A weighty issue : estimation of fire size with geographically weighted logistic regression

Abstract: Size estimations of fires that occurred centuries ago have been the subject of study for many decades. More accurate spatial fire histories from tree rings were possible by either drawing the sample location on detailed topographic maps or using GPS receivers. A popular method of delineating fire sizes is to draw an outline around the fire-scarred samples considering topographic and landscape features. This is a rather subjective method that cannot be replicated. Other more replicable methods have also been suggested to estimate fire size among them methods that use buffers (kernel ranges), grids, or Thiessen polygons. However, even those have a subjective component. Geographically weighted logistic regression (GWLR), not previously used to estimate fire sizes, seemed promising since the method allows for the changing relationships between different topographic, landscape, or socioeconomic features to be considered in the analysis. Logistic regression is done with binomial data: fire/no fire. Geographically weighted regression (GWR) is a relatively new and more objective method that considers the geography of the data. Instead of using one regression coefficient over a whole study area, several regression coefficients are calculated for the different sample locations which might help explain the relationships better. The GWLR analyses consistently found only one variable that explained fire location. This variable changed between the different analyses. The corrected Akaike Information Criterion (AICc) increased in every GWLR analysis when adding more variables (a lower AICc value means a higher quality model) while the R2 value increased (more variables explain more of the variance). The optimal output of such analyses would be that the R2 value increases and the AICc decreases which would mean that the added variables help explain more of the variance AND that the model has higher quality. A probability analysis of whether close trees burn at the same time shows that trees closer to each other have a higher probability of burning compared to trees that are further apart. This is especially true between the years 1400 - 1700 (before human influences on the landscape). Between 1700 and 2000, this clear pattern partially vanished. While GWR could be considered the most objective method of fire-size estimations (of the ones studied), it could not be used to estimate fire sizes. Fire size and location seems to depend more on the distance from fire-scarred trees than on different landscape features. Different methods of estimating fire sizes are more reliable before humans have added to the natural fire regimes. After human influence, the uncertainty of the fire sizes increases between the different methods of calculating fires sizes (up to 46% in this study).