When computing runoff volumes for large catchments, how many standard infiltration indices are typically used in practice?

Introduction:
In hydrologic design, infiltration indices provide simplified, lumped representations of infiltration losses for transforming rainfall to runoff, especially over large basins where spatial detailing is impractical.

Given Data / Assumptions:

• We are concerned with widely used indices in design practice.
• Large-area runoff estimation typically adopts a few standard indices.

Concept / Approach:
The three most commonly referenced indices are: the phi-index (constant loss rate giving the same runoff volume as observed), the W-index (average infiltration rate during periods of rainfall excess, excluding initial abstraction), and the W' (W-prime) index (a refinement accounting for additional abstractions).

Step-by-Step Solution:
Step 1: Identify canonical indices used in design manuals and textbooks.Step 2: Relate their definitions to runoff volume computations for event-based analysis in large catchments.Step 3: Conclude that three indices (phi, W, W') are the standard set commonly cited.

Verification / Alternative check:
Design literature and instructional practice consistently introduce these three for event-loss modeling; additional bespoke indices exist but are not standard in introductory design problems.

Why Other Options Are Wrong:

• 2: Ignores the W' refinement commonly presented with phi and W.
• 4 or 5: Overstates the standard set; more variants exist but are not part of the usual triad.

Common Pitfalls:

• Confusing infiltration indices (loss models) with unit hydrograph scaling or baseflow separation techniques.
• Assuming one index fits all storms without calibration.

Final Answer:
3.