International Journal of Wildland Fire International Journal of Wildland Fire Society
Journal of the International Association of Wildland Fire

Wildland fire probabilities estimated from weather model-deduced monthly mean fire danger indices

Haiganoush K. Preisler A D , Shyh-Chin Chen B , Francis Fujioka B , John W. Benoit B and Anthony L. Westerling C

A USDA Forest Service, Pacific Southwest Research Station, 800 Buchanan St, West Annex, Albany, CA 94710, USA.

B USDA Forest Service, Pacific Southwest Research Station, Riverside, CA 92507, USA.

C Sierra Nevada Research Institute, PO Box 2039, Merced, CA 95344, USA.

D Corresponding author. Email:

International Journal of Wildland Fire 17(3) 305-316
Submitted: 9 December 2006  Accepted: 11 December 2007   Published: 23 June 2008


The National Fire Danger Rating System indices deduced from a regional simulation weather model were used to estimate probabilities and numbers of large fire events on monthly and 1-degree grid scales. The weather model simulations and forecasts are ongoing experimental products from the Experimental Climate Prediction Center at the Scripps Institution of Oceanography. The monthly average Fosberg Fire Weather Index, deduced from the weather simulation, along with the monthly average Keetch–Byram Drought Index and Energy Release Component, were found to be more strongly associated with large fire events on a monthly scale than any of the other stand-alone fire weather or danger indices. These selected indices were used in the spatially explicit probability model to estimate the number of large fire events. Historic probabilities were also estimated using spatially smoothed historic frequencies of large fire events. It was shown that the probability model using four fire danger indices outperformed the historic model, an indication that these indices have some skill. Geographical maps of the estimated monthly wildland fire probabilities, developed using a combination of four indices, were produced for each year and were found to give reasonable matches to actual fire events. This method paves a feasible way to assess the skill of climate forecast outputs, from a dynamical meteorological model, in forecasting the probability of wildland fire severity with known precision.

Additional keywords: FWI, model appraisal, mutual information, NFDRS, semi-parametric logistic regression, spline functions.


We are grateful to J. Roads of the Experimental Climate Prediction Center, University of California, San Diego, for providing model-deduced NFDRS indices. The fire histories used here were developed and updated with support from the National Oceanographic and Atmospheric Administration’s Office of Global Programs via the California Applications Program.


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Appendix A1

The logistic regression lines used to estimate the probabilities of fire occurrence and large fire events are specified in the following equation:


where the subscript v indicates the 1 × 1-degree by 1-month voxel; p is set to either the probability of ignition or conditional probability of large fire given ignition; (lon, lat) are the longitude and latitude of the midpoint of the grid cell; Xm are explanatory fire weather and fire danger variables. The function h is a non-parametric smoothing function (Hastie et al. 2001); g2 is a periodic spline function (for estimating month-in-year effect); and g1 is a thin plate spline function (for estimating the spatial surface as a function of lon and lat). Estimation was done with the R statistical package (R Development Core Team 2004). The procedure within the R package consists of first running the bs (basis spline) function on each of the explanatory variables, then using the outputs from the bs runs as the new explanatory variables in a simple logistic regression routine. A periodic spline function (bs.per) is used for the month variable to allow for a smooth transition between the months of December and January. For the two-dimensional spline function of (lon, lat), the thin plate spline function (ts) is used to produced the necessary variables.

The MI statistic was defined as follows: let Y indicate the occurrence of a fire (or alternatively, a large fire event) and X indicate the logit line (linear predictor) as described in Eqn A1; then the MI statistic is given by


where pX,Y(X, Y), pX(X) and pY(Y) are the joint and marginal distributions of X, Y respectively. For the bivariate normal case, 1 – e–2MIX,Y is the coefficient of determination. In general, MIX,Y = 0 when X and Y are independent and MIX,Y ≤ MIZ,Y if Y is independent of X given Z (Brillinger 2004). A similar and more commonly used statistic for choosing between models is the Akaike information criterion (AIC) given by WF06162_EI7.gif Although AIC and MI often give similar results, as was the case in the present study, AIC does not have the same interpretation as the MI statistic as a measure of the strength of statistical dependence.

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