Understanding Depth-Area-Duration (DAD) Curves

Depth-Area-Duration (DAD) curves are graphical representations used in hydrology to show the relationship between rainfall depth, the area over which it falls, and the duration of the storm.

These curves help hydrologists estimate the maximum rainfall depths expected over various areas for different storm durations.

Relationship Between Storm Duration and Rainfall Depth

A fundamental principle illustrated by DAD curves is that for a given area, rainfall depth generally increases with storm duration. Conversely, for a given duration, rainfall depth decreases as the area increases.

Consider the given information:

• Area: $100 \text{ km}^2$
• Storm Duration 1: 1 day (which is typically considered as 24 hours)
• Maximum average depth for Duration 1: $100 \text{ mm}$

The question asks about the maximum average depth for the same area ($100 \text{ km}^2$) but for a shorter storm duration:

• Storm Duration 2: 3 hours

Comparing Storm Durations

Since 3 hours is a significantly shorter duration than 1 day (24 hours), the amount of rainfall recorded during the 3-hour storm is expected to be less than that recorded during the 1-day storm, assuming similar storm intensity patterns and the same geographical area.

Therefore, the maximum average depth of rainfall over an area of $100 \text{ km}^2$ for a 3-hour storm will be less than the maximum average depth for a 1-day storm over the same area.

Based on this understanding derived from DAD curve principles, the maximum average depth for a 3-hour storm over $100 \text{ km}^2$ will be less than $100 \text{ mm}$.