Forecasting distributions of large federal-lands fires utilizing satellite and gridded weather information
Haiganoush K. Preisler A E , Robert E. Burgan B , Jeffery C. Eidenshink C , Jacqueline M. Klaver D and Robert W. Klaver CA USDA Forest Service, Pacific Southwest Research Station, 800 Buchanan St., West Annex, Albany, CA 94710, USA.
B USDA Forest Service, Rocky Mountain Research Station, 5775 West U.S. Hwy 10, Missoula, MT 59808-9361, USA. [Retired]
C US Geological Survey (USGS), Earth Resources Observation and Science Center (EROS), 25198 479th Ave, Sioux Falls, SD 57198, USA.
D Independent Research Scientist, 2601 S. Holly Ave, Sioux Falls, SD 57105, USA.
E Corresponding author. Email: hpreisler@fs.fed.us
International Journal of Wildland Fire 18(5) 508-516 https://doi.org/10.1071/WF08032
Submitted: 23 February 2008 Accepted: 26 September 2008 Published: 10 August 2009
Abstract
The current study presents a statistical model for assessing the skill of fire danger indices and for forecasting the distribution of the expected numbers of large fires over a given region and for the upcoming week. The procedure permits development of daily maps that forecast, for the forthcoming week and within federal lands, percentiles of the distributions of (i) number of ignitions; (ii) number of fires above a given size; (iii) conditional probabilities of fires greater than a specified size, given ignition. As an illustration, we used the methods to study the skill of the Fire Potential Index – an index that incorporates satellite and surface observations to map fire potential at a national scale – in forecasting distributions of large fires.
Additional keywords: fire business, fire danger, fire distribution, fire mapping, fire occurrence, semi-parametric logistic regression, spatial mapping, statistical comparisons of fire danger indices.
Acknowledgements
We thank the Desert Research Institute Program for Climate, Ecosystem and Fire Applications for the historical fire occurrence and size data.
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Appendix
We used the R statistical package (Ihaka and Gentleman 1996; Development Core Team 2004) to estimate the coefficients in the logit regression lines given in Eqns 2 and 4. In order to estimate the smooth two-dimensional function of the intercepts, we first used a thin plate spline function that transforms the spatial data (x-coordinate, y-coordinate) for each fire to a matrix of the corresponding radial bases functions (Hastie et al. 2001). The required modules for fitting thin plate splines within R were downloaded from the web (Geophysical Statistics Project, National Center for Atmospheric Research, see http://www.cgd.ucar.edu/stats/Software/Fields, accessed 18 June 2009). Once the data are transformed using spline functions, standard logistic regression routine may be used to estimate the coefficients with the bases matrices as the explanatory variables.
The coefficients in Eqn 2 may be estimated simultaneously. However, because we only had FPI values for 3 years, whereas data on fire occurrence and size was available for over 20 years, we chose to do the estimation in two steps. First we estimated the spatial intercepts using 21 years of fire occurrence data using a logistic regression model with spatial location as the only explanatory. Next we used the 3 years of data on fire occurrence and FPI to fit the model in Eqn 2 with the values of the intercepts, Ai, set to their estimates obtained from the first step. It is anticipated that the 21-year dataset would give a better estimate of the historical probabilities than would the 3 years for which FPI is available.
The transformation suggested for day-in-year in Eqn 4 was also obtained using a spline function to account for the non-linear seasonal effect in fire occurrence data. However, in this case, we used a periodic spline function that produces similar estimates for days at the beginning and end of the year.
