| Wildland fire spread models have a long history, but a system is needed to quantify the magnitude, spatial and temporal variability, and statistical characteristics of fire spread modeling errors. This dissertation describes a new methodology to evaluate the uncertainties of fire spread simulations, which can be applied to models that simulate fire growth in two-dimensional space. A characterization of error is proposed that leads to statistical analysis of the error in space and time, and a spatially dependent statistical correction of systematic bias in the spread model. A method is described to construct error bounds on projected fire perimeters, such that the interval between the bounds contains the true perimeter with specified probability.; Hypothetical examples illustrate the application of the error analysis to elliptical fires. This is followed by a comprehensive analysis of errors in the simulation of the Bee Fire, which burned a part of the San Bernardino National Forest, California, on 29 June 1996. The FARSITE fire modeling system simulated the early growth of the Bee Fire from given terrain, fuel, and weather conditions. Different weather scenarios were obtained from a weather station near the fire, and from a high resolution weather model. The resultant fire spread simulations were only partially successful in replicating the Bee Fire. The complex behavior of the actual fire yielded modeling errors that varied considerably in space and time.; The dissertation proposes that random field theory can be used to address spatial and temporal dependencies of fire spread modeling errors. The error dependencies affect the covariance structure of the errors. Random field theory treats the stochastic variability of a geophysical variable across the spatial/temporal spectrum.; The literature describes temporal stochastic variability of fire spread in terms of spread rate power spectra. The Bee Fire data suggest that the spatial stochastic variability of fire spread may be modeled by a Gaussian semivariogram and its spectral equivalent. Random field theory provides a unified framework to analyze spatial and temporal stochastic variations simultaneously, but much work lies ahead. |
