Processes in Clark's method

Clark's method considers two processes in transforming excess precipitation into direct runoff.

1. Translation (movement)

Water from each part of the catchment travels to the outlet without change of shape, only delayed by the travel time. This is represented by the time-area diagram (isochrones). The area between two isochrones contributes a flow $I = 2.78\,A_i/\Delta t$ for 1 cm of excess rain.

How it is achieved: the basin is divided by isochrones at interval $\Delta t$ up to the time of concentration; the strip areas give the translation hydrograph (inflow ordinates).

2. Attenuation (storage)

Storage in the channels, soil surface, and depressions reduces the peaks and spreads the flow in time. This is represented by a single linear reservoir at the outlet, $S = KQ$.

How it is achieved: the translation hydrograph is routed through the linear reservoir using $O_2 = C_0(I_1 + I_2) + C_2 O_1$, with $C_0 = \Delta t/(2K + \Delta t)$ and $C_2 = (2K - \Delta t)/(2K + \Delta t)$. The result is the IUH, and averaging two consecutive ordinates gives the unit hydrograph of duration $\Delta t$.