Question

Given below are two statements:

Statement (I): In the case of moderate rain at non uniform intensities, \(\Phi\)-index will be somewhat higher than the W-index.

Statement (II): These indices vary with initial soil moisture, changes in the depression storage and interception capacity of the area and amount of precipitation.

In light of the above statements, choose the most appropriate answer from the options given below.

• A. Both Statement (I) and Statement (II) are correct.
• B. Both Statement (I) and Statement (II) are incorrect.
• C. Statement (I) is correct but Statement (II) is incorrect.
• D. Statement (I) is incorrect but Statement (II) is correct.

Hint:

Recall that the W-index separately removes surface retention losses that the \(\Phi\)-index does not split out, and both indices are storm specific, not fixed soil properties.

Answer 1

The Correct Option is A

Step 1: The \(\Phi\)-index is defined simply as the average rainfall intensity above which the volume of rainfall equals the volume of runoff, it lumps all the losses, infiltration, interception and depression storage, into one single average rate.

Step 2: The W-index goes a step further and tries to isolate just the infiltration part. It is calculated as (Total rainfall minus runoff minus surface retention) divided by the duration for which rainfall intensity exceeds the infiltration capacity, where surface retention covers interception and depression storage.

Step 3: Because the W-index explicitly subtracts out the surface retention losses while the \(\Phi\)-index does not separate them, the W-index value works out smaller than the \(\Phi\)-index for the same storm, especially under moderate, non uniform rain. So Statement (I) is correct.

Step 4: Both indices are storm dependent numbers, not soil constants. They shift with how wet the soil already is before the storm (initial soil moisture), how much depression storage and interception the land cover provides, and how much total rain falls. So Statement (II) is also correct.

Step 5: Both statements hold true together, so the answer is option 1.