Electronic Thesis and Dissertation Repository

Degree

Doctor of Philosophy

Program

Statistics and Actuarial Sciences

Supervisor

W. John Braun

Abstract

This thesis develops statistical methods and models and applies them
to problems related to forest fires. The unifying goal of the work is to provide a data analytic basis for quantifying the uncertainty surrounding fire ignition and fire growth which builds on existing theory where possible.

The main body of the thesis is comprised of three research papers. The Fire Weather Index (FWI) plays an important role in fire management and is central to the first two papers. In the first instance, the block bootstrap confidence interval method is used to deal nonparametrically with the dependence in the FWI data. Because the actual and nominal confidence levels differ substantially, a double bootstrap is applied and used to calibrate the confidence intervals. The calibration technique focuses on interval length-adjustment instead of level-adjustment.

The second paper systematically develops a sequence of parametric time series models for the FWI, starting from some basic physical observations. The final model developed is a seasonal random effect mixture tailed minification model. Numerical approximations using the model allows for calculation of the survival function for the minimum FWI in one or more consecutive days. Tentative results presented here suggest that fire danger prediction may be more effectively
accomplished using information on runs of moderately large FWI values, instead of simply using a single-day cut-off value.

The third paper studies the fire growth model, Prometheus and re-analyzes the data underlying the associated rate of spread formulas. The main goal of the paper is to incorporate randomness into the deterministic Prometheus model giving rise to a new simulator called Dionysus. The essential idea is a
parametric bootstrap. Burn probability contours can be created quickly by Dionysus. These can help fire managers make suppression resource allocation decisions for fires which are currently burning.


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