Infiltration capacity, phi-index, W-index

(i) Infiltration capacity

The maximum rate at which a soil can absorb water from rain at a given time, under given soil and surface conditions, is the infiltration capacity $f_p$ (mm/h or cm/h). It is high at the start of rain when the soil is dry and decreases to a constant final value $f_c$ as the soil becomes saturated (Horton: $f_p = f_c + (f_0 - f_c)e^{-Kt}$). Actual infiltration $f$ equals the rain intensity if $i < f_p$ and equals $f_p$ if $i \ge f_p$.

(ii) $\Phi$-index

The $\phi$-index is the constant rate of infiltration (loss) in cm/h such that the volume of rainfall above that rate equals the volume of direct runoff. It is found from the hyetograph and the observed runoff depth by trial. It averages all losses (interception, depression storage and infiltration) over the whole storm, so it is a simple approach; it is used for large catchments and to find the rainfall excess.

(iii) W-index

The W-index is the average infiltration rate during the time when rainfall intensity exceeds the infiltration capacity:

$$W = \frac{P - R - S_d}{t_r}$$

where $P$ is total rainfall, $R$ is direct runoff, $S_d$ is depression storage and interception, and $t_r$ is the duration of rain in which intensity exceeds capacity. It is more accurate than the $\phi$-index because it removes the depression storage, but it is a bit smaller than $\phi$ since $S_d$ is removed.