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

This chapter addresses the various models that drive underlying fire behaviour, including fire behaviour models, slope correction, convection, ember generation, fuel moisture and breaks in fuel.

5.1 Behaviour models

5.1.4 Assumptions and limitations

Many of the parameters used in PHOENIX are 'best-estimates' based on a wide range of comparisons between observed fire behaviour and modelled fire behaviour.

FFDI calculations within PHOENIX limit wind speed to 70 km/hr.

5.1.5 User interactions

None.

5.1.6 Description

PHOENIX is a novel fire behaviour simulator utilising some existing published relationships and some conceptual models based on bushfire science and experience. One of the unique features of PHOENIX is how the convective strength of the fire is used to dynamically affect the spread of the fire. Rather than being just a 2-D model or a 3-D model, PHOENIX is somewhere in between (2.5-D). This is a compromise between computational efficiency and producing realistic results.

The development objective was to have a single, universal fire simulator based on a generic description of fine fuels. This was not achieved as there was insufficient information on fuel fineness and fuel strata heights to achieve this, but effectively only two fire models were required in PHOENIX – one for grassy fuel types and one for woody fuel types.

Elements of McArthur Mk 5 (Noble 1980), McArthur prescribed burning guide (McArthur 1962), the Dry Eucalypt Forest Fire Model (Cheney et al. 2012), and CSIRO Grassland (Cheney et al. 1998) have been used. None of these models have been used without modification and all have been used with the addition of some novel components and methods of interaction. As such, PHOENIX should be seen as a new and distinct fire behaviour model.

PHOENIX is mechanistic which means that if all inputs remain the same, the outputs for each run of the simulation will also remain the same. There are no stochastic elements involved. However, distributions of expected outcomes have been used for such things as ember spread, ignition probability and ember release. Many of the parameters used in PHOENIX are 'best-estimates' based on a wide range of comparisons between observed fire behaviour and modelled fire behaviour. Stochasticity can be introduced to the simulations by way of varying the inputs such as has been done in Queensland with SABRE and was done in the Bushfire CRC with FIRE-DST (Cechet et al. 2014).

PHOENIX is dynamic in that there are several forms of feedback that drive the nature of fire behaviour. One of the best examples of this is how the size of the fire and the convective strength drives the spotting process and in turn drives the spread rate of the fire. Another example is how the fine fuel strata are conditionally included in fire behaviour calculations based on the flame height estimated from just the surface fine fuel burning. If flame heights are calculated to meet particular thresholds, the elevated and bark fuels will be added to the fuel being burnt and consequent calculations. If the flame height is less than 1 m, then only the combined surface and near-surface fuels are used in the calculation, and if the flame height is greater than 2 m, then all the combined surface, elevate and bark fine fuels are used in the fire behaviour calculations. For flame heights between 1 and 2 m, the elevated and bark fuels used are calculated proportionally, e.g. if the flame height is 1.8 m, then 80% of the elevated and bark fuels are used in the fire behaviour calculations.

The woody fuel fire spread function uses temperature and humidity values which are from two hours prior to the time step being simulated to account for the time taken for fine fuels to reach equilibrium moisture content under changing conditions (Cohen and Deeming 1985; Matthews 2006). Grass fuels reach equilibria more rapidly due to the higher surface area to volume ratios, so in the grass models, the temperature and humidity corresponding with the time step are used.

Terrain modified winds are used for all perimeter spread calculations and winds in forests are reduced by wind reduction factors specific to the fuel type. Wind reduction factors are only used in grassy type fuels if they are in grassy woodlands.

Fine fuel moisture estimation for woody fuel types is downscaled across the landscape to capture the local effects of canopy shading, incident solar radiation, wind, temperature and relative humidity. This significantly improves the fire spread modelling across the landscape even when the spatial scale of the weather inputs may be several kilometres apart.

To allow the spread functions to be used at any time of day or any time of year, a number of modifications were required. For example, McArthur's model is intended to estimate fire potential at the driest part of the day (between one and four pm) (McArthur 1967). As PHOENIX is intended to be applicable at any time, a solar radiation coefficient is calculated using the digital elevation model (Bird and Riordan 1986) and this is used to incorporate dynamic non-equilibrium diurnal changes in fuel moisture as described by McArthur (1967) (See Section 5.6: Solar Radiation Model).

At FFDIs below 12, PHOENIX uses a fire spread function that grades from the McArthur Mk5 surface fire spread prediction to one more aligned with the McArthur Leaflet 80 surface fire spread prediction. This was an empirically fitted adjustment that accounted for the effects of a reduced exposure of the flames to wind and reduced fine fuel availability at lower intensity fires which together reduced the effective surface fire spread rates. This is unique to the PHOENIX fire spread algorithm.

5.2 Spotting / embers

5.2.4 Assumptions and limitations

The ember module of PHOENIX is designed to simulate both embers lofted in the convection column of a fire and windblown embers. Embers falling less than 200 m ahead of the fire front are assumed to be accounted for in the underlying surface spread functions.

Ember launches are only performed for cells under the influence of a convective centre (see Section 5.9: Convection / Heat Centres). It is assumed that the proportion of available embers launched is dependent on the convective strength at the cell's centre.

Spotting is always run in a fixed 200 m fire grid, regardless of the fire grid size specified by the user. This ensures a consistent effect of spotting on the simulated fire behaviour.

It is assumed that the total number of viable embers reaching the ground is inversely proportional to the convective strength of the launching column and hence the time aloft or maximum ember hang-time.

5.2.5 User interactions

None.

5.2.6 Description

Windblown embers, which result from burning bark detaching from trees, are an important mechanism of fire spread in Australian forests (McArthur 1967, Wilson 1992). McArthur's forest model incorporates short distance ember ignitions as an inherent part of the fire propagation mechanism; however, long-distance convection-driven embers (Albini 1983; Sardoy et al. 2008) are only recognised as a 'maximum spotting distance'. The PHOENIX spotting model accounts for longer distance embers. When a large number of windblown embers start new fires at high densities under extreme conditions, 'mass fire' effects can occur, where fire spread rates and intensities are greatly elevated (Koo et al. 2010; Sharples et al. 2012).

5.2.6.1 Ember launch

The ember module of PHOENIX is designed to emulate embers lofted in the convection column of a fire as well as wind-blown embers travelling more than 200 m; windblown embers travelling less than 200 m at surface level are assumed to be accounted for in the underlying surface spread functions.

When a point along a fire's perimeter impacts a cell, an ember launch event is triggered. Only cells that result in intensity values greater than the self-extinction intensity (120 kW/m) are processed (see Section 6.2: Self-Extinction).

The embers available from the cell is scaled between the arbitrary range of 0 and 60 embers/m2 based on the cell's bark load (McCarthy et al. 1999).

Available Embers=1 / (1+108 * e(-1.2 ×Bark Load) )

Figure 14. Graph showing the relationship between embers available and bark load

Ember launches are only performed for cells under the influence of a convective centre. It is assumed that the proportion of available embers launched is dependent on the convective strength at the cell's centre.

Ember Porportion Launched=1.032- e-.000045 ×Convective Strength

A theoretical maximum ember 'hang-time' in minutes is calculated based on the influencing column's convective strength. This value is intended to represent the maximum time a viable ember can remain aloft, however, it is also used as a scaling mechanism that encapsulates an increased wind speed with altitude (as experienced in the vicinity of the major fires of the 7th February 2009 in Victoria). At these fires, the increased wind speed relative to surface was observed to a height of approximately 5,000 m.

Hang Time=0.6 ×Convective Strength÷10000

Hang-time values increase linearly with convective strength with maximum modelled values achieved in the Kilmore and Murrindindi fires (7 Feb 2009 in Victoria) being 28 and 36 minutes respectively.

5.2.6.1.1 Ember Dispersal

The ember dispersal process can be conceptualised as a cloud of all the available embers from a cell launching simultaneously and being distributed by the prevailing winds. The embers are transported vertically by the convection column then horizontally by the prevailing winds.

Of all the embers launched, it is assumed that only a small proportion will reach the ground in a state that could result in a spot fire with the majority burning up before reaching the ground. It is assumed that the total number of viable embers reaching the ground is inversely proportional to the convective strength of the launching column and hence the time aloft or maximum ember hang-time.

Total Viable Embers=Embers Launched × e-9×(HangTime / 35)

The transport of viable embers is modelled using the reference weather stream rather than the local terrain affected wind as it is assumed to better match the winds aloft.

Without knowing the 'actual' lofting heights, descent rates or vertical wind profile, it is not possible to capture the 'real' transport winds experienced by the spotting material. Instead, an empirically fitted 'resultant' spatial ember density distribution is calculated for each launch event and distributed across the landscape. A Weibull/bimodal distribution provided the best fit to observed spotting patterns (Sardoy et al. 2008). The bimodal distribution captured the medium to long-distance spotting phenomenon better than a traditional exponential decay model which only addresses short distance spotting.

Figure 15. Bimodal ember impact pattern used in PHOENIX. Note, the cumulative probability version of the Weibull function is used to represent this pattern in Phoenix. This graph has been generated using the Weibull probability density function using the same shape and scale parameters as the cumulative function in order to show the change in ember impact pattern with increasing hang time.

In order to determine the proportion of ember impacts in the landscape from the launch cell as the ember cloud disperses, a cumulative Weibull distribution function is used. For small convective values, the majority of embers impacting are assumed to fall within a short time of launch, however, as the hang-time increases, the majority of the viable embers impacting occur at a greater distance. The cumulative Weibull function used to describe the ember distribution takes the following form.

Figure 16. Cumulative Weibull distribution function generates the bimodal ember impact pattern observed as fires increased in convective on the 7th February 2009 and as described in Sardoy et al. 2008.

A Weibull function is also used to represent lateral ember distribution with ember hang-time. Reconstructions of Black Saturday fires show a general transition from a widening spot fire impact pattern with distance, which subsequently narrows for longer distance impacts. It is assumed that these longer distance ignitions are caused by heavier slower-burning spotting material which is less susceptible to turbulent flows in the plume which would widely distribute the smaller and lighter material.

Weibull function parameters were selected to produce an increasing lateral ember distribution for impacts up to seven minutes, which then narrows to the 15-minute mark where it asymptotes (increasingly approaching zero) in order to capture discrete viable long-distance ember impacts (Figure 17).

Figure 17. Lateral spread standard deviation showing that after an initial increasing spread period, the lateral spread decreases.

To ensure viable ember impacts along of the virtual ember cloud's trajectory are at a consistent scale to the Fire Grid, impacts are calculated at a set grid cell resolution interval of 200 m.

Figure 18. Ember impact patterns are shown matching grid resolution with a constant (left), and variable (right) wind direction.

Using the prevailing winds, the time to traverse a cell is calculated. Weather inputs are re-sampled at every cell traversal to capture any change to direction or speed. Each underlying Fire Grid cell is identified, and based on the elapsed time and the time interval, the number of viable embers impacting a cell calculated using the Cumulative Weibull distribution. The impacts are then distributed laterally assuming a normal distribution with a standard deviation derived from the lateral spread Weibull function.

5.3 Slope correction

5.3.4 Assumptions and limitations

None.

5.3.5 User interactions

None.

5.3.6 Description

Fires will spread under the influence of three separate, but interacting factors including wind, slope and fuel continuity. Depending on fuel continuity and fire intensity, fires can spread in the absence of wind and slope. However, if wind or slope affects the fire, then the rate of spread of the fire will change. The effects of wind and slope are non-linear and in addition to the effect of wind and slope alone, there can be an interaction effect.

The spread vector in the direction of the wind (Vws) is first calculated using the component of slope in the direction of the wind. A second 'Residual Slope' spread vector (Vrs) is then calculated using the component of the slope effect not already captured by Vws. This is done by comparing the slope effect on rate of spread in the direction of the wind against the zero-wind slope effect using the following equation which limits maximum slope values to 30 degrees.

Mr = e0.069s

• Where: Mr = rate of spread multiplier;
• And: s = slope relative to wind direction (capped at 30 degrees).

The two spread vectors Vrs and Vws are then added together to produce the resultant slope affected spread vector Vr.

Figure 19. The effect on slope on spread direction as well as rate due to upslope, cross slope and down slope winds.

In the case of the wind blowing directly up a slope, Vrs would be zero and have no effect on the resultant vector Vr, as the slope affect has already been fully captured by Vws. However, in the case where the wind is blowing directly across the slope, Vrs would incorporate the full zero wind slope effect which would point the resultant vector Vr up slope.

5.4 Wind field models

5.4.5 User interactions

None.

5.4.6 Description

Terrain can cause substantial deviations in wind speed and direction from prevailing winds (Forthofer 2007; Butler et al. 2004). These deviations are generally at too fine a scale to be represented in weather forecasts; however, can have large effects on fire behaviour. To compensate for this, PHOENIX can incorporate wind modification layers that represent the deviation in wind speed and direction caused by local topography for winds coming from a particular direction. This allows weather forecasts to be downscaled to a finer resolution.

Wind Ninja 2.1.x (http://www.firemodels.org/index.php/windninja-software/ windninja-downloads) can be used to generate this layer from the DEM layer. It is a mass conservation model and captures the wind speed acceleration up slope, deceleration down slope as well as channelling. It results in a fixed proportional adjustment of speed and direction for a given input direction. It is not a fluid dynamic model and therefore does not model flow separation or lee slope eddies which occur at threshold wind speeds dependent on terrain. The mass conservation approach is computationally simpler than a fluid dynamics approach and only requires terrain and open wind speed and direction inputs to be run. Fluid dynamic wind models are computationally more complex and require a lot more parameterisation of boundary layer conditions to be run. The mass conservation approach still captures some important effects of terrain on wind speed and direction. Wind modifiers are generated at 100 m resolution and exclude areas where elevation varies by less than 10 m.

Modifiers generated by Wind Ninja based on the DEM for each 100 m point across the landscape are contained in a comma-delimited string made up of the paired direction, speed change factors for each 30-degree point around the compass (Table 6) for a reference speed of 10 km/h. Zero or no change values are left blank. Input/output wind speeds and directions are integer values at 10 m above surface. The comma-delimited string for the point represented in Table 6 would be: '2,-2,-3,,5,2,,, etc.' Figure 20 contains a visualisation.

Table 6. Wind modifier values at one point in the landscape using a reference wind speed of 10 km/h.