Analysis of Spatio-Temporal Data for Forest Fire Control

This project aims to establish the relationship of forest fire behavior with ecological/environmental factors, such as forest structure and weather. We analyze records of forest fires during the fire season (May to September) in 1992 from the Forest Fire Management Branch of Ontario Ministry of Natural Resource (OMNR). We start with a preliminary analysis of the data, which includes a descriptive summary and an ordinary linear regression analysis with fire duration as the response. The preliminary analysis indicates that the fire weather index (FWI) used by Natural Resource of Canada is the most relevant together with fire location and starting time. We apply semi-variogram and Moran's I, the conventional methods for exploring spatial patterns, and extend them to investigate spatio-temporal patterns with the fire data. Evaluations of the extended Moran’s I statistic with the residuals of the ordinary linear regression analysis reveal a large departure from the independence and constant variance assumption on the random errors. It motivates two sets of partially linear regression models to accommodate possible nonlinear spatial/temporal patterns of the forest fires. We integrate univariate and bivariate Kernel smoothing procedures with the least squares procedure for estimating the model parameters. Residual analysis indicates satisfactory fittings in both sets of regression analysis. The partially linear regression analyses find that the association of fire duration with FWI varies across different fire management zones, and depends on the fire starting time.