Computers & Geosciences 27 (2001) 815–827 A stochastic ‘‘precipiton’’ model for simulating erosion/sedimentation dynamics A. Crave*, P. Davy Ge ´osciences Rennes, UPR 4661 CNRS, Campus de Beaulieu, 35042 Rennes Cedex, France Received 21 July 1999; received in revised form 29 April 2000; accepted 10 August 2000 Abstract We present a stochastic modelling of erosion–sedimentation processes, based on cellular automata, which mimics the natural variability of climatic events with deterministic transport processes. The numerical procedure calculates the runoff water discharge as a function of the return period of elementary walking elements. This procedure generates water flux distributions at each point of the system, that depends on the local drainage area, and on the walker rainfall, and that are statistically analogous to natural river discharge distributions. It happens that a wide range of non-linear transport processes can be directly simulated in a intuitive way, relating the water flux and the local slope to the sediment transport activity. The present version of the code encompasses the main characteristics of erosion–sedimentation processes, from the simple hillslope diffusive law to the more complex non- linear fluvial transport. To illustrate the versatility of the model to reproduce complex natural dynamics, we calculate several geomorphological instabilities which are crucial in relief dynamics. # 2001 Elsevier Science Ltd. All rights reserved. Keywords: Erosion/sedimentation modelling; Geomorphology; Cellular automata 1. Introduction In this paper, we present a new numerical technique for modelling erosion/sedimentation dynamics over geological time scales. The fundamental objective is to reflect the complexity of transport processes with a simple formulation of the relevant physics. Nonetheless, we aim to introduce a diversity of processes, from diffusive terms operating on hillslopes to non-linear ‘‘advective’’ fluvial processes. This large range of transport processes is expected to produce complex multiscale organization of the relief, and of the sediment paths (drainage network), being a consequence of the growth of incision instabilities. The relationship between such complex dynamics and the transport parameters is still a subject of debate. The non-linearity of the transport equations with respect to the canonical variables, i.e. local slope and water flux, is supposed to be responsible for the development of physical instabil- ities (Smith and Bretherton, 1972). Several three-dimensional 3D models have been published in the recent literature (Ahnert, 1976; Chase, 1992; Howard, 1994a; Kirkby, 1986; Kooi and Beau- mont, 1994; Willgoose et al., 1991) which integrate local transport processes over the system scale. The basic equations are the mass conservation of sediments and water, as well as the erosion/deposition relationships. A major difficulty is taking account of topographic variables, such as the altitude and its spatial gradients, at the same time as hydraulic variables such as the water flux. Smith et al. (1997a, b) propose a general formula- tion of the sediment and water conservation equation, including explicitly the spatial and temporal variability of the flowing water depth. It leads to complex differential expressions, which imply additional hypoth- *Corresponding author. E-mail address: alain.crave@univ-rennes1.fr (A. Crave). 0098-3004/01/$-see front matter # 2001 Elsevier Science Ltd. All rights reserved. PII:S0098-3004(00)00167-9