  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.
