Question

For any time step, when the effective precipitation \( (P_E) \) exceeds infiltration \( (I) \), the total rainfall excess \( (TRE) \) can be computed as:

• A. \( TRE = (P_E - I) \)
• B. \( TRE = (P_E + I) \)
• C. \( TRE = (P_E - I)^2 \)
• D. \( TRE = (P_E + I)^2 \)

Hint:

Rainfall excess = Effective rainfall - Infiltration, if \( P_E>I \).

Answer 1

The Correct Option is A

To compute the total rainfall excess (TRE) when effective precipitation (P_E) exceeds infiltration (I), we analyze the hydrological relationship between these variables.

1. Understanding the Components:
- Effective precipitation \((P_E)\): The portion of rainfall that contributes directly to surface runoff
- Infiltration (I): The process of water entering the soil surface
- Rainfall excess (TRE): The amount of water available for surface runoff

2. The Hydrological Relationship:
When \(P_E > I\) for any time step:
- The rainfall excess is simply the difference between what falls \((P_E)\) and what infiltrates (I)
- This gives the fundamental equation: \(TRE = P_E - I\)

3. Eliminating Incorrect Options:
- TRE = \(P_E + I\) would incorrectly increase runoff with more infiltration
- The squared terms (\(P_E\) - I)² and (\(P_E\) + I)² have no basis in hydrological theory

4. Practical Application:
This simple difference method is widely used in:
- The Soil Conservation Service (SCS) curve number method
- Many hydrological models for runoff estimation

Conclusion:
The correct formula for total rainfall excess is the straightforward difference between effective precipitation and infiltration.

Final Answer:
The correct option is: \(TRE = (P_E - I)\).