analysis of floods

7/29/2019 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

analysis of floods

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