Basin Research (1997) 9, 27–52 Modelling landscape evolution on geological time scales: a new method based on irregular spatial discretization Jean Braun and Malcolm Sambridge Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia ABSTRACT We present simulations of large-scale landscape evolution on tectonic time scales obtained from a new numerical model which allows for arbitrary spatial discretization. The new method makes use of ecient algorithms from the field of computational geometry to compute the set of natural neighbours of any irregular distribution of points in a plane. The natural neighbours are used to solve geomorphic equations that include erosion/deposition by channelled flow and diusion. The algorithm has great geometrical flexibility, which makes it possible to solve problems involving complex boundaries, radially symmetrical uplift functions and horizontal tectonic transport across strike-slip faults. The algorithm is also ideally suited for problems which require large variations in spatial discretization and/or self-adaptive meshing. We present a number of examples to illustrate the power of the new approach and its advantages over more ‘classical’ models based on regular (rectangular) discretization. We also demonstrate that the synthetic river networks and landscapes generated by the model obey the laws of network composition and have scaling properties similar to those of natural landscapes. Finally we explain how orographically controlled precipitation and flexural isostasy may be easily incorporated in the model without sacrificing eciency. evolution on time scales of the order of hundreds of 1 INTRODUCTION thousands, to hundreds of millions of years (Willgoose et al., 1991; Beaumont et al., 1992; Chase, 1992; Howard Many observations of the rate of tectonic processes come from the field of geothermochronometry in which the et al., 1994). However, because geomorphic processes act on time scales of the order of 10 to 100 years, numerical evolution of isotopic systems is used as a proxy for the thermal history of rocks transported towards the surface simulations of landscape evolution require a very fine temporal discretization or, in other words, a large number (Hurford, 1986; Gleadow & Fitzgerald, 1987). It is sometimes overlooked however that rock cooling is not of small time steps. Similarly, geomorphic and tectonic processes also act on very dierent length scales, which only the result of tectonic uplift but also of surface erosion. Therefore, a correct interpretation of thermal means that geomorphic models require a very fine spatial discretization. It is for these reasons that most numerical histories, derived from isotopic data, requires a good understanding of the tectonic and erosional history of a models of landscape evolution are based on a regular spatial discretization of the landscape. Indeed, it is usually given crustal terrain involved in an orogenic event (Brown, 1991; Brown et al., 1994). thought that the level of eciency required to solve large-scale geomorphic problems can only be attained if Recent work ( Jamieson & Beaumont, 1988; Koons, 1989; Beaumont et al., 1992) has also shown that mass a regular rectangular numerical grid is used (Willgoose et al., 1991; Kooi & Beaumont, 1994). redistribution at the surface of the Earth by erosion and deposition plays an important role in determining not In this paper, we show that concepts from the field of computational geometry may be used to develop an only the shape of landscapes but also the large-scale morphology of compressional orogenic belts. Mountain ecient algorithm to solve complex geomorphic problems on large irregular meshes (i.e. of the order of 10 000 building is the result of a balance (or imbalance) between tectonic uplift and surface erosion ( Jamieson & nodes or more). It is not our aim to develop new ‘geomorphic equations’ or rules but instead to present a Beaumont, 1988; Willett et al., 1993). For these reasons, it is no surprise that much work new method that may be used to modify any exist- ing geomorphic model based on a regular spatial has been recently devoted to the modelling of landscape © 1997 Blackwell Science Ltd 27