11 Physically Based Modelling and the Analysis of Landscape Development

Recent interest in the numerical simulation of drainage basin and land surface evolution raises several issues concerning the status of physically based modelling in the analysis of landscape development. Most models use a continuum description for characterizing material transport within and across system boundaries. The scale at which continuum flux models break down is often not considered in the specification of mathematical models of surface development, despite its importance in the modelling of hillslope processes contributing to channel initiation and in the field testing of physically based models. Dimensional analysis and scaling are important modelling techniques, which are still relatively underused in descriptions of landscape development, and can simplify an analysis by eliminating redundant or extraneous variables and terms in governing equations as appropriate for the scales of interest. They can also be used to identify key dimensionless quantities which must have similar values if a laboratory or other quantitative study is to be considered representative of a selected field environment. Many of the constitutive functions for material transport used in contemporary models are ver