Understanding Storm Rainfall and Direct Runoff Calculation

This question involves calculating the total direct runoff from a catchment during a storm, given the hourly rainfall measurements and the $\phi$-index ($\phi$-index).

What is the $\phi$-index?

The $\phi$-index represents the average rate of water loss from a storm, including factors like infiltration, depression storage, and interception. It's a common method used in hydrology to estimate direct runoff. Rainfall intensity exceeding the $\phi$-index during a storm contributes to the direct runoff.

Analyzing the Storm Rainfall Data

We are given the following hourly rainfall data for a four-hour storm:

• Hour 1: 5 cm
• Hour 2: 2 cm
• Hour 3: 4 cm
• Hour 4: 3 cm

The $\phi$-index is given as 3 cm/hour.

Calculating Direct Runoff for Each Hour

To find the direct runoff for each hour, we compare the rainfall intensity for that hour with the $\phi$-index. Direct runoff occurs only when the rainfall intensity is greater than the $\phi$-index. The amount of direct runoff for that hour is calculated as:

Direct Runoff (per hour) = Rainfall Intensity (per hour) - $\phi$-index

If Rainfall Intensity $\leq$ $\phi$-index, then Direct Runoff = 0.

Let's apply this to the given data:

• Hour 1: Rainfall = 5 cm. Since 5 cm > 3 cm ($\phi$-index), Direct Runoff = 5 cm - 3 cm = 2 cm.
• Hour 2: Rainfall = 2 cm. Since 2 cm $\leq$ 3 cm ($\phi$-index), Direct Runoff = 0 cm.
• Hour 3: Rainfall = 4 cm. Since 4 cm > 3 cm ($\phi$-index), Direct Runoff = 4 cm - 3 cm = 1 cm.
• Hour 4: Rainfall = 3 cm. Since 3 cm $\leq$ 3 cm ($\phi$-index), Direct Runoff = 0 cm.

Determining Total Direct Runoff

The total direct runoff is the sum of the direct runoff from each hour:

Total Direct Runoff = (Runoff Hour 1) + (Runoff Hour 2) + (Runoff Hour 3) + (Runoff Hour 4)

Total Direct Runoff = 2 cm + 0 cm + 1 cm + 0 cm

Total Direct Runoff = 3 cm

Therefore, the total direct runoff from the catchment for the storm was 3 cm.