Question

The annual rainfall amounts at a given location have a mean of 152 cm and a standard deviation of 30 cm. Estimate a 100-year annual rainfall amount if the annual rainfall is log-normally distributed.

Answer 1

Answer:

The estimate of 100- year annual rainfall amount is 274.5cm

Step-by-step explanation:

From the question, x (mean) =152 ;  Sx ( standard deviation) = 30, T (time) 100 years, P (period) = 1/T = 1/100 =0.01

The frequency factor is expressed as:

$K_T = w - \frac{2.515517+0.802853w+0.01032w^2}{1+1.432788w+0.189269w^2+0.001308w^3}$

where w= $[In (\frac{1}{P^2} )]^\frac{1}{2}$  for zero is less than P less than or equal to 0.5

w= $[In (\frac{1}{0.01^2} )]^\frac{1}{2}$

= 3.034

$K_T = w - \frac{2.51+0.802w+0.0103w^2}{1+1.432w+0.189w^2+0.0013w^3}$

$K_T = w - \frac{2.51+0.802*3.034+0.0103(3.034)^2}{1+1.432*3.034+0.189(3.034)^2+0.0013(3.034^3}$

$K_T$ = 2.326

$Y_T = Y'' + K_TS_Y$

$Y'' = logx$

$Y'' = log(152)$

=2.18

$S_Y= logSx$

$S_Y = log (30)$

=1.477

∴

$Y_T = Y'' + K_TS_Y$

$Y_T = 2.18 + (1.477*2.326)$

$Y_T = 5.615$

$Y_T = log_e^x$

=$e^5.615$

=274.5cm