A flood is an unusual high stage in a river, normally the level at which the river overflows its banks and inundates the adjoining area. The design of bridges, culvert waterways and spillways for dams and estimation of the score at a hydraulic structure are some examples wherein floodpeak values are required.
To estimate the magnitude of a flood peak the following alternative methods are available:
The extreme value distribution was an introduction by Gumbel (1941) and is commonly known as Gumbel’s distribution. it is one of the most widely used probability distribution functions for extreme values in hydrologic and meteorologic studies for prediction of flood peaks, maximum rainfall, maximum wind speed.
Gumbel defined a flood as the largest of the 365 daily flows and the annual series of flood flows constitute a series of largest values of flows.
Based on the probability distribution.
P(x ≥ x_{0}) =
Where, X_{T} = Peak value of hydrologic data
K = Frequency factor
y_{T} = Reduced variate
y_{T} = log_{∈}log_{∈}(T/T1)
T = Recurrence interval in year
y_{n} = Reduced mean = 0.577
S_{n} = Reduced standard deviation.
S_{n} = 1.2825 for N → ∞
Since the value of the variate for a given return period, xT determined by Gumbel’s method can have errors due to the limited sample data used. An estimate of the confidence limits of the estimates is desirable the confidence interval indicates the limits about the calculated value between which the true value can be said to lie with specific probability based on sampling errors only.
For a confidence probability c, the confidence interval of the variate x_{T} is bounded by value x_{1} and x_{2} given by
X_{2 }/ X_{1} = X_{T }± f(c) . S_{∈}
Where, f(c) is a function of confidence probability ‘C’.
S_{e} = Probability error
Where, N = Sample size
B = factor
σ = Standard deviation
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