Spatial Analysis in Physical Geography and the Challenge of Deterministic Uncertainty

Abstract

The application of complex and nonlinear dynamical systems (NDS) theory in physical geography and geosciences has proceeded through several stages, and has recently entered a phase where field‐testable hypotheses and historical or mechanistic explanations are being generated. However, there are some fundamental challenges. It seems clear that chaos and dynamical self‐organization are present, and may be common in earth surface systems, and that these phenomena have spatial manifestations in the landscape. However, NDS theory and methods have been formulated primarily in the temporal domain and are typically ill‐suited to real‐world spatial data. Spatial analytical methods are not generally capable of distinguishing deterministic complexity and uncertainty from noise. Thus, the detection of the signals of complex deterministic dynamics in real landscapes and spatial data is a major challenge. Entropy‐based methods of spatial analysis can be directly linked to nonlinear dynamics, and are at present the best available method to approach this problem. However, there is evidence in the spatial analysis literature suggesting that development of techniques to detect deterministic uncertainty is possible. Pending such a break‐through, three general approaches are described, based on spatial analysis of chronosequences, the characteriziation of changes in spatial structure over time, and the spatial‐domain testing of specific hypotheses relevant to deterministic uncertainty. Current trends generally suggest a shift in mathematical modeling and spatial analysis in physical geography away from traditional determinism toward approaches that incorporate locational, historical, and scale contingency.