FREQUENCY
ANALYSIS
Siti Kamariah Md Sa’at
PPK Bioprocess..2010
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
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
Frequency distribution analysis
 Gumbel’s Method
 Log-Pearson Type III distribution
 Log normal distribution
General equation
X T  X  K
 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
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
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
Gumbel Equation
QT  Qav   (0.78 y  0.45)
1
1
y   ln[  ln( 1  ), P 
T
T

n
Q2m
(
 Q 2 av)
n 1
n
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
Example 7.4:
 Annual maximum recorded floods in the
river Bhima, tributary of river Krishna, for
period of 1951-1977 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.
Answer:
 n=27 years
 Tp=(n+1)/m
 Qav=4263
 σ=1432.6
 y=2.25037
 Q100=9600
 Q150=10,700