Table of contents

1. Introduction
2. Development philosophy of PHOENIX
3. The Fire Grid
4. Inputs
5. Fire Behaviour
6. Fire Perimeter Propagation
7. Asset Impact
8. Outputs

6. Fire Perimeter Propagation

This chapter addresses models that deal with the spread of the fire perimeter. This includes perimeter expansion, spot fire generation and how fire spread is ameliorated through suppression efforts.

6.1 Point Spread Modeling

6.1.2 Inputs

• Ignition point and time specified by the user;
• Fuel types;
• Fire history;
• Fuel Accumulation;
• Weather;
• Wind reduction factors;
• Wind field model;
• Slope correction;
• Fuel moisture;
• Solar radiation model;
• Road / River / Breaks;
• Self-extinction;
• Reprojection;
• Behaviour models; and
• Topography.

6.1.3 Basis

Each point on the perimeter is dealt with individually using Huygens's wavelet principle as solved by Andersen (Andersen et al. 1982). This mathematical solution to Huygen's principle was implemented in SiroFire (Coleman and Sullivan 1996). The implementation in SiroFire was used in PHOENIX with permission from the Commonwealth Scientific and Industrial Research Organisation (CSIRO). The model has similarity in structure to the operational models FARSITE (Finney 2004) and Prometheus (Tymstra et al. 2010), although it differs in the mathematical solution used.

6.1.4 Assumptions and limitations

There is no perfect solution for point-based fire spread in all circumstances; however, the Anderson solution has fewer artefacts ('tangles').
It is assumed that areas within the perimeter of a fire cannot burn more than once each simulation.

6.1.5 User interactions

The user must specify ignition location and time.
PHOENIX has a tool that can be used to automatically create a uniform ignition grid for doing scenario testing or risk analysis. This ignition grid can be created within the extent of a specified Shapefile, or within an area defined by coordinates and grid spacing.

6.1.6 Description

A fire simulation is started by igniting a fire at a particular place and time. Where point or line ignitions are specified, they are converted to polygons of nominal area. Perimeters are treated as vector (closed) polygons and are simulated to move through a landscape consisting of data at the simulation resolution. As with other Huygen's based models, fires are modelled as perimeters spreading in discrete time steps. At each time step, the locations of all points on the fire perimeter are used to sample the underlying data grids, and weather is sourced for each point. Gridded weather is sampled for each perimeter point using a spatial intersection with the NetCDF weather grid with temporal interpolation used to select the weather for corresponding points in simulation time. Where a non-spatial weather stream is used, the same weather is applied to each vertex, albeit with locally specific wind modifiers computed.

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.

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.

Woody fuel rate of spread @ 20 t/ha= 5 km/h

Grassy fuel rate of spread @ 4t/ha= 12 km/h

Average ROS = ( 5 * 15300 + 12 * 9900 + 0 * 7200 ) / 32400 = 6.03 km/h

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.

6.1.6.1 Perimeter expansion

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.

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.

In concave situations, the resulting points Pp and Pn will often cross over (a 'tangle') resulting in a rotation. This rotation is removed in a later process and the two points are replaced by a single point where the crossing vectors intersect. The parallel vector Vr is not required as it would be eliminated when the rotation is resolved.

6.1.6.2 Perimeter vertex rate of spread

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.

Figure 34. For the resulting perimeter point Pr, its rate of spread Rp the distance covered from the 'current' point divided the time step.

All subsequent fire characteristics are calculated from this rate of spread including intensity, flame height, depth, convection, etc.

6.2 Self-extinction

6.2.3 Basis

It is acknowledged that the real fireline intensity that will result in extinction is closer to 40 kW/m, but it was found that this level for extinction resulted in too many active parts of a fire edge compared with what is observed. Therefore a fire intensity that was consistent with a surface fine fuel moisture content of about 18% was used and this was found to correspond to a fireline intensity of about 120 kW/m.

6.2.4 Assumptions and limitations

The threshold is set at 120 kW/m.

6.2.5 User interactions

The self-extinction threshold is coded into PHOENIX and cannot be altered by the user.

6.2.6 Description

When a perimeter point is moved to its new position, the resulting distance travelled is used to calculate the rate of spread in the direction the point travelled. This rate of spread value is used to calculate the intensity value used in the self-extinction function. Extinct cells cannot reignite. If the fire does not self-extinguish, it will continue to burn until the end of the specified simulation period.

6.3 Reprojection on map

6.3.3 Basis

The Cosine of the slope in the direction of fire travel is calculated and used to convert the distance a perimeter point travelled along the surface to the plan-view distance.

6.3.4 Assumptions and limitations

Uses basic geometric principles.

6.3.5 User interactions

None.

6.3.6 Description

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

6.4.3 Basis

Suppression operations are simulated using an agent-based approach (Hu and Sun 2007) where agents construct an impermeable line around the fire (Smith 1986).

Construction rate limiting factors have been identified for each of the suppression methods (McCarthy et al. 2003) including: fire intensity, terrain, fuel density and in the case of aircraft, turnaround time. In contrast to limiting factors, some elements, such as road proximity, augment construction rates. This is based on field observations at real fires.

6.4.4 Assumptions and limitations

All of the resources are performing at their potential, so their suppression rates are added together.

Suppression rates are a sustained rate of production over at least an eight-hour work period. In reality, the rate would be greater earlier in the fire and lesser later in the fire.

Suppression starts at the first live fire perimeter vertex or point from the most windward (back) point of the fire, with the assumption that the back of the fire is the least intense and therefore most easily suppressed.

While going through a dead fire edge, there is no travel time or suppression effort consumed.

6.4.5 User interactions

Specifying the type and number of suppression resources and the time for them to start suppression work after ignition and the duration of their work in the suppression input data (see Section 4.9: Suppression Resources).

6.4.6 Description

Active agents simulate suppression by constructing a fireline beginning from the rear of the fire (as determined by the most windward point) and progressing forward along each flank, skipping over any previously extinguished points. The weighting of effort between flanks must be pre-specified in the project XML file. In South Eastern Australia, a weighting of 80% sinistral is typically used to account for expected wind changes (Huang and Mills 2006). The weighting of effort between flanks is continuous – hence the suppression approach is not a pure agent approach as suppression units are divisible between flanks.

Suppression rates are determined by evaluating the conditions under which each segment of the perimeter is being suppressed at each time step. The rates for each resource type are considered separately, multiplied by the resource quantity to determine resource-specific rates. The overall line construction rate is the sum of all resource type rates. Fireline construction rates for a resource type are determined by applying the piecewise linear functions specified in the suppression XML file. Examples of attributes that may affect line construction rates include fuel load, level of daylight, slope, proximity to roads and estimated flame cross-sectional area (Albini et al. 1978). Such attributes can add or decrease resource line construction rates (this was discussed in Section 4.9: Suppression Resources). If a suppression rate is calculated to be zero (which may result from extreme simulated fire behaviour), no suppression will occur in that cell.

Suppression is modelled between perimeter spread time steps. For each time step, available suppression agents are determined. The aggregate suppression rate for all active resources is calculated at each perimeter vertex and if suppressible, the fireline is 'built' along the perimeter to the next vertex at that rate. Line construction continues for a period which equates to the perimeter time step length. If a Fire Grid cell boundary occurs before the next point, the suppression rate is recalculated at the boundary. Once part of the fire is considered suppressed, all fire activity is assumed to cease and the fire will not re-ignite at that point.

If a fire perimeter vertex is found to have an intensity or other limiting factors too great to achieve any effective suppression, PHOENIX uses a 'look ahead' function to see if this is just a local aberration. If the local aberration is less than one grid cell ahead, then the suppression effort will 'jump ahead' and continue suppressing the fire perimeter with the aberrant vertices extinguished anyway. If the 'look ahead' indicates that the conditions are not conducive to effective suppression, the suppression progress around the perimeter will stall until conditions become controllable again.

Direct (fire suppression at the edge of the fire) and parallel (construction of fire line a short distance from the fire perimeter) attack are not simulated separately (National Wildfire Coordinating Group 1996). Differences in line construction rates of resulting from these methods can be considered when defining agent properties (see Section 4.9: Suppression Resources); the resolutions of PHOENIX simulations are typically not precise enough to discriminate between the two when creating maps. Indirect suppression methods, such as backburning, and strategic suppression of multiple fires are currently not supported.

6.5 Spot fires

6.5.3 Basis

Spot fire ignition is a function of the cumulative number of embers to enter a cell and the ignition probability (based on fuel type, fuel load and fuel moisture content). When ignition occurs, a new fire polygon will be created at the cell centroid. This is then spread using the same functions as the primary simulation run fire. As with the initial fire, any new ignitions have a build-up phase. Where multiple fires intersect, they will join and become a single fire.

6.5.4 Assumptions and limitations

A separate fire grid is used for the spotting process. It is fixed at 200 x 200 m cell size, regardless of what the user specifies for the general fire simulation grid size. This has been done to maintain a consistent probability of spot fire generation, for a given set of fuel and weather conditions, regardless of the simulation cell size.

Grass fuels have increased flammability due to a high surface area to volume ratio and low bulk density (Hogenbirk and Sarrazin-Delay 1995), so for the determination of ignition potential, the effective fuel load of grass fuels is increased by a factor of four.

Only embers far enough downwind from a fire front (200 m) are processed, those closer are assumed to be subsumed by the main fire and their effect on rate of spread already captured in the surface fire spread rates.

6.5.5 User interactions

None directly, but the user could alter the bark hazard levels in the fuel type definitions to increase or decrease the number of embers being produced. This should only be considered if there is strong evidence to alter the fuel type definitions to better represent the true bark hazard levels.

6.5.6 Description

6.5.6.1 Spot fire ignition grid

Starting a spot fire on every cell that exceeds a spot fire count of one is problematic as the Fire Grid cell resolution can be varied by the user. Halving the resolution will result in up to four times the number of spot fire ignitions which can drastically affect the result. To allow grid cell resolution to change whilst maintaining a consistent spot fire ignition resolution, a 200 m spot fire ignition grid is used to control the density and locating of the resulting ignitions.

When a cell impact is logged, any intersecting ignition grid cells are identified. An area-weighted spot fire density is calculated for each of these ignition grid cells by summing the spot fire densities for each intersected fire cell. If a cell is partially intersected only the intersected area is used. When the resulting spot fire density is greater than or equal to one, the ignition grid cell is flagged as ignited and a spot fire added to the landscape at its centroid.

6.5.6.2 Spot fire ignition threshold

Fuel load is treated as a proxy for the proportion of the fuel bed which has suitable fuel for ember ignition. Grass fuels have increased flammability due to a high surface area to volume ratio and low bulk density (Hogenbirk and Sarrazin-Delay 1995), so for the determination of ignition potential, the effective fuel load of grass fuels is increased by a factor of four. Where more than one fuel type exists in a cell, the cell properties are area-weighted by fuel type.

Fuel moisture content (FMC) is an important factor in the ignition potential of fuel (Ganteaume et al. 2009). McArthur's equations are calibrated for predicting the equilibrium spread rates of 'going' fires; to determine ember ignition potential, forest fuel moisture is estimated using a recently developed formula that directly estimates fine fuel moisture by considering weather inputs and calculated solar radiation (Matthews 2006). Grass fuel moisture is estimated with a grass specific function (Dimitrakopoulos et al. 2010). The ignition of a cell is based on a dynamic threshold incorporating fuel load, fuel moisture and cumulative ember load. Parameters to define the ignition terms have been obtained through iterative adjustment guided by expert opinion.

The FMC ignition probability function is based on a model for line-fire ignitions in Mediterranean grass fuels (Dimitrakopoulos, Mitsopoulos et al. 2010), modified based on the assumption that ember ignitions and forest fuels having a lower surface area to volume ratio will be harder to ignite.

Ignition Probabilty_F = 0.9 / ( 1 + e^{-(4.5 - 0.5 × fmc)} )

Dead fuel moisture content for grass is determined using the fuel moisture function from the CSIRO grassland fire spread meter (Cheney, Gould et al. 1998, Cruz et al. 2015b). The grass FMC ignition probability is the product of a grass FMC ignition probability function and the grass curing coefficient, used to describe the percentage of cured grass. The grass FMC ignition probability function is similarly based on (Dimitrakopoulos, Mitsopoulos et al. 2010) and modified assuming ember based ignitions will be more difficult than direct flame from a drip torch.

Curing_coeff = 1.12 / ( 1 + 59.2 × e^{(-0.124 × Curing - 50)} )

Igniton Probability_fmc = 1 / ( 1 + e^{-(6 - 0.263 × fmc)} )

Ignition Probability_G = Curing_coeff  × Igniton Probability_fmc

The effect of varying fuel loads in t/ha is captured by the following function, with grass loads supplied as a factor of four.

Ignition Probability_FL = 1 / ( 1 + 350 × e^-0.55×Load )