Question

Recorded annual maximum 24-hour rainfall magnitudes at stations 'X' are as under:

$\begin{array}{cc}\text{Years}& \text{Rainfall (cm)}\\ 1960& 12.0\\ 1961& 6.0\\ 1962& 4.8\\ 1963& 7.9\\ 1964& 12.0\\ 1965& 14.2\\ 1966& 13.6\\ 1967& 6.0\\ 1968& 3.7\\ 1969& 2.9\end{array}$

What is the return period, in years, for a 6.0 cm annual rainfall according to (i) Hazen formula and (ii) Weibull formula; respectively?

• A. $\frac{10}{7},\frac{11}{7}$
• B. $\frac{20}{13},\frac{22}{13}$
• C. $\frac{5}{3},\frac{11}{7}$
• D. $\frac{20}{11},\frac{11}{6}$

Answer 1

The correct option is D $\frac{20}{11},\frac{11}{6}$

The data are arranged in descending order

$\begin{array}{cc}\text{Rainfall}& \text{Order (m)}\\ 14.2& 1\\ 13.6& 2\\ 12.0& 3\\ 12.0& 4\\ 7.9& 5\\ 6.0& 6\\ 6.0& 7\\ 4.8& 8\\ 3.7& 9\\ 2.9& 10\end{array}$

Probability,
$P=\left(\frac{m-0.5}{N}\right)\text{Hazen's formula}$

$=\frac{m}{N+1}\text{Weibull's formula}$

Return period
$T=\frac{1}{P}$

For 6.0 cm rainfall m = 6
$\left(\text{i}\right)T=\frac{10}{5.5}=\frac{20}{11}$

$\left(\text{ii}\right)T=\frac{N+1}{m}=\frac{11}{6}$