Flood

An Introduction to F L OO D Mrinmoy Majumder www.baipatra.ws

Definition ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Rational Method ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Time of Concentration ,[object Object],[object Object],t p = C tL (LL ca /(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 t c = 0.01947L 0.77 S -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 ,[object Object],[object Object],K,a,x and m are constants which can be collected from frequency duration curves

Empirical Formula ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Dickens Formula ,[object Object],C D = Dickens Formula with value between 6 - 30

Ryves Formula ,[object Object],C R = Ryves Formula with value between 6.8 – 10.2

Inglis Formula ,[object Object],For Western Ghats in Maharashtra

Fullers Formula ,[object Object],For USA,T = return period, C f is a constant =0.18 – 1.88.

Baird and Mcillwraith(1951) ,[object Object],From maximum rrecorded floods throughout the world

Estimation of Flood from Frequency Analysis ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Analysis .Step.1 : Probability Density Function

Gumbels Method Where the distribution has mode α , mean α + γβ (where γ =0.5772156649... is Euler's constant ), and variance ⅙ β 2π2 If f(x) is probability density function, then, Gumbel’s distribution is given by :

Gumbel’s Distribution Explained ,[object Object],[object Object],[object Object],[object Object]

Normal Distribution = variate = mean = variance P(x) and D(x) is respectively the probability density function and distribution function

Log-Normal Distribution ,[object Object],[object Object],[object Object]

Pearson Type III Distribution = gamma function = variate = mean = = variance = P(x) and Φ (t) is respectively the probability density function and characteristic function = kurtosis = = kurtosis =

Log-Pearson Distribution ,[object Object],[object Object],[object Object]

Analysis.Step.2 : Validation of the PDF by Estimation of Plotting Position of the Event or Plotting Position Probability

Plotting Position Probability (PPP) ,[object Object],[object Object],Where P is the probability of an extreme event and T is the return period of that event. P rn 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 P rn = n C r P r q n-r T= 1/P

Bulletin 17B PPP (InterAgency Advisory Committee on Water Data,1982) ,[object Object],[object Object],Where P is the exceedance probability of an extreme event and T is the return period of that event. i 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 a and b are constants = f(PDF)

Weibull PPP for Uniformly Distributed Dataset ,[object Object],[object Object],Where P is the exceedance probability of an extreme event and T is the return period of that event. i 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 Uniformly distributed dataset means a = b = 0

Hazen PPP for Uniformly Distributed Dataset ,[object Object],[object Object],Where P is the exceedance probability of an extreme event and T is the return period of that event. i 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

Cunnane PPP for Uniformly Distributed Dataset ,[object Object],[object Object],Where P is the exceedance probability of an extreme event and T is the return period of that event. i 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

Synthesis i.e. Determination of the Magnitude

General Equation of Hydrologic Frequency Analysis (Chow,1951) ,[object Object],Where x T 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 You can also apply Gumbel’s Method.

Mathematical Model ,[object Object],Where x is the value of the flood x’ is the mean and σ is the standard deviation K = f (T, frequency distribution) = frequency factor You can also apply Gumbel’s Method. K =(x - x ’)/ σ Note : If x is known then use Eqn.A and if K is known then use Eqn.B ….A ….B

Note ,[object Object],[object Object],[object Object],[object Object]

Rational Equation (modified for urbanization) Q p = 484.1A 0.723 (1+U) 1.516 P E 1.113 T r 0.403 A = drainage area U = fraction of imperviousness P E = volume of excess rainfall T r = duration of rainfall excess

Adjustment for Urbanization Adjusted peak discharge due to observed impervious factor = Observed Peak Discharge multiplied by adjustment factor of the observed imperviousness

Urban Adjustment Factor (Leopold,1968)

Probable Maximum Precipitation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Hershfield Method where X PMP is the PMP for a given station for a specific duration and X¯ n and σ n are the mean and standard deviation for a series of n annual maximum rainfall values of a given duration respectively. K m is the frequency factor and is the largest of all the calculated K values for all stations in a given area.

Frequency Factor Calculation where X 1 , X¯ n −1 and σ n −1 are the highest value, mean and standard deviation respectively excluding the X 1 value from the series.

Homogeneity of Dataset ,[object Object],the ratio of τ to the σ τ gives an indication of trend in the data. For no trend in the data series, this value should lie within the limits of ± 1.96 at the 5% level of significance.

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