Question

A 12-hour storm occurs over a catchment and results in a direct runoff depth of 100 mm. The time-distribution of the rainfall intensity is shown in the figure (not to scale). The $\varphi$-index of the storm is (in mm, rounded off to two decimal places): \includegraphics[width=0.5\linewidth]{image857.png}

Hint:

The $\varphi$-index represents the average rainfall intensity during a storm that produces direct runoff equal to the total rainfall. If all rainfall results in runoff, the $\varphi$-index is zero.

Answer 1

To calculate the $\varphi$-index, we use the following equation: \[ \varphi = \frac{\text{Total rainfall depth} - \text{Direct runoff depth}}{\text{Duration of the storm (in hours)}} \] From the given problem: - Total rainfall depth = 100 mm, - Direct runoff depth = 100 mm, - Duration of the storm = 12 hours. Now, we calculate the $\varphi$-index: \[ \varphi = \frac{100 \, \text{mm} - 100 \, \text{mm}}{12 \, \text{hours}} = 0.00 \, \text{mm/hour}. \] Thus, the $\varphi$-index of the storm is 0.00 mm. \boxed{0.00 \, \text{mm}}