Nonlinear kinematic dispersion in channel network response and scale effects: application of the meta-channel concept

In this paper, we present an application of the “meta-channel” concept to runoff routing at the catchment scale. We are particularly interested in the effects of the underlying geomorphology, implicitly built into the meta-channel formulation through the width function, of spatial heterogeneity built in through downstream variation of hydraulic geometry, and of nonlinearity introduced through the use of discharge dependent celerities and dispersion coefficients. To achieve runoff routing, we use a numerical model of the nonlinear advection-dispersion equation, which is a reasonable approximation to the hydraulic equations governing flow in the meta-channel. We investigate the effects of spatial heterogeneity and nonlinearity on the instantaneous response functions of the channel network due to specified rainfall inputs. Our exploration of spatial heterogeneity and nonlinearity of channel hydraulics indicates that events of small peak intensity undergo mainly translatory movement with minimal dispersion, while large events undergo considerable dispersion due to the presence of strong negative gradients in wave celerities in the downstream direction. We demonstrate that no linear scheme that assumes spatial uniformity of the hydraulic parameters, wave celerity and hydrodynamic dispersivity, can fully capture the actual dispersion exhibited in realistic situations. Nonlinearity and spatial heterogeneity in channel hydraulics manifest themselves in instantaneous response functions that are highly dependent on the magnitude of the rainfall inputs, and this nonlinear dependence is measured in terms of a nonlinear kinematic dispersion coefficient and we also investigate its dependence on catchment size.