A scaling approach to capture sub-time-step rainfall variability in rainfall-runoff and erosion modelling

Scaling in space and time is a fundamental problem in hydrological and erosion modelling. Owing mainly to the lack of adequate data to support modelling at the process timescales, modelling of small time scale processes using coarse time scale data is often undertaken. Generally process descriptions are not modified but rather effective parameter values are used. A similar approach is taken spatially. It is generally recognized that this approach to scaling in process-based modelling can be problematic when non-linear interactions occur. This paper presents a method for modelling surface runoff and erosion processes that accounts for sub-timestep variability in rainfall while retaining a daily timestep and utilizing daily rainfall totals. The method uses the cumulative distribution function (CDF) of rainfall intensities to represent the effect of temporal variability of rainfall at a time-scale of minutes. While any CDF can be used, the rainfall intensity distribution model chosen here is the lognormal distribution. The distribution parameters are determined from daily rainfall totals. The rainfall CDF is modified by the interception, infiltration, and saturation excess processes to derive CDFs of throughfall, infiltration and surface runoff. These are then applied to the erosion algorithm to determine the erosion CDF. The resulting CDFs are integrated to predict respective daily loads. While a specific model is used here, it is worth noting that the approach used for rainfall scaling here is general and could be applied to many (but not all) rainfall-runoff and erosion models.