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Gumble Methods

The document outlines the Gumbel method for frequency analysis of flood peaks, which involves calculating the probabilities of observed flood events using extreme value distribution. It details the steps for arranging flood data, calculating return periods, and determining flood values for various return periods using statistical parameters. An example is provided to illustrate the calculation of a 100-year flood and the return period for a specific flood magnitude using the Gumbel method.

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Gajendra Singh
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62 views10 pages

Gumble Methods

The document outlines the Gumbel method for frequency analysis of flood peaks, which involves calculating the probabilities of observed flood events using extreme value distribution. It details the steps for arranging flood data, calculating return periods, and determining flood values for various return periods using statistical parameters. An example is provided to illustrate the calculation of a 100-year flood and the return period for a specific flood magnitude using the Gumbel method.

Uploaded by

Gajendra Singh
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PPTX, PDF, TXT or read online on Scribd
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Frequency Analysis

by Gumbel Method:
Principle and Steps
Principle and Steps
• As a simple method, frequencies (or probabilities), P(X ≥ x), of the
observed flood peaks could be calculated.
• The Gumbel method of frequency analysis is based on extreme value
distribution and uses frequency factors developed for theoretical
distribution.

x = ẍ + ∆x
Where x is magnitude of flood of some given
probability (P) or return period
x is mean of floods on record
∆x is departure of variate from the mean
• ∆x depends on dispersion characteristics, recurrence interval (T) and
other statistical parameters. It can be expressed as
• ∆x = S K
• where S is standard deviation of the sample and K is frequency factor
Thus, equation (i) above can be expressed as

x = ẍ + KS
Steps Involved in Frequency
Analysis:
• List and arrange annual floods (x) in descending order of magnitude
• Assign rank ‘m’, m = 1 for highest value and so on
• Calculate return period (T) and/or probability of exceedence (P) by
equations n + 1/m and m/n +1 respectively.
• Using tabular form calculate x2 and ∑x and Ex2.
• Now calculate mean x; squared mean x2; mean of squares x2 and
standard deviation S.
• From the table find the frequency factors value for desired return
periods
• Using relation x = x + KS calculate flood values for various return periods
• The annual flood series for a river is available for 21 years. The
observed flood peaks are as given below. Calculate the 100 year flood
using Gumbel’s method.
Solution
Now, using equation x = x + KS and adopting values of x and S from above
and different K and T values from Table flood flows of various return periods
can be calculated
The mean annual flood of a river is 600m3/s and the standard deviation of the annual flood time
series is 150m3/s. Determine the return period of a flood of magnitude 1000m3/s occurring in the
river. Use Gumbel’s method and assume sample size to be very large

• XT= ͞x +KS,
Given that x mean=600m3 /s and s=150 m3 /s and XT=1000 m3 /s, then substituting in the above
equation,

= 1000=600+k 150
400/150=k

K=2.667

K=Yt-Yn /Sn
Given for N large, yn and Sn are 0.577 and 1.2825 respectively

2.667= (Yt-0.577)/1.2825

Yt = 3.9970

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