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Spread from each vertex is processed with the appropriate fire spread function (see Section 5.1: Behaviour Models) and contributing input vectors (e.g. wind speed, wind direction, slope) to determine point spread ellipses (Anderson et al. 1982). These are used to derive subsequent perimeter position for the initialisation of the next time step. If necessary, new vertices are added between existing perimeter points to ensure that the minimum resolution is equal to the simulation grid (Fire Grid) resolution. In PHOENIX, the dynamic time steps are defined by the time for the fastest spreading part of the fire to travel a specified distance, similar to that in Prometheus (Tymstra et al. 2010). This spread distance is a function of the Fire Grid size. The maximum duration of a time step is fixed, and is nominally 5 minutes.
Figure 29. Perimeters are represented by a set of clockwise ordered points which are incrementally expanded based on a specified time step.
Cells can contain a mix of woody fuels, grassy fuels and, bare areas and the resulting spread rate is assumed to be the area-weighted average of all three.
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Key: F – Woody Fuel, G – Grassy Fuel, N – No Fuel
Figure 30. As cell size increases fuel types within a cell can become highly variable. An area-weighted average value for rate of spread will ensure some of this variability is captured compared to a centroid sampling approach.
Take for example a 180 m resolution Fire Grid cell (32,400 m2) that has a fine fuel load of 20 t/ha covering 15,300 m2 and a grass load of 4 t/ha covering 9,900 m2 with the remainder (7,200 m2) bare ground.
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PHOENIX also incorporates a unique 'crawling' process to process perimeter changes between time steps. Between time steps, the movement vector of a perimeter point is recalculated each time it enters a new input grid cell. At the end of a time step, the position which results from the additive spread vectors through all cells crossed is reported. This process ensures that all fuel cells impacted by fire are processed and avoids the issue of rapidly spreading perimeters 'skipping over' cells that have extremely high or low fuel levels. In addition, computational efficiency is retained as points with slow spread rates are only calculated once each time step, and rapidly moving points are calculated more frequently. This reduces the number of calculations required for slow-moving parts of the fire without reducing overall simulation resolution, maximising computational efficiency. Fires spread as perimeters. Areas within the perimeter of the fire cannot burn more than once each simulation.
Figure 31. Unconstrained point spread on the left versus the 'grid crawling' approach on the right for a single time step. In the unconstrained approach, the resulting point has jumped over five cells based on the resulting distance and direction calculated at its original position, failing to capture the effects of five underlying cells. With the grid crawling approach spread rate and direction are recalculated at the intersected cell's boundary, indicated by the green dots. This ensures any changes in fuel types, loads, condition and topography are captured.
Small fires undergo a build-up phase until they reach a particular size where a steady-state rate of spread is achieved (McAlpine and Wakimoto 1991; Finney and McAllister 2011). PHOENIX incorporates this by assessing the conditions shortly after ignition and calculating the time required for an elliptical fire to reach a width of 100 m. This value was used as grassfires have reached equilibrium spread rates under most wind conditions by the time the headfire is 100 m wide (Cheney and Gould 1995). While PHOENIX can simulate multiple fires with a single run, surface (perimeter) spread is based entirely on Hugyen's system, and there are no dynamic interactions of surface fire perimeters (e.g. junction zones, Morvan et al. 2011). Where separate fires meet, they merge into a single fire and are subsequently treated as a single perimeter polygon. While there are no interactions in surface spread, the grid-based approach in the ember module allows the recognition of convective interactions between fires (see Section 5.9: Convection / Heat Centres). This affects ember transport and ignition. Multiple ignitions can be modelled in a single simulation, although for processing efficiency where fires are far enough apart to be considered spatially independent, they should be modelled separately.
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Fire spread calculations start from the most windward point (the back of the fire) and progress clockwise until the perimeter is complete. Each vertex is initially treated as an ignition point with a resultant ellipse determined based on a head-fire rate of spread and time step incorporating any slope that may affect the ellipse orientation. Based on the neighbouring points three vectors are calculated to determine which section of the ellipse will best represent the resultant perimeter segment. Vp is the vector from the previous perimeter point to the current point, Vn is the vector from the current point to the next point and Vr is the resultant vector of Vp + Vn.
Figure 32. The image on the left shows the resultant ellipse for a perimeter point. On the right are the three vectors which will be used to determine which section of the ellipse will best represent the resulting perimeter segment.
The vectors Vp, Vn and Vr are then transposed as touch tangents on to the outside surface of the ellipse with the points at which they touch (Pp, Pr and Pn) being the resulting points on the new perimeter.
Figure 33. The image on the left showing vectors Vp, Vr and Vn being transposed on the outside of the point ellipse. On the right are the resulting new perimeter points Pp, Pr and Pn which are added as ordered points to the new perimeter.
Three points are created when the perimeter shape at the 'current' point is extremely convex as shown in the example above. When the perimeter shape at the 'current' point is relatively straight only the point at resultant vector (Vr) is used. In convex or concave situations, the two points resulting from Vp and Vn are used.
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Generally, the term 'rate of spread' refers to the head-fire rate of spread; however, when modelling a perimeter, the rate of spread will generally vary significantly. To determine the rate of spread of each vertex its distance travelled is divided by the time step.
All subsequent fire characteristics are calculated from this rate of spread including intensity, flame height, depth, convection, etc.
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Figure 35 illustrates the process of converting from the plan view representation of the perimeter on the Fire Grid, to a three-dimensional representation.
Figure 35. The Fire Grid and resulting fire perimeters are plan view representations, whereas fire spreads on the surface of a three-dimensional landscape. Therefore, a conversion is required.
6.4 Suppression model
6.4.1 Purpose
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