A New Quantitative Test of Geomorphic Models, Applied to a Model of Braided Streams

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Abstract
Recent simple cellular models of self‐organized geomorphic patterns embody a new understanding of complex, spatially extended systems. Such models can be difficult to test quantitatively because the statistics traditionally used can be insensitive even to visually obvious variations in a complex pattern. Here we develop a new approach to evaluating such models. We begin by applying to spatial patterns the state‐space reconstruction techniques developed for dynamical systems, producing plots that summarize the patterns in a way that preserves more information than do the statistics usually used in geomorphology. Methods exist for characterizing some aspects of such plots. Here we develop a complementary method for quantitatively comparing state‐space plots in a way that more directly evaluates the similarity between the typical features of spatial patterns. An application of this method to the patterns produced by a cellular braided‐stream model and real braided streams indicates that this approach provides a relatively sensitive way of comparing model‐generated and real spatial patterns.

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