Optimality approaches to describe characteristic fluvial patterns on landscapes

Mother Nature has left amazingly regular geomorphic patterns on the Earth's surface. These patterns are often explained as having arisen as a result of some optimal behaviour of natural processes. However, there is little agreement on what is being optimized. As a result, a number of alternatives have been proposed, often with little a priori justification with the argument that successful predictions will lend a posteriori support to the hypothesized optimality principle. Given that maximum entropy production is an optimality principle attempting to predict the microscopic behaviour from a macroscopic characterization, this paper provides a review of similar approaches with the goal of providing a comparison and contrast between them to enable synthesis. While assumptions of optimal behaviour approach a system from a macroscopic viewpoint, process-based formulations attempt to resolve the mechanistic details whose interactions lead to the system level functions. Using observed optimality trends may help simplify problem formulation at appropriate levels of scale of interest. However, for such an approach to be successful, we suggest that optimality approaches should be formulated at a broader level of environmental systems' viewpoint, i.e. incorporating the dynamic nature of environmental variables and complex feedback mechanisms between fluvial and non-fluvial processes.