Flood routing and Clark IUH method

Flood routing is the procedure for determining how the hydrograph of a flood changes in shape, peak, and timing as it passes through a river reach or reservoir. It uses continuity ($I - O = dS/dt$) and a storage-discharge relation.

Clark IUH method

Clark's method transforms excess rainfall into a catchment outlet hydrograph, using two steps.

1. Translation: isochrones divide the catchment into strips of area $A_i$ between lines of equal travel time. For 1 cm of excess rain, the inflow to the outlet is $I_i = 2.78\,A_i/\Delta t$ (m³/s).
2. Storage: this inflow is routed through a single linear reservoir at the outlet ($S = KO$):

$$O_2 = C_0 (I_1 + I_2) + C_2 O_1,\quad C_0 = \frac{\Delta t}{2K + \Delta t},\quad C_2 = \frac{2K - \Delta t}{2K + \Delta t}$$

The outflow ordinates give the instantaneous unit hydrograph (IUH), and the average of two consecutive ordinates gives the $\Delta t$-hour unit hydrograph. Using the excess rainfall depths and superposition, the flood hydrograph is obtained. The parameters needed are $t_c$, $K$ and the isochrone areas.