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HYDROLOGY
 TOPIC COVERED IN TNPSC AE EXAM UNIT 1- HYDROLOGY

 Hydrology
 Measurement of rainfall
 Evaporation and infiltration
 Estimation of runoff

 Factors affecting runoff

 Computation of volume of runoff and peak flow

 Unit hydrograph
 PREVIOUS YEARS QUESTIONS ON HYDROLOGY

2017
2017

Number of Questions
asked from
Hydrology: 6
 2018

Number of Questions asked from

Hydrology: 4
2019
2019

Number of Questions asked from

Hydrology: 7
DEFINITION AND IMPORTANCE

 Hydrology, by its term meaning is the science of water

 In hydrology, the land unit is the watershed, which also may be referred to as a basin or catchment.
 A watershed is defined as an area of land in which all the incoming precipitation drains (i.e., “sheds”) to
the same place – toward the same body of water or the same topographic low area (e.g., a sinkhole)as a
result of its topography.
Divisions of Hydrology:
 Hydrology can generally be divided into two main branches

 Engineering Hydrology: Engineering hydrology deals with the planning, design and Operation of
Engineering projects for the control and use of water

 Applied Hydrology: Applied hydrology is the study of hydrological cycle, precipitation, runoff, relationship
between precipitation and runoff, hydrographs, Flood Routing

 Chemical Hydrology: Study of chemical characteristics of water.

 Eco-hydrology: Interaction between organisms and the hydrological cycle.

 Hydrogeology: Also referred to as geo-hydrology, is the study of the presence and movement of ground water.

 Hydro-informatics: is the adaptation of information technology to hydrology and water resource applications
 Hydrometeorology: It is the study of the transfer of water and energy between land and water body surfaces
and the lower atmosphere.
 Isotope Hydrology: It is the study of isotropic signatures of water (origin and age of water).
 Surface Water Hydrology: It is the study of hydrologic processes that operate at or near earth’s surface.
 Ground Water Hydrology: It is the study of underground water.
The Hydrologic Cycle
 It refers to the continuous circulation of water within the earth’s hydro-sphere.

The physical processes involved in hydrologic cycle are

▪ Evaporation
▪ Condensation
▪ Sublimation
Sun is source of energy to activate all process
▪ Precipitation
▪ Transpiration,
▪ Interception,
▪ Infiltration,
▪ Percolation and
▪ The runoff
HYDROLOGIC CYCLE
 Evaporation - It involves the vaporization of water from the water sources due to heat energy of
solar radiation. The evaporated water gets converted into cloud. Through which water gets fall on the
earth system in terms of precipitation. In water transfer process about 90% of atmospheric water is
contributed by evaporation.

 Condensation- It refers to the transformation of evaporated water vapours into liquid water
droplets suspended in the air as clouds or fog. It is important process to convert the evaporated
water into liquid state enabling formation of clouds with the aid of condensation nuclei.

 Sublimation- This is the process in which there is direct conversion of solid ice into water vapour.
By this process water mass is also added to atmosphere for cycling.

 Precipitation- It is the fall of atmospheric water to the ground surface. Under this process the water
becomes available for its distribution (surface and sub-surface) and circulation on the above and below
the earth surface. It mostly takes place in the form of liquid (rainfall) and very little in solid form (snow,
sleet, hail fog etc.)
 Transpiration- It is a process of water loss from plants' leaves through respiration. The water loss
through transpiration and evaporation coupled together is referred to Evapotranspiration (ET). In
hydrologic cycle about 10% water or moisture is added to the atmosphere by transpiration process.

 Interception- This is the process in which a part of precipitation is abstracted by the objects lying on
the ground surface. The objects may be the crop, tree, natural vegetations and any other in live or dead
conditions. Intercepted precipitated water is ultimately lost through evaporation process. Rate and quantity
of water loss under this process varied with the type and characteristics of vegetation/objects and climatic
condition, mainly.

 Infiltration- It is defined as the entry of water into the soil by crossing the imaginary boundary between soil
and atmosphere and its rate called infiltration rate. Under this process the precipitated water moves into the soil
media and ultimately joins to the water –table or deposited on impervious layer, if there occurs across water
movement path. It is treated as the input process for ground water occurrence
 Runoff- The flow of joined rain water in the stream is designated as the channel flow or the runoff. The
characteristics associated to the climate and watershed affects the quantum of runoff at the outlet. Runoff is
categorised into surface and sub-surface runoff. In which surface runoff is that part of the runoff which
travels over the ground surface thought the channels/ streams /rivers to reach the basin outlet, and sub-
surface or indirect runoff points to the flow of precipitated water below the soil surface leading to water-
table
Hydrologic Budget
 It consists of inflows, outflows, and storage, presented by the following equation:

 Inflow = Outflow +/- Changes in Storage

 Inflows contribute or add water to the different parts of the hydrologic system, outflows remove water from
them, and storage is the retention of water by parts of the system. Since, water movement is cyclical; therefore,
an inflow for one part of the system is an outflow to another.
 PRECIPITATION
 Clouds- It is the source of precipitation. Precipitation is resulted mainly from two types of clouds. They are the
nimbostratus and cumulonimbus type clouds. The nimbostratus clouds appear at mid height in dark gray colour
result the rainfall throughout day, continuously. The cumulonimbus clouds are low lying in the sky

 Precipitation- The moisture emanating from the cloud and falling to the earth surface is called precipitation.

 Liquid form of Precipitation

 Rainfall- It is in liquid form (drops) falling from the clouds to the earth surface. Size of water droplets is
about to 0.5 mm or little bit bigger. Rate of rainfall varies from time to time. A light rain ranges from
2.5mm/h, moderate rain from 2.5-7.5mm/h and heavy rain above 7.5mm/h. Rainfall is the most important
component of hydrologic cycle which replenishes large percentage of fresh water on earth. Rain and drizzle
are beneficial for plants.
 Drizzle- It is also in liquid form but its droplets size is less than 0.5mm diameter. Its intensity is lesser than
2.5mm/h. It contributes moisture to the lower atmosphere effective for cooling and generating warm air
mass to create cloud in the sky. Drizzle usually falls from low stratus clouds and is frequently accompanied
by fog.
 Acid rain- It occurs when rain becomes mixed with pollutants such as Sulphur Oxides and Nitrous Oxides. It
kills plants and pollutes the water sources lying on the earth surface.
 Solid form of Precipitation
Various forms are the snow, sleet, hail etc,
 Snow- It consists of white or translucent ice crystals. Originally these are highly complex, hexagonal,
branched structures. Snow falls as a combination of individual ice-crystals, fragments of crystals, or clusters
of crystals.

 Snow pellets – These are small hails, appear in the form of white, opaque, round/ conical. Average diameter
varies from 0.08 to 0.2 inch. Have tendency to burst upon striking a hard surface. These occur almost
exclusively in snow showers.

 Hail- These are opaque ball of hard ice, ranging in diameter from 1/8 inch or so to 5 inches or larger. Hails
are basically the ice that falls from the sky, often in round shape. Hailstones are large chunks of ice that fall
from large thunderstorms.
Types Intensity Median diameter
(mm) Numbers of drops (per
(cm/h) sqm)
Fog (0.013) 0.01 67,425,000
Mist 0.005 0.1 27,000
Drizzle 0.025 0.96 151
Light rain 0.10 1.24 280
Moderate rain 0.38 1.60 495
Heavy rain 1.52 2.05 495
Excessive rain 4.06 2.40 818
Cloudburst 10.2 2.85 1,220
 PRECIPITATION TYPES
 Orographic precipitation- This type of precipitation is caused by air masses striling some natural topographic barriers
like mountains. The greater amount of precipitation falls on the windward side. Few important features are given as under:
• Lifting of warm air mass is due to orographic barriers causing formation of cloud and precipitation thereof.Rainfall is steady
rainfall.Southern slope of the Himalayas is a good example of this type of precipitation.Similarly, the winds coming from ocean
strike the western slopes of coastal ranges causing heavy rains are another example of orographic precipitation.The rainfall at u/s
side is intense to that of the d/s side.The d/s orographic precipitation is called Rain shadow.

 Cyclonic precipitation-Cyclone is atmospheric disturbance caused by air mass circulating clockwise in southern and
anticlockwise in northern hemispheres. Basically, cyclone is violently rotating wind storm. The precipitation as result of cyclone is
termed as cyclonic precipitation. Cyclone is very large mass of air ranging from 800 to 1600km in diameter and moving with the
velocity of 50 kmph. Few important features are mentioned below:
• The cyclonic precipitation occurs in the form of drizzle, intermediate rain or steady rain.Precipitation caused by cold front is intense and
of short duration.Precipitation caused by warm front is more continuous

 Convective Precipitation- In this precipitation the lifting of warm air mass is due to convective effect, called convective
uplift. The convective uplift takes place especially when air near to ground gets warm due to sun energy, and begins to rise
upward in the sky. The process of rising of warm air mass and its cooling is governed by adiabatic cooling process. This leads to the
formation of clouds and precipitations, sometimes. In this precipitation the precipitation occurs in the form of showers of high
intensity and for short duration.

 RAINFALL MEASUREMENT

 Rain gauge- The rain gauge is the instrument used for rainfall measurement. The measured rainfall is
termed as the point rainfall. The point rainfall is used for determining the mean areal rainfall by using
various computing methods. The mean aerial rainfall can be used for determining the volume of rainwater
received over the surface area of watershed by multiplying the mean depth of rainfall and area of
watershed/region.
 Types of Rain gauge

 Broadly, it is classified as

1. Non- recording type; and

2. Recording type rain gauge.

SIMON TYPE  Non- Recording Type Rain gauge (Simon type) - It is most
common type of rain gauge, consists of 127mm diameter
cylindrical vessel with a base width 210mm diameter for
making stability. At top a funnel is provided with circular
brass rim which is exactly 127mm to fit into vessel
correctly. This funnel shank is inserted in the receiving
bottle placed below. The height of receiving bottle is 75
to 100mm. The bottle receives the rainfall. Capacity of
receiving bottle is to measure the rainfall depth is
100mm. During heavy rainfall, the rainfall amount is likely
to exceed the bottle capacity. In this condition it is
suggested to take the observations frequently, normally 3
to 4 times in a day. The water collected in the receiving
bottle is measured by a graduated measuring cylinder.
The measuring accuracy of graduated cylinder is being up
to 0. 1mm. The timing of rainfall measurement is
uniformity done, every day at 8:30Am IST
  Recording Type Rain gauge: It records the information about start and end of rainfall event taking
place. With the help of this information, one can determine the rainfall intensity and depth of the
place under measurement. The following rain gauges are commonly used as recording type rain
gauge,

1. Float type rain gauge,

2. Weight type rain gauge, and
3. Tipping bucket type rain gauge.
FLOAT TYPE RAIN GAUGE  It is also known as natural siphon type rain gauge. In India
this rain gauge is adopted as the standard recording rain
gauge. Working of this rain gauge is similar to the weighing
type rain gauge. In this a funnel receives the rain water
which is collected into a container equipped with a float at
the bottom. The position of float rises as the water level
rises in the container depending on rain water coming
into. The movement of float is transmitted to a pen
which traces a curve on the rain chart mounted on a
clockwise rotating drum. When float rises to the top of
container the siphon comes into action and drain the total
water from the container. At this stage the pen traces a
straight line. If rainfall is continued and water is coming
into the container then further float rises up and pen
traces the curve. This process is continued. If rainfall is
stooped the pen traces a horizontal line on the chart. The
obtained curve is the mass curve. View of this rain gauge
is shown in Fig-.
 Weighing Type Rain Gauge- It is most common
self-recording rain gauge, consists of a receiver
(bucket) supported by a spring/ lever balance or
some other weighing mechanism. The movement
of bucket due to its increasing weight because of
accumulation of rainwater is transmitted to a pen,
which traces a curve on the rain chart wrapped on
clock. The obtained rainfall record in terms of
curve is mass curve, i.e. the plot of cumulative
rainfall vs elapsed time. View of rain gage is shown
in Fig-
 Tipping Bucket Type Rain Gauge- It is a 30cm size rain gauge,
used as recording type rain gauge. US weather bureau uses this rain
gauge for measuring the rainfall. Its construction includes a 30cm
diameter sharp edged receiver. At its end a funnel is provided for
directing the rainwater into the receiver. One pair of buckets is
pivoted on a fulcrum below the funnel in such a way that when one
bucket receives 0.25mm depth of rainfall, it tips and empties its
rainfall into the container, and immediately the second bucket comes
below the funnel (Fig..). For single tipping , time involvement is 6 to 7
seconds.
 The rainfall measurement is recorded in terms of number of tips
made for a given rainfall event, which is indicated on a dial
actuated by electrical circuit. .
Rain gauge Installation
 The surrounding exposure of rain gauge station affects the catching of rainfall by a raingauge. Therefore, before
establishment of raingauge, the selection of a suitable place is very important, otherwise the rainfall
measurement would not be accurate as should be. There are few important points to follow for installation of
raingauge station in the area.
1. The ground surface must be level and firm. The places such as the building roof, sloppy surface, and
terrace wall should be avoided.
2. In hilly areas the valley and hill top should not be selected for installation of the raingauge.
3. The site should be representative of the area or watershed.

4. Wind affected site should be avoided.

5. Site should be open from all the sides.

6. In forest area the raingauge should be instated at the distance twice the height of tallest tree from
the forest plantation. Also the gauge’s upper point should make an angle ranging from 20 to 30 degree
from the upper point of the raingauge.
7. The receiver‘s height from the ground surface should be around 75cm.
8. The position of raingauge must be vertical.
  Rain gauge Distribution
 The rain gauge distribution in watershed for measurement of rainfall, in accurate way is very important. If number of rain gauge
differs than the required depending on the areal extent and topography, there is likely to get effects on the results various
estimates. The topography and extent of area of watershed decide the number of rain gauge stations to be there. The number of
rain gauge stations for highly undulating watershed comparatively more to that of the flat topography watershed. Rain gauge
stations as per WMO and IMD is described below,
 As per WMO
1. Flat reasons of temperate mediterrian and tropical reasons Ideal -600 to 900 sq km per raingauge
;Acceptable - 900 to 3000 sq km/per raingauge
2. For mountainous reasons of temperate, mediterrian and tropical reasons Ideal - 100 to 250 sq km/per raingauge
;Acceptable - 250 to 1000 sq km/per raingauge
3. In arid and polar zones – 1500 to 10,000 sq km per raingauge

 As per IMD
1. Plain reasons - 520sqkm/raingauge

2. Reasons of average elevation - 260-360 sq km/per raingauge

3. Pre dominantly hilly reasons with heavy rainfall – 130 sq km/per raingauge

 Note: 10% of total raingauge required is taken as recording type of raingauge for installation.
 Problem (1)- In watershed the tipping bucket type rain gauge is installed for taking measurement.
Determine the depth of rainfall, if rainfall duration is 2.30 hour.

The following standards are involved with the tipping bucket type rain gauge:
1. For single tipping, the time involvement = 6 to 7 seconds
2. Capacity of one compartment is =0.25mm.

 As per above total number of tipping: 2.30 x 60 x 60 / 6 = 1380

 Depth of the rainfall: 1380 x 0.25 = 345 mm

 Normal Rainfall-
It is an average of
the rainfall values
over a 30-year
period. Rainfall
may very often be
either above or
below the
Common Errors in Rainfall Measurement seasonal average,
or "normal."
Few important errors in rainfall measurement by the raingauge are mentioned as under,
1.In non- recording type raingauge (Symons’s type) about 2% error is introduced due to
displacement of water level by measuring scale.
2.Possibility of errors due to initial wetting of dried surface of the catch can or receiver.
3.The dents in catch can or receiver also introduces errors in measurement.
4.A high temperature cause evaporation loss also signifies a kind of errors in rainfall
measurement. The errors may be up to 2%.
5A high wind velocity deflects the rainfall to fall at the mouth of the rain gauge, introduces an
errors in rainfall catching. The research revealed that at the wind velocity of 10mile per hour the
catching of rainfall is declined to the tune of about 17% while at 30mile per hour it may be up
to 60%.
Missing Rainfall Data
 In normal course, sometime what happens, because of several reasons such as absence of
observer, instrumental fault etc there is short breaks in the rainfall records. In this condition to fill
the break the estimation of missing rainfall data is essentially required. The following methods
are commonly used for computing the value of missing rainfall data
1. Arithmetic Mean Method
2. Normal Ratio Method
Arithmetic Mean Method- This method follows following formula for determining the mean aerial rainfall,

in which 'n' is the number of raingauge stations in nearby area, 'Pi' is rainfall depth at ith station and
'Px' is missing rainfall data. Solve example….. illustrates the computation procedure.
Normal Ratio Method- This method is used when normal
annual rainfall at any of the index station differs from the
interpolation station by more than 10%. Missing rainfall
data is predicted by weighing the rainfall of index stations
by the ratios of their normal annual rainfall. Formula is
given as under,
in which Px is the missing rainfall at raingauge station 'x' of
a given rainfall event, Pi is the precipitation for the same
period and same rainfall event of "ith" raingauge station
among group of index stations, Nx the normal annual
rainfall (NAR) of station x and Ni the normal annual rainfall
of 'ith' station.
Problem (2)- In a watershed four rain gage stations namely a, B, C and D are instatlled for recording rainfall data.
The normal annual rainfall of these four stations is 75, 60, 70.5 and 87 cm, respectively. The rain gauge station A
does not have the annual rainfall observation for one year during total length of record, because of disorder of the
rain gauge. Calculate the missing value of rainfall data of rain gauge station A, if the annual rainfall recorded at
other three stations for that particular year was 85, 67.5 and 75 cm, respectively at B, C and D, respectively.

Solution- The variation in normal rainfall data is more than 20% at all the four rain gauge
stations. In this condition, the normal ratio method for computing the missing value of annual
rainfall of station A is suitable. Accordingly, the formula for computing the missing annual
rainfall is given as under.
𝑃1 = 𝑚−1
𝑁1 ( 𝑃2
𝑁2 + 𝑃3 𝑃4 )
𝑁3 + 𝑁4 P1 = (75/ 4-1) ( 85/60 + 67.5/70.5 +
75/ 87)
in which, 𝑃2 = 85𝑐𝑚; 𝑃3 = 67.5𝑐𝑚; 𝑃4 = 75𝑐𝑚, 𝑎𝑛𝑑 𝑁1
= 75𝑐𝑚; 𝑁2 = 60𝑐𝑚; 𝑁3 = 70.5𝑐𝑚; 𝑁4 = 87𝑐𝑚 𝑎𝑛𝑑 𝑚 =
P1 = 81 cm
4. Substituting these values in above formula and
solving , we have,
Mean Areal Rainfall
Average rainfall is the
representative of large area,
which is computed with the Arithmetic Average Method
help of rainfall data generated This method computes arithmetic average of the rainfall by
from well distributed raingauge considering point rainfall observations of all the raingauge stations
installed in the area. This method computes accurate value when
network system of the
rainfall is uniformly distributed in the entire area, as in this situation
watershed. The computing equal weightage of area is assigned to the point rainfall data. Formula
methods are elaborated as is given as under,
under,
1. Arithmetic or station average
method n which 'n' is the number of raingauge stations in
i
2. Thiessen Polygon Method nearby area, 'Pi' is rainfall depth at ith station and
3. Isohyetal Method ‘Px’ average rainfall
 Problem (3)- In a topographically homogeneous watershed total four number of non- recording and one
recording type rain gauges have been installed for recording the rainfall measurements. The point rainfall of four
non- recording type rain gauge stations have been observed to the tune of 250,175,225 and 270mm, respectively
during a given rainfall event. Determine the mean areal rainfall of the watershed for the said rainfall event.

Solution- The mean areal rainfall of the watershed can be computed by using the simple arithmetic
mean method, given as under:
Px = (P1+P2+P3+P4) / 4
= (250+175+225+270)
= (920) /4
= 230 mm
Thiessen Polygon Method
This is a graphical method for computing MAP. It computes by weighing the relative area of each raingauge station
equipped in the watershed. It follows the concept that the rainfall varies by its intensity and duration, spatially. Therefore,
the rainfall recorded by each station should be weighed as per the influencing area (polygons). This method computes
better for the areas having flat topography and size ranging from 500 to 5000 km2. Computing steps are described as
under,
•Plot the locations of raingauge stations on map of the area drawn to a scale.
•Join each station by straight line.
•Draw perpendicular bisectors of each line. These bisectors form polygons around each station. Area enclosed within
polygon is the effective area for the station. For a raingauge station close to the boundary, the boundary lines forms its
effective area.
•Determine effective area of each raingauge station. For this the planimeter can be used.
•Calculate MAP by using the following formula,
in which, Pi is the rainfall depth of raingauge station i and A is the total area of watershed.
 Problem (4)- Compute the mean areal rainfall of the watershed by using Theissen Polygone Method.
The details are cited below
Rain Gauge Station A B C D E

Measured Rainfall( 10.5 11.56 9.57 10.50 11.63

cm)
Area of enclosed 15.0 23.5 35.9 8.5 12.35
polygons( sq.km)
Isohyetal Method
This is also a graphical method, in which an isohyets map is prepared with the help of measured rainfall data of
various raingauge stations located in the watershed. An isohyet map includes a network of isohyet lines. Each line
represents a fixed value of rainfall depth. Computation of MAP under this method is done by using following
steps,
1. Collect the map of area/watershed. The map should to the scal.
2. Draw isohyet map with the help of measured rainfall data of various raingauge stations installed in the
watershed.
3. Find the area enclosed between each isohyet.
4. Multiply the area enclosed between each isohyet by the average precipitation, i..e 𝐴 (𝑃1+𝑃2 ) / 2
5. Find the sum of product of area enclosed and average of rainfall for all segments of Isohyet
map.
6. Divide the sum of the values found in step- 5 by the total area of the watershed to get MAP of
watershed.
Problem (5)- In a watershed total five rain gauge stations (A, B, C, D, and E) are installed for taking rainfall
measurements. Calculate the mean areal rainfall depth using Isohyetal Method for a particular rainfall
event. The details about measured rainfall and area enclosed by respective rain gauge station are given as
under.
 Rainfall Analysis
Mass Curve- It is the plot of accumulated rainfall against time, in chronological order (Fig-). The rainfall
record generated by float type and weighing-bucket type gauges is in terms of mass curve. Mass curve
acts as tool to determine the duration & magnitude and intensity of rainfall event. In case of the
observation of non-recording rain gauges, the mass curve is prepared on the basis of knowledge of
approximate beginning and end of rainfall event and by taking guidance from the mass curve of adjacent
recording raingauge stations.
Double Mass Curve- It is used to check the consistency of many kinds of
hydrologic data. Also, it can be used to adjust inconsistent rainfall data.
The plotting between cumulative data of one variable versus the
cumulative data of a related variable, if produces a straight line indicates
consistency in record, otherwise, break in the double-mass curve shows
inconsistency in record. The break point indicates the time from when
there is development of inconsistency, which could be because of several
reasons like change in original location/ exposure of the instrument/
device used for measurement
 Consistency of Rainfall Data
In the condition when a long time has been to a raingauge establishment, then there is possibility of change
in the surroundings of the rain gauge in reference to the original condition. In result the rainfall to be
measured by the raingauge gets change, and thus the rainfall data becomes inconsistence. The change in
raingauge surroundings may be due to various reasons, such as,
1. Construction of new infrastructures like buildings apartments etc.
2. Plantation of orchards etc.
3. Introduction of instrumental errors.
4. Repetition of observational errors from a certain period.
Consistency test provides the time from when the inconsistency is introduced in the data. It is tested with
the help of double mass analysis method. The stepwise procedure is described as under,
1. Collect the rainfall data (normally annual) of the raingauge station which consistency is to be tested (say station
X) and of the surrounding rain gauge stations.
2. Find the mean of the surrounding rain gauge data called base station data.
3. Calculate the cumulative rainfall of inconsistence raingauge station and of the base stations.
4. Plot the cumulative rainfall of base station on X -axis and corresponding rainfall of station X on Y-axis. It is
shown in Fig-
5. Find the regime where rainfall data are under inconsistence nature. It can be demarcated by getting the change
in slope of the plotted curve.
6. Rectify the inconsistence nature of the data, by multiplying a factor to them. The multiplying factor is the ratio
of slope of straight line of consistence data to the slope of inconsistence data
Hyetograph-Hyetograph is the plot of rainfall intensity vs time presented as bar chart (Fig.). It is derived with the
help of mass curve. Hyetograph represents the characteristics of a rainfall event and acts as a tool to develop a
design storm for predicting extreme floods. Also, a hyetograph casts the information about total depth of rainfall
occurred during rainfall event. Hyetograph is used hydrological analysis of catchment for (i) predicting flood; (ii) for
estimating runoff and (iii) for deriving unit hydrograph.
Problem (6)- The rainfall intensity vs time data derived from the mass curve of a specific rainfall event is
given as under:
Problem (7)- Determine the average depth of rainfall in the watershed of 1000sqkm size by using Depth-
Area relationship, if the highest rainfall at the centre of rain storm is 15cm. Take the constants K=8.256x10-4
and n=6.614x10-1
Rainfall Intensity – Return Period Relationship
Return period or recurrence interval is the number of years in which an event can be expected once. The
relationship between rainfall intensity and return period is very important to determine the rainfall intensity
for different return periods or rainfall frequencies, which is mainly required for computation of runoff rate to be
used for design of hydraulic structures. For example, the soil conservation structures like drop structures, grassed
waterways, farm ponds, reservoirs, dams etc are designed on the basis of runoff rates for different return periods.
The rainfall duration increases when intensity decreases and vice-versa. The rainfall intensity increases when
return period increases and vice-versa. The formula for rainfall intensity – return period is presented by the
following expression.
Problem (8)- Calculate the rainfall intensity of 1000 sqkm size catchment for 25-yeras return period to be used
for design of semi- permanent gully control structure. Take the duration of rainfall is 6.0 hours and constants,
K=45.216; a= 0.50; b=4 and d=0.6870.
Rainfall Frequency
It is also known as plotting position. The design of hydraulic structures, flood control structures, soil
conservation structures, drains, culverts etc are based on probability of occurrence of extreme rainfall
events. The relationship for plotting position/rainfall frequency is given by the Weibul’s equation
presented as under:

Problem (9)- Determine the plotting position of highest rainfall of 50cm during 50 years period.
Solution- The relationship for plotting position is given by the Weibul’s, given as under:
Problem (10)- Determine the length of rainfall record, if return period of highest rainfall of 75 cm is 25
years.
 Rainfall Abstractions and Initial Loss

Initial Loss of Rainwater

In course of rainfall occurrence there is significant water loss from various sources such as interception, evaporation,
transpiration, infiltration, depression storage. In result the overland flow and runoff yield against rainfall gets reduce. These
loses are referred as initial loss. The prediction of initial rainwater loss is very important for determining the runoff and
hydrograph derivation.
Interception- It is the amount of rainwater loss due to abstractions from initially dry surfaces of the objects lying on the
ground surface. The objects may be the live vegetations e.g. herbs, shrubs & trees and any dry surfaces like building etc.
From a tree the interception is mainly from the canopy, is called canopy interception (Fig-)

Intercepted rainwater is lost due to

evaporation is called interception loss. The
extent of interception loss depends on a
host of factors such as types and
characteristics of vegetations, rainfall,
temperature, season of the year, wind
velocity
Interception losses generally occur during the first part of a precipitation event and the interception loss rate trends
toward zero rather quickly

Interception losses are described by the following equation (Horton reprinted by Viessman 1996):
𝐿𝑖 = 𝑆 + 𝐾. 𝐸. 𝑡
in which 𝐿𝑖 is the total volume of water intercepted, S is the interception storage, K is the ratio of the surface area of
the leaves to the area of the entire canopy, E is the rate of evaporation during rainfall and t is the time. This equation
assumes that the rainfall is enough to satisfy the storage capacity of vegetation. Horton equation suggests that the
total interception is dependent on the duration of
rainfall as longer duration rainfall event allows more evaporation from the canopy. Brooks (2003) also suggested
following formula for predicting interception loss,
𝐿𝑖 = 𝑃𝑔 − 𝑇ℎ − 𝑆𝑓
in which 𝐿𝑖 is the canopy interception loss, 𝑃𝑔 is the gross precipitation, 𝑇ℎ is the through fall and 𝑆𝑓 is the stem flow. The
intensity of the storm also plays a role in canopy interception (Viessman 1996); however, there is debate as to whether
intensity increases or decreases interception storage in canopy (Keim 2003).

Interception is mainly at two levels depending on features of vegetation, given as under,

1. Primary interception, and
2. Secondary Interception
Through fall – It is the process of falling of rainwater through the sp[aces of plant canopy. Through
fall is affected by the factors such as plant leaf and stem density, type of precipitation, rainfall intensity and
duration of the rainfall event. Through fall may be bys direct falling of rain water or dropping of intercepted
water through tips of the leaf. The measurement of through fall can be carried out by putting a bucket below the
tree canopy.
Stem flow – In course of rainfall a part of rainwater is also absorbed by the branches and stem of the tree. If
rainfall is continued, then after some time the absorbed water starts flow through the branches and joins to the
soil surface through stem, is called stem flow. By this process a part of rain water is also absorbed by the surfaces
of tree branches and stem, which is lost due to evaporation. The characteristics of tree branches and stem affect
the rate of stem flow. A tree with rough surface of branches /stem involves high level of stem flow loss.
Depression storage- Depressions are the small size low pockets lying on the ground surface. Such appearances
are very common in undulating lands. Presence of depressions on the ground surface cause significant level of
water retention in them, known as depression storage. It also constitutes a kind of rainwater loss because the
retained water is lost due to infiltration and evaporation actions. Depression storage affects the rainfall- runoff
relationship of the area. Linsley (1982) suggested following formula for predicting the volume of retained in
depression storage at any time during a rainfall event
 Infiltration
It is defined as the entry of water into the soil by crossing the imaginary boundary between soil and
atmosphere. Infiltration is treated as one of the most important factors making rainwater loss from the total.
Runoff generating potential of area/ soil is very much affected by infiltration rate. A sandy soil belt involves very
less potential for runoff yield to that of the heavy soil belt, because of the reason that the infiltration rate is
quite high of sandy soil as compared to the heavy soil. The rate of water soaking by the soil is called as
infiltration rate and its maximum rate is termed as infiltration capacity.

Infiltration rate, Initial Infiltration rate and Basic Infiltration rate

The velocity or speed at which water enters into the soil is called infiltration rate. It is usually measured by the
depth (in mm) of the water layer that can enter the soil in one hour. For example an infiltration rate of 15 mm/h
reveals that a 15 mm water depth standing on soil surface will infiltrate into the soil in one hour time. Initially,
infiltration rate is very high and becomes slower as time proceeds. This is because of the reason that at beginning
there is sufficient space or reservoirs are there for storing water in the soil media and likely to get reduce because of
filling of water content in them with time advancement. In dry soil, the water infiltrates rapidly called initial
infiltration rate. As more water replaces the air in the pores, the water from the soil surface infiltrates more slowly
and eventually reaches a steady rate, called the basic infiltration rate.
Field Test for Infiltration Measurement

The most common method to measure

the infiltration rate is by using the
Double Ring Infiltrometer. The diameter
of inner ring is 30 cm and of outer rings 60
cm. View of double ring infiltrometer is
shown in Fig-. Experimental procedure is
described
 Runoff and Its Computation
Runoff is defined as the flow of excess rainwater through a channel, gully, river or any fluvial path. The overland
flow is the main input for generating runoff. On watershed scale, the rainwater after getting satisfied with the
initial losses such as, abstractions, evapotranspiration.

This phenomenon is called overland flow. As soon as the overland flow joins any flow path like channel etc, the
runoff takes place. Since this flow is through channel; therefore, runoff is also called channel flow. The length of
overland flow is limited to a very short distance, normally maximum up to 150 m.
Runoff Classification
It is classified as
1. Direct runoff, and
2. Indirect runoff
Direct Runoff - It is the surface runoff, takes place on the ground surface through the streams / channels etc. Since, it takes place very
soon after start of rainfall event; therefore, it is called as the direct runoff. Direct runoff is also known as surface runoff.
The interflow, in which the infiltrated rainwater joins to the stream flow in terms of influent flow, soon after start of rainfall, is also the
part of surface or direct turnoff. The reason behind this is that the time gap between rainfall occurrence and interflow is very less
Indirect Runoff- This type of runoff takes place below the ground surface. In the course of occurrence of rainfall a part of rain water
which is infiltrated into the soil media moves downward and joins to the water –table. The joined rainwater starts moving or flow along
with ground water to the other places in forward direction, called indirect runoff. Since, this runoff takes place below the ground
surface; therefore, it is also called sub-surface runoff. Sometimes, it is also known as the delayed runoff because of the reason that
there is very large gap between occurrence of rainfall and formation of runoff say for example 1- year or more
 Factors Affecting Runoff
Conceptually, in runoff formation the rainfall is an input and watershed is the system on which rainfall take
place, and runoff is the output. It means that the parameters associated to the rainfall (climate) and
watershed affect the runoff yield. Broadly, the list of factors affecting the runoff are listed in following table-
Form Factor-It is defined as the ratio of average width to the axial length of the watershed. Axial length of
watershed is the distance between outlet and the remotest point of the watershed. Width is determined by
dividing the area of watershed by its axial length.

Compactness factor- It is the ratio of watershed perimeter to the circumference of a circle which area is equal
to the area of watershed. It is given by
Problem (11)- Determine form factor of an elongated watershed, which axial length is 15000m and average
width as 750m.

Problem (12)- Determine compactness factor of an elongated watershed, which perimeter is 2500m and area
is 1.5sqkm.
 Stream Classification
Manly, streams are classified as under,
1. Perennial stream,
2. Intermittent stream, and
3. Ephemeral stream
Perennial stream carries runoff flow throughout the year. In off-season, i.e. summer season the flow of water
is contributed by ground water. Resulted hydrograph is extended for the entire year duration. Intermittent
streams do not have continuous flowing water year-round and are not relatively permanent. Water flowing
water period is limited during wet season (winter-spring) but are normally dry during hot summer months.
The water flow in Ephemeral streams is confined with the occurrence of rainfall. Comparatively, these
streams have less flow than the intermittent stream. Typically these are shallow and have very less flowing
periods.
Effective Rainfall Hyetograph: ERH is the plot of rainfall intensity and time after deducting the Phi – index. It is
plotted in the form of bar diagramme. The area of ERH is the depth of effective rainfall. The time duration of
ERH is the duration ER.

Direct Runoff: It is the runoff directly formed due to rainfall. In other words, the runoff excluding base flow is
the direct runoff. It can be presented in terms of volume and rate both. The depth of effective rainfall
multiplied by area of watershed is the direct runoff volume. The depth of effective rainfall is the area of ERH.

Relationship between ER and DR: In terms of depth both are same. However, the volume of direct runoff is
the product of ER and area of watershed. In other words, area of ERH multiplied with the area of watershed
casts the volume of direct runoff.
 Runoff Computation
There are host of method and empirical formulae for computing the runoff from a watershed, few important
amongst them are listed as under,

1. Rational method,
2. SCS method
3. Cooks method
4. Infiltration Indices method
5. Hydrograph method
6. Empirical formulae
 Rational Method
This method computes the peak runoff of small watershed. Peak runoff is required for design of hydraulic
structures such as culverts, bridges, drop structures, and others. The rational method is appropriate for estimating
peak discharge for small drainage areas of up to about 80 hectares with no significant flood storage. The method
provides the designer with a peak discharge value, but does not provide a time series of flow nor flow volume. This
method follows the hypothesis that

1. Runoff is directly proportional to the area of watershed , and

2. Directly proportional to the rainfall intensity
3. Rainfall intensity must be for the duration equal to time of concentration of watershed. Accordingly, if the area of
watershed is A (-) and rainfall intensity for the time equal to time of concentration of watershed is I then, the
equation of peak runoff (𝑄𝑝) is given as under,

𝑄𝑝 = 𝐶𝐼𝐴
Time of Concentration- The time of concentration (Tc) of watershed is defined as the time required for movement of
rainwater from remotest point to the outlet of watershed. If rainfall duration is equal to or greater than the TOC then
from entire watershed area the excess rainwater or runoff is started to generate, which cumulatively comes to the
watershed outlet. The cumulative runoff joining to the watershed outlet is at highest level, called peak runoff
The following formula given by Kirpitch (1940) can be used for determining the TOC of watershed.

In which 𝑇𝑐 is the time of concentration (minute); L is the longest length of water course (m) and s is the
average slope of water course (m/m).

The above formula is revised by Haan etal (1982) by including the component of overland flow. They reported
that the Rational Method does not compute well when size of watershed is less than 5sqkm area. Such
watersheds are dominated by overland flow rather channel flow or the runoff. In this condition after
incorporating the effect of overland flow the revised formula for TOC is mentioned as under,

In which, Lo is the length of overland flow (m) and n is the Manning’s roughness coefficient and s0 is
the slope of overland flow path (m/m)
Rainfall Intensity- It is the ratio of rainfall depth and duration of rainfall event. As per this definition the
computed rainfall intensity does not fit for rational method. The rainfall duration must be taken as the TOC
of watershed. Accordingly, the rainfall intensity is presented as the ratio of rainfall depth to the TOC.
Sometimes, for design of hydraulic structures such as the drop structure or grassed waterways etc the design
runoff for a given return period or rainfall frequency is required. For such cases the formula for rainfall
intensity – return period is given by the following expression.

in which, i is the rainfall intensity (cm/h) for given return period (T, year) and t is the TOC (h) and K ,a
,b and d are the regional constants
 Runoff Coefficient-
It is the fraction of total rainfall converted into runoff. In other terms it is the ratio of Runoff depth and
total rainfall depth. Its value is dimensionless varies from 0 to maximum 1 in which 0 is for soils having
very high rate of infiltration, i.e. there is no excess rainwater available for generating runoff from the
surface. The value of runoff coefficient for sandy soil may be approaching 1.0 at the beginning of rainfall
occurrence when total rain water is likely to get infiltrated into the soil. And the value of runoff coefficient
as 1.0 which is maximum may be for concrete or any hard formation in which the infiltration of rainwater is
about to zero. However, the runoff coefficient for use in rational method is cited below

The formula for determining the weighted runoff coefficient

In which, 𝐶𝑤 is the weighted runoff coefficient,
A is the total land area and C1 … Cn are runoff
coefficient for the area A1 ….An .
 Assumptions and Limitations- Rational method
Assumptions counted under rational method are as follows,
• Applicable when TOC of watershed is at least equal to or greater than the duration of peak rainfall
intensity.
• The calculated runoff is directly proportional to the rainfall intensity.
• Rainfall intensity is uniform throughout the duration of the storm.
• The frequency of occurrence for the peak discharge is the same as the frequency of the rainfall producing
that event.
• Rainfall is distributed uniformly over the drainage area.
• The minimum duration to be used for computation of rainfall intensity is 10 minutes. If the time of
concentration computed for the drainage area is less than 10 minutes, then 10 minutes should be adopted for
rainfall intensity computations.
• The rational method does not count for storage in the drainage area. Available storage is assumed to be
filled.
Problem (13)- For a watershed of varying land use systems, soils and topography, determine the weighted runoff
coefficient. The requisite details are outlined as under
 Problem (4)- Determine time of concentration of watershed, if

(i) Length of longest water course =1500m ;

(ii) Average longitudinal slope of water course=2.5%.
(iii) Length of overland flow=125m
(iv) Slope of overland flow path =0.02.

Take Manning’s roughness coefficient as 0.15.

Problem (15)- For a watershed of varying land use systems, soils and topography, determine the weighted
runoff coefficient,TOC peak runoff rate. The requisite details are outlined as under:

(i) Length of longest water course =1500m

(ii) Average longitudinal slope of water course=2.5%.
(iii) Length of overland flow=125m
(iv) Slope of overland flow path =0.02.
(v) Rainfall depth =5.0cm
(v)Take Manning’s roughness coefficient as 0.15
 SCS method of Runoff Computation

This method was originally established by the Soil Conservation Services (USA) in the year 1954 for
estimation of runoff based on rainfall depth from agricultural fields. However, it is now used as the method
for computing peak runoff rates and volumes for Urban Hydrology.

It calculates the runoff on the basis of retention capacity of soil, which is predicted by wetness status
(Antecedent Moisture Conditions [AMC]) and physical features of watershed. Method assumes that prior to
formation of runoff the possible initial losses such as interception, infiltration etc are fully satisfied by the
rainfall. The Initial loss (Ia) is taken as 0.2S, in which S is the retention capacity of the soil. Retention capacity
of soil is the function of Curve Number (CN).

The relationship between CN and S is given as under

in which, S is the retention capacity of the soil (cm). The value of CN is obtained from the table..
against given hydrologic soil group, land use, treatment and hydrologic condition of the area or the watershed
.
Problem (16)- Determine the runoff depth in response to a given rainfall of 15cm from the watershed of 500ha
area. Take level of initial abstraction as 1.5cm.
 Cooks Method of Runoff Computation

The method was developed by United States Department of Soil Conservation Services. This is a simple method and
more generalized, but involves similar approach to the estimation of peak runoff to the Rational Method. In Cooks
method the runoff approximation is carried out based on four different characteristics of watershed, namely (i)
Relief, (ii) Infiltration rate, (iii) Vegetal cover, and (iv) Surface depression. Numerical values for above four
characteristics are assigned in respect of extreme, high, normal and low runoff, given in following table (developed
by USDA
Infiltration Indices method
Infiltration of rainwater into the soil media plays a significant effect on surface runoff formation. Although, in case of sub-
surface runoff formation its effect is beneficial because infiltrated rainwater ultimately joins to the water- table via
percolation. Infiltration rate varies with the soil types, land use practices and so many other factors related to soil and
climate.
Runoff = Total rainfall – losses (Infiltration and other losses)
Infiltration Index- It is defined as the average infiltration rate during rainfall when rainfall intensity exceeds the infiltration
rate. The following infiltration indices are used for computing the infiltration rate,
1. ∅ − 𝐼𝑛𝑑𝑒𝑥
2. W- Index
∅ − 𝑰𝒏𝒅𝒆𝒙 - It is the loss of rainwater above which the volume of rainfall is equal to the volume of runoff. It is shown in Fig-. It is
determined from the rainfall hyetograph with the edge of the resulting runoff volume. In other words the ∅ − 𝐼𝑛𝑑𝑒𝑥 is the amount
of water loss from the rainfall, transforming into ER or the direct runoff
of ∅ − index from the rainfall hyetographThe area of ERH multiplied by the area of rainfall contributing catchment is
the volume of direct or surface runoff.
W- Index- It is refined form of ∅ − 𝐼𝑛𝑑𝑒𝑥 . In W- index the surface storage and retention are included. The
following formula can be used for its computation,

Problem (17)- Determine f- index based on the following data.

 Problem (18)- Determine W- index based on following data base,
(i) Depth of rainfall=13.5cm
(ii) Depth of runoff yield =7.0cm
(iii) Duration of rainfall excess=4.5hour
(iv) Depth of initial loss=1.350cm.
 Hydrograph Method
In common terms, hydrograph is a graph presenting the relationship between discharge and corresponding .

A hydrograph plotted between flow stage and time, is called stage hydrograph. The stage hydrograph is used in the
form of a stream gage record.
Hydrograph shows the time distribution of runoff at stream gauging point of watershed. Hydrograph reflects the
complex characteristics of the watershed. The duration or time of runoff flow is about to a constant for a particular
watershed, regardless of the peak flow from a specific storm, assuming constant storm duration.
With the help of hydrograph the runoff can be computed in following way,
1. Runoff volume- The runoff volume formed by a given rainfall event occurred in the watershed is determined by
calculating the area of hydrograph (DRH) resulted from the said rainfall event. In contrast, in case of perennial stream
hydrograph, it is determined by deducting the contribution of base flow from the hydrograph and computing the area of
new hydrograph called DRH.
2. Runoff rate – At any time instant the rate of runoff can be directly read from the hydrograph. In addition, the time of
peak runoff occurrence and what is the extent of peak runoff can also be directly read from the hydrograph.
3. Duration of Runoff: A hydrograph also provides the information about total time of runoff flow at the outlet of
watershed due to a given rainfall event.
 Empirical Formulae
Empirical formulae are developed for a specific condition and area based on the gauged data. These formulae have
limitations about their use unless they are validated for the new condition or watershed. There have been developed
several well recognized empirical formulae developed by different researchers for different regions /watersheds in
India and foreign countries for computing the runoff rate. Few important amongst them are described as under,
Runoff coefficient method

Runoff coefficient is the fraction of rainfall depth converted into runoff presented as C. This fraction is presented in
terms of the coefficient. This varies from place to place or one watershed to another because of variations in
watershed characteristics, soil, vegetations etc. The value of runoff coefficient varies from 0 to maximum 1.0. The
value of C as 0 is for highly coarse textured soils in which total rainwater is likely to get infiltrated. In contrast the C as
little less than 1.0 is for those soils which have very less rainwater loss due to infiltration. Normally, the hard soils
(impervious) are the example of it. Although, there is loss of water, but very small, is counted negligible. The runoff
computing formula can be presented in following form,
𝑅 = 𝑘. 𝑃
in which R is the runoff (depth), k is the coefficient (dimensionless) and P is the rainfall (depth). The value of k is
given in following table.
 Regression Formula
Chow (1964) listed several regression equations as empirical formulae for computing the runoff on the
basis of area of drainage basin. The form of equation is given a sunder,
𝑄 = 𝐶𝐴𝑛
in which Q is the runoff (m3/s), C & n are the empirical constant and A is the area of drainage basin
(sqKm).
Dicken Formula
It is an regression equation model for predicting the runoff. Originally it was developed for design of
bridge. This formula hold good for central and north India. The equation is given as under,

In this formula the value of C varies 2.80 to 5.60 for plain regions and 14 to 28 for mountainous regions.
 Problem (19)-Using Dicken’s formula compute the runoff of small watershed dominated by residential
establishments, if area of watershed is 100sqkm falling within 25km periphery from sea. Take the value of
constant relating the runoff as 2.80.

Ryve’s formula
It is basically modified form of Dickens’ formula, useful for south Indian coastal areas lying within periphery of
25 km from the sea. Formula is given as under,
𝑄 = 𝐶𝐴2/3
In this formula the value of C is taken as 6.8 for flat tracts and 42.40 for western ghat areas.
Problem (20)- Using Ryve’s formula compute the rate of flood flow from a catchment located at the distance of 60Km
from sea coast in south India. The size of catchments is 75sqkm. The value of coefficient is 6.8
 Inglis formula: C.C. Inglis (1940) developed following two empirical formulae for two different areas,
given as under,

Problem (21)- Determine the flood flow rate form the catchment located in Maharashtra. The area of
catchment is about 125sqkm. Use Inglis formula
Khosla formula: This formula was developed by considering the temperature in addition to
precipitation. The formula is given as under,
 Hydrograph
In common terms, hydrograph is a graph presenting the relationship between discharge and corresponding
time. However in broad sense the graph showing the stage, velocity, or other properties of water flow with
respect to time is also called hydrograph. A hydrograph plotted between flow stage and time, is called stage
hydrograph. The stage hydrograph is used in the form of a stream gage record. Hydrograph shows the time
distribution of runoff at stream gauging point of watershed. Hydrograph reflects the complex characteristics of
the watershed. The duration or time of runoff flow is about to a constant for a particular watershed, regardless
of the peak flow from a specific storm, assuming constant storm duration.
Hydrograph included following three characteristics regions,
1. Rising limb,
2. Crest or peak , and
3. Falling limb.
Rising limb- It represents the region of increase in runoff with
respect to enhancement of rainfall duration over the watershed
surface. The plotted curve attains very steep slope. Because of
this reason some times, this region is also called concentration
curve. The watershed and rainfall characteristics both in combine
form affect this region.
Crest or peak- This region of hydrograph includes peak of runoff formed from the watershed due to a given rainfall
event. Extent of this region is for a very short time extended from the point of inflections on rising limb and to a
similar point towards falling limb. This segment is also affected by watershed and rainfall characteristics both in
combine form. A hydrograph with single peak is called single peak hydrograph. Sometimes, due to variation in
rainfall intensity and complicity of watershed shape, the runoff bears more than one peak, and accordingly the
plotted hydrograph contains more than none peak. Such hydrographs are called complex hydrograph. Normally,
for study purposes of the single peak
hydrographs are commonly used. Because of this reason the selection of rainfall event or runoff data should be
done by considering this fact into account.

Falling limb- It starts from the point of inflection at falling limb to the end of runoff yield. The point of inflection
represents the point when rainfall event has been stopped. The flow of runoff at out let is only the stored rainwater
in the stream courses or watershed surface. The rate of runoff flow depends to large extent on the channel
characteristics. Comparatively, this region is largest amongst all.
Factors Affecting Hydrograph Shape
 Depth and Duration of Effective Rainfall
In computation of direct runoff/direct runoff hydrograph or the unit hydrograph the information on effective
rainfall is required. The area of contributing watershed multiplied by the depth of ER is the volume of direct
runoff. The depth of ER is calculated with the help of effective rainfall hyetograph (ERH) which is obtained by
deducting the value of ∅ 𝑖𝑛𝑑𝑒𝑥 from the hyetograph. Area of ERH denotes to the depth of effective rainfall. The
duration of ER is also determined from the ERH, which is determined by counting those time periods for which
rainfall is still remained after deducting the ∅ 𝑖𝑛𝑑𝑒𝑥 , from the hyetograph

Direct Runoff Hydrograph

The hydrograph resulted from direct runoff is called direct runoff hydrograph (DRH). It is also derived with the help
of runoff hydrograph of perennial stream by deducting the base flow contribution. Area of DRH is the volume of
direct runoff. The hydrograph derived from the runoff data of intermittent and ephemeral streams are the DRH as
there is no contribution of base flow in runoff observations
Straight line method: In this method the beginning point of surface/direct runoff and the point representing the end
of direct runoff on recession limb are joined together by a straight line for separating the base flow as shown in Fig-.
The area below the straight line represents the contribution of base flow from the total runoff. In Fig the Point
A is the beginning of direct runoff off and B is the end of direct runoff. The beginning of direct runoff is usually identified
in the view of a sharp change in the runoff rate at the point or time concern. In contrast the exact location of end point B
is difficult. However, the following empirical formula can be used for locating the end point of direct runoff,
𝑁 = 0.83𝐴0.2
in which N is the days from the peak towards recession limb of hydrograph and A is drainage area in (km2). This method
of base-flow separation is the simplest of all the three methods.
Problem (22)-Determine the value of recession constant for interflow, if rate of initial discharge is 120m3/h
and discharge after 2.0 hour is 250m³/h.

Problem (23)- The record of time vs discharge data against a given rainfall event of gauged watershed
denotes the peak runoff taken place after 8 hours from start of runoff. The area of watershed is 50sqkm.
Determine the end time of runoff from watershed.
 Unit Hydrograph
The unit hydrograph of a given watershed is derived with the help of DRH. Unit hydrograph is the DRH of unit depth of
effective rainfall. The depth of ER is determined by the effective rainfall hyetograph. Area of ERH is the depth of ER, and
its duration denotes to the duration of ER. A unit hydrograph is designated for a given duration of ER.

Definition: It is a typical hydrograph of direct runoff generated from unit depth (1cm) of effective
rainfall falling at a uniform rate over the entire drainage basin and is uniformly distributed during a specific
duration
Assumptions:
The main assumptions followed for driving unit hydrograph are as follows
(i) Effective rainfall is uniformly distributed over the entire drainage basin and within its specified duration. The
rainfall events of small duration generally produce an intense and nearly uniform effective rainfall. The
produced hydrograph is of single peak with short time base. Such a storm is termed as “unit storm”, is selected
for unit hydrographdevelopment.
(ii) The effective rainfalls of equal (unit) duration will produce the DRHs having same or constant time base.
(iii) The ordinate of direct runoff hydrograph is directly proportional to the depth of ER. This is assumption is
called as principle of linearity or superposition.
(iv) The DRH of a given effective rainfall will remain invariable irrespective of its time of occurrence. This
assumption is called principle of time invariance.
 Limitations:
These are as below,
(i) Unit hydrograph development is valid and suitable for small watersheds, in which the uniformly distribution of
effective is possible to a large scale within storm duration. The limiting size of the drainage basin is considered to be
5000 sqkm. However, in the condition when area of drainage basin exceeds the limit, the large area is sub-divided into
smaller units (sub- watersheds) and unit hydrograph for each of them is developed. The runoff at the watershed outlet
can then be determined by combining the runoff of sub- watershed using flood routing technique.
(ii) The derivation of unit hydrograph is only feasible for the rainfall events having precipitation in the form of rainfall.
(iii) (iii) Also, for the watershed covered to a large extent by the snow cover the development of unit hydrograph for runoff
estimation is not found suitable.
(iv) (iv)Also, for the watersheds having significant change in land cover or physical characteristics w.r.t. seasons,
development of man-made structures, conditions of flow etc the unit hydrograph theory, i.e. the principle of time
invariance is not satisfied, and thus, the development of unit hydrograph is not found realistic.
(v) It is commonly observed that no two rainfall events have same pattern, temporally and spatially, both; and it is not
practicable to derive separate unit hydrograph for each time- intensity pattern. Therefore, in addition to limiting
drainage basin area up to 5000 sqkm, if storms of shorter duration say for 33 to 25% of peak times are selected, the
runoff pattern does not vary drastically.
(vi) The principle of linearity assumption of unit hydrograph is also not valid because of the reason that there is a large
variation in the quantity of direct or surface runoff formation, even the level of peak runoff due to the rainfall event of
short and large durations for the same watershed.
 Unit Hydrograph for Different Durations

Originally, a unit hydrograph derived for a given watershed is of fixed duration of ER depending on the rainfall event. ER
duration affects the yield of direct runoff from a watershed due to a given rainfall, and accordingly the nature of UHG
also. Because of this reason, sometimes, the requirement of UHG for different ER durations is required for hydrological
analysis of a watershed. A unit hydrograph may be
1. in the multiple of given duration of ER of UHG, and
2. of any ER duration.
Case – 1: When ER duration is in multiple of given ER duration. Superposition
method
In this case the given UHG is superimposed lagged by the given ER duration to (n-1) times in which n is
the multiple numbers. And the time segment -wise ordinates are added together. The obtained
ordinates present the ordinate of DRH, which is divided by the number of superimposition/ lagging.
Example-- illustrates the procedure.
Case-2: For any ER duration
The derivation of UHG for any ER duration, i.e. when desired ER duration is not in term of multiple of original ER
duration of UHG cannot be done by the method of superimposition. For this purpose the S-curve method is
followed to derive the UHG
 Average Unit Hydrograph
The UHG derived for a given watershed are not identical because of temporal and spatial variation in rainfall
pattern. In this condition the UHG derived for different rainfall events are averaged. It is carried out based on
the following information related to derived UHG,
1. Average time to peak
2. Average peak discharge, and
3. Average base width.

Synthetic Unit Hydrograph

It is an artificial unit hydrograph derived for un-gauged watershed, developed by Snyder (1938). Because of this
reason sometimes this hydrograph is also known as Snyder Unit Hydrograph. An un-gauged watershed which is
located at very remote areas does not have the record of rainfall- runoff for the rainfall events taken place, there.
The concept of SIUHG was firstly developed by The SIUHG is derived on the basis of watershed morphology and
rainfall – runoff data of Morpho-hydrologically identical watershed located in the adjoining to the un- gauged
watershed. For this purpose the empirical formulae relating the watershed characteristics and requisite
parameters of UHG are used. The associated formulae for computing SIUGHG parameters are described as under
In order to sketch the SIUHG properly and smoothly the U. S. Corps of Engineers have suggested the widths
of unit hydrographs at 50 and 75% of the peak. The computing formulae are as under,

Problem (24)- Calculate the width of Synthetic Unit Hydrograph at 50 and 75% of the peak flow.
The peak discharge of watershed is 30m3/s and area of watershed is 300sqkm.
 Dimensionless Unit Hydrograph
It is a kind of SIUHG, developed by the Soil Conservation Services in the 1972. In this UHG the ordinate is
expressed by the ratio of discharge (Q) to peak discharge (Qpk) and abscissa by the ratio of time (t) to time of
rise of unit hydrograph (tpk). View of DUHG is shown in Figure-. By using this method the unit
hydrograph can be easily developed for a given peak discharge and lag time. It involves following formulae,
Thank You