1. Hydrology & Water Resources Eng.
ERT 246
Hydrology & Water Resources Eng.
FREQUENCY ANALYSIS
Siti Kamariah Md Sa’at
PPK Bioprocess..2010

2. Flood Frequency Analysis
Statistical Methods to evaluate probability exceeding a particular outcome - P (X >20,000 m3/s) = 10%
Used to determine return periods of rainfall or flows
Used to determine specific frequency flows for floodplain mapping purposes (10, 25, 50, 100 yr)
Used for datasets that have no obvious trends
Used to statistically extend data sets

3. Probability, P P = 100/T, where P in %, T=return period/frequency
Graph plot for Q vs Tr or Q vs P
Equation used to determine flood probability
P(X > x0)n = 1 – (1-1/T)n
Where n = total number of event

4. Frequency distribution analysis
Gumbel’s Method
Log-Pearson Type III distribution
Log normal distribution

5. General equation Where
XT=calue of variate X of a random hydrologic series with return period T
X = mean of variate
σ= standard deviation of variate
K= ferquency factor depend on return period, T and the assume frequency distribution

6. Gumbel’s Extreme-Value distribution
Introduced by Gumbel,1941
Known as Gumbel’s distribution
Most widely used for extreme values in hidrologic studies for prediction of flood peaks, maximum rainfalls, maximum wind speed, etc.
2 method to determine discharge, Q
Graph
Equation

7. Gumbel’s distribution graph
Plotting graph Q vs T at special Gumbel’s graph chart.
The straight line must be intercept at coordinate (2.33years, Qav)
T=(n+1)/m

9. Gumbel Equation Where Qav=average discharge for all flow data
T=return period/frequency
σ = standard deviation
n=total number of event
m=order number of event

12. Example 7.4:
Annual maximum recorded floods in the river Bhima, tributary of river Krishna, for period of is given below. Verify whether the Gumbel extreme value distribution fit the recorded values. Estimate the flood discharge with recurrence interval of i) 100 years ii) 150 years by graphical extrapolation and equation.

14. Answer: n=27 years Tp=(n+1)/m Qav=4263 σ=1432.6 y=2.25037 Q100=9600