FLOOD Mrinmoy Majumder

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 –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 : Q p = C A i Q p 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 (t c ) and an exceedance probability P t c can be expressed as : 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 = L 0.77 S 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 : i t c,p = KT x /(t c +a) m K,a,x and m are constants which can be collected from frequency duration curves

Empirical Formula Regional formula Based on correlation Between flow(Q p ) 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 Q p = C D A 3/4 C D = Dickens Formula with value between

Ryves Formula Q p = C R A 2/3 C R = Ryves Formula with value between 6.8 – 10.2

Inglis Formula Q p = (124A)/(A+10.4) 1/2 For Western Ghats in Maharashtra

Fullers Formula Q Tp = (C f A 0.8 )/(1+0.8logT) For USA,T = return period, C f is a constant =0.18 – 1.88.

Baird and Mcillwraith(1951) Q mp = (3025A)/(278+A) 0.78 From maximum rrecorded floods throughout the world

Flood Frequency Analysis P = m/(N+1) T= 1/P 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

Plotting Position Formula Probability values can be used to determine the position of the event in a probability curve. From which both exceedance and non- exceedance probability of the event can be estimated.

General Equation of Hydrologic Frequency Analysis (Chow,1951) x T = x’ + K.σ 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

Gumbels Method Where the distribution has modemode α, meanmean α+γβ (where γ= is Euler's constant),Euler's constant and variancevariance ⅙ β2π2 If f(x) is probability density function,then,Gumbel’s distribution is given by :

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 and scale parameter β

Normal Distribution

LogNormal Distribution

Pearson Distribution

Log-Pearson Distribution