Adama university, Department of civil Engineering and Architecture Introduction to hydrology (CE-3601) Tessema B; Mekdim M;Belay,Suleman 1 COURSE CONTENT: CHAPTER ONE – INTRODUCTION ...................................................................................................2 1.1 General hydrology: .................................................................................................................2 1.2 Application of Hydrology .......................................................................................................3 1.3 The Hydrologic Cycle .............................................................................................................4 1.4 The basic Hydrologic Equation ..............................................................................................5 CHAPTER TWO - RUNOFF MEASUREMENT AND RATING CURVE .........................................7 2.1 Stream Flow Measurement .....................................................................................................7 2.2 Stage-discharge /Rating Curves ............................................................................................11 2.3 Methods for Extending the Stage - Discharge curve. ...........................................................12 CHAPTER THREE - PROCESSING AND ANALYSIS OF HYDROLOGICAL DATA .................14 3.1 General ..................................................................................................................................14 3.2 Meteorological data ..............................................................................................................14 3.3 Areal Estimation ...................................................................................................................18 3.4 Hydrological Data .................................................................................................................21 CHAPTER FOUR - INTENSITY DURATION FREQUENCY PROCEDURES...............................22 4.1 Intensity-Duration relationship of a Rainfall ........................................................................22 4.2 Depth - Area - Duration (DAD) Relationship.......................................................................23 4.3 Frequency analysis of rainfall (Recurrence interval of a storm)...........................................28 4.4 Intensity - Duration - Frequency Relationship......................................................................31 CHAPTER FIVE - RAINFALL RUNOFF MODELS .........................................................................34 5.1 Introduction ...........................................................................................................................34 5.2 Factors Affecting Runoff ......................................................................................................34 5.3 The hydrograph .....................................................................................................................37 5.4 Methods Used to Estimate Runoff ........................................................................................38 CHAPTER SIX - FLOOD FREQUENCY ANALYSIS ......................................................................44 a. Introduction ...............................................................................................................................44 b. Common flood frequency distributions ....................................................................................45 c. Risk, Reliability and Safety factor: ...........................................................................................50 d. Applied Examples: ....................................................................................................................51 CHAPTER SEVEN – MISCELLANEOUS TOPICS ..........................................................................53 7.1 Introduction ...........................................................................................................................53 7.2 Precipitation ..........................................................................................................................53 7.3 Depression storage ................................................................................................................58 7.4 Interception ...........................................................................................................................59 7.5 Infiltration .............................................................................................................................60 7.6 Evaporation and transpiration ...............................................................................................64
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Adama university, Department of civil Engineering and Architecture
Introduction to hydrology (CE-3601) Tessema B; Mekdim M;Belay,Suleman 1
COURSE CONTENT:
CHAPTER ONE – INTRODUCTION...................................................................................................2
1.1 General hydrology: .................................................................................................................2
1.2 Application of Hydrology .......................................................................................................3
1.3 The Hydrologic Cycle.............................................................................................................4
1.4 The basic Hydrologic Equation ..............................................................................................5
CHAPTER TWO - RUNOFF MEASUREMENT AND RATING CURVE .........................................7
7.6 Evaporation and transpiration ...............................................................................................64
Adama university, Department of civil Engineering and Architecture
Introduction to hydrology (CE-3601) Tessema B; Mekdim M;Belay,Suleman 2
CHAPTER ONE – INTRODUCTION
1.1 General hydrology:
Hydrology is the science that deals with the processes governing the depletion and replenishment of
the water resources of the land areas of the earth. It is concerned with the transportation of water
through the air, the precipitation occurring on the ground as rainfall or snowfall, and the flow of
water over the ground surface and through the underground strata of the earth. It is the science that
treats of the various phases of the hydrologic cycle.
Hydrology is the science, which deals with the occurrence, circulation and distribution of water upon,
over, and beneath the earth surface. Hydrology treats of the water of the earth, their occurrences,
circulation, and distribution, their chemical and physical properties, and their reaction with their
environment, including their relation to living things.
As a branch of earth science, it is concerned with the water in streams and lakes, rainfall and
snowfall, snow and ice on the land and water occurring below the earth’s surface in the pores of the
soil and rocks. Hydrology as a science has thus many components and in the broadest sense would
include the movement of water into, with in and from the atmosphere but these processes is often
considered to be with in the domain of other sciences such as meteorology, climatology and soil
science. The influence of the vegetation is obviously also with in the domain of botany.
Generally the domain of hydrology embraces the full life history of water on the earth. The concept
of water balance and the concept of a catchment are both extremely useful in the applications of
hydrological principles.
We may distinguish several areas of study in hydrology as follows
- The primary process of evaporation , transpiration by vegetation , infiltration and
percolation
- Surface runoff including flow in open channels
- Groundwater hydraulics, including flow in the unsaturated zone
Engineering hydrology includes those segments of the field pertinent to planning, design, and
operation of engineering projects for the control and use of water. It is the study of those aspects of
hydrology which are relevant to the solution of engineering problems in the control of utilization of
water and in the protection of water resources. The term however refers not to a subset of
hydrological studies only but implies as a method of study or analysis which is designed to answer in
a quantitative manner , questions arising in an engineering context but with out necessarily implying
an extension of our understanding of the process involved.
Such problems usually arise and studied under the following categories.
- Forecasting or the estimation of when some hydrological event will occur
- Frequency prediction or the estimation of how often an event will occur
Adama university, Department of civil Engineering and Architecture
Introduction to hydrology (CE-3601) Tessema B; Mekdim M;Belay,Suleman 3
1.2 Application of Hydrology
Knowledge of hydrology is of basic importance for the problems that deal with any water resource
development, and the use and supply of water for any purpose whatsoever. Therefore, hydrology is of
value not only in the field of engineering but also in forestry, agriculture, and other branches of
natural science.
Hydrology is basically an applied science. To further emphasis the degree of applicability, the subject
is sometimes classified as
1. Scientific Hydrology: The study, which is concerned chiefly with academic aspects.
2. Engineering or applied Hydrology: A study concerned with applications of the
hydrological principle in engineering practice.
In general sense, engineering hydrology deals with
i. Estimation of water resources.
ii. The study of hydrologic processes such as precipitation, runoff, evapotranspiration and
their interaction and
iii. The study of problems such as floods and droughts and strategies to combat them.
This course mainly deals with an elementary treatment of engineering hydrology with an introduction
to both surface and ground water hydrology, descriptions that give a qualitative judgment and
techniques that lead to a quantitative evaluation of the hydrologic processes which are of utmost
importance to civil, agricultural and water engineering works.
Adama university, Department of civil Engineering and Architecture
Introduction to hydrology (CE-3601) Tessema B; Mekdim M;Belay,Suleman 4
1.3 The Hydrologic Cycle
The hydrologic cycle is a constant movement of water above, on, and below the earth's surface. It is a
cycle that replenishes ground water supplies. It begins as water vaporizes into the atmosphere from
vegetation, soil, lakes, rivers, snowfields and oceans-a process called evapotranspiration.
As the water vapor rises it condenses to form clouds that return water to the land through
precipitation: rain, snow, or hail. Precipitation falls on the earth and either percolates into the soil or
flows across the ground. Usually it does both. When precipitation percolates into the soil it is called
infiltration; when it flows across the ground it is called surface runoff. The amount of precipitation
that infiltrates, versus the amount that flows across the surface, varies depending on factors such as
the amount of water already in the soil, soil composition, vegetation cover and degree of slope.
Surface runoff eventually reaches a stream or other surface water body where it is again evaporated
into the atmosphere. Infiltration, however, moves under the force of gravity through the soil. If soils
are dry, water is absorbed by the soil until it is thoroughly wetted. Then excess infiltration begins to
move slowly downward to the water table. Once it reaches the water table, it is called ground water.
Ground water continues to move downward and laterally through the subsurface. Eventually it
discharges through hillside springs or seeps into streams, lakes, and the ocean where it is again
evaporated to perpetuate the cycle
Adama university, Department of civil Engineering and Architecture
Introduction to hydrology (CE-3601) Tessema B; Mekdim M;Belay,Suleman 5
1.4 The basic Hydrologic Equation
A fundamental assumption behind the hydrologic equation is that of the hydrologic cycle being a
closed system, i.e., there are no gains or losses of water from the cycle. However, there are many
occasions upon which the hydrologist has to deal with an open system in which can only be described
by a mass balance or water budget equation in which the difference between input I and out put, Q, is
related to the change in storage, dS, with in the time interval dt:
I – Q = dS/dt
In applying this equation care must be taken in defining the so-called control volume or region over
which the budget is applicable. For example, for an open water body, such as a lake or reservoir, the
inputs to the system consist of the inflow Qin, the precipitation, P, on the water surface, and the sub-
surface inflow, Gin, and the outputs include the outflow, Qout, the evaporation from the water surface,
E, and any sub-surface outflow, Gout. If the change in storage over the chosen time period is ∆S,
which may be positive or negative, then,
Gout
Figure 2: A simplified schematization for water budget on an open water body
For the balance of water over a control region such as a catchment the inflow, Qin, can be ignored as
the catchment receives water in form of precipitation. Transpiration by vegetation and interception,
too, can be considered as part of the water budget.
Example 1: A clear lake has a surface area of 708,000m2. For the month of March, the lake had an
inflow of 1.5 m3/s and an outflow 1.25 m
3/s. A storage change of 708,000m3 was recorded during the
month. If the total depth of rainfall recorded at the local rain gauge was 225mm for the month,
estimate the evaporation loss from the lake. State any assumptions that you make in your
calculations.
Solution: The evaporation loss may be computed rearranging the hydrologic equation given above.
That is,
E = P+ Qin-Qout -∆S
Assuming seepage to be negligible,
The precipitation, P = (225/1000X708, 000) m3 = 159,300 m
3,
Inflow, Qin = 1.5 m3/s X 86,400s/d X 31 Days /month = 4,017,600 m
3,
Qin - Qout + P – E + Gin - Gout = ∆S
Or
(Qin + P+ Gin) - (Qout + E + Gout) = ∆S
Qout
Gin
Qin
P E
Adama university, Department of civil Engineering and Architecture
Introduction to hydrology (CE-3601) Tessema B; Mekdim M;Belay,Suleman 6
Outflow, Qout = -1.25 m3/s X 86,400s/d X 31 Days /month = -3,348,000 m
3,
Change in storage, ∆S = +708, 000m3.
Hence, evaporation, E = 159,300 +4,017,600 - 3,348,000 – 708, 000 = 120,900 m3, or
E = 120,900 m3 X 1000mmm/m/708,000 m
2 =171mm over the lake.
In contrast, if the control volume is a catchment or drainage area bounded by its watershed or water
divide, the inputs consist of precipitation, P, and possibly ground water inflow, Gin, and the outputs
comprise the discharge, Q, at the catchment outlet, transpiration from the vegetation growing within
the catchment and evaporation from the precipitation intercepted on the vegetal canopy held in
storage on the ground, E, and possibly groundwater outflow, Gout. The changes in storage, ∆S, to be
considered are principally those in the sub-surface unsaturated and saturated zones leading to
Example 2: During the water year 1998/99, a catchment area with the size of 2500 km2 received
1,300mm of precipitation. The average discharge at the catchment outlet was 30m3/s. Estimate the
amount of water lost due to the combined effects of evaporation, transpiration and percolation to
groundwater. Compute the volumetric runoff coefficient for the catchment in the water year.
Solution: Assuming that the changes in storage, ∆S, are negligible, the above equation for the
catchment area becomes:
E + Gout – Gin = P – Q The runoff, Q = 30m
3/s X86, 400s/d X 365 Days /year X 1000 mm/m/(2500 km
2 X (1000m/km)
2)
= 378mm.
Hence, the combined loss = 1,300 – 378 = 922mm.
The volumetric runoff coefficient, C, is the ratio of the total volume of runoff to the total volume of
rainfall during a specified time interval: in this case,
C = 378/1300 = 0.29, i.e., only 29% of the rainfall reached the catchment outlet with
in the water year.
Q =P – E +Gin –Gout - ∆S
Adama university, Department of civil Engineering and Architecture
Introduction to hydrology (CE-3601) Tessema B; Mekdim M;Belay,Suleman 7
CHAPTER TWO - RUNOFF MEASUREMENT AND RATING CURVE
2.1 Stream Flow Measurement
Definition
Stream flow means the discharge flowing in a river or a stream. It represents the runoff in the river at
the given section and includes surface runoff as well as ground water.
Control section/Gauging station: - is the point selected for measuring /determining the
characteristics of the stream flow. Stream gauging includes determining the river discharge and
velocity over long period of time.
Measurement of stage, velocity and discharge Stage of a stream flow can be measured as the depth of flow in the stream channel, taken from the
bottom of the control point.
Discharge is defined as the volumetric rate of flow through a given section. Mathematically it is
given as: Q = A x V
Where,
Q = discharge, m3/sec
A = cross section of area, m2
V = average flow velocity, m/sec
Discharge can be measured in the following several ways:
1. Velocity area method
2. Weir method
3. Power plant method
4. Dilution method
5. Slope area method
6. And others.
In this lesson discussions will be limited to the first two common and basic methods alone.
1) Velocity area method
This involves estimation of discharge through direct measurement of flow velocity and area of flow.
The velocity of flow can be measured by float method or current meter.
i) Float method - float method of making a rough estimate of the flow in a channel consists of noting
the rate of movement /the advancement of a floating body. A long necked bottle partly filled with
water or a block of wood may be used as a float. A straight section of the channel about 30 meters
long with fairly uniform cross-section is usually selected. Several measurements of depth and width
are made within trial section to arrive at the average cross-sectional area. A string is stretched across
each end of the section at a right angle to the direction of flow. The float is placed in the channel, a
short distance upstream from the trial section. The time the float needs to pass from the upper to
lower section is recorded. Several trials are made to the average time of travel.
Adama university, Department of civil Engineering and Architecture
Introduction to hydrology (CE-3601) Tessema B; Mekdim M;Belay,Suleman 8
Figure 15: A float method illustration
To determine the velocity of water at the surface of the channel, the length of the trial section is
divided by the average time taken by the float to cross it. Since the velocity of the float on the surface
of the water will be greater than the average velocity of the stream, it is necessary to correct the
measurement by multiplying by a constant factor which is usually assumed to be 0.85. That is,
Q = (Vsurface X 0.85) X A, where A is flow area.
ii) Current meter method-The velocity of water in a stream or river may be measured directly
with a current meter. The current meter is a small instrument containing a revolving wheel or vane
that is turned by the movement of water. It may be suspended by a cable for measurements in deep
streams or attached to a rod in shallow streams. The number of revolutions of the wheel in a given
time interval is obtained and the corresponding velocity is reckoned from a calibration table or graph
of the instrument.
For feeding channels or rivers the average flow velocity, Vaverage can be fixed using one of the
following relations.
Where,
VSurface, V0.2, V0.6 and V0.8 are velocities of flow measured at the free surface, 20%, 60% and
80% of the depth of the flow.
Current meter measurements in canals and streams are generally made at metering bridges, at
cableways or at other structures giving convenient access to the stream. The channel at the measuring
section should be straight, with a fairly regular cross section. Structures with piers in the channel are
avoided when possible.
When the mean velocity of a stream is determined with a current meter, the cross section of flow is
divided into a number of sub-areas and separate measurements are made for each sub-area. The width
of sub-areas may vary from 1m to 6m, depending on the size of the stream and precision desired. It
has been found that the average of readings taken at 0.2 and 0.8 of the flow depth below the surface is
an accurate estimate of the mean velocity in a vertical plane.
V Average = V0.6
= (V0.2 +V0.8)/2
= K VSurface
L= about 30 m V average =L/taverage
A float
Adama university, Department of civil Engineering and Architecture
Introduction to hydrology (CE-3601) Tessema B; Mekdim M;Belay,Suleman 9
Figure 16: Division of a river cross-section into sub areas
Both float and current methods, however, have very limited application in the irrigation practice field.
Both methods are used in open channels.
Example 1: The following velocities were recorded in a stream with a current meter.
Depth above the bed, m 0 1 2 3 4
Velocity, m/s 0 0.5 0.7 0.8 0.8
Find the discharge per unit width of the stream near the point of measurement. Depth of the flow at
the point was 5 meters.
Solution:
Yo = 5 m.
Therefore, 0.2Yo = 1 m, V0.2 = 0.5 m/s
0.8Yo = 4 m, V0.8 = 0.8 m/s
Average mean velocity = (V0.2 +V0.8)/2 = (0.5+0.8)/2 = 0.65 m/s.
The discharge per unit width = Ax V = (5 x1) * 0.65 = 3.25 m3/s/m.
Example2: the following data were collected for a stream at a gauging station. Compute the
discharge.
Solution:
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Introduction to hydrology (CE-3601) Tessema B; Mekdim M;Belay,Suleman 10
2) Use of weirs
Weirs are installations used for discharge measurement. There are two kinds of weirs: sharp - crested
& broad - crested weirs. Sharp -crested weirs have knife edge overflow section from where water jet
springs out. Broad -crested weirs have either flat topped or ogee crest profile.
Discharge Formula [m3/s]
Rectangular/ trapezoidal -sharp crested weirs are used to measure large flows, while V-notch weirs
are used for small flows. But sharp-crested weirs are not widely used for rivers carrying high
sediment load as material gets collected in the stilling pool above the weir, thereby rising the velocity
of approach.
For a rectangular sharp-crested weir the discharge formula is
HLgCQ d2
3
23
2= (Without velocity of approach)
H = head of water over the weir crest, m
L = length of the weir crest, m
For a V-notch weir discharge formula is
θθ
,2
tan215
82
5
HgCQ d= is the angle of notch.
H = the head over the notch, m
For a broad -crested weir the discharge formula is
Q = 1.7CdLH3/2
Adama university, Department of civil Engineering and Architecture
Introduction to hydrology (CE-3601) Tessema B; Mekdim M;Belay,Suleman 11
L and H as defined above.
Ogee weir the discharge formula is
Q = 2.2 CdLH3/2
L and H as defined above.
1.1. Coordinate method of measuring discharge from pipes
Figure 17: Coordinate method of measuring discharge from pipes
Q = discharge, m3/s
C = coefficient of contraction ~ 1.0
A = cross sectional area of pipe, m2
X = x-coordinate, m
Y = y-coordinate, m
g = gravitational acceleration, m/s2
V= flow velocity, m/s
2.2 Stage-discharge /Rating Curves
These are the curves that give the relationship between the stage of the river at a given time (gauge
height) and the corresponding discharge. Graphically it is generally represented as follows.
Figure 18: Stage discharge relations
Q = (CAXg1/2
)/ (2Y) 1/2
D
Y
X
V= (Xg 1/2
)/ (2Y) 1/2
X = Vt
Y = (gt2)/2
Gau
ge
hei
ght in
Discharge [m3/s]
Station rating curve
Adama university, Department of civil Engineering and Architecture
Introduction to hydrology (CE-3601) Tessema B; Mekdim M;Belay,Suleman 12
Stage-discharge curves can be prepared for both gauged and ungauged stations. Once the stage-
discharge relationship is established, it can be used to measure the discharge during different stream
flows directly.
2.3 Methods for Extending the Stage - Discharge curve.
a. Logarithmic method:-
If the river cross- section at the site of the gauge is a uniform section (or even approximates a uniform
section) to which can be fitted either a segment of a circle or a trapezoidal or a parabola or a
rectangular section, then this method can be easily adopted. The stage discharge curve for such a
stream can be expressed by an equation of the form
Q = k (g-go) m
where
Q = discharge in m3/s
g = gauge height in meters
go = gauge height in meters corresponding to zero discharge
k and m are constants.
Taking log on both sides, we get
Log Q = log (k (g-go) m
)
= log k + log (g-go) m
= log k + m log (g-go)
This is the equation of a straight line having a slope as m and log k as the intercept on Y - axis as
shown below.
Figure 17: Logarithmic method
The gauge height corresponding to zero discharge is not known and hence a graph is plotted between
log Q and log (g-go) for different assumed values of go other than 0, till a straight line is obtained for
a certain value of go.
b. YA Method (Steven's method)
go
Gau
ge
hei
ght (g
)
Discharge, Q
Adama university, Department of civil Engineering and Architecture
Introduction to hydrology (CE-3601) Tessema B; Mekdim M;Belay,Suleman 13
This method is applicable for wider and shallower streams. For such streams the wetted perimeter,
P=b+2Y ≅ b for Y<<< b (Y flow depth, b channel bottom width). Therefore, the hydraulic mean
radius R (i.e. R = A/P) is equal to A/b = (bY)/b = Y = R.
SRCAQ = (By Chezy Formula)
SRCA=
Qα YA if SC= is constant.
Figure 18: Steven's method
c. General Method
Applicable to all types of river sections, but it is necessary to know the stream cross-section at the
gauging site. The method requires plotting gauge height Vs area curve. From this curve the velocity
curves can be drawn using the relation; Mean velocity, V = Discharge/ Area on the same drawing.
Figure 19: Height: discharge, velocity area relation ship
The mean velocity is given by Manning's Formula as V= SRn
2
1
3
21 . For higher river stages, S
n2
11is
almost constant. Vα R2/3
Q Vs YA
Q
AY
0.5
ht Vs A: Concave down ward
Height Vs Q
ht Vs V: Concave up ward
Gau
ge
Hei
ght, h
t
Discharge, Velocity, Area
Adama university, Department of civil Engineering and Architecture
Introduction to hydrology (CE-3601) Tessema B; Mekdim M;Belay,Suleman 14
CHAPTER THREE - PROCESSING AND ANALYSIS OF HYDROLOGICAL DATA
3.1 General
Hydrological studies require extensive analysis of meteorological, hydrological and spatial data to represent
the actual processes taking place on the environment and better estimation of quantities out of it. Precipitation
is the source of all waters which enters the land. Hydrologists need to understand how the amount, rate,
duration, and quality of precipitation are distributed in space and time in order to assess, predict, and forecast
hydrologic responses of a catchment.
Estimates of regional precipitation are critical inputs to water-balance and other types of models used in water-
resource management. Sound interpretation of the prediction of such models requires an assessment of the
uncertainty associated with their output, which in turn depends in large measure on the uncertainty of the input
values.
The uncertainties associated with a value of regional precipitation consist of:
1. Errors due to point measurement
2. Errors due to uncertainty in converting point measurement data into estimates of regional precipitation
It is therefore, necessary to first check the data for its quality, continuity and consistency before it is
considered as input. The continuity of a record may be broken with missing data due to many reasons such as
damage or fault in recording gauges during a period. The missing data can be estimated by using the data of
the neighboring stations correlating the physical, meteorological and hydrological parameters of the catchment
and gauging stations. To estimate and correlate a data for a station demands a long time series record of the
neighboring stations with reliable quality, continuity and consistency.
3.2 Meteorological data
3.2.1 Principles of Data Analysis
a) Corrections to Point Measurements
Because precipitation is the input to the land phase of the hydrologic cycle, its accurate measurement is the
essential foundation for quantitative hydrologic analysis. There are many reasons for concern about the
accuracy of precipitation data, and these reasons must be understood and accounted for in both scientific and
applied hydrological analyses.
Rain gages that project above the ground surface causes wind eddies affecting the catch of the smaller
raindrops and snowflakes. These effects are the most common causes of point precipitation-measurement.
Studies from World Meteorological Organization (WMO) indicate that deficiencies of 10% for rain and well
over 50% for snow are common in unshielded gages. The daily measured values need to be updated by
applying a correction factor K after corrections for evaporation, wetting losses, and other factors have been
applied. The following equations are recommended for U.S. standard 8-Inch gauges with and without Alter
wind shields.
Correction factor for unshielded rain gauges:
Kru = 100 exp (-4.605 + 0.062 Va
0.58
) (1.1) Correction factor for Alter wind shielded rain gauges:
Kru = 100 exp (-4.605 + 0.041 Va
0.69
) (1.2) Where: Va = Wind speed at the gage orifice in m/s (Yang et al. 1998)
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Errors due to splashing and evaporation usually are small and can be neglected. However, evaporation losses
can be significant in low-intensity precipitations where a considerable amount could be lost. Correction for
wetting losses can be made by adding a certain amount (in the order of 0.03 – 0.10 mm) depending on the type
precipitation.
Systematic errors often associated with recording type rain gauges due to the mechanics of operation of the
instrument can be minimized by installing a non recording type gauge adjacent to each recording gauge to
assure that at least the total precipitation is measured. Instrument errors are typically estimated as 1
– 5% of the total catch (Winter (1981)).
Although difficult to quantify and often undetected, errors in measurement and in the recording and publishing
(personal errors) of precipitation observations are common. To correct the error some subjectivity is involved
by comparing the record with stream flow records of the region.
b) Estimation of Missing Data
When undertaking an analysis of precipitation data from gauges where daily observations are made, it is often
to find days when no observations are recorded at one or more gauges. These missing days may be isolated
occurrences or extended over long periods. In order to compute precipitation totals and averages, one must
estimate the missing values.
Several approaches are used to estimate the missing values. Station Average, Normal Ratio, Inverse Distance
Weighting, and Regression methods are commonly used to fill the missing records. In Station Average
Method, the missing record is computed as the simple average of the values at the nearby gauges. Mc Cuen
(1998) recommends using this method only when the annual precipitation value at each of the neighboring
gauges differs by less than 10% from that for the gauge with missing data.
[ ]....1
321 +++= PPPM
px …… ………… ……… (1.3)
Where:
Px = The missing precipitation record
P1, P2 , …, Pm = Precipitation records at the neighboring stations
M = Number of neighboring stations.
If the annual precipitations vary considerably by more than 10 %, the missing record is estimated by the
Normal Ratio Method, by weighing the precipitation at the neighboring stations by the ratios of normal annual
precipitations.
+++=
m
mx
xN
P
N
P
N
P
N
P
M
Np ....
3
3
2
2
1
1 …… ………… ……… (1.4)
Where:
Nx = Annual-average precipitation at the gage with missing values
N1 , N2 , …, Nm = Annual average precipitation at neighboring gauges
The Inverse Distance Method weights the annual average values only by their
distances, dm, from the gauge with the missing data and so does not require
information about average annual precipitation at the gauges.
∑=
−=m
m
mbdD
1
…… ………… ……… (1.5)
The missing value is estimated as:
Adama university, Department of civil Engineering and Architecture
Introduction to hydrology (CE-3601) Tessema B; Mekdim M;Belay,Suleman 16
m
m
m
mb
x NdP ∑=
−=1
…… ………… ……… (1.6)
The value of b can be 1 if the weights are inversely proportional to distance or 2, if the weights are
proportional to distance squared.
If relatively few values are missing at the gauge of interest, it is possible to estimate the missing value by
regression method.
c) Checking the Consistency of Point Measurements
If the conditions relevant to the recording of rain gauge station have undergone a significant change during the
period of record, inconsistency would arise in the rainfall data of that station. This inconsistency would be felt
from the time the significant change took place. Some of the common causes for inconsistency of record are:
1. Shifting of a rain gauge station to a new location
2. The neighborhood of the station may have undergoing a marked change Obstruction, etc. 4. Occurrence of observational error from a certain date both personal and instrumental
The most common method of checking for inconsistency of a record is the Double-Mass Curve analysis
(DMC). The curve is a plot on arithmetic graph paper, of cumulative precipitation collected at a gauge where
measurement conditions may have changed significantly against the average of the cumulative precipitation
for the same period of record collected at several gauges in the same region. The data is arranged in the reverse
order, i.e., the latest record as the first entry and the oldest record as the last entry in the list. A change in
proportionality between the measurements at the suspect station and those in the region is reflected in a change
in the slope of the trend of the plotted points. If a Double Mass Curve reveals a change in slope that is
significant and is due to changed measurement conditions at a particular station, the values of the earlier period
of the record should be adjusted to be consistent with latter period records before computation of areal
averages. The adjustment is done by applying a correction factor K, on the records before the slope change
given by the following relationship.
changebeforeperiodforSlope
changeafterperiodforSlopeK =
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Introduction to hydrology (CE-3601) Tessema B; Mekdim M;Belay,Suleman 17
a) Double Mass Curves for Bahir b Double Mass Curves for Adet
c) Double Mass Curves for Dangila Figure 1.1: Double Mass Analysis
The updated records are computed using equation as given below:
Pcx = PxK Where the factor K is computed by equation (g) Table 1: Slopes of the DMC and correction factor K
Precipitation records at Bahir Dar and Adet meteorological station beyond November 1998 should be updated
by applying the correction factors 1.25 and 0.75 respectively.
Average slopes
Stations Slope for period after slope
change
Slope for period
before slope change
K
Bahir Dar 1.114 0.892 1.249
Adet 0.752 1.008 0.746
Dangila 1.1986 1.1986 1.000
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Introduction to hydrology (CE-3601) Tessema B; Mekdim M;Belay,Suleman 18
3.3 Areal Estimation
Rain gauges represent only point measurements. in practice however, hydrological analysis requires
knowledge of the precipitation over an area. Several approaches have been devised for estimating areal
precipitation from point measurements. The Arithmetic mean, the Thiessen polygon and the Isohyetal method
are some the approaches.
The arithmetic mean method uses the mean of precipitation record from all gauges in a catchment. The method
is simple and give good results if the precipitation measured at the various stations in a catchment show little
variation.
In the Thiessen polygon method, the rainfall recorded at each station is given a weightage on the basis of an
area closest to the station. The average rainfall over the catchment is computed by considering the
precipitation from each gauge multiplied by the percentage of enclosed area by the Thiessen polygon. The
total average areal rainfall is the summation averages from all the stations. The Thiessen polygon method
gives more accurate estimation than the simple arithmetic mean estimation as the method introduces a
weighting factor on rational basis. Furthermore, rain gauge stations outside the catchment area can be
considered effectively by this method.
The Isohyetal method is the most accurate method of estimating areal rainfall. The method requires the
preparation of the isohyetal map of the catchment from a network of gauging stations. Areas between the
isohyets and the catchment boundary are measured. The areal rainfall is calculated from the product of the
inter-isohyetal areas and the corresponding mean rainfall between the isohyets divided by the total catchment
area.
Example 3.3: compute the mean annual precipitation for the river basin shown in fig 3.16 below by
using Arithmetic method; thiessen polygon method and Isohyets method. The location of the
various rain gauge stations and the point precipitation values are indicated in the table below.
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3.4 Hydrological Data
The availability of stream flow data is important for the model calibration process in catchment modelling.
Measured hydrograph reflects all the complexity of flow processes occurring in the catchment. It is usually
difficult to infer the nature of those processes directly from the measured hydrograph, with the exception of
some general characteristics such as mean times of response in particular events. Moreover, discharge data are
generally available at only a small number of sites in any region where different characteristics of the
catchment are lumped together.
3.4.1 Missing Data and Comparison with the Precipitation Records
The data so far collected do not indicate any missing data. The potential errors in the discharge records would
affect the ability of the model to represent the actual condition of the catchment and calibrating the model
parameters. If a model is calibrated using data that are in error, then the model parameter values will be
affected and the prediction for other periods, which depend on the calibrated parameter values, will be
affected.
Prior to using any data to a model it should be checked for consistency. In data where there is no information
about missing values check for any signs that infilling of missing data has taken place is important. A common
indication of such obvious signs is apparently constant value for several periods suggesting the data has been
filled. Hydrographs with long flat tops also often as sign of that there has been a problem with the
measurement. Outlier data could also indicate the problem.
Even though there is a danger of rejecting periods of data on the basis on these simple checks, at least some
periods of data with apparently unusual behavior need to be carefully checked or eliminated from the analysis.
The available stream flow data for this analysis generally has corresponding match with the precipitation
records in the area. The high flows correspond to the rainy seasons. In some of the years there are remarkably
high flow records, for instance in the month of august 2000 and 2001 the flow records are as high as 100 and
89 m3/s compared to normal rainy season records which is between 30 and 65 m3/s. These data might be real
or erroneous. On the other hand the values match to the days of the peak rainfall records in the area in both the
cases.
Figure 1.2: Koga stream flow record compared with the precipitation record.
However, the stream flow records of 1995 are exceptionally higher and different from flow magnitudes that
had been records for long period of time at Koga River. It is not only the magnitude which is different from the
normal flow record, but also it contradicts with the magnitude of the precipitation recorded during the year.
These records might be modeled or transferred flows. Hence, the flow records of this year are excluded from
being the part of the analysis.
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Introduction to hydrology (CE-3601) Tessema B; Mekdim M;Belay,Suleman 22
CHAPTER FOUR - INTENSITY DURATION FREQUENCY PROCEDURES
Because rainfall varies from year to year in total amounts and in its timing and pattern, each year the
total amount of rain falling at a point is the usual basic precipitation figure available for many
purposes. We require data on rainfall going back sometimes over a hundred years or more for
statistical analysis. Therefore, to make use of such data for statistical analysis, the data should
represented by three important variables such as 1) intensity 2) duration 3) Frequency.
Intensity: - Is the measure of the quantity of rain falling in a given time. It is expressed in cm/hr,
mm/hr, etc.
Duration: - is the period of time during which a particular rain is falling.
Frequency: - refers to the return period of a particular rainfall characterized by a given duration,
intensity or both, falls.
4.1 Intensity-Duration relationship of a Rainfall
An idealized curve showing the intensity variation with time is known as Time-Intensity pattern. A
hyetograph is a plot of the intensity of rainfall against the time interval. The hyetograph is derived
from the mass curve and is usually presented as a bar chart. It is very convenient way of representing
the characteristics of a storm and is particularly important in the development of design storms to
predict extreme floods. The area under a hyetograph represents the total precipitation received in the
period. The time interval used depends on the purpose; for example, in urban drainage problems
small durations are used while in flood flow computations in large catchments the intervals are of
about 6 hours.
Figure 5: Time –Intensity pattern Figure 6: Rain hyetograph
If the total accumulated precipitation is plotted against time, the curve obtained is known as the mass
curve of the storm. Thus the mass curve of rainfall is the plot of the accumulated precipitation against
time plotted in chronological order. Records of float type and weighing bucket type are of this form.
A typical mass curve of rainfall at a station during a storm is shown in the following figure 11. Mass
curves of rainfall are very useful in extracting the information on the duration and magnitude of a
storm. Also intensities at various time intervals in a storm can be obtained from the slope of the
curve. For non-recording rain gauges, mass curves are prepared from the knowledge of the
approximate beginning and end of a storm and by using the mass curves of adjacent recording gauge
station as a guide.
Rai
nfa
ll inte
nsi
ty in c
m/h
r
Time in hours ►
Rai
nfa
ll inte
nsi
ty in c
m/h
r
Time in hours ►
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Introduction to hydrology (CE-3601) Tessema B; Mekdim M;Belay,Suleman 23
Figure 7: Mass curve of rainfall
Point Rainfall: - Point rainfall, also known as station rainfall refers to the rainfall data of a station.
Depending upon the need, data can be listed as daily, weekly, monthly, seasonal or annual values for
various periods. Graphically, these data are represented as plots of magnitude Vs chronological time
in the form of a bar diagram. Such a plot, however, is not convenient for discerning a trend in the
rainfall, as there will be considerable variation in the rainfall. Values of precipitation of three or five
consecutive time intervals plotted at the mid-value of the time interval is useful in smoothing out the
variations and beginning out the trend.
4.2 Depth - Area - Duration (DAD) Relationship
Since precipitation rarely occurs uniformly over an area, variations in intensity and total depth of fall
occur from the center of the peripheries of storm. The areal characteristic of a storm of a given
duration is reflected in its depth - area relationship. Such a relation is represented by a curve shown
below. Different such curves will be obtained for different storms of different duration, as shown in
Fig 13 from which maximum observed DAD curve of a particular duration can be obtained. Different
such curves will be obtained for different storm of a given duration.
Figure 9: Depth - Area – Duration curve
A depth - area duration curve expresses graphically the relation between progressively decreasing
average depth of rainfall over a progressively increasing area from the center of the storm out ward to
its edges for a given duration of rainfall. An immediate purpose of DAD analysis of a particular
storm is to determine the largest average depth of rainfall that fell over various sizes of area during
the standard passage of time in hours or days, such as the largest average depth over 500 sp. km in 1
day.
Effect of first
storm
Effect of
2nd storm
Acc
um
ula
ted p
reci
pitat
ion, cm
Time in days
Rai
nfa
ll d
epth
in
Area in km2
DAD curve for 24 hr (day)
for the given storm
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Introduction to hydrology (CE-3601) Tessema B; Mekdim M;Belay,Suleman 24
Equation of Depth - Area –duration Curve: - in the depth area curve for a rainfall of a given
duration, the average depth decreases with the area in a exponential fashion as given by the equation:
P = P0 (e)- K An
where P = average depth in cm over an area A km2,
P0 = highest amount of rainfall in cm at the storm center,
K and n = constants for the given region.
On the basis of number of severest storms in north Gondor, Debarik and Sanja (1975) have obtained
the following values for K and n for storms of different durations:
Duration K N
1 day 0.0008526 0.6614
2 days 0.0009877 0.6306
3 days 0.001745 0.5961
Since it is very unlikely that the storm center coincides over a rain gauge station, the exact
determination of P0 is not possible. Hence in the analysis of the large area storms the highest station
rainfall is taken as the average depth over an area of 25 km2. The above equation is useful in
extrapolating an existing storm data over an area.
Maximum Depth - Area - Duration Curves: - In many hydrological studies involving estimation of
severe floods, it is necessary to have information on the maximum amount of rainfall of various
durations occurring over various sizes of areas. The development of relationship between maximum
depth - area - duration for a region is known as DAD analysis and forms an important aspect of hydro
- meteorological study.
Figure10: Maximized Depth - Area – Duration curve
The above figure shows typical DAD curves for a catchment. In this the average depth denotes the
depth averaged over the area under consideration. It may be seen that the maximum depth for the
given storm decreases with the area; for a given area the maximum depth increases with the duration.
A brief description of the analysis is given below:
(i) First, the most severe rainstorms that have occurred in the region under question are
considered.
(ii) Isohyetal maps and mass curves of the storms are prepared.
24 hrs duration
12 hrs duration
6 hrs duration
Catchment area
Rai
nfa
ll d
epth
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Introduction to hydrology (CE-3601) Tessema B; Mekdim M;Belay,Suleman 25
(iii) A depth - area curve of a given duration of the storm is prepared.
(iv) From a study of the mass curve of rainfall, various durations and maximum depth of rainfall
in these durations are noted.
(v) The maximum depth - area curve for a given duration D is prepared by assuming the area
distribution of rainfall for smaller duration to the similar to the total storm.
(vi) The procedure is then repeated for different storms and the envelope curve of maximum depth
- area for duration D is obtained.
(vii) A similar procedure for various values of D results in a family of envelope curves of
maximum depth vs. area, with duration as the third parameter. These curves are called DAD
curves.
Example: The following are the rain gauge observation during a storm. Construct:
(a) Mass curve of precipitation
(b) Hyetograph
(c) Maximum intensity- duration curve and develop a formula and
(d) Maximum depth- duration curve.
Time since commencement
of storm (min.)
Accumulated rainfall (cm)
5 0.1
10 0.2
15 0.8
20 1.5
25 1.8
30 2.0
35 2.5
40 2.7
45 2.9
50 3.1
Solution:
(a) Mass curve of precipitation: The plot of accumulated rainfall (cm) Vs time (min.) gives the
mass curve of rainfall.
Mass curve of percipitation
0
0.5
1
1.5
2
2.5
3
3.5
0 5 10 15 20 25 30 35 40 45 50 55
Time (min)
(b) Hyetograph: The intensity of rainfall at successive 5 min. interval is calculated and bar graph
of i (cm/h) Vs t (min.) is constructed; this depicts the variation of the intensity of rainfall with respect
to time and is called the "hyetograph".
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Time, t (min) Accumulated rainfall
(cm) ∆P in time ∆t = 5 min. Intensity,
i = ∆P/∆t x 60 (cm/h)
5 0.1 0.1 1.2
10 0.2 0.1 1.2
15 0.8 0.6 7.2
20 1.5 0.7 8.4
25 1.8 0.3 3.6
30 2.0 0.2 2.4
35 2.5 0.5 6.0
40 2.7 0.2 2.4
45 2.9 0.2 2.4
50 3.1 0.2 2.4
Hyetograph
1.2 1.2
7.2
8.4
3.6
2.4
6
2.4 2.4 2.4
0
1
2
3
4
5
6
7
8
9
0 5 10 15 20 25 30 35 40 45 50 55
Time (min)
Intenisty(cm/hr)
(c) Maximum depth - duration curve: By inspection of time (t) and accumulated rainfall (cm)
the maximum rainfall depths during 5, 10, 15, --------------, 50 min. duration are 0.7, 1.3, 1.6, 1.8, 2.3,
2.5, 2.7, 2.9, 3.0 and 3.1 cm respectively. The plot of the maximum rainfall depths against different
duration on a log-log paper gives the maximum depth - duration curve, which is a straight line.
Time
(min.)
Acc
rainfall
(cm)
change
in ppt
Intensity
(cm/hr) Maximum Intensity of each duration (cm/hr)