Research Program: Fire Hazard Estimation using Point Process Methods.

Principal Investigator: Rick Paik Schoenberg

This is an NSF/EPA-sponsored project aimed at investigating fire hazard in the Los Angeles basin using techniques from multivariate point process analysis. Our strategy is to model fire occurrence as a marked spatial-temporal point process whose conditional rate of events depends not only on the record of previous fires but on other covariates as well. These covariates include local environmental factors such as temperature, altitude, humidity, precipitation, vegetation, and soil characteristics, as well as conglomerate indices such as the Burning Index (BI). Various Departments have been very helpful in supplying data, including the Los Angeles County Fire Department, Los Angeles County Department of Public Works, the USDA Forest Service, the National Park Service, and UCLA's Department of Atmospheric Science and Institute of the Environment.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

An important component of this research is the assessment of various different models via likelihood analysis (based on past data) and the evaluation of forecasting performance (employing data obtained after the models are fitted). Using the models which perform best, we intend to construct quantitative conservative predictions of local fire hazard accompanied by estimates of uncertainties in these predictions. Of statistical interest is the use of modern techniques in point process theory such as the application of multi-dimensional branching, Markovian, and multi-stage point process models and the use of multi-dimensional random rescaling in assessing these models. Our methods are similar to those used to model other natural events including earthquakes, volcanos, hurricanes, etc.

Click here for wildfire hazard estimates for LA County for 2003, and other recent results.

Some related statistical papers are listed below.

-- Peng, R. D., Schoenberg, F. P., Woods, J. (2003). Multi-dimensional point process models for evaluating a wildfire hazard index. JASA, in review.

-- Peng, R., and Schoenberg, F.P. (2003). Estimation of the fire interval distribution for Los Angeles County, California. . Environmetrics, in review.

-- 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 in Los Angeles County, California. Int. J. Wildland Fire 12(1), 1--10.

-- Schoenberg, F.P., Peng, R., and Woods, J. (2003). On the distribution of wildfire sizes. Environmetrics, to appear.

-- Schoenberg, F.P., Brillinger, D.R., and Guttorp, P.M. (2002). Point processes, spatial-temporal. in Encyclopedia of Environmetrics, Abdel El-Shaarawi and Walter Piegorsch, editors. Wiley, NY, vol. 3, pp 1573--1577.

-- Schoenberg, F. (2001). Evidence for threshold-type relationships between fire incidence and ecological factors. Proc. Forest Fires 2001: Operational Mechanisms, Firefighting Means and New Technologies, Athens, Greece, March 13-16.

-- Schoenberg, F.P. (2003). Multi-dimensional residual analysis of point process models for earthquake occurrences. JASA (in review).

-- Schoenberg, F.P. (2003). Testing separability in multi-dimensional point processes. Biometrics (in review).

-- Vere-Jones, D. and Schoenberg, F.P. (2003). Rescaling marked point processes. Australian & New Zealand Journal of Statistics (to appear).

-- Schoenberg, F.P. (2003). Consistent parametric estimation of the intensity of a spatial-temporal point process. JSPI (in review).

-- Schoenberg, F.P. (2003). Characterization of non-simple marked point processes. Characterization and simplification of non-simple marked point processes. (in preparation).

-- Schoenberg, F.P. (2002). On rescaled Poisson processes and the Brownian bridge. Ann. Int. Stat. Math. , 54(2), 445--457.

-- Schoenberg, F. (1999). Transforming spatial point processes into Poisson processes. Stochastic Processes and their Applications, 81(2), p. 155--164.