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Estimation of subgrid scale kinematic wave parameters for hillslopes
Author(s) -
Willgoose Garry,
Kuczera George
Publication year - 1995
Publication title -
hydrological processes
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.222
H-Index - 161
eISSN - 1099-1085
pISSN - 0885-6087
DOI - 10.1002/hyp.3360090316
Subject(s) - kinematic wave , kinematics , scale (ratio) , surface runoff , parameterized complexity , surface roughness , geology , meteorology , mathematics , physics , algorithm , ecology , biology , classical mechanics , quantum mechanics
The 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 m 2 ) and large‐scale catchments (1 km 2 ) 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, c r and e m , to yield the discharge Q = c r A cs emS 0.5 with S being the slope and A cs 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 c r and e m , yet is not readily apparent in small‐scale data. Unfortunately, using small‐scale data c r and e m 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.