How Should Mathematical Models of Geomorphic Processes be Judged?

Mathematical models of geomorphic processes can have value as both predictive tools and precise conceptual frameworks. Well-posed mechanistic models have great conceptual value because they link geomorphic processes to universal scientific principles, such as conservation of energy, momentum, and mass. Models without this linkage (e.g., models based exclusively on cellular rules or empirical correlations) have less conceptual value but offer logical methodology for making practical predictions in some circumstances. Clear tests of the predictive power of mechanistic models can be achieved in controlled experiments, whereas natural landscapes typically have uncontrolled initial and boundary conditions and unresolved geological heterogeneities that preclude decisive tests. The best mechanistic models have a simplicity that results from minimizing assumptions and postulates, rather than minimizing mathematics, and this simplicity promotes conclusive tests. Optimal models also employ only parameters that are defined and measured outside the model context. Common weaknesses in geomorphic models result from use of freely coined equations without clear links to conservation laws or compelling data, use of fitted rather than measured values of parameters, lack of clear distinction between assumptions and approximations, and neglect of the four-dimensional (space + time) nature of most geomorphic processes. Models for predicting landslide runout illustrate principles and pitfalls that are common to all geomorphic modeling.