Question

For a given storm, the relation between the highest rainfall $P_0$ and average rainfall depth $P$ in cm over an area $A \, \text{km}^2$, where $K$ and $n$ are storm constants, is given by:

• A. $P = P_0 \exp(-K A^n)$
• B. $P = P_0 K \exp(A^n)$
• C. $P = P_0 K^{-A}$
• D. $P = P_0 K A^n$

Hint:

For rainfall area-depth relationships, use $P = P_0 K \exp(A^n)$ when $K$ and $n$ are defined constants for specific storms.

Answer 1

The Correct Option is A

The relationship connecting maximum rainfall $P_0$, average rainfall depth $P$, and area $A$ (in km\textsuperscript{2}) is:
\[P = P_0 \exp(-K A^n)\]
In this equation:
$P_0$ represents the maximum rainfall (cm),
$P$ denotes the average rainfall depth (cm),
$A$ is the region's area (km\textsuperscript{2}),
$K$ and $n$ are storm constants, which vary with storm characteristics.
The correct formula is $P = P_0 \exp(-K A^n)$ (Option 1).