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:
[tex]K_T = w - \frac{2.515517+0.802853w+0.01032w^2}{1+1.432788w+0.189269w^2+0.001308w^3}[/tex]
where w= [tex][In (\frac{1}{P^2} )]^\frac{1}{2}[/tex] for zero is less than P less than or equal to 0.5
w= [tex][In (\frac{1}{0.01^2} )]^\frac{1}{2}[/tex]
= 3.034
[tex]K_T = w - \frac{2.51+0.802w+0.0103w^2}{1+1.432w+0.189w^2+0.0013w^3}[/tex]
[tex]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}[/tex]
[tex]K_T[/tex] = 2.326
[tex]Y_T = Y'' + K_TS_Y[/tex]
[tex]Y'' = logx[/tex]
[tex]Y'' = log(152)[/tex]
=2.18
[tex]S_Y= logSx[/tex]
[tex]S_Y = log (30)[/tex]
=1.477
∴
[tex]Y_T = Y'' + K_TS_Y[/tex]
[tex]Y_T = 2.18 + (1.477*2.326)[/tex]
[tex]Y_T = 5.615[/tex]
[tex]Y_T = log_e^x[/tex]
=[tex]e^5.615[/tex]
=274.5cm
