Landform evolution models were initially developed as a means of understanding the links between environmental processes acting on a landform (primarily runoff and erosion) and the form of the landscape resulting from the longterm action of those processes (i.e. the geomorphology). With their use we are able to (1) identify the geomorphological fingerprint of an individual process, so that aspects of the natural process acting on that landform can be identified and/or calibrated (or at least constrained) from the landform statistics, and (2) relate geomorphological scaling and organization principles to process, allowing simplified, but still physically-based, representations of catchment-scale processes. More recent developments have seen these models used for practical erosion modelling applications. It is these recent developments that will be the focus of this chapter. We first provide some context for the original models because their capabilities are underpinned by the science agenda justifying their original and continued development. Gilbert (1909) was the first to note that hillslopes subjected to an erosion process with a rate that increased with slope, but which was inde-pendent of distance downslope, resulted in slopes with convex profiles (hereafter a convex slope is one that has a downward curvature in its elevations in the direction of flow, while a concave slope has an upward curvature). Kirkby (1971) was the first to quantify the process interaction between distance down a hillslope and slope, defining the hillslope profile and its concavity in terms of causal processes. Kirkby did this by solving a differential equation for hillslope elevations and erosion processes, constructing in the process a simple landform evolution model.In Kirkby's work, hillslopes were assumed to have parallel flow lines with a fixed downstream boundary condition (determined by the river bed elevation) so that neither flow convergence and divergence nor interaction with a dynamic river were considered in his solutions. Ahnert (1976) constructed the first landform evolution model where flow convergence was allowed, and applied it to understanding the evolution of mountain ranges (e.g. Ahnert, 1984).The modern generation of landform evolution models is generally considered to have started with those presented by Willgoose et al. (1991a) andHoward (1994). These models simulated entire catchments rather than a single hillslope, the simultaneous evolution of the hillslopes and channels by different processes (and channel extension and retreat), and allowed for flow convergence on slopes. Moglen and Bras (1994) built on the work of Willgoose to allow
Handbook of Erosion ModellingEdited by R.P.C. Morgan and M.A. Nearing