# The Spotting Distribution of Wildfires
## 1 Introduction
### The Havoc Caused by Spotting  
Spotting is not important in all fire contexts, but in a variety of ecosystems worldwide its importance varies from a minor concern, to the primary front spread mechanism or the primary breaching mechanism from wildland to urban structures. The type of fire, classified according to the structure of the fire's convection column, is also very important, and we will discuss this in detail in Section 1.4. In Boreal forests of North America, for example, there are vast continuous stretches of coniferous forests, which can create incredibly intense fires, called _crown fires_[3; 4]. These crown fires are capable of prolific spotting, and highly variable rates of spread. In the most extreme tinder-dry burning conditions, spotting may occur with sufficient frequency beyond a minimum distance, such that it influences the rate of spread. In addition, the prolific release of flaming needles [5] presents another mechanism, which might speed up a fire's local progression. Either of these mechanisms may describe the high variability in observed rates of spread for Boreal crown fires as outlined in [3]. While writing this article, a huge crown fire of high intensity is unfolding in Fort McMurray in Alberta, Canada. Spotting has allowed the fire to enter the city and more than 1600 homes were destroyed. As another example, in the chapparal brush of California, spotting from brushfires annually threatens property in the wildland-urban interface [6; 7]. The warm, dry _foelnt_ winds which pass through the great basin in Southern California [8], lead to extreme fire spreading scenarios in which spotting can play an important role. In fact, examples of foehn winds are found in many other regions, such as the Chinook winds East of the Rocky Mountains, or the Vento del Sur winds in Spain. In Australia, spotting is a major issue for fires in Eucalyptus-grassland forests [9; 10; 11]. In certain instances, severe burning conditions have led to the observation that the fire's boundary \"appears to be moving as a continual coalescence of spot fires\" [9]. In these cases, spotting seems to drive the fire front; such situations will be globally described as _spotting dominated cases_. An example of a  
Figure 1: (**a**) Caricature of the spotting process. A cohort of firebrands are launched to various heights \(z\) above a spreading ambient forest fire. The \(x\)-direction denotes the mean ambient wind direction. The firebrands are then released and transported in the ambient windfield: combusting, falling downward due to gravity, experiencing drag and possibly buoyancy, until they finally come to rest downwind of the main fire. Depending on the local conditions for fuel and weather at the landing site, a new fire may be ignited if the firebrand is still combusting. Such a fire is called a _spot fire_, and the process is called _spotting_; (**b**) Determining the “flight and burning” distribution \(L\) from the vertical launch distribution \(\phi\). The term “flight and burning” refers to the physical details of firebrand flight and combustion, which we will discuss in detail in the Appendix. Shown in the vertical is a cross-section of the launching distribution \(\phi(z,m)\) for some fixed \(m>0\). A possible asymptotic landing distribution \(\mathbb{L}(x,m)\) is plotted here in the horizontal. spotting dominated case are conflagrations, where fire spreads rapidly in an urban setting, as with post-earthquake fires which occurred in San Francisco (1906) or Tokyo (1923) [12]. Spotting is often the cause of a fire _breaching_ across an extended obstacle to local spread, such as roads, rivers, or man-made fuel breaks [13]. Naturally, then, spotting is also the most frequent mechanism for the escape of prescribed fires, the latter used by fire ecologists and management, to promote ecological diversity and mitigate potential large fires through fuel management [14].