FLOOD
Mrinmoy Majumder
www.baipatra.ws
Definition
• High stage in river when the river overflows and inundates
the adjoining area
• Flood peak and frequency of the peak is an important
consideration in hydraulic design
• Magnitude and time of the flood varies with change in
watershed characteristics
• Peak flood depends on rainfall, discharge or watershed
area and type
• Magnitude of flood can be estimated in
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Rational method
Empirical method
Unit hydrograph technique
Flood frequency studies
Rational Method
• Assumptions :
– Area of watershed must be less than 50 Sq.Km
– Rainfall continues beyond time of concentration
– Catchment is homogeneous
• The equation for peak flood, according to
rational method :
Qp = C A i
Qp is the peak discharge, C is coefficient of runoff (runoff/rainfall), i is rainfall intensity
which depends on time of concentration and exceedance probability, A is drainage
area in Sq.Km
Time of Concentration
• Rainfall intensity is found to be a function
of time of concentration (tc) and an
exceedance probability P
• tc can be expressed as :
tp = CtL(LLca/(S)1/2)n
where,
C is a constant,
L is the distance from farthest point of the catchment to
basin divide,Lca is the distance of gage from centroid
of the watershed,S is slope between farthest point and
outlet,n is the manning’s constant
tc = 0.01947L0.77S-0.385
where,
time of concentration (minutes),L is maximum
length from farthest point to outlet and S is slope
of catchment(from highest point to lowest point)
Rainfall Intensity
• The rainfall intensity is thus represented
by :
itc,p = KTx/(tc+a)m
K,a,x and m are constants which can be collected
from frequency duration curves
Empirical Formula
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Regional formula
Based on correlation
Between flow(Qp) and catchment properties
Almost all use area(A)
Neglects flood frequency
The reason why empirical formulas are all
regional and gives approximate results when
applied to other regions
Dickens Formula
Qp = CDA3/4
CD = Dickens Formula with value between 6 30
Ryves Formula
Qp = CRA2/3
CR = Ryves Formula with value between 6.8 – 10.2
Inglis Formula
Qp = (124A)/(A+10.4)1/2
For Western Ghats in Maharashtra
Fullers Formula
QTp = (CfA0.8)/(1+0.8logT)
For USA,T = return period, Cf is a constant =0.18 – 1.88.
Baird and Mcillwraith(1951)
Qmp = (3025A)/(278+A)0.78
From maximum rrecorded floods throughout the world
Flood Frequency Analysis
P = m/(N+1)
Prn = nCrPrqn-r
T= 1/P
T= 1/P
Where P is the probability of an extreme event and T is the return period of that event. Prn is the
occurrence of the event for r times in n successive years
m is the rank of the event with respect to other events of the year or decade or greater time span.
N = total number of events in the dataset
C =combination of n and r and q = 1-P
Plotting Position Formula
• Probability values can be used to determine the position of the event
in a probability curve. From which both exceedance and nonexceedance probability of the event can be estimated.
General Equation of Hydrologic Frequency Analysis
(Chow,1951)
xT = x’ + K.σ
Where xT is the value of the flood in T return period
x’ is the mean and σ is the standard deviation
K = f (T, frequency distribution) = frequency factor
Gumbels Method
If f(x) is probability density function,then,Gumbel’s distribution is given by :
Where the distribution has
mode α,
mean α+γβ (where γ=0.5772156649... is Euler's constant),
and
variance ⅙β2π2
Gumbel’s Distribution Explained
• There are essentially three types of Fisher-Tippett extreme value
distributions.
• The most common is the type I distribution, which are sometimes
referred to as Gumbel types or just Gumbel distributions.
• The term "Gumbel distribution" is used to refer to the distribution
corresponding to a minimum extreme value distribution (i.e., the
distribution of the minimum ).
• The Gumbel distribution has a location parameter α
parameter β
and scale
Normal Distribution
LogNormal Distribution
Pearson Distribution
Log-Pearson Distribution