The drainage areas and the log-normal distribution parameters including mean and
ID: 1845258 • Letter: T
Question
The drainage areas and the log-normal distribution parameters including mean and standard deviation of the annual flood series for 5 watersheds are shown in the following table. Establish the power-model regression equations for the mean and standard deviation as functions of the drainage area; Compute the 2-, 10-, and 100-year peak discharges for a watershed with a drainage area of 30 mi^2 based on the log-normal distribution and the established regression equations for distribution parameters.Explanation / Answer
DRAINAGE AREA: A drainage basin or catchment basin is an extent or an area of land where surface water from rain, melting snow, or ice converges to a single point at a lower elevation, usually the exit of the basin, where the waters join another waterbody, such as a river, lake, reservoir, estuary, wetland, sea, or ocean.
Log-normal distribution: normal distibution of the logarithum of variate.
Mean and stand deviation is estimated with the help of logarithum of the varities.
The proable density function and distribution function is adjusted accordingly.
Drainage area(m2) 7.2 13.65 22.5 49.8 82.5
Mean 2.06 2.35 2.45 2.75 2.95
Standard deviation 0.24 0.22 0.19 0.17 0.13
0.24+0.22+0.19+0.17+0.13=0.95
7.2+20.85+43.35+93.15+175.65=0
/332.7813.51=24.632
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