Modeling the spatial variability of forest fuel arrays

Abstract

This project focuses on the need for a comprehensive approach for forest fuels mapping based on spatial interpolation techniques. Instead of working only with the fuel-model concept, this investigation is focused on the generation of four different fuel maps. Three of them are based on fuel timelag (measure of the rate at which a specified size of dead fuel gains or loses moisture) [1-HR, 10-HR and 100-HR fuel classes]. The fourth one corresponds to the live-fuels category [Live Woody]. This allowed better definition of the spatial variations in fuels, even within an area classified into the same fuel-model class. A total of twelve interpolation options were compared, five statisticals (spline, polygonal mapping, inverse distance weighting [power 1 and 2]) and seven geostatisticals (ordinary kriging, universal kriging [1st and 2nd degree], cokriging, point kriging and block kriging), in order to get the continuous surfaces that more precisely represent the spatial distribution for each of the mentioned fuel classes. The ancillary data required in cokriging were gathered from a Digital Elevation Model, a Landsat 5 TM and a forest inventory. Field data were collected from the "ejido" El Largo y Anexos, Cd. Madera (Chihuahua, México). These variables were analyzed to define more significant auxiliary variables. The four fuel classes showed significant autocorrelation and cross-correlation, thus it was possible to model the spatial continuity of each of the four fuel classes. The average spatial dissimilarity between data points allowed defining a structural distribution (variogram), with the corresponding sill, range and nugget effect. Traditional "conditionally positive definite" models were good enough to characterize the pattern of spatial continuity, and to define weighting factors for both kriging and cokriging. Based on the mean square error values, in general, geostatistical techniques performed better than the traditional alternatives. As a result, three out of the four fuel classes (1-HR, 100-HR, LW) were better modeled through cokriging, with elevation as an ancillary variable. The ancillary variables that showed the best performance when cokriged with fuel classes were elevation and principal component 3. Inverse distance weighting (IDW, power 1) was the best alternative to define the spatial distribution of 10-HR fuel. Although, it was not possible to establish a unique "best" spatial interpolation method, IDW showed a more constant performance. The worst results were obtained using spline, and Thiessen interpolation techniques. Since there was not a spatially explicit fire behavior model that could use the four fuel-type maps, a spatial simulation model (SSM) was developed under a raster approach. This model was compared with FARSITE, an existing spatially explicit fire behavior model that is based on the fuel-model concept. The required fuel-model map for FARSITE was developed under the "Conditional Fuels Loading Concept" (CFLC), which considers that each fuel-model has a characteristic fuels loading combination. There were some differences in fire behavior, such as rate of spread and reaction intensity, when comparing the simulation model of this study (SSM) versus FARSITE, which was the result of the variation of fuel loading. Forest fire phenomena are complex, thus a more accurate prediction of fire behavior should consider not only the evaluation of more variables, but also determine their spatial inter-dependencies. It is recommended that future fuels evaluation should be based on the integration of a multi-resource approach and geostatistical techniques. Furthermore, nonlinear kriging techniques should be tested in the interpolation of forest fuels. On the other hand, geostatistical techniques can be used to monitor and predict changes in the spatial distribution of forest fuels. Also the CFLC should be further tested not only regarding the "Timber litter" fuel complex, but also with the other fuel groups. Further research is needed to define the more adequate sample design when interpolating fuels' spatial distribution.