By UWIMPUHWE

Charlotte
CHAP 7. FLOOD HYDROGRAPH
 Introduction
 A hydrograph is a graph showing how some measure
of water changes over time.
 Time is the independent variable and is therefore,
always located on the X-axis.
 The dependent variable, or whatever is doing the
changing over time, goes on the Y-axis.
 i.e:
 discharge hydrograph (showing how the rate of
flow in a stream changes with time),
 stage hydrograph,
 runoff hydrograph ….
Introduction
 Introduction
 Depending upon the unit of time involved, there are:
 annual hydrographs showing the variation of daily or weekly or
10 daily mean flows over a year;
 Monthly hydrographs showing the variation of daily mean
flows over a month;
 Seasonal hydrographs depicting the variation of the discharge
in a particular season such , as the monsoon season or dry
season; and
 Flood hydrographs or hydrographs due to a storm representing
stream flow due to a storm over a catchment.
 Each of these types has particular applications. Annual and
seasonal hydrographs are of use in: Calculating the surface
water potential of stream, Reservoir studies and Drought
studies.
 Flood hydrographs are essential in analyzing stream
characteristics associated with floods.
 Components of hydrograph
 Hydrograph is a graph showing discharge (i.e., stream
flow at the concentration point) versus time.
 The various components of a natural hydrograph:
 At the beginning, there is only base flow (i.e., the ground
water contribution to the stream) gradually depleting in an
exponential form.
 After the storm commences, the initial losses like
interception and infiltration are met and then the surface
flow begins.
 Then, the hydrograph gradually rises (The rising limb has
its steepness determined by the rate of surface runoff. The
higher the peak, and the shorter the basin lag, the steeper
will be the rising limb. The gradient of the profile reflects
the rate of rising flood.)
 Components of hydrograph
 The various components of a natural hydrograph:
 Components of hydrograph
 The various components of a natural hydrograph:
 Time of concentration of a drainage basin is the time required
by the water to reach the outlet from the most remote point of
the drainage area.
 Lag Time: Lag is the time between the peak flow and the
centroid of rainfall.
 Storm runoff occurs during flood. It is really flood water,
collected from surface runoff and quick subsurface flow during
heavy rain.
 The recession limb indicates the rate of passing flood.
 Effective rainfall refers to the percentage of rainfall which
becomes available to plants and crops
 Net Rainfall is the portion of rainfall which reaches a stream
channel or the concentration point as direct surface flow
2 Factor affecting flood hydrograph
 Factors affecting the shape of runoff hydrograph:
 Size of catchment;
 Nature of catchment;
 Shape of catchment;
 Intensity and/or duration of rain;
 Direction of storm (wind);
 Distribution of rain and/or drainage network,
 Type of rain; and
 Groundwater contribution
 Unit Hydrograph Theory
 Hydrograph is a graphical relation between flow rate
(m3/s) or level against time (t in hr).
 If two identical rains fall on a drainage basin, the
hydrographs of runoff from the 2 storms would be the
same. This is the basis for the Unit Hydrograph (UH).
 A unit hydrograph is defined as the hydrograph of runoff
produced by excess rainfall of 1cm occurring uniformly
over the entire drainage basin at a uniform rate over the
entire specified duration.
 In other word, Unit Hydrograph (UH) is a simple
hydrograph model for response of catchment to rainfall. It
is a hydrograph of runoff produced by a rainstorm of
specific duration called Unit Duration, resulting in a
runoff depth of 1cm on the entire basin (catchment area).
 Unit Hydrograph Theory
 Application of unit hydrograph
1. A unit hydrograph is used to estimate stream flow or
discharge given a basin average rainfall
2. The development of flood hydrograph for extreme rainfall
magnitude
3. Extension of flood flow record based on rainfall record
4. Development of flood forecast and warning system based on
rainfall
 Limitation of application of hydrograph
1. unit hydrographs assume uniform distribution of rainfall over
the catchment and uniform intensity during the duration of
rainfall excess, these two conditions are never satisfied
2. the size of the catchment imposes an upper limit on the
applicability of the unit hydrograph
3. the upper limit for use of the unit hydrograph method is
5000km2
 Unit Hydrograph Theory
 Why Construct & Analyze Hydrographs?
 To find out discharge patterns of a particular drainage
basin, to help predict flooding events therefore influence
implementation of flood prevention measures
 We know that after a period of heavy rainfall, the
discharge increases.
 One of the formula using for estimating peak /maximum
discharge
 we know that where we have peak discharge when we
reach at peak point.
 Derivation of Unit Hydrograph
 We have observed hydrograph (discharge of observed
hydrograph), also called TRO—Total runoff ordinate =
gauged discharge of stream
 Then separate BFO—Base flow ordinate
 then find DRH: Direct Runoff Hydrograph and sum of all
DRH, also called DRO—Direct runoff ordinate = TRO—
B.F.O
 after we find VDR: volume of direct of runoff, also called
UGO—Unit hydrograph ordinate
 Unit hydrograph: DRO/UNIT DEPTH or Pnet
 Pnet=ΣDRO *t/A
Derivation of Unit Hydrograph
 Derivation of Unit Hydrograph
 Element of unit hydrograph
 Derivation of Unit Hydrograph
 Illustrative
Example
 The runoff data at
a stream gauging
station for a flood
are given below.
The drainage area
is 40 km2. The
duration of rainfall
is 3 hours. Derive
the 3-hour unit
hydrograph for the
basin and plot the
same
 Derivation of Unit Hydrograph
 Illustrative Example
 Derivation of Unit Hydrograph
 Illustrative Example
Instantaneous unit hydrograph
 The difficulty of using a unit hydrograph of a known
duration has been obviated by the development of the
instantaneous unit hydrograph (IUH).
 The IUH is a hydrograph of runoff resulting from the
instantaneous application of 1 cm net rain on the drainage
basin.
 The IUH in conjunction with the design storm can be used
to obtain the design flood by using a convolution integral.
 The IUH was first proposed by Clark in 1945.
 The IUH can be developed either directly from the
observed data or by adopting conceptual models
Estimate the design Unit Hydrograph
 Estimate the design Unit Hydrograph Depending upon the
data availability and characteristics of flood hydrograph
etc,
 the unit hydrograph may be derived using any of the
following techniques:
 1. Simple method of unit hydrograph derivation from a
flood event with isolated peak
 2. Collin’s method
 3. Nash method
 4. Clarke model.
 In case of insufficient data, synthetic unit hydrograph may
be derived
Application of unit hydrograph
 The application of unit hydrograph consists of two
aspects:
 (i) From a unit hydrograph of a known duration to obtain a
unit hydrograph of the desired duration, either by the S-
curve method or by the principle of superposition.
 (ii) From the unit hydrograph so derived, to obtain the
flood hydrograph corresponding to a single storm or
multiple storms. For design purposes, a design storm is
assumed, which with the help of unit hydrograph, gives a
design flood hydrograph
Review –
CHAP 8. DESIGN FLOOD
ESTIMATION
 Introduction
 Whenever an area stands under water over a certain
period of time (which can vary from place to place)
leading to disruption of normal activities and lost of
property and life,
it is said to be flooded.
 Generally, every area must have its natural drainage
system in a form of drains, rivers and other tributaries,
lakes, etc. to carry the surface runoff resulting from
rainfall.
 What are the causes of flood?
 Do we have a history to tell?
 Is it possible to know the magnitude and frequency of the floods
over watershed?
 Is it possible to minimize damages caused by flood ?
 Introduction
Floods generally occur due to inadequate drainage capacity :
 Excessive rainfall leading to extraordinary runoff
 Poor drainage system and drains of inadequate capacities
 Highly meandering rivers and unstable rivers often change
their course
 Tidal rivers - when excessive rain coincides with a high tide.
This causes the water level to rise and if there is not enough
space to absorb this water, the consequence would be flooding
 Sea waves due to extraordinary storm (hurricanes, cyclones
etc)
 Excessive snowmelt combined with rainfall can cause flooding
 Sudden failure of water retaining structures such as dams,
embankments, barrages etc.
 Land/Hill slides into river valleys have also often created
temporary dam-like structures leading to flooding of the
upstream areas
 Introduction
A man lifting a lady to cross the flooded On 19/05/2010, the flood was
area in Nyabugogo observed in Jenda Sector, Nyabihu
district
 Design Flood
 Definition: Design Flood is the flood discharge adopted
for the design of a hydraulic structure after careful
considerations of economic and hydrologic factors
 The Design Flood for a hydraulic structure may also be
defined in a number of ways, like:
 The maximum flood that any structure can safely pass.
 The flood considered for the design of a structure
corresponding to a maximum tolerable risk.
 The flood which a project (involving a hydraulic structure)
can sustain without any substantial damage, either to the
objects which it protects or to its own structures.
 The largest flood that may be selected for design as safety
evaluation of a structure.
 Design Flood
 Design Flood is also known as the Inflow Design Flood (IDF).
 It is the flood adopted for design purpose, and could be:
 The entire flood hydrograph, that is, the possible values of
discharge as a function of time.
 The peak discharge of the flood hydrograph
 The IDF’s (Inflow Design Flood or Design Flood) for different
types of structures constructed across rivers are different.
 Some of the structures which are of importance to water
resources engineering are:
 Storage Dams.
 Barrages and Weirs
 Diversion Works and Coffer dams
 Cross drainage works
 Choice of design flood
 Choice of design flood may be chosen from either one of
the following:
 Probable Maximum Flood (PMF) called also Most
Probable Flood (MPF),
 Standard Project Flood (SPF), and
 Flood of a specific return period
 Choice of design flood
 The methods for evaluating PMF and Standard Project
flood (SPF) fall under the hydrometeorological approach,
using the unit hydrograph theory.
 Flood of a given frequency (or return period) is obtained
using the statistical approach, commonly known as flood
frequency analysis.
 In every method, adequate data for carrying out the
calculations are required.
 The data which are required include:
 long term and short term rainfall and runoff values,
 annual flood peaks series,
 catchment physiographic characteristics, etc.
 Choice of design flood
 Most Probable Flood (MPF)
 The Most Probable Flood (MPF) which is also called The
Maximum Probable Flood (MPF) is the flood which may be
expected from the most severe combination of critical
meteorological and hydrological conditions that are reasonably
possible to occur on a certain region
 The PMF is computed by using the Probable Maximum Storm
(PMS) which is an estimate of the physical upper limit to storm
rainfall over the catchment.
 This is obtained from the studies of all the storms that have
occurred over the region and maximizing them for the most
critical atmospheric conditions.
 The critical time sequence of the design storm rainfall is
superimposed on the derived design unit hydrograph to give
the direct hydrograph, when added to the base flow, gives the
probable maximum flood hydrograph
 Choice of design flood
 Standard Project flood (SPF): This is the flood resulting
from the most sever combination of meteorological and
hydrological conditions considered reasonably
characteristic of the region.
 Flood of a specific return period: This flood is estimated
by frequency analysis of the annual flood values of
adequate length.
 Sometimes when the flood data is inadequate, frequency
analysis recorded storm data is made and the storm of a
particular frequency applied to the unit hydrograph to
derive the design flood. This flood usually has a return
period greater than the storm.
 Choice of design flood
 Data requirement for PMF/SPF studies:
1. Watershed data
 Total watershed area, snowbound area, minimum and
maximum elevations above the mean sea level and length
of river up to the project site;
 Lag time, travel times of reaches, and time of
concentration;
 Contributing areas, mean overland flow distances and
slopes;
 Design storm water losses, evaporation, infiltration,
depression and interception losses, infiltration capacities.
 Land use practices, soil types, surface and subsurface
divides.
 Choice of design flood
 Data requirement for PMF/SPF studies:
2. Channel data
 Channel and valley cross sections at different places under
consideration to fix the gauge discharge rating curves.
 Manning’s n or the data required to estimate channel
roughness coefficient.
3. Runoff data
 Base flow estimates during design floods.
 Available historical data on floods along with the
precipitation data including that of self-recording rain
gauges, if available
 Choice of design flood
 Data requirement for PMF/SPF studies:
4. Storm data
 Daily rainfall records of all rain gauge stations in and
around the region under study
 Rainfall data of self-recording rain gauges
 Data of the storm dew point and maximum dew point
temperatures
Methods for Design Flood Estimation
 In general, the methods used in estimation of the flood
design can be grouped as under:
 Increasing the maximum observed flood by a certain
percentage,
 Envelop curves,
 Empirical flood formulae,
 Rational method,
 Unit hydrograph application, and
 Frequency analysis (Or statistical methods)
Methods for Design Flood Estimation
 Rational Method
 In this method, it is assumed that the maximum flood flow
is produced by a certain rainfall intensity, I, which lasts
for a time equal to or greater than the period of
concentration time, tc.
 When a storm continues beyond concentration time, every
part of the catchment would be contributing to the runoff
at outlet and therefore it represents condition of peak
runoff.
Methods for Design Flood Estimation
 Rational Method
 The runoff rate corresponds to this condition is given by:(This
is expressed in the rational formula as)
 Q = KCIA
 Where:
 Q = peak flow (m3/s),
 C = runoff coefficient (dimensionless),
 I = rainfall intensity (cm/hr),
 A = catchment area (ha),
 K = conversion factor = 0.0278.
 The product of rainfall intensity, I, and watershed area, A, is the
inflow rate for the system, IA, and the ration of this rate of peak
discharge, Q, (which occurs at time tc) is termed runoff
coefficient, C (0 < C ≤ 1).
Methods for Design Flood Estimation
 Rational Method
 For different subcatchments, the peak runoff is then
computed using the following form of the rational
formula:

 Where:
 Aj denotes the areas of the sub-catchment; and
 Cj denotes the runoff coefficients of each sub-catchment.
 m is the number of sub-catchments drained by the drain.
Methods for Design Flood Estimation
 Rational Method
Rainfall intensity: from “The Intensity-Duration-Frequency
(IDF) curves”
 After the time of concentration has been determined, the
rainfall intensity may then be approximated.
 Several mathematically similar expressions may be fitted to
describe IDF relationships.
 The simplest relate the average rainfall intensity over 24hrs
(mm/h) and duration t (min) for a fixed return period T (yr):

Where:
 I= intensity (mm/hour),
 t= storm duration (min),
 a b, and c are regression coefficients obtained graphically or by
least squares
Methods for Design Flood Estimation
 Rational Method
 Rainfall intensity
 The rainfall intensity is estimated by the following formulas:

 Kumasi

 Wench

 Where:
 I10 is intensity in (mm/hr) for the return period of 10 years and
 tc is time of concentration in mins.
 The applied method assumes that the maximum runoff rate in a
catchment is reached when all parts of the catchment are contributing
to the outflow. This happens when the time of concentration is
reached
Methods for Design Flood Estimation
 Rational Method
Time of concentration
 The Kirpich/Ramser formula is mostly used to calculate
the time of concentration:

 where:
 tc= Time of concentration [min],
 L = Length of main river [km],
 S = Average slope of main stream [m/m].
Methods for Design Flood Estimation
 Rational Method
 Illustrative example
 A culvert is proposed across a stream draining an area of
185 ha. The intensity of rainfall for this catchment is
112mm/hr. Assuming a runoff coefficient of 0.35, estimate
the peak discharge to be drained by this culvert.
Methods for Design Flood Estimation
 Rational Method
 Illustrative example
Methods for Design Flood Estimation
 Rational Method
 Example
 A culvert is proposed across a stream draining an area of
185 ha. The catchment has a slope of 0.004 and the length
of travel for water is 1150 m. Estimate the 25 years flood
if rainfall intensity is given by:

 • Where i (mm/hr); Tr (years) and t (min). Assume a

runoff coefficient of 0.35
 Methods for Design Flood Estimation
 Flood Frequency analysis
 To minimize flood damage, we need to know the magnitude
and frequency of the floods a watershed is likely to get.
 We need to relate the magnitude of extreme events to their
frequency of occurrence through the use of probability
distributions.
1
Magnitude 
Frequency of occurence
 Most of the measurements we make in Hydrology (flow rate,
rainfall intensity) cannot be predicted with certainty. They are
Random Variables (parameter that cannot be predicted with
certainty).
Methods for Design Flood Estimation
 Flood Frequency analysis
 Basic to all frequency analyses, is the concept that there is
a collection of data, called the ‘population’
 For flood frequency studies, this population are taken as
the annual maximum flood occurring at a location on a
river (called the site).
 Since the river has flooded during the past years and is
likely to go on flooding over the coming years (unless
something exceptional like drying up of the river
happens!), the recorded flood peak values which have
been observed for a finite number of years are only a
sample of the total population
 Methods for Design Flood Estimation
 Flood Frequency analysis
 Here, ‘flood peak’ means the highest recorded discharge value
for the river at any year.
 The following assumptions are generally made for the data:
 The sample is representative of the population. Thus, it is
assumed that though only a finite years’ data of peak flow has
been recorded, the same type of trend was always there and
would continue to be so in future.
 The data are independent. That is, the peak flow data which has
been collected are independent of each other.
 Thus, the data set is assumed to be random. In a random
process, the value of the variant does not depend on previous or
next values
Methods for Design Flood Estimation
 Flood Frequency analysis
 Flood frequency analysis starts by checking the
consistency of the data and finding the presence of
features such as trend, jump, etc.
 The next step is to apply a convenient probability
distribution curve to fit the data set.
 There are a number of probability distributions f (x),
which has been suggested by many statisticians. Of these,
the more common are:
 Normal Distribution
 Log – normal
 Pearson Type III
 Gumbel Distribution
Methods for Design Flood Estimation
 Flood Frequency analysis
 Normal Distribution
 The Normal distribution is one of the most important
distributions in statistical hydrology. This is used to fit
empirical distributions with skewness coefficient close to zero.
The probability density function (PDF) of the distribution is
given by:

 Where, μ is the location parameter and σ is the scale parameter.

 The cumulative distribution function (CDF) of the normal
distribution is given by:

.
Methods for Design Flood Estimation
 Flood Frequency analysis
 Log – normal
 If the logarithms, ln x, of a variable x are normally distributed,
then the variable x is said to be log normally distributed so that:

 Where, μy and σy are the mean and standard deviation of the

natural logarithm of x.
 Log normal distributions can be applied to a wide variety of
hydrologic events especially in the cases in which the
corresponding variable has a lower bound, the frequency
distribution is not symmetrical and the factors causing those are
independent and multiplicative
Methods for Design Flood Estimation
 Flood Frequency analysis
 Log – normal
 If the variable x has a lower boundary x0, different from
zero, and the variable z=x - x0 follows a lognormal
distribution, then x is log normally distributed with three
parameters:

 Where, μy, σy and x0 are called the scale, the shape and
the location parameters, respectively. Parameter x0 is
generally estimated by trial and error
Methods for Design Flood Estimation
 Flood Frequency analysis
 Pearson Type III
 Pearson type III is a three parameter distribution, also known
as Gamma distribution with three parameters. The PDF of the
distribution is given as:

 The CDF of the Pearson Type III distribution is given by:

 Where x0, β, and γ are location, scale and shape parameters,

respectively.
Methods for Design Flood Estimation
 Flood Frequency analysis
 Gumbel Distribution
 Gumbel distribution is a member of family of Extreme
Value distributions with the value of parameter k = 0. It is
a two parameter distribution and is widely used in
hydrology.
 The PDF is given as:

 Where, u and α are location and shape parameters,

respectively
Selection of return period of a design flood
 Frequency analysis makes use of the observed data in the
past to predict the future flood events along with their
probabilities or return period.
 In the annual series the largest flood observed in each
water year only is taken.
 When estimates of very frequent events with return
periods of less than 5 years are required, (for example in
the design of coffer dams, urban drainage, etc) the partial
series is preferable to annual series.
 In partial series all flood events above a selected base
value are included
 When two consecutive events are not independent only the
higher of the two peaks is considered
Risk Associated with design flood Selection
 The prob. of an occurrence in one year p = 1/T
 The probability of at least one occurrence of the T-year event
in n years is called the Risk.
 The Risk is the sum of probs. of one such flood, two floods,
three floods, …, n floods.
 From the probabilistic nature of rainfall events, the risk (R) of
failure in design flood estimation is given by:

 Where:
 Tr(years) = return period of the design flood
 N(years) = Lifetime of the hydraulic structure
 R(fraction or %) = risk in design flood selection
Risk Associated with design flood Selection
 Illustrative example
 A coffer dam is designed for a 25 years flood and
constructed. If it takes 5 years to complete the
construction of main dam, what is the risk that the coffer
dam may fail before the end of the construction period?
 What return period in the design of coffer dam would have
reduced the risk to 10%?
Risk Associated with design flood Selection
 Illustrative example
Review