ONOSAKPONOME, OGAGA ROBERT

PG/M.ENG/2008/48538

PG/M. Sc/09/51723

COMPARATIVE STUDY OF DIFFERENT METHODS

OF RUNOFF DISCHARGE ESTIMATION FOR

DRAINAGE DESIGN

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OCTOBER, 2009

COMPARATIVE STUDY OF DIFFERENT METHODS

OF RUNOFF DISCHARGE ESTIMATION FOR

DRAINAGE DESIGN

BY

ONOSAKPONOME, OGAGA ROBERT

PG/M.ENG/2008/48538

DEPARTMENT OF CIVIL ENGINEERING

UNIVERSITY OF NIGERIA, NSUKKA

OCTOBER, 2009.

CERTIFICATION

This is to certify that this research is an authentic work of

Onosakponome, Ogaga Robert and has been approved under the supervision

of Engr. (Prof.) J.C. Agunwamba as part of the requirement for the award of

the Master of Engineering in Water Resources and Environmental

Engineering in the Department of Civil Engineering, at the University of

Nigeria, Nsukka.

Engr. (Prof.) J.C. Agunwamba ______________ __________

Supervisor Signature Date

Engr. (Prof.) J.C. Agunwamba ______________ __________

Head of Department Signature Date

____________________ _____________ __________

External Examiner Signature Date

DEDICATION

This work is dedicated to my Lord and saviour, JESUS CHRIST to

whom I will forever remain eternally grateful. The KING OF kings, LORD

of Lords, who also is my life – in HIM I live, move and have my whole

being!

ACKNOWLEDGEMENT

I express my sincere gratitude and thanks to my supervisor and head

of department of civil Engineering, Engr. (Prof.) J.C. Agunwamba for his

concern, advice and contribution to my success. I owe many thanks to my

dearly and wonderful sisters, Mrs. Mercy Lilian Akomah for her care and

financial support.

A special thanks to the engineers and staff members of the department of

physical planning unit, UNN for enabling me obtain a copy of the

topographical map of the UNN campus. I also appreciate the kind gesture of

Mr. Onu and the entire department of crop science, UNN for allowing me

retrieve necessary hydrologic data required for this work. I will not forget to

appreciate the effort of Mr. Eze who contributed immensely to this project.

May the works of your hands be blessed and multiplied in Jesus name

– Amen!

ABSTRACT

This project is a comparative study of the different established empirical and

predictive methods used in the estimation of runoff discharge. A catchment

area was selected within the campus (University of Nigeria, Nsukka) and

data were collected to determine the peak flow (runoff discharge). Observed

peak discharge was compared to discharges computed for each of the

empirical methods discussed. From the results, the unit hydrograph gave the

best estimates, followed by the Khosla`s formula, the rational method was

the last.

TABLE OF CONTENTS

Certification----------------------------------------------------------------------------i

Dedication-----------------------------------------------------------------------------ii

Acknowledgement-------------------------------------------------------------------iii

Abstract--------------------------------------------------------------------------------iv

Table of Contents---------------------------------------------------------------------v

CHAPTER ONE: INTRODUCTION-------------------------------------------1

1.1 Significance of the Research----------------------------------------------2

1.2 Research Objectives--------------------------------------------------------3

1.3 Scope and Limitation of the Research-----------------------------------4

1.4 Description of Catchment area--------------------------------------------4

CHAPTER TWO: LITERATURE REVIEW---------------------------------5

2.1 Runoff------------------------------------------------------------------------5

2.1.1 Sources and components of Runoff--------------------------------------6

2.1.1.1 Channel Precipitation------------------------------------------------------8

2.1.1.2 Overland Flow--------------------------------------------------------------8

2.1.1.3 Interflow---------------------------------------------------------------------9

2.1.1.4 Groundwater flow---------------------------------------------------------10

2.1.1.5 Snowmelt------------------------------------------------------------------10

2.1.1.6 Quickflow and Baseflow-------------------------------------------------11

2.2 Types of stream-----------------------------------------------------------11

2.3 The Runoff Process------------------------------------------------------12

2.3.1 The Horton Runoff Model---------------------------------------------13

2.3.2 The Hewlett Runoff Model---------------------------------------------15

2.3.3 Variable Source Areas---------------------------------------------------16

2.4 Factors Affecting Runoff-----------------------------------------------17

2.4.1 Factors Affecting the Total Volume of Runoff----------------------17

2.4.2 Factors Affecting the Distribution of Runoff in Time--------------18

2.4.2.1 Meteorological factors--------------------------------------------------18

2.4.2.2 Types of Precipitation--------------------------------------------------19

2.4.2.3 Rainfall Intensity and Duration----------------------------------------19

2.4.2.4 Rainfall Distribution ---------------------------------------------------21

2.4.3 Catchment Factors-------------------------------------------------------21

2.4.3.1 Topography--------------------------------------------------------------22

2.4.3.2 Geology ------------------------------------------------------------------24

2.4.3.3 Soil------------------------------------------------------------------------25

2.4.3.4 Vegetation----------------------------------------------------------------26

2.4.3.5 Drainage network--------------------------------------------------------27

2.4.4. Human Factors-----------------------------------------------------------28

2.4.4.1 Hydraulic Structures----------------------------------------------------28

2.4.4.2 Agricultural Techniques------------------------------------------------29

2.4.4.3 Urbanization-------------------------------------------------------------30

2.4.4.4 Severity of Flooding----------------------------------------------------30

2.5 Variations of Runoff----------------------------------------------------31

2.5.1 Areal Variations---------------------------------------------------------32

2.5.2 Seasonal Variations-----------------------------------------------------32

2.5.2.1 Simple Regimes---------------------------------------------------------32

2.5.2.2 Complex I Regimes-----------------------------------------------------34

2.5.2.3 Complex II Regimes----------------------------------------------------34

2.6 Hydrograph---------------------------------------------------------------35

2.6.1 Unit Hydrograph Method-----------------------------------------------37

2.6.2 Construction of Unit Hydrograph -------------------------------------39

2.6.3 Assumptions--------------------------------------------------------------41

2.6.4 Limitations of Unit Hydrograph Method-----------------------------42

2.7 The Estimation, Prediction, and Fore-casting of Runoff------------43

2.7.1 Annual and Seasonal Runoff--------------------------------------------45

2.7.2 Peak Flows-----------------------------------------------------------------46

2.8 Empirical formulae-------------------------------------------------------47

2.8.1 Rational Method----------------------------------------------------------48

2.8.1.1 Assumptions of the Rational Method----------------------------------49

2.8.1.2 Rainfall Intensity (I)------------------------------------------------------50

2.8.1.3 Runoff Coefficient (C)---------------------------------------------------55

2.8.1.4 Catchment Area (A)------------------------------------------------------57

2.8.1.5 Design Computations-----------------------------------------------------57

2.8.1.6 Time of Concentration---------------------------------------------------58

2.8.2 Khosla’s Formula--------------------------------------------------------62

2.8.3 Inglis Formulae for Hilly and Plain Areas-----------------------------62

2.8.4 Lacey’s Formula----------------------------------------------------------62

2.8.5 Statistical Method---------------------------------------------------------63

2.9 Direct Measurement of Runoff -----------------------------------------69

2.9.1 Velocity-Area Method---------------------------------------------------70

2.9.2 Weirs and Flumes---------------------------------------------------------71

CHAPTER THREE: METHODOLOGY-------------------------------------73

3.1 Gauge Stations--------------------------------------------------------------73

3.2 Empirical Formulae--------------------------------------------------------74

3.3 Velocity-Area Method------------------------------------------------------74

3.4 Unit Hydrograph Method---------------------------------------------------75

CHAPTER FOUR: RESULTS AND ANALYSIS---------------------------76

4.1 Unit Hydrographs-----------------------------------------------------------80

4.2 Rational Formulae----------------------------------------------------------82

4.3 Relationship between Estimated and Measured Runoff Discharge- 85

CHAPTER FIVE: CONCLUSION AND RECOMMENDATION -----86

5.1 Conclusion--------------------------------------------------------------------86

5.2 Recommendation------------------------------------------------------------87

References--------------------------------------------------------------------88

Appendices-------------------------------------------------------------------94

CHAPTER ONE

INTRODUCTION

The design of a drainage structure requires hydrologic analysis of

precipitation amount and duration, peak rate of runoff and the time

distribution of runoff from a given basin or catchment. Many hydrologic

methods are available for estimating peak flows (runoff) from a catchment

area, and no single method is applicable to all catchments. There is usually

disparity between measured values and those determined from other

methods, viz; the unit hydrograph method, simulation or the rational method.

Often, extensive hydraulic analysis and design are needed to reduce

the impact of highway and bridge crossings on floodways and drainage,

there is potential for stormwater runoff to create or increase flood and water

quality problems. Many government agencies are trying to mitigate the

increased runoff and diminished water quality associated with transportation

infrastructure through better design of drainage structures. Detention

structures and channel improvements have often helped to manage runoff

volume and maintain water quality. Various types of drainage structures are

necessary to protect human life, highways and highway structures, adjacent

structures, and the flood-plain environment from surface and subsurface

water. Drainage structures are designed to convey water in a manner that is

efficient, safe and least destructive to the highway and adjacent areas.

(Washington State Department of Transportation; 1997).

The VDOT design manual (Virginia Department of Transportation,

2002) recommends that transportation engineers follows several well-

documented, standard engineering methods to estimate runoff volumes and

peak flows from small drainage basins. The appropriate method of

determination of runoff depends on its applicability to the area concerned,

the quantity and type of data available, the detail and accuracy required, and

the importance of the structure. Usually, the unit hydrograph method,

simulation or the rational method is applied (Agunwamba, 2001).

Although, (Agunwamba, 2001), (VDOT, 2002), recommend the use

of the rational method for estimating the design-storm peak runoff from

small basins with areas up to 200 acres and for up to 300 acres in low-lying

tide water areas, this study was conducted to determine the reliability of

methods recommended as to ascertain the most appropriate as the case may

be. Data collected at the catchment were analyzed and compared to the ones

obtained by empirical methods. The results of this study should be similar to

results obtained by comparable studies in other areas of the metropolis.

1.1 SIGNIFICANCE OF THE RESEARCH

The purpose of this research is to present a comparison of design

estimates of runoff discharge to observed peak flow, obtained through data

collected within the catchment area of the Nsukka campus. This report

describes the results of a small basin runoff study conducted in 2009 and

presents a summary of peak-flow data within the metropolis. This report also

presents background information on the processes that control runoff from

drainages with various soil, geologic, topographic and land-use

characteristics; comparison of runoff characteristics (time flow) observed

and estimated by various methods from storm data to runoff characteristics.

A more effective method for the estimation of the runoff discharge is

expected to emerge at the end of the research, which will serve as a major

contribution to the body of knowledge.

1.2 RESEARCH OBJECTIVES

The objectives of this study are:

1. To review the various methods available for estimation of run-off

discharge required for drainage design.

2. To use available data obtained from the catchment area to compute

for the runoff discharge using the empirical methods reviewed.

3. To compare the results obtained through these empirical methods

with the observed runoff discharge at the catchment, in order to

determine which method gives a more accurate value of the runoff

discharge.

1.3 SCOPE AND LIMITATION OF THE RESEARCH

The scope of the project will be limited to investigations and data

collection with regards to the catchment (i.e., the University of Nigeria,

Nsukka campus).

1.4 DESCRIPTION OF CATCHMENT AREA

Two broad categories of factors affect runoff: precipitation

characteristics and basin or watershed characteristics. Basin characteristics

are; size, shape, topography, soils, geology, and land use (Schwab and

others, 1997). Other factors such as site accessibility, proximity to site, and

capability to be instrumented with monitoring equipment also were

considered in selecting the area within the University of Nigeria, Nsukka

campus as the study basin. Land use for the study watershed consists of

combined road and ditch, pasture, residential and recreational areas.

CHAPTER TWO

LITERATURE REVIEW

2.1 RUNOFF

Runoff or streamflow comprises the gravity movement of water in

channels which may vary in size from the one containing the smallest ill-

defined trickle to the ones containing large rivers. Precipitation is the

primary natural supplier of water to a basin. Runoff is that part of the

precipitation that exits the basin as streamflow at a concentrated point. A

hydrograph is a geographical representation of streamflow (runoff) plotted

with respect to time (Langbein and Iseri, 1960) and can be used to analyze

runoff characteristics associated with a basin and storm. The hydrograph

shows the integrated effects of the physical basin characteristics and storm

characteristics within the basin boundaries (Chow, 1964; Freeze, 1974), and

the separation of a hydrograph in terms of time can be useful for hydrologic

analysis of drainage structures.

The single most important property of the hydrograph that is essential

to drainage structure design is the peak rate of runoff (Wigham, 1970). The

design of a drainage structure requires the hydrologic analysis of the peak

rate of runoff, the volume of runoff and the time distribution of flow from

the contributing drainage area (Virginia Department of Transportation, 2002;

Washington State Department of Transportation, 1997). However, the

relation between the amount of rainfall over a drainage basin and the amount

of runoff from the basin is complex and not well understood. The hydrologic

analysis allows for estimates of runoff characteristics such as peak rate of

runoff or runoff volume, but exact solutions to drainage design problems

should not be expected (Virginia Department of Transportation, 2002).

Errors in runoff estimates can result in either an undersized drainage

structure that causes potential hazards, inconvenience, and drainage

problems; or an oversized, inefficient drainage structure.

Runoff, which may be variously referred to as streamflow, stream or

river discharges or catchment yield, norm ally expressed as a volume per

unit of time. The cumec, i.e, one cubic metre per second is a commonly used

unit. Runoff may also be expressed as a depth equivalent over a catchment,

i.e., millimeters per day or month or year.

2.1.1 SOURCES AND COMPONENTS OF RUNOFF

The persistent misuse of runoff terminology has resulted in much

confusion and ambiguity about the sources and components of runoff.

(Freeze, 1972) provided a consistent aid unambiguous terminology which

has been adopted with only slight modification. The total runoff from a

typically heterogeneous catchment area may be conveniently divided into

four component parts: channel precipitation, over land flow, interflow, and

groundwater flow.

The runoff process is represented diagrammatically as shown in figure 2.1

below

BASIN PRECIPITATION

(excluding storage, interception and other losses)

CHANNEL

PRECIPITATION

OVERLAND

FLOW

INTERFLOW

(SUBSURFACE

STEM FLOW)

GROUND

WATER

FLOW

SURFACE

RUNOFF SUBSURFACE

RUNOFF

DELAYED

INTERFLOW RAPID

INTERFLOW

Channel

flow Channel

flow Channel

flow

Channel

flow

INFILTRATION

Fig. 2.1 Diagrammatic representation of the runoff process.

2.1.1.1 CHANNEL PRECIPITATION

Direct precipitation onto the water surfaces of streams, lakes, and

reservoirs makes an immediate contribution to streamflow. In relation to the

other components, however, this amount is normally small in view of the

small percentage of catchment area normally covered by water surfaces. The

water surface for most catchments does not exceed 5 per cent of the total

area even at high water levels (Linsley et al, 1938). However, (Rawitz and

others, 1966), in an analysis of ten storms over a small Pennsylvania

watershed, estimated that channel precipitation accounted for between 3 and

61 percent of total runoff. In catchments containing a large area of lakes or

swamps, channel precipitation may make a substantial contribution to

streamflow.

2.1.1.2 OVERLAND FLOW

Overland flow comprises the water which, failing to infiltrate the

surface, travels over the ground surface towards a stream channel either as

quasi-laminar sheet flow or, more usually as flow anatomizing in small

trickles and minor rivulets. The main cause of over-land flow is the inability

of water to infiltrate the surface and in view of the high value of infiltration

characteristic of most vegetation-covered surfaces, it is not surprising that

overland flow is a rarely observed phenomenon. Conditions in which it

assumes considerable importance include the saturation of the ground

surface, the hydrophobic nature of some very dry soils, the deleterious

effects of many agricultural practices on infiltration capacity and freezing of

the ground surface. Surface runoff may then be defined as that part of the

total runoff which travels over the ground surface to reach a stream channel

and thence through the channel to reach the drainage basin outlet.

2.1.1.3 INTERFLOW

Water which infiltrates the soil surface and then moves laterally

through the upper soil horizons towards the stream channels, either as

unsaturated flow or, more usually , as shallow perched saturated flow above

the main ground water level is known as interflow. Alternative terms used

include; subsurface storm flow, storm-seepage, and secondary base flow.

The general condition favouring the generation of interflow is one in which

lateral hydraulic conductivity in the surface horizons of the soil is

substantially greater than the overall vertical hydraulic conductivity through

the soil profile. Then during prolonged or heavy rainfall, water will enter the

upper part of the profile more rapidly than it can pass vertically through the

lower part, thus forming a perched saturated layer from which water will

‘escape’ laterally, i.e., in the direction of greater hydraulic conductivity.

In addition, some hydrologists argue that water may travel down slope

through old root holes and animal burrows and other subsurface pipes. In

view of the variety of possible interflow routes, it is to be expected that some

will result in a more rapid movement of water to the stream channels than

will others, so that it is sometimes helpful to distinguish between rapid and

delayed interflow (see fig. 2.1). Experimental evidence has long indicated

that interflow may account for up to 85 percent of total runoff (Hertzler,

1939).

2.1.1.4 GROUNDWATER FLOW

Most of the rainfall which percolates through the soil layer to the

underlying groundwater will eventually reach the main stream channels as

groundwater flow through the zone of saturation. Since water can move only

very slowly through the ground, the outflow of groundwater into the stream

channels may lag behind the occurrence of precipitation by several days,

weeks, or often years. In general, groundwater flow represents the main

long-term component of total runoff and is particularly important during dry

spells when surface runoff is absent.

2.1.1.5 SNOWMELT

In some areas, particularly at high altitude or in high latitudes, a large

proportion of streamflow may be derived from the melting of snows and

glaciers. Where this melting occurs gradually, over a long period of time, the

resulting contribution to stream flow will resemble that of groundwater flow.

Where, however, it occurs suddenly, a large volume of water will enter the

streams during a short period of time, giving a runoff peak which closely

resembles that derived from storm rainfall.

2.1.1.6 QUICKFLOW AND BASEFLOW

Quickflow or direct runoff, is the sum of channel precipitation,

surface runoff and rapid interflow and will clearly represent the major runoff

contribution during storm periods and is also the major contributor to most

floods. Baseflow or base runoff may be defined as the sustained or fair-

weather runoff (Chow, 1964) and is the sum of groundwater runoff and

delayed interflow, although some hydrologists prefer to include the total

interflow as illustrated by the broken line in fig. 2.1.

2.2 TYPES OF STREAM

The long-term relationship between baseflow and quickflow

determines the main characteristics of a stream or river; whether, for

example, it will flow steadily or flashily through the year, whether, indeed, it

will flow throughout the year or only for part of the time; and this provides a

basis for classifying streams into three main types, i.e., ephemeral,

intermittent, or perennial (Wisler and Brater, 1959).

Ephemeral streams are those which comprise quickflow only and

which, therefore, flow only during and immediately after rainfall or

snowmelt.

In the case of intermittent streams, which flow during the wet season,

but which dry up during the seasons of drought, streamflow consists mainly

of quickflow, but baseflow makes some contribution during the wet season,

when the water table rises above the bed of the stream.

Finally, as the term suggests, perennial streams flow throughout the

year, because even during the most prolonged dry spell, the water table is

always above the bed of the stream, so that groundwater flow can make a

continuous and significant contribution to total runoff at all times.

2.3 THE RUNOFF PROCESS

The broad relationship between precipitation and streamflow is

obvious and has been evident since the work of Mariotte in the Seine basin

during the seventeenth century. On a seasonal basis streamflow tends to

reach a maximum during the wet season and declines slowly during the drier

part of the year. It usually peaks sharply during a storm and declines

relatively slowly after the end of rainfall. In other words, quite clearly,

streamflow results from precipitation and some water arrives in the channel

quickly while some arrives much more slowly and continues to arrive even

during prolonged dry periods. A successful model of the runoff process must

incorporate and explain these two facts.

For many years, most explanations and analyses of runoff behaviour

have been made in terms of the infiltration theory of runoff developed by

Horton (Horton,1933). Recently, however, this classical model has been

seriously questioned and is now seen to be applicable only in specific

circumstances. A more realistic dynamic model of the runoff process

developed by Hewlett, Hursh and others in the United States in the fifties is

now believed to provide a more accurate representation of the runoff process

over a wide orange of conditions.

2.3.1 THE HORTON RUNOFF MODEL

The Horton infiltration theory of runoff (Horton, 1933) considers

average conditions over an entire catchment area. It is assumed that at the

end of a dry period most streamflow will be derived from groundwater flow,

although Horton also recognized that baseflow could be supplied from other

storage such as that in lakes, marshes, snow, and ice. As groundwater flow

takes place, the groundwater reserves will be depleted and this, in turn, will

lead to a gradual reduction in groundwater flow to the stream channels. This

condition is represented by section AX of the hydrograph in fig. 2.2 below.

10-

8-

6-

Y

Z

B

Run

off

(cu

mec

s)

4-

2-

A X

0

1 2 3 4 5 6

Time (days)

Fig 2.2 Short-period storm hydrograph for a hypothetical catchment.

The Horton model assumes that during a prolonged storm of constant

intensity there will be a continuous exponential decrease of infiltration

capacity which Horton assumed was largely the result of factors operating at

the soil surface such as compaction, structural change, and the inwashing of

fine particles. Eventually a constant low value of infiltration capacity is

reached over the entire catchment area. If this value falls below that of

rainfall intensity, so that rain is falling at a faster rate than the soil can

absorb it, overland flow and subsequently surface runoff will occur.

Overland flow, having built up to a sufficient depth, will reach the stream

channels quite quickly giving rise to the marked increase in streamflow

represented by the line XY in fig. 2.2 above.

Soon after the end of rainfall, the surface runoff will begin to

diminish, rapidly in the initial stages, and later more slowly, as first the

minor channels, and then the larger ones begin to drain dry (see section YZ,

fig. 2.2). Any water which is left on the surface as depression storage will

soak into the soil and may perhaps percolate to the groundwater. Finally,

once all the surface runoff has been disposed of, the flow in the steams will

again consist almost entirely of groundwater flow (see section ZB), which

gradually decreases as the reserves are used up.

2.3.2 The Hewlett runoff model

The Hewlett runoff model embodying the variable source area

concept makes the basic assumption that infiltration is seldom a limiting

factor, i.e., that only in special conditions rainfall intensity exceed

infiltration capacity. Hewlett derived this basic premise from a number of

fundamental field evidence that most precipitation infiltrated the ground

surface, particularly in well-vegetated areas. Even during a 100-year storm

which delivered more than 500mm of rain in five days on one Coweeta

watershed, no overland flow was detected (Hewlett and Nutter, 1970).

Secondly, only about 10 per cent of the annual precipitation in humid areas

such as the eastern United States appears as quickflow in headwater streams

(Woodruff and Hewlett 1970). Thirdly, most of this quickflow leaves the

drainage basins hours after the cessation of rainfall. Fourthly, Hewlett

described as the most intriguing of all the findings at Coweeta, the evidence

that unsaturated soil moisture movement may account entirely for baseflow

from some mountain watersheds.

Essentially the core of the Hewlett runoff model is the response of the

channel system to precipitation. A further proposition of the Hewlett runoff

model is that the shallow subsurface movement of water, resulting from the

very large percentage of total precipitation infiltrating the surface, makes a

vital contribution to the recession limb of the hydrograph as well as to the

rising limb and peak. In some circumstances the contribution of interflow

may entirely account for recession flows which have been explained as the

result of groundwater flow.

2.3.3 Variable Source Areas

It is now widely accepted that widespread Hortonian overland flow

resulting from saturation when rainfall intensity exceeds the infiltration

capacity of the ground surface is more. A number of authors have discussed

the relationships between rainfall intensity and infiltration capacity and have

demonstrated that over a wide range of conditions, typical rainfall intensities

are less than the infiltration capacities of many soils and that in any case

normal storm duration tends to be shorter than the time required for most

soils to become saturated at the surface (Freeze,1972). The concept of

variable (or partial) source areas is an attempt to reconcile the absence of

widespread overland flow with the rapid response of most streams to

precipitation by postulating that over-the-surface movement of water is

restricted to limited areas of a drainage basin.

2.4 Factors Affecting Runoff

It will be convenient at the outset of this discussion of the factors

affecting runoff to differentiate between those factors which combined to

influence the total volume of runoff over, say, a period of several years, and

those other factors which combined to influence the distribution of runoff in

time say, over a period of one year or less.

2.4.1 Factors Affecting the Total Volume of Runoff

The most obvious and probably the most effective influence on the total

volume of runoff is the long-term balance between the amount of water

gained by catchment area in the form of precipitation, and the amount of

water lost from that catchment area in the form of evapotranspiration. In

this sense, the climate of the catchment area sets the broad upper limits to

the total volume of streamflow leaving the area, but this relationship

between annual totals and means of rainfall and evapotranspiration may be

modified by short-term factors, such as the manner in which precipitation

occurs, and sudden changes in the vegetation cover.

In addition to the water balance of the catchment area, a second group

of factors influencing the total amount of runoff comprises aspects of the

physique of the catchment area. Chief amongst these, naturally, is the area of

the catchment since, other factors being equal, this determines the total

amount of precipitation caught. It should be noted, however, that the effect

of area may depend upon the prevailing climatic regime.

Slope, soil, and rock type may indirectly influence the total runoff

from a catchment through their effects in delaying water movement after

precipitation thereby possibly affecting the amount of evapotranspiration. In

general, the highest annual runoff would be expected from steeply sloping

areas having thin soils and impermeable rocks. Finally, the average height of

the catchment may affect total runoff, again indirectly, through its direct

orographic influence on precipitation amounts.

2.4.2 Factors Affecting the Distribution of Runoff in Time

From the hydrologist’s point of view, climate, which it has been

suggested sets the broad upper limits to total runoff, is a comparatively

stable environmental factor; even more so are the catchment factors which

have been discussed. It is, then, the second group of factors which influence

the distribution of runoff in time, and which, themselves, tend sometimes to

be more variable and unpredictable, which have attracted the most attention.

2.4.2.1 Meteorological Factors

In the sense that precipitation forms the raw material of streamflow,

meteorological factors are obviously of great importance and their variation

with time tends to be closely related to similar variations of runoff.

2.4.2.2 Types of Precipitation

For the purpose of this discussion, it may be considered that

precipitation occurs either as rainfall or as snowfall, other forms, such as hail

and sleet may be conveniently grouped with rainfall; hail, for example, often

occurs in conditions which favour rapid melting at the ground surface, and

the snow content of sleet will normally tend to liquefy soon after contact

with the ground.

The most important feature of a snow blanket is its storage capacity,

and the resulting time interval between the occurrence of runoff. Thus, in a

simple and rather obvious example, precipitation falling as snow during the

winter months between December and February will not contribute to runoff

until melting occurs during the spring.

Precipitation falling as rain may, of course contribute directly to

runoff, but the extent to which it does so will depend upon the interaction of

numerous meteorological and other factors, the most important of which will

be discussed below.

2.4.2.3 Rainfall Intensity and Duration

It has already been shown that, in some circumstance, the intensity

with which rain falls, may be an important factor in determining the

proportions of the rainfall which go to overland flow, interflow, and

groundwater flow and, therefore, the speed with which water may reach the

stream channel. The duration of rainfall is important, particularly in relation

to the hydrologically responsive areas of a catchment and particularly in flat,

low-lying areas. Here, if rainfall is sufficiently prolonged, infiltration may

raise the surface of saturation to the ground surface itself, thereby reducing

the infiltration capacity to zero and causing a sudden increase of surface

runoff.

The duration of rainfall also becomes significant when considered in

relation to the mean travel time of a drop of water from its points of impact

on the catchment area as rainfall, to its exit from the catchment area as

streamflow. If the rainfall duration is equal to or grater than this mean travel

time, then the whole of the catchment area is likely to be contributing to

runoff during the later stages of the storm, so that the potential runoff is at a

maximum. If on the other hand, the duration of rainfall is less than the mean

travel time, then the potential runoff will be lower than the maximum

because only part of the catchment will be contributing to runoff before

rainfall ceases. In this context, it is apparent that the importance of rainfall

duration will tend to vary with the size and nature of the catchment. In a

small catchment with steep slopes, maximum potential runoff is likely to be

caused by a rainfall of much shorter duration than would be required in a

large, gently undulating catchment.

2.4.2.4 Rainfall Distribution

The time relationship between rainfall and runoff may be greatly

affected by the distribution of rainfall over the catchment area. A given

volume of rainfall, which is uniformly distributed over the whole of a

catchment, will have lower intensities and is, therefore, less likely to

produce quickflow than is the same volume of rain falling on a small,

localized part of the catchment. The first type of rainfall distribution will

tend to result in an increase in baseflow, and consequently a long-term

increase in streamflow, while the second sort of distribution will tend to give

larger volumes of quickflow and thus, a more sudden, short-lived increase in

streamflow.

When discussing rainfall distribution, one is rarely concerned with a

stationary pattern. Much of the rainfall in the British isles, for example, is

related to series of depressions moving in from the Atlantic, causing belts of

frontal main to cross the country. In this way, a rainstorm may begin in one

part of a catchment area, and end in another, and the direction of movement

of the storm may be very important.

2.4.3 Catchment Factors

The various meteorological factors which have been discussed can all

be measured with reasonable accuracy thus facilitating their correlation with

runoff characteristics. It is, however, much more difficult to apply such

precise determinations to many catchmnent factors. Furthermore, some of

these factors, such as shape, topography, and soil type, remain fairly

constant over long periods while others , such as those associated with land

use, may change very rapidly. The main problems, however, arise partly

from the fact that the various components of runoff may be differently

affected by each of the catchment factors, so that the net effect of any one

catchment factor on variations of total runoff with time are difficult to

establish, and partly from the fact that only limited, hydrologically

responsive areas of a catchment make a substantial contribution to

quickflow, so that is the influence of catchment factors in these limited

areas; and not over the whole of the catchment, which must be determined.

The fact that the variable source areas within a catchment are difficult to

define, means that the present discussion must be largely qualitative in

nature.

2.4.3.1 Topograhy

One of the several factors which may be included under this rather

general heading is the shape of the catchment area, which is known to

influence runoff through its effects on flood intensities, and on the mean

travel time of a drop of water from its point of impact on the surface of the

catchment to its point of exit in the main stream. In a generally square or

circular catchment area, the tributaries often tend to come together and join

the main stream near the centre of the area (Parde, 1955). Consequently, the

separate runoff peaks generated by a heavy fall are likely to reach the main

stream in approximately the same locality at approximately the same time,

thereby resulting in a large and rapid increase in the discharge of the main

stream. If on the other hand, the catchment area is long and narrow, the

tributaries will tend to be relatively short, and are more likely to join the

main stream at intervals along its length. This means that, after a heavy

rainfall over the area, the runoff peaks of the lower tributaries will have left

the catchment before those of the upstream tributaries have moved very far

down the main stream. Elongated catchments are thus less subject to high

runoff peaks.

Synder (1938) suggested that one way to express the effective shape

of a catchment was to draw isopleths of travel time of the water above the

drainage outlet and to plot the area between isopleths against time. The

resulting curve would then express the shape of the catchment by giving the

increment of the area that is at any particular travel-time distant from the

outlet.

A second pertinent topographical factor is the slope of the catchment

area which, as has already been suggested, may affect the relative

importance of predominantly vertical movement of water by means

infiltration and the predominantly lateral movement of water by means of

interflow and over land flow, the former tending to be more important in flat

areas, the latter in steeply sloping areas. Furthermore, because the speed of

water movement will tend to increase with slope, runoff in steeply sloping

areas will reach stream channels quickly.

The shape of the runoff hydrograph depends not only on the speed

with which water gets into the stream channel but also on the speed with

which it moves down the channel to the outlet of the catchmnent. Channel

slope may therefore be as important as catchment slope and has frequently

yielded more significant correlations with runoff characteristics.

2.4.3.2 Geology

By its very nature, the geology of a catchment area will exert a

fundamental influence on runoff which will be felt in many ways. Two

aspects are, however, of chief importance – the type of rock in which the

catchment area has been eroded, and the main structural features of the area.

The influence of rock type on runoff may be seen in the close

relationships which often exist between geology and the texture of drainage.

Thus studies in Pennsylvania showed that high runoff peaks occurred in

shale and sandstone catchments while catchments having extensive, thick

limestone generated extremely low runoff peaks (White,1970). Where

subsurface water movement through limestone is very rapid, however,

runoff peaks may be substantially greater than in other geological areas.

2.4.3.3 Soil

The influence of soil type on infiltration characteristics and its

consequent effect upon the disposition of rainfall as either overland flow,

interflow or groundwater flow cannot be over-emphasized. Open-textured

sandy soils will tend to be associated with higher infiltration values than

fine-grained, closely compacted clay soils and will, therefore, tend to

generate smaller volumes of quickflow.

Soil profile characteristics are important in relation to their effects

upon infiltration and the generation of interflow. In particular, marked

reductions of hydraulic conductivity with depth, especially in the upper

horizons, facilitate the formation of interflow and, during prolonged rainfall,

the saturation of the soil surface and the generation of overland flow. On the

other hand, deep uniformly permeable soils tend to encourage continued

vertical infiltration and the dominance of baseflow over quickflow.

Hydrologists have for a long time reorganized the relationship

between the amount of runoff (especially quickflow) produced by a given

rainfall and the moisture content of the soil, expressed either as a direct

measurement or indirectly as an antecedent precipitation index. Earlier

workers, using Hortonian concepts, tended to ascribe this relationship to the

reduction of infiltration capacity which accompanies the increase of soil

moisture content. In the light of modern views on runoff formation,

however, it will be appreciated that, in general, the source areas within a

catchment will tend to expand as the catchment becomes wetter and that this

is a much more likely explanation of observed relationships between runoff

and catchment moisture indices.

2.4.3.4 Vegetation

The effect of vegetation on the distribution of runoff with time has

probably received more attention from hydrologists than the effect of any

other catchment factor and yet because of the complexity of the interaction

involved, there is still much confusion. The complexity of the problem

becomes evident when it is considered that the total effect of vegetation on

runoff is comprised of its individual effects on interception,

evapotranspiration, soil moisture movement (particularly in terms of

infiltration and interflow), and also the pattern of snow accumulation and

melt. By way of illustration, let us compare a forested and a non-forested

area on which all precipitation falls as rain and which are identical, apart

from vegetation differences. In the non-forested area, transpiration and

interception losses will probably be lower, thus producing wetter soils with a

reduced capacity for additional water storage, and thereby resulting in higher

volumes of dry season quickflow and higher instantaneous peak flows. In

the wet season, the storage capacity of the soils under both vegetation types

will be at a minimum so that the response of runoff to rainfall will be similar

from both areas. In a less direct way, vegetation may influence runoff

through its effect on soil type.

2.4.3.5 Drainage Network

The character of the drainage pattern is important because of the

extent to which it may reflect many of the physical characteristics of

catchment areas. In a catchment where sub surface storage and hydraulic

conductivity are low, the ground surface will be prone to saturation resulting

both from the downslope movement of interflow and the increase in

elevation of shallow water tables during and immediately after precipitation.

In this situation, the channel network will expand rapidly during

precipitation, or, stated in alternative terms, a large proportion of the

precipitation will be evacuated as overland flow. On the other hand, in a

catchment where subsurface storage and hydraulic conductivity are high,

deep infiltration will be encouraged, channel network expansion during

precipitation will be small, and only a small proportion of the precipitation

will be evacuated as overland flow. Consequently, the surface, topographic

expression of overland flow, i.e., interconnection depressions, hills and

valleys, will be correspondingly smaller.

A final point which can be made in connection with the influence of

the drainage network on runoff concerns the presence of lakes and swamps

in a catchment area. Where these occur, they tend to ‘absorb’ high runoff

peaks and thus to exert a moderating influence on the hydrograph, which is

particularly beneficial in catchments which generate large volumes of

quickflow.

2.4.4 Human Factors

There are very few areas of the world in which runoff is not affected

to some extent by the influence of man. In remote uplands, dams have been

constructed for water supply and hydro-electric power generations.

Elsewhere, former grasslands have been ploughed up, more land have been

forested, semi-desert areas have been irrigated, swamps have been drained,

and everywhere there has been a great increase in urbanization, and the

resulting spread of artificial, impermeable surfaces. In all these ways, the

response of catchment areas to rainfall and, consequently, the pattern and

distribution of runoff has been changed.

2.4.4.1 Hydraulic Structures

The flow of many of the world’s large rivers is controlled or modified

by dams and reservoirs which have been constructed for power, water

supply, or irrigation purposes. The effect of these structures has been similar

to that of natural lakes to the extent that flood peaks are normally ‘absorbed’

by the artificial lakes and subsequently gradually released. An additional

effect, in some instances, has been a marked diminution of flow, particularly

where multipurpose schemes are in operation in which the impounded water

is used not only for water supply and power but also for irrigation.

Streamflow may also be affected by artificial modifications to stream

prone to flooding. Such modifications commonly include channel

straightening and enlargement and the construction of relief and by-pass

channels in order to reduce both discharge and water levels at critical points.

2.4.4.2 Agricultural Techniques.

A second aspect of human influence on runoff may result from the

application of specific agricultural techniques and practices, particularly

where these cause a sudden change in catchment characteristics, e.g.,

vegetation cover. Some of these changes have been brought about

deliberately, as conservation measures; other changes have brought about

‘accidentally’ and sometimes initially surprising hydrological results. In

Russia, for example, experiments showed that autumn ploughing may

decrease runoff by as much as 45 percent, and a 20 percent reduction in

runoff resulted in some areas from the cultivation of virgin lands (Lvovitch,

1958). Again, Ayers (1965) reported that in southern Ontario ploughed soils

in good management yielded much less runoff during the winter months than

grass-covered areas.

Some of the most dramatic land use changes are those associated with

afforestation and deforestation, the hydrological effects of which continue to

engender considerable controversy. In general, it has been shown that runoff

is reduced when deciduous trees are replaced by conifers and increased

when forest is replaced by lower growing vegetation such as grass or crops.

2.4.4.3 Urbanization

The effects on runoff of the spread of settlement and ancillary features

such as roads, pavements, and airfields calls for serious attention. Over large

areas, infiltration capacity is considerably reduced, falling precipitation is

caught by rooftops and roads, and is passed through drainage systems which

have been designed to dispose of it into nearby streams as rapidly as

possible. The result is that, immediately below large urban areas, there tends

to be a marked and rapid build-up of surface runoff which will be

accentuated where slopes are steep. Increases in the magnitude of peak flows

are thus a result of partly an increase in the volume of quick flow and partly

of the more rapid movement of runoff which is possible in an urbanized

area. Apart from peak flows, urbanization also affects water quality and

wide range of other hydrological variables.

2.4.4.4 Severity of Flooding

In conclusion, it is of interest to note that it is largely the human

factors which have been discussed above which are believed to be

responsible for the apparent increased severity of floods during recent times.

Floods, which may be defined as unusually high rates of discharge often

leading to the inundation of land adjacent to the streams, are nearly always

the result of quickflow, rather than baseflow, and are thus usually caused by

intense or prolonged rainfall, snowmelt, or a combination of these factors.

Any increase in the severity of floods is, therefore, likely to be caused

by increased rainfall intensity, or duration, reduced infiltration capacity, or

the changed efficiency of the drainage network. There is some evidence to

suggest that storms are increasing in intensity; the effect of urbanization in

reducing infiltration capacities have already been noted and, in addition,

such factors as forest clearance and burning, accidentally or otherwise, of

large areas of peat moorland must also be taken into account. Finally, the

efficiency of drainage channels is likely to be impeded by bridges, levees,

flood walls, and similar structures, and although the individual effect of each

may be small, their combined effect in large built-up areas may be

surprisingly significant (Wisler and Brater, 1959).

2.5 Variations of Runoff

Preceding discussions have shown that many factors combine to

influence runoff. So numerous are these factors, indeed, that all variations of

runoff are unique since no combination of all the variables are ever likely to

be repeated. However, certain general similarities and patterns may be

observed both in the spatial variation of annual runoff totals and in the

variation of runoff with time at one particular place.

2.5.1 Areal Variations

Areal variations of runoff are associated with varying runoff values

over a geographic sphere. An outstanding feature of this distribution is the

very low values representative of some regions where rainfall is low and

evaporative losses are generally high. At other regions, there could be high

values, and there is a fairly rapid transition between the areas of high and

low runoff.

2.5.2 Seasonal Variations

Most rivers show a seasonal variation in flow which, although

influenced by many factors, is largely a reflection of climatic variations and,

in particular, of the balance between rainfall and evaporation. The pattern of

seasonal variations which tends to be repeated year after year is often known

as the regime of the river or stream. Thus, equatorial rivers tend to have a

fairly regular regime, tropical rivers show a marked contrast between runoff

in the rainy and dry season, while in other climatic areas complications may

arise from the fact that precipitation falls as snow and does not, therefore,

contribute directly to runoff until melting occurs. In this way, river regimes

may be considered in relation to the climatic zones from which they

principally derive.

2.5.2.1 Simple Regimes

Simple regimes are those variations of river flow throughout the year

in which a simple distinction may be made between one period of high water

levels and runoff, and one period of low water levels and runoff. Such

regimes may result from one of several contrasting factors: thus, in many of

the oceanic areas of Europe, rainfall is fairly evenly distributed throughout

the year, but the peak of evapotranspiration during the summer months

results in low runoff during this season, in contrast to high runoff values

during the winter months when evapotranspiration is small. In tropical areas,

on the other hand, evapotranspiration tends to be uniformly high through the

year, so that the rainfall distribution is the main determinant of the river

regimes, with high runoff occurring as a result of the summer rains.

6-

5-

4-

3-

2-

1-

0

J F M A M J J A S O N D J

Time (months)

Fig2.3 Simple regimes hydrograph for a typical tropic rainfall

Runoff

(cu

mec

s)

2.5.2.2. Complex I regimes

Complex I regimes are characterized by at least four, and sometimes

as many as six, hydrological phases, although normally there are two low

runoff and two high runoff periods. In the case of European streams, the first

high runoff period, resulting perhaps from snowmelt, may occur in spring

and then be followed by a period of low runoff. Later in the year, a second

period of high water levels and runoff may occur in the summer as a result

of, say, convectional rainfall over a ‘continental’ area, or in autumn as a

result of Mediterranean storms, or in winter as the result of an excess of

rainfall over evapotranspiration in an oceanic area. This sequence results,

then, in two periods of peak runoff which are separated by two periods of

lower discharge, giving four distinct hydrological phases through the year.

2.5.2.3 Complex II regimes

Complex II regimes form the third and probably the most important

group in Parde’s classification and are found on most of the world’s large

rivers. Since these normally flow through several distinct relief and climatic

regions, and may receive the waters of large tributaries which themselves

flow over varied terrain, rivers comprising this group normally have a

simple or a complex I regime in their headwater reaches but, downstream,

are gradually influenced by a variety of factors such as snow or glacier melt,

rainfall, and evaporation regimes which may emphasize the trends found in

the headwater regime of which, because they work in opposite ways, may

cancel each other out.

2.6 Hydrograph

The hydrograph is a graph of discharge against time (i.e., specified

time). Discharge graphs are known as flood or runoff graphs. Each

hydrograph has a reference to a particular river site. The time period for

discharge hydrography may be hour, day, week or month.

Hydrograph of stream or river will depend on the characteristics of the

catchment and precipitation over the catchment. A hydrograph will assess

the flood flow of rivers hence it is essential that anticipated hydrograph

could be drawn for river for a given storm. A hydrograph indicates the

power available from the stream at different times of day, week or year. A

typical hydrograph is shown in the figure below.

A M J J A S O N D J F M A

Time

Fig. 2.4 A Typical hydrograph.

The main features of a hydrograph resulting from a single storm on a

basin are rising limb, a peak and a recession limb. Multiple peaks often

Rising Limb

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - -

Peak or crest

Point of inflexion

Point of inflexion

Recession Limb

Dis

char

ge

resulting from rain storms separated by periods of little or no rain or by areal

variation in storms are sometimes noticed.

The rising segment depends on the duration and intensity distribution

of rainfall and the antecedent condition of the drainage area. The peak of the

hydrograph represents the highest runoff in the drainage basin. It occurs at a

certain time after the rain has ended. The point of inflexion on the falling

segment is assumed to mark the time at which the surface inflow to the

channel system ceases. The recession represents the withdrawal of water

from the storage after all inflow of water from the storage into the channel

has ceased. It is more or less independent of the time variations, rainfall and

infiltration. It may be slightly dependent on area-rainfall distribution and it

depends heavily on the ground condition.

Generally, the hydrograph is used in computing storage and outflow

from reservoirs. Based on this research work, the concept of unit hydrograph

is of uttermost importance, as it offers opportunity of estimating runoff

discharge. This will be discussed extensively in later chapters.

2.6.1 Unit hydrograph method

The peak flow alone does not give sufficient information about the

runoff since it (peak flow) represents a momentary value. Therefore, it is

necessary to understand the full hydrography of flow. The basic concept of

unit hydrograph is that the hydrographs of runoff from two identical storms

would be the same. In practice, identical storms occur very rarely. The

rainfall generally varies in duration, amount and areal distribution. This

makes it necessary to construct a typical hydrograph for a basin which could

be used as a unit of measurement of runoff.

A unit hydrograph may be defined as the direct runoff hydrograph

corresponding to an effective unit precipitation (such as 1cm of rainfall) in a

specified time duration. The precipitation is assumed to occur uniformly

over the entire catchment. The important conditions implied in the above

definition must be effective;

(1) The precipitation must be effective.

Therefore, the total precipitation volume must equal the volume

indicated by the hydrograph curve. For the unit hydrograph, the direct runoff

corresponds to unity.

(2) The time of occurrence of the unit precipitation is a specified one.

This could be 3hrs, 4hrs, or 6hrs. For each time duration, the shape of the

unit hydrograph would be different. Also a 4-hr unit hydrograph corresponds

to an effective precipitation of 1/4cm/hr for 4hrs uniformly. Hence, it is

necessary to specify the duration of a unit hydrograph.

(3) The unit hydrograph is used to correlate the direct runoff with the

excess precipitation. Therefore, the resulting hydrograph does not include

the base flow.

The application of U.H method consists of two aspects;

(1) To arrive at the unit hydrograph of a suitable duration for the

catchment under consideration.

(2) To use the U.H derived for finding out the flood hydrograph

corresponding to any storm. For design purposes a design storm is

assumed which will with the help of the U.H give a design flood

hydrograph.

2.6.2 Construction of unit hydrograph.

The following steps are used for the construction of unit hydrograph:

(1) Choose an isolated intense rainfall of unit duration from past

records.

(2) Plot the discharge hydrograph for outlet from the rainfall records.

(3) Deduce the base flow from stream discharge hydrograph to get

hydrograph of surface records.

(4) Find out the volume of surface runoff which would correspond to

the area under the direct runoff hydrograph and convert this

volume into cm of runoff by dividing by the catchment area. This

runoff depth is the effective precipitation depth over the basin.

(5) Measure the ordinates of surface runoff hydrograph.

(6) Divide these ordinates by obtained run-off in cm to get ordinates of

unit hydrograph.

Thus for any catchment, unit hydrograph can be prepared once. Then

whenever peak flow is to be found out, multiply the maximum ordinate of

unit hydrograph by the runoff value expressed in cm. Similarly to obtain

runoff hydrograph of the storm of the same unit duration multiply the

ordinates of the unit hydrograph by the runoff value expressed in cm. If the

storm is of longer duration calculate the runoff in each unit duration of the

storm. Then super-impose the runoff hydrographs in the same order giving a

lag of unit period between each of them. Finally, draw a summation

hydrograph by adding all the overlapping ordinates. Generally, the

computations are done in a tabular form before the hydrograph is plotted.

The direct runoff depth or the effective precipitation depth is given

by;

Direct runoff depth = 0.36 X Σ0 X t

A (cm) …(2.1)

where;

Σ0 = Summation of DRO ordinates in cumecs

t = Time interval in hours between successive ordinates.

A = area of basin in km2.

The U.H ordinates will be

U.H ordinates = ordinates of DRO

depth of DRO ...(2.2)

Effective duration = 6 hours.

Unit

hydrograph

Peak

flow

Runoff hydrograph

Runoff time (hours)

Surf

ace

runoff

(m

3/s

)

Fig.2.5 showing how a runoff hydrograph is constructed from a unit

hydrograph.

2.6.3 Assumptions

The following assumptions have been made in the unit hydrograph

method:

(1) The base period of a direct runoff hydrograph corresponding to the

storm of the same duration but different intensities, is always

constant.

(2) The direct runoff hydrograph from a catchment corresponding to a

given period of rainfall reflects all the physical characteristics of

the basin lumped together. Hence, the unit hydrograph can be

viewed as the catchment response to an input precipitation of 1 cm

in same specified time.

(3) The principle of linearity applies. This means that the direct runoff

at any instant is directly proportional to the intensity of

precipitation.

(4) The principle of superposition applies. This means that the

combined hydrograph of the successive rainfalls can be obtained

by finding the direct runoffs for each rainfall period separately and

then superposing all such hydrograph.

2.6.4 Limitations of unit hydrograph method.

The limitations of the application of the unit hydrograph method are

that:

(1) Its use is limited to areas about 5000sq. kilometers since similar

rainfall distribution over a large area from storm- to- storm is

rarely possible.

(2) The odd-shaped basins (particularly long and narrow) have very

uneven rainfall distribution. Therefore, unit hydrograph method is

not adopted to such basins.

(3) In mountain areas, the areal distribution is very uneven; even then

unit hydrograph method is used because the distribution pattern

remains same from storm to storm.

2.7 The estimation, prediction and forecasting of runoff

Ideally, all hydrological problems would be solved by the use of

measured data, thus obviating the necessity for estimation, prediction, and

forecasting. There are many circumstances, however, in which the use of

these techniques becomes necessary. Thus, for example, there may be a

deficiency of measured data for a particular area, but there may be the

possibility of extrapolating future runoff trends either from existing runoff

data relating to adjacent or nearby areas or from precipitation data.

Alternatively, measured data may be collected too late to be of any use. Such

is the case in areas where peaks of quickflow constitute a flood problem

which must be viewed and solved in the light, not only of hydrological

factors, but also of factors of settlement and communications, agriculture,

and economics. Inevitably, the relevant measured data cannot become

available until the flood peaks themselves have occurred and so, in these

circumstances, the need is for techniques for accurately forecasting the

volume and timing of quickflow peaks. Again, in areas where water supplies

for agriculture, industry, or domestic uses are likely to be limited at times of

low flow; the need is for accurate forecasts of the magnitude of dry-weather

flows, and the time occurrence of minimum flow.

The main requirements, therefore; are for techniques to forecast, for a

given point within a drainage basin, both the total volume of runoff and the

magnitude of the instantaneous peaks normally associated with sudden

increases of quickflow and also to forecast the timing and magnitude of the

minimum flows which are likely to be associated with decreasing volumes

of baseflow, particularly groundwater flow. Most of the techniques currently

in use were developed before the newer concepts of runoff formation, which

shall be presented in this chapter, had been accepted or, in some cases, had

even emerged. Interestingly, however, many of these methods yield

reasonable results despite being conceptually weak or even erroneous. Such

successes may be fortuitous but techniques are either highly empirical, and

are often applicable only to restricted areas, or else are based upon factors

which, although not directly cause-related to the patterns of runoff under

consideration, are themselves directly affected by the real runoff-forming

factors.

Although, in normal English usage, the terms forecasting and

prediction are clearly synonymous, they are sometimes used in a more

restricted sense by hydrologists. Thus, as Smith (1972) observed, prediction,

in this context, refers to the application of statistical concepts to long periods

of data, usually relating to extreme events, with a view to defining the

statistical probability or return period of a given magnitude of flow. In other

words, there is no indication of when this particular flow will occur.

Forecasting, on the other hand, refers to specific runoff events, whether

floods or low flows, and to the use of current hydro-meteorological data in

order to provide a forecast of the magnitude of the runoff event and also, in

many cases, of its timing. As far as possible, this distinction will be

preserved in the ensuring discussions.

There are many techniques of runoff prediction and forecasting. Some

of these are in widespread use, either because they work reasonably well

over a wide range of conditions or else are easy to apply. The use of other

techniques may be restricted to specific areas or to specific users, such as a

particular Government agency. Most methods have little merit and yield

poor results. It would clearly be impossible to deal with all methods or even

a representative selection of the better ones. Indeed, in the present context

this would not, in any case, be appropriate. Instead, the main lines of

approach to the problem of runoff prediction and forecasting will be briefly

reviewed in general terms and will be illustrated, where appropriate, by

specific examples.

2.7.1 Annual and Seasonal Runoff

Reasonably accurate estimates of annul and seasonal runoff totals for

given catchment areas may, in some cases; be made from annual or seasonal

rainfall totals, using a simple straight line regression between the two

variables. Normally, however, such simple correlations between rainfall and

runoff may be expected to yield forecasts of only token accuracy and

certainly for shorter periods of hours, days or even weeks, more refined

techniques must be used.

Some improvement on the simple rainfall-runoff relationship may be

derived from procedure such as that proposed by Thonthwaite (Thornthwaite

and Mather, 1957). It was shown that a reasonably accurate forecast of

monthly and even shorter period runoff totals for a small drainage basin in

eastern England could be obtained from a simple consideration of rainfall

and potential evapotranspiration values (Ward, 1972).

Finally, it may in some cases be appropriate to consider vegetation

type as an indicator of potential runoff. Satterlund (1967) investigated the

use of forest vegetation in this respect and concluded that, in relation to the

USA, the technique would be more useful where water supplies are scanty,

as in the south-west, and useful where a considerable excess of water over

plant needs is available, as in Southern Appalachia.

2.7.2 Peak Flows

It has earlier been shown that increases in runoff after rainfall or

snowmelt tend to be rapid, leading quickly to a short-lived or instantaneous

peak, which is followed by a rather longer period of declining runoff. Since

it is likely to be the peak flow which causes damage to structures, or

flooding of agricultural land adjacent to streams, the main problems of

forecasting and prediction concern the magnitude and timing of this peak,

and the frequency with which it is likely to occur, although, it may also be of

interest to know in advance, say, the total volume of runoff, and there length

of the period between the beginning and the end of quickflow. Several

techniques may be used, and in the ensuing discussion, these will be

considered. The choice of method will normally be determined by the

purpose for which it is required, by the available data, and by the area and

characteristics of the drainage basin. In relation to the last point, for

example, there is clearly a major difference between a drainage basin of

1km2, where the runoff-producing storm may cover the entire area, and a

basin of several thousands of square kilometers, where a flood peak

generated on a small headwater stream by an isolated thunder storm will

move down the drainage system and where the main problem is to forecast

its change in shape and magnitude as it does so.

2.8 Empirical Formulae

In this method an attempt is made to derive a direct relationship

between the rainfall and subsequent run-off. For this purpose, some

constants are established which give fairly accurate results for a specified

region. Virtually all methods of runoff prediction and forecasting contain an

element of approximation and empiricism; the heading of this section may

be considered misleading. However, as with equality, so with empiricism,

some methods are more empirical than others. The main weaknesses of such

methods are normally their non-generality and the difficulty of knowing the

exact conditions under which they may be used. One of the earliest and best-

known attempts to estimate peak flows was the so-called rational formula.

2.8.1 Rational Method

The Rational method is an empirical relation between rainfall

intensity and peak flow that is widely accepted by hydraulic engineers;

however, the origin of the method is unclear. In the United States, Kuichling

(1889) was the first to mention the method in the scientific literature, yet

some engineers attribute the principles of the method to Mulvaney (1851). In

England, the method is often referred to as the Lloyd-Davis method, which

was published in 1906 (Chow, 1964).

The Rational Method is based on the theory that, for a given storm

frequency, the maximum runoff rate results from a rainfall intensity of

duration equal to the time of concentration of the particular basin. The

simplicity of the equation is misleading because “the critical value of the

rainfall intensity, through the medium of concentration time, entails a

consideration of such factors as basin size, shape, and slope; channel length,

shape, slope, and conditions; as well as variation in rainfall intensity,

distribution, duration, and frequency; all of which can and should be

considered in determining its value” (National Resources Committee, 1939).

Virginia Department of Transportation (VDOT) (2002) recommends

use of the Rational Method for estimating the design-storm peak runoff from

small basins with area up to 200 acres(2ha) and for up to 300 acres(3ha) in

low-lying tidewater areas. The method uses an empirical equation that

incorporates basin and precipitation characteristics to estimate peak

discharges (Chow, 1964). The Rational Method is relatively simple to apply;

however, its concepts are sophisticated. Considerable engineering

knowledge is required to select representative hydrologic characteristics that

will result in a reliable design discharge (Virginia Department of

Transportation, 2002). Validation of the Rational Method is difficult because

direct measurement of some hydrologic characteristics used in the method is

not easily accomplished.

2.8.1.1 Assumptions of the Rational Method

The rational method assumes that (Merit, 1976):

(1) The maximum rate of runoff for a particular rainfall intensity occurs if

the duration of rainfall is equal to or greater than the time of concentration;

(2) The maximum rate of runoff from a specific rainfall intensity whose

duration is equal to or greater than the time of the rainfall intensity;

(3) The frequency of occurrence of the peak discharge is the same as that of

the rainfall intensity from which it was calculated;

(4) The peak discharge per unit drainage area increases and the intensity of

rainfall decreases as its duration increases;

(5) The coefficient of runoff remains constant for all storms on a given

watershed.

(6) Precipitation is uniform over the time or space;

(7) Precipitation does not vary with time or space;

(8) Time of concentration is relatively short and independent of storm

intensity;

(9) Runoff is dominated by overland flow;

(10) Basin storage effects are negligible. (U.S Geological Survey, 2005)

The rational formula is given by;

Q = 0.278 CIA …(2.3)

where,

Q is the quantity of runoff in (m3/s);

C is the coefficient of runoff;

I is the rainfall intensity in (mm/hr);

A is the tributary or catchment area in (km2)

For the application of the above formula, C, I and A must be known, and A

in (m2), then;

Q = CIA in (m3/s). (Agunwamba, 2001)

2.8.1.2 Rainfall intensity (I)

The Rational Method uses a rainfall intensity to represent the average

intensity for a storm of a given frequency for a selected duration (Viessman

and others; 1977). As noted, assumptions of the method include that the

rainfall intensity is constant over the entire basin and uniform for the time of

concentration. Of all the assumptions associated with the Rational Method,

the assumptions of constant, uniform rainfall intensity are the least valid in a

natural environment. However, the variability of rainfall intensity during a

storm and over a basin becomes less as the size of the basin decreases such

that these assumptions become more valid. The variability of rainfall

intensity in time and space is a major reason for an upper limit on basin size

when using the Rational Method to estimate peak flow.

Rainfall intensity is selected from an intensity-duration-frequency

(IDF) curve generated from point rainfall data collected in the local area.

This is, however, possible if both the duration (Tc) and the storm return

period (T) are known. These curves are generated by fitting annual

maximum rainfall intensities for specified durations to a Gumbel-probability

distribution, usually by plotting the data on extreme-value-probability paper

(Mckay, 1970). Figure 2.6 is an example of an IDF curve plotted on

arithmetic paper. The rainfall intensity is estimated by transferring the basin

time of concentration as duration in minutes through the desired storm

frequency curve in the same manner as shown in figure 2.6. For example, if

the hypothetical IDF curve in figure 2.6 is valid for the basin being analyzed

and it is determined that a basin has a time of concentration of 20 minutes,

then the rainfall intensity for the 25-year storm is 5.2 in/hour.

Oyebande and Longe (1990) obtained an empirical formula by using

Gumbel Extreme value distribution. In order to overcome the problem of

inadequate length of available records and poor aerial coverage of

hydrological data, data from individual stations of areas with similar rainfall

distribution were pooled together.

The equation obtained for rainfall intensity expressed in mm/hr is;

I = KTmtn

1-1

…(2.4)

where

K, m, and n1 are parameters dependent on the regions as classified in

Table 2.1;

T is the return period (yrs); and

t is the rainfall duration in (hrs).

If t<1, n1 is replaced by n2.

Table 2.1: Values of the parameters for computing rainfall intensity for

different regions.

Regions/stations Parameters

K M N1 N2

Group I

Port Harcourt, Calabar,

Umudike

54

0.26

-0.86

-0.38

Group II

Warri, Benin

47

0.28

-0.85

-0.38

Group III

Lagos, Ikeja, Oshodi

34

0.30

-0.89

-0.47

Group IVa

Oshogbo, Ondo, Ilora, Ibadan

40

0.28

-0.87

-0.51

Group IVb

Markudi, Enugu

38

0.32

-0.90

-0.48

Group VI

Bida, Ibi, Yola

38

0.32

-0.90

-o.52

Group VIIa

Lokoja, Minna

32

0.25

-0.90

-0.60

Group VIIb

Sokoto, Yelwa

33

0.27

-0.87

-0.61

Group VIII

Kano, Gusau, Zaria, Bauchi,

Samaru

33

0.32

-0.88

-0.60

Group IX

Potiskum, Maiduguri

32

0.30

-0.89

-0.59

Group X

Nguru, Karsina

30

0.32

-0.95

-0.64

Source: Oyebande and Longe (1990).

12-

11-

10-

9-

8-

7-

6-

5-

4-

3-

2-

50-yr

2-yr

5-yr

10-yr

25-yr

100-yr

Storm Frequency

RA

INF

AL

L I

NT

EN

SIT

Y, IN

CH

ES

PE

R H

OU

R

1-

0 10 20 30 40 50 60 70

Fig. 2.6 Hypothetical intensity-duration-frequency (IDF) curve. (plotted

from data provided by the U.S Geological Survey for small basins in Central

Virginia). (U.S.G.S, 2005).

The return period is chosen from 2 to 5 years, if damage due to

flooding is small, and from 20 – 100 years

when the damage is great (e.g when basements in commercial areas can be

flooded). Typical frequency (return) periods of storm sewers for different

districts are shown in Table 2.2 below (Agunmamba, 2001).

Table 2.2: Frequency periods of storm sewers for different areas.

Areas Frequency Period

Residential Areas 2-10 years

Commercial and high value district 10-50 years

Flood protection works 50 years

Urban roads 5 years

Source: Federal Republic of Nigeria Highway Manual Part 1.

2.8.1.3 Runoff coefficient (C)

The runoff coefficient, c is a dimensionless empirical coefficient

related to the abstractive and diffusive properties of the basin. Basin

abstractions including infiltration, depression storage, evapotranspiration,

and interception are lumped into the coefficient. Runoff diffusion is a

measure of the attenuation of the flood peak attributable to basin runoff

characteristics (Ponce, 1989). The runoff coefficient ranges between 0 and

1.0, where a value of 0 indicates that none of the rain falling on the basin

generates runoff, and a value of 1.0 indicates that all of the rain falling on

the basin generates runoff. A basin that has low land-surface slopes, high

infiltration rates, high ground-water storages, and extensive vegetation and

surface storage will have a low runoff coefficient. A steep basin with an

impervious surface, little vegetation, and no surface storage will have a high

runoff coefficient. Values of coefficient of runoff (C) for different vegetative

covers and slopes are given in Table 2.3.

Table 2.3: Runoff coefficient values for urban areas

Flat Rolling hilly

2-10% 10%

Pavement and roofs 0.90 0.90 0.90

Earth shoulders 0.50 0.50 0.50

Drives and walks 0.75 0.80 0.85

Gravel pavement 0.50 0.55 0.60

City business areas 0.80 0.85 0.85

Apartment dwelling areas 0.50 0.60 0.70

Normal Residential areas 0.40 0.50 0.55

Dense Residential areas 0.50 0.65 0.70

Lawn, sandy soil areas 0.10 0.15 0.20

Lawn, heavy soil areas 0.20 0.25 0.35

Grass shoulders 0.25 0.25 0.25

Side turfed slopes 0.30 0.30 0.30

Cultivated land (clay and loam) 0.50 0.55 0.60

Cultivated land (sand and gravel) 0.25 0.30 0.35

Industrial area 0.50 0.70 0.80

Parks and Cemeteries 0.10 0.15 0.20

Play grounds 0.20 0.25 0.30

Woodland and forests 0.10 0.15 0.20

Meadows and pasture land 0.25 0.30 0.35

Unimproved areas 0.10 0.30 0.30

Source: Federal Republic of Nigeria Highway Manual Part I ‘Drainage

Design’ section I.

2.8.1.4 Catchment Area (A)

This is the area contributing runoff into the drain. It is determined

from the topographical map by breaking the area into regular figures,

calculating each and summing up. A planimeter may also be used.

2.8.1.5 Design Computations

The VDOT (2002) design manual recommends use of the Rational

method for peak discharge design for acres up to 200 acres(2ha) except in

low-lying tide water areas where the method can be used for areas up to 300

acres(3ha). The form of the Rational Equation recommended by VDOT

(2002) is;

Q=Cf.C.I.A …(2.5).

where,

Q is the peak flow in (ft3/s),

Cf is the design storm frequency adjustment factor (dimensionless),

C is the runoff coefficient (dimensionless),

I is average rainfall intensity from an intensity-duration-frequency

curve for a duration equal to tc in (in/hour),

A is areas in acres,

Tc is time of concentration in minutes.

The only difference in this form of the Rational Equation and equation

(2.4) is inclusion of the storm frequency adjustment factor, Cf. Many

investigators have concluded – in contrast to the basic assumptions of the

Rational method – that the runoff coefficient varies with rainfall intensity

and duration (Ponce, 1989; Beadles, 2002; Pilgrim and Cordery, 1993), and

recommend that the runoff coefficient be adjusted for design of less frequent

floods. Values for Cf are selected from a chart, see fig. 4.10. A value of 1.0

is used when the combined value of C+Cf is greater than 1.0.

2.8.1.6 Time of Concentration

Time of concentration has several definitions. The minimum time

required after runoff begins for the entire basin to contribute flow to the

outlet is the definition preferred by the authors. Other definitions are the

time required for a particle of water to travel from the most hydraulically

distant point in the basin to the outlet (Wigham, 1970), and the time required

for a flood wave to travel from the most hydraulically distant point to the

outlet (National Resources Committee, 1939).

VDOT (2002) defines time of concentration as the time required for

water to flow from the hydraulically most distant point to the outlet.

Determination of time of concentration consists of combining flow times for

overland flow, channel flow, and conveyance flow in pipes, as appropriate,

at several locations within the basin. Overland flow computations should be

limited to approximately 200ft(61m) and either the Seelye method or

kinematic wave method used to compute flow times. For channel flow

computations, VDOT (2002) recommend use of the nomograph developed

by P.Z. Kirpich. No recommendations are given for determining flow time

through pipes.

The rainfall duration is assumed equal to the time of concentration

which is the time required for water to flow from the most remote part of the

area to the outlet. The time of the overland flow is influenced mainly by the

ground slope, surface cover and flow length.

The rainfall duration is assumed equal to the time of concentration

which is the time required for stormwater to flow from the most remote part

of the area to the outlet where measurements are being considered. The time

of overland flow is influenced mainly by the ground slope, surface cover and

flow length.

The time of concentration is the sum of the inlet time (ti) (time

required for runoff to gain entrance to the drain, assumed to vary from 1 to

20mins) and the flow time (tf) (time required by the stormwater to flow from

the beginning of the drain to the end). The time of concentration (mins) may

be expressed as,

Tc = 0.0078(L)0.77

(S)0.5

...(2.6)

where,

L is the flow path distance (ft) from the remotest part of the water

catchment to the drain outlet, while

S is the surface shape (slope).

These parameters are determined from the topographical map of the

project area. After metric conversion of L to meters,

Tc = 0.01947(L)0.77

(S) 0.5

… (2.7)

Tc and T are known, I can be determined from a rainfall duration

curve (e.g., fig. 4.9). where T is the storm return period in years. In some

areas where these graphs do not exist or cannot be produced because of lack

of data, it is usual to use rainfall-duration curves of other areas of similar

rainfall distribution.

The time of concentration, Tc and rainfall intensity may also be

computed using Izzard method (1946). That is,

Tc = 526.423bL1/3

(CrI)2/3

…(2.8)

The equation is valid only for laminar flow conditions where the product. IL

is less than 3871.

The coefficient b is expressed by

b = 2.8 X105 I Cr

S1/3

…(2.9)

The parameter Cr is the retardance coefficient with values 0.07 for

smooth asphalt surface, 0.012 for concrete pavement, 0.017for Tar and

gravel pavement and 0.060 for dense blue grass turf. Obtaining I using the

Izzard method (equation 2.8) involves trial and error since Tc is expressed as

a function of I.

Empirical relationships between rainfall duration and I also exist. For

instance,

I = a

t + b … (2.91)

where a and b are locality constants; a = 1846 and b = 3.6 for eastern part of

Nigeria.

For t>12 mins.

I = Co

ts …(2.92)

Typical value are s = ½ and Co = 446.

2.8.2 Khosla’s Formula:

R=P-4.811T …(2.93)

where,

R = annual runoff in (mm)

P = annual rainfall in (mm)

T = mean temperature in degree centigrade

2.8.3 Inglis Formulae for hilly and plain areas:

For hilly region

R = 0.88P – 304.8 ... (2.94)

For plain region,

R = (P – 177.8) X P

2540 ...( 2.95)

2.8.4 Lacey’s Formula:

R = P

1+3084F

PS ….(2.96)

where,

R = monsoon runoff in (mm)

P = monsoon rainfall in (mm)

S = catchment area factor

F = monsoon duration factor.

Values of S for various types of catchment area given below;

Types of catchment Values of S

Flat, cultivated and black cotton soils. 0.25

Flat, party cultivated, various soils. 0.60

Average catchment. 1.00

Hills and places with little cultivation 1.70

Very hilly and steep, with hardly any cultivation. 3.45

Values of F for various durations of monsoon are given below;

Class of monsoon Values of F

Very short 0.50

Standard length 1.00

Very long 1.50

2.8.5 Statistical Method

Hazen (1914) was one of the first to apply statistical methods to low

flow forecasting. As with peak flows, statistical methods are based on the

assumption that conditions recorded in the past will be repeated in the future

so that the reliability of these methods has inevitably improved considerably

since Hazen’s initial work simply because of the availability of longer and

more widespread flow records (Hudson and Hazen, 1964). Forecasting

procedures may be concerned with evaluating the minimum flow which is

likely to occur in the most severe drought conditions but are more frequently

concerned with estimating the probability of occurrence of low flows of a

given magnitude and with the duration of flows below a certain threshold

value.

An elementary but useful method is to plot a runoff duration curve,

either for the catchment whose low flow is to be predicted, or for adjacent

catchments, if no runoff records are available for the area in question.

An estimate of the frequency with which a given magnitude of runoff

may be exceeded in the future is based upon consideration of the recorded

historical pattern of runoff events. Unfortunately, the duration of runoff

records is normally so short that it is difficult to extrapolate them with a high

degree of reliability. In essence the main problem is that flood frequency

estimation involves the estimation of the tail of a probability distribution

curve from a sample of values which usually does not include values within

this tail (Melentijevich, 1969). However, statistical methods of extreme

value frequency analysis have been designed to extract the maximum

information from the recorded data and to evaluate the likely nature of the

distribution of the parent population from which the sample has been drawn

(Bruce and Clark, 1966).

Various methods of plotting extreme value data and of drawing

frequency curves through the plotted points have been devised, including

several types of special plotting paper on which the data will plot as a

straight line and are therefore, easier to extrapolate (Bruce and Clark, 1966).

One of the simplest and most practical methods of computing flood

frequency is as illustrated in Table 2.3 and Fig. 2.7. In this hypothetical

example the problem is to predict the likelihood of a certain sized runoff

peak occurring during a specified time, on a stream whose flow has been

measured for, say, 24 years. Using the annual maximum series, the peak

flows recorded during that period are arranged in descending order of

magnitude and the recurrence interval and probability are determined as

shown in Table 2.3. If the size of the peak flow and the probability are then

plotted on log-probability paper, as shown in fig. 2.7A, it will be seen that an

approximately straight line is described, which it is possible to extend in

order to predict floods with probability factors, within or outside the range

represented by the sample data. Alternatively, runoff may be plotted against

recurrence interval on semi-logarithmic coordinates as shown in fig. 2.7B.

Mathematical analyses have demonstrated that the mean annual flood has a

recurrence interval of 2.33 years, i.e., on average, the annual maximum flow

will exceed the mean maximum flow once every 2.33 years, and this

recurrence interval is indicated by the broken line.

This type of technique is quite successful provided that a long

sequence of recorded data is available. Where, however, the records are brief

or intermittent there is a considerable danger that the sample data will be

inadequate, and that extrapolations based upon them will be grossly

inaccurate. One frequently used method of reducing sampling error is

regional analysis, whereby data from within homogeneous area, or from

adjacent similar areas, are combined to increase the sample size, and thus to

improve the quality of the result (Alexander, 1963; Satter lund, 1967). A

homogeneity test was developed by Langbein (1947) to define a

homogeneous region and various methods of regional analysis have been

developed, including the construction of regional flood frequency curves

(Dalrymple, 1960).

Table 2.3 Probability and recurrence interval calculated from a 24 year

annual maximum series for a hypothetical stream

Runoff Peak

(cumecs)

Order number

(m)

Probability m_

n+1

(Percent)

Recurrence Interval

n+1

m (years)

150000 1 4 25.00

135000 2 8 12.50

126000 3 12 8.33

117000 4 16 6.25

114000 5 20 5.00

108000 6 24 4.17

105000 7 28 3.57

102000 8 32 3.13

100500 9 36 2.78

96000 10 40 2.50

93000 11 44 2.27

91500 12 48 2.08

87000 13 52 1.92

84000 14 56 1.79

81000 15 60 1.67

79500 16 64 1.56

78000 17 68 1.47

75000 18 72 1.39

72000 19 76 1.32

70500 20 80 1.25

66000 21 84 1.19

63000 22 88 1.14

57000 23 92 1.09

51000 24 96 1.04

where n is the number of years o record and m is the rank of the item in the

array.

300 -

200 -

150 -

100 -

50 -

30 - Runoff

in c

um

ecs

(thousa

nds)

-

10 -

99.99 99.8 98 80 50 20 2.0 0.2 0.0

Probability (percent)

Fig. 2.7A Log-Probability graph of peak flows listed in Table 3.4

220 -

200 -

180 -

160 -

Runoff

in c

um

ecs

140 -

120 -

100 -

80 -

60 - Q2.33

1 2 3 5 10 20 30 50 100 200 300

Recurrence interval (return period) in years

Fig. 2.7B Recurrence interval graph of peak flows listed in Table 2.3.

2.9 Direct Measurement of runoff.

The reliability of many hydrological measurements, e.g., rainfall and

evapotranspiration, depends upon the representativeness of the catchment, in

the case of rainfall, or the loss, in the case of evapotranspiration, from a very

small sample area. Only a minute part of the total volume of rain falling on a

catchment area, for example, is caught by even an extremely dense network

of gauges, and yet large varieties of rainfall over small distances is usually

recorded.

In the case of measurements of runoff, however, inaccuracies

resulting from this type of sampling do not occur, since the total volume of

streamflow which passes a given point may be measured. If the measuring

device is located at the lowest point in a catchment area, and providing there

is no leakage of underground water across the divides, it may be assumed

that all the streamflow from the catchment area will pass the measuring

point. From this point of view, therefore, runoff data should be more reliable

than any other of the basic hydrological data.

2.9.1 Velocity – area method

The velocity-area method comprises three related operations. The first

involves the determination of the height or stage of the stream surface; the

second the determination of the mean velocity of the stormwater flow in the

stream channel; and the third the derivative of a known relationship between

stage and the total volume of discharge.

The discharge of a stream, i.e, the total volume of water flowing past a

given point in a known unit of time, is the product of the cross-sectional area

of the stream and the speed with which the water is flowing. Provided that

the stream bed and banks have been accurately surveyed at the point of

measurement, only data on the storage of the stream is needed to enable the

cross-sectional area of the water in the stream channel to be rapidly

calculated. Thereafter, the volume of discharge may be readily calculated if

the mean velocity of the current is known.

The measurement of current velocity in streams and rivers is normally

accomplished by means of a current meter. Alternatively, current velocities

may be determined directly using deflecting vanes, pitometers or floats or

may be estimated by means of one of the commonly used theoretical flow

equations for the steady flow of water in open channels such as that

proposed by Manning (1889) or Chezy.

2.9.2 Weirs and Flumes

On streams where a physical obstruction in the channel is permissible,

e.g., small tributaries and drainage channels which are not used for

navigation, discharge may be accurately measured by means of a weir or

flume. These are rigid structures whose cross-sectional area is closely

defined and stable and which, therefore act as a permanent control. Since the

velocity of falling water (or indeed of any other substance) depends solely

on the height of fall and the acceleration due to gravity (i.e., V2 = 2gh), and

since the acceleration due to gravity is constant, it follows that, in order to

measure accurately the velocity of a stream, it is only necessary to cause the

water to fall (as over a weir or through a flume), and to measure the head of

water by means of a continuous recorder at an appropriate point. Insofar as

this basic theory of measurement is concerned, the only significant

difference between weirs and flumes is that there is a loss of head (and of

kinetic energy) over the weir, whereas there is a considerable recovery of

head (preservation of kinetic energy) in the case of the flume.

There are two main types of weirs, which are; sharp-crested and

broad-crested, the former being more commonly used where precise

measurement is required. One important advantage of the flume is that it is

self-cleansing because of the high velocity through and below the control

section. Because of this, it is particularly suited to discharge measurement in

silt and debris-laden water.

CHAPTER THREE

METHODOLOGY

The studys for which the available data were obtained was aimed at

estimating runoff discharge using the unit hydrograph method, rational

method, Khosla and Inglis formulae. For the present case, the aim is to

compare the results of these methods with the measured peak discharge at

the catchment outlets. The available data was obtained from series of field

measurements through the use of the current meter and the meter rule, to

determine the velocity and depth of flow respectively.

3.1 Gauge Stations

The catchment area was divided into four sub-areas. This was done

such that the time of concentration increases from one sub-area to the next.

Thus the times of concentration for the sub-areas I, II, III and IV are 30min,

33min, 36min and 40min respectively. Thus, in the first 30min, only the sub-

area I contributes the discharge at outlet. In the next 3min, both the areas I

and II contribute, and so on. Hence, each sub-areas contributes to the total

discharge from the catchment during the entire storm period.

Runoff then can be computed from the discharge and time as in the

hydrograph method.

3.2 Empirical Formulae

In this method an attempt is made to derive a direct relationship

between the rainfall and subsequent run-off. For this purpose some constants

are established which give fairly accurate result for a specified region.

Virtually all methods of runoff prediction and forecasting contain an element

of approximation and empiricism; the heading of this section may be

considered misleading. However, as with equality, so with empiricism, some

methods are more empirical than others. The main weaknesses of such

methods are normally their non-generality and the difficulty of knowing the

exact conditions under which they may be used. One of the earliest and best-

known attempts to estimate peak flows was the so-called rational formula.

3.3 Velocity – area method

The velocity-area method comprises three related operations. The first

involves the determination of the height or stage of the stream surface; the

second is the determination of the mean velocity of the water flowing in the

stream channel; and the third the derivative of a known relationship between

stage and the total volume of discharge.

The discharge of a stream, i.e, the total volume of water flowing past a

given point in a known unit of time, is the product of the cross-sectional area

of the stream and the speed with which the water is flowing. Provided that

the stream bed and banks have been accurately surveyed at the point of

measurement, only data on the storage of the stream is needed to enable the

cross-sectional area of the water in the stream channel to be rapidly

calculated. Thereafter, the volume of discharge may be readily calculated if

the mean velocity of the current is known.

The measurement of current velocity in streams and rivers is normally

accomplished by means of a current meter. Alternatively, current velocities

may be determined directly using deflecting vanes, pitometers or floats or

may be estimated by means of one of the commonly used theoretical flow

equations for the steady flow of water in open channels such as that

proposed by Manning, (1889).

3.4 Unit hydrograph method

The peak flow alone does not give sufficient information about the

runoff since it (peak flow) represents a momentary value. Therefore, it is

necessary to understand the full hydrography of flow. The basic concept of

unit hydrograph is that the hydrographs of runoff from two identical storms

would be the same. In practice, identical storms occur very rarely. The

rainfall generally varies in duration, amount and areal distribution. This

makes it necessary to construct a typical hydrograph for a basin which could

be used as a unit of measurement of runoff.

0

1

2

3

4

5

6

0 3 6 9 12 15 18 21 24 27 30

Time (Hrs)

3Hrs-Unit-Hydrograph

0

0.05

0.1

0.15

0.2

0.25

0 3 6 9 12 15 18 21 24 27 30

Times (Hrs)

Dis

ch

arg

e (

cu

me

cs

)

(cu

me

cs

)

Fig. 4.1: A 3-hr Effective Duration of Storm

Hydrograph

STATION I D

isc

harg

e (

cu

me

cs

)

CHAPTER FOUR

RESULTS AND ANALYSIS

4.1 Unit Hydrographs

Fig. 4.2: A 3-hr Unit Hydrograph

3Hrs-Storm Hydrograph

0

1

2

3

4

5

6

0 3 6 9 12 15 18 21 24 27 30

Time (Hrs)

Dis

ch

arg

e (

cu

me

cs

)

3-Hrs-Unit Hydrograph

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 3 6 9 12 15 18 21 24 27 30

Time (Hrs)

Dis

ch

arg

e (

cu

nm

ec

s)

Fig. 4.4: A 3-hr Unit Hydrograph

STATION II

Fig. 4.3: A 3-hr Effective Duration of Storm

Hydrograph

STATION III

3-Hrs storm Hydrograph

0

1

2

3

4

5

6

0 3 6 9 12 15 18 21 24 27 30

Time (Hrs)

Dis

ch

arg

e (

cu

me

cs

)

3-Hrs Unit Hydrograph

0

0.02

0.04

0.06

0.08

0.1

0.12

0 3 6 9 12 15 18 21 24 27 30

Time (Hrs)

Dis

ch

arg

e (

cu

me

cs

)

Fig. 4.6: A 3-hr Unit Hydrograph

Fig. 4.5: A 3-hr Effective Duration of Storm

Hydrograph

STATION IV

3-Hrs Storm Hydrograph

0

1

2

3

4

5

6

0 3 6 9 12 15 18 21 24 27 30

Time (Hrs)

Dis

ch

arg

e (

cu

me

cs

)

3-Hrs Unit Hydrograph

0

0.01

0.02

0.03

0.04

0.05

0.06

0 3 6 9 12 15 18 21 24 27 30

Time (Hrs)

Dis

ch

arg

e (

cu

me

cs

)

Fig. 4.8: A 3-hr Unit Hydrograph

Fig. 4.7: A 3-hr Effective Duration of Storm

Hydrograph

4.2 Rational Formula

Intensitiy -Duration Frequency Curve

0

50

100

150

200

250

300

350

400

450

500

30 60 90 120

Duration of Rainfall (min)

Rain

fall

in

ten

sit

y (

mm

/hr)

2-Yr rainfall intensity (mm/hr)

5-Yr rainfall intensity (mm/hr)

10-Yr rainfall intensity (mm/hr)

100-Yr rainfall intensity(mm/hr)

Fig.4.9: Intensity-Duration Frequency (IDF) curve of Nsukka campus.

The catchment area was obtained from the topographical map, I from

fig. 4.9 while C was obtained from a table (Agunwamba, 2001). These

values and the corresponding discharges obtained from the rational formula

are given in Table 4.1.

Table 4.1 Discharge obtained from Rational formula.

STATION Area, A

(km2)

Rainfall

Intensity, I

(mm/hr)

Coefficient of

Runoff,C

Discharge

(cumecs)

I 0.765 220 0.40 18.715

II 0.573 210 0.40 13.381

III 0.383 200 0.40 8.519

IV 0.191 190 0.40 4.035

DESIGN STORM FREQUENCY ADJUSTMENT FACTOR [Cf]

The maximum rainfall intensity, Imax = 446.2 mm/hr. Using a storm frequency

adjustment factor (Cf) of 0.30 for the maximum storm intensity (since runoff

coefficient varies with rainfall intensity and duration and constitute about

30% of basin losses) (VDOT, 2002).

Cf=Ip X 0.30 …(4.1)

Imax

where, Ip = peak storm intensity for the year.

Year Ip (mm/hr) Imax (mm/hr) Cf

1973 446.20 446.20 0.30

1981 439.70 ,, 0.30

1974 429.60 ,, 0.29

1979 404.20 ,, 0.27

1980 373.30 ,, 0.25

1972 372.70 ,, 0.25

1971 364.90 ,, 0.25

1978 364.90 ,, 0.25

2007 327.66 ,, 0.22

1975 327.30 ,, 0.22

2008 326.02 ,, 0.22

2006 313.94 ,, 0.21

1982 312.90 ,, 0.21

1976 306.70 ,, 0.20

1977 251.20 ,, 0.17

1983 241.20 ,, 0.16

0.30 –

0.20 –

0.1 –

0 20 40 60 80 100 120 140 160 180 200 220

Mean Annual Rainfall Intensity

(mm/hr)

Des

ign

sto

rm-f

req

uen

cy a

dju

stm

ent

fact

or

(Cf)

Fig. 4.10: Design storm frequency adjustment factor chart

Design Computations

The modified rational formula is given by;

Q = 0.278 Cf CIA

where, Cf = design storm frequency adjustment factor (obtained from chart)

Table 4.2 Discharge obtained by the various methods.

STATION Modified

Rational

method

Khosla’s

Formula

Inglis Formula Velocity

Area

method

(measured)

Cf Discharge

(cumecs)

T

(oC)

Discharge

(cumecs)

P

(mm)

Discharge

(cumecs)

Discharge

(cumecs)

I 0.17 3.182 25.5 0.861 220 0.032 0.188

II 0.18 2.409 25.5 0.773 210 0.024 0.144

III 0.19 1.619 25.5 0.684 200 0.015 0.102

IV 0.19 0.767 25.5 0.596 190 0.008 0.050

0

0.5

1

1.5

2

2.5

3

3.5

1 2 3 4

Stations

Dis

ch

arg

e (

cu

me

cs

)

Modified Rational Formula

Khosla

Inglis

Measured

Unit Hydrograph

Fig. 4.11: A graph of Discharges against Station for all the methods used.

4.3 Relationship between Estimated and Measured Runoff

Discharge

Qe = 17.6Qm – 0.135 ---------------------------- Rational Formula

Qe = 1.115Qm ----------------------------------- Unit Hydrograph Method

Qe = 1.93Qm + 0.494--------------------------- Khosla’s Formula

where, Qe = Estimated runoff discharge at the catchment.

Qm = measured runoff discharge at the catchment.

From the results obtained above, the unit hydrograph method gave

the best estimation of the runoff discharge when compared with other

methods, for all the sub-catchments. Only the Inglis formula gave discharge

estimates below the observed discharges at each of the sub-catchments. It is

therefore not suitable for these catchments.

CHAPTER FIVE

CONCLUSION AND RECOMMENDATION

5.1 CONCLUSION

This project work reviewed and compared the different methods

of runoff discharge estimation for drainage design. The design of a drainage

structure requires hydrologic analysis of precipitation amount and duration,

peak rate of runoff, and the time distribution of runoff from a given basin.

Many hydrologic methods are available for estimating peak flows from a

basin, and no single method is applicable to all basins. Although, of all the

methods reviewed, the unit hydrograph method gave a much closer

estimation of the basin peak flows, it is however not widely applied owing to

the disadvantages of non-availability of runoff data for a minimum of

25years for a particular catchment and the cost for obtaining such data.

Although, the Khosla’s formula proved relatively effective in the estimation

of the basin peak flow, it is however, limited in application since basin

hydrological characteristics vary significantly from catchment to catchment.

The rational formula, though it over-estimates, is commonly used

to estimate the design-storm peak discharge. The advantages of this method

are its simplicity in application, relative availability of data and low cost of

obtaining these data. Once a basin rainfall intensities for a minimum of 25

years are available, the rational formula can then be applied. With the

modification in the rational formula, it is therefore considered appropriate

for the estimation of runoff discharge in many basins particularly in regions

were sufficient hydrologic data are not available.

5.2 RECOMMENDATIONS

(1) The unit hydrograph method is recommended for a basin whose

runoff data are available for a minimum of 25 years.

(2) Where these data are insufficient, the improved rational formula

can be applied.

(3) In applying the modified rational formula, effort should be made

to obtain the design storm frequency adjustment factor (Cf) chart peculiar to

the region of interest.

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international Hydrological Programme (IHP) Maiduguri, 26th

– 28th

, pp. 335.

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Civil engineers, London.

APPENDIX I

Rainfall intensity of the University of Nigeria, Nsukka Campus.

Rainfall intensity for the year 2006.

Month Rainfall intensity

(mm/hr)

No. of rain (days)

January 36.32 1

February 4.06 2

March 103.12 4

April 51.05 5

May 243.83 16

June 259.60 16

July 213.86 21

August 195.58 19

September 190.50 25

October 313.94 19

November 1.54 1

December - -

Mean Rainfall Intensity = 146.67mm/hr.

2007

Month Rainfall intensity

(mm/hr)

No. of rain (days)

January - -

February 9.91 1

March 39.12 4

April 121.66 8

May 193.55 11

June 327.66 16

July 62.99 14

August 323.60 17

September 169.67 19

October 267.20 18

November 55.12 4

December - -

Mean Rainfall Intensity = 157.05mm/hr.

APPENDIX II

2008.

Month Rainfall intensity No. of rain (days)

(mm/hr)

January - -

February - -

March 61.23 4

April 143.30 11

May 254.01 12

June 186.43 15

July 246.10 14

August 203.20 19

September 326.02 22

October 198.63 11

November 8.38 2

December 10.93 2

Mean Rainfall Intensity = 163.82mm/hr.

1983

Month Temperature

(oC)

Wind

speed

(km/day)

Sunshine

(hours)

Humidity

(%)

Rainfall

(mm/month)

Max. Min.

January 30.0 18.0 223.0 4.7 20.0 0.0

February 34.0 20.0 156.9 5.7 54.0 0.0

March 35.0 21.0 168.3 3.2 51.7 0.0

April 35.0 21.0 183.9 5.2 68.8 13.7

May 31.0 19.0 156.1 1.5 78.0 114.9

June 28.0 19.0 133.6 0.8 86.0 168.5

July 27.0 18.0 122.0 0.6 89.0 158.3

August 26.0 18.0 96.7 1.0 92.0 102.4

September 28.0 18.0 67.6 1.4 67.0 241.2

October 29.0 17.0 75.6 2.0 79.0 55.8

November 31.0 19.0 96.8 1.8 75.0 33.1

December 31.0 18.0 99.3 1.9 67.0 11.2

Mean Rainfall intensity = 99.90 mm/hr.

APPENDIX III

1982

Month Temperature

(oC)

Wind

speed

(km/day)

Sunshine

(hours)

Humidity

(%)

Rainfall

(mm/month)

Max. Min.

January 32.0 21.0 127.0 6.5 40.0 17.3

February 33.0 22.0 149.7 5.9 59.0 55.7

March 32.0 22.0 157.8 6.1 51.0 56.4

April 32.0 22.0 169.2 6.3 76.0 83.4

May 30.0 21.0 114.1 5.4 81.0 217.2

June 27.0 20.0 119.8 4.2 86.0 225.4

July 27.0 19.0 113.8 3.1 90.0 312.9

August 26.0 19.0 136.3 2.3 90.0 180.9

September 27.0 19.0 88.5 2.5 88.0 228.5

October 28.0 19.0 97.8 4.3 65.0 303.1

November 30.0 18.0 99.8 6.6 64.0 19.0

December 32.0 18.0 108.5 6.7 66.0 0.0

Mean Rainfall intensity = 154.53 mm/hr

1981

Month Temperature

(oC)

Wind

speed

(km/day)

Sunshine

(hours)

Humidity

(%)

Rainfall

(mm/month)

Max. Min.

January 31.0 19.0 142.5 6.0 45.0 4.8

February 34.0 24.4 172.8 6.2 68.0 0.0

March 33.0 23.0 186.3 5.4 75.0 53.7

April 33.0 23.0 196.3 6.1 73.0 26.2

May 31.0 22.0 145.0 5.0 89.0 286.9

June 29.0 22.0 147.0 4.9 83.0 84.3

July 27.0 21.0 146.7 3.1 80.0 184.7

August 27.0 21.0 132.9 2.6 81.0 271.7

September 28.0 21.0 98.4 2.6 77.0 439.7

October 29.0 21.0 102.2 4.8 76.0 234.3

November 30.0 19.0 111.7 6.8 64.0 32.5

December 32.0 19.7 107.2 7.3 61.0 0.0

Mean Rainfall intensity = 161.88 mm/hr

APPENDIX IV

1980

Month Temperature

(oC)

Wind

speed

(km/day)

Sunshine

(hours)

Humidity

(%)

Rainfall

(mm/month)

Max. Min.

January 33.0 21.0 137.4 7.6 63.0 0.0

February 34.0 23.0 146.8 4.9 68.0 7.6

March 33.0 23.0 177.5 5.7 68.0 63.5

April 32.0 23.0 175.1 5.7 60.0 118.7

May 30.0 23.0 133.2 5.2 82.0 146.8

June 29.0 22.0 138.2 5.3 84.0 182.9

July 27.0 22.0 128.9 3.2 88.0 346.6

August 27.0 21.0 114.6 3.3 91.0 362.3

September 28.0 21.0 85.6 3.4 84.0 373.3

October 29.0 21.0 91.9 4.5 82.0 190.3

November 30.0 21.0 92.9 6.1 76.0 38.6

December 30.0 20.0 139.3 6.6 58.0 0.0

Mean Rainfall intensity = 183.06 mm/hr

1979

Month Temperature

(oC)

Wind

speed

(km/day)

Sunshine

(hours)

Humidity

(%)

Rainfall

(mm/month)

Max. Min.

January 33.0 20.0 131.4 8.2 56.0 0.0

February 32.0 23.0 149.3 6.2 76.0 48.8

March 33.0 23.0 147.1 5.1 73.0 23.9

April 33.0 23.0 174.8 0.0 73.0 100.6

May 30.0 22.0 126.0 5.6 80.0 198.5

June 29.0 22.0 144.7 4.8 83.0 135.6

July 28.0 21.0 148.3 3.4 85.0 326.2

August 27.0 21.0 150.6 2.7 90.0 404.2

September 28.0 21.0 96.8 4.1 82.0 300.7

October 29.0 21.0 100.6 5.1 82.0 269.5

November 30.0 23.0 98.2 6.1 81.0 57.0

December 31.0 18.0 127.4 7.8 47.0 0.0

Mean temp. = 25.5 oC, mean rainfall intensity 186.5 mm/hr.

APPENDIX V

1978

Month Temperature

(oC)

Wind

speed

(km/day)

Sunshine

(hours)

Humidity

(%)

Rainfall

(mm/month)

Max. Min.

January 32.2 20.0 110.3 8.8 33.0 0.3

February 33.9 23.3 101.2 6.8 45.0 17.1

March 32.8 22.8 106.8 7.1 50.0 51.6

April 30.6 21.7 95.5 5.5 67.0 245.9

May 30.0 21.7 82.0 6.5 70.0 364.9

June 28.3 20.6 85.6 5.1 73.0 242.4

July 26.7 20.6 101.7 3.0 77.0 167.8

August 27.2 21.1 97.9 3.4 77.0 178.3

September 28.0 21.0 124.4 3.2 76.0 217.3

October 30.0 21.0 105.3 5.0 76.0 217.3

November 30.0 19.0 116.6 8.3 74.0 39.0

December 31.0 20.0 105.3 8.2 68.0 6.1

Mean Rainfall intensity = 150.26 mm/hr

1977

Month Temperature

(oC)

Wind

speed

(km/day)

Sunshine

(hours)

Humidity

(%)

Rainfall

(mm/month)

Max. Min.

January 27.6 21.7 141.5 5.8 51.0 9.4

February 32.8 22.2 154.7 6.1 61.0 3.3

March 33.3 22.8 180.4 2.9 62.0 42.7

April 32.2 23.3 181.8 4.6 74.0 31.8

May 31.1 22.2 186.2 6.3 77.0 143.3

June 28.3 21.1 176.4 4.7 85.0 140.3

July 27.2 20.6 170.1 4.0 86.0 239.2

August 26.7 20.6 163.2 3.3 89.0 131.3

September 27.8 21.1 126.2 3.2 81.0 251.2

October 28.9 21.7 112.8 5.6 82.0 187.7

November 35.0 20.6 129.4 8.9 63.0 0.0

December 31.1 18.9 170.1 8.9 48.0 13.7

Mean Rainfall intensity = 108.54 mm/hr.

APPENDIX VI

1976

Month Temperature

(oC)

Wind

speed

(km/day)

Sunshine

(hours)

Humidity

(%)

Rainfall

(mm/month)

Max. Min.

January 31.1 19.4 162.6 6.4 57.0 0.0

February 31.1 22.2 193.0 6.1 78.0 134.5

March 30.6 22.2 177.9 5.8 80.0 32.2

April 30.6 22.2 170.3 5.1 82.0 123.1

May 28.9 21.7 153.3 4.1 82.0 212.3

June 28.3 20.4 155.6 5.4 84.0 124.6

July 26.1 20.0 174.5 3.0 91.0 117.6

August 26.1 20.6 171.4 2.5 90.0 104.4

September 27.8 21.1 154.0 3.8 86.0 268.5

October 27.8 21.1 138.0 3.4 86.0 306.7

November 29.4 21.1 142.8 6.2 78.0 46.2

December 31.1 20.6 137.9 6.2 73.0 59.4

Mean Rainfall intensity = 139.05 mm/hr.

1975

Month Temperature

(oC)

Wind

speed

(km/day)

Sunshine

(hours)

Humidity

(%)

Rainfall

(mm/month)

Max. Min.

January 31.1 18.3 191.0 5.3 37.0 0.0

February 32.8 22.2 185.3 6.8 63.0 1.5

March 32.2 22.8 205.8 5.0 75.0 55.8

April 31.1 22.8 190.2 7.2 74.0 68.4

May 29.4 21.1 158.6 6.1 81.0 205.0

June 28.9 21.1 173.7 4.5 83.0 211.7

July 27.2 20.6 168.0 3.5 88.0 146.1

August 26.1 20.6 197.3 3.6 88.0 150.5

September 26.7 20.0 156.6 3.3 86.0 327.3

October 28.3 20.6 130.5 4.5 81.0 187.9

November 29.4 21.7 135.5 5.6 76.0 20.5

December 30.6 17.8 170.3 5.3 37.0 31.6

Mean Rainfall intensity = 127.85 mm/hr.

APPENDIX VII

1974

Month Temperature

(oC)

Wind

speed

(km/day)

Sunshine

(hours)

Humidity

(%)

Rainfall

(mm/month)

Max. Min.

January 30.6 18.9 152.8 4.9 53.0 0.0

February 32.8 21.7 178.3 6.4 64.0 29.7

March 32.8 27.2 201.6 4.6 72.0 38.4

April 31.1 21.7 185.5 6.0 78.0 134.6

May 29.4 21.1 158.6 4.9 78.0 254.0

June 28.3 21.1 161.9 4.5 79.0 186.6

July 27.2 20.6 162.0 3.1 86.0 178.4

August 27.2 21.1 189.0 3.1 86.0 132.4

September 27.2 20.6 163.2 3.9 85.0 429.6

October 28.3 20.6 148.0 4.5 84.0 301.3

November 30.6 20.6 148.0 6.9 73.0 1.8

December 30.6 18.3 182.0 4.8 48.0 0.0

Mean Rainfall intensity = 168.68 mm/hr.

1973

Month Temperature

(oC)

Wind

speed

(km/day)

Sunshine

(hours)

Humidity

(%)

Rainfall

(mm/month)

Max. Min.

January 31.7 21.7 158.2 4.7 66.0 8.1

February 33.3 23.3 180.1 6.4 70.0 2.2

March 33.3 23.3 210.1 5.8 65.0 25.1

April 32.2 22.8 187.9 4.7 72.0 96.0

May 30.0 21.7 163.6 5.5 78.0 267.7

June 28.3 21.1 155.3 3.4 84.0 326.6

July 27.8 21.1 180.2 3.7 84.0 103.5

August 27.8 21.1 212.2 4.2 86.0 165.7

September 27.8 23.9 138.3 3.3 85.0 446.2

October 28.9 20.6 127.5 3.5 81.0 200.3

November 31.1 19.4 137.6 5.8 61.0 50.8

December 30.6 21.7 145.7 4.6 76.0 33.3

Mean Rainfall intensity = 146.79 mm/hr.

APPENDIX VIII

1972

Month Temperature

(oC)

Wind

speed

(km/day)

Sunshine

(hours)

Humidity

(%)

Rainfall

(mm/month)

Max. Min.

January 31.7 20.0 152.8 5.4 71.0 21.5

February 32.2 22.8 178.3 6.0 84.0 31.0

March 31.7 22.8 200.0 2.8 54.0 41.4

April 30.0 21.7 185.5 4.5 80.0 161.0

May 30.0 21.7 156.9 6.2 68.0 172.5

June 28.3 21.1 164.7 4.6 83.0 216.6

July 27.8 21.1 145.5 3.9 85.0 100.9

August 26.7 20.6 116.9 3.2 88.0 163.0

September 27.2 21.1 134.1 3.1 87.0 372.7

October 28.3 20.6 123.9 5.5 81.0 201.6

November 31.1 18.9 130.7 8.7 64.0 0.0

December 31.1 20.0 160.3 8.7 62.0 19.6

Mean Rainfall intensity = 136.53 mm/hr.

1971

Month Temperature

(oC)

Wind

speed

Sunshine

(hours)

Humidity

(%)

Rainfall

(mm/month)

Max. Min. (km/day)

January 31.1 20.0 150.7 5.1 57.0 0.0

February 32.2 22.2 176.7 6.9 73.0 10.2

March 32.2 22.2 200.0 6.5 74.0 21.9

April 31.1 22.2 183.9 6.6 76.0 120.1

May 31.0 21.0 156.9 6.3 80.0 206.0

June 27.8 20.6 162.3 3.3 83.0 251.5

July 26.7 20.6 162.5 3.1 88.0 288.5

August 26.1 20.6 187.4 3.6 90.0 364.9

September 27.2 20.0 161.5 4.1 86.0 321.9

October 28.9 21.1 146.4 6.0 82.0 160.0

November 31.1 20.6 146.4 6.7 67.0 0.0

December 31.1 19.4 180.4 4.5 51.0 4.1

Mean Rainfall intensity = 174.91mm/hr

Unit Hydrograph Data

Run-off Discharge, UNN, July 2009

STATION 1

Time (hrs) Run-off (cumecs)

0 0.5

3 1.1

6 2.3

9 3.0

12 5.5

15 3.5

18 2.3

21 1.8

24 1.2

27 0.9

30 0.5

Time (hrs) Run-off

(cumecs) (1)

Base flow

(2)

Ordinate of DRO

(3) = (1) - (2)

Ordinate of U.H

(4) = (3) ÷ 24.14

0 0.5 0.5 0 0

3 1.1 0.5 0.6 0.02

6 2.3 0.5 1.8 0.07

9 3.0 0.5 2.5 0.10

12 5.5 0.5 5.0 0.21

15 3.5 0.5 3.0 0.12

18 2.3 0.5 1.8 0.07

21 1.8 0.5 1.3 0.05

24 1.2 0.5 0.7 0.03

27 0.9 0.5 0.4 0.02

30 0.5 0.5 0 0

ΣO = 17.10

Run-off (cumecs)

Time (hrs) Station II Station III Station IV

0 0.5 0.5 0.5

3 1.0 0.9 0.8

6 2.1 2.1 2.0

9 3.0 2.8 2.7

12 5.2 5.1 5.0

15 3.2 3.1 3.0

18 2.1 2.0 2.0

21 1.6 1.5 1.4

24 1.1 1.1 1.0

27 0.7 0.6 0.6

30 0.5 0.5 0.5

Ordinate of U.H

Time (hrs) Station II Station III Station IV

0 0.0 0.0 0.0

3 0.017 0.010 0.004

6 0.055 0.039 0.019

9 0.086 0.055 0.028

12 0.161 0.111 0.057

15 0.092 0.063 0.032

18 0.055 0.036 0.019

21 0.038 0.024 0.011

24 0.021 0.014 0.006

27 0.007 0.002 0.001

30 0 0 0

Velocity – Area Data

STATION I

Table 4.11; Velocity Measurement

S/No. Rev. Time (s) Rev/time (n) Depth of

flow

1 327 30 10.90 300

2 591 60 9.85 310

3 339 30 11.30 300

4 316 30 10.53 280

5 321 30 10.70 310

STATION II

Table 4.12: Velocity Measurement

S/No. Rev. Time (s) Rev/time (n) Depth of

flow

1 321 30 10.70 220

2 310 30 10.33 240

3 312 30 10.40 250

4 316 30 10.53 240

5 307 30 10.23 250

Width of drainage = 1000mm

Discharge, Q = 0.144 cumecs

STATION III

Table 4.13: Velocity Measurement

S/No. Rev. Time (s) Rev/time (n) Depth of

flow

1 300 30 10.00 210

2 305 30 10.17 200

3 311 30 10.37 190

4 308 30 10.27 200

5 302 30 10.07 200

Width of drainage = 1000mm

Discharge, Q = 0.102 cumecs

STATION IV

Table 4.14: Velocity Measurement

S/No. Rev. Time (s) Rev/time (n) Depth of

flow

1 165 30 5.50 150

2 200 30 6.67 130

3 178 30 5.93 160

4 202 30 6.73 160

5 152 30 5.07 150

Width of drainage = 1000mm

Discharge, Q = 0.050 cumecs