Spatial lumping of a distributed rainfall-sediment-runoff model and its effective lumping scale

This paper proposes a method to spatially lump a distributed rainfall-sediment-runoff model at the catchment scale. Based on a kinematic wave rainfall-sediment-runoff model, the proposed method spatially integrates (1) a rainfall-runoff model that simulates unsaturated, saturated subsurface and surface runoff processes and (2) a rainfall-sediment-runoff model that simulates soil erosion and transport processes induced by raindrops and surface flow detachment, respectively. The method deductively derives a set of lumped equations that relates the streamflow discharge and the catchment storage of water and sediment, which are then used together with continuity equations to predict the sediment runoff fluxes from the catchment outlet. The main advantage of the method is that the derived lumped model parameters are reflected by the spatially distributed topographical and soil property information, and yet the model can be implemented with a much less computational load compared to the original distributed model. Thus, the model gives a possibility of its numerous applications?-?such as the application to real-time flood forecasting, sediment yield-flood prediction for hydraulical structure designing, and for a climate change impact analysis on hydrological responses?-?coupled with the risk and uncertainty analyses which require a number of simulations. The developed lumped model successfully simulated the original distributed model outputs, as well as the observed streamflow and sediment at the Lesti River Catchment (381?km2), a tributary of the Brantas River Basin in Indonesia. After validating the proposed lumped model, the most effective lumping scale was then investigated by conducting multiple simulations, the results of which suggested that approximately 200?km2 is the ideal lumping scale for this model. Copyright (C) 2011 John Wiley & Sons, Ltd.