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):
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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.
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}}
