analysis of floods
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Analysis of Floods
Kedara v bhadrudu.vujji
ME(Hydraulics, Coastal & Harbour Engineering)
Departmint of Civil Engineering, Andhra university
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Overview of Presentation
Introduction
Definition
Max Flood Discharge Which probability distribution fits the
flood data?
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Introduction
Common problems in hydrologic design
Ungauged sites
Inadequate at-site information at gauged sites
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Flood
An overflow or inundation that comes from a
river or other body of water and causes or
treatens demage.
Any relatively high streamflow overtopping
the natural or artificial banks in any reach of a
stream.
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Max Flood Discharge
By physical indication of past floodsBy actual gaugings
By flood discharge formulae
By unit hydrograph
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By physical indication of past floods
These are more reliabe provided good recordsof such flood levels are available in differentyears.
Situated on river banks always bear past floodmarks.
Old people in the villages situated on the bank
of the river may contacted to know themaximum flood level attained in the pastyears.
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By actual gaugings
This is the best method proded a record of
actual measurements .
Discharges of the river is available for atleast
35 years from which the highest value.
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By flood discharge formulae
(a) Peak discharge formulae involving
drainage area only
(b) Peak discharge formulae involving
drainage area and its shape
(c) Peak discharge formulae involving rainfall
intensity and drainage area
( ) P k di h f l i l i
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(a) Peak discharge formulae involving
drainage area only
Dickens formulaQp Peak discharge in m3/s
Qp =CA3/4 A Catchment area in km2
C - Constant
C=11.5 (North India); 14-19.5 (Central India); 22 to 26 (Western Ghats of India)
Ryves formula
Qp = CA2/3
C = 6 8 for catchment areas within 80 km from thecoast= 8.8 for catchment areas within 80-2400 km from the coast
(b) k di h f l i l i
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(b) Peak discharge formulae involving
drainage area and its shape
Pettis formula
Q =C(PB)5/4
P Probable 100 year maximum 1 dayrainfall in cm
C = 1.5 ( humid areas); 0.2 ( desert areas)
C - Constant
( ) P k di h f l i l i
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(c) Peak discharge formulae involving
rainfall intensity and drainage area
Rational formula
Qp =CiA
Qp Peak discharge in cfs
A Catchment area in acres
C Runoff coefficient (0 C1)
i Intensity of rainfall in inches/hr
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By unit hydrograph
Involves developing regression relationships
between The physical characteristics of catchments
and parameters of their unit hydrographs, to arrive
at a synthetic unit hydrograph for estimation of
design flood.
Whi h b bili di ib i fi h
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Which probability distribution fits the
flood data?
Procedures for Identification
Probability papers
L-moment ratio diagram
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Probability papers
Flood data are plotted on probability paper to checkif a frequency distribution fits the data
Probability papers are specifically designed for thefrequency distributions
-One of the axes represents the values of peak flows- other axis represents exceedence or non-exceedenceprobability associated with peakflows, or return period
The plotted data appears close to a straight line if
the frequency distribution fits the data Flood quantile is estimated graphically by
interpolation or extrapolation of the determined
linear relationship between abscissa and ordinate
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L-moment ratio diagram
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Probability distributions
Normal family
Normal, lognormal, lognormal-III
Generalized extreme value family
EV1 (Gumbel), GEV, and EVIII (Weibull)
Exponential/Pearson type family
Exponential, Pearson type III, Log-Pearson type III
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Normal distribution Central limit theorem if X is the sum of n independent and
identically distributed random variables with finite variance, thenwith increasing n the distribution of X becomes normal regardless
of the distribution of random variables
pdf for normal distribution
Hydrologic variables such as annual precipitation, annual average
streamflow, or annual average pollutant loadings follow normal
distribution
2
2
1
2
1)(
x
X exf
http://upload.wikimedia.org/wikipedia/commons/1/1b/Normal_distribution_pdf.png -
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Standard Normal distribution
A standard normal distribution is a normal
distribution with mean () = 0 and standard
deviation () = 1
Normal distribution is transformed to standardnormal distribution by using the following formula:
z is called the standard normal variable
X
z
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Lognormal distribution
If the pdfof X is skewed, its not
normally distributed
If the pdf of Y = log (X) is normally
distributed, then X is said to be
lognormally distributed.
xlogyandxy
xxf
y
y
,02
)(exp
2
1)(
2
2
Hydraulic conductivity, distribution of raindrop sizes in storm follow lognormal
distribution
http://upload.wikimedia.org/wikipedia/commons/4/46/Lognormal_distribution_PDF.png -
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Pearson Type III
Named after the statistician Pearson, it is also called three-
parameter gamma distribution. A lower bound is introduced
through the third parameter (e)
It is also a skewed distribution first applied in hydrology for
describing the pdf of annual maximum flows.
functiongammaxexxfx
;)(
)()(
)(1
e
ee
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Log-Pearson Type III
If log X follows a Person Type III distribution, then X is said to
have a log-Pearson Type III distribution
e
e e
xlogyey
xfy
)(
)()(
)(1
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THANK YOU
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