A number of analyses have shown the effects of fire suppression on fire growth where the fire shape remains constant (Albini et al. 1978, Bratten 1978, Mees 1985, Anderson 1989, Fried and Fried 1996). Effects of direct attack and parallel attack have shown that attacking the head of a fire reduces burned area more than an attack from the back and can result in different fire shapes. Direct attack occurs at the flaming front whereas parallel attack maintains a constant distance from the active fire front. Although none of the analytical models can be applied to fire shapes that arise under non-uniform environmental conditions, they do give ready comparisons for output of simulations of suppression with uniform fire conditions.
Many factors are known to affect the rate of fireline production. Fuel type, soil type, topography, weather influences on working conditions, crew size, equipment, fatigue, and crew experience have been found to have an effect (Hirsch and Martell 1996). Of these factors, most of the variation in line construction rate can probably be explained from fuel type, crew size, and equipment. Their effect on line production has also been the most consistently documented compared to other possible factors (Haven et al. 1982, Phillips and Barney 1984, Phillips et al. 1988, Quintilio et al. 1988, Fried and Gilless 1989, Barney et al. 1992, Hirsch and Martell 1996). Simulation control over line production rate was restricted to these factors.
The simulation of horizontal rate of fireline production is assumed only to be a function of fuel type and slope for an arbitrary crew type and size. On sloping terrain the horizontal rate is computed as the product of the horizontal rate and the cosine of slope in the direction of travel. This assumes that the horizontal rate is constant in a plane parallel with the slope but that less line will be produced on steep slopes in the horizontal plane.
The effect of direct attack on an active fire front is simulated using the known fire perimeter positions at two successive time steps t1 and t2. The idea is to compute the position at t2 of an attack crew building line at a given rate from its position on the fire perimeter at t1 (Figure X). The computation assumes that the range of possible solutions is defined by a quadrilateral of perimeter vertices (2 successive points at t1 and their new positions at t2). The fire perimeter points will move to their respective positions at t2 without suppression. Because this quadrilateral is obtained while adhering to the time and space resolutions set for the simulation, the suppression effects on the fireline will also be calculated within those tolerances.
On flat terrain, the effect of suppression can be represented as an circle or arc of potential solutions with a constant radius L determined by the product of the line construction rate and the time difference between t2 and t1. On sloping terrain, the arc would be eccentric along the fall-line of the slope given the above assumption of constant line production. Solutions to the suppression problem occur where the arc of suppression intersects the legs of the quadrilateral. Some potential solutions are illogical. Different methods are required to obtain some solutions depending on the length of the suppression line L relative to the dimensions of the quadrilateral.
The first case occurs when the suppression arc intersects the fire perimeter segment of t2 within bounds of the quadrilateral (L is smaller than the diagonal of the quadrilateral but greater than the spread distance). Solving for this point is done iteratively (item A in Figure). The second case occurs if the suppression arc exceeds the bounds of the quadrilateral without intersecting it. This happens when the line production rate is large compared to the spread rate and larger than the diagonal of the quadrilateral. The solution in this case is to incrementally compute the progress of line building over shorter time steps such that the length L falls within the quadrilateral (item B in Figure). The third case occurs when the rate of line production is much slower than the fire spread rate. In reality, a flanking action would be taken by a fire crew. The simplest way to "flank" the fire spread is to compute the point at which the line production parallels the route of the suppression starting point from t1 to t2 (item C in Figure).
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Method for constructing fireline during direct attack. Pairs of vertices on a fire perimeter at time 1 and time 2 form a quadrilateral as shown in items A, B, and C. Fireline is shown as line L (radius of the arc, dotted black line) and is the product of the time step and the line production rate in a particular fuel type. Item A shows the solution if fireline production is less than the diagonal of the quadrilateral (dotted red line) but greater than the spread distance between t1 and t2. Item B shows the solution if fireline is greater than the diagonal. Item C shows one possible solution when line production is much less than the spread distance between t1 and t2. |
Indirect attack is simulated by the incremental lengthening of an impermeable fireline along a predetermined route. The length of line produced is determined by 1) the rate of line production in a given fuel type, 2) the slope in the direction of travel, and 3) the time step. The distance resolution set for the simulation will interrupt the line production, forcing it to sample the landscape for information on fuel type and topography, if the length of the line in a given time step exceeds that resolution. The distance resolution also determines the width of the fireline that can't be breached by the fire spread distance in a given time step. The constructed fireline is represented as a closed stationary polygon for which mergers with active fire fronts are computed as described above (see Mergers). When a merger is detected, the vertices from the fire that have entered the interior of the fireline polygon are "turned off".
Burnout, "firing out", or "back firing" is simulated on one side of the indirect line by adding a line fire incrementally to the simulation, but behind the advancing edge of the fireline by an adjustable distance. Each incremental line fire is then merged with the existing fire fronts.
A parallel or tangential attack is simulated using a combination of the direct and indirect methods discussed above. Since a parallel attack is designed to maintain line production at a fixed distance from the fire front, the algorithm from the Direct Attack methods is used to calculate the fireline path. As described by Fried and Fried (1996), this tactic has the same theoretical solution as for direct attack. The path taken by the parallel attack in FARSITE is however, computed along the convex hull of a fire perimeter. A convex hull is the ordered set of vertices that defines the globally convex outermost edge of a polygon. The convex hull will be the same as all or part of a fire that is convex (eg. an ellipse or circle). This feature has the benefit of minimizing the horizontal length of fireline constructed and it allows for automatic burnout of unburned fuels in concave regions. Once the route for fireline production is computed, the fireline is constructed the same way as for the Indirect Attack. Burnout is accomplished in the same fashion as with the Indirect Attack methods described above.
Numerous studies have shown that the effectiveness of a retardant drop depends on density of the retardant applied to a specific fuel type. Heavy fuels such a timber or slash require higher retardant densities or coverage levels than uniformly fine fuels such as grass. George (19...) classifies retardant densities into six coverage levels. Coverage levels 1-6 correspond to 1-6 US gallons per 100 ft2 of ground surface (George ..).
Both simulations and field trials have shown that the length of a drop pattern is related to the volume of retardant and the density of its application (George...). Aircraft with multiple tanks or compartments can choose to open all tanks at once to apply a high concentration of retardant onto a short pattern or combinations of sequential discharges for lesser coverage and a longer pattern. For a given volume of retardant, higher densities are found toward the middle of the drop pattern and have substantially shorter length of coverage. The relationships between retardant volume, drop height, air speed, aircraft type have been incorporated into simple slide calculators (George19..).
There is a finite duration of effectiveness for all retardant applications regardless of the type (water, thickened, or foam). As retardant dries, its effectiveness in stopping fire spread is reduced. The limited duration is an important tactical consideration in scheduling retardant drops. Drops too far ahead of the fire may evaporate or dry before the fire gets there. Retardant applied to timber fuels with holdover potential may not be effective without subsequent attention from ground crews.
Obviously there are many other factors that actually affect the application and effectiveness of air attack. Air temperature, wind speed and direction, angle of aircraft approach, drop height, aircraft speed, and fire behavior