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

Look at how each index is built rather than memorising which is bigger. The \(\Phi\)-index is a rough, single average loss rate, rainfall in minus runoff out, spread over the whole storm duration, with no attempt to separate infiltration from interception or depression storage. The W-index tries to be more precise, it removes the surface retention term (interception plus depression storage) from the numerator before dividing by time, and it only considers the period when rainfall intensity is above the infiltration capacity.

Because the W-index has already stripped out part of the losses that the \(\Phi\)-index still carries inside its single average, the W-index naturally comes out a bit lower, which makes the \(\Phi\)-index somewhat higher for moderate, uneven rain. That confirms Statement (I).

Neither index is a fixed property of a watershed. Antecedent soil moisture changes how much water infiltrates, the depression storage and interception capacity of the surface change how much water is held back before it can run off, and simply having more or less total rainfall changes the numbers too. That confirms Statement (II).

\[\boxed{\text{Both Statement (I) and Statement (II) are correct}}\]