Question

For Indian black soils under AMC-I conditions, the best relationships among Initial Abstraction (\(I_a\)) and the Potential Maximum Retention (\(S_m\)) is given by the popular SCS-CN method. Select the best from options given below

• A. \(I_a = 0.1 S_m\)
• B. \(I_a = 0.2 S_m\)
• C. \(I_a = 0.3 S_m\)
• D. \(I_a = 0.15 S_m\)

Hint:

Initial Abstraction ratio:
US Standard: $I_a = 0.2 S$.
Indian standard Black soils: $I_a = 0.1 S$ or $I_a = 0.3 S$ (AMC-III).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The Soil Conservation Service Curve Number (SCS-CN) method relates direct surface runoff to total storm rainfall, potential maximum retention, and initial abstraction.
Key Formula or Approach:
\[ Q = \frac{(P - I_a)^2}{P - I_a + S} \quad (P > I_a) \]
\[ I_a = \lambda S \quad (\lambda = 0.2 \text{ in US standard; } \lambda = 0.1 \text{ for Indian black soils / CWC}) \]

Step 2: Detailed Explanation:
In the original US-SCS methodology, initial abstraction (interception, depression storage, and initial infiltration) was empirically set as \(I_a = 0.2 S\).
However, extensive hydrological research in Indian watersheds (by Ministry of Agriculture, ICAR, and Central Water Commission), particularly in high-swelling, cracking black soils (Vertisols), proved that \(I_a = 0.2 S\) significantly underestimates runoff.
Consequently, the Indian standard relation for black soils (under dry antecedent moisture conditions AMC-I and AMC-II) was officially revised and calibrated to \(I_a = 0.1 S_m\) (\(\lambda = 0.1\)).

Step 3: Final Answer:
Therefore, the best relationship for Indian black soils is \(I_a = 0.1 S_m\), corresponding to option (A).