Infiltration index concept in hydrology The relation P − Q = φ * t_e is used to estimate the constant infiltration index (φ-index), where P is total storm rainfall depth, Q is direct-runoff depth, and t_e is the duration of rainfall excess. This equation for determining infiltration capacity was suggested by:

Introduction / Context:
The φ-index is a practical hydrologic tool used to convert a storm's total rainfall into rainfall excess by assuming a constant infiltration rate over the effective duration. This question asks who is credited with the widely used constant-infiltration approach summarized by P − Q = φ * t_e.

Given Data / Assumptions:

• P = total storm rainfall depth.
• Q = direct runoff (rainfall excess) depth reaching the stream.
• t_e = duration during which rainfall intensity exceeds infiltration.
• φ = constant infiltration index to be back-calculated.

Concept / Approach:
The equation assumes a uniform, constant rate of infiltration during the effective period, allowing direct computation of φ from measured rainfall and runoff. The approach is rooted in early infiltration research and practical runoff separation methods.

Step-by-Step Solution:

Verification / Alternative check:
If more detailed infiltration data are available, one may compare the constant φ approximation with Hortonian infiltration-capacity curves i_f(t) that decline exponentially; the φ-index then approximates the time-average of i_f over the effective period.

Why Other Options Are Wrong:

• Horner and Lloyd are not associated with this constant-infiltration runoff separation.
• Bernard is associated with the distribution (mass) graph of runoff, not the φ-index.

Common Pitfalls:
Using P (gross rainfall) and Q (direct runoff) from mismatched durations; φ must be based on the effective period only. Also, confusing φ-index with W-index (which additionally accounts for initial losses).

Final Answer:
Horton