A Cellular Automaton Fluvial and Slope Model of Landscape Evolution

T.J.Coulthard, M.J.Kirkby and M. Macklin
School of Geography, University of Leeds, Leeds LS2 9JT, United Kingdom

An increasingly popular paradigm for modelling is the 'cellular automata' (Wolfram, 1984). Cellular automata (CA) models represent the landscape as a series of fixed size cells each of which corresponds to an area of the land surface. Each cell acts independently according to the influence of it immediate neighbours . This technique has been widely used for ecological population modelling (e.g. life models) but with the exception of Murray & Paola (1994) has rarely been applied to geomorphological models.

There are many processes acting in the evolution of a valley landscape such as mass movement and soil creep, but the interactions of these with the fluvial system are especially important. The valley floor and channel act a 'conveyer belt' removing and storing eroded material from the system. The interplay between these processes gives rise to landforms and fluvial features such as bar, braiding, terrace sets and alluvial fans. From a modelling perspective this presents a problem, as there are a variety of processes acting at a wide range of scales, both temporally and spatially. This paper describes a simple CA model representing an upland valley and the stream(s) flowing down it. The cells in this CA model are represented by altitudes in a landscape as per a DEM. Water and sediment discharges are applied to several upstream input points, and routed down through the landscape according to suitable approximations of the relevant laws of motion. A sediment budget for each cell then calculates the amount of material eroded from itself for the processes of fluvial erosion, mass movement and soil creep.

This CA framework provides a unique, generic and simple method of combing these processes to not only replicate fluvial features such as bars, terraces and alluvial fans, but is intended to ascertain the varying implications of' climate change and anthropogenic influence on the landscape. As for CA models in other fields, the simple laws applied here can yield complex non-linear behaviour and subjectively realistic results.