Watershed hydrograph model based on surface flow diffusion

[1] Based on the diffusion equation and Darcy’s law, Criss and Winston (2008b) developed the one-parameter analytical subsurface flow diffusion hydrograph model to represent the theory of rapid displacement of ‘‘old’’ aquifer water and shallow pore water following rainfall events. We developed a two-parameter analytical surface flow diffusion hydrograph model for urban or other basins that generate surface runoff similar to flash floods following a sharp pulse of rainfall at the watershed inlet. The model uses two time parameters that are based on watershed scale, flow diffusivity, and flow celerity to control the shape of the hydrograph and time to discharge peak. The two-parameter analytical surface flow diffusion model was mathematically and experimentally compared with the one-parameter analytical subsurface diffusion hydrograph model proposed by Criss and Winston (2008b). We demonstrated that the one-parameter model represented one extreme case of the two-parameter model when the advection of subsurface flow was zero and that the two-parameter model was applicable for both surface and subsurface flow hydrograph simulations. The two-parameter model was tested on several watersheds and was shown to have a high efficiency in simulating hydrograph timing and peak discharge as well as in matching rising and falling limb inflection points. Fitting the two-parameter surface flow diffusion hydrograph model to a watershed runoff event helps to quantify the role of advective and diffusive transport on discharge and how it changes with changing storm and land cover characteristics.