Non-linearity and spatial resolution in a cellular automaton model of a small upland basin

Abstract

The continuing development of computational fluid dynamics is allowing the high resolution study of hydraulic and sediment transport processes but, due to computational complexities, these are rarely applied to areas larger than a reach. Existing approaches, based upon linked cross sections, can give a quasi two-dimensional view, effectively simulating sediment transport for a single river reach. However, a basin represents a whole discrete dynamic system within which channel, floodplain and slope processes operate over a wide range of space and time scales. Here, a cellular automation (CA) approach has been used to overcome some of these difficulties, in which the landscape is represented as a series of fixed size cells. For every model iteration, each cell acts only in relation to the influence of its immediate neighbours in accordance with appropriate rules. The model presented here takes approximations of existing flow and sediment transport equations, and integrates them, together with slope and floodplain approximations, within a cellular automation framework. This method has been applied to the basin of Cam Gill Beck (4.2 km2) above Starbottom, upper Wharfedale, a tributary of the River Wharfe, North Yorkshire, UK. This approach provides, for the first time, a workable model of the whole basin at a 1 m resolution. Preliminary results show the evolution of bars, braids, terraces and alluvial fans which are similar to those observed in the field, and examples of large and small scale non-linear behaviour which may have considerable implications for future models.