Regional flood estimation: Identify the correct Ryve’s empirical formula In catchment hydrology, Ryve’s formula is used for estimating peak flood discharge (in m^3/s, i.e., cumecs) from drainage area A (in km^2). Which expression correctly represents Ryve’s relation between Q and A?

Introduction / Context:
Empirical regional flood formulas relate peak discharge Q to catchment area A using a coefficient C that embeds climatic, topographic, and catchment-response effects. Ryve’s formula is one such Indian regional relation, historically applied in parts of southern India for preliminary peak flood estimates where stream-gauged data are scarce.

Given Data / Assumptions:

• Q is in m^3/s (cumecs).
• A is in km^2.
• C is an empirical coefficient dependent on region/catchment characteristics.
• Intended for quick, reconnaissance-level estimation, not detailed design without checks.

Concept / Approach:

Regional flood formulas adopt power laws: Q = C * A^n. The exponent n reflects how catchment size scales with peak discharge. For Ryve’s formula, n is taken as 2/3, distinct from other Indian formulas such as Dickens (3/4) or Inglis (state-specific forms). Correctly recognizing n is essential to avoid systematic over- or underestimation across scales.

Step-by-Step Solution:

Verification / Alternative check:

Typical hydrology handbooks list major Indian empirical relations and emphasize regional calibration; Ryve’s is consistently quoted with the 2/3 exponent for A (in km^2).

Why Other Options Are Wrong:

• A^(3/4), A^(1/2), A^(1/4), A: These exponents correspond to other forms or unrealistic scaling; they do not represent Ryve’s formula.

Common Pitfalls:

• Using Dickens’ exponent (3/4) in place of Ryve’s (2/3).
• Mixing units (e.g., converting A but not adjusting C).

Final Answer:

Q = C * A^(2/3).