Applied Hydrology.pptx

Wollega University
College of Engineering and Technology
Hydraulic and water Resources Engineering Department
Course Title- Applied Hydrology
Course Code- HENG-6121
Degree Programme- Master of Science in Hydraulic
Engineering
Module- Applied Hydrology and Water System Planning
and Management
ECTS Credits-6
Contact Hours per week-6

Hydrology Defined
Hydrology is an earth science.
It encompasses
 the origin (occurrence),
 distribution,
 movement, and
 properties of the waters of the earth.
 A knowledge of hydrology is one of the key ingredients in decision
making processes where water is involved.
 The study of water can mean different things to different professions.
 To a chemist, a water molecule is a stable chemical bond of two atoms
of hydrogen and one atom of oxygen;

Hydrology Defined
 the chemist will be interested in the properties of water and its role
in chemical reactions.
 The climatologist will be interested in the effect of the water stored
in the soil and lakes on climatic processes.
 To those involved in the design of hydraulic machinery, the study of
the properties of water will concentrate on the forces exerted by
water in a dynamic state.
 To the mechanical engineer, the properties of water in the form of
steam can be important
 The ground water hydrologist will be interested in the movement of
water in transporting pollutants.

Hydrology Defined
 Even geographers and historians may be interested in water, at least
in terms of how its availability and accessibility has shaped
development and culture.
 However, our interest herein is in the narrow field of hydrologic
engineering analysis and design
 Engineering hydrology encompasses those aspects of hydrology that
relate to the design and operation of engineering projects for the
control and use of water.
 In an attempt to overcome the problems created by the variations in
the temporal and spatial variations in water availability, engineers
and hydrologists attempt to make predictions of water availability.

Hydrology Defined
 These predictions are used in the evaluation of alternative means of
preventing or solving problems. A number of factors contribute to the
ineffectiveness of these engineering designs.
 First, the occurrence of rainfall cannot be predicted with certainty.
That is, it is not possible to predict exactly how much rain will occur
in one time period (for example, day, month, and year).
 The uncertainty of extreme variation in rainfall amounts is even
greater than the uncertainty in the rainfall volumes occurring in the
more frequent storm events.
 It is difficult to design engineering works that will control the water
under all conditions of variation in both the time and spatial
distribution.

Hydrology Defined
 Second, even if we had perfect information, the cost of all of the
worthwhile projects needed to provide the optimum availability of
water is still prohibitive.
 Therefore, only the most efficient and necessary projects can be
constructed.
 Third, hydrologic processes such as rainfall and runoff are very
complex and a complete, unified theory of hydrology does not exist.
 Therefore, measurements of observed occurrences are used to
supplement the scant theoretical understanding of hydrologic
processes that exists.
 However, given the limited records of data, the accuracy of many
engineering designs is less than we would like.

Hydrology Defined
 These three factors (hydrologic uncertainty, economic limitations,
and lack of theory and observed data) are just some of the reasons
that we cannot provide solutions to all problems created by
undesirable variations in the spatial and temporal distributions of
water.

Engineering application
Hydrology finds its greatest application in the design and operation of
engineering projects, such as:
1. Irrigation 4. Hydropower plants
2. Water supply 5. Navigation
3. Flood control
 In all these projects hydrological investigations for the proper
assessment of the following factors are necessary.
1. The capacity of storage structures such as reservoirs
2. The magnitude of flood flows to enable safe disposal of the excess
flow

3.The minimum flow and quantity of flow available at various seasons
4.The interaction of the flood wave and hydraulic structures, such as
levees, reservoirs, barrages and bridges
 Engineering application of principles of hydrology also include
 the design of culverts (for example, a pipe that crosses under a road
or embankment), surface drainage inlets, and bridges that cross over
rivers and streams
 Those involved in the design of structures must understand the basic
concepts of hydrologic analysis because design of these structures
require consideration of the fundamental concepts of hydrology.

 For proper drainage of storm runoff the fundamental knowledge of
hydrology is required.
 There are many other hydrologic analyses required in building
construction
 When clearing land for development:
 Provision of sediment control facilities to ensure that eroded soil
does not enter into waterways and wetlands.
 Sediment control depends:
 on the area of the land being cleared,
 the amount of rainfall that can be expected during the period where
the soil will be exposed to rainfall impact,

and site characteristics such as
the slope and soil type.
In addition to hydrologic considerations during the land development
stage, site development must consider drainage patterns after
development.
The design must consider meteorological factors, geomorphological
factors, and the economic value of the land, as well as human value
considerations such as aesthetic and public safety aspects of the
design.
The design of a storm water detention basin should also consider the
possible effects of inadequate maintenance of the facility.

 The hydrologic designs discussed in the preceding paragraphs are
based primarily on rainfall and the resulting surface runoff.
 Dams and the water stored in the reservoirs behind the dams provide
many benefits, such as
 power generation, recreation,
 flood control,
 irrigation, and
 the maintenance of low flows for water quality control.
 In addition to estimating the volume of inflow into the reservoir, dam
design requires assessment of the evaporation losses from the
reservoir.

 For reservoirs with large surface areas,
 evaporation losses can be significant.
 Failure to consider evaporation losses during the design could result
 in overestimating the water that would be available for the
purposes stated above.
 Thus, failure to understand the processes of the hydrologic cycle
may render the design inadequate.

The Hydrologic cycle
 The physical processes controlling the distribution and movement of
water are best understood in terms of the hydrologic cycle.
 Although there is no real beginning or ending point of the hydrologic
cycle, we can begin the discussion with precipitation
 The hydrologic cycle is a global process whereby water is
transported from the oceans to the atmosphere to the land and back to
the sea.

 The ocean is the earth’s principal reservoir; 97% of the terrestrial water
 Water is evaporated by the sun, incorporated into clouds as water vapor,
falls to the land and sea as precipitation, and ultimately finds its way
back to the atmosphere through a variety of hydrologic processes.
 The hydrologic cycle can be considered a closed system for the earth
because the total amount of water in the cycle is fixed even though its
distribution in time and space varies.
 There are many sub-cycles within the worldwide system, however, and
they are generally open ended.
 It is these subsystems that give rise to the many problems of water
supply and allocation that confront hydrologists and water managers.

 The hydrologic cycle is usually described in terms of six major
components:
 Precipitation (p),
 Infiltration (I),
 evaporation (E),
 Transpiration (T),
 surface runoff (R), and
 groundwater flow (G).
 For computational purposes, evaporation and transpiration are
sometimes lumped together as evapotranspiration (ET).

0= evaporation from ocean
1=rainwater evaporation
2= interception
3= transpiration
4= Evaporation from land
5=Evaporation from water bodies
6=Surface Runoff
7=Infiltration
8= Groundwater
9= Deep percolation
 The above figure illustrates that some precipitation evaporates before
reaching the earth and remains in the atmosphere as water vapor.
 Water also evaporates after reaching the earth.
 Plants take up infiltrated water and groundwater and return a portion of
it to the atmosphere through their leaves, a process known as
transpiration.

Some infiltrated water may emerge to surface water bodies as
interflow, while other portions may become groundwater flow.
 Groundwater may ultimately be discharged into streams or may
emerge as springs.
After an initial filling of interception and depression storages and
providing that the rate of precipitation exceeds that of infiltration,
overland flow (surface runoff) begins.
The magnitude and duration of a precipitation event determine the
relative importance of each component of the hydrologic cycle during
that event.
The hydrologic cycle, while simple in concept, is in reality, very

 The hydrologic cycle, while simple in concept, is in reality, very
complex.
 Paths taken by precipitated droplets of water are many and varied
before the sea is reached.
 The time scale may be of the order of seconds, minutes, hours, days,
or even years.

Hydrologic Abstractions
The collective term given to the various processes that act to remove
water from the incoming precipitation before it leaves the watershed
as runoff is abstractions.
These processes are
evaporation,
transpiration,
interception,
infiltration,
depression storage, and
detention storage.

Hydrologic Abstractions
The most important abstractions in determining the surface runoff
from a given precipitation event are
infiltration,
depression storage, and
detention storage.
Evaporation
 Evaporation is the process by which water from the land and water
surfaces is converted into water vapor and returned to the
atmosphere.
 It occurs continually whenever the air is unsaturated and temperatures
are sufficiently high.

Evaporation
Air is 'saturated' when it holds its maximum capacity of moisture at the
given temperature.
Saturated air has a relative humidity of 100 percent.
Evaporation plays a major role in determining the long-term water
balance in a watershed.
 However, evaporation is usually insignificant in small watersheds for
single storm events and can be discounted when calculating the
discharge from a given rainfall event.
Transpiration
Transpiration is the physical removal of water from the watershed by
the life actions associated with the growth of vegetation.

Transpiration
In the process of respiration, green plants consume water from the
ground and transpire water vapor to the air through their foliage.
As was the case with evaporation, this abstraction is only significant
when taken over a long period of time, and has minimal effect upon
the runoff resulting from a single storm event for a watershed.
Interception
 Interception is the removal of water that wets and adheres to objects
above ground such as buildings, trees, and vegetation.
 This water is subsequently removed from the surface through
evaporation.
 Interception can be as high as 2 mm during a single rainfall event,
but usually is nearer 0.5 mm.

Interception
The quantity of water removed through interception is usually not
significant for an isolated storm, but, when added over a period of
time, it can be significant.
It is thought that as much as 25 percent of the total annual PPT is lost
through interception during the course of a year.

Infiltration
Infiltration is the flow of water into the ground by percolation
through the earth's surface.
The process of infiltration is complex and depends upon many
factors such as soil type, vegetal cover, antecedent moisture
conditions or the amount of time elapsed since the last precipitation
event, precipitation intensity, and temperature.
Infiltration is usually the single most important abstraction in
determining the response of a watershed to a given rainfall event.
As important as it is, no generally acceptable model has been
developed to accurately predict infiltration rates or total infiltration
volumes for a given watershed.

Depression Storage
Depression storage is the term applied to water that is lost because it
becomes trapped in the numerous small depressions that are
characteristic of any natural surface.
When water temporarily accumulates in a low point with no
possibility for escape as runoff, the accumulation is referred to as
depression storage.
The amount of water that is lost due to depression storage varies
greatly with the land use. A paved surface will not detain as much
water as a recently furrowed field.
The relative importance of depression storage in determining the
runoff from a given storm depends on the amount and intensity of
precipitation in the storm.

Depression Storage
 Typical values for depression storage range from 1 to 8 mm (0.04 to
0.3 in) with some values as high as 15 mm (0.6 in) per event.
 As with evaporation and transpiration, depression storage is generally
not directly calculated in highway design.
Detention Storage
 Detention structures store water for a relatively short period of time.
 These facilities drain primarily by discharging either overland or
directly to a man-made or natural watercourse.
 Examples of detention structures include detention basins,
subsurface structures for temporary storm water storage, and (on a
larger scale) flood control reservoirs.

Detention Storage
Natural ponds, lakes, and stream channels also provide detention of
water as it moves over the face of the earth.
Detention storage is water that is temporarily stored in the depth of
water necessary for overland flow to occur.
The volume of water in motion over the land constitutes the
detention storage.
The amount of water that will be stored is dependent on a number of
factors such as land use, vegetal cover, slope, and rainfall intensity.
Typical values for detention storage range from 2 to 10 mm, but
values as high as 50 mm have been reported.

Retention structures
 Retention structures: generally hold water for a relatively long
period of time.
 Stored water in retention systems is depleted overtime primarily by
infiltration or evaporation.
 The distinguishing characteristic of retention facilities is that they
do not have a surface discharge for most flows (although they may
be designed with an overflow provision for extreme storm events).
 Examples of retention structures include recharge basins or ponds
(sometimes referred to as infiltration basins), subsurface recharge
systems such as dry wells and infiltration galleys, and water quality
swales designed for infiltration.

Total Abstraction Methods
 While the volumes of the individual abstractions may be small, their
sum can be hydrologically significant.
 Therefore, hydrologic methods commonly lump all abstractions
together and compute a single value.
 The SCS curve number method lumps all abstractions together, with
the volume equal to the difference between the volumes of rainfall and
runoff.
 The phi-index method assumes a constant rate of abstraction over the
duration of the storm.
 These total abstraction methods simplify the calculation of storm
runoff rates.

Hydro-meteorological measurement and data analysis
a. Units of Measurements:
 stream and river flows are usually recorded as cubic meter per second
(m3/s).
 Groundwater flows and water supply flows are commonly measured in
m3 or liters per unit time and flows used in agriculture or related to
water storage are often expressed as depth per unit time.
 Volumes are given as cubic meters, liters or cubic centimeters.
 Precipitation depths are recorded in inches or centimeters, whereas
precipitation rates are given in inches or centimeters per unit time.
 Evaporation, Transpiration and infiltration rates are also given as
inches or centimeters of depth per unit time.

Hydro-meteorological measurement and data
analysis
b. Hydrological data:
 data on hydrological variables are fundamental to analyses,
forecasting, and modeling.
c. General climatological data:
 The most readily available sources of data on temperature, solar
radiation, wind, relative humidity and precipitation in Ethiopia is the
National Meteorological Service Agency (NMSA).
 The data is available on daily basis.
 There are also some web sites where data can be downloaded for
certain use in some software like SWAT.

d. Precipitation Measurement and data analysis:
 Precipitation is the primary source of fresh water supply and its
records are the basis of most studies dealing with water supply in all
its forms, floods, and droughts.
 Of all hydrological data, data on precipitation are most readily
available and have been collected for the longest periods.
 Precipitation is all meteoric water (water of direct atmospheric origin)
that falls on the Earth’s surface, whether in liquid form (rain or
drizzle), solid form (snow, ice pellets, hail), or occult form (frost, dew,
hoarfrost).

The formation of precipitation requires a four step process:
(1) Cooling of air to approximately the dew-point temperature;
(2) Condensation on nuclei to form cloud droplets or ice crystals;
(3) Growth of droplets or crystals into rain drops, snowflakes or
hailstones and
(4) Importation of water vapor to sustain the process of precipitation
geographically, temporally, and seasonally.
 This regional and temporal variation in precipitation are important in
water resources planning and hydrologic studies.
 The amount fallen is usually expressed in terms of precipitation depth
per unit of horizontal area [mm] or in terms of intensity[mm/h], which

 Precipitation is usually measured with a rain gauge placed in the
open space.
 The catch of a gauge is influenced by the wind, which usually
causes low readings.
 Gauges for measuring rainfall may be recording or non-recording.
 The most commonly non-recording gauge is the US Weather
Bureau Standard 8-inch gauge.
 They cannot be used to indicate the time distribution of rainfall.
 Time variation in rainfall intensity is extremely important in the
rainfall-runoff process.
 Recording gauges continuously sense the rate of rainfall and its time

 These gauges are either of the weighing-recording type or the tipping-
bucket type.
 Weighing type gauges usually run for a period of one week, at which
time their charts must be changed.
 Rainfall measurements can also be made using satellite sensors and
radar.
Types of Precipitation (by Origin)
 Precipitation can be classified by the origin of the lifting motion that
causes the precipitation.
 The three major types of storms are classified as convective storms,
orographic storms, and cyclonic storms

A) Convective Storms
 Precipitation from convective storms results as warm moist air rises
from lower elevations into cooler overlying air.
 The characteristic form of convective precipitation is the summer
thunderstorm.
 The surface of the earth is warmed considerably by mid- to late
afternoon of a summer day, the surface imparting its heat to the
adjacent air.
 The rapid condensation may often result in huge quantities of rain
from a single thunderstorm spawned by convective action, and very
large rainfall rates and depths are quite common beneath slowly
moving thunderstorms.

B) Orographic Storm
 Orographic precipitation results as air is forced to rise over a fixed-
position geographic feature such as a range of mountains.
 Mountain slopes that face the wind (windward) are much wetter than
the opposite (leeward) slopes.

C) Cyclonic Storms
 Cyclonic precipitation is caused by the rising or lifting of air as it
converges on an area of low pressure.
 Air moves from areas of higher pressure toward areas of lower
pressure. In the middle latitudes, cyclonic storms generally move
from west to east and have both cold and warm air associated with
them.
 These mid-latitude cyclones are sometimes called extra-tropical
cyclones or continental storms.

Processing and Analysis of Precipitation Data
Point Precipitation
 Precipitation events are recorded by gauges at specific locations.
 The resulting data permit determination of the frequency and
character of precipitation events in the vicinity of the site.
 Point precipitation data are used collectively to estimate areal
variability of rain and are also used individually for developing
design storm characteristics of small urban and other watersheds.
 Point rainfall data are used to derive intensity-duration- frequency
curves.
 Failure of any rain gauge or absence of observer from a station
causes short break in the record of rainfall at the station.

 These gaps are to be estimated first before we use the rainfall data
for any analysis.
 The surrounding stations located within the basin help to fill the
missing data on the assumption of hydro-meteorological similarity
of the group of stations.
 The general equation of the weightage transmission of the rainfall of
the nearby stations to the missing station (Xi) can be represented as:

Where,
 Pi is the normal rainfall of ith surrounding station, i= 1, 2, … n are
the surrounding gauge numbers which are used for filling the gaps,
 ai the weighting factor of the station Pi and Pxi is the data
required to be filled up.
 The methods mostly to be used in hydrology for filling the missing
data are, Arithmetic mean method, normal ratio method, and
distance power methods are generally used for filling up the
missing rainfall data.
a) Arithmetic Mean Method
This method is used when:

(i) The normal annual rainfall of the missing station x is within 10% of
the normal annual rainfall of the surrounding stations,
(ii) Data of at least three surrounding stations, called index station are
available within the basin,
(iii)The index stations should be evenly spaced around the missing
station and should be as close as possible,
(iv)The missing rainfall data of station x is computed by simple
arithmetic average of the index stations in the form:

 In which are the precipitations of index stations and px
that of the missing station, n the number of index stations.
 The word normal means average of 30 years of data, i.e., 30 values
of the latest records.
 For example, for a station when the last 30 years of June month
rainfall is averaged, we call it as normal rainfall for the month of
June for that station.
b) Normal Ratio Method
 This method is used when the normal annual precipitation of the
index stations differ by more than 10% of the missing stations.

 In the normal ratio method, the rain fall RA at station A is estimated
as a function of the normal monthly or annual rainfall of the station
under question and those of the neighboring stations for the period of
missing data at the station under question.
 The rainfall of the surrounding index stations are weighted by the
ratio of normal annual rainfall by using the following equation:

Where,
RA is the estimated rainfall at station A
Ri is the rainfall at surrounding stations
NRA is the normal monthly or seasonal rainfall at station A
NRi is the normal monthly or seasonal rainfall at station i
n is the number of surrounding stations whose data used for
estimation
c) Distance power method:
In this method, the rainfall at a station is estimated as a weighted
average of observed rainfall at the neighboring stations.

The weights are taken as equal to the reciprocal of the distance of
some power of the estimator station.
Where, RA and Ri has the same notation as in case of normal ratio
method and Di is the distance of the estimator station from the
estimated station.

d) Inverse Distance Methods
 In this method a rectangular coordinate system is superimposed over
the map marked with rain gauge stations in such a way that the origin
(0, 0) represents the missing station.
 The surrounding index station lies within the quadrants to the point
for which rainfall is to be estimated.
 The distance of index stations from the missing station gives a
weightage of the station by which missing rainfall is estimated. The
following relation may be used.

Where, wi =1/D2, D2 = ( is the distance of the station I in x and y
coordinates taking missing rainfall station at (0, 0) position. This is
the most acceptable method and is widely used for determining the
missing rainfall for any scientific analysis.
e) Regression method
Using regression technique, a linear equation of the form Y=a + bx is
fitted, where

Areal Distribution of Rainfall
 For most hydrologic analyses, it is important to know the areal
distribution of precipitation.
 average depths for representative portions of the watershed are
determined and used for this purpose.
 The most direct approach is to use the arithmetic average of gauged
quantities.
 This procedure is satisfactory if gauges are uniformly distributed
and the topography is flat.
Spatial Averaging of Rainfall Data
 Precipitation observations from gauges are point measurements.
 However, in the hydrological analysis and design, we frequently
require mean areal precipitation over an area.

 A characteristic of the precipitation process is that it exhibits
appreciable spatial variation though the values at relatively short
distances may have good correlation.
 Numerous methods of computing areal rainfall from point
measurements have been developed.
 While using precipitation data, one often comes across missing data
situations.
 Data for the period of missing rainfall could be filled using various
techniques.
 Due to the spatial structure of precipitation data, some type of
interpolation making use of the data of nearby stations is commonly
adopted.

 Using a linear interpolation technique, an estimate of precipitation
over the area can be expressed by:
Where, Wi is the weight of the ith station
The most commonly used methods for Spatial Averaging of
Precipitation Data are:
(a) Arithmetic average,
(b) Thiessen polygon method, and
(c) Isohyetal method.

The choice of the method depends on
 the quality and nature of data,
 importance of use and required precision,
 availability of time and computer.
Arithmetic Average
 It is applied for a basin where the gauges are uniformly distributed
and the individual gauge catches do not vary much from the mean.
 The basin should be reasonably flat area.
 The assumption made is that all gauges weigh equally.
 This method gives fairly good results if the topographic influences on
precipitation and aerial representativeness are considered while
selecting the gauge site.

 It is the simplest form in which the average depth of precipitation
over the basin is obtained by taking simple arithmetic mean of all the
gauged amounts within the basin.
 The simplest technique to compute the average precipitation depth
over a catchment area is to take an arithmetic average of the observed
precipitation depths at gauges within the catchment area for the time
period of concern. The average precipitation is:

 Where, P is the average catchment precipitation from the data of n
stations, Pi is the precipitation at station i, and Wi is the weight of
ith station.
 If the gauges are relatively uniformly distributed over the
catchment and the rainfall values do not have a wide variation, this
technique yields good results.
 Where,
P is the average catchment precipitation from the data of n stations,
Pi is the precipitation at station i, and Wi is the weight of ith station.

 If the gauges are relatively uniformly distributed over the catchment
and the rainfall values do not have a wide variation, this technique
yields good results.
 Thiessen Polygon
 The Thiessen Polygon method is based on the concept of proximal
mapping.
 All the stations in and around the basin are considered and a linear
variation in the precipitation between two gauge stations is assumed.
 In this method weightage is given to all the measuring gauges on the
basis of their aerial coverage on the map thus eliminating the
discrepancies in their spacing over the basin.

 Weights are assigned to each station according to the catchment area
which is closer to that station than to any other station.
 This area is found by drawing perpendicular bisectors of the lines
joining the nearby stations so that the polygons are formed around
each station.
 It is assumed that these polygons are the boundaries of the catchment
area which is represented by the station lying inside the polygon.

 The area represented by each station is measured and is expressed as
a percentage of the total area.
 The weighted average precipitation for the basin is computed by
multiplying the precipitation received at each station by its weight
and summing.
 The weighted average precipitation is given by:
 in which Wi = Ai/A, where Ai is the area represented by the station i
and A is the total catchment area. Clearly, the weights will sum to
unity.

An advantage of this method is that the data of stations outside the
catchment may also be used if these are believed to help in capturing
the variation of rainfall in the catchment.
The method works well with non-uniform spacing of stations.
Isohyetal Method
The isohyetal method employs the area encompassed between
isohyetal lines.
Rainfall values are plotted at their respective stations on a suitable
base map and contours of equal rainfall, called isohyets, are drawn.
 In regions of little or no physiographic influence, drawing of
isohyetal contours is relatively simple matter of interpolation.

The isohyetal contours may be drawn take into account the spacing
of stations, the quality, and variability of the data.
In pronounced orography where precipitation is influenced by
topography, the analyst should take into consideration the orographic
effects, storm orientation etc. to adjust or interpolate between station
values.
 Computers are being used to draw isohyetal maps these days, by
using special software.
 As an example, the isohyetal map for an area is shown in Fig
below.

The total depth of precipitation is computed by measuring the area
between successive isohyets, multiplying this area by the average
rainfall of the two isohyets, and totaling.
The average depth of precipitation is obtained by dividing this sum
by the total area. The average depth of precipitation (Pi) over this
area is obtained by:
Where, Ai is the area between successive isohyets and Pi is the
average rainfall between the two isohyets.

Optimum Rain-gauge Network Design
Ideally a basin should have as many numbers of gauges possible to
give a clear representative picture of the aerial distribution of the
precipitation.
Factors like economy, topography, accessibility, and rainfall
variability govern the number of stations for a basin.
There is no definite rule as to how many gauge are needed for a
complete ungauged basin.
WMO recommends certain density of gauges to be followed for
different types of catchments.
The optimum rain-gauge network design is to obtain all quantitative
data averages and extremes that define the statistical distribution of the
hydro-meteorological elements, with sufficient accuracy.

 When the mean areal depth of rainfall is calculated by the simple
arithmetic average, the optimum number of rain-gauge stations to be
established in a given basin is given by the equation :
 Where, N = optimum number of rain gauge stations to be established
in the basin,
 CV = Coefficient of variation of the rainfall of the existing rain
gauge stations (say, n),
 p = desired degree of percentage error in the estimate of the average
depth of rainfall over the basin.

Coefficient of variation can be calculated in the following steps from
the data of existing n stations:
1) Calculate the mean of rainfall from the equation,
2) Calculate the standard deviation as,
3) compute the coefficient of variation as,

If the allowable percent of error in estimating the mean rainfall is
taken higher, then a basin will require fewer numbers of gauges and
vice-versa.
The allowable percent of error is normally taken as 10%.
 The number of additional rain-gauge stations (N–n) should be
distributed in the different zones (caused by isohyets) in proportion
to their areas, i.e., depending upon the spatial distribution of the
existing rain-gauge stations and the variability of the rainfall over
the basin.
 Testing and Adjustment of Precipitation Records
 Rainfall data reported from a station may not be consistent always.
Over the period of observation of rainfall records,

Testing and Adjustment of Precipitation Records
there could be:
(i) unreported shifting of the rain gauge site by as much as 8 km aerially
or 30m in elevation,
(ii) significant construction work in the area might have changed the
surroundings
(iii) change in observational procedure incorporated from a certain
period or,
(iv) a heavy forest fire, earth quake or land slide might have taken place
in the area.
Such changes at any station are likely to affect the consistency of data from a
station.
Use of double mass curve checks the consistency of the record and helps to correct
the rainfall data for the station.

 Over a period of observation of rainfall records, there could be
(i) unreported shifting of the rain gauge site by as much as 8 km
aerially or 30m in elevation,
(ii) significant construction work in the area might have changed the
surroundings
(iii) change in observational procedure incorporated from a certain
period or,
(iv) a heavy forest fire, earth quake or land slide might have taken place
in the area, Such changes at any station are likely to affect the
consistency of data from a station.
(v) Use of double mass curve checks the consistency of the record and
helps to correct the rainfall data for the station.

Double-mass analysis:
The consistency of records at the station in question (say, X) is tested
by a double mass curve by plotting the cumulative annual (or
seasonal) rainfall at station X against the concurrent cumulative
values of mean annual (or seasonal) rainfall for a group of
surrounding stations, for the number of years of record.
In this method, the accumulated annual rainfall of a particular station
is compared with the concurrent accumulated values of mean rainfall
of groups of 5 to 8 surrounding base stations.
The basis of such an exercise is that a group of sample data (for any
period) drawn from its population will be the same.

 From the plot, the year in which a change in regime (or environment)
has occurred is indicated by the change in slope of the straight line
plot.
 The rainfall records of the station x are adjusted by multiplying the
recorded values of rainfall by the ratio of slopes of the straight lines
before and after change in environment.
 Procedure of computation is as follows
 From the plot, the year in which a change in regime (or environment)
has occurred is indicated by the change in slope of the straight line
plot.

 The rainfall records of the station x are adjusted by multiplying the
recorded values of rainfall by the ratio of slopes of the straight lines
before and after change in environment.
 Procedure of computation is as follows:
Step 1: a computation table is prepared with the following columns
Column 1: The years are represented in a decreasing order, i.e., with the
latest year as a first entry in the column.
Column 2: Yearly precipitation values of station whose consistency
needs to be checked are entered in column 2
Column 3: the cumulative annual rainfall of station whose consistency
is in question are entered

Column 4: mean annual precipitation of the group of stations
surrounding the station whose consistency has to be checked are
computed and entered.
Column 5: cumulative mean annual precipitation of group of stations
surrounding the station whose consistency has to be checked is
entered.
Step 2: A graph is plotted taking the cumulative mean annual
precipitation of a group of stations along abscissa (x-axis) and
cumulative annual precipitation of station A along the ordinate (y-
axis). Consecutive points are joined by a straight line.

Step 3: If the consistency of station A has undergone changes from any
year, then it can be noticed from the change in slope of the plotted
points.
 The straight line joining the initial points of the graph are extended
by a dotted line and correction (C/Ci) is computed
Step 4: Annual rainfall (recorded at station A) of subsequent years from
the year of deviation are corrected by multiplying by the correction
factor.

Presentation of Precipitation Data
Rainfall is usually presented in the form of the following graphs. Such
graphs are useful for analysis and design purpose.
1.Moving average curve
2.Mass curve
3.Rainfall hyetograph
4.Intensity-Duration-Frequency curves
Moving Average:
 Rainfall data are plotted chronologically with time in x-axis and
rainfall magnitude in y-axis.
 An event of rainfall is always associated with randomness.
 In order to overcome the random component in rainfall magnitudes,
a simple moving average of order 3 or 5 is used.

 This helps to isolate the trend in rainfall data.
 If there is any dry or wet cyclic trend associated with rainfall, then
such a trend can be clearly visible from the moving average plot of
the data.
 If x1, x2, x3, x4, x5, x6, x7, etc. are the annual precipitation at a
station in the chronological sequence and a 5-year moving average is
applied to the time series, then the 5-year moving mean are
computed as:

The 5-year moving average data x1, x2, x3, etc. obtained as above
can be presented from third year onward only.
For example, if data are available from 1961 t0 1996, then a 5-year
moving average can be represented from the year 1963 to 1994.
The data corresponding to the first two years (1961and 1962) and
the last two years (1995 and 1996) are lost in the moving average
process.

Mass Curve
 Mass curve is a graphic representation of rainfall data in which
time is represented along the abscissa and the cumulative
precipitation is represented along the ordinate.
 Plot of a mass curve gives information regarding rainfall intensity,
duration, magnitude, onset and cessation of precipitation of any
storm.
 All self-recording rain gauges automatically record the mass
curve of precipitation at a place over time.
 Therefore, all information about the storm at the place is known
from the graph record.

Rainfall Hyetograph
 The variation of rainfall with respect to time may be shown
graphically by a hyetograph.
 A hyetograph is a bar graph showing the intensity of rainfall with
respect to time and is useful in determining the maximum
intensities of rainfall during a particular storm as is required in
land drainage and design of culverts.
 During a storm, intensity always changes with time.
 On a mass curve any two points can be marked and the depth of
rainfall (∆y) between these two points are noted from the y-axis.

 Time between these two points (∆t) are recorded from x-axis. The
depth divided by time i.e., (∆y/(∆t) is the intensity of rainfall for the
period under consideration.
 When the plot of rainfall intensity with time is presented in the
form of a bar graph such a graph is known as hyetograph.
 The plot is very useful for flood studies and calculation of rainfall
indices.

Intensity-Duration- Frequency Curve
 Rainfall during a year or season (or a number of years) consists of
several storms.
 The characteristics of a rainstorm are
 (i) intensity (cm/hr),
 (ii) duration (min, hr, or days),
 (iii) frequency(once in 5 years or once in 10, 20, 40, 60 or 100
years), and
 (iv) areal extent (i.e., area over which it is distributed).
 Suppose a number of years of rainfall records observed on recording
and non-recording rain-gauges for a river basin are available; then it
is possible to correlate
 (i) the intensity and duration of storms, and (ii) the intensity,

duration and frequency of storms.
 An intensity-duration-frequency curve is a three parameter curve
in which duration is taken on x-axis, intensity on y-axis and the
return period or frequency as a third parameter.
 By fixing the return period of say 10, 50, 100 years or any other
period, a particular curve between intensity and duration can be
obtained for the area. Through such a curve, an exponential
equation of the following order can be fit.
T
a
C
I   
 d
a
d
b
D
CT
B
D





Where, T is the return period or frequency in years
I is the intensity of precipitation in cm/hr or mm/hr
D is the duration in hours
A, b and d are constants
 If there are storms of different intensities and of various durations,
then a relation may be obtained by plotting the intensities (i, cm/hr)
against durations (t, min, or hr) of the respective storms either on the
natural graph paper, or on a double log (log-log) paper.

Depth-Area- Duration Curve (DAD) curve
 The depth-area-duration (DAD) relationships provide the designer
with important information on temporal and spatial variation of
rainfall for a given area
 DAD also provide one of the simplest methods of transposing of
the storm data.
 For a given storm with one centre the depth-area relationship is
derived using the isohyets as boundaries of individual areas,
working from the centre outwards.
 Depth of precipitation of a storm is related to the area of its
coverage and duration of a storm.
 DAD analysis is carried out to obtain a curve relating the depth of
precipitation, D, area of its coverage, A, and

duration of occurrence of the storm, D.
 A DAD curve is a graphical representation of the gradual decrease of
depth of precipitation with a progressive increase of the area of the
storm away from the storm center, of a given duration taken as a
third parameter.
 It gives a direct relationship between depth, area and duration of
precipitation over the region for which the analysis is carried out.
 The main aim of the DAD analysis is to determine the maximum
precipitation amounts that have occurred over various sizes of
drainage area during the passage of storm periods of say 6hr, 12hr,

24hr or other durations.
 There are two methods of carrying out the DAD analysis.
 They are mass curve method and incremental-isohyetal method.
 The second method is most popular and is extensively used by the
hydrologists.
 The procedure of DAD analysis is given herein.
Step1: All the major storms of the area are identified
Step 2: the duration of the storms are noted. For example, if the
duration is chosen as 1-day, then all the storms occurring for 1-day
period are selected.
Further when a storm has occurred, say for 3 days, then the maximum
one day precipitation out of the three days is also noted.

Step 3: Isohyetal patterns for all 1-day storms are prepared on maps.
Step 4: for each 1-day storm considered, the area bounded within the
highest isohyet is determined.
 This is called the eye-area of the storm.
 Then the area bounded between the largest and the second largest
isohyets is determined.
 The depth of precipitation in the area covering up to the second
largest isohyets is obtained as d2= (Pm1A1+ Pm2A2)/(A1+A2),
where, Pm1 is the mean precipitation over the area A1 bounded
within the highest isohyets and pm2 is the mean precipitation over
the area A2 bounded between the largest and the second largest
isohyets.

 Similarly, for the area covering up to the 3rd largest isohyets, the
depth of precipitation d3 can be obtained by the relation d3=
(Pm1A1+Pm2A2+Pm3A3)/ A1+A2+A3) where pm3 is the mean
precipitation between the second largest and the 3rd largest isohyets
covering an area A3 between them.
 The procedure is repeated to cover the remaining isohyets of the area.
Step 5 : All the area- depth precipitations are recorded in a table
Step 6: step 4 is repeated for all other 1-day storms considered for the
area.
Step 7: A graph is plotted taking area along the abscissa and maximum
average depths of precipitation as ordinate covering the depth-area data
of all 1-day storms of step 5.

Step 8: Such an exercise may also be taken up for 6-hr, 12-hr, 2-day,
and 3-day storms of the region.
 The curves are plotted on the same paper as in step 6
Step 9: if a semi-log graph paper is used with area plotted on log scale
then the curve will plot close to a straight line.

Types of Streams
(i) Perennial streams:
 Are streams which have some flow at all times of a year due to
considerable amount of base flow into the stream during dry periods
of the year.
 The stream bed is, obviously, lower than the ground water table in
the adjoining aquifer (i.e., water bearing strata which is capable of
storing and yielding large quantity of water).
 When the surface runoff begins, the river level rises rapidly.
 As a consequence the piezometeric gradient reverses and flow
occurs from the stream into bank storage.
 As the river level falls, the water from the banks starts to drain back
into the river.

Types of Streams
(ii) Intermittent streams:
 These streams have limited contribution from the ground water and
that too during the wet season only when the ground water table is
above the stream bed and, therefore, there is base flow contributing
to the stream flow.
 Excepting for some occasional storm that can produce short duration
flow, such streams remain dry for most of the dry season periods of
a year.

Types of Streams
(iii) Ephemeral streams:
 These streams do not have any contribution from the base flow. The
annual hydrograph, in the Fig. below, is of such a stream which
shows series of short duration hydrographs indicating flash flows in
response to the storm and the stream turning dry soon after the end
of the storm.
 Such streams, generally found in arid zones, do not have well
defined channels.

Types of Streams
 The most satisfactory determination of the runoff from a catchment
is by measuring the discharge of the stream draining it, which is
termed as stream gauging.
 A gauging station is the place or section on a stream where
discharge measurements are made.
Streamflow Measurement
 The total runoff consisting of surface flow, subsurface flow,
groundwater or base flow, and the precipitation falling directly on
the stream is the stream flow or the total runoff of a basin.

 When the rate of rainfall or snowmelt exceeds the interception
requirements and the rate of infiltration, water starts to accumulate
on the surface.
 At first the excess water collects into the small depressions and
hollows, until the surface detention requirements are satisfied.
 After that water begins to move down the slopes as a thin film and
tiny streams.
 This early stage of overland flow is greatly influenced by surface
tension and friction forces.
 With continuing rainfall the depth of surface detention and the rate of overland
flow increase, Streamflow representing the runoff phase of the hydrologic
cycle is the most important basic data for hydrologic studies.

 Streamflow is the only part of the hydrologic cycle that can be
measured accurately.
 It is measured in units of discharge (m3/s) occurring at a specified
time and constitutes a historical data.
 The measurement of discharge in a stream forms an important
branch of Hydrometry, the science and practice of water
measurement.
 Streamflow measurement techniques can be broadly classified into
two categories as
 (a) Direct determination of stream discharge and
 (b) Indirect determination. Under each category there are a host of
methods.

a) Direct method of streamflow measurement
1) Area velocity method
(2) Dilution Technique
(3) electromagnetic method and
(4) Ultrasonic method
b)Indirect determination of streamflow measurement
1)Hydraulic structures, such as weirs, flumes, and gated structures and
2)Slope area method
The flow characteristics of a stream depend upon
(i) the intensity and duration of rainfall besides spatial and temporal
distribution of the rainfall,

ii) shape, soil, vegetation, slope, and drainage network of the
catchment basin, and
(iii) climatic factors influencing evapotranspiration. Based on the
characteristics of yearly hydrograph, (graphical plot of discharge
versus time in chronological order is plotted).
A) Direct Measurement
i)Area velocity method
The area of cross-section of flow may be determined by sounding and
plotting the profile. The mean velocity of flow (V) may be
determined by making velocity measurements.

ii)STAGE-DISCHARGE-RATING CURVE
 The measurement of discharge by the direct method involves a
two-step procedure, the development of the stage –discharge
relationship which forms the first step is of at most importance.
 Once the stage-discharge (G-Q) relationship is established, the
subsequent procedure consists of measuring the stage (G) and
reading the discharge (Q ) from the (G-Q) relationship.
 This second part is a routine operation.
 The stage discharge relationship is also known as rating curve.
 The measured value of discharges when plotted against the
corresponding stages gives relationship that represents the
integrated effect of a wide range of channels and flow parameters

Is termed as control.
 If the (G: Q) relationship for a gauging section is constant and does
not change with time, the control is said to be permanent.
 If it changes with time, it is called shifting control.
Permanent Control
 A majority of streams and rivers exhibits permanent control. For
such a case, the relationship between the stage and the discharge is
a single valued relation which is expressed as,
 Where, Q= stream discharge
 G= gauge height (stage)

a= a constant which represent the gage reading corresponding to zero
discharge
cr and are rating curve constants.
This relationship can be expressed graphically by plotting the
observed relative stage (G: Q) against the corresponding discharge
values in an arithmetic or logarithmic plots

Correlation coefficient,

 A river is gauged by current meter throughout the rainy season (for
about 3 months) at different stages (water levels) of the river.
 The water stage can be read on the enamel painted staff gauges
(gauge posts) erected at different levels at a gauging station.
 It may be noted that corresponding graduation of gauge posts at two
locations are fixed at the same level.
 A curve is drawn by plotting ‘stream discharge ‘Q vs. gauge height
h’ which is called the ‘stage discharge rating curve’ as shown in
Figure below.
 From this rating curve, the stream discharge corresponding to staff
gauge readings taken throughout the year/s can be obtained, as long
as the section of the stream at or near the gauging site has not

Periodical gauging (say, once in three years) are conducted to verify
the rating curve, or to revise the rating curve if any change in section
has been noticed.
Figure gauge posts on river banks

B) Indirect method of streamflow measurement
 Under this category are included those methods which make use
of the relationship between the flow discharge and the depths at
specified locations.
 The field measurement is restricted to the measurements of depths
only. Two broad classifications of these indirect methods are
(1) flow measuring structures
(2) Slope-area method
Flow Measuring Structures
(a) Venturiflumes or standing wave flumes (critical depth meter) for
small channels.

 A venturi flume is a structure in a channel which has a contracted
section called throat, downstream of which followed a flared
transition section designed to restore the stream to its original width.
 It is a structure which is used for measuring discharge in open
channels.
 The discharge Q flowing through the channel can be calculated by
measuring the depths of flow at the entrance and the throat of the
flume and applying the following formula:

 In which A, a, and H, h are the areas and depths of flow section at
entrance and throats of the flume respectively and k is the discharge
coefficient of the flume.
 The discharge coefficient must be determined by calibration through
the entire range of head.
(b) Weirs
 A weir is the name given to a concrete or masonry structure built
across a river or stream in order to raise the level of water on the
upstream side and to allow the excess water to flow over its entire
length to the downstream side.
 Weirs are used for measuring the rate of flow of water in rivers or
streams.

 For computing the discharge of water flowing over the weir the
following relation can be used.
Q=CLH3/2
Where, Q = stream discharge, C = coefficient of weir, L = length of
weir, H = head (depth of flow) over the weir crest.
(c) Slope-area method
 During very high floods, a site may become inaccessible or the
gauge-discharge setup may be fully inundated.
 Under such situations, discharge measurements can be accomplished
using slope-area method.

 The previous peak flood stages at two locations can be collected
from the flood marks in the river courses which give the water
surface slope of the peak flood.
 By knowing the distance between the two points along the river,
slope Sf can be computed.
 Manning’s equation can be used to calculate the discharge as
 Q = AV
V=C RS Chezy’s formula
V= S
R
n
2
/
1
3
/
2
1
Manning’s formula

Chezy’s C= R
n
6
/
1
1
, R=
P
A
Where, C = Chezy’s constant
N = Manning’s coefficient of roughness
R = hydraulic mean radius
A = cross-sectional area of flow
P = wetted perimeter
S = water surface slope (= bed slope)
 The cross-sectional area A is obtained by taking soundings below the
water level at intervals of, say, 6 m and plotting the profile of the
cross-section and drawing the high flood level or water surface
level.

The water surface slope is determined by means of gauges placed at
the ends of the reach, say 1 km upstream of the gauging station and 1
km downstream of the gauging station(in a straight reach; if Δh is the
difference in water levels in a length L of the reach, then S =Δh/L.
The slope may also be determined by means of flood marks on either
side or their subsequent leveling.
The slope-area method is often used to estimate peak floods where
no gauging station exists.
(d) Contracted area methods: The drop in water surface in contracted
sections as in bridge openings, canal falls etc. is measured and the
discharge is approximately given by:

Contracted area methods
Q = Cd A1  
ha
h
g 

2
Where, Cd = coefficient of discharge
A1 = area of the most contracted section
Δh = difference in water surface between the upstream and downstream
ends (of the pier)
ha = head due to the velocity of approach.
The hydrologic Budget
 The area of land draining into a stream or a water course at a given
location is known as catchment area.
 It is also called a drainage basin.
 Catchment area is separated from its neighboring areas by a ridge

The Hydrologic Budget
Thus, the catchment area is a logical and convenient unit to study
various aspects relating to hydrology and water resources of a region.
Rainfall can be viewed as an input to the surface of Earth.
The surface can be viewed as a series of storage elements, such as
storage on the surface of vegetation and depression storage.
Runoff from the surface can be viewed as an output from surface
storage elements.
This would be a systems representation of the physical processes
controlling surface runoff.

If river channel processes are the important elements of the
hydrologic design, then the surface runoff can be viewed as the input,
the channel itself as the storage element, and the runoff out of the
channel (into another channel, a lake, or an ocean) as the output from
the system.
 A water budget is an accounting of water movement into and out of,
and storage change within, some control volume.
 The universal concept of mass conservation of water implies that
water-budget methods are applicable over any space and time scales
(Healy et al., 2007).

 The water budget of a soil column in a laboratory can be studied at
scales of millimeters and seconds.
 A water-budget equation is also an integral component of
atmospheric general circulation models used to predict global
climates over periods of decades or more.
 Water-budget methods represent the largest class of techniques for
estimating recharge.
 Most hydrologic models are derived from a water-budget equation
and can therefore be classified as water-budget models.
 For a given problem area, say a catchment, in an interval of time ∆t,
the continuity equation for water in its various phases is written as:

Mass inflow-mass outflow = change in mass storage
 Inflows add water to the different parts of the hydrologic system,
while outflows remove water.
 Storage is the retention of water by parts of the system. Because
water movement is cyclical, an inflow for one part of the system is
an outflow for another.
 The conceptual representation of hydrologic systems can be stated
in mathematical terms.
 Letting I, 0, S, and t denote the input, output, storage, and time,
respectively, the following equation is known as the linear storage
equation:

 The derivative on the right-hand side of the above Equation can be
approximated by the numerical equivalent ∆S/ ∆t, when one wishes
to examine the change in storage between two times, say t2 and t1.
 In this case, the above Equation becomes:
in which S2 and S1 are the storages at times t2 and t1, respectively.
 The earth's water supply remains constant, but man is capable of
altering the cycle of that fixed supply.
 Population increases, rising living standards, industrial and economic
growth have placed greater demands on our natural environment.

Our activities can create an imbalance in the hydrologic equation and
can affect the quantity and quality of natural water resources
available to current and future generations.
The storage equation can be used for other types of hydrologic
problems.
Estimates of evaporation losses from a lake could be made by
measuring: all inputs, such as rainfall (I1), inflow from streams (I2),
and ground-water inflow (I3); all outputs, such as streamflow out of
the lake (O1), ground-water flow out of the lake (O2), and
evaporation from the lake (O3); and the change in storage between
two time periods, Mathematically, the water balance is:

The hydrologic budget is a convenient way of modeling the elements
of the hydrologic cycle. It will be used frequently in describing the
problems of analysis and design.

According to estimates (Seckler et al., 1998), the annual average
depth of precipitation on the land surface is about 108*103 km3. Out
of this, about 61*103 km3 is returned to the atmosphere as
evapotranspiration and the runoff from land to oceans is 47*103 km3.
 As far as the water balance of oceans is concerned, the depth of
precipitation over them is about 410*103 km3 , 47 *103 km3 of
water is received as runoff from the land, and 457*103 km3 is lost as
evaporation.
 If we consider the water balance of atmosphere, 457*103 km3 of
water is received as evaporation from oceans and 61*103 km3 from
land. The precipitation over oceans is 410*103 km3 and it is 108*103
km3 over land.

Global Water Balance
 The hydrologic equation may be applied for areas of any size, but
the complexity of computation greatly depends on the extent of the
area under study.
 The smaller is the area, the more complicated is its water balance
because it is difficult to estimate components of the equation.
 Finally, the components of the hydrologic equation may be
expressed in terms of the mean depth of water (mm), or as a volume
of water (m3), or in the form of flow rates (m3/s or mm/s).

Infiltration
Estimating the quantity of flow allows us to determine the fraction of
the rainfall that will contribute to surface runoff, and the fraction that
will feed the groundwater flow and thus recharge the aquifers.
 Infiltration is the transfer of water through the surface layers of the
soil after it has been subjected to rain or has been submerged.
The infiltrating water initially fills the interstices in the surface soil
and then penetrates the soil under the forces of gravity and soil
suction.
The rate at which net precipitation enters the soil surface depends on
several soil surface conditions and the physical characteristics of the
soil itself.

Infiltration
Infiltration affects many aspects of hydrology, agricultural
engineering and hydrogeology.

Infiltration
The maximum rate at which water can enter the soil surface is called
infiltration capacity.
Infiltration capacity diminishes over time in response to several
factors that affect the downward movement of the wetting front.
The size of individual pores and the total amount of pore space in a
soil generally decrease with increasing soil depth.
The actual infiltration rate equals the infiltration capacity only when
the rate of rainfall or snowmelt equals or exceeds the infiltration
capacity.
When rainfall or snowmelt rates exceed infiltration capacity, surface
runoff or ponding of water on the soil surface occurs.

Infiltration
When rainfall intensity is less than the infiltration capacity, the rate of
infiltration equals rainfall intensity.
In these instances, water enters the soil and is either held within the
soil if soil moisture content is less than the field capacity or percolates
downward under the influence of gravity when soil moisture content is
greater than the field capacity.
The infiltration capacity of a soil depends on several factors including
texture, structure, surface conditions, the nature of soil colloids, organic
matter content, soil depth or the presence of impermeable layers, and
the presence of macro-pores within the soil.
Macro-pores function as small channels or pipes within a soil and are
non-uniformly distributed pores created by processes such as

Infiltration
earthworm activity, decaying plant roots, the burrowing of small
animals, and so forth.
Rate of infiltration i (t): also called the infiltration regime, is the rate
of flow of water penetrating the soil.
 It is usually expressed in mm/h.
 The rate of infiltration depends above all on the mode of inputs
(irrigation, rain) but also on the properties of the soil.
Cumulative infiltration, I(t): is the total volume of water infiltrated in
a given time period.
 It is equal to the integral over time of the rate of infiltration,

Infiltration
Where, I(t) is the cumulative infiltration at time t [mm] and i(t) is the
rate of infiltration for time t [mm/h].
Figure General Evolution of the rate of infiltration and of cumulative
infiltration over time (Ks = saturated hydraulic conductivity)

Infiltration
Saturated hydraulic conductivity (Ks): is a key parameter of
infiltration.
 It represents the limit value of the rate of infiltration if the soil is
saturated and homogeneous.
 This parameter is part of many equations for calculating infiltration.
Infiltration capacity or absorption capacity: is the maximum amount
of water flow that the soil can absorb through its surface, when it
receives an effective rainfall or is covered with water.
 It depends on texture and structure of the soil, and also on the initial
conditions, which is to say, the initial water content of the soil profile
and the water content imposed on the surface.

Infiltration
Many equations have been proposed to express the curves fp(t) or
Fp(t) for use in hydrological analysis.
Four such equations will be discussed:
a)Horton’s Equation: According to Horton (1933), the expression
used to find infiltration capacity is given as:
Where, fp =the infiltration capacity (depth/time) at some time t
K= a constant representing the rate of decrease in f capacity
fc= a final or equilibrium capacity
f0= the initial infiltration capacity

Infiltration
b)Philip’s Equation(1957):
Where, s= a function of soil suction potential and called sorptivity
K= Darcy’s hydraulic conductivity
 Infiltration capacity could be expressed as:
c)Kostiakov equation (1932): Kostiakov model expresses cumulative
infiltration capacity as:
Where a and b are local parameters with a>0 and 0<b<1

Infiltration
The infiltration capacity would be expressed as:
d)Green-Ampts equation(1911):Green and Ampts proposed a model
for infiltration capacity based on Darcy’s law as:
Where, porosity of the soil
Sc=capillary suction at the wetting front and
K= Darcy’s hydraulic conductivity

Percolation and effective rainfall
Percolation: indicates the vertical flow of water in the soil
(unsaturated porous media) towards the groundwater table, mostly
under the influence of gravity.
 This process follows infiltration and directly determines the water
supply to underground aquifers.
Precipitation excess or effective rainfall: is the quantity of rain that
flows only on the surface of the soil during a rain.
 The net storm rain is deducted from the total rainfall, minus the
amounts that are intercepted by vegetation or stored in depressions
in the soil, and minus the fraction that infiltrates.

Factors Influencing Infiltration
 Infiltration is affected by the following main factors:
a) Type of soil (structure, texture, porosity): The characteristics of
the soil matrix influence the forces of capillarity and adsorption giving
rise to the force of suction, which in part governs infiltration.
b) Compaction of the soil surface: is the result of the impact of rain
drops or other causes (thermal and anthropogenic).
 For example, heavy machinery in agricultural land can degrade the
structure of the surface soil layer and cause the formation of a
dense and impermeable crust to a certain depth (this can be the
result of plowing, for example).

 The Figure below illustrates some examples of the evolution of the
infiltration rate over time as a function of the soil type.
Figure Infiltration regime as a function of time for different soil types (based on Musy and
Soutter, 1991)

c) Soil cover: Vegetation has a positive influence on infiltration by
slowing down surface runoff and giving the water more time to
penetrate the soil.
 In addition, the root systems improve the permeability of the soil.
Lastly, foliage protects the soil from the impact of the rain drops, and
so decreases surface sealing.
d) Topography and morphology: Slope, for example, has the opposite
effect of vegetation. A steep slope increases surface flow at the expense
of infiltration.
e) Water Supply: This is the intensity of precipitation or the irrigation
water rate.

f) Initial water content of the soil: The water content of the soil is an
essential factor affecting the infiltration rate, because the force of
suction is a function of the moisture content in the soil.
 The infiltration rate over time will evolve differently depending on
the initial condition (wet or dry) of the soil.
 The moisture content of the soil is usually understood by studying the
precipitation that fell in a given time period preceding rain.
 The Antecedent Precipitation Indices (IAP) are often used to establish
the moisture content of the soil preceding a rain.
 In summary, for the same type of topography, the most influential
factors affecting infiltration are the soil type, the soil cover, and the
initial water content.

Infiltration Indices
 In hydrological calculations involving floods it is found convenient to
use a constant value of infiltration rate for the duration of the storm.
 The defined average infiltration rate is called infiltration index and
two types of indices are in common use.
Φ-Index
 Infiltration indexes generally, assume that infiltration occurs at some
constant or average rate throughout a storm.
 Consequently, initial rates are underestimated and final rates are
overestimated if an entire storm sequence with little antecedent
moisture is considered.
 The Φ-index is the average rainfall above which the rainfall volume is
equal to the runoff volume.

 The Φ-index is derived from the rainfall hyetograph with the
knowledge of the resulting runoff volume.
 If the rainfall intensity is less than Φ, then the infiltration rate is equal
to the rainfall intensity; however, if the rainfall intensity is larger than
Φ the difference between the rainfall and infiltration in an interval of
time represents the runoff volume.
 The amount of rainfall in excess of the index is called rainfall excess.
 In connection with runoff and flood studies it is also known as
effective rainfall.
 The Φ-index accounts for the total abstraction and enables magnitudes
to be estimated for a given rainfall hyetograph.

 The Φ-index is derived from the rainfall hyetograph with the
knowledge of the resulting runoff volume.
 If the rainfall intensity is less than Φ, then the infiltration rate is
equal to the rainfall intensity; however, if the rainfall intensity is
larger than Φ the difference between the rainfall and infiltration in an
interval of time represents the runoff volume.
 The amount of rainfall in excess of the index is called rainfall
excess.
 In connection with runoff and flood studies it is also known as
effective rainfall.
 The Φ-index thus accounts for the total abstraction and enables
magnitudes to be estimated for a given rainfall hyetograph.

Mathematically, the Φ-index can be expressed as:
Where,
p= total storm precipitation (mm or cm)
R= total direct surface runoff (mm or cm)
te= duration of the excess rainfall, i.e., the total time in which the total
intensity is greater than Φ (in hours), and
Φ= uniform rate of infiltration (mm/hr or cm/hr)

W-Index
 In an attempt to refine the Φ-index, the initial losses are separated
from the total abstractions and an average value of infiltration rate
(called the w-index) is calculated as given below:
Where, p= total storm precipitation (cm)
R=total storm runoff (cm)
Ia= initial losses (cm)
te= duration of the excess rainfall (in hours), i.e., the total time
in which the rainfall intensity is greater than infiltration capacity and

w= average rate of infiltration (cm/hr)
 The minimum value of W-index obtained under very wet soil
conditions, representing the constant minimum rate of infiltration of
the catchment, is known as Wmin.
 It is to be noted that both the -index and W index vary from storm
to storm.
Rainfall-Runoff Relation
 When rain falls on the earth’s surface, some of that rain is
intercepted by the surfaces of vegetation located in its path
(interception)
 Depending on soil characteristics and amount of rainfall, some or all
of the remaining rainfall will enter the ground through pores in the

surface soils (infiltration).
 As the remaining water, if any, flows overland, irregularities in the
surface of the land trap some of this water as depression storage.
 The portion of this overland flow that reaches the watershed outlet
is called direct runoff, or storm water runoff.
 This relationship can be expressed as a storm event water balance,
by the following equation:
 Runoff = Precipitation - Interception - Infiltration - Depression
Storage-Evapotranspiration
 This very basic relationship is the basis for most methods used to
estimate runoff.

 In hydrologic analysis, interception, infiltration, and depression
storage are sometimes referred to as “abstractions”.
 Thus, runoff is what remains of rainfall, after accounting for
abstractions.
 When we estimate runoff, we are concerned with the quantities of
runoff volume and runoff rate.
Runoff Volume
 The volume of surface runoff that will occur on a site during a given
rainfall event depends on a number of factors:
 For very large watersheds, the volume of runoff from one storm event
may depend on rainfall that occurred during previous storm events.

 In addition to rainfall, other factors affect the volume of runoff are:
Basin characteristics
 Size, Shape, Slope, Altitude (elevation), Topography, Geology (type
of soil), Land use/land cover /vegetation, Orientation, Type of
drainage network , Proximity to ocean and mountain ranges.
Storm characteristics
 Amount of precipitation; Rainfall event, duration and intensity; Type
or nature of storm and season, Intensity of storm, Duration and Areal
extent (distribution), Frequency antecedent precipitation and
Direction of storm movement.
Storage characteristics
Depressions Pools and ponds / lakes Stream Channels, Check dams,

(in gullies), Upstream reservoir /or tanks Flood plains, swamps Ground
water storage in pervious deposits (aquifers In analyzing the hydrology
of an area, several runoff volume quantities are of interest.
For instance:
 The runoff volume associated with a storm event;
 The runoff volume over an extended time (e.g., annual runoff);
 A runoff volume for water quality treatment.
 Runoff volumes are generally estimated in terms of “watershed
meters”, cubic meters (m3), or acre-feet.
 A “watershed -meter” is equivalent to a one-meter depth of water
spread over the entire contributing watershed.

 An “acre-foot” is equivalent to one foot of water spread over an acre
of area.
Methods Commonly used for Estimating Runoff Volume
 The volume of runoff that will occur on a site during a given rainfall
event depends on a number of factors:
 The area of land from which runoff occurs (known as the
watershed);
 amount of precipitation;
 the duration and intensity (volume per unit of time) at which
precipitation falls;
 the soils at and near the land surface; and
 the surface cover (combination of exposed earth, vegetation, pavement and roofs).

 The rate at which runoff discharges from a given site is known as the
runoff rate or discharge rate. The rate of runoff depends on the
following factors
 the roughness of the surface, which is determined by the type of
surface cover;
 the location of the impervious area in the watershed in relation to the
point of analysis;
 slope of the ground surface (flatter slopes result in slower rates of
flow over the ground, steeper slopes result in faster rates of flow);
 total distance the runoff must travel to the point of analysis.
How is Runoff Related to Rainfall?

 When rain falls on the earth’s surface, some of that rain is intercepted
by the surfaces of vegetation located in its path (interception).
 Depending on soil characteristics and amount of rainfall, some or all
of the remaining rainfall will enter the ground through pores in the
surface soils (infiltration).
 As the remaining water, if any, flows overland, irregularities in the
surface of the land trap some of this water as depression storage.
 The portion of this overland flow that reaches the watershed outlet is
called direct runoff, or storm water runoff.
This relationship can be expressed as a storm event water balance, by the
following equation:
 Runoff = Precipitation - Interception - Infiltration - Depression

 This very basic relationship is the basis for most methods used to
estimate runoff.
 In hydrologic analysis, interception, infiltration, and depression
storage are sometimes referred to as “abstractions”.
 Thus, runoff is what remains of rainfall, after accounting for
abstractions.
 Anything that affects the “abstraction” processeswill affect the amount
of runoff.
Runoff Volume
 The volume of surface runoff that will occur on a site during a given
rainfall event depends on a number of factors:
 Watershed area;

Runoff Volume
 Rainfall event duration and intensity (volume per unit of time);
 Surface soils characteristics; and
 and-use surface cover.
 Runoff volumes are generally estimated in terms of “watershed
inches”, cubic feet (ft3), or acre-feet.
 A “watershed inch” is equivalent to a one-inch depth of water spread
 over the entire contributing watershed.
 An “acre-foot” is equivalent to one foot of water spread over an acre
of area.
Methods Commonly used for Estimating Runoff
 There are many methods available for the estimation of runoff
volumes and rates.

 Runoff volume and rate can be estimated using Soil Conservation
Service (SCS, now the Natural Resources Conservation Service)
methods, assuming the necessary underlying assumptions of the SCS
models are satisfied.
 The selection of methods depends on a number of factors, including:
 Whether the method will be used to estimate total runoff volumes,
peak rates, or variations of flow rate with time over the duration of a
storm event;
 Whether the values obtained by the method will be used for sizing
storm drain pipes,
 detention facilities, water quality treatment facilities, or other purpose;
 Limitations inherent in each method;

 Data available for performing the calculations; and
 Whether the method requires calibration to actual field data.
The Rational Method
The SCS Curve Number/Unit Hydrograph Method
The Rational Method:
 is generally used for estimating peak flows, to develop designs for
conveyance systems such as culverts, piped storm drains, and open
channel systems.
 While there is an adaptation of the rational method that may be used
for estimating detention storage volumes, the method is cumbersome
to use in comparison to other available modeling tools.

The Rational Method
 Also, it is not generally appropriate for development of peak rate
control devices such as detention and retention basins.
 For those interested in how to use the Rational Method,
 Applicability:
 Required output: peak discharge only
 Drainage area: less than or equal to 20 acres
 The Rational Method is used for determining peak discharges from
small drainage areas.
 This method is traditionally used to size storm sewers, channels, and
other storm water structures, which handle runoff from drainage areas
less than 20 acres.
 The Rational Formula is expressed as q=C*i*A

The Rational Method
where:
q = Peak rate of runoff in cubic feet per second
C = Runoff coefficient, an empirical coefficient representing a
relationship between rainfall and runoff
i = Average intensity of rainfall in inches per hour for the time of
concentration (Tc) for a selected frequency of occurrence or return
period.
Tc = The rainfall intensity averaging time usually referred to as the time
of concentration, equal to the time required for water to flow form the
hydraulically most distant point in the watershed to the point of design.
A = The watershed area in acres

Runoff Estimation Rational Method
Description of Step Reference
Step 1 Identify Analysis Points
Step 2 Delineate Watershed of Each Analysis Point
Step 3 Characterize Each Watershed:
 Total area (A), expressed in acres
Land cover type, soils, and slope condition –
corresponding to table of runoff coefficients
Area of each cover/soils/slope complex
Step 4 Determine Runoff Coefficient (C)
 Determine c for each unique sub-area, based on cover/soils/slope
complex

Runoff Estimation Rational Method
 Determine weighted c for each watershed
Step 5 Determine Time of Concentration (tc)
Note that this time is sometimes expressed in hours, and sometimes in
minutes, and may need to be converted to appropriate units for
computing intensity
Step 6 Determine Rainfall Intensity (i)
Note that intensity must be expressed in units of
inches/hour
Step 7 Determine Peak Discharge (q, expressed in cfs)
Use Rational Formula:
q = C * i * A

Assumptions in Runoff Estimation Using Rational
Method
1.The peak rate of runoff at any point is a direct function of the tributary
drainage area and the average rainfall intensity during the time of
concentration to that point.
2. The return period of the peak discharge rate is the same as the return
period of the average rainfall intensity or rainfall event.
3. The rainfall is uniformly distributed over the watershed.
4. The rainfall intensity remains constant during the time period equal
to Tc.
5. The relationship between rainfall and runoff is linear.
6. The runoff coefficient, C, is constant for storms of any duration or
frequency on the watershed.

Limitations
1.When basins become complex, and where sub-basins combine, the
Rational Formula will tend to overestimate the actual flow
2. The method assumes that the rainfall intensity is uniform over the
entire watershed. This assumption is true only for small watersheds and
time periods, thus limiting the use of the formula to small watersheds.
3The results of using the formula are frequently not replicable from
user to user. There are considerable variation in interpretation and
methodology in the use of the formula.
4. The Rational Formula only produces one point on the runoff
hydrograph, the peak discharge rate.

The SCS Curve Number Method
 In 1972, the soil conservation service developed a method for
computing abstractions from storm rainfall, considering the storm as
a whole, the depth of excess precipitation or direct runoff Pe is
always less than or equal to the depth of precipitation P.
 Similarly, after runoff begins, the additional depth of water retained
in the watershed Fa is less than or equal to the potential maximum
retention S.
 There is some amount of rainfall in the form of initial abstraction
before ponding Ia, for which no runoff will occur.
 Hence, the potential runoff is P-Ia.

The SCS Curve Number Method
 For many peak discharge estimation methods, the input includes
variables to reflect the size of the contributing area, the amount of
rainfall, the potential watershed storage, and the time-area
distribution of the watershed.
 These are often translated into input variables such as the drainage
area, the depth of rainfall, an index reflecting land use and soil type,
and the time of concentration.
 In developing the SCS rainfall-runoff relationship, the total rainfall
was separated into three components: direct runoff (Q), actual
retention (F), and the initial abstraction (Ia).
 The retention (F) was assumed to be a function of the depths of
rainfall and runoff and the initial abstraction.

Hypothesis of the SCS method
 The ratio of actual additional depth of water retained in the watershed
Fa to the potential maximum retention S is equal to the ratio of the
actual depth of excess of precipitation or direct runoff Pe to the
potential runoff (P-Ia). That is,
(1)
 Applying the principle of continuity, we have, Depth of
precipitation= Depth of excess precipitation or direct runoff + depth
of initial abstraction before ponding +additional depth of water
retained in the watershed
( 2)

From equation (1) (3)
From equation (2)
(4)
Substituting the value of Fa in equation (4) in equation (3) we have

 This equation is the basic equation for computing the depth of excess
rainfall or direct runoff from a storm by SCS method.
 By study of results from many small experimental watershed, an
empirical relation was developed.
Ia =0.2S
Substituting Ia =0.2S in equation

Where,
P = depth of precipitation, mm (in)
Ia = initial abstraction, mm (in)
S = maximum potential retention, mm (in)
The retention S should be a function of the following five factors:
land use, interception, infiltration, depression storage, and antecedent
moisture.
 The above equation represents the basic equation for computing the
runoff depth, Q, for a given rainfall depth, P.
 It is worthwhile noting that while Q and P have units of depth, Q
and P reflect volumes and are often referred to as volumes.

Additional empirical analyses were made to estimate the value of S. The
studies found that S was related to soil type, land cover, and the
hydrologic condition of the watershed. These are represented by the
runoff curve number (CN), which is used to estimate S by:
Empirical analyses suggested that the CN was a function of three
factors: soil group, the cover complex, and antecedent moisture
conditions.

Soil Group Classification
 SCS developed a soil classification system that consists of four
groups, which are identified by the letters A, B, C, and D.
 Soil characteristics that are associated with each group are as follows:
Group A: deep sand, deep loess; aggregated silts
Group B: shallow loess; sandy loam
Group C: clay loams; shallow sandy loam; soils low in organic content;
soils usually high in clay
Group D: soils that swell significantly when wet; heavy plastic clays;
certain saline soils
Cover Complex Classification:
 The SCS cover complex classification consists of three factors: land
use, treatment or practice, and hydrologic condition.

Cover Complex Classification
 Many different land uses are identified in the tables for estimating
runoff curve numbers.
 Agricultural land uses are often subdivided by treatment or
practices, such as contoured or straight row; this separation reflects
the different hydrologic runoff potential that is associated with
variation in land treatment.
 The hydrologic condition reflects the level of land management; it is
separated into three classes: poor, fair, and good.
 Not all of the land uses are separated by treatment or condition.

 To standardize the SCS curves, a dimensionless curve number CN is
defined such that 0 ≤ CN ≤ 100.
 The curve for dry conditions (AMC I) or wet conditions (AMCIII),
equivalent curve numbers can be computed by:
and
 The range of antecedent moisture conditions for each classes is
shown in the following table.
CN (I) =  
 
II
CN
II
CN
058
.
0
10
2
.
4


Table: Classification of antecedent moisture classes (AMC) for the SCS
method of rainfall abstractions
AMC group Total 5-day antecedent rainfall(inches)
Dormant seasons Growing seasons
I <0.5 <1.4
II 0.5 to 1.1 1.4 to2.1
III >1.1 >2.1
Runoff Rate
 The term runoff rate refers to the volume of runoff discharging from
a given watershed per unit of time.

Runoff Rate
 The rate at which runoff discharges from a given watershed depends
on the following factors in addition to those affecting runoff volume:
Surface roughness (determined by the type of surface cover);
 Location of impervious area in the watershed relative to the point of
analysis;
 Slope of the ground surface;
 Distance the runoff must travel to the point of analysis.
 Runoff rates (volume of runoff in a unit time) are usually estimated
or measured in cubic meter per second (m3/s).
Runoff Depth Estimation
 A common assumption in hydrologic modeling is that the rainfall
available for runoff is separated into three parts:

Runoff Depth Estimation
direct (or storm) runoff, initial abstraction, and losses.
 Factors that affect the split between losses and direct runoff include
the volume of rainfall, land cover and use, soil type, and antecedent
moisture conditions.
 Land cover and land use will determine the amount of depression
and interception storage.
 The following equation can be used to compute a peak discharge
with the SCS method:
 Where, qp = peak discharge, m3/s (ft3/s
 qu = unit peak discharge, m3/s/km2/mm (ft3/s/ mi2/in)
 A = drainage area, km2 (mi2) Q = depth of runoff, mm (in).

Base Flow Separation
 The first step in developing a unit hydrograph is to plot the
measured hydrograph and separate base flow from the total runoff
hydrograph
 In perennial streams the base flow is not assumed to be part of the
runoff from a given rainfall and is separated first
 The separation of the base flow, however, is not an easy task.

Base Flow Separation
c) Method III: In this method the base flow curve existing prior to the
commencement of the surface runoff is extended till it intersects the
ordinate drawn at the peak point. Then this point is joined to point C
by a straight line

2.RESPONSE FUNCTIONS OF LINEAR SYSTEMS
UNIT HYDROGRAPH CONCEPTS
 The hydrograph is the response of a given catchment to a rainfall
input
 The interactions of various storms and catchments are in general
extremely complex
 Two different storms in a given catchment produce hydrographs
differing from each other
 Similarly identical storms in two catchment produce hydrographs
that are different
 These complex hydrographs are the result of storm and catchment
peculiarities and their complex interaction.
 Hence, simple hydrographs resulting from isolated storms are preferred for

 The unit hydrograph is a simple linear model that can be used to
derive the hydrograph resulting from any amount of excess rainfall.
 First proposed by Sherman (1932), the unit hydrograph originally
named unit-graph of a watershed is defined as a direct runoff
hydrograph (DRH) resulting from 1’’ (usually taken as 1 cm in SI
units) of excess rainfall generated uniformly over the drainage area at
a constant rate for an effective duration.
 Sherman originally used the word “unit” to denote a unit of time.
But since that time it has often been interpreted as a unit depth of excess
rainfall.

 Sherman classified runoff into surface runoff and groundwater runoff
and defined the unit hydrograph for use only with surface runoff
 The unit hydrograph is a widely used element of hydrological studies
and applies to runoff from rainfall only, not to that from melting of
snow or ice.
 The UH refers to runoff from a rainfall excess uniformly distributed
over the entire catchment.
 Isolated storm results single peak hydrograph and complex storm
yields multiple peak hydrograph
The following basic assumptions are inherent in this model;
 1. Rainfall excess of equal duration are assumed to produce
hydrographs with equivalent time bases regardless of the intensity of the rain,

2. Direct runoff ordinates for a storm of given duration are assumed
directly proportional to rainfall excess volumes.
3. The time distribution of direct runoff is assumed independent of
antecedent precipitation,
4. Rainfall distribution is assumed to be the same for all storms of equal
duration, both spatially and temporally.
Sherman based his formulation on three postulates:
(a)Constant base length: This means that for a given catchment the
duration of runoff is essentially constant for all rainfalls of a given
duration and independent of the total volume of runoff.
(b) Proportional ordinates. It is assumed that for a given duration and catchment
the ordinates of the runoff hydrograph are proportional to the total volume of

Applied Hydrology.pptx

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to Applied Hydrology.pptx

Similar to Applied Hydrology.pptx (20)

Recently uploaded

Recently uploaded (20)

Applied Hydrology.pptx