On the nonlinearity of the catchment instantaneous response function: Insights obtained from dynamic wave modeling

In the unit hydrograph theory, the catchment response function f to a unit rainfall is described invariant. However, real catchment response is nonlinear in that f varies with rainfall excess rate i_e. In particular, the peak f(t_p) and peak time t_p of f are known to follow power functional relationships with i_e. We investigated two fundamental knowledge gaps in the emergence of the nonlinearity: (1) the role of hydrodynamics and (2) the linkage with the linear convolution principle. Employing a sophisticated hydrodynamic model of the tRIBS-FEaST, the power-law nonlinearity was captured in simulations for a series of catchments. We found further that the time of concentration decreases with i_e, again following a power law. Nevertheless, we found significant limitations in f obtained by deconvoluting S-hydrographs, as it fails to capture the known tendency of the growing skewness with i_e. Further, the hydrographs reproduced with the linear convolution, even the nonlinearity is seen in f, deviates from the continuous simulation results. Alternatively, a series of f was directly simulated as hydrographs from the hydrodynamic model, initiated with varying initial water depth h_o all over the catchment, but no additional water or rainfall imposed. This alternative method successfully reproduces not only the nonlinear peak variation but also the skewness variation with h_o, which is attributed to the relaxation of the linear convolution framework.