Mathematical modeling of whole landscape evolution

The mathematical modeling of landform evolution consists of two components: the processes represented (i.e., considered dominant) in the model and the (typically computer) model representation of these processes. This review discusses the current debates surrounding processes represented in landform evolution. The potential impact on both evolving landforms and computer model structure is discussed. Issues specifically discussed include (a) the fundamental nature of mass conservation and the role of detachment- and transport-limited processes in mass conservation equations, (b) the interaction between detachment- and transport-limitation in channels, (c) the role of hillslope erosion and soil properties and their interaction with channel processes, (d) the interactions with tectonics when applying these models at large scale, (e) depositional structures and implications for paleo-climatic interpretation, (f) engineering applications of these models, and (g) numerical issues in the computer implementations. This review is not a model comparison. However, many applications are at the boundaries of computer capabilities so a comparison of existing models is provided.