Point process modeling of wildfire hazard in Los Angeles county, California. (English) Zbl 1223.62168

Xu, Haiyong; Schoenberg, Frederic Paik

Ann. Appl. Stat. 5, No. 2A, 684-704 (2011).

Summary: The Burning Index (BI) produced daily by the United States government’s National Fire Danger Rating System is commonly used in forecasting the hazard of wildfire activity in the United States. However, recent evaluations have shown the BI to be less effective at predicting wildfires in Los Angeles County, compared to simple point process models incorporating similar meteorological information. We explore the forecasting power of a suite of more complex point process models that use seasonal wildfire trends, daily and lagged weather variables, and historical spatial burn patterns as covariates, and that interpolate the records from different weather stations. The results are compared with models using only the BI. The performance of each model is compared by Akaike Information Criterion (AIC), as well as by the power in predicting wildfires in the historical data set and residual analysis. We find that multiplicative models that directly use weather variables offer substantial improvement in fit compared to models using only the BI, and, in particular, models where a distinct spatial bandwidth parameter is estimated for each weather station appear to offer substantially improved fit.

MSC:

62P12	Applications of statistics to environmental and related topics
60G55	Point processes (e.g., Poisson, Cox, Hawkes processes)
65C60	Computational problems in statistics (MSC2010)

Keywords:

burning index; conditional intensity; residual analysis

Software:

pyuvdata

References:

[1]	Akaike, H. (1977). On entropy maximization principle. In Applications of Statistics (P. R. Krishnaiah, ed.) 27-41. North-Holland, Amsterdam. · Zbl 0388.62008
[2]	Andrews, P. L. and Bradshaw, L. S. (1997). FIRES: Fire Information Retrieval and Evaluation System-a program for fire danger rating analysis. Gen. Technical Report INT-GTR-367. Ogden, UT; U.S. Dept. Agriculture, Forest Service, Intermountain Research Station. 64 p.
[3]	Andrews, P. L., Loftsgaarden, D. O. and Bradshaw, L. S. (2003). Evaluation of fire danger rating indexes using logistic regression and percentile analysis. Int. J. Wildland Fire 12 213-226.
[4]	Baddeley, A., Turner, R., Møller, J. and Hazelton, M. (2005). Residual analysis for spatial point processes (with discussion). J. Roy. Statist. Soc. Ser. B 67 617-666. · Zbl 1112.62302 · doi:10.1111/j.1467-9868.2005.00519.x
[5]	Bradshaw, L. S., Deeming, J. E., Burgan, R. E. and Cohen, J. D. (1983). The 1978 National Fire-Danger Rating System: Technical Documentation . United States Dept. Agriculture Forest Service General Technical Report INT-169. Intermountain Forest and Range Experiment Station, Ogden, Utah. 46 p.
[6]	Burgan, R. E. (1988). 1988 revisions to the 1978 National Fire-Danger Rating System. USDA Forest Service, Southeastern Forest Experiment Station, Research Paper SE-273.
[7]	Daley, D. and Vere-Jones, D. (1988). An Introduction to the Theory of Point Processes . Springer, New York. · Zbl 0657.60069
[8]	Daley, D. and Vere-Jones, D. (2003). An Introduction to the Theory of Point Processes. Vol. 1: Elementary Theory and Methods . Springer, New York. · Zbl 1026.60061 · doi:10.1007/b97277
[9]	Deeming, J. E., Burgan, R. E. and Cohen, J. D. (1977). The National Fire-Danger Rating System - 1978 . Technical Report INT-39, USDA Forest Service, Intermountain Forest and Range Experiment Station.
[10]	Haines, D. A., Main, W. A., Frost, J. S. and Simard, A. J. (1983). Fire-danger rating and wildfire occurrence in the Northeastern United States. Forest Science 29 679-696.
[11]	Haines, D. A., Main, W. A. and Simard, A. J. (1986). Fire-danger rating observed wildfire behavior in the Northeastern United States. Res. Pap. NC-274. St. Paul, MN: U.S. Dept. Agriculture, Forest Service, 23 p.
[12]	Härdle, W. (1994). Applied Nonparametric Regression . Cambridge, Cambridge University Press.
[13]	Helmers, R., Magku, I. W. and Zitikis, R. (2003). Consistent estimation of the intensity function of a cyclic Poisson process. J. Multivariate Anal. 84 19-39. · Zbl 1038.62037 · doi:10.1016/S0047-259X(02)00008-8
[14]	Keeley, J. E. (2000). Chaparral. P. 203-253 in North American Terrestrial Vegetation , 2nd ed. (M. G. Barbour and W. D. Billings, eds.). Cambridge University Press, Cambridge.
[15]	Keeley, J. E. and Fotheringham, C. J. (2003). Impact of past, present, and future fire regimes on North American Mediterranean shrublands. In: Fire and Climatic Change in Temperate Ecosystems of the Western Americas (T. T. Veblen, W. L. Baker, G. Montenegro and T. W. Swetnam, eds.) 218-262. Springer, New York.
[16]	Mandallaz, D. and Ye, R. (1997a). A new dryness index and the non-parametric estimate of forest fire probabilities. Schweiz. Z. Forstwes. 148 809-822.
[17]	Mandallaz, D. and Ye, R. (1997b). Prediction of forest fires with Poisson models. Can. J. For. Res. 27 1685-1694.
[18]	Mardia, K. V. and Jupp, P. E. (2000). Directional Statistics . Wiley, New York. · Zbl 0935.62065
[19]	Mees, R. and Chase, R. (1991). Relating burning index to wildfire workload over broad geographic areas. Int. J. Wildland Fire 1 235-238.
[20]	Ogata, Y. (1978). The asymptotic behaviour of maximum likelihood estimators for stationary point processes. Ann. Inst. Statist. Math. 30 243-261. · Zbl 0451.62067 · doi:10.1007/BF02480216
[21]	Peng, R. and Schoenberg, F. P. (2008). Estimating fire interval distributions using coverage process data. Environmetrics . Unpublished manuscript.
[22]	Peng, R. D., Schoenberg, F. P. and Woods, J. (2005). A space-time conditional intensity model for evaluating a wildfire hazard index. J. Amer. Statist. Assoc. 100 26-35. · Zbl 1117.62411 · doi:10.1198/016214504000001763
[23]	Rathbun, S. L. and Cressie, N. (1994). Asymptotic properties of estimators for the parameters of spatial inhomogeneous Poisson point processes. Adv. Appl. Probab. 26 122-154. · Zbl 0811.62090 · doi:10.2307/1427583
[24]	Schoenberg, F. P., Brillinger, D. R. and Guttorp, P. M. (2002). Point processes, spatial-temporal. In Encyclopedia of Environmetrics (A. El-Shaarawi and W. Piegorsch, eds.) 3 1573-1577. Wiley, New York.
[25]	Schoenberg, F. P., Chang, C., Keeley, J., Pompa, J., Woods, J. and Xu, H. (2010). A critical assessment of the burning Index in Los Angeles County, California. Int. J. Wildland Fire .
[26]	Schoenberg, F. P., Peng, R., Huang, Z. and Rundel, P. (2003). Detection of nonlinearities in the dependence of burn area on fuel age and climatic variables. Int. J. Wildland Fire 12 1-10.
[27]	Schoenberg, F. P., Peng, R. and Woods, J. (2003). On the distribution of wildfire sizes. Environmetrics 14 583-592.
[28]	Schoenberg, F. P. and Xu, H. (2008). Directional kernel regression for wind and fire data. Environmetrics . Unpublished manuscript.
[29]	Schroeder, M. J., Glovinsky, M., Hendricks, V., Hood, F., Hull, M., Jacobson, H., Kirkpatrick, R., Krueger, D., Mallory, L., Oertel, A., Reese, R., Sergius, L. and Syverson, C. (1964). Synoptic weather types associated with critical fire weather. Institute for Applied Technology, National Bureau of Standards, U.S. Dept. Commerce, Washington, DC.
[30]	Silverman, B. W. (1986). Kernel Density Estimation and Data Analysis . Chapman and Hall, London. · Zbl 0617.62042
[31]	Viegas, D. X., Bovio, G., Ferreira, A., Nosenzo, A. and Sol, B. (1999). Comparative study of various methods of fire danger evaluation in Southern Europe. Int. J. Wildland Fire 9 235-246.
[32]	Warren, J. R. and Vance, D. L. (1981). Remote Automatic Weather Station for Resource and Fire Management Agencies. United States Dept. Agriculture Forest Service Technical Report INT-116. Intermountain Forest and Range Experiment Station.