Estimation of subgrid scale kinematic wave parameters for hillslopes

Abstract

AbstractThe kinematic wave approximation is commonly used in the new generation of so‐called physically based, distributed rainfall‐runoff models. However, although the kinematic wave approximation is commonly accepted for channel and experimental flows, its applicability to actual hillslopes remains unvalidated. Because it is not possible to measure, nor model, all of the details of the flow on any realistic surface, we use subgrid approximations to provide an effective parameterization of the processes that occur on scales smaller than those that can be modelled. This paper explores different effective parameterizations, the data required to identify the correct parameterization, and the implications of not being able to identify all of the parameters on the scale dependence of flood hydrology. Data from small‐scale plot experiments (100 m2) and large‐scale catchments (1 km2) are used to explore these issues. It has been found that infiltration parameters can be adequately calibrated from small‐scale plots. However, it is more difficult to calibrate the kinematic wave parameters using small‐scale data alone. The conveyance properties of the hillslope cross‐sections are parameterized by two kinematic wave parameters, cr and em, to yield the discharge Q = cr A S0.5 with S being the slope and Acs the cross‐sectional area. It is shown that these two parameters are highly correlated, particularly when inferred from small‐scale data. The surface roughness, amount of rilling and undulations of the surface all influence the kinematic wave parameters. The runoff response at large scales is very sensitive to changes in cr and em, yet is not readily apparent in small‐scale data. Unfortunately, using small‐scale data cr and em cannot be estimated with acceptable precision to reliably extrapolate to larger scales. The significance of this behaviour is demonstrated and some possible solution strategies are discussed.