Procrustes based metrics for spatial validation and calibration of two-dimensional perimeter spread models: A case study considering fire

A number of phenomena in natural systems exhibit spread from a point source facilitated by a transport vector. Such occurrences are an important focus of landscape management, and include fires, wind driven disease and pollutant spills. Two-dimensional dynamic spread models are used to simulate the impacts of such events, determine risks and optimise responses. These models produce spatially coherent outputs that are not easily verified through traditional regression approaches. Validation of predictions is an essential part of model development and is necessary for the improvement of predictive performance. Current methods of evaluation are rarely systematic and are typically undertaken through subjective comparison of simulation outputs with observed features. There are few methods suitable for the objective analysis of freeform spread patterns, and it is proposed that a pseudo-landmark approach be adopted to allow the use of landmark based analysis methods. Vector driven spread patterns exhibit a degree of spatial structure, with distinct origin points and elongate shapes resulting from the predominant vector trajectory. These can be used as references to generate analogous landmarks for perimeter comparison. To describe differences, three indices derived from Procrustes analysis are proposed. These provide metrics to evaluate differences in perimeter orientation, size and shape. A case study simulating wildfire spread was used to demonstrate the proposed methodology. It was found to be effective for the description of perimeter differences and has potential for the validation and calibration of spread models. A number of assumptions were recognised and limitations in assigning pseudo-landmarks considered. (C) 2012 Elsevier B.V. All rights reserved.