Quantifying rare events in spotting: How far do wildfires spread?

TL;DR

This paper compares methods for predicting rare firebrand landing distances in wildfires, introducing a large deviation theory approach that efficiently estimates low probability tail events crucial for fire spread prediction.

Contribution

It proposes a novel large deviation theory method for accurately quantifying rare firebrand landing distances, improving over traditional Monte Carlo and importance sampling techniques.

Findings

LDT accurately estimates tail probabilities of firebrand landing distances.

Most probable landing distance scales linearly with wind velocity.

Explicit formula for relative landed mass enables quick assessment of fire spread risk.

Abstract

Spotting refers to the transport of burning pieces of firebrand by wind which, at the time of landing, may ignite new fires beyond the direct ignition zone of the main fire. Spot fires that occur far from the original burn unit are rare but have consequential ramifications since their prediction and control remains challenging. To facilitate their prediction, we examine three methods for quantifying the landing distribution of firebrands: crude Monte Carlo simulations, importance sampling, and large deviation theory (LDT). In particular, we propose an LDT method that accurately and parsimoniously quantifies the low probability events at the tail of the landing distribution. In contrast, Monte Carlo and importance sampling methods are most efficient in quantifying the high probability landing distances near the mode of the distribution. However, they become computationally intractable for quantifying the tail of the distribution due to the large sample size required. We also show that the most probable landing distance grows linearly with the mean characteristic velocity of the wind field. Furthermore, defining the relative landed mass as the proportion of mass landed at a given distance from the main fire, we derive an explicit formula which allows computing this quantity as a function of the landing distribution at a negligible computational cost. We numerically demonstrate our findings on two prescribed wind fields.