Curve Number Method Runoff Relationship

The Curve Number (CN) method is a widely used empirical approach in hydrology to estimate direct runoff ($Q$) from rainfall ($P$). The relationship involves initial abstraction ($I_a$) and potential maximum storage ($S$).

Understanding the Curve Number Formula

The fundamental relationship between runoff ($Q$), rainfall ($P$), and initial abstraction ($I_a$) is:

$Q = P - I_a \quad \text{for } P > I_a$

If rainfall is less than or equal to the initial abstraction ($P \le I_a$), there is no runoff ($Q = 0$).

The initial abstraction ($I_a$) is empirically related to the storage capacity ($S$) by the following equation:

$I_a = 0.2S$

Substituting this expression for $I_a$ into the basic runoff equation provides a more refined formula for calculating runoff:

$Q = \frac{(P - I_a)^2}{P - I_a + S}$

By substituting $I_a = 0.2S$, the equation becomes:

$Q = \frac{(P - 0.2S)^2}{P - 0.2S + S}$

Simplifying the denominator ($P - 0.2S + S = P + 0.8S$), the final expression for runoff is:

$Q = \frac{(P - 0.2S)^2}{P + 0.8S}$

This equation represents the relationship between rainfall, initial abstraction, storage capacity, and actual runoff in the Curve Number method.