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

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

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 - (2.515517+0.802853w+0.01032w^2)/(1+1.432788w+0.189269w^2+0.001308w^3)`

where w=
`[In ((1)/(P^2) )]^(1)/(2)` for zero is less than P less than or equal to 0.5

w=
`[In ((1)/(0.01^2) )]^(1)/(2)`

= 3.034

`K_T = w - (2.51+0.802w+0.0103w^2)/(1+1.432w+0.189w^2+0.0013w^3)`

`K_T = w - (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