By depth-area-duration analysis, the maximum average depth of rainfall over a $10^3\text{ km}^2$ catchment due to a 6-hour storm is $80\text{ mm}$. For the same storm, the maximum average depth of rainfall for a $10^4\text{ km}^2$ catchment, in mm, is

Question

Prepp Team · Accepted Answer

Depth-Area Rainfall Analysis

Depth-Area-Duration (DAD) analysis examines how rainfall amounts relate to the size of the area and the duration of a storm.

A fundamental concept in DAD analysis is that for a constant storm duration, the maximum average rainfall depth typically decreases as the catchment area grows larger. Intense rainfall is often localized, so averaging over a wider area results in a lower average depth.

Problem Details

Storm Duration: 6 hours
Catchment Area 1 ($A_1$): $10^3\text{ km}^2$
Maximum Average Depth for $A_1$ ($D_1$): $80\text{ mm}$
Catchment Area 2 ($A_2$): $10^4\text{ km}^2$
Maximum Average Depth for $A_2$ ($D_2$): Unknown

Analysis

The question asks for the maximum average rainfall depth ($D_2$) over a larger area ($A_2 = 10^4\text{ km}^2$) compared to a smaller area ($A_1 = 10^3\text{ km}^2$) during the same 6-hour storm.

Based on the DAD principle, since $A_2 > A_1$, the average rainfall depth $D_2$ must be less than $D_1$.

Thus, $D_2 < 80\text{ mm}$.

The maximum average depth of rainfall for the $10^4\text{ km}^2$ catchment is lesser than $80\text{ mm}$.