Quantifying Spatio-Temporal Errors in Forest Fire Spread Modelling Explicitly

Forest fire growth models (FGMs) are widely used in both research and operations. FGMs involve modelling complex physical-chemical dynamic processes over large spatially heterogeneous forest landscapes and long periods under changing weather conditions. Because of their complexity, it is difficult to validate these models. A typical approach is to graphically compare predicted boundaries to the corresponding boundaries of actual fires, which provides is a visual rather than quantitative evaluation of modelling errors of forest fire spread. In this paper, we propose a method to quantify two-dimensional spread process modelling errors, in this case for forest fire spread modelling. We introduce several indices that can be used to quantify spatio-temporal modelling errors of two-dimensional spread processes explicitly and to evaluate overall modelling errors. We demonstrate the effectiveness of the indices through a case study in which the modelling errors of a forest fire simulated by a FGM are compared with those of a reference fire. The case study illustrates that the spatio-temporally explicit indices do work to quantify modelling errors of forest fire spread compared to a reference model and that this error analysis is not only useful for validating FGMs but also provides a basis for improving them. Because of the similarity of other two-dimensional spread processes to forest fire spread, we suggest potential applications of the method in other spatial spread processes, such as the spread of forest insect and contagious disease. The limitations of the method are presented.