses, bacteria, protozoa and helminths. The cost of testing for all these organisms is prohibitive and the most common test is for Escherichia coli whose presence is an indicator of the potential for other pathogenic organisms. Results of testing for E coli are recorded as the most probable number (MPN)/100 ml)

3. Relation oriented data

Any kind of relationship between two or more variables is classified as relation oriented data. The relationship can be of any mathematical form which is the result of regression or a calibration exercise. The variables themselves may form a time series but it is their relationship rather than their occurrence in time which is the principal focus of the data and their storage and management in the HIS.

Relation-oriented data include the following:

1. General 2. Flow Data

Stage discharge data Stage discharge rating parameters

3. Sediment data Discharge sediment concentration/load data Discharge concentration/load rating parameters

1. General

A mathematical relationship between two or more hydrological variables can be established for the purpose of validation and in-filling of the data for another period. Relationships between stages at two adjacent gauging stations, between the average rainfall in a catchment and the resulting flow are typical examples. In some instances relationships may be established between water quality parameters and discharge to determine chemical loads. The parameters of the relationship along with the ranges of independent variables, error statistics and the period of applicability are required to be available for any relationship established.

2. Flow data

Stage discharge data : Stage discharge data are the most common example of this type of data, although in this case special provision must be made, for the inclusion of

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ancillary gauging station information and for various types of correction. Stage-discharge observations are the primary data for establishing the relationship between the stage and discharge, called the rating curve, at any river gauging station. Individual current meter measurement results in the computation of paired values of stage and discharge and ancillary information for its interpretation. Data from many gauging results in a series of such paired data - the summary stage discharge data. The Secondary Validation tolls of eSWIS provides a means of deriving rating relationships based on these paired values and ancillary information.

Stage discharge rating parameters : Analysis of stage discharge observations results in the production of parametric relationships. For simple relationships this may be expressed in parabolic or in power form. For a given station and time, more than one equation may be required to characterize the relationship and the relationships may change with time. There is thus a need for a means of storing coefficients of equations, range of level applicability and period of validity

3. Sediment data

Movement of solids transported in any way by a flowing liquid is termed as the sediment transport. From the aspect of transport it is the sum of the suspended load transported and the bed load transported. From the aspect of origin it is the sum of the bed material load and the wash load. As the discharges are related with the corresponding stages, discharge-sediment data also fit the classification of relation-oriented data. However, the relationship exhibited is often not as strong as that between stages and discharges for obvious reasons.

Sediment may be divided into two types of material:

bed material forming the bed or transported as bed load and as suspended load

wash load material, only transported as suspended load

The traditional classification as per ISO (ISO 4363: 1993) is shown in Fig. 4.1 as below:

Fig. 1: Definition of sediment loads and transports (ISO 4363: 1993)

In India suspended load and bed material are being sampled till recently. Bed load measurements are likely to be started at some stations. Near bed load transport measurements might become needed in future in relation with special problems.

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The information on sediment includes the sediment size and the sediment concentration for the transported load: bed load and suspended load.

Flow/ sediment concentration load summary:

When stable flow discharge - sediment concentration relationships exist, observations of flow and sediment in a station in a given period may be stored as relation oriented data and result in the production of a parametric relationship. This may be the case for stations with predominantly wash load transported in suspension.

Flow sediment relationships - a word of warning:

Sediment originates from various sources, including river basin soil erosion, mass wasting or river bed and bank erosion. The sediment may be temporarily stored and mobilized again, depending on its source and on the flood events. Consequently sediment transport rates will depend on many factors, and may differ from the sediment transport capacity because of sediment availability, and sediment concentration is not necessarily closely linked to the flow discharge. In many rivers, unstable relationships between flow discharge and sediment concentration display loop effects, the intensity of which may vary from one flood to another.

Flow sediment rating parameters:

Where parametric relationships are possible, they may be expressed by an exponential, parabolic or power form. As for the stage discharge rating, more than one equation may be required to characterize the relationship; the breaking points may or may not be the same. The coefficients need to be stored with their domain of applicability (range of stage) and period of validity.

Sediment size data: Distinction has to be made between information on bed material and on transported sediment load. Bed material data may be considered as space-oriented data only when the river bottom is bedrock. River bed sediment sizes may change during the flood events by selective erosion and have to be considered as time-oriented. In the absence of direct bed load transport measurements, size distribution of bed material is required for their calculation. The changes with time of bed sediment sizes must be available. Data on size distribution must also be available for sediment transported as bed load.

For sediment transported as suspended load, data on sediment size distribution are not available because of the small sizes of the samples. Only the percentage of that load is given for three fractions:

the coarse fraction (particles above 0.2 mm diameter) the medium fraction (particles between 0.075 and 0.2 mm diameter) the fine fraction (particles below 0.075 mm diameter)

An alternative way of classifying data in the Hydrological Information System is to categories them as:

Static or semi-static data: These include most space-oriented data including catchment boundaries, topographic features, station location etc., which may be said to be static. Some features such as physical characteristics of rivers, lakes or reservoirs etc. do change in time but often very gradually and can be considered as semi-static in nature.

Time oriented data: On the other hand, all hydro-meteorological quality and quantity data including relationships between them can be considered as time oriented data as

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they change regularly in time. Time-oriented data are grouped as meteorological data, hydrological data, water quality data and sediment data.

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Chapter 3: Primary Validation for Rainfall Data

Data validation is the process to ensure that the final figure stored is the best possible representation of the true value of the variable at the measurement site at a given time or in a given interval of time. Validation recognizes that values observed or measured in the field are subject to errors which may be random, systematic or spurious.

Improvement in computing facilities now enables such validation to be carried out whereas in the past the volume of data the time required to carry out comprehensive manual validation was prohibitive.

Primary validation of rainfall data will be carried out at the Sub-divisional level using Primary module of dedicated data processing software and is concerned with data comparisons at a single station:

for a single data series, between individual observations and pre-set physical limits between two measurements of a variable at a single station, e.g. daily rainfall from a

daily gauge and an accumulated total from a recording gauge

Data entry checks will already have been carried out to ensure that there have been no transcription errors. Some doubtful values may already have been flagged.

The high degree of spatial and temporal variability of rainfall compared to other climatic variables makes validation of rainfall more difficult. This is particularly the case on the Indian sub-continent, experiencing a monsoon type of climate involving convective precipitation.

More comprehensive checks can be carried out on daily and longer duration rainfall data by making comparisons with neighboring stations. This will be described under secondary validation and carried out at Divisional offices.

1. Instruments and observational methodsThe method of measurement or observation influences our view of why the data are suspect. To understand the source of errors we must understand the method of measurement or observation in the field and the typical errors of given instruments and techniques.

Data validation must never be considered a purely statistical or mathematical exercise. Staff involved in it must understand the field practice.

Three basic instruments are in use at climatologically stations for measurement of daily and shorted duration rainfall:

1. standard daily raingauge 2. syphon gauge with chart recorder 3. tipping bucket gauge with digital recorder

These will be separately described with respect to the typical errors that occur with each gauge or observation method, and the means by which errors may be detected (if at all).

1. Daily rainfall gauge (SRG) Daily rainfall is measured using the familiar standard gauge (SRG). This consists of:

a circular collector funnel with a brass or gun metal rim and a collection area of either 200 cm2 (diameter 159.5 mm) or 100 cm2 (diameter 112.8 mm), leading to a,

base unit, partly embedded in the ground and containing,

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a polythene collector bottle

The gauge is read once or twice daily and any rain held in the polythene collector is poured into a measuring glass to determine rainfall in millimeters.

Typical measurement errors Observer reads measuring glass incorrectly Observer enters amount incorrectly in the field sheet Observer reads gauge at the wrong time (the correct amount may thus be allocated to

the wrong day Observer enters amount to the wrong day Observer uses wrong measuring glass (i.e., 200 cm2 glass for 100 cm2 gauge, giving

half the true rainfall or 100 cm2 glass for 200 cm2 gauge giving twice the true rainfall. Observed total exceeds the capacity of the gauge. Instrument fault - gauge rim damaged so that collection area is affected Instrument fault - blockage in raingauge funnel so that water does not reach collection

bottle and may overflow or be affected by evaporation Instrument fault - damaged or broken collector bottle and leakage from gauge

It may readily be perceived that errors from most of these sources will be very difficult to detect from the single record of the standard raingauge, unless there has been a gross error in reading or transcribing the value. These are described below for upper warning and maximum limits.

Errors at a station are more readily detected if there is a concurrent record from an autographic raingauge (ARG) or from a digital record obtained from a tipping bucket raingauge (TBRG). As these too are subject to errors (of a different type), comparisons with the daily raingauge will follow the descriptions of errors for these gauges.

The final check by comparison with raingauges at neighbouring stations will show up further anomalies, especially for those stations which do not have an autographic or digital raingauge at the site. This is carried out under secondary validation at the Divisional office where more gauges are available for comparison.

2. Autographic raingauge (natural syphon)

In the past short period rainfall has been measured almost universally using the natural syphon raingauge. The natural syphon raingauge consists of the following parts:

a circular collector funnel with a gun metal rim, 324 cm2 in area and 200 mm in diameter and set at 750 mm above ground level, leading to ,

a float chamber in which is located a float which rises with rainfall entering the chamber,

A syphon chamber is attached to the float chamber and syphon action is initiated when the float rises to a given level. The float travel from syphon action to the next represents 10 mm rainfall

a float spindle projects from the top of the float to which is attached, a pen which records on, a chart placed on A clock drum with a mechanical clock.

The chart is changed daily at the principal recording hour. During periods of dry weather the rainfall traces a horizontal line on the chart; during rainfall it produces a sloping line, the steepness of which defines the intensity of rainfall. The chart is graduated in hours and the observer extracts the hourly totals from the chart and enters it in a register and computes the daily total.

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Typical measurement errors

Potential measurement faults are now primarily instrumental rather than caused by the observer and include the following:

Funnel is blocked or partly blocked so that water enters the float chamber at a different rate from the rate of rainfall

Float is imperfectly adjusted so that it syphons at a rainfall volume different from 10 mm. In very heavy rainfall the float rises and syphons so frequently that individual

pen traces cannot be distinguished. Clock stops; rainfall not recorded or clock is either slow or fast and thus timings are

incorrect. Float sticks in float chamber; rainfall not recorded or recorded incorrectly. Observer extracts information incorrectly from the pen trace.

In addition differences may arise from the daily raingauge due to different exposure conditions arising from the effect of different level of the rim and larger diameter of collector. It has been traditional to give priority to the daily SRG where there is a discrepancy between the two.

3. Tipping bucket raingauge

Short period rainfall is more readily digitized using a tipping bucket raingauge. It consists of the following components.

A circular collector funnel with a brass or gunmetal rim of differing diameters, leading to a

Tipping bucket arrangement which sits on a knife edge. It fills on one side, and then tips filling the second side and so on.

A reed switch actuated by a magnet registers the occurrence of each tip A logger records the occurrence of each tip and places a time stamp with the

occurrence

The logger stores the rainfall record over an extended period and may be downloaded as required. The logger may rearrange the record from a non-equidistant series of tip times to an equidistant series with amounts at selected intervals. The digital record thus does not require the intervention of the field observer. For field calibration, a known amount of rainfall is periodically poured into the collector funnel and checked against the number of tips registered by the instrument.


· Funnel is blocked or partly blocked so that water enters the tipping buckets at a different rate from the rate of rainfall

· Buckets are damaged or out of balance so that they do not record their specified tip volume

· Reed switch fails to register tips · Reed switch double registers rainfall tips as bucket bounces after tip. (Better equipment

includes a denounce filter to eliminate double registration. · Failure of electronics due to lightning strike etc. (though lightning protection usually

provided) · Incorrect set up of measurement parameters by the observer or field supervisor

Differences may arise from the daily raingauge (SRG) for reasons of different exposure conditions in the same way as the autographic raingauge.

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2. Comparison of daily time series for manual and autographic or digital data

General description:

At stations where rainfall is measured at short durations using an autographic or a digital recorder, a standard raingauge is always also available. Thus, at such observation stations rainfall data at daily time interval is available from two independent sources. The rainfall data at hourly or smaller interval is aggregated at the daily level and then a comparison is made between the two. Differences which are less than 5% can be attributed to exposure, instrument accuracy and precision in tabulating the analogue records and are ignored. Any appreciable difference (more than 5%) between the two values must be probed further. The observation made using standard raingauge has generally been taken as comparatively more reliable. This is based on the assumption that there is higher degree of possibility of malfunctioning of autographic or digital recorders owing to their mechanical and electromechanical systems. However, significant systematic or random errors are also possible in the daily raingauge as shown above.

If the error is in the autographic or digital records then it must be possible to relate it either to instrumental or observational errors. Moreover, such errors tend to repeat under similar circumstances.

Data validation procedure and follow up actions:

This type of validation can be carried out in tabular or graphical form. For both approaches, the values of hourly data are aggregated to daily values to correspond to those observed using a standard raingauge. A comparison is made between the daily rainfall observed using standard and automatic gauges. Percent discrepancy can be shown by having a second axis on the plot. Tabular output for those days for which the discrepancy is more than 5% can be obtained. A visual inspection of such a tabulated output will ensure screening of all the suspect data with respect to this type of discrepancy.

The following provides a diagnosis of the likely sources of error with discrepancies of different sorts:

(a) Where the recording gauge gives a consistently higher or lower total than the daily gauge, then the recording gauge could be out of calibration and either tipping buckets (TBRG) or floats (ARG) need recalibration.

Accept SRG and adjust ARG or TBRG

(b) Where agreement is generally good but difference increases in high intensity rainfall suggests that for the ARG:

the syphon is working imperfectly in high rainfall, or the chart trace is too close to distinguish each 10 mm trace (underestimate by

multiples of 10 mm)

For the TBRG: gauge is affected by bounce sometimes giving double tips

Accept SRG and adjust ARG or TBRG

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Where a day of positive discrepancy is followed by a negative discrepancy and rainfall at the recording gauge was occurring at the observation hour, and then it is probable that the observer read the SRG at a different time from the ARG. The sum of SRG readings for successive days should equal the two-day total for the TBRG or ARG

Accept TBRG or ARG and adjust SRG

Where the agreement is generally good but isolated days have significant differences, then the entered hourly data should be checked against the manuscript values received from the field. Entries resulting from incorrect entry are corrected. Check that water added to the TBRG for calibration is not included in rainfall total. Otherwise there is probable error in the SRG observation.

Accept ARG or TBRG and adjust SRG

However, it will be very interesting to note that in certain cases the values reported for the daily rainfall by SRG and ARG matches one to one on all days for considerable period notwithstanding the higher rainfall values etc. It is very easy to infer in those situations that there has been at attempt by the observer to match these values forcefully by manipulating one or both data series. It is not expected that both these data series should exactly match in magnitude. Since such variation must be there due to variance in the catch and instrumental and observation variations. And it is therefore highly undesirable that such matching is effected by manipulation.

Fig. 3.1: Graphical comparison of daily rainfall obtained from SRG and ARG at the same station.

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Following points can be noticed:

(a) The difference in daily values from SRG and ARG varies considerably; from a very reasonable deviation to unacceptably high values.

(b) In this example, the resulting errors can be categorized in three types major classes:

There are many instances where a larger difference is caused by the shifting of one of the data series by one day. This shift is not present before and after this period. Such errors are not exactly due the differences in the two observations but are the result of recording or entering one of the data series inappropriately against wrong date. However, even if this time shift were not present, then also there would have been substantial differences in the corresponding values as can be easily inferred from the tabulated values.

There are a few instances where the difference is due to mistake in recording or entering or might even be due to failure of ARG. Such errors are very easy to be detected also.

There is lot of instances where the percent difference is moderate to high which can be attributed to observational errors, instrumental errors and the variation in the catch in the two raingauge. Most of these high percentage differences are for the very low rainfall values which also highlights the variation in the catch or the accuracy of equipment at such low rainfall events.

Following actions must be taken as a follow-up of data validation:

(a) The cause of the shift in one of the data series can be very easily detected and removed after looking at the dates of the ARG charts and corresponding tabulated data.

(b) Cause of mistake can be removed if ARG chart also shows comparable rainfall. If ARG data is found correct according to the chart and there does not seem to be any reason to believe instrumental failure etc. then the daily rainfall as reported by the SRG can be corrected to correspond to the ARG value. Else, if there is any scope of ambiguity then the daily data has to be flagged and it has to be reviewed at the time of secondary validation on the basis on rainfall recorded at the adjoining stations.

(c) Moderate to large differences (more than 5%) in the two data series are to be probed in detail by looking at the ARG chart and corresponding tabulations. Any errors in tabulations are to be corrected for. Inspection of the differences in this case shows that there is no particular systematic error involved. Sometime the SRG value is more by a few units and sometimes ARG is more by similar magnitude. Sometimes this might be due to observation SRG at non-standard times or incorrect tabulation of the ARG chart. At low rainfall these differences can also be due to variation in the catch or due to inaccuracy of the equipment. In both circumstances, it must be ensured whether standard equipment and exposure conditions are maintained at the station.

4. Checking against maximum and minimum data limits

3.4.2 General description:

Rainfall data, whether daily or hourly must be validated against limits within which it is expected to physically occur. Such limits are required to be quite wide to avoid the possibility of rejecting true extreme values. For rainfall data, it is obvious that no data can be less than zero which perfectly serves as the limiting minimum value. However, it is quite difficult to assign an absolute maximum limit for the rainfall data in a given duration occurring at a particular station. Nevertheless, on the basis of past experience and physical laws governing

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the process of rainfall it is possible to arrive at such maximum limits which in all probability will not be exceeded. The limit may be set as the maximum capacity of the raingauge, but care should be taken in rejecting values on this basis where the gauge observer has read the gauge several times to ensure the gauge capacity was not exceeded.

Maximum limits also vary spatially over India with climatic region and orography. Also, this maximum limit has a strong non-linear relationship with rainfall duration. For example, for any place, the maximum limit for daily rainfall is not equal to 24 times the maximum limit for hourly rainfall. It is certainly much lower than this amount. For this reason, it is essential to set maximum limits for rainfall for durations other than 1-day. Limits for 1-day and 1-hour should be set and this will generally be sufficient to identify gross errors over the intervening range of duration.

For 1-day duration, the India Meteorological Department and Indian Institute of Tropical Meteorology have prepared atlas for 1 day Probable Maximum Precipitation (PMP) which gives the expected maximum amount that can physically occur in a given duration at a given location. Values extracted from this map should be applied or else could be derived as the historical maximum value from the long term records now available for most of the regions. Though there might be some variation in the values obtained from both these atlases but for the purpose of prescribing the maximum limit here such differences may be ignored. Alternatively, the derived information on observed maximum 1-Day point rainfall, which is available for scores of stations across the country from long term records, can be used as a reasonably good estimate of the maximum limit of rainfall.

Similarly, use can be made of the maps showing 50 year – 1 hour maximum rainfall, as developed by India Meteorological Department, for presecribing the maximum data limit for the case of hourly rainfall data. Such initial estimates can be adjusted on the basis of local judgement adjusted on the basis of experience or of local research studies based on either:

· storm maximisation by considering precipitable moisture and inflow of moist air · Statistical analysis of observed extreme values for shorter durations.

Data validation procedure and follow up actions: Setting minimum and maximum limits in eSWIS ensures filtering of values outside the specified limits. Such values are considered suspect. They are first checked against manuscript entries and corrected if necessary. If manuscript and entry agree and fall outside prescribed limits, the value is flagged as doubtful. Where there are some other corroborative facts about such incidents, available in manuscript or notes of the observer or supervisor then they must be incorporated with the primary data validation report. This value then has to be probed further at the time of secondary data validation when more data from adjoining stations become available.However, when the current data is being entered in subsequent month and there happens a entries which are more than the prescribed maximum limit and such heavier rainfall events are also very fresh in the minds of data processing staff then it implies that the earlier maximum has been crossed in reality. In such circumstances the maximum limit is reset to a suitable higher value. In such cases there will surely be a few adjoining stations recording similar higher rainfall and will support such inferences. However, if no such basis is available for justification of such very high values then the value is reported in the form of a remark which can be reviewed at the secondary validation stage.

Fig. 4.1: Graphical plot showing physical significance of maximum limit and upper warning level

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5. Checking against upper warning level


Validation of rainfall data against an absolute maximum value does not discriminate those comparatively frequently occurring erroneous data which are less than the prescribed maximum limit. In view of this, it is advantageous to consider one more limit, called the upper warning level, which can be employed to see if any of the data value has violated it. This limit is assigned a value with an intention of screening out those high data values which are not expected to occur frequently. The underlying purpose of carrying out such a test is to consider a few high data values with suspicion and subsequently scrutinising them.

For the daily rainfall data this limit can be set statistically, for example, equal to 99 percentile value of the actual rainfall values excluding zero rainfall values. In other words, it leads to screening out those values which are higher than that daily rainfall value which is exceeded only once in 100 rainfall events on an average. Say, if the data for 30 years is available and there are 3456 non-zero daily rainfall values then 99 percentile value will be about 34 th

highest in the lot. It indicates that rainfall value which is equalled or exceeded, on an average, once in every 100 rainfall events.

Similar statistic can be employed for obtaining suitable value for upper warning level for hourly rainfall data. The central idea while setting these upper warning levels is that the higher rainfall data is screened adequately, that is the limits must be such that it results in not too many and not too less data values being flagged for validation.

Data validation procedure and follow up actions:

Setting warning limits in the Primary module (like maximum limits) results in filtering values outside specified limits. Values are checked against manuscript entries and corrected if necessary. Remaining values are flagged as doubtful, and any associated field notes or corroborative facts are incorporated with the primary validation report and forwarded to the Divisional Data Processing Centre for secondary validation.

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Chapter 4: Secondary Validation of Rainfall Data

After primary validation of Rainfall data, Secondary validations will use to comparisons with neighboring stations to identify suspect values. Some of the checks which can be made are oriented towards specific types of error known to be made by observers, whilst others are general in nature and lead to identification of spatial inconsistencies in the data.

Rainfall poses special problems for spatial comparisons because of the limited or uneven correlation between stations. When rainfall is convectional in type, it may rain heavily at one location whilst another may remain dry only a few miles away. Over a month or monsoon season such spatial unevenness tends to be smoothed out and aggregated totals are much more closely correlated.

Spatial correlation in rainfall thus depends on:

duration (smaller at shorter urations), distance (decreasing with distance), type of precipitation, andphysiographic characteristics of a region.

Example 1:

The effect of aggregation of data to different time interval and that of the inter-station distances on the correlation structure is illustrated here.

The scatter plot of correlation between various rainfall stations for the daily, 10 daily monthly and yearly rainfall data is shown in Fig. 1.1, Fig. 1.2, Fig. 1.3 , and Fig. 1.4. respectively.

From the corresponding correlation for same duration in these three figures it can be noticed that aggregation of data from daily and monthly further to yearly level increases the level of correlation significantly. At the same time it can also be seen that the general slope of the scatter points becomes flatter as the aggregation is done. This demonstrates that the correlation distance for yearly interval is much more than that for monthly intervals.

Fig. 1.1: Daily Rainfall of Multiple stations

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Fig. 1.2: 10Daily Rainfall of Multiple stations

Fig. 1.3.: Monthly Rainfall of Multiple stations (Line)- For a year

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Fig. 1.4.1: Yearly Rainfall of Multiple stations (Scatter) - For a year

Fig. 1.4.2: Yearly Rainfall of Multiple stations (Bar) - For a year

Spatial correlation can be used as a basis for spatial interpolation and correction.

However, there is a danger of rejecting good data which is anomalous as well as accepting bad data. A balance must be struck between the two. In considering this balance, it is well to give weight to the previous performance of the station and the observer.

One must particularly be wary of rejecting extreme values, as true extreme values are for design purposes the most interesting and useful ones in the data series. True extreme values (like false ones) will often be flagged as suspect by validation procedures. Before rejecting such values it is advisable to refer both to field notes and to confer with Sub-divisional staff.

2. Screening of data seriesAfter the data from various Sub-Divisional offices has been received it is organized and imported into the temporary databases of secondary module of dedicated data processing software. The first step towards data validation is making the listing of data thus for various stations in the form of a dedicated format. Such listing of data is taken for two main objectives: (a) to review the primary validation exercise by getting the data values screened against desired data limits and (b) to get the hard copy of the data on which any remarks or observation about the data validation can be maintained and communicated subsequently to the State/Regional data processing centre.

Moreover, for the case of validation of historical data for period ranging from 10 to 40 years this listing of the screening process is all the more important. This screening procedure involves, for example for daily rainfall data, flagging of all those values which are beyond the maximum data limits or the upper warning level. It also prepares the data in a well-organized matrix form in which various months of the year are given as separate columns and various days of the month are given as rows. Below this matrix of data the monthly and yearly basic statistics like total rainfall, maximum daily rainfall, number of rainy days etc. are listed. Also, the number of instances where the data is missing or has violated the data limits is also given.

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This listing of screening process and basic statistics is very useful in seeing whether the data has come in the databases in desired manner or not and whether there is any mark inconsistency vis-à-vis expected hydrological pattern.

Example: 2.1:An example of the listing of screening process for Dhalegaon station for the year 2010 is given in Table 2.1.

Table 2.1: Result of the screening process of daily rainfall data for one year:

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A few days of high rainfall shows that these values have crossed the Maximum Warning Level. Such flagged values can then be subsequently attended to when comparing with adjoining stations. This particular year shows a few days of very heavy rainfall, one in fact making the recorded maximum daily rainfall (i.e. 98 mm on 1st July).

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3. Scrutiny by multiple time series graphsInspection of multiple time series graphs may be used as an alternative to inspection of tabular data. Some processors may find this a more accessible and comprehensible option. This type of validation can be carried out for hourly, daily, monthly and yearly rainfall data. The validation of compiled monthly and yearly rainfall totals helps in bringing out those inconsistencies which are either due to a few very large errors or due to small systematic errors which persist unnoticed for much longer durations. The procedure is as follows:

(a) Choose a set of stations within a small area with an expectation of spatial correlation. (b) Include, if possible, in the set one or more stations which historically have been more

reliable. (c) Plot rainfall series as histograms stacked side by side and preferably in different colours

for each station. Efficient comparison on the magnitudes of rainfall at different stations is possible if the individual histograms are plotted side by side. On the other hand a time shift in one of the series is easier to detect if plots of individual stations are plotted one above the other. Stacking side-side is presently possible with the software.

(d) After inspection for anomalies and comparing with climate, all remaining suspect values are flagged, and comment inserted as to the reason for suspicion.

Example 3.1:

Consider that a few of the higher values at Mahi at Mataji station of during June, July and August 2006 are suspect. Comparison with adjoining available stations Tikapara, and Narmada at Mortakka is made for this purpose. Fig. 3.1 gives the plot of daily rainfall for these multiple stations during the period under consideration.

Comparison of Daily Rainfall at Multiple Stations

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Fig. 3.1.: Comparison of multiple time series plot of daily rainfall data

The data correction also confirmed when the ARG record is compared with the SRG record. Thus inspection of the record sheets, visit to site and interaction with the observation can be helpful in getting more insight into the probable reasons of such departures.

4. Scrutiny by tabulations of daily rainfall series of multiple stations

In the case of rainfall (unlike other variables), a tabular display of monthly rainfall some year, listing several stations side by side can reveal anomalies which are more difficult to see on multiple time series graphs (see below), plotted as histograms. Scanning such tabular series will often be the first step in secondary data validation. Anomalies to look out for are:

Do the daily blocks of rainy days generally coincide in start day and finish day?

Are there exceptions that are misplaced, starting one day early or late? Is there a consistent pattern of misfit for a station through the month? Are there days with no rainfall at a station when (heavy) rainfall has occurred at

all neighboring stations?

Field entry errors to the wrong day are particularly prevalent for rainfall data and especially for stations which report rainfall only. This is because rainfall occurs in dry and wet spells and observers may fail to record the zeros during the dry spells and hence lose track of the date when the next rain arrives. When ancillary climate data are available, this may be used to compare with rainfall data. For example a day with unbroken sunshine in which rain has been reported suggests that rainfall has been reported for the wrong day. However, most comparisons are not so clear cut and the processor must be aware that there are a number of possibilities:

rainfall and climate data both reported on the wrong day - hence no anomaly between them but discrepancy with neighboring stations.

rainfall data only on the wrong day - anomalies between rainfall and climate and between rainfall and neighboring rainfall

rainfall and climate both reported on the correct day - the anomaly was in the occurrence of rainfall. For example no rainfall at one site but at neighboring sites. In this case climatic variables are likely to have been shared between neighboring stations even if rainfall did not occur.

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5. Checking against data limits for totals at longer durations

5.1 General description:

Many systematic errors are individually so small that they cannot easily be noticed. However, since such errors are present till suitable corrective measures are taken, they tend to accumulate with time and therefore tend to be visible more easily. Also, some times when the primary data series (e.g. daily rainfall series) contains many incorrect values frequently occurring for a considerable period (say a year of so) primarily due to negligence of the observer or at the stage of handling of data with the computer then also the resulting series compiled at larger time interval show the possible incorrectness more visibly. Accordingly, if the observed data are accumulated for longer time intervals, then the resulting time series can again be checked against corresponding expected limits. This check applies primarily to daily rainfall at stations at which there is no recording gauge.

5.2 Data validation procedure and follow up actions:

Daily data are aggregated to monthly and yearly time intervals for checking if the resulting data series is consistent with the prescribed data limits for such time intervals.

Together with the upper warning level or maximum limit, for monsoon months and yearly values use of lower warning level data limit can also be made to see if certain values are

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unexpectedly low and thus warrants a closer look. Aggregated values violating the prescribed limits for monthly or annual duration are flagged as suspect and appropriate remarks made in the data validation report stating the reasons for such flagging. These flagged values must then validated on the basis of data from adjoining stations.

Example 5.1:

The daily data of a station can be considered and the yearly totals are derived. The period of 2005 to 2007 is taken for the compilation where in some years of data, is missing for some stations.

For example, In any case, if the mean of the 26 yearly values is about 660 mm with an standard deviation of 320 mm with a skewness of 0.35. With an objective of only flagging a few very unlikely values for the purpose of scrutiny, a very preliminary estimate of the upper and lower warning levels is arbitrarily obtained by taking them as:

Lower warning level = mean – 1.5 x (standard deviation) = 660 – 1.5 x 320 = 180 mm

and

Upper warning level = mean + 2.0 x (standard deviation) = 660 + 2.0 x 320 = 1300 mm

The multipliers to the standard deviation for the lower and upper warning levels have been taken differently in view of the data being positively skewed with a finite lower bound. Such limits can be worked out on a regional basis on the basis of the shape of distribution and basically with the aim to demarcate highly unlikely extremes.

These limits have been shown in the plot of the yearly values and it may be seen that there are a few instances where the annual rainfall values come very close or go beyond these limits.

After screening such instances of extreme values in the data series compiled at longer time intervals, it is then essential that for such instances the values reported for the station under consideration is compared with that reported at the neighboring stations. For this, the yearly data at five neighboring stations including the station under consideration, is tabulated together as Table 5.1 for an easier comparison.

Table 5.1: Tabulation of yearly rainfall at five neighboring stations

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It may be seen from this table that for the year 2006 at most of the neighboring stations the reported rainfall is very high and is even about 279.6mm for 010217005 station. At two other stations also it is in the range of 85 to 200 mm except that for 010215024 Thus, as far as the suspect value of for any station is concerned, the suspicion may be dropped in view of similar higher values reported nearby. Comparison for the year some other years though all the stations. Such a situation warrants that the basic daily data for this test station must be looked more closely for its appropriateness.

6. Rainfall missed on days with low rainfall – rainy days check

6.1. General description:

Whilst it is required that observers inspect the raingauge for rain each day, the practice of some observers may be to visit the gauge only when they know that rain has occurred. This will result in zeros on a number of days on which a small amount of rain has occurred. Totals will be generally correct at the end of the month but the number of rainy days may be anomalously low. In addition spatial homogeneity testing may not pick up such differences.

-Owing to spatial homogeneity with respect to the occurrence of rainfall within the day, it is expected that the number of rainy days in a month or year at the neighbouring stations will not differ much. Presently, there are two definitions for number of rainy days: some agencies consider a minimum of 0.1 mm (minimum measurable) in a day to be eligible for the rainy day whereas some use 2.5 mm and above as the deciding criteria. The later is used more often in the agriculture sector. For the hydrological purpose it is envisaged that the definition of minimum measurable rainfall (i.e. 0.1 mm) will be used for the data validation.It is good to ehavio this fact to see if the observed data follow such characteristic. A graphical or tabular comparison of the difference in the number of rainy days for the neighbouring stations for the monthly or yearly period will be suitable in bringing out any gross inconsistency. The tolerance in the number of rainy days between the stations has to be based on the variability experienced in the region and can easily be established using historical data. If the difference is more than the maximum expected, the data may be considered suspect. Any gross inconsistency noticed must then be probed further by looking at the manuscript and seeking a report on, or inspecting the functioning and ehavior of the observer.

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6.2. Data validation procedure and follow up actions:

First of all, with the help of historical daily rainfall data, belonging to a homogenous region, the expected maximum variation in the number of rainy days for each month of the year and for year as a whole is found out. A group of stations being validated is then chosen and the number of rainy days at each station within the month(s) or year obtained. The number of rainy days at each station is then compared with every other station in the group. All those instances when the expected variation is exceeded by the actual difference in the number of rainy days is presented in tabular or graphical form. It is appropriate to present the output in a matrix form in which the stations are listed as rows and columns of the table or the graph. In case the presentation is on the monthly basis then each tabular or graphical matrix can accommodate a period of one year.

Any glaring departure in the number of rainy days, at one or more stations, can be apparent by inspecting the matrix. The station for which the number of rainy days is much different from others will have the column and row with lower (or occasionally higher) values. The data pertaining to such months or years of the station(s) for which the difference in the number of rainy days is beyond the expected range is considered suspect and has to be further probed. The original observer’s manuscript for the suspect period can be compared with the values available in the database. Any discrepancy found between the two can be corrected by substituting the manuscript values. Where the manuscript matches with the data available in the database then comparison with other related data like temperature and humidity at the station, if available, can be made. Together with analytical comparison, feedback from the observer or supervisor will be of a great value in checking this validation especially where it is done within one or two months of the observations. If the related data corroborate the occurrence of such rainy days then the same can be accepted.

Where there is strong evidence to support the view that the number of rainy days derived from the record is incorrect, then the total may be amended by reference to neighbouring stations. Such action implies that there are unreported errors remaining in the time series, which it has not been possible to identify and correct. A note to this effect should be included with the station record and provided with the data to users.

As a follow up measure a report can be sought on the functioning and ehavior of the observer.

7. Checking for systematic shifts using double mass analyses


Double mass analysis is a technique that is effective in detecting a systematic shift, like abrupt or gradual changes in the mean of a series, persisting in the record for a considerable period of time . Rainfall record contains such inconsistencies which may exist for a considerable period of time. Inconsistencies present in the rainfall data of a station can occur for various reasons:

· The raingauge might have been installed at different sites in the past · The exposure conditions of the gauge may have undergone a significant change due

to the growth of trees or construction of buildings in its proximity · There might have been a change in the instrument, say from 125 mm to 200 mm

raingauge · The raingauge may have been faulty for a considerable period etc.

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Such inhomogeneity in the data set must be removed before any statistical inference can be drawn. The double mass analysis tests the record for its inconsistency and accuracy and provides a correction factor to ensure that the data series is reasonably homogeneous throughout its length and is related to a known site. A note may be available in the station registers of the known changes of site and instruments and can corroborate the detection of inconsistency using this technique. The application of double mass analysis to rainfall data will not be possible until a significant amount of historical data have been entered to the database.

7.2. Description of method

Double mass analysis is a technique to detect possible in homogeneities in series by investigating the ratio of accumulated values of two series, viz.:

· the series to be tested, and · the base series

The base series is generally an artificial series, i.e. the average of reliable series of nearby stations (usually 3 as minimum) which are assumed to be homogenous.

First of all the accumulated test and base series are obtained as two vectors (say Y i and Xi respectively, for i = 1, N). The double mass analysis then considers the following ratio:

i

Y j

rci ji1

X

jj1

or expressed as a ratio of the percentages of the totals for N elements:

i N

Yj .

X j

pc j 1

.j1

N ii

Yj

X j

j1 j1

These ratios in absolute and percent form gives the overall slope of the double mass plot from origin to each consequent duration of analysis.

A graph is plotted between the cumulative rainfall of the base series as abscissa and the cumulative rainfall of test station as the ordinate. The resulting plot is called the double mass curve. If the data of test station is homogeneous and consistent with the data of the base series, the double mass curve will show a straight line. An abrupt change in the test-series will create a break in the double mass curve, whereas a trend will create a curve. Graphical inspection of the double mass plot provides the simplest means of identifying such inconsistencies but significance tests may also be used to identify breaks and jumps. A change in slope is not usually considered significant unless it persists for at least 5 years and there is corroborating evidence of a change in location or exposure or some other change. There is a regional consistency in precipitation pattern for long periods of time but this consistency becomes less pronounced for shorter periods. Therefore the double mass technique is not recommended for adjustment of daily or storm rainfalls. It is also important to mention here that any change in regional meteorological or weather conditions would not

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have had any influence on the slope of the double mass curve because the test station as well as the surrounding base stations would have been equally affected.

It must also be emphasised here that the double mass technique is based on the presumption that only a part of the data under consideration is subjected to systematic error. Where the whole length of the data being considered has such an error then the double mass analysis will fail to detect any error.

7.3. Data validation procedure and follow up actions:

For analysing the rainfall data for any persistent systematic shift, the accumulated rainfall for longer duration at the station under consideration (called the test station) is compared with another accumulated rainfall series that is expected to be homogeneous. Homogeneous series for comparison is derived by averaging rainfall data from a number of neighbouring homogenous stations (called base stations).

Accumulation of rainfall can be made from daily data to monthly or yearly duration. The double mass plot between the accumulated values in percent form at test and base station is drawn and observed for any visible change in its slope. The tabular output giving the ratio between the accumulated values at test and base station in absolute and percent is also obtained. In case, there are some missing data points within each duration of analysis, a decision can be made about the number of elements which must essentially be present for that duration to be considered for analysis. The analysis, if required, can also be carried for only a part of the years or months.

Where there is a visible change in the slope of the double mass plot after certain period then such a break must be investigated further. Possible reasons for the inhomogeneity in the data series are explored and suitable explanation prepared. If the inhomogeneity is caused by changed exposure conditions or shift in the station location or systematic instrumental error then the data series must be considered suspect. The data series can then be made homogeneous by suitably transforming it before or after the period of shift as required.

Transformation for inconsistent data is carried out by multiplying it with a correction factor which is the ratio of the slope of the adjusted mass curve to the slope of the unadjusted mass curve.

Example 7.1:

Double mass analysis for DHALEGAON station is carried out considering two neighbor stations Narmada at Mortaka and Mahi at Mataji as the base stations. A period of only three months from July to September (92 days) 2006 has been taken into consideration while carrying out the analysis. Though the reliability of records and the homogeneity of these base stations have to be ascertained before considering them for the analysis but here it has been assumed that they are reliable stations.

It can be seen from double mass plot of this analysis, as shown in Fig. 7.1, that the data of DHALEGAON station is fairly consistent throughout the period of analysis (2005 to 2012) with respect to the other two base stations. Baring a few short-lived very small deviations from the ideal curve , the plot shows a similar trend throughout the period.

The result of this analysis on yearly basis is given in Table 7.1.

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Fig. 7.1: Double mass plot showing near consistent trend at test station

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Chapter 5: Correct and Complete of Rainfall Data

After secondary validation a number of values can be flagged as incorrect or doubtful. Some records may be missing due to non-observation or loss on recording or transmission. Incorrect and missing values will be replaced where possible by estimated values based on other observations at the same station or at neighboring stations. The process of filling in missing values is generally referred to as ‘completion’.

It must be recognized that values estimated from other gauges are inherently less reliable than values properly measured. Doubtful original values will therefore be generally given the benefit of the doubt. Where neighboring observations or stations are not available, missing values will be left as ‘missing’ and incorrect values will be set to ‘missing’

Procedures for correction and completion depend on the type of error and the availability of suitable source records with which to estimate.

1. Use of ARG and SRG data at one or more station:All observational stations equipped with autographic raingauge (ARG) also have an ordinary or standard raingauge (SRG) installed. One instrument can be used as a back-up and for correcting errors in the other in the event of failure of the instrument or the observer. The retention of an SRG at stations with an ARG is based on the view that the chances of malfunctioning of automatic type of equipment are higher.

Where an autographic record at a station is erroneous or missing and there are one or more adjoining stations at which autographic records are available these may possibly be used to complete the missing values.

1.1 . Data correction or completion procedure:

Correction and completion of rainfall data using ARG and SRG data depends on which has failed and the nature of the failure. The procedure to be followed in typical situations is explained below:

1.1.1. SRG record missing or faulty - ARG available

The record from the standard raingauge may be missing or faulty due to poor observation technique, a wrong or broken measuring glass or a leaking gauge. In these circumstances, it is reasonable to correct the erroneous standard raingauge data or complete them using the autographic records of the same station. The standard raingauge data in such cases are made equal to that obtained from the autographic records. The standard raingauge are normally observed at one or two times in the day i.e. at 0830 hrs or 0830 and 1730 hrs.. The estimated values for such observations can be obtained by aggregating the hourly autographic records corresponding to these timings.

Example 1.1

We have rainfall data for both SRG and ARG, it is possible to make a one-to-one comparison of daily rainfall totals obtained from both the equipment. For this, the hourly data series obtained from ARG is used to compile the corresponding daily totals. Then the daily rainfall thus obtained from SRG and ARG are tabulated together for an easy comparison as given in Fig. 2.1.

Fig. 2.1: Daily rainfall series obtained from SRG & ARG for the station Haralahalli of August 2011

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Both the above mentioned suspicions are cleared after examining the graph. Rainfall obtained from SRG (data type MPS) and ARG (data type MPA) on 21.08.2011 is 6.5 mm and 1 mm respectively. At this stage the manuscript of SRG record and hourly tabulation of ARG record is referred to and confirmation made. Assuming that in this case the daily value of ARG record matches with the manuscript and a look at the corresponding chart record confirms proper hourly tabulation, then the daily value is according corrected from 6.5 mm to 1 mm as equal to ARG daily total.

2.2.2 ARG record missing or faulty - SRG available

The autographic record may be missing as a result for example of the failure of the recording mechanism or blockage of the funnel. Records from autographic gauges at neighbouring stations can be used in conjunction with the SRG at the station to complete the record. Essentially this involves hourly distribution of the daily total from the SRG at the station by reference to the hourly distribution at one or more neighbouring stations. Donor (or base) stations are selected by making comparison of cumulative plots of events in which autographic records are available at both stations and selecting the best available for estimation.

Consider that the daily rainfall (from 0830 hrs. on previous day to 0830 hrs. on the day under consideration) at the station under consideration is Dtest and the hourly rainfall for the sameperiod at the selected adjoining station are Hbase,i (i = 1, 24). Then the hourly rainfall at the station under consideration, Htest,i is obtained as:

H D H base,i test,i test. 24

H base,i i 1The procedure may be repeated for more than one base station and the average or resulting hourly totals calculated.

Example 2.2

Hourly rainfall data at Tapi at Burhanpur station is considered for the period of July-August 2004. Though there is no missing data in this period under consideration, it is assumed that the rainfall values during 27–29 July are not available and are thus tried to be estimated on the basis of hourly distribution of rainfall at neighbouring stations.

Three neighboring stations (Tapi at Hatnur, Tapi at Bhusawal and Purna at Gopalkhera) are available around this Tapi at Burhanpur station at which two days of hourly rainfall is required to be estimated. For this, first of all the hourly rainfall pattern of Tapi at Burhanpur station is tried to be correlated with one or more of the neighbouring stations. Data of a rainfall event in the area during 5-7 August 2004 is considered for identifying suitable neighboring stations for estimates of hourly distribution.

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Fig. 2.1 shows the comparison of cumulative hourly rainfall between these Four neighboring stations. Purna at Gopalkhera is show quite a high level of similarity with the RAHIOL station.

3. Correcting for entries to wrong days


Daily rainfall data are commonly entered to the wrong day especially following a period when no rainfall was observed. Identification of such mistakes is explained under secondary validation which identifies the occurrence of the time shift and quantifies its amount.

Correction for removing the shift in the data is done by either inserting the missing data or deleting the extra data points causing the shift (usually zero entries). While inserting or deleting data points care must be taken that only those data values are shifted which are affected by the shift. Though this type of correction is required frequently for daily data a similar procedure may be employed for other time intervals if a shift is identified.

Data correction procedure:

There are two important things to be considered while correcting the data for the identified shift in the data series.

· the amount of shift and · the extent of data affected by the shift.

The amount of shift is the number of days by which a group of daily data is shifted. The extent of data affected by the shift is the number of data in the group which are affected by the shift. For example, if the daily data in a certain month is shifted forward 2 days, then the amount of shift is 2 days. The extent of shift may be the full monthly period or a period of days within the month. The data must be corrected by deleting the two unwanted data from the desired location in the month. This deletion must be followed by shifting the affected data backward to fill up the deleted locations. Obviously, this will result in making a gap before the period where rainfall values were entered to the correct day. These must be filled with suitable entries (normally zero). Where the shift extends to the end of the month then the last 2 data in the month must similarly be filled up with suitable entries. Where the shift

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continues into the following month, the first two values of the next month are transferred to the last two values of the previous month and the process is continued.

4. Apportionment for indicated and unindicated accumulationsGeneral description:

Where the daily raingauge has not been read for a period of days and the total recorded represents an accumulation over a period of days identified in validation, the accumulated total is distributed over the period of accumulation by reference to rainfall at neighbouring stations over the same period.

Data correction procedure:

The accumulated value of the rainfall and the affected period due to accumulation is known before initiating the correction procedure. Consider that:

number of days of accumulation = Nacc accumulated rainfall as recorded = Racc

Estimates of daily rainfall, for each day of the period of accumulation, at the station under consideration is made using spatial interpolation from the adjoining stations (in the first instance without reference to the accumulation total) using:

N base b (P

ij Di ) N base b

i1

(1/ Di )

Pest, j

(Pij

) N base

Nbase

(1 Dib ) i 1 (1/ Di

b )

i1 i 1 Where:

estimated rainfall at the test station for jth dayPest,j =Pij = observed rainfall at ith neighbour station on jth dayDi = distance between the test and ith neighbouring stationNbase = number of neighbouring stations considered for spatial interpolation.b = power of distance used for weighting individual rainfall value. Usually taken as2.

The accumulated rainfall is then apportioned in the ratio of the estimated values on the respective days as:

P

Pest, j

* P

tot

j 1 to NN

accappor, j acc

Pest, j

j 1

Where:= accumulated rainfall as recordedPtot

Nacc = number of days of accumulationPappor,j = apportioned rainfall for jth day during the period of accumulation

5. Adjusting rainfall data for long term systematic shiftsGeneral description :

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The double mass analysis technique is used in validation to detect significant long-term systematic shift in rainfall data. The same technique is used to adjust the suspect data. Inconsistency in data is demonstrated by a distinct change in the slope of the double mass curve and may be due to a change in instrument location or exposure or measurement technique. It does not imply that either period is incorrect - only that it is inconsistent. The data can be made consistent by adjusting so that there is no break in the resulting double mass curve. The existence of a discontinuity in the double mass plot does not in itself indicate which part of the curve should be adjusted (before or after the break). It is usual practice to adjust the earlier part of the record so that the entire record is consistent with the present and continuing record. There may be circumstances however, when the adjustment is made to the later part, where an erroneous source of the inconsistency is known or where the record has been discontinued. The correction procedure is described below.

Data correction procedure :

Consider a double mass plot shown in Fig. 5.1. There is a distinct break at point A in the double mass plot and records before this point are inconsistent with present measurements and require adjustment. The adjustment consists of either adjusting the slope of the double mass curve before the break point to confirm to the slope after it or adjusting the slope in the later part to confirm with that of the previous portion. The decision for the period of adjustment to be considered depends on the application of data and on the reasons for the exhibited in-homogeneity. For example, if the change in behaviour after a certain point in time is due to an identified systematic error then obviously the portion are the break point will be adjusted. On the other hand, if shift is due to the relocation of an observation station in the past then for making the whole data set consistent with the current location the portion before the break needs to be corrected.

Fig. 5.1: Definition sketch for double mass analysis

Considering the double mass plot shown in Fig. 5.1, the break points occurs at time T 1 and if the start and end times of the period under consideration are T0 and T2 respectively, then the slopes of the curve before and after the break point can be expressed as:

T1

1

Ptest,i

i0

T

1

Pbase,i

andi0

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T2 T1

Ptest,i P

test,i

2 iT0 iT0

T2 T1

Pbase,i P

base,i

iT0 iT0

In case the earlier portion between T0 and T1 is desired to be corrected for then the correction factor and the corrected observations at the test station can be expressed respectively as:

Pcorr,i

Ptest,i

2

1

After making such correction the double mass curve can again be plotted to see that there is no significant change in the slope of the curve. The double mass curve technique is usually applied to aggregated monthly (rather than daily) data and carried out annually. However there are circumstances where the technique might be applied to daily data to date the beginning of an instrument fault such as a leaking gauge. Once an inconsistency has been identified, the adjustment should be applied to all data intervals

6.1Using spatial interpolation to interpolate erroneous and missing values

General description

Missing data and data identified as erroneous by validation can be substituted by interpolation from neighbouring stations. These procedures are widely applied to daily rainfall. Estimated values of the rainfall using such interpolation methods are obtained for as many data point as required. However, in practice usually only a limited number of data values will require to be estimated at a stretch. Three analytical procedures for estimating rainfall using such spatial interpolation methods are described below.

(a) Arithmetic average method

This method is applied if the average annual rainfall of the station under consideration is within 10% of the average annual rainfall at the adjoining stations. The erroneous or missing rainfall at the station under consideration is estimated as the simple average of neighbouring stations. Thus if the estimate for the erroneous or missing rainfall at the station under consideration is P test and the rainfall at M adjoining stations is Pbase,i (i = 1 to M), then:

1P

test

M (P

base,1 P

base,2 P

base,3 ....P

base,M )

Usually, averaging of three or more adjoining stations is considered to give a satisfactory estimate.

(b) Normal ratio method

This method is preferred if the average (or normal) annual rainfall of the station under consideration differs from the average annual rainfall at the adjoining stations by more than 10%. The erroneous or missing rainfall at the station under consideration is estimated as the weighted average of adjoining stations. The rainfall at each of the adjoining stations is weighted by the ratio of the average annual rainfall at the station under consideration and average annual rainfall of the adjoining station. The rainfall for the erroneous or missing value at the station under consideration is estimated as:

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P 1

(

Ntest

P

Ntest

P

Ntest

P ....

Ntest

PN N Ntest M N

base,1

1base

base,2

base,2

base,3

base,3

base,M

base,M

Where:Ntest = annual normal rainfall at the station under considerationNbase,i = annual normal rainfall at the adjoining stations (for i = 1 to M)

A minimum of three adjoining stations must be generally used for obtaining good estimates using normal ratio method.

It may be seen from the above estimation results that on an average the observed and estimated rainfall matches fairly well. Since, the above is a very small sample for judging the performance of the two averaging method, but the suitability of the normal ratio method is implied since it would maintain the long term relationship between the three stations with respect to the station normal rainfalls.

(c) Distance power method

This method weights neighbouring stations on the basis of their distance from the station under consideration, on the assumption that closer stations are better correlated than those further away and that beyond a certain distance they are insufficiently correlated to be of use.. Spatial interpolation is made by weighing the adjoining station rainfall as inversely proportional to some power of the distances from the station under consideration. Normally, an exponent of 2 is used with the distances to obtain the weighted average.

In this method four quadrants are delineated by north-south and east-west lines passing through the raingauge station under consideration, as shown in Fig. 6.1. A circle is drawn of radius equal to the distance within which significant correlation is assumed to exist between the rainfall data, for the time interval under consideration. The adjoining stations are now selected on the basis of following:

The adjoining stations must lie within the specified radius having significant spatial correlation with one another.

A maximum number of 8 adjoining stations are sufficient for estimation of spatial average. An equal number of stations from each of the four quadrants is preferred for minimising any

directional bias. However, due to prevailing wind conditions or orographic effects spatial heterogeneity may be present. In such cases normalised values rather than actual values should be used in interpolation.

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Fig. 6.1: Definition sketch of Test and Base (neighbouring) stations

The spatially interpolated estimate of the rainfall at the station under consideration is obtained as:

8.1 base

Pi , j / Di b P

est, j i 1

Mbase

1/Di b

i1

Where:= estimated rainfall at the test station at time jPest,j

Pi,j = observed rainfall at the neighbour station i at time jDi = distance between the test and the neighbouring station iMbase = number of neighbouring stations taken into account.b = power of distance D used for weighting rainfall values at individual station

6.4.1 Correction for heterogeneity

To correct for the sources of heterogeneity, e.g. orographic effects, normalised values must be used in place of actual rainfall values at the adjoining stations. This implies that the observed rainfall values at the adjoining stations used above are multiplied by the ratio of the normal annual rainfall at the station under consideration (test station) and the normal annual rainfall at the adjoining stations (base stations). That is:

Pcorr,i , j

( N

test /

N

base,i )P

i, j

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Where:Pcorr,i,j = for heterogeneity corrected rainfall value at the neighbour station i at time jNtest = annual normal rainfall at the station under considerationN base,i = annual normal rainfall at the adjoining stations (for i = 1 to Mbase)

Station normals are either found from the historical records and are readily available. Otherwise, they may be computed from established relationships, as a function of altitude, if sufficient data is not available at all stations for estimating station normals. The relationship for station normals as a function of the station altitude (H) is of the form:

Ni a1 b1 . Hs H s H1

Ni a2 b2 . Hs H s > H1

After scrutiny and checking rainfall series the incorrect and missing values will be replaced where possible by estimated values based on other observations at the same station or at neighboring stations. The process of filling in missing values is generally referred to as ‘completion’. Where no suitable neighboring observations or stations are available, missing values will be left as ‘missing’ and incorrect values will be set to ‘missing’. Procedures for correction and completion depend on the type of error and the availability of suitable source records with which to estimate, what should have been studied using the tools described in the previous section The judgment of the hydrologist is critical at this stage. The newly calculated value will then be marked and not anymore as missing. A label attached to the data value, saying this data value is a completed value, will be stored in the database.Gap Filling & Correction allows the user to carry out the data correction and completion of the selected series using different process and tools:

1. Relation curves2. Constant correction3. Using existing records4. Time shifting 5. Drift correction

1.1 Relation curvesUsing tools of Time Series Analysis/General Inspection of Series the relationship between stations is studied.The regression curves analyzed are stored if the user considers them adequate.The best regression curve for each interval should be used for filling gaps. The user will select it/them from a list of correlations.

· Linear. Only fill series with few gaps: For Rainfall this method is recommended only for Hourly

· Polynomial

· Power

· Exponential

Example 1.1:Completion gaps of one station at Narmada Basin, using data of an adjacent station. The regression curves generated in previous stages should be used.Fig(bellow):

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Table(bellow):DATETIME VALUE REMARK COMPUTED

01-Oct-2007 8:30 AM 0.708 GAP FILLED BY USING X = 0.0 ON -0.004573223207763986 X² + 0.7492417073237746 X + 0.7075985562684594 Yes































1.2 constant correction

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Filling-in data according to the “block type filling” option comprises the replacement of missing data by the last non-missing value before any gap. If the completion starts at the beginning of the series, it will be filling with the first value non-missing.Each fitting must be checked using goodness test: mean quadratic error.

Example 1.2:Completion of gaps of one station at Narmada Basin, using non-missing data of the same station the generated graph and report table(for March 2014) is bellow:

DATETIME VALUE REMARK

01-Mar-2014 8:30 AM 0 Computed Block-type filling-in










11-Mar-2014 8:30 AM 0



14-Mar-2014 8:30 AM 13



17-Mar-2014 8:30 AM 156.4

18-Mar-2014 8:30 AM 156.4 Computed Block-type filling-in










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1.1 using existing recordsTo fill data of series with series of different time steps, from the same station, using aggregated series.

SRG record missing or faulty - ARG available: The record from the standard rain-gauge may be missing or faulty due to poor observation technique, a wrong or broken measuring glass or a leaking gauge. In these circumstances, it is reasonable to correct the erroneous standard rain-gauge data or complete them using the autographic records of the same station. The standard rain-gauge data in such cases are made equal to that obtained from the autographic records. The standard rain-gauges are normally observed at one or two times in the day i.e. at 0830 hrs or 0830 and 1730 hrs. The estimated values for such observations can be obtained by aggregating the hourly autographic records corresponding to these timings.

1.2 shiftingTo correct entries of wrong data, showing by tabulation the test series with shift data and the series of the nearby stations.Shift errors in rainfall series can often be spotted in the tabulated or plotted multiple series, especially if they are repeated over several wet/dry spells. It is assumed that no more than one of the listed series will be shifted in the same direction in the same set.There are two important things to be considered while correcting the data for the identified shift in the data series:

· The amount of shift

· The extent of data affected by the shift

Example 1.4:Wherein during validation by tabulation a time shift was found in a station Narmada at Barman, comparing with the station Narmada at Rajghat and Narmada at Mortakka of Narmada Basin. The tabulation of the data series of the nearby stations allows checking and correcting data. Bellow is the result in tabular and graphical form:

.1.3 Drift correction

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The pen of the autographic recorder may gradually drift from its true position. In this case, analogue observations may show deviation from the staff gauge observations. This deviation can be static or may increase gradually with time.Where a digital record is produced from an analogue record using a pen-follower digitizer, the annotated clock and recorder time and level can be fed into the digitizing program and an accumulative adjustment spread over the level record from the time the error is thought to have commenced till the error was detected or the chart removed. However, such procedure is not recommended to be followed as the actual reasons for the shift may still be unknown at the time of digitizing the charts. It is always appropriate to tabulate/digitize the chart record as it is in the first instance and then apply corrections thereafter.This option for correcting the gradual spread of error in digital records extracted from a chart recorder, with a growing adjustment from the commencement of the error until error detection. Let the error be ΔX observed at time t = i+k and assumed to have commenced at k intervals before, then the applied correction reads:Xcorr,j = Xmeas,j - ((j - i)/k)ΔX for j = i, i+1, ......., i+k (8.1)Example 1.5:

To correct the gradual spread of error in digital records extracted from a chart recorder, with a growing adjustment from the commencement of the error until error detection. Taking in account the station “Narmada at Mortakka” and bellow is the Drift correction parameters:

Bellow is the generated graph:

Below is the review series:

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Chapter 6: Compile Rainfall Data

1. GENERALRainfall compilation is the process by which observed (or generated) rainfall is transformed:· from one time interval to another· from one unit of measurement to another· from point to areal valuesCompilation is required for validation, reporting and analysisThe tool with these functions is: Compilation & Generation, including:· Aggregation· Disaggregation· Creation of derived series· Computation of areal rainfall

1.1. AGGREGATION OF DATA TO LONGER DURATIONSRainfall from different sources is observed at different time intervals, but these are generally one day or less. For the standard rain-gauge, rainfall is measured once or twice daily. For autographic records, a continuous trace is produced from which hourly rainfall is extracted. For digital rainfall recorders rainfall is recorded at variable interval with each tip of the tipping bucket. Hourly data are typically aggregated to daily; daily data are typically aggregated to weekly, ten daily, 15 daily, monthly, seasonally or yearly time intervalsAggregation to longer time intervals is required for validation and analysis. For validation small persistent errors may not be detected at the small time interval of observation but may more readily be detected at longer time intervals.

Aggregation of daily to weekly: Aggregation of daily to weekly time interval is usually done by considering the first 51 weeks of equal length (i.e. 7 days) and the last 52nd week of either 8 or 9 days according to whether the year is non-leap year or a leap year respectively. The rainfall for such weekly time periods is obtained by simple summation of consecutive sets of seven days rainfalls. The last week’s rainfall is obtained by summing up the last 8 or 9 days daily rainfall values.For some application it may be required to get the weekly compilation done for the exact calendar weeks (from Monday to Sunday). In such a case the first week in any year will start from the first Monday in that year and thus there will be 51 or 52 full weeks in the year and one or more days left in the beginning and/or end of the year. The days left out at the end of a year or beginning of the next year could be considered for the 52nd of the year under consideration. There will also be cases of a 53rd week when the 1st day of the year is also the first day of the week (for non-leap years) and 1st or 2nd day of the year is also first day of the week (for leap years).

Aggregation of daily to ten daily: Aggregation of daily to ten daily time interval is usually done by considering each month of three ten daily periods. Hence, every month will have first two ten daily periods of ten days each and last ten daily period of either 8, 9, 10 or 11 days according to the month and the year. Rainfall data for such ten daily periods is obtained by summing the corresponding daily rainfall data. Rainfall data for 15 daily periods is also be obtained in a similar manner for each of the two parts of every month.

Aggregation from daily to monthly: Monthly data are obtained from daily data by summing the daily rainfall data for the calendar months. Thus, the number of daily data to be summed up will be 28, 29, 30 or 31 according to the month and year under consideration. Similarly, yearly rainfall data are obtained by either summing the corresponding daily data or monthly data, if available.Hourly to other intervals: From rainfall data at hourly or lesser time intervals, it may be desired to obtain rainfall data for every 2 hours, 3 hours, 6 hours, 12 hours etc. for any specific requirement. Such compilations are carried out by simply adding up the corresponding rainfall data at available smaller time interval.

2. Hourly to other intervals

From rainfall data at hourly or lesser time intervals, it may be required to obtain rainfall data for every 2 hours, 3 hours, 6 hours, 12 hours etc. for any specific requirement. Such compilations are carried out by simply adding up the corresponding rainfall data at available smaller time interval.

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Example 2.1:

Daily rainfall at Tapi at Bhuswal is observed with Autographic Raingauge (ARG). Standard Raingauge (SRG) is also available at the same station for recording rainfall continuously and hourly rainfall data is obtained by tabulating information from the chart records.

It is required that the hourly data is compiled to the daily interval corresponding to the observations synoptic observations at 0830 hrs. This compilation is done using the aggregation option and choosing to convert from hourly to daily interval. The observed hourly data and compiled daily data, Monthly data and Yearly data is shown in Fig. 2.1, Fig. 2.2, Fig. 2.3 and Fig. 2.4 respectively.

Fig. 2.1: Plot of observed hourly rainfall data

Fig. 2.2: Compiled daily rainfall from hourly data tabulated from SRG charts

Similarly, daily data observed using SRG is required to be compiled at weekly, ten-daily, monthly and/or yearly interval for various application and for the purpose of data validation. For this, the daily data obtained using SRG is taken as the basic data and compilation is done to weekly, ten-daily, monthly and yearly intervals. These are illustrated in Fig. 2.3, Fig. 2.4, Fig. 2.5 and Fig. 2.6 respectively

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Fig. 2.3: Compiled Weekly data from daily data obtained from SRG records

Fig. 2.4: Compiled Ten Daily data from daily data obtained from SRG records

Fig. 2.5: Compiled monthly data from daily data obtained from SRG records

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Fig. 2.6: Compiled monthly data from daily data obtained from SRG records

Options available while Aggregation:· Value of first time step

When 'Value of first time step' is checked the aggregation values will be taken as the first value of the new time step When, for example, daily values are aggregated to monthly values, the aggregated monthly values will be equal to the first value of each month.

· Time ShiftThe Time Shift option is introduced to change the start time of the aggregated series, by default the time shift is 0. The time shift can be changed by using the spin button or by entering a value in the text box. The time shift values must be integer values, between -1000 and +1000.This option can be useful when aggregating hourly rainfall values to daily values. When you aggregate hourly values from 1-1-2000 8:00 to 2-1-2000 8:00 the aggregated daily rainfall value will, by default, be set to 1-1-2000. In many countries the meteorological service uses a different procedure, the aggregated daily rainfall value is set to 2-1-2000.

· Ignore Missing Values. The user decided what to do with missing values (-999)

DISAGREGATION OF DATA TO SHORTER INTERVALSFor disaggregating series different methods available:• Equal value: basic and dis-aggregated series data are equal,• Fractions of the basic series: if there are n disaggregated series elements in a basic series interval, then the fraction is 1/n: disaggregated series data = 1/n * basic series data,• Interpolation: the dis-aggregated series data are interpolated linearly. between the mid-point values of the basic series dataExample 1.1:It is required that a station with the daily data is compiled to the hourly interval. This compilation is done using the disaggregation option and selecting to convert from daily to hourly interval. Daily rainfall at Tapi at Bhuswal is changing to hourly data

CREATION OF DERIVED SERIESThe annual, seasonal or monthly maximum series of rainfall is frequently required for flood analysis, whilst minimum series may be required for drought analysis. This process allows the user to get data series from different data series selected previously. It will be possible getting this type of data series:· Data series of maximum values· Data series of minimum values· Data series of average values

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· Data series of median values· Data series from a series multiplying by a value· Data series from addition of several data series· Data series from subtraction of several seriesFollowing is the tabular view of MIN, MAX, MEAN and MEDAN values for TIKARAPARA station:

3. COMPUTATION OF RAINFALL AREARain-gauges generally measure rainfall at individual points. However, many hydrological applications require the average depth of rainfall occurring over an area which can then be compared directly with runoff from that area. The area under consideration can be a principal river basin or a component sub-basin. Occasionally, average areal rainfall is required for country, state or other administrative unit, and the areal average is obtained within the appropriate political or administrative boundary.Since rainfall is spatially variable and the spatial distribution varies between events, point rainfall does not provide a precise estimate or representation of the areal rainfall. The areal rainfall will always be an estimate and not the true rainfall depth irrespective of the method.There are a number of methods which can be employed for estimation of the areal rainfall including:- Weighted average method - Thiessen polygon method. These methods for estimation of areal average rainfall compute the weighted average of the point rainfall values; the difference between various methods is only in assigning the weights to these individual point rainfall values, the weights being primarily based on the proportional area represented by a point gauge. Methods are outlined below:

3.1.1. Weighted averageThis is the simplest of all the methods and as the name suggests the areal average rainfall depth is estimated by simple averaging of all selected point rainfall values for the area under consideration. That is: Where:Pat= estimated average areal rainfall depth at time tPit = individual point rainfall values considered for an area, at station i ( for k = 1,N) and time t,Ck = weight assigned to individual rain-gauge station k (k = 1,N).N = total number of point rainfall stations consideredSometimes all point rainfall stations are allocated weights of equal magnitude, equal to the reciprocal of the total number of stations considered. Generally, stations located within the area under consideration are taken into account. However, it is good practice also to include such stations which are outside but close to the areal boundary and thus to represent some part of the areal rainfall within the boundary. This method is also sometimes called as unweighted average method when all the stations are given the same weights irrespective of their locations.This method gives satisfactory estimates and is recommended when:• The area under consideration is flat• The spatial distribution of rainfall is fairly uniform

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• The variation of individual gauge records from the mean is not greatThe tool with this function is: Compilation & Generation / Computation of areal rainfall

With 'Definition Areal Series Weights' the user can make generate relations by selecting Series Codes for the Areal Series and for the Point Series. The function gives the possibility to enter equal weights or to specify station weights.

Example 1.5.1: Fig.1.1 is a graph for Tapi basin by areal rainfall “Equal station weight”

Fig. 1.1: Areal Rainfall

3.1.2. Thiessen polygonThis widely-used method was proposed by A.M. Thiessen in 1911. The Thiessen polygon method accounts for the variability in spatial distribution of gauges and the consequent variable area which each gauge represents. The areas representing each gauge are defined by drawing lines between adjacent stations on a map. The perpendicular bisectors of these lines form a pattern of polygons (the Thiessen polygons) with one station in each polygon. Stations outside the basin boundary should be included in the analysis as they may have polygons which extend into the basin area. The area of a polygon for an individual station as a proportion of the total basin area represents the Thiessen weight for that station. Areal rainfall is thus estimated by first multiplying individual station totals by their Thiessen weights and then summing the weighted totals as follows:

Where:Pm= estimated average areal rainfall depthPi= Individual Rainfall valuesAi = the area of Thiessen polygon for station i A = total area under consideration

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The polygons are computed based on the catchment boundary contour and the station locations. The catchment boundary is a characteristic of a Catchment which is selected from the catchment list box. If for a time step at one or more of the point rainfall stations an observation is missing then automatically a missing value will be entered for the areal rainfall.The combination of point rainfall stations and weights to compute the areal rainfall are stored in the database to be used at a later stage for different time periods.The Thiessen method is objective and readily computerized but is not ideal for mountainous areas where physiographic effects are significant or where rain-gauges are predominantly located at lower elevations of the basin. Altitude weighted polygons (including altitude as well as areal effects) have been devised but are not widely used.Example 1.5.1:Areal average rainfall for a basin in Tapi catchment is required to be compiled on the basis of rainfall data observed at a number of rain-gauges in and around the region. Areal average is worked out using Thiessen method. Figure 1.1 is a graph of areal rainfall:

Fig. 1.1: Areal Rainfall

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Chapter 7: Primary Validation for Climatic Data

Data validation in its simplest form involves inspection of a data set and being able to say what is realistic and what is unrealistic and correcting the unrealistic if it is possible.

The question can then be asked - what is realistic? To the uninitiated it is just a set of numbers. How do we know that one set of numbers is better or worse than the ones which have been provided? To illustrate some general principles a simple example is used of a climatic number set. We are given dry bulb temperatures at a station at hourly intervals;

0700 25.0oC0800 28.0oC0900 40.0oC

We could reasonably assume that there was a mistake in one or more of the readings, probably the last. We don’t expect the temperature to rise by 12oC in one hour. If the next reading at 1000 was 32oC we would be even more confident that the figure of 40oC entered for 0900 was incorrect and that the most likely cause was that the observer had incorrectly read 40oC for 30oC (or had read it correctly but written it down wrong). From this simple example we can draw several lessons.

· The numbers in a data set are representative of a variable and the sequence of the variable represents a physical process which has physical behaviour and physical limits. In the example above the numbers represent a physical process of atmospheric warming under the influence of solar radiation. A rise in temperature of 12oC in one hour is quite unrealistic. The lesson is that if we want to know what is realistic we must first understand the physical process, its behaviour and limits.

· The method of measurement or observation influences our view of why the data are suspect. In the example above, we can make a reasonable guess of the source of the error because we know that the measurement was taken manually by an observer. Observers are not infallible; they make mistakes - even the best observers. The lesson here is that to understand the source of errors we must understand the method of measurement or observation in the field and the typical errors of given instruments and techniques.

· Data validation must never be considered a purely statistical or mathematical exercise. Staff involved in it must understand the physical process and field practice.

· Graphical inspection permits detection of errors which are more difficult to identify by numerical techniques. Take for example a variation on the above set of temperatures. Say, the temperature listed in the data set at 0900 was 35oC would we still consider that the value was a mistake? Perhaps yes, but we would not be so certain; we would consider it suspicious but not impossible. If such a value were plotted on a graph for the day as available in eSWIS, an error both for 40oC and for 35OC becomes a near certainty

Primary validation can be considered, variable by variable, looking in summary at the physical process, behavior and limits, and then its field measurement and typical errors, for the following variables:

1. Temperature 2. Humidity 3. Wind speed 4. Pan evaporation 5. Atmospheric pressure 6. Sunshine

1. Primary validation of temperature

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1.1. Temperature variation and controls

Temperature is a measure of the ability of a body (in this case the atmosphere) to communicate heat to other bodies and to receive heat from them (IMD definition). Temperature varies primarily with the magnitude of solar radiation and observes cyclic diurnal and seasonal patterns. It is influenced at particular times by prevailing air masses and by the incursion of air masses from other source areas with different insolation properties and by prevailing cloudiness which limits incoming radiation. These factors limit the maximum and minimum temperatures which are expected at a given location for given season and time of day. They also limit the rates of change expected from hour to hour and from day to day.

With respect to location, temperature varies with latitude (which controls solar radiation), altitude and proximity to the ocean. Generally temperature is a spatially conservative element which has strong correlation (at least on an averaged basis) with neighbouring stations within the same air mass. There is normally a regular decrease in mean temperature with altitude at a rate of approximately 0.6oC per 100 metres for moist air and 0.9oC for dry air. Stations in close proximity to the sea have their temperature moderated by its influence so that maxima tend not to be so high, minima not so low, thus giving a reduced diurnal range.

Specific site conditions also affect the temperature measured. Stations in topographic hollows may experience temperature inversions in calm conditions, reversing the normal lapse rate of temperature with altitude. Stations sited in urban areas have generally higher temperatures than adjacent rural areas. The nearby prevailing ground cover, whether bare or vegetated, influences the measured temperature - including the proximity of trees which shade the site or of buildings which alternately shade and reflect heat to the station.

Validation based on location and site conditions are best considered in the comparison between stations and is discussed under secondary validation.

1.2. Temperature measurement

Temperature is periodically observed (once or twice daily) using a set of four thermometers, located in a thermometer (or Stevenson) screen, which from its construction and installation provides a standard condition of ventilation and shade. The four thermometers are:

Dry bulb thermometer - measuring ambient air temperature

Wet bulb thermometer - which provides a basis for calculating relative humidity Maximum thermometer - to indicate the highest temperature reached since the last settingMinimum thermometer - to indicate the lowest temperature reached since the last

setting.

Graduations are etched on the glass stem of the thermometer. In the case of the dry bulb, wet bulb and maximum thermometers, observations are of the position of the end of the mercury column but in the case of the minimum thermometer, the reading is taken of the position of the end of the dumb-bell shaped index furthest from the bulb. Each thermometer has a calibration card which shows the difference between the true temperature and that registered by the thermometer. Corrections for a given temperature are applied to each observation. When the maximum and minimum thermometers have been read they are reset (twice per day for minimum; once per day for maximum) using a standard procedure.

Temperature is also measured continuously using a thermograph in which changes in temperature are recorded through the use of a bi-metallic strip. The temperature is registered on a chart on a clock-driven revolving drum and the measurement (chart) period may be

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either one day or one week. The observer extracts temperatures at a selected interval from the chart. The manually observed reading on the dry bulb thermometer is measured and recorded at the beginning and end of the chart period and if these differ from the chart value, a correction is applied to the chart readings at the selected interval.

1.3. Typical measurement errors

Observer error in reading the thermometer, often error of 1oC (difficult to detect) but sometimes 5oC or 10oC. Such errors are made more common in thermometers with faint graduation etchings.

Observer error in registering the thermometer reading Observer reading meniscus level in minimum thermometer rather than index Thermometer fault - breaks in the mercury thread of the dry, wet or maximum

thermometer Thermometer fault - failure of constriction of the maximum thermometer Thermometer fault - break in the spirit column of minimum thermometer or spirit

lodged at the top or bubble in the bulb. Thermograph out of calibration and no correction made.

Thermometer faults will result in individual or persistent systematic errors in temperature.

1.4. Error detection

Many of the above faults will have been identified by the field supervisor or at data entry but others may be identified by setting up appropriate maximum minimum and warning limits for the station in question. These may be altered seasonally. For example, summer maximum temperature can be expected not to exceed 50oC nor winter maximum temperature to exceed 33oC.

Other checks carried out by eSWIS include:

Dry bulb temperature should be greater than or (rarely) equal to the wet bulb temperature.

Maximum temperature should be greater than minimum temperature Maximum temperature measured using the maximum thermometer should be greater

than or equal to the maximum temperature recorded by the dry bulb during the interval, including the time of maximum observation. The value of the maximum will be set to the observed maximum on the dry bulb if this is greater.

Minimum temperature should be less than or equal to the minimum temperature recorded by the minimum thermometer during the interval, including the time of observation of the minimum thermometer. The value of the minimum will be set to the observed minimum on the dry bulb if this is lower.

Thermograph readings at time of putting on and taking off should agree with the manually observed readings.

2. Primary validation of humidity2.1. Humidity variations and control

The standard means of assessing the relative humidity or moisture content of the air is by means of the joint measurement of dry bulb and wet bulb temperature. From these two measurements, the dew point temperature, actual and saturated vapour pressures may also be calculated. The relative humidity (%) is the ratio of the actual vapour pressure to saturated vapour pressure corresponding to the dry bulb temperature. Whilst the actual vapour pressure may vary little during the day (except with the incursion of a new air mass), the

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relative humidity has a regular diurnal pattern with a minimum normally coinciding with the highest temperature (when the saturation vapour pressure is at its highest). It also shows a regular seasonal variation.

Generally relative humidity is a spatially conservative element which has strong correlation (at least on an average basis) with neighbouring stations within the same air mass. Stations in close proximity to the sea have higher relative humidities than those inland and a smaller daily range.

2.2. Humidity measurement

Wet and dry bulb thermometers used for temperature assessment also used for calculating various measures of humidity. The wet bulb is covered with a clean muslin sleeve, tied round the bulb by a cotton wick which is then led to a water container, by which the wick and muslin are kept constantly moist.

The observer calculates the relative humidity from the wet bulb depression using a set of tables.

Relative humidity may also be measured continuously by means of hygrograph in which the sensor is human hair whose length varies with relative humidity. The humidity is registered on a chart on a clock-driven revolving drum and the measurement (chart) period may be either one day or one week. The observer extracts humidity at a selected interval from the chart. A manually computed reading from dry and wet bulb thermometers is recorded at the beginning and end of the chart period and if these differ from the chart value, a correction is applied to the chart readings at the selected interval.


Measurement errors using dry and wet bulb thermometers in the assessment of humidity are the same as those for temperature. In addition an error will occur if the muslin and wick of the wet bulb are not adequately saturated. Similarly there will be an error if the muslin becomes dirty or covered by grease. These defects will tend to give too high a reading of wet bulb temperature and consequently too high a reading of relative humidity. Errors in the hygrograph may also result from poor calibration or the failure to correct for manually observed values at the beginning and end of the chart period.


Errors may be detected by setting up upper and lower warning limits appropriate to the station and season. The maximum is set at 100%. If the wet bulb is greater than dry bulb and the resulting calculated relative humidity is greater than 100%, then the observation will be rejected by eSWIS. Graphic inspection of the daily series can be used to identify any anomalous values.

The observer calculated values of relative humidity may be compared with those calculated by the computer. However in view of the fact that the calculation can be done very simply in the office there seems little point in continuing the field calculation except in those cases where it is used to calibrate the hygrograph.

Accompanying field notes should be inspected for observations by the supervisor of errors in the thermometers or of a dry or dirty muslin. Hygrograph records can be inspected for departures of starting and finishing values measured by manual methods.

3. Primary validation of wind speed

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3.1. Wind speed variations and controls

Wind speed is of particular importance in hydrology as it controls the advective component of evaporation. Wind speed exhibits wide variation not only from place to place but also shows strong diurnal variation at the same place. Wind flow and speeds are controlled by local pressure anomalies which in turn are controlled by the temperature. It may also be influenced by local topographic features which may funnel the wind and increase it above the areal average; conversely some stations will have wind speeds reduced by shelter. Extraordinary wind speeds may be experienced in some parts of the country through the incursion of tropical cyclones.

3.2. Measurement of wind speed and direction

Wind speed is measured using an anemometer, usually a cup counter anemometer. The rate of rotation of the anemometer is translated by a gear arrangement to read accumulated wind total (km) on a counter. By observing the counter reading at the beginning and end of a period, the wind run over the period can be determined and the average speed over the interval can be determined by dividing by the time interval. Standard Indian practice is to measure the wind speed over a three minute period as representing an effectively instantaneous wind speed at the time of observation. Daily wind run or average wind speed is also calculated from counter readings on successive days at the principal observation times.

Wind direction is commonly measured and may be used in the calculation of evapo-transpiration with respect to finding the fetch of the wind. It is observed using a wind vane and reported as 16 points of the compass either as a numerical figure or an alpha character


Errors in windspeed might arise as the result of observer errors of the counter total, or arithmetic errors in the calculation of wind run or average wind speed. Instrumental errors might arise from poor maintenence or damage to the spindle which might thus result in reduced revolutions for given wind speed.


Because of extreme variability in wind speed in space and time, it is difficult to set up convincing rules to detect suspect values. Nevertheless simple checks are as follows:

Wind speeds should be zero where the direction is reported as ‘0’ (calm) Wind speeds cannot exceed 5 km/hr when the wind speed is reported as variable. Wind speeds in excess of 200 km per hour should be considered suspect and will

result in a warning flag.

4. Primary validation of atmospheric pressure

4.1. Atmospheric pressure variations and controls

Atmospheric pressure is a measure of the weight of the air column vertically above a unit area. The principal variation is with altitude but a correction is always made to reduce the observed measurement of pressure to a standard sea level pressure so that spatial variations can be more readily investigated.

Pressure changes within a relatively narrow range and rates of change are comparatively slow. Lowest pressures and the most rapid rates of change are experienced in tropical cyclones.

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Variations in atmospheric pressure are of great importance in weather forecasting but its influence on evapotranspiration is very limited and can often be assessed with acceptable accuracy with the use of a mean value of atmospheric pressure. It is of importance for pressure correction where non-vented pressure transducers are used for the measurement of water level.

4.2. Measurement of Atmospheric pressure

Atmospheric pressure is usually measured using a mercury barometer where the weight of the mercury column represents the atmospheric pressure. Commonly the Kew pattern barometer is used in India. It is read using a Vernier scale. Corrections are made for index error and for temperature (reducing to a standard temperature of 0oC using a set of tables. It is also reduced to mean sea level pressure.

A barograph is also used for the continuous measurement of pressure. It consists of an aneroid sensor which expands and contracts with changes in pressure. These are registered on a clock-driven drum chart. Values of pressure may be extracted at hourly or other intervals from the chart and it is calibrated and set up to correspond with the reading using the more accurate mercury barometer.


Observer errors may result from incorrect observation incorrect registration or in the application of corrections for temperature or reduction to sea level. Observation problems can result from the use of the Vernier scale.

Instrumental errors result from the entry of air into the space above the mercury and mechanical defects in the Vernier head.


Primary validation is mainly through the setting up of upper and lower warning and maximum and minimum limits. Values outside the maximum and minimum limits are rejected; values outside the warning limits are flagged.

5. Primary validation of sunshine duration5.1. Sunshine variations and controls

Sunshine duration is a very important contributor to the evapotranspiration equation and is widely used in the absence of direct measurements of radiation. The potential maximum sunshine duration varies regularly with latitude and with season. Actual sunshine also varies with ambient weather conditions and is generally lower during the monsoon than during the dry season. In urban areas the amount of bright sunshine may be reduced by atmospheric pollution and in coastal areas it may be reduced by sea mists.

5.2. Measurement of sunshine

The only instrument in common use in India for sunshine measurement is the Campbell Stokes sunshine recorder. This consists of a glass sphere mounted on a section of a spherical bowl. The sphere focuses the sun’s rays on a card graduated in hours, held in the grooves of the bowl which burns the card linearly through the day when the sun is shining. The card is changed daily after sunset. Hence the sunshine recorder uses the movement of the sun instead of a clock to form the time basis of the record. Different grooves in the bowl

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must be used in winter summer and the equinoxes, taking different card types. The total length of the burn in each hour gives an hourly sunshine duration.


The instrument is very simple in principle and the use of the sun rather than a clock as a time base avoids timing errors. Potential errors may arise from the use of the wrong chart which may result in the burn reaching the edge of the chart, beyond which it is not registered. Possible errors may result from extraction of information from the chart by the observer.


eSWIS may be used to detect and if necessary reject suspect values. Thus:

Values of hourly sunshine greater than 1.0 or less than 0.0 are not permitted Sunshine records before 0500 and after 1900 are rejected and hence daily

totals greater than 14.0 hours are rejected.

Daily warning limits may be set seasonally within eSWIS based on the maximum possible sunshine for the location and time of year.

6. Primary validation of pan evaporation

6.1. Pan evaporation variations and controls

Evaporation is the process by which water changes from the liquid to the vapour state. Pan evaporation provides an estimate of open water evaporation. It is a continuous process in which the rate of evaporation depends on a wide range of climatic factors:

amount of incoming solar radiation (represented by sunshine hours) temperature of the air and the evaporating surface saturation deficit - the amount of water that can be taken up by the air before it

becomes saturated (represented in measurement by the wet bulb depression) wind speed

Evaporation again maintains a regular seasonal pattern with highest totals before the onset of the monsoon, during which evaporation is suppressed by decreasing saturation deficit.

6.2. Measurement of pan evaporation

The standard measurement in India is made using the US Class A pan evaporimeter. It is a circular pan 1.22 m in diameter and 0.255 m deep. It rests on a white painted wooden stand and is maintained level. The pan is covered by a wire mesh to avoid loss of water due to birds and animals. The inner base of the pan is painted white. A stilling well is situated in the pan within which there is a pointer gauge. Measurement must take account not only of evaporation losses but also gains due to rainfall; the raingauge nearby is used to assess the depth of rain falling in the pan.

On days without rain at daily (or twice-daily) reading, water is poured into the pan using a graduated brass cylinder (cup) to bring the level up precisely to the top of the pointer gauge. The number of cups (and part cups) is recorded and represents a depth of evaporation.

On days with rain since the last observation the rainfall may exceed evaporation and water must be removed from the pan to bring it to the hook level. The adjacent raingauge is used to assess the rainfall inflow.

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On days with forecast heavy rainfall a measured amount of water may be removed from the pan in advance of the rainfall occurrence (to avoid pan overflow)


Observer errors - the observer over- or underfills the pan - such values will be compensated for the following day

Instrument errors Leakage: this is the most serious problem and it occurs usually at the joint betweenthe

base and the side wall. Small leaks are often difficult to detect in the field but may have a significant systematic effect on measured evaporation totals.

Animals may gain access to the pan, especially if the wire mesh is damaged Algae and dirt in the water will reduce the measured rate of evaporation Errors arise in periods of high rainfall when the depth caught by the raingauge is

different in depth from the depth caught in the pan as a result of splash or wind eddies round the gauges.


Warning and maximum limits may again xxxbe allocated to screen spurious values arising from observer error, leakage, animal interference or dirty water.

Where leakage has been identified and is recorded in the field record book, the records for a period preceding the discovery will be inspected and flagged as suspect and for review under secondary validation

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Chapter 8: Secondary Validation for Climatic Data

Data validation is the process to ensure that the final figure stored is the best possible representation of the true value of the variable at the measurement site at a given time or in a given interval of time.

1. Methods of Secondary validation

· Multiple station validation

Comparison Plots Of Stations Balance Series Regression Analysis Double Mass Curve

· Single station validation tests for homogeneity

mass curves residual mass curves a note on hypothesis testing

The section on multiple station validation is placed first in the text as it is generally chronologically first to be carried out at the Divisional office.

2. Screening of data series

After the data from various Sub-Divisional offices has been received at the respective Divisional office, it is organized and imported into the temporary databases of secondary module of dedicated data processing software. The first step towards data validation is making the listing of data thus for various stations in the form of a dedicated format. Such listing of data is taken for two main objectives: (a) to review the primary validation exercise by getting the data values screened against desired data limits and (b) to get the hard copy of the data on which any remarks or observation about the data validation can be maintained and communicated subsequently to the State/Regional data processing centre.

Moreover, for the case of validation of historical data for period ranging from 10 to 40 years this listing of the screening process is all the more important. This screening procedure involves, for example for daily pan evaporation, minimum or maximum temperature data, flagging of all those values which are beyond the maximum data limits or the upper warning level. It also prepares the data in a well-organized matrix form in which various months of the year are given as separate columns and various days of the month are given as rows. Below this matrix of data the monthly and yearly basic statistics like total and maximum pan evaporation etc. are listed. Also, the number of instances where the data is missing or has violated the data limits is also given.

This listing of screening process and basic statistics is very useful in seeing whether the data has come in the databases in desired manner or not and whether there is any mark inconsistency vis-à-vis expected hydrological pattern.

3. Multiple station validation

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3.1. Comparison plots

The simplest and often the most helpful means of identifying anomalies between stations is in the plotting of comparative time series. This should generally be carried out first, before other tests. For climate variables the series will usually be displayed as line graphs of a variable at two or more stations where measurements have been taken at the same time interval, such as 0830 dry bulb temperature, atmospheric pressure or daily pan evaporation.

In examining current data, the plot should include the time series of at least the previous month to ensure that there are no discontinuities between one batch of data received from the station and the next - a possible indication that the wrong data have been allocated to that station.

For climatic variables which have strong spatial correlation, such as temperature, the series will generally run along closely parallel, with the mean separation representing some locational factor such as altitude. Abrupt or progressive straying from this pattern will be evident from the comparative plot which would not necessarily have been perceived at primary validation from the inspection of the single station. An example might be the use of a faulty thermometer, in which there might be an abrupt change in the plot in relation to other stations. An evaporation pan affected by leakage may show a progressive shift as the leak develops (Fig. 1). This would permit the data processor to delimit the period over which suspect values should be corrected.

Comparison of series may also permit the acceptance of values flagged as suspect in primary validation because they fell outside the warning range . Where two or more stations display the same behaviour there is strong evidence to suggest that the values are correct. An example might be the occurrence of an anomalous atmospheric pressure in the vicinity of a tropical cyclone.

Comparison plots provide a simple means of identifying anomalies but not of correcting them. This may be done through regression analysis, spatial homogeneity testing (nearest neighbour analysis) or double mass analysis.

3.2. Balance series

An alternative method of displaying comparative time series is to plot the differences . This procedure is often applied to river flows along a channel to detect anomalies in the water balance but it may equally be applied to climatic variables to detect anomalies and to flag suspect values or sequences. Considering Zi as the balance series of the two series Xi and Yi , the computations can be simply done as:

Zi = Xi - Yi

ESWIS provides this option under “Balances”. Both the original time series and their balances can be plotted on the same figure. Anomalous values are displayed as departures from the mean difference line.

3.3. Derivative series

For scrutinising the temporal consistency it is very useful to check on the rate of change of magnitude at the consecutive time instants. This can be done by working out a derivative series. The derivative of a series is defined as the difference in magnitude between two time steps. The series ZI of a series XI is simply the difference between the consecutive values calculated as:

Zi = Xi - Xi-1

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Together with the original series the derivative series can be plotted against the limits of maximum rate of rise and maximum rate of fall. This gives a quick idea of where the rate of rise or fall is going beyond the expected values.

3.4. Regression analysis

Regression analysis is a very commonly used statistical method. In the case of climatic variables where individual or short sequences of anomalous values are present in a spatially conservative series, a simple linear relationship with a neighbouring station of the form:

Yi = a Xi + c

may well provide a sufficient basis for interpolation.

In a plot of the relationship, the suspect values will generally show up as outliers but, in contrast to the comparison plots, the graphical relationship provides no indication of the time sequencing of the suspect values and whether the outliers were scattered or contained in one block.

The relationship should be derived for a period within the same season as the suspect values. (The relationship may change between seasons). The suspect values previously identified should be removed before deriving the relationship, which may then be applied to compute corrected values to replace the suspect ones.

Validation section provides a section on “Relation Curves” which gives a number of variants of regression analysis including polynomial regression and introduction of time shifts, generally more applicable to river flow than to climate. A more comprehensive description of regression analysis is given in the Chapter on “Series completion and regression”

3.5. Double mass curves

Double mass curve analysis has already been described in the secondary validation of rainfall and a full description will not be repeated here. It may also be used to show trends or inhomogeneities between climate stations but it is usually used with longer, aggregated series. However in the case of a leaking evaporation pan, described above, the display of a mass curve of daily values for a period commencing some time before leakage commenced, the anomaly will show up as a curvature in the mass curve plot.

This procedure may only be used to correct or replace suspect values where there has been a systematic but constant shift in the variable at the station in question , i.e., where the plot shows two straight lines separated by a break of slope. In this case the correction factor is the ratio of the slope of the adjusted mass curve to the slope of the unadjusted mass curve. Where there has been progressive departure from previous behaviour, the slope is not constant as in the case of the leaking evaporation pan, and the method should not be used.

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Chapter 9: Analysing of Climatic Data

Evaporation is the process by which water is lost to the atmosphere in the form of vapour from large open free water bodies like ponds, rivers, lakes and reservoirs.

Transpiration is the process by which water leaves the body of a living plant and reaches the atmosphere as water vapour. The water present as soil moisture in the root zone is extracted by the vegetation through its roots and is passed through the stem and branches and is eventually lost as transpiration from the leaves. For hydrological purposes, evaporation and transpiration processes are commonly considered together as evapotranspiration

Potential evapotranspiration (PE) is usually defined as the water loss which will occur from a surface fully covered by green vegetation if at no time there is a deficiency of water in the soil for the use of vegetation. It is primarily dependent on climatic conditions.

Actual evapotranspiration (AE) is the real evapotranspiration at a location dependent on the available moisture in the soil which is in turn dependent on soil characteristics. It may be calculated from PE for the specific conditions at the site.

Evaporation from a free water surface and potential evapotranspiration are the principal variables of interest in hydrology. Evaporation estimates may be based on measurement of losses from an evaporation pan or on theoretical and empirical methods based on climatological measurements. Practical estimation of potential evapotranspiration depends on estimation from climatological data. Several researchers have developed empirical formulae for estimation of evaporation and evapotranspiration from climatic data. These formulae range from simple regression type equations to more detailed methods such as those representing water budget, energy budget and mass transfer approaches; the principal methods in use are based on the Penman equation and methodology as discussed in full.

Climatic data (with the exception of measured pan evapotranspiration) are thus not themselves of interest in hydrology but they are required for the estimation of evaporation from open water and evapotranspiration.

1. Analysis of pan evaporation

1.1. Pans for estimating open water evaporation

Evaporation measured by pans does not represent the evaporation from large water bodies such as lakes and reservoirs. Pans have the following limitations:

· Pans differ from lakes and reservoirs in the heat storage characteristics and heat transfer. Pans exposed above ground are subject to heat exchange through the sides

· The height of rim in an evaporation pan affects the wind action over the surface.

· The heat transfer characteristics of the pan material is different from that of the reservoir

Since heat storage in pans is small, pan evaporation is nearly in phase with climate, but in the case of very large and deep lakes the time lag in lake evaporation may be up to several months. Estimates of annual lake evaporation can be obtained by application of the appropriate lake – pan coefficient to observed pan evaporation.

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The lake – pan coefficient is given by El / E p where El is the evaporation from the lake andE p is the evaporation from the pan. Pan - lake coefficients show considerable variation

from place to place and from month to month for the same location (WMO Technical Note 126). The variation from month to month precludes the use of a constant pan coefficient.

Monthly pan coefficient depends on climate, and lake size and depth, and range will generally vary from 0.6 to 0.8. For dry seasons and arid climates the pan water temperature is less than the air temperature and the coefficient may be 0.60 or less whilst for humid seasons and climates where the pan water temperature is higher than air temperature pan coefficients may be 0.80 or higher. The average value used is generally 0.7. Based on the studies carried out in India, the average pan - lake coefficient for the Indian Standard pan was found to be 0.8 ranging from 0.65 to 1.10. Ramasastri (1987) computed open water evaporation using pan – lake coefficients for whole of India based on the evaporation data of 104 US Class A pan evaporimeters.

1.2. Effects of mesh screening

The top of the standard pan in use in India is covered fully with a hexagonal wire netting of galvanised iron to protect the water in the pan from birds. The screen has an effect to reduce pan evaporation by about 14 % as compared to that from an un-screened pan. Although a correction factor of 1.144 is commonly applied, it seems preferable, to retain the originally measured values in the archive, to indicate that this is the case in reports, and to leave mesh corrections to users. This is to allow for the possibility that future amendments may be made to the correction factor.

1.3. Pans for estimating reference crop evapotranspiration

Estimation of reference crop evapotranspiration from:

E t K P .E pan 1

where

KP = pan coefficient (FAO (1977) publication No 24)Epan = pan evaporation in mm / day

The pan coefficient is a function of relative humidity, daily windrun and the fetch . The fetch depends on the dryness or wetness of the upwind land surface as illustrated in Fig. 1. There are two cases:

· for case 1 the fetch is the length of the upwind green crop from the pan· for case 2 the fetch is the length of the upwind dry surface between the crop and the pan

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Fig. 2.1: Definition sketch for computing pan coefficient

1.4. Pan evaporation references

Gupta, Shekhar; Vasudev and P. N. Modi (1991) ‘A regression model for potential evapotranspiration estimation’, Journal of Indian Water Resources Society, Vol 11, No 4, pp 30 – 32

Ramasastri, K. S. (1987) ‘Estimation of evaporation from free water surfaces’ Proceedings of National Symposium on Hydrology Roorkee (India), pp ll – 16 to ll – 27

Venkataraman, S. and V. Krishnamurthy (1965) ‘Studies on the estimation of Pan evaporation from meteorological parameters’, Indian Journal of Meteorology and Geophysics, Vol.16 , No.4 pp 585 - 602

World Meteorological Organisation (1966) ‘Measurement and estimation of evaporation and evapo-transpiration’ WMO Technical Note No. 83

World Meteorological Organisation (1973) ‘Comparison between pan and lake evaporation WMO Technical Note No. 126

2. Estimation of potential evapotranspiration

2.1. General

The Penman method, in wide use for estimation of potential evapotranspiration arose from earlier studies of methods to estimate open water evaporation. In turn, both depend on the combination of two physical approaches which have been used in calculating evaporation from open water:

the mass transfer method, sometimes called the vapour flux method, which calculates the upward flux of water vapour from the evaporating surface

the energy budget method which considers the heat sources and sinks of the water body and air and isolates the energy required for the evaporating process

The disadvantage of these methods is the requirement for data not normally measured at standard climatological stations. To overcome this difficulty Penman (1948) developed a formula for calculating open water evaporation, combining the physical principles of the mass transfer and energy budget methods with some empirical concepts incorporated, to enable standard meteorological observations to be used. The method was subsequently adapted to

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estimate potential evapotranspiration and to substitute alternative more commonly measured climatic variables for those less commonly measured.

2.2. The Penman method

The Penman formula may be presented in a number of formats but may be conveniently expressed as follows:

E

R n

f (u)(es ea ) 2

where:

E = reference crop evapotranspiration (mm/day)· = slope of es - t curve at temperature t (mb/oC) · = psychometric constant (mb/oC) Rn = net radiation (mm/day)f(u) = wind related functiones = saturation vapour pressure at mean air temperature (mb)ea = actual vapour pressure (mb)

The vapour pressure-temperature gradient is computed from:

des

4098 es

3(237.3 dT T )2

where:

T = t + 273.16 (oKelvin)t = air temperature (oC)

and

17.27 T

es (T ) 0.6108 exp 4 237.3T

The psychometric constant is computed from:

e (Tw

) e (T )

cp ps aa

T Tw

where:

cp = specific heat of air (=1.005 kJkg-1)p = atmospheric pressure (kPa)

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= ratio of molecular masses of water vapour and dry air = 0.6225.1 = latent heat of vaporisation (kJkg-1)

Where the air pressure is not measured, it is estimated as:

p

T 0.0065 H 5.256

101.3 T

Where

H = elevation relative to m.s.l (m)

Where net radiation Rn is not available (as is normally the case in India), it can be substituted in turn by net shortwave and net longwave radiation, and then by bright sunshine totals which are more commonly measured at standard climatological stations. Thus net radiation can be computed from:

Rn Rns Rnl 7

where:

Rns = net shortwave radiationRnl = net longwave radiation

and in turn net shortwave radiation is:

Rns (1 ) Rs 8

where:

= albedoRs = shortwave radiation

If the shortwave radiation is not available it is computed from:

Rs Ra (a1 b1 n / N ) 9

where:

Ra = extra terrestrial radiation (available from tables dependent on latitude and time ofyear)

n/N = actual to maximum bright sunshine duration (from Campbell Stokes sunshinerecorder)

a1 , b1 = coefficients

If the net longwave radiation is not available it is estimated from:

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Rnl T 4 (a2 b2 ea )(a3 b3 n / N ) 10

where:

5.2 = Boltzmann constant ( = 2.10-9) a2, b2 = coefficients in vapour terma3, b3 = coefficients in radiation term

The wind function f(u), as proposed by FAO is given by:

f (u) 0.26 (1 U 24 / 100) 11

where:

U24 = 24 hour wind run (km/day) measured at 2 m above ground level

The actual vapour pressure is computed by one of the following three formulae depending on which time series is available. For current data the formula using wet and dry bulb temperature is used even if relative humidity and dew point have already been calculated by the observer; this is to avoid incorporating observer’s calculation errors. The other formulae may be required for historic data where wet and dry bulb temperatures are no longer available.

ea es . rh /100 12

ea es (t wb ) (t db t wb ) 13

ea es (t dew ) 14

where:

rh = relative humidity in %twb, tdb = wet and dry bulb temperature (oC)tdew = dew point temperature (oC)

Daily potential evapotranspiration using the Penman formula may thus be computed using the following observations at standard Indian climatological stations:

tmax , tmin to obtain tmean as (tmax ,+ tmin)/2 in (oC)

twb, tdb to obtain actual and saturated vapour pressures (ea , es)

U24 to obtain the wind function f(u)

n actual daily bright sunshine duration using Campbell Stokes sunshinerecorder to compute net shortwave and net longwave radiation (Rns , Rnl )

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3. Other potential evapotranspiration formulae

A large number of empirical and theoretical formulae have been proposed for the calculation of potential evapotranspiration and several of these are available in eSWIS. These will not form a part of routine processing but may be used for special applications. The following methods are available:

Christiansen method

FAO radiation method

Makkink radiation method

Jensen-Haise method

Blaney-Criddle method

Mass transfer method

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Chapter 10: Primary Validation of Water Level Data

Data validation is the means by which data are checked to ensure that the final figure stored is the best possible representation of the true value of the variable at the measurement site at a given time or in a given interval of time. Validation recognizes that values observed or measured in the field are subject to errors which may be random, systematic or spurious.

Stage or water level is the elevation of water surface above an established datum; it is the basic measure representing the state of a water body. Records of stage are used with a stage-discharge relation in computing the record of stream discharge. The reliability of the discharge record is dependent on the reliability of the stage record and on the stage discharge relation. Stage is also used to characterize the state of a water body for management purposes like the filling of reservoirs, navigation depths, flood inundation etc. Stage is usually expressed in meters or in hundreds or thousandths of a meter.

1. Instruments and observational methods:

Three basic instruments are in use at river gauging stations for measurement of water level:

1. Staff gauges

2. Autographic water level recorders

3. Digital water level recorders

1. Staff gauges

Instrument and procedure:

The staff gauge is the primary means of measurement at a gauging station, the zero of which is the datum for the station. It is a manually read gauge and other recording gauges which may exist at a station are calibrated and checked against the staff gauge level. Staff gauges are located directly in the river. An additional staff gauge may be situated within the stilling well but this must not be used to calibrate recording instruments as it may be affected by blockage of the intake pipe. Where the staff gauge is the only means of measurement at a station, observations are generally made once a day in the lean season and at multiple times a day during a flood period - even at hourly intervals during flood season on flashy rivers.

Typical measurement errors:

Staff gauges like other manual measurements, are dependent on the observer’s ability and reliability and it must not be assumed that these are flawless . Checking on the performance of the observer is mainly the task of the field supervisor, but the data processor must also be aware of typical errors made by observers.

A common problem to note is the misplacement of decimal point for readings in the range

.01 to .10. For example a sequence of level readings on the falling limb of a hydrograph: 4.12, 4.10, 4.9, 4.6, 4.3, 4.1, 3.99 - should clearly be interpreted as:4.12, 4.10, 4.09, 4.06, 4.03, 4.01, 3.99.

Experience suggests that where the record is maintained by a single observer who is left unsupervised for extended periods of time, that it may contain some ‘estimated’ readings,

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fabricated without visiting the station. This may show up as sequences which are hydrologically inconsistent. Typical indicators of such ‘estimates’ are:

Abrupt falls or a sudden change in slope of a recession curve.

Long periods of uniform level followed by a distinct fall.

Uniform mathematical sequences of observations, for example, where the level falls regularly by 0.05 or 0.10 between readings for extended periods. Natural hydrographs have slightly irregular differences between successive readings and the differences decline as the recession progresses.

In addition, precise water level measurement may be difficult in high flows, due to poor access to the gauge and wave action and, in flood flows the correspondence between staff gauges and recording gauges may not be as good as in low flows. Quality of gauge observations is of course, also affected if the gauge is damaged, bent or washed away. The station record book should be inspected for evidence of such problems.

2. Automatic water level recorders

Instrument and procedure:

The vast majority of water level recorders in use in India use a float and pulley arrangement in a stilling well to record the water level as a continuous pen trace on a chart. The chart is changed daily or weekly and the recorder level is set to the current level on the staff gauge, which is also written on the chart at the time of putting on and taking off.

Typical measurement errors:

Automatic water level recorders are subject to errors resulting from malfunction of the instrument or the stilling well in which it is located. Many of these errors can be identified by reference to the chart trace or to the level figures which have been extracted from it.

The following are typical malfunctions noted on charts and possible sources of the problems.

(a) Chart trace goes up when the river goes down

Float and counterweight reversed on float pulley

(b) Chart trace goes up when the river goes down Tangling of float and counterweight wires

Backlash or friction in the gearing Blockage of the intake pipe by silt or float resting on silt

(c) Flood hydrograph truncated Well top of insufficient height for flood flows and float sticks on floorboards of gauging hut or recorder box.

Insufficient damping of waves causing float tape to jump or slip on pulley.

(d) Hydrograph appears OK but the staff gauge and chart level disagree. There are many possible sources including operator setting problems, float system, recorder mechanism or the operation of the stilling well, in addition to those noted above. The following may be considered.

Operator Problems

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Chart originally set at the wrong level Float system problems

Submergence of the float and counterweight line (in floods) Inadequate float diameter and badly matched float and counterweight Kinks in float suspension cables

Build up of silt on the float pulley affecting the fit of the float tape perforations in the sprockets

Recorder problems Improper setting of the chart on the recorder drum Distortion and/or movement of the chart paper (humidity) Distortion or misalignment of the chart drum Faulty operation of the pen or pen carriage

Stilling well problems

Blockage of intake pipe by silt. Lag of water level in the stilling well behind that in the river due to insufficient diameter of the intake pipe in relation to well diameter.

(e) Chart time and clock time disagree Chart clock in error and should be adjusted

In particular it should be noted that the partial blockage of the stilling well or intake pipe will result in a serious systematic error in level measurement.

3. Digital water level recorders

Instrument and procedure

Like the chart recorder many DWLRs are still based on a float operated sensor operating in a stilling well. One significant improvement is that the mechanical linkage from the pulley system to the chart is replaced by the shaft encoder which eliminates mechanical linkage errors and the imprecision of a pen trace. The signal from the shaft encoder is logged as level at a selected time interval on a digital logger and the information is downloaded from the logger at regular intervals and returned for processing. The level is set and checked with reference to the staff gauge.

Alternative sensors for the measurement of water level do not require to be placed in still water, notably the pressure transducer. Loggers based on such sensors have the advantage that they do not need to be placed in a stilling well and thus can avoid the associated problems.


Measurement except for the sensors noted above is still subject to the errors caused by the float system and by the operation of the stilling well. Many of the same or equivalent checks are therefore necessary to ensure the continuity and accuracy of records. In particular the comparison and noting of staff gauge and logger water levels (and clock time and logger time) at take off and resetting, in the Field Record Book are essential for the interpretation of the record in the office.

Procedures in the office for checking the reliability of the record since the previous data download will depend on the associated logger software but should include a graphical inspection of the hydrograph for indications of malfunction (e.g. flat, stepped or truncated trace). Comparisons as for the chart recorder should be made with the observer’s readings and bad or missing data replaced by manual observations.

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2. Scrutiny of tabular and graphical data - single record

2.1. General description

The first step in validation is the inspection of individual records from a single recorder or manual measurement for violations of preset physical limits or for the occurrence of sequences of data which represent unacceptable hydrological behaviour.

Screening of some unacceptable values will already have been carried out at the data entry stage to eliminate incorrectly entered values.

Numerical tests of physical limits may be considered in three categories:

(a) Absolute maximum and minimum limits

(b) Upper and lower warning limits

(a) Absolute maximum and minimum limits

Checking against maximum and minimum limits is carried out automatically and values violating the limits are flagged and listed. The values of the absolute maximum and minimum levels at a particular station are set by the data processor such that values outside these pre-set limits are clearly incorrect. These values are normally set for the full year and do not vary with month or season.

The cross-section plot of the river gauging line in conjunction with the cross section of the control section at higher flow depths provides an appropriate basis for setting these minimum and maximum limits. With respect to minimum values for stage records, since it is normal to set the zero of the gauge at the level at which flow is zero then, for many stations a zero gauge level may be set as the absolute minimum. However, for some natural channels and controls negative stage values may be acceptable if the channel is subject to scour such that flow continues below the gauge zero. Such conditions must be confirmed by inspection of the accompanying Field Record Book.

Similarly, the absolute maximum is set at a value after considering the topography of the flood plains around the control section and also the previously observed maximum at the station. If long term data on water levels is already available (say for 15 –20 years) then the maximum attained in the past can be taken as an appropriate maximum limit.

(b) Upper and lower warning limits

Validation of stage data against an absolute maximum limit does not discriminate those unusually high or low values which are less than the maximum limit but which may be incorrect. Less extreme upper and lower warning limits are therefore set such that values outside the warning range are flagged for subsequent scrutiny. The underlying objective while setting the upper and lower warning levels must be that such limits are violated 1–2 times every year by a flood event. This would ensure that on an average the one or two highest flood or deepest troughs are scrutinised more closely for their correctness. These limits may also be worked out using suitable statistics but care must be taken of the time interval and the length of data series under consideration. Statistics like 50% ile value of the collection of peak over the lowest maximum annual values used to set the upper warning level for the case of hourly data series of say 15-20 years. Of course, such statistics will also be subjected to the nature or shape of hydrograph which the station under consideration experiences. And therefore the appropriateness of such limits have to be verified before adopting them.

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(c) Graphical inspection of hydrographs

Visual checking of time series data is often a more efficient technique for detecting data anomalies than numerical checking and must be applied to every data set with an inspection of the stage hydrograph on screen. Screen display will also show the maximum and minimum limits and the upper and lower warning levels. Potential problems identified using numerical tests will be inspected and accepted as correct, flagged as spurious or doubtful and corrected where possible. An attempt must be made to interpret identified anomalies in terms of the performance of observer, instruments or station and where this has been possible to communicate this information to field staff for field inspection and correction. A few examples cases are discussed below:

Case 1Case 1 represents a false recording of a recession curve (Fig. 3.4) caused by:

3.2.5 An obstruction causing the float to remain hung

3.2.6 Blockage of the intake pipe 3.2.7 Siltation of the stilling well

This also shows where the obstruction was cleared. It may be possible to interpolate a true recession.

Case 2Case 2 involves steps in the stage recording because of temporary hanging of the float tape or counterweight as the result of mechanical linkages in the recorder (Fig. 3.5). Such deviations can be easily identified graphically and true values can be interpolated.

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Case 3Spurious peaks and troughs (spikes) in the hydrograph. These may be generated by observer error or occasionally by electronic malfunction of transducers or shaft encoders. It should be noted however that in some instances real variations of a similar nature may be generated:

In rivers with small flow, switching on and off of pumps immediately upstream from the observation station will generate rapid changes

The building of a bund or obstruction upstream from a station and its subsequent failure or release will generate first a negative spike followed by a positive one. In this case the levels as observed are correct.

(d) Validation of regulated rivers

Rivers which are unaffected by river regulation and abstraction have a flow pattern which is determined by the rainfall and the transformation and storage of that rainfall on that basin on its way to the outlet. The hydrograph at such stations follows a natural pattern on which errors and inconsistencies can readily be identified.

Such natural rivers are not common in India; they are influenced artificially to a greater or lesser extent. One example is listed above (Case 3) More generally on regulated rivers the natural pattern is disrupted by reservoir releases which may have abrupt onset and termination, combined with multiple abstractions and return flows.

The influences are most clearly seen in low to medium flows where in some rivers the hydrograph appears entirely artificial; high flows may still observe a natural pattern. In such rivers validation becomes more difficult and the application of objective rules may result in the listing of many queries where the observations are in fact correct. It is therefore recommended that the emphasis of validation on regulated rivers should be graphical screening by which data entry and observation errors may still be readily recognised.

The officer performing validation should be aware of the principal artificial influences within the basin, the location of those influences, their magnitude, their frequency and seasonal timing, to provide a better basis for identifying values or sequences of values which are suspect.

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1. Comparison of daily time series for manual and autographic or digital data


At stations where water level is measured at short durations using an autographic or a digital recorder, a staff gauge reading is always also available. Thus, at such observation stations water level data at daily time interval is available from at least two independent sources. Discrepancies between reading may arise either from the staff gauge readings, the recorder readings or from both. The typical errors in field measurement have been described above and these should be considered in interpreting discrepancies. In addition errors arising from the tabulation of levels at hourly intervals from chart records or from data entry are possible.

1.2. Validation procedure

Two or more series representing the same level at a site are plotted on a single graph, where the two lines should correspond. A residual series may also be plotted showing the difference between the two methods of measurement. The following in particular should be noted:

· If there is a systematic but constant difference between staff gauge and recorder, it is probable that the recorder has been set up at the wrong level. Check chart annotations and the field record book. Check for steps in the hydrograph at the time of chart changing. The recorder record should be adjusted by the constant difference from the staff gauge.

· If the comparison is generally good but there are occasional discrepancies, it is probably the result of error in the staff gauge observations by the observer or incorrect extraction from the chart.

· If there is a change from good correspondence to poor correspondence in flood conditions, a failure associated with the stilling well or the recorder should be suspected and the staff gauge record is more likely to be correct and may therefore be used to correct or interpolate missing records in the recorder record.

· A gradual increase in the error may result simply from the recorder clock running fast or slow. This can be easily observed from the graphical plot and the recorder record should be adjusted.

2. Multiple graphs of water level at adjacent stations

Comparison of records between stations will normally be carried out as part of secondary validation at Divisional level and will not only be done with respect to discharge but also for stages. However an initial inspection may be done at Sub-divisional level where records for a few neighbouring stations are available. Such stations, especially if on the same river will show a similarity in their stage plot and inspection may help in screening out outliers.

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Chapter 11: Secondary Validation of Water Level Data

1.General: After Primary Validation of water level data, Secondary validation at will mostly emphasis on comparisons with neighboring stations to identify suspect values. Special attention will be given to records already identified as suspect in primary validation

The assumption, while carrying out secondary validation, is that the variable under consideration has adequate spatial correlation. Since the actual value of water level is controlled by specific physical conditions at the station, the amount of secondary validation of level is limited. Most of the check comparisons with neighboring stations must await transformation from level to discharge through the use of stage discharge relationships. Only as discharge can volumetric comparisons be made. However validation of level will identify serious timing errors.

Secondary validation of level will be used to identify suspect values or sequences of values but not usually to correct the record, except where this involves a simple shift (time or reference level) of a portion of a record.

The main comparisons are between water level series at successive points on the same river channel. Where only two stations are involved, the existence of an anomaly does not necessarily identify which station is at fault. Reference will be made to the historic reliability of the stations.

Comparisons will also be made between incident rainfall and level hydrographs.

2. Scrutiny of multiple hydrograph plotsGraphical inspection of comparative plots of time series provides a very rapid and effective technique for detecting timing anomalies and shifts in reference level. Such graphical inspection will be the most widely applied validation procedure.

For a given time period several level time series for neighboring stations are plotted in one graph. For routine monthly validation, the plot should include the time series of at least the previous month to ensure that there are no discontinuities between one batch of data received from the station and the next. The time interval of observation rather than averaged values should be displayed. In general, peaks and troughs are expected to be replicated at several stations with earlier occurrence at upstream stations and the lag between peaks, based on the travel time of the flood wave, approximately the same for different events. It should be noted that level values at downstream stations are not necessarily higher than upstream stations - the actual value depends on physical conditions at the stations. Where peaks occur at one station but not at its neighbor or where the lag time between stations is widely different from the norm, an error at one station may be suspected. However it must be recognized that the quality of the relationship between neighboring hydrographs depends not only on the accuracy of the records but on a variety of other factors including:

rainfall and inflow into the intervening reach between stations. If the intervening catchment is large or the rainfall high in comparison to that over the upstream basin, a very poor relationship may result.

river regulation and abstractions between the stations may obscure natural variations, though high flows are usually less affected than low or medium flows.

An average lag between successive stations can be used in making comparisons but the actual lag is variable, generally diminishing up to bankfull stage and increasing again with overbank flow.

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one station may suffer backwater effects on the stage hydrograph and not another, obscuring the effects of differences in flow. Where such effects are known to occur, comparison should await transformation to discharge.

Anomalies identified from comparative hydrograph plots are flagged for further stage validation or to await validation as discharge.

Example 2.1:

Application of the above described technique is demonstrated for the stations SITAMARH and MIRZAPUR on Ganga river. The stations lateral inflow in between the sites is small compared to the river flow. The hydrographs of hourly water levels for the month August 2014 are shown in Figure 2.1 From the plot some anomalies are observed. Make sure to have always a tabulated output of the water level observations available when carrying out such analysis to note down possible anomalies.

From the Figure 2.1 two types of errors may be observed:

spurious errors originating from transcription errors in the field or in the office, and errors in the occurrence of peaks

Particular with respect to the last type of error additional information is required to determine which parts of the hydrographs are faulty. Fortunately upstream as well as downstream of the stations hydrometric stations are available.

Multiple hydrograph plot (2 Station)

Figure 2.1 Multiple hydrograph plot

Example 2.2:

The hydrograph plot presented in Figures 2.1a and b is now extended with the hydrographs of the stations VARANASI, SITAMARI, ALLAHABAD and MIRZAPUR on river Ganga. The

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hydrographs are shown in Figure 2.2a. and the detail for the same period of Figure 2.1b in Figure 2.2b.

Multiple hydrograph plot (4 series)

Figure 2.2a Multiple hydrograph plot, 4 stations

Multiple hydrograph plot (4 series)

Figure 2.2b Detail of Figure 2.2a.

It is observed from Figure 2.2b that the first 1 peaks originate from upper WATRAK. These peaks are due to releases from an upstream reservoir.

Where peaks occur at one station but not at its neighbor or where the lag time between stations is widely different from the norm, an error at one station may be suspected. However it must be recognized that the quality of the relationship between neighboring hydrographs depends not only on the accuracy of the records but on a variety of other factors including

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3. Combined hydrograph and rainfall plotsThe addition of rainfall to the comparative plots provides a means of assessing timing errors and of investigating the effects of inflow into the intervening reach between stations. Comparison may be made using an average rainfall determined using Thiessen polygons or other methods over the entire basin or for the intervening sub-basin corresponding to various gauging stations. Where the basin is small or the number of rainfall stations limited, individual rainfall records may be plotted.

In general a rise in river level must be preceded by a rainfall event in the basin and conversely it is expected that rainfall over the basin will be followed by rise in level. There must be a time lag between the occurrence of rainfall and the rise in level.

Where these conditions are violated, an error in rainfall or in the level hydrograph may be suspected. However the above conditions do not apply universally and the assumption

of an error is not always justified especially for isolated storms in arid areas. For example:

An isolated storm recorded at a single raingauge may be unrepresentative and much higher than the basin rainfall. The resulting runoff may be negligible or even absent.

Where storm rainfall is spatially variable, it may be heavy and widespread but miss all the raingauges, thus resulting in a rise in river level without preceding measured rainfall.

The amount of runoff resulting from a given rainfall varies with the antecedent catchment conditions. Rainfall at the onset of the monsoon on a very dry catchment may be largely absorbed in soil storage and thus little reaches the river channel.

The use of comparative plots of rainfall and level is therefore qualitative but it provides valuable ancillary information with the multiple hydrograph plots.

Example 3.1:

An example of a combined hydrograph and rainfall plot is presented in Figure 3.1, which displays the water level record of station Narmada at Hoshangabad together with the rainfall records of station Narmada at Mortakka

Combined Rainfall and hydrograph plot

Figure 3.1 Combined hydrograph and rainfall plot

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From the graph it is observed that the first peak is preceded by substantial rainfall. The remainder, however, shows suspect combinations of hydrographs of stage and rainfall, where hydrograph appears to occur before the rainfall and where the response to the rainfall is delayed. One may be tempted to doubt the rest of the record. However, in this case the peaks may as well be caused by releases from an upstream reservoir. Therefore, in this case additional information is required about the reservoir releases to conclude on the series. Nevertheless, the delayed response to the second rainfall peak remains suspicious.

4. Relation curves for water level

4.1. General

A relation curve gives a functional relationship between two series of the form:

o Yt = F(Xt+t1)

To account for the lag between level changes at one station and the next downstream, it may be necessary to introduce a time shift (t1) between the two time series.

Relation curves will normally be applied to water level data rather than discharge. However it may be appropriate on occasions to use them for discharge data, especially where one or both stations are affected by backwater conditions.

If there is a distinct one to one relationship between two series, random errors will be shown in a relation curve plot as outliers.

By comparing two relation curves, or data of one period with the curve of another period, shifts in the relationship, e.g., in the water level series due to changes in the gauge zero can be detected.

4.2. Application of relation curves to water level

If two water level stations are located on the same river and no major branch joins the main stream between the two locations, a relation can be expected between the recordings at the two locations. With the help of this relation, the stage at a particular station can be derived from the available data series of the adjacent station. A sample plot of such relationship between the two stations is shown in example Fig. 4.

Two important conditions need to be satisfied to obtain a high degree of relationship between the stage data of adjacent stations. These are:

No major tributary joins the main stream in between the two adjacent stations. Time of travel of the flood wave between the two stations is taken into consideration.

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Figure 4 Example of relation curve

As noted above for comparative hydrograph plots, the occurrence of lateral inflow between stations limits the quality of the relationship between neighboring stations. The lateral inflow may occur as a main tributary inflow or distributed over the reach as surface and groundwater inflows. In either case if it is a significant proportion of the downstream flow or variable, then good correlation may not be obtained.

4.3. Determination of travel time

With respect to the second condition, the relationship between the two station time series must incorporate a time shift, representing the mean travel time of a flood wave between the stations. Plotting without a time shift results in a looped relationship as shown in Example 4.1. The time shift may be assessed using:

(a) physical reasoning, or (b) from an analysis of the time series.

Example 4.1

A relation curve is to be established between the stations CC000G4(MUSIRI) and CC00017(KODUMUDI). The hydrographs for the period for which the relation curve is to be established is presented in Figure 4.1a. It is observed that the hydrograph at the downstream site is lagging behind. Plotting the observations at the two sites without a correction for travel time of the flood wave results in a looped scatter plot vas displayed in Figure 4.1b

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Figure 4.1a Hydrographs of CC000G4 (MUSIRI) and CC00017 (KODUMUDI)

Figure 4.1b Scatter plot of CC000G4(MUSIRI) and CC00017(KODUMUDI)

4.3.1. From physical reasoning

The time of travel of a flood wave can be approximately determined by the division of the interstation distance by the estimated flood wave velocity. Consider a relation curve of daily water levels of stations X and Y which are spaced at a distance s km from each other along the same river, X upstream of Y. Let the average flow velocity (assessed from current meter gaugings at the stations) be u m/s, then the propagation velocity or celerity of the flood wave c is approximately equal to 1.7 (Br/Bs).u, where Br is the river width and Bs is the storage width (river+flood plain). So, if the river is in-bank, celerity becomes equal to 1.7u, and the time shift to be applied between X and Y for a one to one relationship amounts to distance/celerity = -s * 1000/(1.7 u) sec. When the river expands in the flood plain, the celerity is different from 1.7.u and should be multiplied with B r/Bs ; consequently, a different time shift will result.

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4.3.2. From cross correlation analysis

Another computational procedure to derive the time shift between the two related series is based on cross-correlation analysis. The estimate of the cross-correlation function (Rxy t) between the time series X(t) and Y(t) of two stations is computed for different lags . The lag time corresponding to the maximum of the cross correlation function indicates the travel time between the two stations.

A plot is made between the lag time and the related cross correlation coefficient . The lag time corresponding to the maximum of the cross-correlation function indicates the travel time between the two cross sections. After calculating the time shift, it can be applied by entering the data of station X at time T and corresponding it with the data of station Y at time T + . It is then advisable to plot the resulting X-Y relationship:

4.4. Fitting the relation curve

The X-Y data can be fitted in eSWIS using a relation equation of polynomial type:

Yt = c0 + c1 Xt+t1 + c2 Xt+t12 + c3 Xt+t1

3 + .......

After inspection of the scatter plot the form of the relationship (the degree of the polynomial) can be decided. It is recommended to use a polynomial not greater than order 2 or 3; in many instances a simple linear relationship will be acceptable. The least squares principle is applied to estimate the coefficients.

Where inspection of the scatter plot indicates the presence of breakpoints, then separate relationships may be established for different ranges of X (analogous to different ranges of the stage discharge relationship) with a maximum of 3 intervals of X.

4.5. Using relation curve for data validation

Relation curves can be displayed and plotted and relation equations valid for different periods can be compared. Shifts in the relationship between the two series indicate a physical change at one of the stations, such as shifts in gauge zero, changes in cross section or even relocation of station.

Where such shifts in relation curve are accompanied by changes in the stage discharge relationship at one station, the changed relation curve is acceptable. However, where no such accompanying change in stage discharge has been notified, an explanation should be sought from Sub-divisional staff or the field supervisor.

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Chapter 12: Correct and Complete Water Level Data

1.GeneralAfter validation a number of values can be marked as incorrect or doubtful. Some records may be missing due to non-observation or loss on recording or transmission. Incorrect and missing values will be replaced where possible by estimated values based on interpolation or other observations at the same station or neighbouring stations. The process of filling in missing values is generally referred to as ‘completion’.

Values identified as suspect by numerical validation tests will be inspected and corrected if necessary or the flag removed if they are found to be acceptable. Numerical test of records with respect to maximum, minimum and warning limits and rates of rise will have identified suspect values (and flagged them) during primary validation. Unless these were due to entry error, they will not have been corrected and will thus require further inspection and correction and completion if necessary.

Where multiple level records at the same station are thus flagged, but the observations agree, then the records may be assumed to be correct. Other suspect values outside warning limits are inspected for violations of typical hydrological behavior but are also checked against neighboring stations before correction or acceptance.

It must be recognized that values estimated from other gauges are inherently less reliable than values properly measured. Doubtful original values will therefore be generally given the benefit of the doubt and will be retained in the record with a flag. Where no suitable neighboring observations or stations are available, missing values will be left as ‘missing’ and incorrect values will be set to ‘missing’

2. Correction using river level or discharge:Correction and completion may be carried out with respect to the water level series or it may await transformation to discharge using a stage discharge relationship. The choice of water level or discharge for correction depends on the type of error, the duration of missing or faulty records and the availability of suitable records with which to estimate. Correction as level has the advantage that it is the primary measurement whereas error in the discharge may result either from error in the level record or in the stage discharge relationship; it has the disadvantage that it provides no volumetric water balance checks.

Conditions where correction and completion will usually be carried out as level include the following:

If the level record is complete but the recorder has gone out of adjustment and periodic check observations are available

If the level record is correct but shifted in time If the primary record (e.g., from a digital water level recorder) is missing but an

alternative level record of acceptable quality is available at the same station

If the record is missing but the duration is short during a period of low flow or recession.

Correction and completion may be carried out as level includes:

If a record is available from a neighboring station with little lateral inflow or abstraction between the stations

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Correction and completion will normally be carried out as discharge:

If a record is available only from a neighboring station with much lateral inflow or abstraction

If one or both stations are affected by variable backwater If the only available means of infilling is from catchment rainfall and the use of a

rainfall runoff model.

Records completed as stage will receive further validation as discharge and may require further correction.

3. Comparison of staff gauge and autographic or digital recordsIf two or more measurements of the same variable are made at a station, one record may be used to correct or replace the other where one is missing. If more than one record exists but they differ, the problem in the first instance is to determine which record is at fault. Typical measurement errors from each source are described under ‘primary validation’ and guidelines are provided for identifying which record is at fault. Suspect values are flagged during validation. Errors and their correction may be classified as follows:

observer errors recorder timing errors pen level errors errors arising from stilling well and intake problems

3.1. Observer errors

Staff gauge and autographic or digital records can be displayed together graphically as multiple time series plots. Differences can also be displayed. Simple and isolated errors in reading and transcription by the observer (e.g., 6.57 for 5.67) can be identified and replaced by the concurrent measurement at the recording gauge. Persistent and erratic differences from the recording gauge (negative and positive) indicate a problem with the observer’s ability or record fabrication. They should be notified to the Sub-division for corrective action; the full staff gauge record for the period should be flagged as doubtful, left uncorrected and the recording gauge record adopted as the true stage record for the station.

3.2. Recorder timing errors

When the clock of the recording gauge runs fast or slow, the rate at which the recorder chart moves in the time direction under the pen will also be fast or slow. This can be detected by comparing with staff gauge readings, e.g. if observations are taken daily at 0800 and the clock of the recording instrument is running slower, then the observer’s stage record at 0800 will correspond to the same observation in the recording gauge before 0800, say 0700 Clock times and recorder times annotated on the chart or recorded in the Field Record book at the time of putting on or taking off the chart can be used to determine the time slippage during the record period.

3.2.1 Correction Procedure

For time corrections, it is assumed that a clock runs fast or slow at a constant rate. Where a digital record is produced from an analogue record using a pen-follower digitiser, the annotated clock and recorder time and level can be fed into the digitising program and the level record expanded or contracted as required to match the clock duration.

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Where a digital record is extracted manually at a fixed interval from a chart, it will result in extra records for a fast clock and deficient records for a slow clock. This can be expediently corrected by removing or inserting (interpolating) records at appropriate intervals, e.g. if the clock runs 4 hours fast in eight days, and hourly data have been extracted, then one data point should be removed at 2 day intervals.

3.3. Pen level errors

The pen of the autographic recorder may gradually drift from its true position. In this case, analogue observations may show deviation from the staff gauge observations.This deviation can be static or may increase gradually with time.

3.3.1 Correction ProcedureWhere a digital record is produced from an analogue record using a pen-follower digitiser, the annotated clock and recorder time and level can be fed into the digitising program and an accumulative adjustment spread over the level record from the time the error is thought to have commenced till the error was detected or the chart removed. However, such procedure is not recommended to be followed as the actual reasons for the shift may still be unknown at the time of digitising the charts. It is always appropriate to tabulate/digitise the chart record as it is in the first instance and then apply corrections thereafter.

eSWIS provides such facility for correcting the gradual spread of error in digital records extracted from a chart recorder, with a growing adjustment from the commencement of the error until error detection. Let the error be X observed at time t = i+k and assumed to have commenced at k intervals before, then the applied correction reads:

Xcorr,j = Xmeas,j - ((j - i)/k)X for j = i, i+1, ......., i+k

Prepare the time-series plot of deviation of staff gauge observations from the recording gauge observations. If the deviation is static with time, then the difference must be settled (increased or decreased) directly from the analogue gauge observations. However, if the deviation increases gradually with time, then corrections for the difference between the pen observation and the staff gauge reading are made in the same way as time corrections. For example, assume that the pen trace record gradually drifted 0.08 m away (recording lower levels) from the corresponding staff gauge record in a period of 10 days. This shows that the pen readings has an error which is increasing gradually from 0 to 8 cms in 10 days period. Now error in such a data can be compensated by adding a proportionate amount of 8 mm per day from the starting point of the error.

3.4. Errors arising from stilling well and intake problems

Problems with stilling well or intake pipe may be intermittent or persistent and can be serious. In extreme floods, the hydrograph may be truncated due to inadequate height of the well, restricting the travel of the float, or counterweight reaching the well bottom. Blockage of the intake pipe with silt will result in a lag between river level (as recorded by the staff gauge) and well level, or a flat trace.

3.4.1. Correction procedure

The recorder trace is replaced by the observer’s staff gauge record if the time interval is sufficiently small in relation to the changes in the water levels. If the staff gauge record is intermittent or frequent changes in the levels are expected to be present then use of relation curves, as described in subsequent sections, is to be preferred for correcting the water level record.

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3.5. Miscellaneous instrument failures

Unacceptable recorder traces may result from a wide variety of instrument problems. These are often displayed as stepped or flat traces and may be corrected by interpolating a smooth curve on the hydrograph plot.

Figure 3.1 False recording of recession curve

Fig. 3.1 represents false recording of the recession curve because of: a) silting of stilling well; or b) blocking of intakes; or c) some obstruction causing the float to remain hung. The figure also shows the time when the obstruction is cleared. The correct curve can be estimated by reading the smooth curve that joins the first and last reading during the period of obstruction.

Figure 3.2 Correction of stepped hydrograph

Figure 3. 2 shows small steps in the stage records because of the temporary hanging of the float tape or counterweight, or kinks in the float tape. Such deviations can be easily identified and true values can be interpreted by reading the smooth curve in the same way as for recession curve.

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4. Linear interpolation of short gaps

Where only a single record is available at a station, gaps may occur due to instrument failure, observer sickness, station maintenance, etc. Gaps may be infilled by simple linear interpolation where they occur during periods of low flow or during recession and the difference between the level at the beginning and end of the gap is small. During periods of low flow, gaps of one to several days may be infilled in this way but it is recommended that infilling by linear interpolation during the monsoon or on a heavily regulated river should not exceed 6 hours.

For longer periods of missing data during a recession when the runoff is result only of outflow from a groundwater reservoir, the flow shows an exponential decay, which, when plotted as discharge on a sem-logarithmic scale, plots a a straight line. Using the stage discharge relationship it is possible to infill the series as water level rather than flow, but infilling as flow is conceptually simpler. Gaps of a month or more may be filled in this way.

5. Use of relation curves with adjacent stations5.1. General

The use of relation curves for water level data validation is also an effective way of infilling missing records and of correcting suspect ones especially for sequential stations on a river with little lateral inflow between. The following are typical uses.

infilling of missing records identifying and correcting misreadings in one series identifying and correcting shift in gauge zero or change in cross section

5.2. Infilling of Missing Records

A relation curve based on the data of two series can be used to infill the missing data in the dependent variable of the relationship. The relation curve is used to calculate the missing value(s) at the station corresponding to the observed values at the adjacent station An example is given in Figure 5.1.

Figure 5.2 Infilling of missing data with relation curve

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Figure 5.1 shows that the relation curve did not provide a good connection between the existing record and the infilled part. These situations do sometimes happen, particularly, when the standard error is more than a few centimetres. Therefore, one should always verify the correctness of the infilled part.

5.3. Identifying and correcting misreadings

If, after taking the lag between stations into account, there is a strong relationship between the two series, incidental misreading or incorrect booking will show up as outliers in the relation curve plot. Having identified its occurrence it is then required to determine in which series the problem has arisen and the actual value at fault, taking into account the lag time between stations. A corrected value is estimated using the relation curve or relation equation and substituted in the time series.

5.4. Identifying and correcting shift in gauge zero or change in cross section

Shifts in water level observations due to change in gauge zero or changes in cross section conditions can be detected by comparing two relation curves or the plot of one period with that of another. For routine validation and completion, the comparison will be between data for the current period and an established curve for the station. If the new relation differs and there is a new stable relationship between the records and the deviation from the previous relation is constant, then a shift in the reference gauge is suspected. The time of its occurrence can be identified from the comparative plots. If there is a change in slope of the relation curve compared with the standard curve, then a change in cross section at one of the stations may be suspected.

On the identification of such changes, consultation should be made with sub-divisional staff and the Field Record Book inspected. If the conditions of change had been previously recognised in the field and adjustments made to the rating curve to account for the shift in gauge zero (or change in station location) or altered cross section, then no further action need be taken. If the change had not been recognised in the field then, since the analysis does not indicate which station is in error, then further action is necessary on following lines:

Where additional stations are available for comparison, further relation curves may be developed and the station in error identified.

Field staff are requested to re-survey gauges and the cross section at both stations If, after survey the gauge zero at one station is found to have inadvertently altered,

then it should be reset to its former level. The stage level during the period between gauge shift and resetting should be corrected by the deviation shown by survey (and confirmed by the constant difference in relation curves).

If no change in gauge zero is found but the cross section at one station has altered, then field staff are requested to intensify current meter gauging to establish a new stage discharge relationship. Usually the stage record will not be changed but the revised rating curve applied over the period from the occurrence of the change in cross section (usually during a flood).

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Chapter 13:Primary Validation of Stage Data

1. General

Flow measurement in this module refers to individual measurements of discharge made by current meter which are used in the plotting and fitting of a stage discharge relationship or rating curve.

Initial calculation is carried out in the field and the completed field sheets are returned monthly to the Sub-divisional office where they are entered to computer using Primary module of dedicated hydrological data processing system (eSWIS) and the discharge recomputed.

Primary validation consists of:

inspection of field sheets and Field Record Book

comparison of field and office computed discharge

comparison of computed discharge with existing rating curve comparisons of cross sectional and velocity profiles

1. Inspection of field sheets and Field Record Book

Each current meter measurement of discharge contains multiple observations or calculations of width, depth, velocities, slope, areas, flows, etc., and the information is entered to the standard “Discharge Measurement Sheet” (Fig. 2.1). Before checking the arithmetic calculations, it is necessary to check ancillary information on the form and in the Field Record Book to ensure that it is complete and that any change at the station which may have influenced the relationship between stage and discharge is available for interpretation of the computed discharge. Information which may be relevant includes:

1. rates of rise and fall in level during measurement (possible unsteady flow effect)

2. backwater due to very high stages (i.e. flooding) in receiving river or contributing tributary downstream of gauging station

3. flood in deposition or scour of the channel at the gauge or at the downstream control, based on observer observations.

4. gravel extraction at the station or downstream 5. bunding or blockage in the downstream channel 6. weed growth in the channel 7. change in datum at the station, adjustment or replacement of staff gauges.

The stage recorded at the beginning and end and during the gauging must be compared with the hourly or other stage observation by recorder or manually. Any discrepancy must be investigated by reference to the field supervisor. The error maybe in the continuous record or in the observation during current meter gauging; if the latter then the mean stage in the summary form for the current meter measurement must be amended.

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Fig. 2.1: Specimen “discharge measurement sheet”

3. Comparison of field and office computed discharge

The calculation of discharge from current meter measurements is initially carried out in the field by the gauging team. On receipt in the office, individual observations made during the

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measurement are entered to computer and the discharge is re-computed. If the total discharge determined from the two calculations differs, the source of the difference must be identified and correction made. In particular line by line comparisons of the two calculations should be made to identify data entry errors to computer. If none are found, arithmetic errors should be sought in the field calculation. Other potential sources of discrepancy are in the use of the wrong current meter rating in one of the calculations or incorrect entry of current meter rating parameters to the ratings datafile.

Any errors in the field computation should be notified to the field supervisor.

4. Comparison of computed discharge with existing rating curve

Validated gaugings are entered to the stage-discharge summary data file in a form suitable for graphical plotting and inspection. The new gauging can then be compared graphically with existing rating curve and the previous current meter gaugings (Fig. 4.1); a table can also be obtained of the actual and percentage deviation of the gauging from the previously established rating.

Deviations may be due to:

the reliability of the individual gauging the general accuracy with which measurements can be made at a station actual changes in the stage discharge relationship

It is important to distinguish the difference. Early identification is necessary so that gauging practice can be adjusted or, in the case of rating changes, so that gauging can be intensified to establish a new relationship.

The percentage deviation of a gauging which requires further action will depend on the physical characteristics of the station and the assumed accuracy with which individual measurements can be made. For example in a station with sensitive control and a regular gauging section and error of 5% may be achieved but at irregular sections with erratic velocity distribution an error of 10% may be acceptable. In general the individual gauging should be investigated further if the deviation from the previous rating exceeds 10% or, if a sequence of gaugings shows persistent positive or negative deviations from the established rating.

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Fig. 4.1: Scatter plot of stage-discharge data

4.1. Deviations due to reliability of individual gaugings

The individual gauging may be unreliable due, for example, to:

1. an inadequate number of verticals taken to define total area and mean velocity 2. very low velocities in the section not measured accurately by available equipment 3. no air/wet line corrections made to depth measurement in high flow 4. no angle correction for gaugings taken oblique to the flow 5. a faulty current meter

Items (a) to (d) can be identified from the tabulated gauging. The use of a faulty current meter (e) cannot be so identified but may be identified from field inspection or by persistent differences between the results from the specified meter and other meters at the same station. A plot of cross sectional velocity can be made for individual gaugings and a comparison made between gaugings at the same stage

4.2. Deviations due to physical properties of gauging section

The general accuracy with which gaugings can be made at a station depends to a large extent of the regularity of the bed and banks at the gauging cross section and approach conditions - both bed roughness and the existence of a bend - whether or not these are subject to change. These control the velocity distribution across the section and how it differs from a smooth trapezoidal channel. Irregularities may result in deviation from a typical logarithmic velocity profile in the vertical so that neither 0.6d nor (0.2d + 0.8d)/2 represent the mean flow. They may also cause rapid velocity variations across the section such that the number of verticals chosen may not be an adequate sample to represent the mean flow.

The velocity distribution in the cross section may be investigated by plotting velocity contours or velocity vectors across the cross section if sufficient observations have been made.

4.3. Deviations due to actual changes in the stage discharge relationship

Deviation from a simple power relationship at a gauging station may arise for a number of reasons including the following:

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Unsteady flow causing hysteresis with rising and falling floods. This can be identified by plotting the rate of rise (+) of fall (-) during gauging alongside the plotted point on the stage discharge graph. Higher flow for given level may be expected in rising flows when the energy slope is greater but is generally only evident in reaches with low channel slope.

Changes in cross section at the control section due to natural scour or deposition or gravel extraction. Such changes may be identified by plotting sequential cross-sections for the control section where available but otherwise for the gauging section. It is changes in the control section which are critical, but these are often accompanied by changes in cross section at the station also and these can give an indication of the existence of scour or deposition At least two cross sections are conducted each year before and after the monsoon period. These may be compared. In addition, a cross sectional profile is available from each current meter gauging and these may also be compared and may indicate the presence of scour or deposition at the station. Reference should be made to gauging notes and to the Field Record Book for observations of field staff.

Introduction of a new rating or the use of the shift procedure should be considered.

Discharge for given level may also be affected by downstream bed changes even if no change is found at the station itself. In channels of low slope the control may extend to many kilometres downstream for which no cross sectional information exists. Comparison of mean velocity between sequential gaugings across the width of the channel at the gauging section will help to identify such changes (though backwater may exhibit the same effect - see below). Scour or gravel extraction downstream will result in increased velocity for given gauge level; bunding and blockage will result in a decrease. Reference should again be made to gauging notes. Introduction of a new rating or the use of the shift procedure should be considered.

Similarly discharge for given level may be affected by downstream backwater conditions caused for example by a confluence or by tidal effects. The effect may also be illustrated by comparison of velocity profiles. Unlike the effects of downstream bed changes, the effect may not persist from one gauging to the next. For stations affected by backwater, rating curves with backwater corrections should be applied.

Weed growth at or downstream from the station may also be identified by changes in the mean velocity profile across the section. Weed growth decreases the velocity for a given level. Reference should be made to gauging notes. If weed growth causes significant variation from the mean rating, the introduction of the shift procedure should be considered.

Where bed profile and mean velocity profiles remain sensibly constant from one gauging to another but the plotted point deviates from the previous rating, then a change in the datum or a shift in the staff gauges should be suspected. Reference should be made to the Field Record Book and gauging notes. Field staff should be requested to carry out a check survey of the staff gauges. If necessary a new rating can be introduced with a simple change in the ‘a’ parameter.

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Chapter 14: Secondary Validation of Stage Data

1. GeneralRating curves are usually developed and validated with respect to current metering observations at an individual station. It is often necessary to extrapolate the relationship beyond the measured range.

One means of providing a further check on the reliability of the extrapolated rating curve is to make comparisons of discharges computed using the stage discharge relationships between neighboring stations. If there is an inconsistency or an abrupt change in the relationship between discharge time series at sequential stations on a river or around a confluence, then the most likely source is the stage discharge relationship at one or more of the compared stations. Where such inconsistencies are observed, rating curves and their extrapolations must be reviewed.

2. Review of rating curve on the basis of balancesAfter finalizing rating curves, observed stage time series are converted to discharge. Discharge time series are then aggregated and compiled to successively longer time intervals - from hourly to daily to ten-daily and monthly. Discharge time series at consecutive stations on a river should then show a consistent pattern of relationship and water balance, taking into consideration the intervening catchment area, major tributary inflows and abstractions. The balance of flows can be checked using the average discharge or flow volumes during a time interval. Generally better and less variable relationships are obtained using longer time intervals. Comparison plots of discharge time series provide a helpful means of identifying anomalies.

In addition a residual series can be plotted (Fig. 2.1a-h) alongside the comparison plots as the difference between discharges at the two stations.

Residual series generally provide a better means of detecting anomalies. Where inconsistencies occur, the station at fault may not be immediately evident. A potential source, which should be investigated, are periods when rating curve extrapolation has been used at one or both stations.

In the Figures 2.1a to 2.1h an application of the technique is outlined. In Figure 2.1a the hourly water level time series of the stations KODUMUDI and MuSIRI in the Cauvery basin are show. Both stations are located along the same river. The rating equations fitted to the stage-discharge data available for 1995 are shown in Figures 2.1b and c. Next, the hourly water level time series have been transformed into hourly discharge time series using the rating curves presented in Figures 2.1b and c. The results are shown in Figures 2.1d and e, where the latter is a detail. The differences are far better exposed if the difference between the series is plotted, see Figure 2.1f. It is noted that particularly with sharp rises of the hydrograph and little inflow in between the stations the peak at the upstream station advances the downstream one, hence creating negative values in the balance, which is apparent from the first peak. Large positive values as is observed for the second peak is likely due to lateral inflow (provided that timing errors in the water level hydrograph do not exist).

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Figure 2.1a Hourly water level time series

Figure 2.1b Stage-discharge rating curve KODUMUDI 1995

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Figure 2.1b Stage-discharge rating curve MUSIRI 1995

Figure 2.1d Hourly discharge time series MUSIRI and KODUMUDI

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Figure 2.1e Hourly discharge time series MUSIRI and KODUMUDI (detail)

Figure 2.1f MUSIRI and KODUMUDI hourly discharge series

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Figure 2.1g Daily discharge time series MUSIRI and KODUMUDI

Figure 2.1h MUSIRI and KODUMUDI daily discharge series

The eliminate these travel time problems in the water balance the water balance for the discharge time series should be executed at a higher aggregation level. Provided that no water is being abstracted from the river, the reasons could be:

· Either the water series at one or at both sites are erroneous, or · The rating curves established for one or both sites are biased for that period, or · Both water level series and rating curves are incorrect.

These possibilities then have to be investigated in detail. If the anomaly is due to one or both rating curves, more segments have to be incorporated in the rating curves or the rating curves for shorter periods of time have to be developed.It is noted here that for the peaks some negative values in the water balance may occur due to damping of the flood wave. The damping per unit length is approximately:

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dQmax

(3 / 5)3

( Bs / Br )2

2

Q

dx 2 K m2 hmax1/3 S 02 t 2

where : Bs

= total width of river and flood plain

Br = width of the main riverKm = K-Manning (=1/n)hmax = flow depth for the flood peakS0 = slope of the river bed

To get an impression of the magnitude assume that the shape of the flood wave can be approximated by the following cosinus function:

2t 2Q a0 4 2

Q(t ) Q0 a0 (1 cos()) hence : 2 2

t

TT Q max

With the above, the damping per unit of length becomes:

dQmax

(3/ 5)34 2 (Bs / Br )2 a0

dx 2 K m2 hmax1/3 S0

2 T 2

The equation shows that the damping is large if:

· Bs/Br is large, i.e if the a wide flood plain is present · Km is small, i.e. Manning’s n is large that is a hydraulically rough river bed · S0 is small; in steep rivers the attenuation is small · The amplitude a0 of the wave is large and its period T (duration) is short, i.e. rapidly rising

and falling hydrographs.

Using this for the second flood peak of the example with:

· Q0 = 400 m3/s, a0 = 750 m3/s and T = 36 hrs · Bs/Br = 1 (no flood plain), Km = 40, hmax = 5 m and S0 = 8x10-4

Then dQmax /dx = 1.1x10-4 m3/s/m and the damping over a distance of 11 km is approximately 1.2 m3/s, which is negligible. For a bed slope of 10 -4, the damping would have been 64 times as large, whereas a flood plain would have increased the damping further.

3. Review of rating curve on the basis of double mass analysisDouble mass curve analysis has already been described in the secondary validation of rainfall and climate . It can also be used to show trends or inhomogeneities between (a) flow records at neighbouring stations or (b) observed flow records and flows computed on the basis of regression relationships with rainfall and is normally used with aggregated series (usually monthly). It can again be used to identify potential problems in the rating curve of one or more stations.

A distinct break of slope in the double mass curve between neighbouring stations suggests inhomogeneity in one of the records. Inspection for rating changes at the time of the break of

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slope will help to identify the source. It should be noted however that inhomogeneities also arise from artificial changes in the catchment, for example the commencement of abstraction for an irrigation scheme.

4. Review of rating curve on the basis of relation curves between stages at adjacent stations

Relationship between stages at adjoining stations for steady state conditions can be established. At both such stations relation between stages and corresponding discharges would have been also established. It can then be possible to combine these three relationships together in the following way. MUSIRI and KODUMUDI in the Cauvery, which are two adjoining stations on a river reach. Figure bellow shows the relationship between stages MUSIRI and KODUMUDI.

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Chapter 15: Secondary Validation of Discharge Data

1. GeneralAfter transformation of stage to discharge data (in Summery stage-discharge data under Hydrological module of eSWIS) secondary validation can be started for Discharge data. The suspect (based on assessment of stage), corrected, or missing values require to be reviewed, corrected, or inserted.

The quality and reliability of a discharge series depends primarily on the quality of the stage measurements and the stage discharge relationship from which it has been derived. In spite of their validation, errors may still occur which show up in discharge validation. Validation flags which have been inserted in the validation of the stage record are transferred through to the discharge time series. These include the data quality flags of ‘good’, ‘doubtful’ and ‘poor’ and the origin flags of ‘original’, ‘corrected’ and ‘completed’. This transfer of flags is necessary so that stage values recognized as doubtful or poor can be corrected as discharge.

Wrong stage discharge relationship can arise Discharge errors, causing discontinuities in the discharge series, or in the use of the wrong stage series.

The Secondary Validation will be emphasis in the comparison of the time series with neighboring stations but preliminary validation of a single series is also carried out against data limits and expected hydrological behavior.

2. Single station validationSingle station validation is to inspection of the data in tabular and graphical form. The displays will illustrate the status of the data with respect to quality and origin, which may have been inserted at the stage validation stage or identified at discharge validation. Validation emphasize on identifying errors and, following investigation, for correcting and completing the series.

· Validation against data limits

Data will be checked numerically against, absolute boundaries, relative boundaries and acceptable rates of change, and individual values in the time series will be flagged for inspection.

Absolute boundaries: Values may be flagged which exceed a maximum specified by the user or fall below a specified minimum. The specified values may be the absolute values of the historic series. The object is to screen out spurious extremes, but care must be taken not to remove or correct true extreme values as these may be the most important values in the series.

Relative boundaries: A larger number of values may be flagged by specifying boundaries in relation to departures ( and ) from the mean of the series (Qmean ) by some multiple of the standard deviation (sx), i.e.

Upper boundary Qu = Qmean + sx

Lower boundary Ql = Qmean - sx

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Whilst Qmean and sx are computed by the program, the multipliers and are inserted by the user with values appropriate to the river basin being validated. The object is to set limits which will screen a manageable number of outliers for inspection whilst giving reasonable confidence that all suspect values are flagged. This test is normally only used with respect to aggregated data of a month or greater.

Rates of change. Values will be flagged where the difference between successive observations exceeds a value specified by the user. The specified value will be greater for large basins in arid zones than for small basins in humid zones. Acceptable rates of rise and fall may be specified separately, generally allowable rates of rise will be greater than allowable rates of fall.

For looking at the possible inconsistencies, it is very convenient if a listing of only those data points which are beyond certain boundaries is obtained.

2.2 Graphical validation

Graphical inspection of the plot of a time series provides a very rapid and effective technique for detecting anomalies. Such graphical inspection will be the most widely applied validation procedure and will be carried out for all discharge data sets.

The discharge may be displayed alone or with the associated stage measurement (Fig. 2.1). Note that in this example the plot covers 2 months to reveal any discontinuities which may appear between successive monthly updates of the data series.

The discharge plots may be displayed in the observed units or the values may be log-transformed where the data cover several orders of magnitude. This enables values near the maximum and minimum to be displayed with the same level of precision. Log-transformation is also a useful means of identifying anomalies in dry season recessions. Whereas the exponential decay of flow based on releases from natural storage are curved in natural units, they show as straight lines in log-transformed data

Figure 2.1 Q(t) and h(t) of station Khed for consecutive months

The graphical displays will also show the absolute and relative limits. The plots provide a better guide than tabulations to the likely reliability of such observations.

The main purpose of graphical inspection is to identify any abrupt discontinuities in the data or the existence of positive or negative ‘spikes’ which do not conform with expected

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hydrological behavior. It is very convenient to apply this test graphically wherein the rate of change of flow together with the flow values are plotted against the expected limits of rate of rise and fall in the flows. Examples are:

· Use of the wrong stage discharge relationship (Fig. 2.2). Note that in this example, discharge has been plotted at a logarithmic scale

· Use of incorrect units (Fig. 2.3) · Abrupt discontinuity in a recession (Fig. 2.4). · Isolated highs and lows of unknown source (Fig. 2.5) but may be due to recorder

malfunction with respect to stage readings

Figure 2.2 Use of incorrect rating for Figure 2.3 Use of incorrect unitsPart of the year

Figure 2.4 Unrealistic recession Figure 2.5 Isolated ‘highs’ and ‘lows’

2.3 Validation of regulated rivers

The problems of validating regulated rivers have already been mentioned with respect to stage data and should also be borne in mind in validating discharge data. Natural rivers are not common in India; they are influenced artificially to a greater or lesser extent. The natural pattern is disrupted by reservoir releases which may have abrupt onset and termination, combined with multiple abstractions and return flows. The influences are most clearly seen in low to medium flows where in some rivers the hydrograph appears entirely artificial; high flows may still observe a natural pattern. Officers performing validation should be aware of the principal artificial influences within the basin, the location of those influences, their

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magnitude, their frequency and seasonal timing, to provide a better basis for identifying values or sequences of values which are suspect.

3. Multiple station validation.3.1 Comparison plots

The simplest and often the most helpful means of identifying anomalies between stations are in the plotting of comparative time series. eSWIS permits the plotting of multiple for a given period in one graph. There will of course be differences in the plots depending on the contributing catchment area, differing rainfall over the basins and differing response to rainfall. However, gross differences between plots can be identified.

The most helpful comparisons are between sequential stations on the same river. The series may be shifted relative to each other with respect to time to take into account the different lag times from rainfall to runoff or the wave travel time in a channel.

In examining current data, the plot should include the time series of at least the previous month to ensure that there are no discontinuities between one batch of data received from the station and the next - a possible indication that the wrong data have been allocated to the station.

Comparison of series may permit the acceptance of values flagged as suspect because they fell outside the warning ranges, when viewed as stage or when validated as a single station. When two or more stations display the same behavior there is strong evidence to suggest that the values are correct, e.g. an extreme flood peak.

Figure 3.1 Plot of multiple discharge series of adjacent stations

Comparison plots provide a simple means of identifying anomalies but not necessarily of correcting them. This may best be done through regression analysis, double mass analysis or hydrological modelling.

3.2 Residual series

An alternative way of displaying comparative time series is to plot their differences. This procedure may be applied to river flows along a channel to detect anomalies in the water balance . eSWIS

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provides a means of displaying residual series under the option ‘Balance’. Both the original time series and their residuals can be plotted in the same figure.

Water balances are made of discharge series of successive stations along a river or of stations around a junction, where there should be a surplus, balance or deficit depending on whether water is added or lost. The basic equation is expressed as:

Yi = a.X1,i b.X2,i c.X3,i d.S4,i

Where:

a, b, c, d = multipliers entered by the user (default = 1) = sign entered by user (default = +)

A maximum of four series is permitted. An example for the series presented in Figure 3.1 is shown in Figure 3.2 where the comparison is simply between two stations, upstream and a downstream. Reference is also made to module 30. Any anomalous behavior should be further investigated. Sharp negative peaks may be eliminated from the plot by applying the appropriate time shift between the stations or to carry out the analysis at a higher aggregation level.

Figure 3.2 Example of water balance between two adjacent stations

Double mass curves

Double mass curve can also be used to show trends or in homogeneities between flows records at neighboring stations and is normally used with aggregated series.

A difficulty in double mass curves with streamflow is in the identification of which if any station is at fault; this may require intercomparisons of several neighboring stations. There may also be a legitimate physical reason for the in homogeneity, for example, the construction of a major irrigation abstraction above one of them. In the latter case no correction should be applied unless one is attempting to ‘naturalize’ the flow. (Naturalization is the process of estimating the flow that would have occurred if one, several or all abstractions, releases or land use changes had not occurred).

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4. Comparison of streamflow and rainfallThe principal comparison of streamflow and rainfall is done through hydrological modeling. However, a quick insight into the consistency of the data can be made by graphical and tabular comparison of areal rainfall and runoff. Basically the basin rainfall over an extended period such as a month or year should exceed the runoff (in mm) over the same period by the amount of evaporation and changes in storage in soil and groundwater. Tabular comparisons should be consistent with such physical changes. For example an excess of runoff over rainfall either on an annual basis or for monthly periods during the monsoon will be considered suspect.

Graphical comparison on a shorter time scale can be made by plotting rainfall and streamflow on the same axis. In general the occurrence of rainfall and its timing should be followed by the occurrence of runoff separated by a time lag but precise correspondence should not be expected owing to the imperfect assessment of areal rainfall and to the variable proportion of rainfall that enters storage.

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Chapter 16: Compute Discharge Data

With limited exceptions, discharge cannot be measured both directly and continuously. Instead measurements of stage (or level) are made continuously or at specified intervals at a gauging station and these are converted to discharge by the use of stage discharge relationships.

Computation of discharge normally be carried out monthly on the stage data from the previous month but will always be reviewed annually before transferring to the archive.

Computation of discharge will be carried out at Divisional offices and reviewed at the State Data Management Centre.

2. Station ReviewBefore computing discharge, it is essential to have available a summary of all the relevant information for the station, including:

the stage record - to ensure that it is complete and without abrupt discontinuities. a listing of stage discharge relationships to check that periods of application do not

overlap or have gaps between ratings. Ancillary information based on field records (Field Record Book) or on information

from validation of stage or stage discharge relationships. In particular field information on datum changes, scour and deposition, blockage and backwater effects should be assembled along with any adjustments or corrections applied during validation.

3. Transformation of stage to dischargeThe procedure used to transform stage to discharge depends on physical conditions at the station and in the river reach downstream The following alternatives are considered:

· single channel rating curve · compound channel rating curve · rating curves with unsteady flow correction · rating curves with constant fall backwater correction · rating curves with normal fall backwater correction

3.1. Single channel rating curve

When unsteady flow and backwater effects are negligibly small the stage discharge data are fitted by a single channel relationship, valid for a given time period and water level range. Rating equations will have previously been derived either as parabolic or power law equations; it is assumed that in the vast majority of cases the recommended power law relationship will have been applied. Equations for standard and non-standard gauging structures may also be re-computed in this form with little loss of accuracy.

The basic equations are as follows:

(a) For the power type equation used for curve fitting.

Q c (h a1,i

)b1,i (1)

t 1,i t

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(b) For the parabolic type of equation used for curve fitting

Q a2,i b2,i ht c2,t ht2 (2)

Where:discharge at time t (m3/sec)Qt =

ht = measured water level at time t(m)a1,b1,c1 = parameters of the power equationa2,b2,c2 = parameters of the parabolic equation

i =index for water level interval for which the parameters are valid (1 i 4)

The parabolic form of rating equation is however not recommended for use while establishing the rating curves.

eSWIS permits a maximum of 5 equations applicable over different level ranges in a single stage discharge relationship; normally three will be sufficient. One equation may require to be used for the situation where water is ponded at the gauge and a non-zero level has been measured but the flow is zero. In this case an equation may be introduced for the range from h = 0.0 to h at minimum flow, taking the power law form with c = 0.0, a = 0.0 and b = 1.0

3.2. Compound channel rating curve

The compound channel rating curve is used to avoid large values of the parameter b and very low values of the c-parameter in the power equation at levels where the river begins to spill over from its channel to the floodplain.

When a compound channel rating has been applied, the discharge for the flood plain interval will be computed by adding the discharge computed for the river section up to the maximum flood plain level using the parameters for the one but last interval, and the discharge computed for the flood plain section for the last interval. That is:

Qtot Q

r Q

fp (3)Where:

= total dischargeQtot

Qr = discharge flowing through the main river section up to the maximum waterlevel

Qfp = discharge flowing through the flood plain section.

3.3. Rating curve with unsteady flow correction

Where an unsteady flow correction is required, the application of the simple rating curve first yields a discharge for steady flow which must then be multiplied by the unsteady flow correction to give the discharge for the required rate of change of water level. The stage-discharge transformation used for this case is:

where:= is the required discharge corresponding to the observed stage ht and rate ofQt

change of stage (dht/dt)Qst = is the steady state discharge as obtained from the available steady state

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rating curve.

The expression (1/S0c) is expressed in the form of parabolic equation as:

1 a b h ch 2 and h h (5)

3 t t minS0 c

3 3 t

a3, b3, c3 = parameters of the equationHmin = the lowest water level below which the correction is not to be applied.

The parameters of the above parabolic equation and that of the steady state equation are available from the established rating curve.

The rate of change of stage with respect to time (dht/dt) at time t can be obtained from the stage time series as:

3.4. Rating curve with constant fall backwater correction

Where the station is affected by backwater and the rating curve with constant fall type of backwater correction has been established for it then the stage-discharge transformation is carried out using the following equation:

3.5. Rating curve with normal fall backwater correction

Where the station is affected by backwater and the rating curve with normal fall type of backwater correction has been established for it, then the stage-discharge transformation is carried out using the equation:

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· = is the exponent in the above equation and is available as the parameter of the established rating curve

Ft = h1t – h2t

· is the measured fall between the stages at the station under consideration (h1t) and the reference station (h2t). The stages used for calculating the fall have to be precisely synchronised in time.

The reference fall, Frt in this case is expressed as:

Frt a4 b4 ht c4 ht2 and ht hmin (9)

The parameters a4, b4 and c4 are available from the established rating curve and the reference fall is evaluated for any stage above the minimum stage hmin below which the control is not affected by the backwater.

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Chapter 17: Correct and Complete Discharge Data

1. General Data validation is the process to ensure that the final figure stored is the best possible representation of the true value of the variable at the measurement site at a given time or in a given interval of time. Validation recognizes that values observed or measured in the field are subject to errors which may be random, systematic or spurious.Incorrect and missing values will be replaced where possible by estimated values based on interpolation or other observations at the same station or neighbouring stations. The process of filling in missing values is generally referred to as ‘completion’. It must be recognised that values estimated from other gauges are inherently less reliable than values properly measured. Doubtful original values will therefore be generally given the benefit of the doubt and will be retained in the record with a flag. Where no suitable neighbouring observations or stations are available, missing values will be left as ‘missing’ and incorrect values will be set to ‘missing’ Procedures for correction and completion depend on the type of error, its duration, and the availability of suitable source records with which to estimate.

2. Completion from another record at the same station

All streamflow stations equipped with autographic or digital recorders have a back-up of level observations made by the observer. Where there is an equipment failure the observer’s record is used to complete the instrument record. However this is normally done as level rather than as discharge.

3. Interpolating discharge gaps of short duration

Unlike rainfall, streamflow shows strong serial correlation; the value on one day is closely related to the value on the previous and following days especially during periods of low flow or recession.

Where gaps in the record are short, during periods of low flow (say, less than 2 days), it may be acceptably accurate to use linear interpolation between the last value before the gap and the first value after it. To confirm that this is acceptable, a graphical display of the hydrograph at the station and one or more neighbouring stations is inspected to ensure that that there are no discontinuities in the flow sequence over the gap.

4. Interpolating gaps during recessions

During periods of recession when the flow is dependent on surface and sub-surface storage rather than rainfall, the flow exhibits a pattern of exponential decay giving a curved trace on a simple plot of Discharge versus Time, but a straight line on a logarithmic plot. During long recession periods, interpolation between the logarithmically transformed points before and after the gap will result in a more realistic recession than simple linear interpolation. It is possible to make this interpolation as stage rather than as discharge but, as the principle is based on depletion of a storage volume, it is conceptually simpler to apply the interpolation to discharge rather than to stage.

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The slope of the logarithmically transformed flow recession (also called a reaction factor), from the last value before the gap Qt 0 at time t0 to the first value after the gap Qt 1 at time t1 is:

The gap is filled incrementally with no discontinuity at the beginning and end of the gap. In suitable conditions periods of a month or more may be interpolated in this way.

5. Interpolation using regression

During periods of variable flow or in longer gaps, simple interpolation should not be used and relation/regression equations may be applied to fill in missing data, provided there are suitable stations on the same river or on a neighbouring catchment. Regression relations may be obtained for annual, monthly or daily series.

Since relations between stations may change seasonally, eSWIS offers the option of fitting and applying a relation only to a limited period in the year, e.g. daily or monthly values of one to a few months for sequential years. Where two or more such relations are applied to fill a single gap, the resulting interpolated hydrograph is inspected to ensure that there is no serious discontinuity at the junction between the periods of application.

A time shift may be applied to a series to allow for the average lag time between a station represented by the dependent series and the independent station series where they are on the same river - or the difference in rainfall response time if on neighbouring catchments. The time shift may be computed by the user based on the physical properties of the channel or an optimal time shift may be computed using eSWIS.

For a user computed shift (t1) between an upstream station X and a downstream one Y, spaced at a distance of s km, the following may be applied. Given the average flow velocity of u m/sec (possibly available from gauging), the propagation velocity or celerity of the flood wave c is approximately 1.7u and the time shift to be applied between X and Y is:

t1= - 1000 s / (1.7 u)

(secs), or

t1 = -0.00772 s / u (days)

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When the river is in flood and especially when the river extends over the floodplain the celerity may differ from 1.7u and a different time shift may be necessary.

ESWIS also provides an analytical procedure to compute time shift on the basis of cross correlation analysis. Correlation coefficients are derived for sequential time shifts. A parabolic relationship is fitted between shift time and correlation coefficient and the maximum of this parabola is displayed as the optimum time shift.

As described in the validation by regression module, eSWIS provides a range of regression relations as follows:

· Single independent variable simple linear polynomial logarithmic power exponential hyperbolic

· Multiple independent variables

linear multiple linear stepwise

To establish the spread of the relationship between X and Y and to view its functional form, a scatter graph should first be plotted. In general a simple linear relationship should be tried first, then a polynomial - but rarely exceeding order 3After the time period of analysis is specified, the parameters of the relation curve of selected functional form are computed and the graph displayed of the fitted relationship. An example is shown of Fig. 2. Once an acceptable relationship has been established, the parameters may be stored for further use in computing missing values of Y from X

Multiple regression may be applied, for example, between:

downstream station and two or more upstream tributaries

downstream station and upstream station and rainfall

upstream station anddownstream station and intervening tributary

Irrespective of the scatter, regression analysis will produce a functional relationship, but if the relationship is poor it should not be used to in-fill missing values. What criteria then, should be used for acceptance? It is suggested that a correlation coefficient r of less than 0.90 be generally considered the lower limit for acceptance but reference should also be made to the standard error of estimate. Where no acceptable relationship is found, the missing values should be left ‘missing’ or an alternative method of in-filling used.

Application of regression analysis may also produce a discontinuity between observed flows before and after the gap and the in-filled values due to error in the relationship. The in-filled hydrograph plot should be inspected for such discontinuities and suitable

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adjustment applied. Water balance approach for in-filling/correcting, which is explained in the following section, would be preferred as it will have better physical basis.

6. Water balance and flow routing methods Regression analysis may be used to estimate long periods of missing values or to extend a record. However, in-filling missing values by regression does not ensure water balance between neighbouring stations . Thus application may give significantly less volume at a downstream station than upstream (taking outflows into consideration). To check the water balance, ESWIS provides an option to compare upstream and downstream stations or multiple stations around a junction and to display the balance graphically. If the balance conflicts with common sense, the functional relationship should be reviewed and if necessary rejected.

Alternatively, to achieve a satisfactory balance between stations flow routing methods may be applied.

The mass-balance equation for a system states that the difference between the input and output is equal to the rate of change in storage.. In flow routing, routing two parameters K and X are determined from measured hydrographs at upstream and downstream stations and applied to route the flow from upstream to a missing downstream station. Inflows and abstractions from the intervening reach can be incorporated to achieve a water balance. Flow routing is usually applied to floods but can be extended for use in low flows. An example of the classical Muskingum method of flow routing follows. More sophisticated alternatives are available using a third parameter6.1 Muskingum method of flow routing

The Muskingum method of flow routing is based on the continuity equation:

I Q dS

(4)dt

and

S K[ XI (1 X )Q] (5)

where I = inflow, Q = outflow, S = storage, X = weighting factor, K = storage coefficient, and t = time.

The values of storage at time t and t+1 can be written, respectively, as

St K[ XI t (1 X )Qt ] (6)and

St1 K[ XI t 1 (1 X )Qt 1 ] (7)

Using eqs. (6) and (7), the change in the storage over time interval t is

St1 St K[ XIt 1 (1 X )Qt 1 ] K [ XIt (1 X )Qt ] (8)

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Considering the variation of inflow and outflow over the interval is approximately linear, the change in storage can also be expressed using eq. (4) as:

St1

S

t (I t I t 1 ) t (Qt Qt1 ) t (9)Coupling of Eqs. (8) and (9) in finite difference forms leads to

Qt 1

C

0 I

t1

C

1I

t

C

2Q

t

(10)where C0, C1, and C2 are routing coefficients in terms of t, K, and X as follows:

(t / K ) 2XCo (11a)

2(1 X ) (t / K )(t / K ) 2X

C1 (11b)2(1 X ) (t / K )

C2 2(1 X ) (t / K )

(11c)2(1 X ) (t / K )

Since (C0+C1+C2)=1, the routing coefficients can be interpreted as weighting coefficients.

If observed inflow and outflow hydrographs are available for a river reach, the values of K and X can be determined. Assuming various values of X and using known values of the inflow and outflow, successive values of the numerator and denominator of the following expression for K, derived from eq. (8) and (9).

K

0.5 t [( It 1 I t ) (Q j 1 Q j )]

(12)X (I j1 I j ) (1 X ) (Q j1 Q j )

The computed values of the numerator and denominator are plotted for each time interval. With numerator on the vertical axis and the denominator on the horizontal axis. This usually produces a graph in the form of a loop. The value of X that produces a loop closest to a single line is taken to be the correct value for the reach, and K, according to eq. (12), is equal to the slope of the line. Since K is the time required for the incremental flood wave to traverse the reach, its value may also be estimated as the observed time of travel of the peak flow through the reach.

The application of Muskingum method is demonstrated with the help of the following example.

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An inflow hydrograph to a channel is shown in Col. 2 of Table 1. Using Muskingum method, route this hydrograph with K=2 days and X=0.1 to calculate an outflow hydrograph. Assume baseflow is 352 m3/s.

Table 1 shows the computation of outflow using Muskingum method. For given values of K=2 days and X=0.1 (derived from the historical record of inflow and outflow sets), C0=0.1304 (Eq. 7a), C1=0.3044 (Eq. 7b), and C2=0.5652 (Eq. 7c). It is noted that the sum of these routing coefficients is equal to 1.0. Taking Q1 = 352 m3 /s which is the baseflow, partial flows shown in columns 3 through 5 of Table 1 can be computed and summed up to obtain total outflow given in Col. 6.

The principal difficulty in applying routing methods to infilling missing values is in the assessment of ungauged lateral inflows and outflows, and the method should not be used where these are large and variable.

7. Using rainfall runoff simulation

Regression analysis and flow routing imply that neighbouring flow records are available for infilling. Where no such records are available but the catchment contains sufficient raingauges to calculate areal rainfall, simulation modelling may be used to infill missing records or to extend the recordThe Sacramento model which is incorporated in eSWIS has been outlined in the previous module. With respect to application to infilling missing records, it is assumed that the model has already been calibrated and the parameters selected and optimised and that rainfall data series are available for the period of the missing flow record. The model is again run with the given rainfall (and evapotranspiration) input and parameters to give the outflow record at the specified time step for the missing record period.

Like regression analysis the quality of the generated record cannot be guaranteed. It may be limited by the reliability of the rainfall and flow record during the calibration period. Generally a correlation coefficient of less than 0.70 between observed and simulated flow for the calibration period should not be applied for infilling. Such records should be left missing.

Table 1. Muskingum routing

Time Inflow Partial flows Total Outflow(day) (m3/s) (m3/s) (m3/s)

C0I2 C1I1 C2Q1

1 2 3 4 5 60 352.0 - - - 3521 587.0 76.5 107.1 199.0 382.62 1353.0 176.4 178.7 216.3 571.43 2725.0 355.3 411.9 322.9 1090.14 4408.5 574.9 829.5 616.1 2020.55 5987.0 780.7 1341.9 1142.0 3264.66 6704.0 874.2 1822.4 1845.2 4541.8

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7 6951.0 906.4 2040.7 2567.0 5514.18 6839.0 891.8 2115.9 3116.6 6124.39 6207.0 809.4 2081.8 3461.4 6352.6

10 5346.0 697.1 1889.4 3590.5 6177.011 4560.0 594.6 1627.3 3491.3 5713.212 3861.5 503.5 1388.1 3229.1 5120.713 3007.0 392.1 1175.4 2894.2 4461.814 2357.5 307.4 915.3 2521.8 3744.515 1779.0 232.0 717.6 2116.4 3066.016 1405.0 183.2 541.5 1732.9 2457.717 1123.0 146.4 427.7 1389.1 1963.218 952.5 124.2 341.8 1109.6 1575.619 730.0 95.2 289.9 890.6 1275.720 605.0 78.9 222.2 721.0 1022.1

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Chapter 18: Compile Discharge Data

1. GeneralDischarge compilation is the process by which discharge at its observational or recorded time interval and units is transformed:

to another time interval

from one unit of measurement and especially from discharge (a rate of flow) to volume or runoff (a depth over the catchment)

Computations for aggregation of data from one time interval to another depends on the data type. If the data is of instantaneous nature then the aggregation is effected by computing the arithmetic average of the individual constituent data values. Whereas when the data type is of accumulative nature then the constituents values are arithmetically summed up for obtaining the aggregated value.

Compilation is required for validation, analysis and reporting. Compilation is carried out at Divisional offices; it is done prior to validation if required, but final compilation is carried out after correction and ‘completion’.

2. Aggregation of data to longer durationDischarge and its precursor water level is observed at different time intervals, but these are generally one day or less. Manual observation may be daily, hourly for part of the day during selected seasons, or some other multiple of an hour. For automatic water level recorders a continuous trace is produced from which hourly level and hence discharge is extracted. For digital water level recorders level is usually recorded at hourly intervals though for some small basins the selected interval may be 15 or 30 minutes. Sub-hourly, hourly and sub-daily discharges, computed from levels, are typically aggregated to daily mean. For example, the daily mean discharge (Qd) is computed from hourly values (Qi) by:

124

Qd Qi (1)

24 i 1

For a given day the mean is normally calculated for hours commencing 0100 and finishing 2400. For some purposes daily discharge averages are calculated over the day from 0800 to 0800 (i.e. for hourly measurements the average of observations from 0900 to 0800) to enable direct comparison to be made with daily rainfall.

Daily data are typically averaged over weekly, ten daily, 15 daily, monthly, seasonally or yearly time intervals. In general,

1Nd

QNd Qi (2)

Nd i1

where,QNd is the discharge for Nd days duration,Qi is the discharge of ith day in duration of Nd days.

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Time intervals used while aggregating the data generally corresponds to the month or year ending. For example a ten daily data series corresponds to three parts of every month in which the first two parts are the 1-10 and 11-20 days of the month and the third part is the remaining part of the month. Thus every third value in the series corresponds to 8,9,10 or 11 days (the last part of the month) depending on the total days in the month. Similarly, weekly data depending on its objective is the taken in two ways: (a) as four parts of the months where first three parts are of seven days each and the fourth part is of 7, 8, 9 or 10 days period (as per the total days in the month) or (b) as 52 parts of a year where first 51 weeks are of 7 days each and the last week is of 8 or 9 days depending upon whether the year is a leap or a non-leap year. Such culmination are often desirable for the operational purpose as the time interval is reset to the 1st of a month or year every time.

Averaging over longer time intervals is required for validation and analysis. For validation small persistent errors may not be detected at the small time interval of observation but may more readily be detected at longer time intervals.

3. Computation of volumes and runoff depthTo facilitate comparisons between rainfall and runoff it is usual to express values of rainfall and flow in similar terms. Both may be expressed as a total volume over a specified period (in m3, thousand m3, (Tcm) or million m3 (Mcm)). Alternatively, discharge may be expressed as a depth in millimetres over the catchment.

Volume is simply the rate in m3/sec (cumecs) multiplied by the duration of the specified period in secs., i.e. for daily volumes in cubic metres with respect to daily mean flow Qd in cumecs following equation may be used:

Vd (cum) = (24 x 60 x 60 seconds) Qd (cumecs) = 86400 Qd (cum) (3)

Runoff depth is the volume expressed as depth over the specified catchment area with a constant to adjust units to millimetres; i.e. for daily runoff:

Rd (mm) Vd (cum) x 103

Vd (mm)

86.4 Qd

(4)Area (km2 ) x 10 6 Area (km2 ) x 10 3 Area (km2 )

Runoff depths provide not only a ready comparison with rainfalls; they also provide a comparison with other catchments standardised by area. Such comparions may be made for monthly, seasonal and annual totals but are not generally helpful for daily or shorter duration depths, where basins respond at different time scales to incident rainfall.

For the purposes of annual reporting it is usual to compare the monthly and annual runoff from a station with the long term average, maximum and minimum monthly runoff derived from the previous record. This requires the annual updating of runoff statistics with the concatenation of the previous year with earlier statistics

Volumes and runoff depths may also be required for irregular periods to compare with rainfall depths over a storm period. Providing sufficient measurements are available over the period, the runoff over the storm period can be expressed simply as:

0.001N

R(mm) (Qi t ) (5)Area i 1

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Where:= Number of observations in the periodN

t = Time step in secondsA = Catchment area in km2

Qi = Discharge at time i in m3 / sec

It is not generally necessary to use more complex procedures such as Simpson’s rule, to account for the non-linear variation of flow between observations.

For the purposes of storm analysis, it is also generally necessary to separate the storm flow, resulting from the incident rainfall, and the base flow originating from continuing groundwater sources. Various methods have been suggested for such separation; they are described in standard texts and not discussed further here.

Another unit which is sometimes used to standardise with respect to area is specific discharge which may be computed with respect to instantaneous discharges or the mean discharge over any specified duration as discharge over area (m3/sec per km2).

Imperial and other units are regarded as obsolete and should not be used; these include Mgd (million gallons per day), acre-feet and ft3 /sec (cusecs).

4. Compilation of maximum and minimum seriesThe annual, seasonal or monthly maximum series of discharge is frequently required for flood analysis, whilst minimum series may be required for drought analysis. Options are available for the extraction of maximum and minimum values for the following time periods:

· day · month · year · period within a year

For example if the selected time period is ‘month’ and the time interval of the series to be analysed is ‘day’, then the minimum and maximum daily value is extracted for each month between a start and end date.

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Chapter 19: Analyse Discharge Data

1. General

The types of analysis considered in this module are:

computation of basic statistics empirical frequency distributions and cumulative frequency distributions (flow

duration curves) fitting of theoretical frequency distributions Time series analysis

· moving averages · mass curves · residual mass curves · balances

regression/relation curves double mass analysis series homogeneity tests rainfall runoff simulation

2. Computation of basic statistics Basic statistics are widely required for validation and reporting. The following are commonly used:

· arithmetic mean

1

N

X

i (1)XN

i 1

· median - the median value of a ranked series Xi · mode - the value of X which occurs with greatest frequency or the middle value of the

class with greatest frequency · standard deviation - the root mean squared deviation Sx :

· skewness or the extent to which the data deviate from a symmetrical distribution

N N ( X X )3

CX i

(N 1)( N 2)3

i1 SX

· kurtosis or peakedness of a distribution

(N 2 2N 3) N ( Xi

X ) 4

K X ( N 1)( N 2)( N 3)

4

i 1 SX

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3. Empirical frequency distributions (flow duration curves)A popular method of studying the variability of streamflow is through flow duration curves which can be regarded as a standard reporting output from hydrological data processing. Some of their uses are:

· in evaluating dependable flows in the planning of water resources engineering projects · in evaluating the characteristics of the hydropower potential of a river · in assessing the effects of river regulation and abstractions on river ecology · in the design of drainage systems · in flood control studies · in computing the sediment load and dissolved solids load of a river · in comparing with adjacent catchments.

A flow-duration curve is a plot of discharge against the percentage of time the flow was equalled or exceeded. This may also be referred to as a cumulative discharge frequency curve and it is usually applied to daily mean discharges. The analysis procedure is as follows:

Taking the N years of flow records from a river gauging station there are 365n daily mean discharges.

1. The frequency or number of occurrence in selected classes is counted (Table 1). The class ranges of discharge do not need to be the same.

2. The class frequencies are converted to cumulative frequencies starting with the highest discharge class.

3. The cumulative frequencies are then converted to percentage cumulative frequencies. The percentage frequency represents the percentage time that the discharge equals or exceeds the lower value of the discharge class interval.

4. Discharge is then plotted against percentage time. Fig. 1 shows an example based on natural scales for the data in Table 1. A histogram plot may also be made of the actual frequency (Col. 2) in each class, though this is not as useful as cumulative frequency.

5. The representation of the flow duration curve is improved by plotting the cumulative discharge frequencies on a log-probability scale (Fig. 2). If the daily mean flows are log normally distributed they will plot as a straight line on such a graph. It is common for them to do so in the centre of their range.

Table 1 Derivation of flow frequencies for construction of a flow duration graph

Daily discharge Frequency Cumulative Percentageclass frequency cumulative

frequency1 2 3 4

Over 475 3 3 0.21420-475 5 8 0.44365-420 5 13 0.89315-365 8 21 1.44260-315 25 46 3.15210-260 36 82 5.61155-210 71 153 10.47120-155 82 235 16.08105-120 52 287 19.64

95-105 42 329 22.5285-95 50 379 25.9475-85 58 427 29.9165-75 83 520 35.59

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50-65 105 625 42.7847-50 72 697 47.7142-47 75 772 52.8437-42 73 845 57.8432-37 84 929 63.5926-32 103 1032 70.6421-25 152 1184 81.0416-21 128 1312 89.8011-16 141 1453 99.45Below 11 8 1461 100.00

Total days = 1461

From Fig 2 percentage exceedence statistics can easily be derived. For example the 50% flow (the median) is 45 m3 /sec and flows less than 12 m3 / sec occurred for 2% of the time

The slope of the flow duration curve indicates the response characteristics of a river. A steeply sloped curve results from very variable discharge usually for small catchments with little storage; those with a flat slope indicate little variation in flow regime.

Comparisons between catchments are simplified by plotting the log of discharge as percentages of the daily mean discharge (i.e. the flow is standardised by mean discharge)(Fig. 3). A common reporting procedure is to show the flow duration curve for the current year compared with the curve over the historic period. Curves may also be generated by month or by season, or one part of a record may be compared with another to illustrate or identify the effects of river regulation on the river regime.

Flow duration curves provide no representation of the chronological sequence. This important attribute, for example the duration of flows below a specified magnitude, must be dealt with in other ways.

4. Fitting of frequency distributions4.1. General description

The fitting of frequency distributions to time sequences of streamflow data is widespread whether for annual or monthly means or for extreme values of annual maxima or minima. The principle of such fitting is that the parameters of the distribution are estimated from the available sample of data, which is assumed to be representative of the population of such data. These parameters can then be used to generate a theoretical frequency curve from which discharges with given probability of occurrence (exceedence or non-exceedence) can be computed. Generically, the parameters are known as location, scale and shape parameters which are equivalent for the normal distribution to:

· location parameter mean (first moment)· scale parameter standard deviation (second moment)· shape parameter skewness (third moment)

Different parameters from mean, standard deviation and skewness are used in other distributions. Frequency distributions for data averaged over long periods such as annual are often normally distributed and can be fitted with a symmetrical normal distribution, using just the mean and standard deviation to define the distribution.

Data become increasingly skewed with shorter durations and need a third parameter to define the relationship. Even so, the relationship tends to fit least well at the extremes of the data which are often of greatest interest. This may imply that the chosen frequency

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distribution does not perfectly represent the population of data and that the resulting estimates may be biased.

Normal or log-normal distributions are recommended for distributions of mean annual flow.

4.2. Frequency distributions of extremes

Theoretical frequency distributions are most commonly applied to extremes of time series, either of floods or droughts. The following series are required:

· maximum of a series: The maximum instantaneous discharge value of an annual series or of a month or season may be selected. All values (peaks) over a specified threshold may also be selected. In addition to instantaneous values maximum daily means may also be used for analysis.

· minimum of a series: With respect to minimum the daily mean or period mean is usually selected rather than an instantaneous value which may be unduly influenced by data error or a short lived regulation effect.

The object of flood frequency analysis is to assess the magnitude of a flood of given probability or return period of occurrence. Return period is the reciprocal of probability and may also be defined as the average interval between floods of a specified magnitude.

A large number of different or related flood frequency distributions have been devised for extreme value analysis. These include:

· Normal and log-normal distributions and 3-parameter log-normal · Pearson Type III or Gamma distribution · Log-Pearson Type III · Extreme Value type I (Gumbel), II, or III and General extreme value (GEV) · Logistic and General logistic · Goodrich/Weibull distribution · Exponential distribution · Pareto distribution

Different distributions fit best to different individual data sets but if it is assumed that the parent population is of single distribution of all stations, then a regional best distribution may be recommended.

It is clear that there is no single distribution that represents equally the population of annual floods at all stations, and one has to use judgement as to which to use in a particular location depending on experience of flood frequency distributions in the surrounding region and the physical characteristics of the catchment. No recommendation is therefore made here.

A standard statistic which characterises the flood potential of a catchment and has been used as an ‘index flood’ in regional analysis is the mean annual flood, which is simply the mean of the maximum instantaneous floods in each year. This can be derived from the data or from distribution fitting. An alternative index flood is the median annual maximum, similarly derived. These may be used in reporting of general catchment data.

Flood frequency analysis may be considered a specialist application required for project design and is not a standard part of data processing or validation. Detailed descriptions of the mathematical functions and application procedures are not described here.

5. Time series analysis

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Time series analysis may be used to test the variability, homogeneity or trend of a streamflow series or simply to give an insight into the characteristics of the series as graphically displayed. The following are described here:

1. moving averages 2. esidual series 3. residual mass curves 4. balances

5.1 Moving averages

To investigate the long term variability or trends in series, moving average curves are useful. A moving average series Yi of series Xi is derived as follows:

1j i M

Yi X

j

(2M 1) j i M

where averaging takes place over 2M+1 elements. The original series can be plotted together with the moving average series. An example is shown in Table 2 and Fig. 5

Table 2. Computation of moving averages (M = 1)

I Year Annual Totals for moving average Moving averagerunoff (mm) =Xi-1 + Xi + Xi+1 Yi = Col 4 / 3

1 2 3 4 51 1970 5202 1971 615 520+615+420 = 1555 518.33 1972 420 615+420+270 = 1305 435.04 1973 270 420+270+305 = 995 331.75 1974 305 270+305+380 = 955 318.36 1975 380 305+380+705 = 1390 463.37 1976 705 380+705+600 = 1685 561.78 1977 600 705+600+350 = 1655 551.79 1978 350 600+350+550 = 1500 500.0

10 1979 550 350+550+560 = 1460 486.711 1980 560 550+560+400 = 1510 503.312 1981 400 560+400+520 = 1480 493.313 1982 520 400+520+435 = 1355 451.714 1983 435 520+435+395 = 1350 450.015 1984 395 435+395+290 = 1120 373.316 1985 290 395+290+430 = 1115 371.717 1986 430 290+430+1020 =1740 580.018 1987 1020 430+1020+900 =2350 783.319 1988 900

5.2 Mass curves and residual mass curves

These methods are usually applied to monthly data for the analysis of droughts.

For mass curves, the sequence of cumulative monthly totals are plotted against time. This tends to give a rather unwieldy diagram for long time series and should not be used.

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Residual mass curves or simply residual series are an alternative procedure and has the advantage of smaller numbers to plot. An example is shown in Fig. 6. With respect to reservoir design (Fig. 7), each flow value in the record is reduced by the mean flow and the accumulated residuals plotted against time. A line such as AB drawn tangential to the peaks of the residual mass curve would represent a residual cumulative constant yield that would require a reservoir of capacity CD to fulfil the yield, starting with the reservoir full at A and ending full at B.

5.3 Run length and run sum characteristics

Related properties of time series which are used in drought analysis are run-length and run-sum. Consider the time series X1 ................Xn and a constant demand level y as shown in Fig. 8. A negative run occurs when Xt is less than y consecutively during one or more time intervals. Similarly a positive run occurs when Xt is consecutively greater than y. A run can be defined by its length, its sum or its intensity. The means, standard deviation and the maximum of run length and run sum are important characteristics of the time series.

5.4 Storage analysis

Use of sequent peak algorithm can be made for computing water shortage or equivalently the storage requirements without running dry for various draft levels from the reservoir. The procedure used in the software is a computerised variant of the well known graphical Ripple technique. The algorithm considers the following sequence of storages:

Si = Si-1 + (Xi - Dx) Cf for i = 1, 2N ; S0 = 0

where:

Xi = inflowDi = DL mxmx = average of xi , i = 1, NDL = draft level as a fraction of mx

Cf = multiplier to convert intensities into volumes (times units per time interval)

The local maximum of Si larger than the preceding maximum is sought. Let the locations be k2 and k1 respectively with k2 > k1. Then the largest non-negative differences between Sk1

and Si , i = k1 …, K2 …, is determined, which is the local range. This procedure is executed for two times the actual series Xi = XN+i . In this way initial effects are eliminated.

5.5 Balances

This method is used to check the consistency of one or more series with respect to mass conservation. Water balances are made of discharge series at successive stations along a river or of stations around a junction. The method has already been described in detail with an example in Module 36

6. Regression /relation curvesRegression analysis and relation curves are widely used in validation and for the extension of records by the comparison of the relationship between neighbouring stations.

7. Double mass analysisThe technique of double mass analysis is again widely used in validation of all climatic variables.

8. Rainfall runoff simulation

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Rainfall runoff simulation for data validation is described in Module 38 with particular reference to the Sacramento model which is used by ESWIS. The uses of such models are much wider than data validation and include the following:

· filling in and extension of discharge series · generation of discharges from synthetic rainfall · real time forecasting of flood waves · determination of the influence of changing landuse on the catchment (urbanisation,

afforestation) or the influence of water use (abstractions, dam construction, etc.)

Fig. 1 Flow duration curve plotted on a natural scale

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Fig. 2 Flow duration curve plotted on a log-probability scale (after Shaw 1995)

Fig. 3 Flow duration curve standardised by mean flow (after Shaw 1995)

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Fig. 4 Flow frequency curve showing discharge plotted against return period (top) and probability (Lower) (after Shaw, 1995)

Fig. 5 Moving average of annual runoff

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Fig. 6 Example of a residual mass curve

Fig. 7 Residual mass curve used in drought analysis

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Fig. 8 Definition diagram of run-length and run-sum

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Chapter 20: Stage Discharge Rating Curve

1.GeneralAlthough, flow is the variable usually required for hydrological analysis but, continuous measurement of flow past a river section is usually impractical or prohibitively expensive. However, stage can be observed continuously or at regular short time intervals with comparative ease and economy. Fortunately, a relation exists between stage and the corresponding discharge at river section. This relation is termed a stage-discharge relationship or stage-discharge rating curve or simply, rating curve.

A rating curve is established by making a number of concurrent observations of stage and discharge over a period of time covering the expected range of stages at the river gauging section.

At many locations, the discharge is not a unique function of stage; variables such as surface slope or rate of change of stage with respect to time must also be known to obtain the complete relationship in such circumstances.

The rating relationship thus established is used to transform the observed stages into the corresponding discharges. In its simplest form, a rating curve can be illustrated graphically, as shown in Figure 1.1, by the average curve fitting the scatter plot between water level (as ordinate) and discharge (as abscissa) at any river section.

Figure 1.1 Example of stage-discharge rating curve

If Q and h are discharge and water level, then the relationship can be analytically expressed as:

Q = f(h) (1)

Where; f(h) is an algebraic function of water level. A graphical stage discharge curve helps in visualising the relationship and to transform stages manually to discharges whereas an algebraic relationship can be advantageously used for analytical transformation.

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Because it is difficult to measure flow at very high and low stages due to their infrequent occurrence and also to the inherent difficulty of such measurements, extrapolation is required to cover the full range of flows. Methods of extrapolation are described in a later module.

2. The station control· The shape, reliability and stability of the stage-discharge relation are controlled

by a section or reach of channel at or downstream from the gauging station and known as the station control. The establishment and interpretation of stage discharge relationships requires an understanding of the nature of controls and the types of control at a particular station.

· Fitting of stage discharge relationships must not be considered simply a mathematical exercise in curve fitting. Staff involved in fitting stage discharge relationships should have familiarity with and experience of field hydrometrics.

The channel characteristics forming the control include the cross-sectional area and shape of the stream channel, expansions and restrictions in the channel, channel sinuosity, the stability and roughness of the streambed, and the vegetation cover all of which collectively constitute the factors determining the channel conveyance.

2.1. Types of station control

The character of the rating curve depends on the type of control which in turn is governed by the geometry of the cross section and by the physical features of the river downstream of the section. Station controls are classified in a number of ways as:

· section and channel controls · natural and artificial controls · complete, compound and partial controls · permanent and shifting controls

2.1.1. Section and channel controls

When the control is such that any change in the physical characteristics of the channel downstream to it has no effect on the flow at the gauging section itself then such control is termed as section control. In other words, any disturbance downstream the control will not be able to pass the control in the upstream direction. Natural or artificial local narrowing of the cross-section (waterfalls, rock bar, gravel bar) creating a zone of acceleration are some examples of section controls (Figs. 2.1 and 2.2). The section control necessarily has a critical flow section at a short distance downstream.

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Figure 2.1 Example of section control

Figure 2.2 Example of section control. (low-water part is sensitive, while high-water part is non-sensitive)

A cross section where no acceleration of flow occurs or where the acceleration is not sufficient enough to prevent passage of disturbances from the downstream to the upstream direction then such a location is called as a channel control. The rating curve in such case depends upon the geometry and the roughness of the river downstream of the control (Fig. 2.3). The length of the downstream reach of the river affecting the rating curve depends on the normal or equilibrium depth he and on the energy slope S (L he/S, where he follows from Manning Q=KmBhe 5/3S1/2 (wide rectangular channel) so he = (Q/KmS1/2)3/5). The length of channel effective as a control increases with discharge. Generally, the flatter the stream gradient, the longer the reach of channel control.

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Figure 2.3 Example of channel control

2.1.2. Artificial and natural controls

An artificial section control or structure control is one which has been specifically constructed to stabilise the relationship between stage and discharge and for which a theoretical relationship is available based on physical modelling. These include weirs and flumes, discharging under free flow conditions (Fig. 5). Natural section controls include a ledge of rock across a channel, the brink of a waterfall, or a local constriction in width (including bridge openings). All channel controls are ‘natural’.

Figure 2.4 Example of an artificial control

2.1.3. Complete, compound and partial controls

Natural controls vary widely in geometry and stability. Some consist of a single topographical feature such as a rock ledge across the channel at the crest of a rapid or waterfall so forming a complete control. Such a complete control is one which governs the stage-discharge relation throughout the entire range of stage experienced. However, in many cases, station controls are a combination of section control at low stages and a channel control at high stages and are thus called compound or complex controls. A partial control cases, station controls are a combination of section control at low stages and a is one which operates over a limited range of stage when a compound control is present, in the transition between section and channel control. The section control begins to drown out with rising tailwater levels so that over a transitional range of stage the flow is dependent both on the elevation and shape of the control and on the tailwater level.

2.1.4. Permanent and shifting controls

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Where the geometry of a section and the resulting stage-discharge relationship does not change with time, it is described as a stable or permanent control. Shifting controls change with time and may be section controls such as boulder, gravel or sand riffles which undergo periodic or near continuous scour and deposition, or they may be channel controls with erodible bed and banks. Shifting controls thus typically result from:

· scour and fill in an unstable channel · growth and decay of aquatic weeds · overspilling and ponding in areas adjoining the stream channel.

The amount of gauging effort and maintenance cost to obtain a record of adequate quality is much greater for shifting controls than for permanent controls. Since rating curves for the unstable controls must be updated and/or validated at frequent intervals, regular and frequent current meter measurements are required. In contrast, for stable controls, the rating curve can be established once and needs validation only occasionally. Since stage discharge observations require significant effort and money, it is always preferred to select a gauging site with a section or structure control. However, this is not practicable in many cases and one has to be content with either channel control or a compound control.

3. Fitting of rating curves

3.1. General

A simple stage discharge relation is one where discharge depends upon stage only. A complex rating curve occurs where additional variables such as the slope of the energy line or the rate of change of stage with respect to time are required to define the relationship. The need for a particular type of rating curve can be ascertained by first plotting the observed stage and discharge data on a simple orthogonal plot. The scatter in the plot gives a fairly good assessment of the type of stage-discharge relationship required for the cross section. Examples of the scatter plots obtained for various conditions are illustrated below.

If there is negligible scatter in the plotted points and it is possible to draw a smooth single valued curve through the plotted points then a simple rating curve is required. This is shown in Fig. 3.1.

Figure 3.1 Permanent control

However, if scatter is not negligible then it requires further probing to determine the cause of such higher scatter. There are four distinct possibilities:

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· The station is affected by the variable backwater conditions arising due for example to tidal influences or to high flows in a tributary joining downstream. In such cases, if the plotted points are annotated with the corresponding slope of energy line (surface slope for uniform flows) then a definite pattern can be observed. A smooth curve passing through those points having normal slopes at various depths is drawn first. It can then be seen that the points with greater variation in slopes from the corresponding normal slopes are located farther from the curve. This is as shown in Fig. 3.2a and b.

Figure 3.2a Rating curve affected by Figure 3.2b Rating curve affected by

variable backwater (uniform channel)variable backwater (submergence of low-

water control)

· The stage discharge rating is affected by the variation in the local acceleration due to unsteady flow. In such case, the plotted points can be annotated with the corresponding rate of change of slope with respect to time. A smooth curve (steady state curve) passing through those points having the least values of rate of change of stage is drawn first. It can then be seen that all those points having positive values of rate of change of stage are towards the right side of the curve and those with negative values are towards the left of it. Also, the distance from the steady curve increases with the increase in the magnitude of the rate of change of stage. This is as shown in Fig. 3.3.

Figure 3.3 Rating curve affected by unsteady flow

· The stage discharge rating is affected by scouring of the bed or changes in vegetation characteristics. A shifting bed results in a wide scatter of points on the graph. The changes are erratic and may be progressive or may fluctuate from scour in one event and deposition in another. Examples are shown in Fig. 3.4.

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Figure 3.4 Stage-discharge relation Figure 3.5 Stage-discharge relationaffected by scour and fill affected by vegetation growth

· If no suitable explanation can be given for the amount of scatter present in the plot, then it can perhaps be attributed to the observational errors. Such errors can occur due to non-standard procedures for stage discharge observations.

Thus, based on the interpretation of scatter of the stage discharge data, the appropriate type of rating curve is fitted. There are four main cases:

· Simple rating curve: If simple stage discharge rating is warranted then either single channel or compound channel rating curve is fitted according to whether the flow occur essentially in the main channel or also extends to the flood plains.

· Rating curve with backwater corrections: If the stage discharge data is affected by the backwater effect then the rating curve incorporating the backwater effects is to be established. This requires additional information on the fall of stage with respect to an auxiliary stage gauging station.

· Rating curve with unsteady flow correction: If the flows are affected by the unsteadiness in the flow then the rating curve incorporating the unsteady flow effects is established. This requires information on the rate of change of stage with respect to time corresponding to each stage discharge data.

· Rating curve with shift adjustment: A rating curve with shift adjustment is warranted in case the flows are affected by scouring and variable vegetation effects.

3.2. Fitting of single channel simple rating curve

Single channel simple rating curve is fitted in those circumstances when the flow is contained the main channel section and can be assumed to be fairly steady. There is no indication of any backwater affecting the relationship. The bed of the river also does not significantly change so as create any shifts in the stage discharge relationship. The scatter plot of the stage and discharge data shows a very little scatter if the observational errors are not significant. The scatter plot of stage discharge data in such situations, typically is as shown in Fig. 1.1. The fitting of simple rating curves can conveniently be considered under the following headings:

equations used and their physical basis determination of datum correction(s) number and range of rating curve segments

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determination of rating curve coefficients estimation of uncertainty in the stage discharge relationship

3.2.1. Equations used and their physical basis

Two types of algebraic equations are commonly fitted to stage discharge data are:

1. Power type equation which is most commonly used:

c (h a)b (2)

2. Parabolic type of equation

Q c (hw

a) 2 c (hw

a) c(3)2 1 0

where: Q = discharge (m3/sec)h = measured water level (m)a = water level (m) corresponding to Q = 0ci = coefficients derived for the relationship corresponding to the station

characteristics

It is anticipated that the power type equation is most frequently used in India and is recommended. Taking logarithms of the power type equation results in a straight line relationship of the form:

log (Q) log (c) b log (h a)(4)

or A (5)Y B X

That is, if sets of discharge (Q) and the effective stage (h + a) are plotted on the double log scale, they will represent a straight line. Coefficients A and B of the straight line fit are functions of a and b. Since values of a and b can vary at different depths owing to changes in physical characteristics (effective roughness and geometry) at different depths, one or more straight lines will fit the data on double log plot. This is illustrated in Fig. 3.6, which shows a distinct break in the nature of fit in two water level ranges. A plot of the cross section at the gauging section is also often helpful to interpret the changes in the characteristics at different levels.

Figure 3.6 Double logarithmic plot of rating curve showing a distict break

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The relationship between rating curve parameters and physical conditions is also evident if the power and parabolic equations are compared with Manning’s equation for determining discharges in steady flow situations. The Manning’s equation can be given as:

Q 1

AR 2/ 3 S1/2 (1

S 1/ 2 )( AR 2/ 3 )m

n n (6) function of (roughness & slope) & (depth & geometry)

Hence, the coefficients a, c and d are some measures of roughness and geometry of the control and b is a measure of the geometry of the section at various depths. The value of coefficient b for various geometrical shapes are as follows:

For rectangular shape: about 1.6For triangular shape : about 2.5For parabolic shape : about 2.0For irregular shape : 1.6 to 1.9

Changes in the channel resistance and slope with stage, however, will affect the exponent b. The net result of these factors is that the exponent for relatively wide rivers with channel control will vary from about 1.3 to 1.8. For relatively deep narrow rivers with section control, the exponent will commonly be greater than 2 and sometimes exceed a value of 3. Note that for compound channels with flow over the floodplain or braided channels over a limited range of level, very high values of the exponent are sometimes found (>5).

3.2.2 Determination of datum correction (a)

The datum correction (a) corresponds to that value of water level for which the flow is zero. From eq. (2) it can be seen that for Q = 0, (h + a) = 0 which means:a = -h.

Physically, this level corresponds to the zero flow condition at the control effective at the measuring section. The exact location of the effective control is easily determined for artificial controls or where the control is well defined by a rock ledge forming a section control. For the channel controlled gauging station, the level of deepest point opposite the gauge may give a reasonable indication of datum correction. In some cases identification of the datum correction may be impractical especially where the control is compound and channel control shifts progressively downstream at higher flows. Note that the datum correction may change between different controls and different segments of the rating curve.

For upper segments the datum correction is effectively the level of zero flow had that control applied down to zero flow; it is thus a nominal value and not physically ascertainable.

Alternative analytical methods of assessing “a” are therefore commonly used and methods for estimating the datum correction are as follows:

· trial and error procedure · arithmetic procedure · computer-based optimisation

However, where possible, the estimates should be verified during field visits and inspection of longitudinal and cross sectional profiles at the measuring section:

Trial and error procedure

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This was the method most commonly used before the advent of computer-based methods. The stage discharge observations are plotted on double log plot and a median line fitted through them. This fitted line usually is a curved line. However, as explained above, if the stages are adjusted for zero flow condition, i.e. datum correction a, then this line should be a straight line. This is achieved by taking a trial value of “a” and plotting (h + a), the adjusted stage, and discharge data on the same double log plot. It can be seen that if the unadjusted stage discharge plot is concave downwards then a positive trial value of “a” is needed to make it a straight line. And conversely, a negative trial value is needed to make the line straight if the curve is concave upwards. A few values of “a” can be tried to attain a straight line fit for the plotted points of adjusted stage discharge data. The procedure is illustrated in Fig.3.7. This procedure was slow but quite effective when done earlier manually. However, making use of general spreadsheet software (having graphical provision) for such trial and error procedure can be very convenient and faster now.

Figure 3.7 Determination of datum correction (a) by trial and error

Arithmetic procedure:

This procedure is based on expressing the datum correction “a” in terms of observed water levels. This is possible by way elimination of coefficients b and c from the power type equation between gauge and discharge using simple mathematical manipulation. From the median curve fitting the stage discharge observations, two points are selected in the lower and upper range (Q1 and Q3) whereas the third point Q2 is computed from Q2

2 =Q1.Q3, such that:

Q1

Q2 (7)

Q2 Q3

If the corresponding gauge heights for these discharges read from the plot are h 1, h2 and h3 then using the power type, we obtain:

c (h1 a)

c (h2 a) (8)

c (h2 a) c (h3 a)

Which yields:

a

h2 h h32 1

(9)h1 h3 2h2

From this equation an estimated value of “a” can be obtained directly. This procedure is known as Johnson method which is described in the WMO Operational Hydrology manual on stream gauging (Report No. 13, 1980).

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Optimisation procedure:

This procedure is suitable for automatic data processing using computer and “a” is obtained by optimisation. The first trial value of the datum correction “a” is either input by the user based on the field survey or from the computerised Johnson method described above. Next, this first estimate of “a” is varied within 2 m so as to obtain a minimum mean square error in the fit. This is a purely mathematical procedure and probably gives the best results on the basis of observed stage discharge data but it is important to make sure that the result is confirmed where possible by physical explanation of the control at the gauging location. The procedure is repeated for each segment of the rating curve.

3.2.3 Number and ranges of rating curve segments: After the datum correction “a” has been established, the next step is to determine if the rating curve is composed of one or more segments. This is normally selected by the user rather than done automatically by computer. It is done by plotting the adjusted stage, (h-a) or simply “h” where there are multiple segments, and discharge data on the double log scale. This scatter plot can be drawn manually or by computer and the plot is inspected for breaking points. Since for (h-a), on double log scale the plotted points will align as straight lines, breaks are readily identified. The value of “h” at the breaking points give the first estimate of the water levels at which changes in the nature of the rating curve are expected. The number and water level ranges for which different rating curves are to be established is thus noted. For example, Fig. 3.6 shows that two separate rating curves are required for the two ranges of water level – one up to level “h1” and second from “h1” onwards. The rating equation for each of these segments is then established and the breaking points between segments are checked by computer analysis (See below).

3.2.4 Determination of rating curve coefficients:

A least square method is normally employed for estimating the rating curve coefficients. For example, for the power type equation, taking and as the estimates of the constants of the straight line fitted to the scatter of points in double log scale, the estimated value of the logarithm of the discharge can be obtained as:

ˆ X (10)Y

The least square method minimises the sum of square of deviations between the logarithms of measured discharges and the estimated discharges obtained from the fitted rating curve. Considering the sum of square the error as E, we can write:

N N

ˆ)

2

(Yi X i )2

(11)E (Yi Yi

i1 i1

Here i denotes the individual observed point and N is the total number of observed stage discharge data.

Since this error is to be minimum, the slope of partial derivatives of this error with respect to the constants must be zero. In other words:

N

E

{(Yi X i ) 2 }

(12)i 1

0

andN

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E

{(Yi X i ) 2}

(13)i1

0

This results in two algebraic equations of the form:

N N

Yi N X i 0 (14)

i1 i1

andN N N

( X

i Yi ) X i ( X i ) 2 0 (15)i1 i 1 i1

All the quantities in the above equations are known except and . Solving the two equations yield:

N N N

N ( X i Yi ) ( X i ) (Yi )i1 i1 i 1 (16)

N N

N ( X i ) 2 ( X i ) 2

andi1 i1

N N

Yi

X i (17)i 1 i 1

NThe value of coefficients c and b of power type equation can then be finally obtained as:

b = and c = 10 (18)

Reassessment of breaking points

The first estimate of the water level ranges for different segments of the rating curve is obtained by visual examination of the cross-section changes and the double log plot. However, exact limits of water levels for various segments are obtained by computer from the intersection of the fitted curves in adjoining the segments.

Considering the rating equations for two successive water level ranges be given as Q = f i-1(h) and Q = fi (h) respectively and let the upper boundary used for the estimation of f i-1 be denoted by hui- 1 and the lower boundary used for the estimation of f i by hli . To force the intersection between fi-1 and fi to fall within certain limits it is necessary to choose: hu i-1 > hli . That is, the intersection of the rating curves of the adjoining segments should be found numerically within this overlap. This is illustrated in Fig. 3.8 and Table 3.1. If the intersection falls outside the selected overlap, then the intersection is estimated for the least difference between Q = fi-1(h) and Q = fi (h). Preferably the boundary width between hu i-1 and hli is widened and the curves refitted.

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It is essential that a graphical plot of the fit of the derived equations to the data is inspected before accepting them.

Figure 3.8 Fitted rating curve using 2 segments

3.3 Compound channel rating curve

If the flood plains carry flow over the full cross section, the discharge (for very wide channels) consists of two parts:

Qriver (h Br ) (K mr h2 / 3 S 1 / 2 ) (24)

and

Q (hh ) ( BBr

) [Kmf

(h h ) 2 / 3 S 1/ 2 ] (25)floodplain 1 1

assuming that the floodplain has the same slope as the river bed, the total discharge becomes:

Qtotal h Br (K mr h2 / 3 S1/ 2 ) (h h1 ) (B Br ) [K mf (h h1 )2 / 3 S1 / 2 ] (26)

This is illustrated in Fig. 3.9. The rating curve changes significantly as soon as the flood plain at level h-h 1

is flooded, especially if the ratio of the storage width B to the width of the river bed B r is large. The rating curve for this situation of a compound channel is determined by considering the flow through the floodplain portion separately. This is done to avoid large values of the exponent b and extremely low values for the parameter c in the power equation for the rating curve in the main channel portion.

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Figure 3.9 Example of rating curve for compound cross-section

The last water level range considered for fitting rating curve is treated for the flood plain water levels. First, the river discharge Qr will be computed for this last interval by using the parameters computed for the one but last interval. Then a temporary flood plain discharge Qf

is computed by subtracting Qr from the observed discharge (Oobs) for the last water level interval, i.e.

Qf = Qobs - Qr. (27)

This discharge Qf will then be separately used to fit a rating curve for the water levels corresponding to the flood plains. The total discharge in the flood plain is then calculated as the sum of discharges given by the rating curve of the one but last segment applied for water levels in the flood plains and the rating curve established separately for the flood plains.

The rating curve presented in Figure 3.9 for Jhelum river at Rasul reads:

For h < 215.67 m + MSL: Q = 315.2(h-212.38)1.706

For h > 215.67 m + MSL: Q = 315.2(h-212.38)1.706 + 3337.4(h-215.67)1.145

Hence the last part in the second equation is the contribution of the flood plain to the total river flow.

3.4 Rating curve with backwater correction

When the control at the gauging station is influenced by other controls downstream, then the unique relationship between stage and discharge at the gauging station is not maintained. Backwater is an important consideration in streamflow site selection and sites having backwater effects should be avoided if possible. However, many existing stations in India are subject to variable backwater effects and require special methods of discharge determination. Typical examples of backwater effects on gauging stations and the rating curve are as follows:

· by regulation of water course downstream. · level of water in the main river at the confluence downstream · level of water in a reservoir downstream

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· variable tidal effect occurring downstream of a gauging station · downstream constriction with a variable capacity at any level due to weed growth etc. · rivers with return of overbank flow

Backwater from variable controls downstream from the station influences the water surface slope at the station for given stage. When the backwater from the downstream control results in lowering the water surface slope, a smaller discharge passes through the gauging station for the same stage. On the other hand, if the surface slope increases, as in the case of sudden drawdown through a regulator downstream, a greater discharge passes for the same stage. The presence of backwater does not allow the use of a simple unique rating curve. Variable backwater causes a variable energy slope for the same stage.

Discharge is thus a function of both stage and slope and the relation is termed as slope-stage-discharge relation.

The stage is measured continuously at the main gauging station. The slope is estimated by continuously observing the stage at an additional gauge station, called the auxiliary gauge station. The auxiliary gauge station is established some distance downstream of the main station. Time synchronisation in the observations at the gauges is necessary for precise estimation of slope. The distance between these gauges is kept such that it gives an adequate representation of the slope at the main station and at the same time the uncertainty in the estimation is also smaller. When both main and auxiliary gauges are set to the same datum, the difference between the two stages directly gives the fall in the water surface. Thus, the fall between the main and the auxiliary stations is taken as the measure of surface slope. This fall is taken as the third parameter in the relationship and the rating is therefore also called stage-fall-discharge relation.

Discharge using Manning’s equation can be expressed as:

Q K m R 2 / 3 S 1/ 2 A (28)

Energy slope represented by the surface water slope can be represented by the fall in level between the main gauge and the auxiliary gauge. The slope-stage-discharge or stage-fall-discharge method is represented by:

Qm

Sm

p F p

m

(29)Q S F

r r r

where Qm is the measured (backwater affected) dischargeQr is a reference dischargeFm is the measured fallFr is a reference fallp is a power parameter between 0.4 and 0.6

From the Manning’s equation given above, the exponent “p” would be expected to be ½. The fall (F) or the slope (S = F/L) is obtained by the observing the water levels at the main and auxiliary gauge. Since, there is no assurance that the water surface profile between these gauges is a straight line, the effective value of the exponent can be different from ½ and must be determined empirically.

An initial plot of the stage discharge relationship (either manually or by computer) with values of fall against each observation, will show whether the relationship is affected by variable slope, and whether this occurs at all stages or is affected only when the fall reduces below a particular value. In the absence of any channel control, the discharge would be affected by variable fall at all times and the correction is applied by the constant fall method. When the

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discharge is affected only when the fall reduces below a given value the normal (or limiting) fall method is used.

3.4.1 Constant fall method: The constant fall method is applied when the stage-discharge relation is affected by variable fall at all times and for all stages. The fall applicable to each discharge measurement is determined and plotted with each stage discharge observation on the plot. If the observed falls do not vary greatly, an average value (reference fall or constant fall) Fr is selected.

Manual computation

For manual computation an iterative graphical procedure is used. Two curves are used (Figs. 3.10 and 3.11):

· All measurements with fall of about Fr are fitted with a curve as a simple stage discharge relation (Fig.3.10). This gives a relation between the measured stage h and the reference discharge Qr.

· A second relation, called the adjustment curve, either between the measured fall, Fm, or the ratio of the measured fall for each gauging and the constant fall (Fm / Fr), and the discharge ratio (Qm / Qr) (Fig. 3.11)

· This second curve is then used to refine the stage discharge relationship by calculating Qr from known values of Qm and Fm/Fr and then replotting h against Qr .

· A few iterations may be done to refine the two curves.

Figure 3.10 Qr=f(h) in constant fall rating Figure 3.11 Qm/Qr = f(Fm/Fr)

The discharge at any time can be then be computed as follows:

· For the observed fall (Fm) calculate the ratio (Fm/Fr) · read the ratio (Qm / Qr) from the adjustment curve against the calculated value of (Fm/Fr) · multiply the ratio (Qm / Qr) with the reference discharge Qr obtained for the measured

stage h from the curve between stage h and reference discharge Qr.

Computer computation

For computer computation, this procedure is simplified by mathematical fitting and optimisation. First, as before, a reference (or constant) fall (Fr) is selected from amongst the most frequently observed falls.

A rating curve, between stage h and the reference discharge (Qr), is then fitted directly by estimating:

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F p

Qr

r

(30)Q

m F

m

where p is optimised between 0.4 and 0.6 based on minimisation of standard errors.

The discharge at any time, corresponding to the measured stage h and fall Fm , is then calculated by first obtaining Qr from the above relationship and then calculating discharge as:

F p

Q

m

(31)Q

r F

r A special case of constant fall method is the unit fall method in which the reference fall is assumed to be equal to unity. This simplifies the calculations and thus is suitable for manual method.

3.4.2 Normal Fall Method:

The normal or limiting fall method is used when there are times when backwater is not present at the station. Examples are when a downstream reservoir is drawn down or where there is low water in a downstream tributary or main river.

Manual procedureThe manual procedure is as follows:

· Plot stage against discharge, noting the fall at each point. The points at which backwater has no effect are identified first. These points normally group at the extreme right of the plotted points. This is equivalent to the simple rating curve for which a Qr -h relationship may be fitted (where Qr in this case is the reference or normal discharge) (Fig. 3.12).

Figure 3.12 Qr-h relationship for Normal Fall Method

· Plot the measured fall against stage for each gauging and draw a line through those observations representing the minimum fall, but which are backwater free. This represents the normal or limiting fall Fr (Fig. 3.13). It is observed from Figure 3.13 that the line separates the backwater affected and backwater free falls.

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Figure 3.13 Fr-h relationship

· For each discharge measurement derive Qr using the discharge rating and Fr , the normal fall from the fall rating.

· For each discharge measurement compute Qm/Qr and Fm/Fr and draw an average curve (Fig. 3.14).

Figure 3.14 Qm/Qr - Fm/Fr relationship

· As for the constant fall method, the curves may be successively adjusted by holding two graphs constant and re-computing and plotting the third. No more than two or three iterations are usually required.

The discharge at any time can be then be computed as follows:·· From the plot between stage and the normal (or limiting) fall (Fr), find the value of Fr

for the observed stage h · For the observed fall (Fm), calculate the ratio (Fm/Fr) · Read the ratio (Qm / Qr) from the adjustment curve against the calculated value of· (Fm/Fr)· Obtain discharge by multiplying the ratio (Qm / Qr) with the reference discharge Qr

obtained for the measured stage h from the curve between stage h and reference discharge Qr.

Computer procedureThe computer procedure considerably simplifies computation and is as follows:

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· Compute the backwater-free rating curve using selected current meter gaugings (the Qr -h relationship).

· Using values of Qr derived from (1) and Fr derived from:

Q 1/ p

Fr r

Fm Q (32)m

a parabola is fitted to the reference fall in relation to stage (h) as:

Fr a b h c h2 (33)

The parameter p is optimised between 0.4 and 0.6.

The discharge at any time, corresponding to the measured stage h and fall Fm , is then calculated by:

· obtaining Fr for the observed h from the parabolic relation between h and Fr · obtaining Qr from the backwater free relationship established between h and Qr · then calculating discharge corresponding to measured stage h as:

F p(34)

Q m

Qr F r

3.5 Rating curve with unsteady flow correction

Gauging stations not subjected to variable slope because of backwater may still be affected by variations in the water surface slope due to high rates of change in stage . This occurs when the flow is highly unsteady and the water level is changing rapidly. At stream gauging stations located in a reach where the slope is very flat, the stage-discharge relation is frequently affected by the superimposed slope of the rising and falling limb of the passing flood wave. During the rising stage, the velocity and discharge are normally greater than they would be for the same stage under steady flow conditions. Similarly, during the falling stage the discharge is normally less for any given gauge height than it is when the stage is constant. This is due to the fact that the approaching velocities in the advancing portion of the wave are larger than in a steady uniform flow at the corresponding stages. In the receding phase of the flood wave the converse situation occurs with reduced approach velocities giving lower discharges than in equivalent steady state case.Thus, the stage discharge relationship for an unsteady flow will not be a single-valued relationship as in steady flow but it will be a looped curve as shown in the example below. The looping in the stage discharge curve is also called hysteresis in the stage-discharge relationship. From the curve it can be easily seen that at the same stage, more discharge passes through the river during rising stages than in the falling ones.

3.5.1 Application For practical purposes the discharge rating must be developed by the application of adjustment factors that relate unsteady flow to steady flow. Omitting the acceleration terms in the dynamic flow equation the relation between the unsteady and steady discharge is expressed in the form:

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Qr is the steady state discharge and is obtained by establishing a rating curve as a median curve through the uncorrected stage discharge observations or using those observations for which the rate of change of stage had been negligible. Care is taken to see that there are sufficient number of gaugings on rising and falling limbs if the unsteady state observations are considered while establishing the steady state rating curve.

Rearranging the above equation gives:

1

(Qm / Qr ) 2 1(36)

c S0 dh / dt

The quantity (dh/dt) is obtained by knowing the stage at the beginning and end of the stage discharge observation or from the continuous stage record. Thus the value of factor (1/cS0) can be obtained by the above relationship for every observed stage. The factor (1/cS0) varies with stage and a parabola is fitted to its estimated values and stage as:

1 a b h ch2 (37) c S0

A minimum stage hmin is specified beyond which the above relation is valid. A maximum value of factor (1/cS0) is also specified so that unacceptably high value can be avoided from taking part in the fitting of the parabola.

Thus unsteady flow corrections can be estimated by the following steps:

· Measured discharge is plotted against stage and beside each plotted point is noted the value of dh/dt for the measurement (+ or - )

· A trial Qs rating curve representing the steady flow condition where dh/dt equals zero is fitted to the plotted discharge measurements.

· A steady state discharge Qr is then estimated from the curve for each discharge measurement and Qm , Qr and dh/dt are together used in the Equation 35 to compute corresponding values of the adjustment factor 1 / cS0

· Computed values of 1 / cS0 are then plotted against stage and a smooth (parabolic) curve is fitted to the plotted points

For obtaining unsteady flow discharge from the steady rating curve the following steps are followed:

· obtain the steady state flow Qr for the measured stage h · obtain factor (1/cS0) by substituting stage h in the parabolic relation between the two · obtain (dh/dt) from stage discharge observation timings or continuous stage records

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· substitute the above three quantities in the Equation 35 to obtain the true unsteady flow discharge

The computer method of analysis using eSWIS mirrors the manual method described above.

It is apparent from the above discussions and relationships that the effects of unsteady flow on the rating are mainly observed in larger rivers with very flat bed slopes (with channel control extending far downstream) together with significant rate change in the flow rates. For rivers with steep slopes, the looping effect is rarely of practical consequence. Although there will be variations depending on the catchment climate and topography, the potential effects of rapidly changing discharge on the rating should be investigated in rivers with a slope of 1 metre/ km or less. Possibility of a significant unsteady effect (say more than 8–10%) can be judged easily by making a rough estimate of ratio of unsteady flow value with that of the steady flow value.

Example

The steps to correct the rating curve for unsteady flow effects is elaborated for station MAHEMDABAD on WAZAK river. The scatter plot of stage discharge data for 1997 is shown in Figure 3.15a. From the curve is apparent that some shift has taken place, see also Figure 3.15b. The shift took place around 24 August.

Figure 3.15a Stage-discharge data of station Mahemdabad on Wazak river, 1997

Figure 3.15 b Detail of stage discharge data for low flows, clearly showing the shift

In the analysis therefore only the data prior that date were considered. The scatter plots clearly show a looping for the higher flows. To a large extent, this looping can be attributed to unsteady flow phenomenon. The Jones method is therefore applied. The first fit to the scatter plot, before any correction, is shown in Figure 3.15c.

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Figure 3.15c First fit to stage-discharge data, prior to adjustment

Based on this relation and the observed discharges and water level changes values for 1/cS0 were obtained. These data are depicted in Figure 3.15d. The scatter in the latter plot is seen to be considerable. An approximate relationship between 1/cS0 and h is shown in the graph.

Figure 3.15 d Scatter plot of 1/cS0 as function of stage, with approximate relation.

With the values for 1/cS0 taken from graph the unsteady flow correction factor is computed and steady state discharges are computed. These are shown in Figure 3.15e, together with the uncorrected discharges. It is observed that part of the earlier variation is indeed removed. A slightly adjusted curve is subsequently fit to the stage and corrected flows.

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Figure 3.15e Rating curve after first adjustment trial for unsteady flow.

Note that the looping has been eliminated, though still some scatter is apparent.

3.6 Rating relationships for stations affected by shifting control

For site selection it is a desirable property of a gauging station to have a control which is stable, but no such conditions may exist in the reach for which flow measurement is required, and the selected gauging station may be subject to shifting control. Shifts in the control occur especially in alluvial sand-bed streams. However, even in stable stream channels shift will occur, particularly at low flow because of weed growth in the channel, or as a result of debris caught in the control section.

In alluvial sand-bed streams, the stage-discharge relation usually changes with time, either gradually or abruptly, due to scour and silting in the channel and because of moving sand dunes and bars. The extent and frequency with which changes occur depends on typical bed material size at the control and velocities typically occurring at the station. In the case of controls consisting of cobble or boulder sized alluvium, the control and hence the rating may change only during the highest floods. In contrast, in sand bed rivers the control may shift gradually even in low to moderate flows. Intermediate conditions are common where the bed and rating change frequently during the monsoon but remain stable for long periods of seasonal recession.

For sand bed channels the stage-discharge relationship varies not only because of the changing cross section due to scouring or deposition but also because of changing roughness with different bed forms. Bed configurations occurring with increasing discharge are ripples, dunes, plane bed, standing waves, antidunes and chute and pool (Fig. 3.16). The resistance of flow is greatest in the dunes range. When the dunes are washed out and the sand is rearranged to form a plane bed, there is a marked decrease in bed roughness and resistance to the flow causing an abrupt discontinuity in the stage-discharge relation. Fine sediment present in water also influences the configuration of sand-bed and thus the resistance to flow. Changes in water temperature may also alter bed form, and hence roughness and resistance to flow in sand bed channels. The viscosity of water will increase with lower temperature and thereby mobility of the sand will increase.

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Figure 3.16 Bed and surface configurations configurations in sand-bed channelsFor alluvial streams where neither bottom nor sides are stable, a plot of stage against discharge will very often scatter widely and thus be indeterminate (Fig. 3.17) However, the hydraulic relationship becomes apparent by changing the variables. The effect of variation in bottom elevation and width is eliminated by replacing stage by mean depth (hydraulic radius) and discharge by mean velocity respectively. Plots of mean depth against mean velocity are useful in the analysis of stage-discharge relations, provided the measurements are referred to the same cross-section.

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Figure 3.17 Plot of discharge against stage for a sand-bed channel with indeterminate stage-discharge relation

These plots will identify the bed-form regime associated with each individual discharge measurement. (Fig. 3.18). Thus measurements associated with respective flow regimes, upper or lower, are considered for establishing separate rating curves. Information about bed-forms may be obtained by visual observation of water surfaces and noted for reference for developing discharge ratings.

Figure 3.18 Relation of mean velocity to hydraulic radius of channel in Figure 3.17

There are four possible approaches depending on the severity of scour and on the frequency of gauging:

· Fitting a simple rating curve between scour events · Varying the zero or shift parameter · Application of Stout’s shift method · Flow determined from daily gauging

3.6.1 Fitting a simple rating curve between scour events

Where the plotted rating curve shows long periods of stability punctuated by infrequent flood events which cause channel adjustments, the standard procedure of fitting a simple logarithmic equation of the form Q = c1(h + a1)b1 should be applied to each stable period. This is possible only if there are sufficient gaugings in each period throughout the range of stage.

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To identify the date of change from one rating to the next, the gaugings are plotted with their date or number sequence. The interval in which the change occurred is where the position of sequential plotted gaugings moves from one line to the next. The processor should then inspect the gauge observation record for a flood event during the period and apply the next rating from that date.

Notes from the Field Record book or station log must be available whilst inspection and stage discharge processing is carried out. This provides further information on the nature and timing of the event and confirms that the change was due to shifting control rather than to damage or adjustment to the staff gauge.

3.6.2 Varying the zero or shift parameter

Where the plotted rating curve shows periods of stability but the number of gaugings is insufficient to define the new relationship over all or part of the range, then the parameter ‘a’ in the standard relationship Q = c1(h + a1 )b1 may be adjusted. The parameter ‘a1’ represents the datum correction between the zero of the gauges and the stage at zero flow. Scour or deposition causes a shift in this zero flow stage and hence a change in the value ‘a1’..

The shift adjustment required can be determined by taking the average difference (a) between the rated stage (hr) for measured flow (Q m) and measured stage (hm) using the previous rating. i.e.

n

a (hr hm ) / n (39)i 1

The new rating over the specified range then becomes:

Q = c1(h + a1 + a)b1 (40)

The judgement of the processor is required as to whether to apply the value of a over the full range of stage (given that the % effect will diminish with increasing stage) or only in the lower range for which current meter gauging is available. If there is evidence that the rating changes from unstable section control at low flows to more stable channel control at higher flows, then the existing upper rating should continue to apply.

New stage ranges and limits between rating segments will require to be determined. The method assumes that the channel hydraulic properties remain unchanged except for the level of the datum. Significant variation from this assumption will result in wide variation in (hr - hm) between included gaugings. If this is the case then Stout’s shift method should be used as an alternative.

3.6.3. Stout’s shift method (Not Recommended to be Applied )

For controls which are shifting continually or progressively, Stout’s method is used. In such instances the plotted current meter measurements show a very wide spread from the mean line and show an insufficient number of sequential gaugings with the same

trend to split the simple rating into several periods. The procedure is as follows:

· Fit a mean relationship to (all) the points for the period in question.

· Determine hr (the rated stage) from measured Qm by reversing the power type rating curve or from the plot:

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hr = (Qm / c)1/b - a (41)

· Individual rating shifts (h), as shown in Fig. 3.19, are then:

h = hr - hm (42)

· These h stage shifts are then plotted chronologically and interpolated between successive gaugings (Fig. 3.19) for any instant of time t as ht.

· These shifts, ht ,are used as a correction to observed gauge height readings and the original rating applied to the corrected stages, i.e.

Qt = c1(ht +ht + a1)b1 (43)

Figure 3.19 Stout’s method for correcting stage readings when control is shifting

The Stout method will only result in worthwhile results where:

(a) Gauging is frequent, perhaps daily in moderate to high flows and even more frequently during floods.

(b) The mean rating is revised periodically - at least yearly.

The basic assumption in applying the Stout’s method is that the deviations of the measured discharges from the established stage-discharge curve are due only to a change or shift in the station control, and that the corrections applied to the observed gauge heights vary gradually and systematically between the days on which the check measurements are taken. However, the deviation of a discharge measurement from an established rating curve may be due to:

(a) gradual and systematic shifts in the control, (b) abrupt random shifts in the control, and (c) error of observation and systematic errors of both instrumental and a personnel nature.

Stout’s method is strictly appropriate for making adjustments for the first type of error only. If the check measurements are taken frequently enough, fair adjustments may be made for the second type of error also. The drawback of the Stout’s method is that all the errors in current meter observation are mixed with the errors due to shift in control and are thus incorporated in the final estimates of discharge. The Stout method must therefore never be used where the rating is stable, or at least sufficiently stable to develop satisfactory rating curves between major shift events; use of the Stout method in such circumstances loses the advantage of a

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fitted line where the standard error of the line Smr is 20% of the standard error of individual gaugings (Se). Also, when significant observational errors are expected to be present it is strongly recommended not to apply this method for establishing the rating curve.

3.6.4 Flow determined from daily gauging

Stations occur where there is a very broad scatter in the rating relationship, which appears neither to result from backwater or scour and where the calculated shift is erratic. A cause may be the irregular opening and closure of a valve or gate in a downstream structure. Unless there is a desperate need for such data, it is recommended that the station be moved or closed. If the station is continued, a daily measured discharge may be adopted as the daily mean flow. This practice however eliminates the daily variations and peaks in the record.

It is emphasised that even using the recommended methods, the accuracy of flow determination at stations which are affected by shifting control will be much less than at stations not so affected. Additionally, the cost of obtaining worthwhile data will be considerably higher. At many such stations uncertainties of 20 to 30% are the best that can be achieved and consideration should be given to whether such accuracy meets the functional needs of the station.

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Chapter 21: Validate Rating Curve

1. GeneralValidation of a rating curve is required both after the relationship has first been fitted and subsequently when new gaugings have been carried out, to assess whether these indicate a change in rating. Validation is also used to assess the reliability of historical ratings.

Current meter gauging is carried out with variable frequency depending on previous experience of the stability of the control and of the rating curve. As a minimum it is recommended that six gaugings per year are carried out even with a station with a stable section and previously gauged over the full range of level. At unstable sections many more gaugings are required. The deviation of such check gaugings from the previously established relationship is computed and any bias assessed to determine whether they belong to the same population as the previous stage-discharge relationship.

Graphical and numerical tests are designed to show whether gaugings fit the current relationship equally and without bias over the full range of flow and over the full time period to which it has been applied. If they do not, then a new rating should be developed, but taking into account the deficiencies noted in validation.

2. Graphical validation testsGeneral

Graphical tests are often the most effective method of validation. These include the following:

Stage/discharge plot with the new gaugings Period/flow deviation scattergram Stage/flow deviation scattergram Cumulative deviation plot of gaugings. Stage/discharge plots with gaugings distinguished by season

2.1. Stage/discharge plot with new gaugings

The simplest means of validating the rating curve with respect to subsequent gaugings is to plot the existing rating curve with the new check gaugings. This is shown in the example for Station Pargaon. A rating curve is established for the period 30/6 – 3/8/97, see Figure 2.1. New data are available for the period 4-23/8/97. The new data with the existing rating curve are shown in Figure 2.2. From this plot it is observed that the new gaugings do not match with the existing curve. In Figure 2.3 the new gaugings are shown with the rating curve and its the 95% confidence limits (derived as t-times the standard error Se). From this plot it can be judged if most check gaugings lie inside the confidence limits

and thus whether they can be judged acceptable with respect to deviation. It is expected that 19 out of 20 observations will lie inside the limits if the standard error is considered at 5% significance level. However, except insofar as one can see whether all the new points lie

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above or below the previous regression line, the graph does not specifically address the problem of bias. For example, if some 25 new gaugings may all lie scattered within 95% confidence limits, it does not show any significant change in behaviour. However, if these points are plotted and sequence of each observation is also considered and if upon that a certain pattern of deviation (with respect to time) is perceivable and significant then such situation may warrant new ratings for different periods of distinct behaviour. For the Pargaon-

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case the plot confirms earlier observations that the new gaugings significantly differ from the existing rating.

2.2. Period/flow deviation scattergram A period/flow deviation scattergram (Figure 2.4) is a means of illustrating the negative and positive deviation of each current meter gauging from the present rating curve and whether there has been a gradual or sudden shift in the direction of deviations within the period to which the rating has been applied. It also shows whether recent additional gaugings show deviation from previous experience. In the example shown in Fig. 2.4, percentage deviations are very high; there are far more gaugings with positive than with negative deviations. The rating is therefore biased and a revision of the rating is strongly recommended.

Figure 2.4 Period-flow deviation scatterdiagram for Pargaon rating curve data and new gaugings

2.3. Stage/flow deviation diagram

A similar scattergram plot shows the percentage deviation with stage (Figure 2.5) and is a means of illustrating whether over certain ranges of stage the relationship is biased. Most recent gaugings can also be placed within this context.

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Figure 2.5 Stage-flow deviation scatterdiagram for Pargaon rating curve data and new gaugings

In the example shown in Fig. 2.5, there is some difference in deviation at different stages; particularly at the lower stages the differences are substantial. This plot also confirms the necessity for revision of the rating curve.

2.4. Cumulative deviation plot of gaugings

A plot of the cumulative deviation of gaugings from the rating curve give another indication of bias and whether that bias changes with time. Fig. 2.6 shows such a plot for the example of station Pargaon. From the upward trend of the line for the new gaugings it is concluded that the new gaugings produce consistently higher flow values for the same stages than before.

2.5. Stage discharge plots with gaugings distinguished by season.

It is sometimes helpful to separate gaugings between seasons to demonstrate the effect of varying weed growth or other seasonal factors on the stage discharge relationship. The effects of weed growth may be expected to be at a maximum in low flows before the onset of the monsoon; monsoon high flows wash out the weed which increases progressively from the end of the rains. The discharge for given level may thus differ from one month to another. This shows up more clearly in rivers where winter low flows are little affected by weed growth than summer low flows and thus show much smaller spread. Where an auxiliary gauge is available, a backwater rating curve (normal fall method) may be used. Otherwise a simple rating curve may be used in weed absent periods and Stout’s shift method during periods of variability.

3. Numerical validation tests

3.1. Test for absence from bias in signs

A well-balanced rating curve must ensure that the number of positive and negative deviations of the observed values from the rating curve is evenly distributed. That is, the difference in number between the two should not be more than can be explained by chance fluctuations. The test is employed to see if the curve has been established in a balanced manner so that the two sets of discharge values, observed and estimated (from the curve), may be reasonably supposed to represent the same population.

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This test is performed by counting observed points falling on either side of the curve. If Q i is the observed value and Qc the estimated value, then the expression, Q i - Qc , should have an equal chance of being positive or negative. In other words, the probability of Q i - Qc being positive or negative is ½. Hence, assuming the successive signs to be independent of each other, the sequence of the differences may be considered as distributed according to the binomial law (p+q) N, where N is the number of observations, and p and q, are the probabilities of occurrence of positive and negative values are ½ each. The expected number of positive signs is positive signs is Np. Its standard deviation is

(Npq). The “t” statistic is then found by dividing the difference between the actual number of positive signs N1 and expected number of positive signs Np by its standard deviation(Npq):

The resulting value is compared with the critical value of “t” statistic for 5% significance level for the degrees of freedom equal to the total number of stage discharge data. If the value of the critical “t” statistic is more than that obtained for the observed data then it can be considered that the data does not show any bias with respect to sign of the deviations between observed and computed discharges.

3.2. Test for absence from bias in values

This test is designed to see if a particular stage discharge curve, on average, yields significant under estimates or over estimates as compared to the actual observations on which it is based. (Compare the graphical test using the period/flow deviation and stage /flow deviation scattergrams) The percentage differences are first worked out as:

P = 100 (Qi - Qc ) / Qc (4)

If there are N observations and P1, P2, P3, …, PN are the percentage differences and Pav isthe average of these differences, the standard error of Pav is given by:

The average percent Pav is tested against its standard error to see if it is significantly different from zero. The “t” statistic for in this case is computed as:

t = (Pav – 0) / Se (6)

If the critical value of “t” statistic for 5% significance level and N degrees of freedom is greater than the value computed above then it may be considered that there is no statistical bias in the observed values with respect to their magnitudes as compared with that obtained by the rating curve.

The percentage differences have been taken as they are comparatively independent of the discharge volume and are approximately normally distributed about zero mean value for an unbiased curve.

3.3. Goodness of fit test

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Due to changes in the flow regime, it is possible that long runs of positive and/or negative deviations are obtained at various stages. This may also be due to inappropriate fitting of the rating curve. This test is carried out for long runs of positive and negative deviations of the observed values from the stage-discharge curve. The test is designed to ensure a balanced fit in reference to the deviations over different stages. (Compare the graphical tests using stage/flow deviation scattergram and cumulative deviation plot of gaugings)

The test is based on the number of changes of sign in the series of deviations (observed value minus expected or computed value). First of all, the signs of deviations, positive or negative, in discharge measurements in ascending order of stage are recorded. Then starting from the second sign of the series, “0” or “1” is placed under sign if the sign agrees or does not agree respectively with the sign immediately preceding it. For example,

+ - + + + + - - - - + + + + - 1 1 0 0 0 1 0 0 0 1 0 0 0 1

If there are N numbers in the original series, then there will be (N – 1) numbers in the derived series 11000100010001

If the observed values are regarded as arising from random fluctuations about the values estimated from the curve, the probability of a change in sign could be taken to be ½. However, this assumes that the estimated value is the median rather than the mean. If N is fairly large, a practical criterion may be obtained by assuming successive signs to be independent (i.e. by assuming that they arise only from random fluctuations), so that the number of “1”s (or “0”s) in the derived sequence of (N – 1) members may be judged as a binomial variable with parameters (N – 1) and ½.

From the above derived series, the actual number of changes of sign is noted. The expected number of changes of sign is computed by multiplying total possible numbers (i.e. N –1 ) with the probability of change of sign (i.e. ½). The statistical significance of the departure of the actual number of change of signs from the expected number is known by finding the “t” statistic as follows:

where N’ denotes the actual number changes of sign.

If the critical value of “t” statistic, for (N – 1) degrees of freedom, is more than that computed above then it can be considered to be having adequate goodness of fit. Otherwise, the results will indicate that there is significant bias in the fitted curve with respect to long runs of positive or negative deviations.

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Chapter 22: Extrapolate Rating Curve

1. General

Extrapolation of rating curves is required because the range of level over which gauging has been carried out does not cover the full range of observed levels . The rating curve may fall short at both the lower and the upper end. Extreme flows are often the most important for design and planning and it is important that the best possible estimates are made.

Calibration at very high instantaneous flows is particularly difficult as they occur infrequently and are of short duration. They may occur at night. Peak flow gauging requires the gauging team to be on site when the flood arrives - which may not be possible. It also requires that facilities are available for flood gauging in safety. In practice, the gauging site may be inaccessible, the gauging facilities no longer serviceable and the river may have spread from a confined channel to an inaccessible flood plain.

Extrapolation is not simply a question of extending the rating from existing gaugings to extreme levels (although in some cases this may be acceptable); a different control may apply, the channel geometry may change, flow may occur over the floodplain and form and vegetation roughness coefficients may change.

Applicable methods of extrapolation depend on the physical condition of the channel, whether inbank or overbank and whether it has fixed or shifting controls. Consideration must also be given to the phenomenon of the kinematic effect of open channel flow when there may be reduction in the mean velocity in the main channel during inundation of the flood plain. Methods given below are suitable for rivers with defined banks and fixed controls, as well as for a channel with spill.

Extrapolation of stage discharge relationships will be carried out at the State Data Processing Centre.

2. High flow extrapolationThe following methods are considered below:

double log plot method stage-area / stage-velocity method the Manning’s equation method the conveyance slope method

2.1. The double log plot method

Where the hydraulic characteristics of the channel do not change much beyond the measured range, then simple extrapolation of the logarithmic stage discharge relationship may be applied. Graphically, the relationship in this case can simply be extended beyond the measured range by projecting the last segment of the straight line relationship in log-log domain. Such an extrapolation is illustrated by the dashed straight line in Fig. 2.2 for the cross-sectional profile shown in Figure 2.1.

Cross Section Khamgaon

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Figure 2.1 Cross-section of river at Khamgaon used in examples in this module

2.2. Stage-area / Stage-velocity method

Where extrapolation is needed either well beyond the measured range, or there are known changes in the hydraulic characteristics of the control section, then a combination of stage-area and stage-velocity curves may be used. Stage-area and stage-mean velocity curves are extended separately. For stable channels the stage-area relationship is fixed and is determined by survey up to the highest required stage. The stage-velocity curve is based on current meter gaugings within the measured range and, since the rate of increase in velocity at higher stages diminishes rapidly this curve can be extended without much error for in-bank flows. Discharge for a given (extended) stage is then obtained by the product of area and mean velocity read using extrapolated stage-area and stage-mean velocity curves (Fig. 2.3). This method may be used for extrapolation at both the upper and lower end of the rating.

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Figure 2.3 Extrapolation based on stage-area/stage-velocity technique

The mean velocity curve can also be extrapolated by the use of a logarithmic plot of mean velocity against hydraulic radius. The hydraulic radius can be found for all stages from the

cross section by survey. The logarithmic plot of mean velocity and hydraulic radius generally shows a linear relationship and thus can be extended linearly beyond the extent of measurements. Mean velocity in the extrapolated range can be obtained from this curve. Extrapolated discharge as before is obtained as the product of mean velocity thus estimated and the corresponding area from the stage-area curve.

2.3. The Manning’s equation method

A slight variation of the stage-area-velocity method is the use of Manning’s equation for steady flow. In terms of the mean velocity the Manning equation may be written:

v = Km R2/3 S1/2 (1)

Since for higher stages the value of Km S1/2 becomes nearly constant, the equation can be rewritten:

v = K* R2/3 (2)

or K* = v / R2/3 (3)

The relationship of stage (h) to K* is plotted from discharge measurements. This curve often approaches a constant value of K* at higher stages (Fig. 2.4). This value of K* may then be used in conjunction with extrapolated relationships between h and A and, h and R2/3 based on survey. Discharge for extrapolated stage is then obtained by applying the Manning equation with K* and extrapolated values of A and R2/3

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Figure 2.4 K* versus gauge height

Above bankfull stage the discharge on the floodplain must be determined separately by assuming an appropriate Km value as done using the conveyance slope method.

This method was applied to the Khamgaon river cross-sectional data shown in Figure 2.1 and observed discharges. The results are shown in the Figures 2.5 to 2.7. From Figure 2.5 it is observed that K* indeed tends to an approximately constant value for the higher stages,

which was subsequently applied in the extrapolation. Together with the cross-sectional area and the hydraulic radius the river the flow through the main section was computed. For the flood plain the Manning equation was applied separately. The result is shown in Figure 2.7. In this Figure also the result of the double logarithmic extrapolation technique is shown for reference purposes. It is observed that the flow through the main river is approximately the same between the two methods, however the total flow with the Manning technique is larger since in this method due account is given to the flood plain flow.

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2.4. The conveyance slope method

In the conveyance slope method, the conveyance and the energy slope are extrapolated separately. It has greater versatility than the methods described above and can be applied in sections with overbank flow. It is therefore recommended for use. It is normally, again, based on the Manning equation:

Q = Km R2/3 S1/2 A (4)

or: Q = K S1/2 (5)

where the conveyance is

K = KmA R2/3 (6)

For the assessment of K for given stage, A and R are obtained from field survey of the discharge measurement section and values of n are estimated in the field. Values of K are then plotted against stage up to the maximum required level (usually on natural graph paper) (Fig. 2.8)

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Figure 2.8 Conveyance as f(h) Figure 2.9 Slope extrapolation

Values of S, which is the energy gradient are usually not available but, for measured discharges, S1/2 can be computed by dividing the measured discharge by its corresponding K value. S is then calculated and plotted against stage on natural graph paper and extrapolated to the required peak gauge height, in the knowledge that S tends to become constant at higher stages at the limiting slope of the stream-bed, (see Figure 2.9 for the Khamgaon case).

The discharge for given gauge height is obtained by multiplying the corresponding value of K from the K curve by the corresponding value of S1/2 from the S curve. It should be noted that in this method, errors in estimating Km have a minor effect, because the resulting percentage

error in computing K is compensated by a similar percentage error in the opposite direction in computing S1/2.

The whole procedure can be accomplished in various stages as given below:

Computation of cross-sectional data

First of all the cross-sectional contour is obtained from:

distance (x) from an initial point

depth (y) and depth correction (yc)

The depth correction yc may be introduced to evaluate quickly the effects of changes in the cross-section on geometric and hydraulic parameters.

The actual depth ya is computed from:

ya = y + yc

A plot can be made of the cross section and for levels at fixed interval the following quantities are computed

These parameters may be determined for the whole cross-section or for parts of cross-section, e.g. for main river and flood plain separately.

It must be noted that when the cross-section is divided, the wetted perimeter for each part may be determined in two ways:

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the water boundary not considered: - for flood plain : Pfloodplain = ABC- for the main river: Priver = CEFG

the water boundary is treated as a wall: - for the flood plain : Pfloodplain = ABCD- for the river : Priver = DCEFG

To account for the lateral transport of momentum between river and flood plain the latter option appears to be more realistic. It reduces generally the discharge capacity of the main channel. However, to obtain consistency with hydraulic computations, where generally the first approach is used, both options are included.

Computation of hydraulic quantities in the measured range

Next, the geometric and hydraulic quantities are obtained in one of the following ways:

from stage-discharge database, provided that the cross-sectional parameters are also given

from a combination of the cross-section profile and the rating curve

The following parameters are obtained for various depths:

surface width, (B) wetted perimeter, (P) cross-sectional area, (A) hydraulic radius, (R): R = A/P factor {area x (hydraulic radius)2/3}, (AR2/3) discharge, (Q) average velocity. (v): v = Q/A Conveyance, (K): K = (1/n)(AR2/3) ; where n is an estimated value Slope (S): S = (v/K)2

Estimation of discharge in the extrapolated range

The estimated values of slope (S) in the measured range is plotted against stages and since this curve is asymptotic to the bed slope at higher stages extrapolation is accordingly. The conveyance curve is also plotted making use of the estimated values of K in the full range of stages. Now, for any stage in the extrapolated range the value of K and S are read from the two curves and the product of these two quantities and the area of cross section (A) yield the estimated value of discharge (Q).

After synthetic data stage-discharge data have been obtained for the extrapolated range, these data are incorporated in the set of stage-discharge data. Subsequently, new attempts can be made to fit rating equation to the measured and estimated stage-discharge data.

3. Low flow extrapolationManual low flow extrapolation is best performed on natural graph paper rather than on logarithmic graph paper because the co-ordinates of zero flow can not be plotted on such paper. An eye-guided curve is drawn between the lowest point of the known rating to the known point of zero flow, obtained by observation or by survey of the low point of the control. There is no assurance that the extrapolation is precise but improvement can only come from further low flow discharge measurements. However low flows persist for a sufficient period for gaugings to be carried out and there is little physical difficulty in obtaining such measurements.

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In eSWIS the power type equation used for the lowest segment with stage-discharge observations is assumed applicable also below the measured range. The shift parameter ‘a’ is either determined based on the measurements by the system or is introduced based on

cross-sectional information

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e - surface water information system - secondary...

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