Boston Society of Civil Engineers (B.S.C.E.) runoff relation (expressed in cumecs per square kilometre): This empirical relation primarily depends on which factors?

Introduction / Context:
Regional empirical relations for design discharge often appear in the form of unit discharge (cumecs per km^2). The Boston Society of Civil Engineers (B.S.C.E.) relation is a classical example linking peak runoff to catchment size and rainfall. Recognizing the governing variables helps engineers apply such formulae appropriately and understand their limitations.

Given Data / Assumptions:

• Discharge is expressed as cumecs per square kilometre (unit discharge).
• Empirical form generally uses rainfall intensity or an index storm parameter and drainage area.
• Question asks which factors it is based upon.

Concept / Approach:
Unit discharge normalizes by area, so remaining primary drivers are rainfall (intensity/duration appropriate to the basin response) and catchment properties. In these simplified relations, area is always present; rainfall is the forcing input. Basin shape or total runoff volume are not typically the core variables in the simple B.S.C.E. peak relation stated per unit area.

Step-by-Step Reasoning:
Identify required variables for peak runoff generation: rainfall forcing + catchment size.Other details (shape, slope, infiltration) are often embedded in empirical coefficients; they are not the explicit paired factors in the simplest expression.

Verification / Alternative check:
Many historical US and regional formulae express Q = C * P^m * A^n; when cast per unit area, Q/A primarily scales with P and weakly with A through the exponent or coefficient. This supports option (a).

Why Other Options Are Wrong:

• Total runoff volume is not the input for an instantaneous peak relation.
• Drainage area alone omits the meteorological driver.
• Wind speed and humidity are not primary controls for short-term peak runoff estimates.

Common Pitfalls:

• Assuming unit discharge depends only on area after normalization.
• Applying empirical formulae beyond their validated hydro-climatic region.

Final Answer:
Rainfall characteristics and drainage area