online_uh_cascade:   Unit hydrograph by the cascade of linear reservoirs Formulas C = tr/K          C1 = C/(2+C)           C2 = (2-C)/(2+C) Qj+1n+1 = 2C1(Qaverage)j + C2Qj+1n
 Reference

 RATIONALE Every catchment or basin of a given drainage area A has a unit hydrograph (1 cm of runoff) for a given [unit] effective rainfall of duration tr (i.e., the unit hydrograph duration is tr). The shape of the unit hydrograph is characterized by its peak discharge and catchment lag. These properties of the unit hydrograph are a function of the amount of runoff diffusion in the catchment or basin. In turn, runoff diffusion depends on the diffusivity characteristics of the basin. Steeper basins have less diffusion; consequently, they have higher peaks and shorter time lags. Milder basins have more diffusion; therefore, lesser peaks and longer time lags. In practice, steeper basins are modeled with higher values of Courant number C = tr/K and lower values of N. The largest practical value of C is 2; the minimum value of N is 1. Milder basins are modeled with a lower C and a higher N. For steeper basins, C > 1 and N < 3. For milder basins, C < 0.4 and N > 7. Considerable experience is required in order to estimate the values of C and N for a given application. Unit hydrograph shapes for various values of C and N are given by Ponce (1980). For a gaged stream, where a measured tr-hr unit hydrograph may be available, online_uh_cascade can be used to calibrate the parameters C and N. The resulting cascade unit hydrograph can be convoluted with the effective storm pattern to calculate the composite flood hydrograph.

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