Department of Civil Engineering School of Engineering, University of Nairobi

Lecture Notes Hydrology

Dulo S.OE-mail: sodulo@uonbi.ac.ke

Department of Civil Engineering School of Engineering, University of Nairobi

Precipitation Rainfall

PrecipitationThe common forms of precipitations: Drizzle/Mist: water droplets of diameters less than 0.5 mm. Snow: ice crystals combining to form flakes with average specific gravity of about 0.1. Sleet: rain water drops falling through air at or below freezing temperatures, turned to frozen rain drops. Hail: precipitation in the form of ice balls of diameter more than about 8 mm.

Precipitation cont.Rain:

Is precipitation in the form of water drops of size larger than 0.5 mm to 6mm

The rainfall is classified in to Light rain if intensity is trace to 2.5 mm/h Moderate if intensity is 2.5 mm/hr to 7.5 mm/hr Heavy rain above 7.5 mm/hr

PrecipitationThe formation of precipitation requires the lifting of an air mass in the atmosphere so that it cools and some of its moisture condenses. The 3 main mechanisms of air mass lifting are Frontal Lifting: warm air mass rises to pass over cooler air by frontal passage. Orographic Lifting: an air mass rises to pass over a mountain range. Convective Lifting: air is drawn upwards by convective action.

The Formation of PrecipitationWater droplets in clouds are formed by nucleation of vapor on aerosols, then go through many condensationevaporation cycles as they circulate in the cloud, until they aggregate into large enough drops to fall through the cloud base.

Introduction.Snow:

Snow is formed from ice crystal masses, which usually combine to form flakesHail

(violent thunderstorm)

precipitation in the form of small balls or lumps usually consisting of concentric layers of clear ice and compact snow. Hail varies from 0.5 to 5 cm in diameter and can be damaging crops and small buildings.

Rainfall MeasurementRainfall

gauges (WMO standard

types Rainfall recorders Dines Tilting Syphon Tipping bucket gauge

Rainfall Measurement

Tipping bucket rain gauge

How it rains The

surface is heated by the sun Air rises Air expands and cools Air condenses Water droplets grow to form raindrops Air can rise in different ways

Relief rainfall

Cyclonic Rainfall Depressions

are areas of low pressure formed when cold and warm air meet The warm air rises above the cold air to form a front There are two types of fronts depending on the way in which the air masses are

Cyclonic Rainfall: Fronts Warm

fronts form where warm air moves towards cold air Cold fronts form where cold air moves towards warm air As air rises at fronts both are responsible for rain

Convectional rainfall Common

on hot summer days inland Hot air rises quickly and condenses to form cumulonimbus Water freezes at the top of the cloud forming hail Associated with lightning

Fair Weather Fair

weather is produced by high pressure High pressure forms anticyclones Air sinks and prevents the formation of rain clouds Anticyclones cause heat waves in summer and frosty/foggy

Forecasting the Weather Modern

forecasts use computers to simulate the likely weather based on careful observations from 100s of weather stations round the world Satellite images and radar give a better picture of the weather over

A Satellite Image

A Radar Image Cyclonic

rainfall moving in from the west The brighter the colour, the heavier the rainfall Mountains intensify the rain such as over the Scottish Highlands

Rainfall Measurement

Rain gaugeA rain gauge collects rain and measures it.

PrecipitationVariation of Precipitation Precipitation varies in Time Space

According to The general pattern of atmospheric circulation Local factors The average over a number of years of observations of a weather variable is called its normal value.

Temporal Variation of rainfall at a particular site Total Rainfall amount = 6.17 cm 14 Rainfall Intensity, cm/hr 12 10 8 6 4 2 0 0 20 40 60 80 100 120 140 Time, min

L o n g te r m P r e c ip ita tio n v a r ia tio n a t A r b a M in c h45 40 35 Annual rainfall, mm 30 25 20 15 10 5 0 1986 1988 1990 1992 1994 1996 Ye a rs 1998 2000 2002 2004 2006

A n n u a l P r e c ip it a t io n a v e r a g e p r e c ip it a t io n

Precipitation variation

Mean annual precipitation

Seasonal Precipitation variation

Normal monthly distribution of precipitation

PrecipitationVariety of Precipitation

Mean annual precipitation of the world in mm. (1977)

Rainfall Isohyetal MapsRainstorms vary greatly in space and time. Rainfall can be represented by Isohyetal Map. Isohyet is a contour of constant rainfall. Isohyetal maps are prepared by interpolating rainfall data recorded at gauged point.

Rainfall Hyetograph ; cumulative HyetographComputation of rainfall depth and intensity at a point=1.17-0.00 =1.67-0.02

=3.81-0.00 =4.17-0.02

The rainfall data in 5-minute increments from gage 1-Bee in the Austin storm.

=3.81-0.00 =8.22-0.02

Computations of max rainfall depth and intensity give index of how severe a particular storm is, compared to other storms recorded at the same location, and they provide useful data for design of control structures.

=0.76/(5/60)

=8.20/2

RainfallRainfall Depth (mm)

Rainfall Hyetograph Cumulative Rainfall Hyetograph0.76 inch

Incremental Rainfall in mm per 5 minutes

Rainfall Hyetograph: Is a plot of rainfall depth or intensity as a function of time.

Time in minutes

RainfallRainfall Hyetograph Cumulative Rainfall HyetographCumulative Rainfall in inches

Cumulative Rainfall Hyetograph /Rainfall Mass Curve: Is a plot of cumulative rainfall as a function of time.=6.22-3.15 =8.22-0.02

=6.73-1.17

Time in minutes

2.3. Measurement of RainfallRainfall

and other forms of precipitation are measured in terms of depth, the values being expressed in millimeters. One millimeter of precipitation represents the quantity of water needed to cover the land with a 1mm layer of water, taking into account that nothing is lost through drainage, evaporation or absorption. Instrument used to collect and measure the precipitation is called raingauge.

Rainfall measurement

Precipitation gauge 1 - pole 2 - collector 3 - support- galvanized metal sheet 4 funnel 5 - steel ring

1. Non recording gauge

2. Recording gauge / graphic raingaugeThe

instrument records the graphical variation of the fallen precipitation, the total fallen quantity in a certain time interval and the intensity of the rainfall (mm/hour). It allows continuous measurement of the rainfall. The graphic rain gauge1-receiver 2-floater 3-siphon 4-recording needle 5-drum with diagram 6-clock mechanism

3. Tele-rain gauge with tilting basketsThe

tele-rain gauge is used to transmit measurements of precipitation through electric or radio signals. The sensor device consists of a system with two tilting baskets, which fill alternatively with water from the collecting funnel, establishing the electric contact. The number of tilting is proportional to the quantity of precipitation hp

Tipping bucket rain gauge 1 - collecting funnel 2 - tilting baskets 3 - electric signal 4 - evacuation

4. Radar measurement of rainfallThe

meteorological radar is the powerful instrument for measuring the area extent, location and movement of rainstorm. The amount of rainfall overlarge area can be determined through the radar with a good degree of accuracy The radar emits a regular succession of pulse of electromagnetic radiation in a narrow beam so that when the raindrops intercept a radar beam, its intensity can easily be known.

Raingauge NetworkSince

the catching area of the raingauge is very small as compared to the areal extent of the storm, to get representative picture of a storm over a catchment the number of raingauges should be as large as possible, i.e. the catchment area per gauge should be small. There are several factors to be considered to restrict the number of gauge: Like economic considerations to a large extent

Raingauge Network..

World

Meteorological recommendation:

Organization

(WMO)

In flat regions of temperate, Mediterranean and tropical zones Ideal 1 station for 600 900 km2 Acceptable 1 station for 900 3000 km2

mountainous regions of temperate In Mediterranean and tropical zonesIdeal 1 station for 100 250 km2 Acceptable 1 station for 250 1000 km2

,

In arid and polar zone1 station for 1500 10,000 km2

10

% of the raingauges should be self recording to know the intensity of the rainfall

ARIAL RAINFALL DETERMINATION

Mean Precipitation over an areaRaingauges

rainfall represent only point sampling of the areal distribution of a storm The important rainfall for hydrological analysis is a rainfall over an area, such as over the catchment To convert the point rainfall values at various stations to in to average value over a catchment, the following methods are used: arithmetic mean the method of the Thiessen polygons

Arithmetic Mean Method

When the area is physically and climatically homogenous and the required accuracy is small, the average rainfall ( P ) for a basin can be obtained as the arithmetic mean of the hi values recorded at various stations. Applicable rarely for practical purpose P1 + P2 + ..... + Pi + .....Pn 1 N P = = Pi N N i =1 This method is suitable if the rain gauge stations are uniformly distributed over the entire area and the rainfall variation in the area is not large.

Method of Thiessen polygonsThe method of Thiessen polygons consists of attributing to each station an influence zone in which it is considered that the rainfall is equivalent to that of the station. The influence zones are represented by convex polygons. These polygons are obtained using the mediators of the segments which link each station to the closest neighbouring stations

Arial RainfallThiessen Polygon MethodThe catchment is plotted to scale The gauging stations are then inserted on the plot The lines joining adjacent stations are then bisected by perpendiculars Each stations is then surrounded by a polygon

Thiessen polygons .

Thiessen polygons .

P A7 7

P6

P2

A A2 6

A P8 8

A1

P1

A5

P3

A3

A4

P5

P4

Thiessen polygons .

P1 A1 + P2 A2 + ..... + Pm Am P = ( A1 + A2 + ..... + Am )Generally for M station

P

=

P Ai =1 i

M

i

Atotal

=

Ai Pi A i =1

M

Ai The ratio A is called the Thiessen coefficient

(weightage factor) of station i

Arial RainfallThiessen Polygon Method The method is better than the arithmetic mean method

since it assigns some weightage to all rain gauge on area basis. The rain gauge stations outside the catchment can also be used effectively. Once the weightage factors (thiessen coefficient)for all the rain gauge stations are computed, the calculation of the average rainfall depth P is relatively easy for given network of stations.

Arial Rainfall - Isohyetal Method The catchment is plotted to scale The gauging stations are then inserted on the plot Points of equal rainfall are joined to form the isohyets Since this method considers actual spatial variation of rainfall, it is considered as the best method for computing average depth of rainfall.

Arial Rainfall - Isohyetal MethodAn isohyet is a contour of equal rainfall. Knowing the depths of rainfall at each rain gage station of an area, assuming linear variation of rainfall between any two adjacent stations, one can draw a smooth curve passing through all points indicating the same value of rainfall. The area between two adjacent isohyets is measured with the help of a planimeter. Average depth of rainfall, P

[ Area between two adjacent isohyets ] X 1 P= A [mean pptof two adjacent isohyte values ]

Isohyetal Method

An isohyet is a line joining points of equal rainfall magnitude. 10. 8 0 D a12 6 C 5 9.2 12 a4 a3 7.0 B 4 7.2 A E a2 10. 9.1 4.0 a1 0 F 8 6 4

2.6 Intensity Duration Frequency (IDF) RelationshipMass Curve of RainfallMass curve of rainfall accumulated precipitation, mm 60 50 40 30 20 10 0 0 20 40

1st storm, 16 mm

2nd storm, 60 80 16 mmTime, hour

100

120

Hyetograph

IDF .

-is a plot of the accumulated precipitation against time, plotted in chronological orderHyeto g rap h o f a sto rm 0.5 Intensity, cm/hr 0.4 0.3 0.2 0.1 0 0 8 8 16 16 24 24 32 32 40 40 48 Time, ho urs

Total depth = 10.6 cm Duration = 46 hr

IDF . In

many design problems related to watershed such as runoff disposal, erosion control, highway construction, culvert design, it is necessary to know the rainfall intensities of different durations and different return periods. The curve that shows the inter-dependency between i (cm/hr), D (hour) and T (year) is called IDF curve. The relation can be expressed in general form as:

i =

( D + a)

kT

x n

i Intensity (cm/hr) D Duration (hours) K, x, a, n are constant for a given catchment

IDF .Typ ical IDF Curve14Intesity, cm/hr

12 10 8 6 4 2 0 0 1 2 3 4 5 6Duration, hr

T = 25 years T = 50 years T = 100 years

k = 6.93 x = 0.189 a = 0.5 n = 0.878

Preparation of Data Before using rainfall data, it is necessary to check the data for continuing and consistency Missing data Record errors Estimation of Missing Data Given annual precipitation values P1, P2, P3, Pm at neighboring M stations of station X 1, 2, 3 & m respectively The normal annual precipitation given by N1, N2, N3,, Nm, Ni (including station X) To find the missing precipitation, Px , of station X

Nx Px = M

P1 Pm P2 + + ... + Nm N1 N 2

Interpretation of Rainfall DataEstimating of Missing DataRainfall data must be checked for continuity consistency before they are analyzed for any purpose. The missing annual precipitation, Px2 3

N P P P 1 Px = x [ 1 + 2 + .... + m ] Px = (P1 + P2 + .... + Pm ) M N1 N2 Nm MPx = a + b1 1 + b 2P2 + .... + b mPm PMultiple Linear Regression

x1 m

a0Nx bi MNi1, 2, 3,.,M = neighbouring rainfall stations P1, P2, P3,.,Pm = annual rainfall values N1, N2, N3,.,Nm = average rainfall values

Interpretation of Rainfall DataTest for Consistency of Precipitation DataChanges in relevant conditions of a rain gauge -Gauge location -Exposure -Instrumentation -Observation techniques -Surroundings may cause a relative change in the rainfall catchment of the rain gauge. The consistency of the rainfall data needs to be examined.

Test for record consistencySome

of the common causes for inconsistency of record include: Shifting of a raingauge station to a new location, The neighborhood of the station undergoing a marked change.

Test for consistency record(Double mass curve techniques) Let a group of 5 to 10 base stations in the neighbourhood of the problem station X Arrange the data of X stn rainfall and the average of the neighbouring stations in reverse chronological order (from recent to old record) Accumulate the precipitation of station X ( P ) and the average values of the group base stations starting from the latest record.x

( P )avg

Test for consistency record(Double mass curve techniques)

Plot the ( Px ) against ( Pavg ) as shown on the next figure A decided break in the slope of the resulting plot is observed that indicates a change in precipitation regime of station X, i.e inconsistency. Therefore, is should be corrected by the factor shown on the next slide

Double Mass Curve Analysis5accumulated annual rainfall of X stn in 10^3 cm

Test for consistency record.

4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 0 0.5 1 1.5 2 2.5Accumulated annual rainfall of neigbouring stns in 10^3 cm

c

a

Mc c = Ma a

Mc Pcx = Px Ma

Pcx corrected precipitation at any time period t1 at stationX Px Original recorded precp. at time period t1 at station X Mc corrected slope of the double mass curve

Assumption in the DMCIt

is apparent that the more homogeneous the base station records are, the more accurate will be the corrected values at station X. A change in slope is normally taken as significant only where it persists for more than five years.

Depth-Area-Duration CurveThe

technique of depth-areaduration analysis (DAD) determines primarily the maximum falls for different durations over a range of areas. The data required for a DAD analysis are shown in the following figure.

To

demonstrate the method, a storm lasting 24h is chosen and the isohyets of the total storm are drawn related to the measurements from 12 recording rain gauge stations. The accumulated rainfalls at each station for four 6-h periods are given in the table. To provide area weightings to the gauge values, Thiessen polygons

Step-by-step procedures for drawing DAD curvesFirst,

the areal rainfall depths over the enclosing isohytal areas are determined for the total storm. The duration computations then proceed as in the following table, where the area enclosed (10km2) by the 150mm isohyet is considered first. The areal rainfall over the 10km2 for the whole storm is 155mm.

The

computations are continued by repeating the method for the areas enclosed by all the isohyets.

Depth-Area-Duration (DAD)curveDAD curves are plots of accumulated average precipitation versus area for different durations of a storm period.

Example 3Arial RainfallStation P2 P3 P4 P5 Total Observed rainfall within the area (mm) 20 30 40 50 140

Average Rainfall=140/4=35 mm

Arithmetic-Mean Method

Example 4Arial RainfallStationA1

Observed Area rainfall (mm) (km2) 10 20 30 40 50 0.22 4.02 1.35 1.60 1.95 9.14

Weighted rainfall (mm) 2.2 80.4 40.5 64.0 97.5 284.6

P1A5 A2

P2 P3 P4 P5 Total

A4

A3

Average Rainfall=284.6/9.14=31.1 mm

Thiessen Method

Example 5Arial RainfallIsohyets Area Enclosed (km2) 0.88 1.59 2.24 3.01 1.22 0.20 Average Rainfall (mm) 5* 15 25 35 45 53* 9.14 Rainfall Volume 4.4 23.9 56.0 105.4 54.9 10.6 255.2

10 20 30 40Total

50

Average Rainfall=255.2/9.14=27.9 mm Isohyetal Method

Example 6Arial RainfallThe average depth of annual rainfall precipitation as obtained at the rain gage stations for a specified area are as shown in figure. The values are in cm. Determine the average depth of annual precipitation using (1) The arithmetic mean method

P= =

1 [20.3 + 88.1+ 60.9 + 54.7 + 48.1+ 45.6 + 60.0 + 84.0 + 93.2 + 1406 + 1540] . . 11 1 (8495) = 77.23 cm . 11

Example 7Arial RainfallRainfall Guage 1 Station 2 3 4 5 6 7 8 9 10 11 Total Rainfall, Pi (cm) 20.3 88.1 60.9 54.7 48.1 45.6 60.0 84.0 93.2 140.6 154.0 Area of Polygon, Ai 22 2 (km ) 0 0 0 62 373 338 373 286 236 254 1,944 Weightage Factor (%), 1.13 Ai/ Aix100 0 0 0 3.19 19.19 17.39 19.19 14.71 12.41 13.07 100.01 PiAi/Ai 0.23 0 0 0 1.53 8.75 10.43 16.12 13.71 17.07 20.13 87.97

(2) Thiessen Polygon Method

Average Annual Precipitation = Pi

Ai = 87.97 cm A i

Example 8Arial RainfallIsohyets (cm) 150 Total Net Area, Ai Average Precipitation, Pi PiAi (cm) (km2) 96 25 2,400 600 610 360 238 40 1,944 45 75 105 135 160 27,000 45,750 37,800 32,130 6,400 151,480

(3) Isohyetal Method 151 ,480 Average Annual Pr ecipitation for the ba sin = 1944 , = 77.92 mm

Example 9

No 1 2 3

Annual Station 1 S 1,486.20 1,475.70 1,403.80Sta.1 Sta.3 Sta.2Annual Rainfall (mm/yr) Cumulative Annual Rainfall (mm/yr)

Double Mass Curve

Example 9Accumulative Annual Rainfall of Station1 (mm)40,000

Double Mass CurveStation 1 Accumulative Annual Rainfall of Station1 (mm)80,000

35,000 30,000 25,000 20,000 15,000 10,000 5,000 0 0 10,000 20,000 30,000 40,000

Station 270,000 60,000 50,000 40,000 30,000 20,000 10,000 0

50,000Accumulat ive Annual Rainfall of 1t ion S at

0

10,000

20,000

30,000

40,000

50,00

Accumulative Annual Rainfal of 3 station Mean (mm)

Accumulative Annual Rainfal of 3 station Mean (mm)30,000

Sat n 3 t io25,000

The past response is to be related to the present conditions.

20,000

(mm )

15,000

10,000

5,000

0 0 10,000 20,000 30,000 40,000

50,000