Spatial Modelling of Catchment Dynamics

In the previous chapter, we addressed the issues associated with data and sampling of physical phenomena as well as methods for the interpolation of spatial patterns. We believe that these spatial observations are vital to improving our understanding of catchment hydrological response. But measured patterns (or patterns interpolated from measurements) are of limited use without a framework within which they can be exploited. We need to use the patterns in a way that lets us test hypotheses. Mathematical modelling provides a powerful tool for this purpose. This modelling can take many forms, the most relevant to the topic of this book being spatially explicit models of catchment surface and subsurface response. These models are used for a range of purposes from tools for testing hypotheses about the behaviour of natural systems and putting data from research catchments into a consistent framework (the chapters in this book are examples), to practical applications such as erosion and transport modelling and simulation of the effect of land use change – in fact anything influenced by hydrological response. This chapter is about the basic structure of, and approaches to process representation in, spatial models. We introduce the concepts of model calibration and testing, focussing on the way in which spatial patterns can be used to inform model development and reduce model uncertainty. Finally we look at approaches to the evaluation of spatial predictions from spatially explicit models.