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

5. Fire Behaviour

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.

Input Direction in degrees	Topographically modified direction	Topographically modified speed	Pair direction, speed change
0	2	8	2,-2
30	27	10	-3,
60	65	12	5,2
90	90	10	,
etc

To apply the modifiers to an input wind, the proportion change is calculated and applied. For example, an input wind speed of 25 km/h at 0 degrees would result in:

Resulting speed=25 x ( -2 +10 ) / 10 = 20 km/h

Resulting direction=0 + 2 = 2 degrees

If the input wind direction falls between reference directions, then the resulting value is interpolated based on the two adjacent values.

Figure 20.Visualisation of the effect of a mountain range on wind speed and direction as captured by the wind modifier layer for an input wind speed of 40 km/h at 315 degrees. The range is evident by the line of increased wind speeds shown in red stretching from the bottom left corner to the top right corner of the figure.

5.5 Road, river and break impact

5.5.1 Purpose

Linear fuel elements with no fuel such as roads and streams can be highly disruptive to fire spread, with their effect far exceeding the area they represent. PHOENIX implements a process that attempts to capture this effect.

5.5.2 Inputs

• Fuel disruption;
• Point spread model; and
• Spot fires model.

5.5.3 Basis

Discontinuities in the fuel, mapped as linear vector fuel disruptions, are analysed on a grid cell basis. Grid cell disruption values are calculated by sampling within the cell to determine the combined disruptive width for the cell. Following this, breaches of fuel disruptions are modelled for both embers and fire perimeters.

5.5.4 Assumptions and limitations

Although disruptions are stored as a linear feature with a north-south orientation in the centre of the cell, they are assumed to affect fire spread anywhere within the cell and be orientated perpendicular to the direction of fire spread.

5.5.5 User interactions

None, except to include/exclude disruption layer from input datasets.

5.5.6 Description

Discontinuities in the fuel, mapped as linear vector fuel disruptions are converted into a raster data grid (usually 30m or 25m resolution) using GIS software (see Section 4.7: Fuel Disruption). The resultant input data file is typically called 'Disruption.zip'. This disruption data layer is then analysed on a Fire Grid cell basis. For each cell, the effective area of disruptions is calculated by using an intersection function to find the total linear length of disruptions in each Fire Grid cell which is then multiplied by the length-weighted widths from the attributes of the disruption layer. This is transposed into a single polygon with a length equivalent to the grid cell resolution and a width based on the total area of disruptions within the cell.

Figure 21. Fire Grid cell disruption values are calculated by sampling the Disruption input data cells within the Fire Grid cell to determine the combined disruptive width for that Fire Grid cell.

Fire Grid cell breaching is assessed in two ways; 'ember breaching' and 'flame breaching'.

5.5.6.1 Ember breaching

Firstly, the cell's spot fire ignition probability is checked. Then, to capture 'in-cell' or short distance spotting (< 200 m), the maximum spotting distance for the cell is calculated directly using the McArthur fire behaviour function including the subsequent spotting factor modification for bark load (McCarthy et al. 1999).
If either the cell's spot fire ignition probability is greater or equal to one (pc≥1) or the maximum spotting distance exceeds the cells disruption width, then the disruptive elements are considered breached and the fire continues unhindered.

5.5.6.2 Flame breaching

The barrier will be breached via flame if the disruption width is less than a specified multiple of the simulated flame height (Mees et al. 1993).

5.6 Solar radiation model

5.6.1 Purpose

PHOENIX incorporates a solar radiation model to determine the amount of solar radiation at each cell of the Fire Grid. Solar radiation is required as an input into the fuel moisture and suppression models.

5.6.2 Inputs

• Fuel type; and
• Topography (DEM).

5.6.3 Basis

The solar radiation model is based on the functions contained in the 'solrad.xls' Excel spreadsheet developed by Greg Pelletier of the Washington State Department of Ecology, Olympia, Washington. It is a part of the NOAA JavaScript implementation of the Bird and Hulstrom solar radiation model (Bird and Hulstrom 1981).
The cell wind reduction factor (see Section 4.2: Wind Reduction Factors) is used to determine leaf area index (LAI) used to calculate shading based on Beer's law (Silberstein, Sivapalan et al. 2003).

5.6.4 Assumptions and limitations

In the absence of cloud cover data, it is assumed that there is no cloud cover reducing the solar radiation reaching the ground, or if forecast cloud cover data is available, then it is assumed that the forecast is correct in time and space. The model incorporates slope and aspect, but not orographic shading from surrounding hills or ranges.

5.6.5 User interactions

None.

5.6.6 Description

The functions below describe the wind reduction factor to LAI conversion and the LAI to transmittance conversion.

LAI = 0.2333 Wrf² - 0.4333 Wrf+0.2

Where: LAI = leaf area index
Wrf = wind reduction factor

t = e - LAI

Where: t = transmittance (0-1)
LAI = leaf area index

5.7 Fuel accumulation

5.7.1 Purpose

Fuel levels are considered in a dynamic manner, using the time since the last fire to moderate total fuel levels for each stratum. These are then used in fire behaviour calculations.

5.7.2 Inputs

• Ignition;
• Fuel type;
• Fire history;
• Wind reduction factor;
• Solar radiation; and
• Weather.

5.7.3 Basis

Within PHOENIX, once a fuel type has been determined from the fuel input data grid, a lookup table ('FuelTypes.xml') is used to calculate the fuel levels for the 'combined surface', 'elevated' and 'bark' fuel strata. This calculation is based on the fuel type and the time since last fire. The fuel lookup table stores three parameters of a negative exponential fuel accumulation curve for each fuel type. These values are then combined and used in the Fire Grid for use by the PHOENIX simulation.
Assumptions and limitations

After a fire, the fuel level in each stratum (surface, elevated fuel and bark) is assumed to follow a modified Olson accumulation pattern (Olson 1963; Birk and Simpson 1980) with the modification that the value at time zero is not necessarily zero. That is to account for the fact that there is often some residual fine fuel after the passage of fire.
In Victoria, the peak fuel levels and the rate of accumulation after an understorey fire have been based on a lot of fuel sampling across the State over a 40 or so year period. However, the accumulation rates are very general and do not reflect all the variation in geographic conditions across the distribution of each fuel type and they do not reflect variation in accumulation rates due to the nature of the seasonal conditions following a fire event. Over time, some refinements of these accumulation rates have been made based on local observations.
In NSW, fuel accumulation rates in forested areas were specifically studied and incorporated into their fuel lookup table. However, non-forest fuel types have been treated more like the Victorian process. Fuel accumulation rates in other states have been derived in a similar way as they have been in Victoria. This has provided a good working base with the expectation that values in the fuel lookup tables will be refined and improved over time.
At present, there is no distinction made between fires of different intensities on fuel accumulation rates. The assumption currently used with fuel accumulation rates is that they are the rates expected after a surface or understorey type fire. Users should be aware that intense fires that have resulted in structural changes to the vegetation may result in fuel accumulation rates different to those generally used in PHOENIX.

User interactions

Users may modify the parameters for the fuel accumulation curves and the wind reduction factors in the fuel lookup table (FuelTypes.xml) using an editing tool in PHOENIX; however, it is not recommended to be done without careful consideration.

Description

Fuel loads are considered in a dynamic manner, using the time since the last fire (see Section 4.3: Fire History) to estimate the accumulated fuel load. After a fire, each stratum of fine fuel (surface, elevated fuel and bark) is assumed to follow a modified Olson curve accumulation pattern (Olson 1963; Birk and Simpson 1980). Fuel accumulation rates and the overall equilibrium levels are specified in the fuel description file (FuelTypes.XML) for each fuel stratum within each fuel type using a three-parameter negative exponential curve. Fuel types also include a Wind Reduction Factor (Wind RF), designed to capture the varying effect different fuels have on wind speed at 1.5 m above the ground (Figure 22, also see Section 4.2 Wind Reduction Factors).

Figure 22. Fuel type lookup table showing surface, elevated and bark re accumulation rates for fuel type 7.

Fuel levels are expressed in hazard classes (HC) based on the Overall Fire Fuel Hazard Guide (McCarthy et al. 1999). Parameters r, k and c determine the current hazard class based on the equation below.

HC = r1 - e - kt + c

Where: HC = hazard class (0-5)
r = range of change in hazard class
k = reaccumulation rate
t = years since last fire
c = post-fire hazard class (= effective minimum hazard class immediately after fire)
r + c = equilibrium (maximum) hazard class

Internally, fuel hazard classes are converted to an equivalent fuel load (t/ha) using the following equations

ls = ( -22.17HC ) / ( -9.605 + HC )

Where: ls = surface fuel or grass load in t/ha
HC = hazard class

le = 11.49 / ( 1 + 1107.8e^-1.78HC )

Where: le = elevated fuel load in t/ha
HC = hazard class

lb = 7.431 / ( 1 + 937.8e^-1.905HC )

Where: lb = bark fuel load in t/ha
HC = hazard class

5.8 Fuel moisture

5.8.1 Purpose

Fine fuel moisture is an important component for fire behaviour calculations. PHOENIX incorporates a fine fuel moisture model.

5.8.2 Inputs

• Fuel;
• Wind reduction factor;
• Solar radiation; and
• Weather.

5.8.3 Basis

The PHOENIX fine fuel moisture model has been adapted from a Python script provided by Stuart Matthews of CSIRO (Matthews, Gould et al. 2010). It is a simplification of his multiple-layer process model, but more complex than the fuel moisture model used in Project VESTA. The PHOENIX adaption has not been published.
Grass fuel moisture is estimated with a grass specific function (Dimitrakopoulos et al. 2010).

5.8.4 Assumptions and limitations

Grass fuel moisture is assumed to react instantaneously to changes in temperature and relative humidity (Cheney and Sullivan 2008) and therefore does not directly include solar radiation affects.
Woody fuel moisture is assumed to have a two-hour lag time in response to changes in atmospheric temperature and relative humidity. Therefore, weather data two hours prior to the ignition time is used to run the simulation in wood fuels.

5.8.5 User interactions

None.

5.8.6 Description

The PHOENIX fine fuel moisture model uses screen (1.5m) weather (see Section 5.2: Wind Reduction Factors) and surface solar radiation (see Section 5.6: Solar Radiation) to determine fine fuel moisture content. Forest fine fuel moisture is calculated for each Fire Grid cell.
Forecast weather data does not incorporate the effect of the fire on the atmosphere. Large fires can entrain enormous amounts of air into the convection column and can heat cool air as it passes over the burning area, preventing or at least delaying the landscape downwind from experiencing forecast changes.
Fire behaviour lag time in response to fire weather conditions is addressed in PHOENIX by implementing a two-hour lag for temperature and relative humidity values. This two-hour lag attempts to capture the effect of the coupling between the fire and atmosphere on downwind weather conditions and the moisture diffusion rate in the fine fuels.
Grass fuel moisture is assumed to react instantaneously to changes in temperature and relative humidity (Cheney and Sullivan 2008) and does not directly include solar radiation. Grass fuel moisture is estimated with a grass specific function (Dimitrakopoulos et al. 2010):

Mf = -0.19625t + 0.1356r + 9.575

Where: Mf = grass fuel moisture (%odw)
t = air temperature in °C
r = relative humidity %

5.9 Convection / heat centres

5.9.1 Purpose

The outputs of the convection model are used in conjunction with wind speed and direction to support the simulation of ember lofting and distribution. The resulting ember impacts are used to start spot fires (see Section 6.5: Spot Fires) as well as in asset impact calculations (see Chapter 7: Asset Impact).

5.9.2 Inputs

• Fire perimeter propagation model; and
• Weather.

5.9.3 Basis

PHOENIX has developed a simple, empirically derived representation of convection processes. There were no existing simple models for bushfire plumes that predict their convective strength or their effects on spotting, air quality or destructive potential. The PHOENIX model has made several advances in describing the convective elements of bushfires. Empirical validation of modelled convective centres, based on observed physical damage to trees and buildings, shows a good match between predicted location and extent and those observed in real bushfires.

5.9.4 Assumptions and limitations

The convection heat centres model assumes that convection columns will form over the hottest 25% of a fire perimeter.
Whilst the PHOENIX convection model shows promising results it is important to recognise its underlying functions are based on a simplified atmospheric boundary layer conditions and are fitted to events of a single day.

5.9.5 User interactions

None.

5.9.6 Description

With any fire, columns of convecting gases develop as a result of the heat being released. As fires become larger and more intense, these convection columns become substantial, reaching high into the atmosphere and affecting surface wind fields (Potter 2012).
The computation of fire-atmosphere interactions in fire models requires substantial processing due to the need to consider the interactions and feedbacks between fire, the landscape and the atmosphere in three dimensions (Coen et al. 2013). Currently, WRF-Fire and Access-FIRE have been developed to capture the full fluid dynamic effects of a coupled fire-atmosphere system, but the computational overheads of these models restrict their use to research (Chong et al. 2012bd). At the time of PHOENIX development, there were no simple models for bushfire plumes that predict their convective strength or their effects on spotting, air quality or destructive potential. Therefore, one was developed as part of PHOENIX. To keep processing times to within operational requirements, PHOENIX uses a simple, empirically derived representation of convection processes, and has made several advances in describing the convective elements of bushfires. In PHOENIX development, efforts to date have focused on identifying surface level, dominant heat centres (convective centres) and using them as a predictor of plume locations and strength for ember dispersal. The algorithm performs a surface level aggregation of fire perimeter segments (heat centres) where they are deemed close enough to interact and act as one.
The model developed has been used to provide more realistic results in the PHOENIX ember dispersal and house loss probability model (Chong et al. 2012d). For details on the validation of this model, refer to PHOENIX RapidFire 4.0's Convection Plume Model (Chong et al. 2012d) University of Melbourne and Bushfire CRC technical report.

5.9.6.1 Heat segments

The first step in identifying potential convection columns or plumes is to locate relatively hot parts of a fire's perimeter (heat segments). This has been defined as the perimeter segments having an average intensity value in the top 25% of perimeter intensity values.
A PHOENIX fire perimeter consists of a series of ordered vertices, forming a polygon. A vertex intensity value for the identification of a heat segment is its average value for the preceding time step. Input and output data for PHOENIX are stored in the Fire Grid, the size of which is specified by the user. A vertex may traverse multiple grid cells, each resulting in a different rate of spread and resulting intensity value.
A heat segment's intensity value is smoothed out using a running average over 10 perimeter points or 10% of the total perimeter points, whichever is smaller. The heat segment begins when the intensity of the cell exceeds the 25% threshold and ends where a cell drops below this threshold.

Figure 23. The fire perimeter is shown in green with dots representing vertices, white pixels indicate a section that has been identified as being in the top 25% of perimeter intensities. The running 10-point average in red is shown traversing the perimeter, entering and exiting the 25% threshold value.

Multiple ignitions, topography, varying fuel types and load and variable weather can generate complex fire perimeters, and these often generate more than one active convection column.

Figure 24. Early stages of the Bunyip Ridge fire on 7 Feb 2009 showing two distinct convective centres. Photo by Lex Wade.

The PHOENIX convection model allows for multiple distinct heat segments to be identified within a fire to reflect the multiple active fire fronts that can exist within a bushfire.

Figure 25. Results from three separate ignitions that have merged resulting in a complex perimeter shape with multiple active fronts, behaviour which regularly occurs in large bushfires where spotting and highly variable topography or fuel is prevalent.

5.9.6.2 Column merging

Heat segments individually do not necessarily reflect the size and strength of a fire's dominant convection columns. For a single regularly shaped elliptical fire this is expected to be the case, however regularly shaped fire perimeters are the exception rather than the rule in naturally occurring bushfires. A large fast-moving bushfire can have multiple active fronts and spot fires each with their own associated convection column. In these cases, any convection columns forming are likely to be an aggregate of multiple local heat sources merged to produce a locally dominant column. The PHOENIX convection model attempts to reproduce this phenomenon by aggregating heat segments where they are deemed to be close enough to interact.

Figure 26. The image on the left shows heat segments identified after three regularly shaped elliptical fires have merged compared to the image on the right that shows heat segments identified in a fire modelled in a natural landscape with has resulted in significant spot fires.
Note the irregular shape and spatial distribution of the heat segments in the right-hand image.

PHOENIX utilises a recursive merging algorithm that aggregates heat segments where they are deemed to interact. Each heat segment is first identified as a potential convection column whose heat output is that of the perimeter vertices it contains. Vertex point intensity (kW/m) is converted to total heat output in kilowatts (kW) by averaging the values between two vertices and multiplying by their distance apart. Column convective output is expressed in megawatts (MW).

A column's 'centre of gravity' is calculated using vertex locations weighted by their intensity. A minimum bounding box is determined for the heat segment. The single segment column's area of influence is expressed as its effective radius (Columner) which is set as a function of its minimum binding boxes dimensions (E). This radius is inclusive of the area of convective indraught effect outside of the burning area which is assumed to be an additional 10% of the burning area radius.

Column_er =  1.1 × ( E_h + E_w ) / 2

Single heat segment columns are then sorted in descending order based on convective output. Starting with the strongest, each is tested against lesser columns and merged if within their effective radius.

When a heat segment is merged into a column, a new minimum bounding box is recalculated based on the vertices of the new heat segment, the additional heat output is added, and the column's location or centroid is adjusted to reflect the new heat source.

The merging process is recursive and continues until all merging is complete.

Figure 27. Series of images showing the development of three fires in a flat, homogenous landscape. Circles show estimated position of convection columns as they merge (darker circles indicate greater convective output).
Columns are initially independent but as fires get progressively closer, they merge to form a single column.

All heat segments, including those from separate fires (spot fires or multiple ignitions), are processed in the same recursive algorithm to capture the heat distribution in the landscape (Figure 28).

Figure 28. Diagram showing how the recursive merging algorithm processes heat segments from separate fires.