Question

By using Gumbel's method, the flood discharge with a return period of 500 years at a particular township neighbourhood was estimated as $18000m^3/s$ with a probable error of $2000m^3/s$. What are the 95% confidence probability limits of the 500 year flood at the location?
(f(c) = 1.96 for 95% confidence probability)

• A. $16100m^3/sto19900m^3/s$
• B. $17050m^3/sto18950m^3/s$
• C. $14080m^3/sto21920m^3/s$
• D. $13600m^3/sto22400m^3/s$

Answer 1

The correct option is C $14080m^3/sto21920m^3/s$

For confidence probability C, the confidence interval (if variate $x_T$ is bounded by values $x_1$ and $x_2$) is given by:
$x_1=x_T-f\left(c\right)S_e$
$x_2=x_T+f\left(c\right)S_e$
Given,
$x_T=1800m^3/s$
$S_e=2000m^3/s$

For 95% confidence probability f(c) = 1.96
$\therefore x_1=18000-1.96\times 2000=14000m^3/s$
$x_2=18000+1.96\times 2000=21920m^3/s$