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 correct relation between the highest rainfall $P_0$, average rainfall depth $P$, and area $A$ (in km\textsuperscript{2}) is:
\[P = P_0 \exp(-K A^n)\]
Here:
$P_0$ is the highest rainfall (in cm),
$P$ is the average rainfall depth (in cm),
$A$ is the area of the region (in km\textsuperscript{2}),
$K$ and $n$ are storm constants that depend on the characteristics of the storm.
Final Answer: $P = P_0 \exp(-K A^n)$ (Option 1)