Overview

Illustration of the vertical fuel layers that can define a forest fuel complex.

Background

There are many Australia-specific bushfire behavior models that predict how fire will move across a landscape under local fuel, weather & topographic conditions. This is a reflection of the diversity of fire regimes across the country: the spread rates and intensities of bushfires are driven by different factors in eucalyptus forests than in grasslands.

As a result, each bushfire model requires a different set of input datasets that are tuned to the requirements of the model and to the ecosystem where it will be run. These can generally be categorized into the following groups:

• Patterns of ecosystem structure, like vegetation height and canopy cover, which moderate wind behavior and the likelihood of canopy torching.
• Estimates of fuel abundance/density, like leaf litter and and bark fuel density, which predict energy release and spread rate.
• Normalized hazard scores, which use semi-empirical methods to estimate how fuel abundance and ecosystem structure interact (these are normally scaled from 0-5).

We have plenty of experience modeling the patterns of ecosystem structure that are inputs to several of these fire spread models, but less experience estimating fuel abundance and density.

We've been provided with a series of documents regarding now NSW RFS estimates these patterns—with empirically-derived fuel accumulation curves—and this document is a review of the a) how these models work and b) how we'll develop custom fuel abundance maps.

---

The negative exponential model

Fuel accumulation curves are based on a few key premises:

1. As plants grow and senesce, they drops leaves and branches that accumulate on the ground.
2. The rate of accumulation is driven by two factors: 1) the rate of decomposition and 2) how much time has elapsed since the last fire.
3. The rate of decomposition can be empirically estimated on an ecosystem-by-ecosystem basis.
4. There is a limit to the maximum amount of litter that can accumulate in an area. This occurs when an ecosystem enters a steady-state condition: accumulation occurs at the same rate as decomposition.
5. Fires reduce the total amount of fuel on the landscape through combustion, though the total amount consumed varies with the intensity of a fire. The amount of fuel that remains post-fire is considered the "initial" fuel amount.
6. Fuel accumulates faster in the years that immediately follow a fire and slows as the ecosystem approaches its steady-state.
7. Fuel accumulates at different rates for different strata. The majority of fuel accumulates in the surface stratum, but the amount of herbaceous and shrubby vegetation can be estimated using this method, too (which is characterized in the near-surface and elevated strata).

These premises are encoded in a negative exponential model form, which is represented as:

c = i + [(l_max - i) x (1 - e^(-k x t))]

Where

• c = Current fuel density estimate (in tons/ha)
• i = Initial or post-fire fuel density (tons/ha)
• l_max = Limit or maximum fuel density (tons/ha)
• k = Annual fuel accumulation rate (0-1 fraction, estimated as k = l / l_max, where l = the amount of fuel that accumulates in a year)
• t = Time since last fire (years)

Put simply, the amount of available fuel at a location approaches the maximum fuel density as a function of the annual fuel accumulation rate and the amount of time elapsed since the last fire.

The parameters l_max and k have been estimated for many veg forms and sub-forms. We'll be using previously-published values for these instead of trying to re-estimate them ourselves, but we'll use satellite fire detections to create our own time-since-fire maps.

---

Fuel strata

These parameters are estimated separately for each of the different vertical fuel strata that are represented in bushfire models. The primary strata are:

• litter or surface fuels – leaves, twigs, bark and other dead plant material lying on the ground, with a predominantly horizontal orientation. This layer may contain partly-decomposed matter, and usually contributes the bulk of the fuel available for burning.
• near-surface fuels – grasses, low shrubs, creepers and collapsed understorey whose orientation includes a mixture ranging from horizontal to vertical.
• elevated fuels – tall shrubs and other understorey plants with a primarily upright orientation.
• bark fuels – flammable bark on tree boles and branches.

The majority of field work has been done to estimate surface fuel parameters, which was synthesized in this 2012 review by Penny Watson. The next most information is on bark parameters, synthesized in this 2012 review by Horsey and Watson.

Watson's 2012 review provided parameters for near-surface and elevated fuel loads, but they should probably be thought of as "reasonable estimates from an expert in the field" and not "precise quantitative estimates numerically derived from data." That's to say there's the most uncertainty around these values.

These sources provide a wide array of data for each parameter, detailing how the data were collected, the quality ratings, and the methods used to translate numbers to consistent units. But fields were often missing or available for only a subset of forms/subforms, meaning we had to make choices as to how to fill in data where there was none.

---

Our approach to estimating fuel accumulation

We've created a table with a list of parameters for each form/sub-form, and I've added notes in this section describing how we did this and why we made certain choices.

Watson 2012 provided measured estimates of litter fuel parameters for l_max and k for several subforms within each veg formation. For example, data were available for Cool Temperate Rainforests, Subtropical Rainforests and Northern Warm Temperate Rainforests, which make up 3 of the 9 Rainforest sub-forms. She then recommended a weighted average value for each parameter be used for the whole formation.

We are instead using the measured parameters for each sub-form where data are available. Sub-forms with custom measurements are marked in the table as Measured == 1. Sub-forms with Measured == 0 use the formation-level recommended averages.

Near surface and elevated fuels

From these formation-level litter fuel parameters, Watson then estimated rates for litter + near surface and elevated fuels. The litter + near surface values are often very close to the standalone litter values, and the elevated rates were typically much lower than the litter values (because litter accumulates each year, and the elevated fraction represents mostly live, upright vegetation).

Since the litter + near surface and elevated parameters are only estimated at the formation level, we need a way to estimate them for the sub-forms that have measured litter parameters. We did this by computing a linear scalar that represents the relationship between litter and the remaining two parameters.

The form of the scalers is simple: scaler_elevated = param_elevated / param_litter (this is applied to both elevated and litter + near_surface)

The example above shows the formation-level parameter estimates for Wet Sclerophyll Forests. The scaling factor to convert between k_elevated and k_litter is 0.15/0.45, or 0.33. The Southern Escarpment sub-form has a measured k_litter value of 0.38—lower than the form-level value—and after applying the scaling factor, k_elevated for this subform would be 0.38 * 0.33, or 0.127.

These scaling factors allow us to compute litter + near surface and elevated fuel loads with more precision in the subforms where field measurements have been made. The assumption behind this approach is that the relationships between accumulation rates in different strata are stationary within formation types.

Forms without parameters

Watson 2012 provided estimates for the parameters i, l_max and k for six vegetation forms:

• Rainforests
• Wet sclerophyll forests (grassy subforms)
• Wet sclerophyll forests (shrubby subforms)
• Dry sclerophyll forests (grassy subforms)
• Dry sclerophyll forests (shrubby subforms)
• Grassy woodlands

Gordon and Price provided parameter estimates for a few classes in two forms:

• Heathlands
• Forested wetlands

Several sub-forms from the above contain no parameter estimates. Additionally, there are 8 other formations where this detailed information is unavailable. Yet we still need to estimate them.

Fortunately, RFS 2019 published a guide to estimating fuel hazard scores for the Vesta Mk2 model that includes summary table with aggregated l_max parameters that include surface + elevated.

Cross-referenced with the forms estimated in Watson 2012, these numbers are the sum of l_max for litter, near surface and elevated. This table includes aggregated l_max numbers for the 10 forms without fine-grained parameters, and we'll use these aggregated numbers to and estimate appropriate parameters for each vertical strata.

There will be a bit of uncertainty regarding the estimated l_max numbers. But the litter strata dominates the signal, and in all the other veg. forms the parameters for near surface and elevated are often so closely related to the litter numbers that we can typically use the same estimation approach used by Watson 2012:

• l_max for the litter + near surface is usually 0-1 tons/ha greater than litter alone
• k for litter + near surface is within ± 0.1 of the litter value for k
• l_max for elevated is typically in the range of 2.5-5 for shrub-dominant formations, and in the range of 0-2 for forms without heavy shrub cover
• k for elevated ranges from 0.15-0.25, and it appears that ecosystem productivity is the main driver of variation (with higher k values in more productive systems)

Approximating k values

Since RFS 2019 only provides information for aggregated l_max scores, we're left without empirical guidance as to the appropriate value for k in the 10 formations without parameters. This means that we'll have the highest uncertainty around these numbers.

This uncertainty is mitigated to a degree: k is typically most important in areas that have recently experienced fire, as it estimates the fuel accumulation rate based on the time since fire, and the majority of recent fires have been in areas with measured k values. So most areas are likely to be in steady-state conditions (i.e., approximating l_max).

Still, we have to estimate this parameter. I've chosen to do so by comparing the bioclimatic conditions in forms without k estimates to the conditions in forms with k estimates.

Since k represents the rate of accumulation over time, with high values in productive ecosystems (0.7 in rainforests, 0.45 in wet sclerophyll forests, 0.2-0.3 in dry sclerophyll forests), I'll be using my best judgment to consider how temperature, cloud cover, and LAI patterns might determine the productivity of a system, and match unestimated k values to the most climatically-similar formation's k values.

Formations that are hot and dry with low vegetation cover will receive low k scores. Cooler, wetter and more productive systems will receive higher k scores.

Salo-estimated parameter justification

The l_max parameter that is reported in RFS 2019 is the sum of l_max for the litter, near surface and elevated strata. In estimating these parameters, I've ensured the assigned values sum to the value estimated by RFS 2019.

Semi-arid woodlands (Grassy subformation). Hot and arid system with very low l_max from RFS 2019. Set low l_max for all classes, and low fuel accumulation rate, especially in the elevated stratum because this is a grass-dominated system.

Semi-arid woodlands (Shrubby subformation). Hot and arid like the grassy subform, but with higher litter productivity indicated by a higher l_max in RFS 2019. Set l_max higher across the board, especially in the elevated stratum, while keeping k values low across the board to track slow annual accumulation in this arid system.

Semi-arid woodlands (Mallee subforms). This is an inland subform that supports higher total canopy cover from Eucalyptus spp. and was assigned a higher l_max than the other shrubby subforms above. Minor increases in i, l_max and k for all stratum relative the the semi-arid shrubby subforms.

Coastal Swamp Forests. High l_max value, presumably with much of the litter accumulation stored in seasonally-flooded soils. Akin to the Rainforests formation, I set a high k rate to indicate high productivity and rapid decomposition. There's only minor accumulation in the near surface stratum. The elevated stratum was assigned a high l_max but a low k to track slow understory recovery/high potential biomass storage in swamp systems.

Forested Wetlands. Much lower l_max values than the Coastal Swamp Forests. Kept k values high in the spirit of high productivity/rapid decomposition, while assuming most of the accumulation will occur in the litter stratum. Due to limited shrub cover, l_max is low for the elevated stratum.

Heathlands (tall heath per RFS 2019). The highest l_max of all formations. This subform occupies a cool, wet climate that supports vigorous vegetation growth, indicating high fuel accumulation rates. This is a dense-shrubland system, so the elevated stratum was assigned a high l_max, though I think we should double check the maximum estimate for how many tons/ha could possibly be stored in shrubby biomass. And while the l_max scores are high, the k rates are about average, tracking that this system can accumulate large amounts of fuel after a long-ish period post-disturbance.

Heathlands (short heath). Assigned around half of the l_max score of the tall heath class. We removed the majority from the litter and near surface strata, keeping a relatively high l_max for the elevated stratum, and keeping the k values pretty similar to the tall heaths (slow growth, high max accumulation).

Arid shrublands (Acacia subformation). Arid system without sufficient precipitation to support trees. Low overall l_max scores were more evenly-split that usual between the litter and elevated stratum on the assumption that these evergreen shrubs don't cycle leaves often and a lot of the biomass is stored in standing vegetation.

Arid shrublands (Chenopod subformation). Akin to the Acacia subform, this is an drought-adapted system without much turnover and without much annual vegetation growth. Low l_max, low k, and 0 i values on the assumption that a fire in these systems will consume the litter bed.

Freshwater wetlands. Annually flooded systems with few trees. Low l_max likely due to rapid decomposition or storage in underwater peat. Assigned a high k value for each stratum assuming rapid recovery in flooded system.

Alpine complex. This formation is mostly dominated by low-and-slow growing plants, so near surface values of l_max were higher than they usually are above the litter values. Low values across the board for the elevated stratrum, due to low shrub cover. Alpine Heaths were assigned the parameters from the short heath forms (per RFS 2109).

Grasslands. Medium l_max values, assigned mostly to litter and near surface strata, with very low elevated accumulation. Relatively high k values were assigned because grassland systems recovery quickly post-fire.

Saline wetlands. We're totally winging it here: there's no l_max estimate published by RFS 2019. So we're using the Coastal Swamp Forest parameters for the Saline Mangroves, and the Forested Wetlands parameters for the rest.

Bark fuel loads

I'll let Penny Watson introduce bark fuels:

Bark is one of the most variable features across Eucalypt species. At the broadest scale Eucalypts can be divided into those that shed their dead bark annually (the smooth barks) and those that retain their dead bark, which accumulates year by year on the trunk and branches (the rough barks). Within the latter category, the persistent bark varies widely in texture, fibre length and thickness. Between these two categories are species, commonly referred to as “half‐barks”, whose bark is persistent to variable heights on part, or all, of the trunk.

Here's why it's critical to estimate bark loads for predicting fire behavior:

Bark contributes to bush fire behaviour through three particular mechanisms. First, dead bark retained on trees contributes to the overall fine fuel load of a forest. Bark which has been completely shed is usually considered a part of the surface fuel load, in some cases making a considerable contribution). Second, bark can act as a “ladder fuel”, by carrying flames vertically from the surface into the tree canopy, leading to crown fires. Third, certain bark types are the major contributor to the “spotting” process in which glowing or flaming pieces of fuel are transported by wind and convection currents to propagate new, spot fires beyond the fire front

Bark fuel density can be estimated using the negative exponential model. Horsey and Watson 2012 wrote a synthesis document with guidance for mapping bark fuel loads with this approach, providing empirical estimates for the i and l_max parameters.

Based on the finding that charring rates vary between ecosystems—meaning that different amounts of charred bark persist following a fire in different formations—they insist that the i parameter is critical for bark mapping.

Less critical, however, was estimating different accumulation rates between formations. Based on the data available, they concluded that uniformly setting k to 0.1 was sufficiently general. We're taking their word for it.

They provided parameters for 39 classes within the Wet & Dry Sclerophyll Forests, for both grassy and shrubby subforms, as well as for Grassy Woodlands. We use those exactly as-is, and I took a guess as some parameters for the rest of the classes without measurements.

All Alpine, Grassland, Cleared, and Arid classes were set to 0 on the presumption that Eucalypts are sparsely dispersed in these areas. Likewise for all Wetlands formations. So I was mostly guessing parameters for the forest/heath/semi-arid forms.

Rainforests used the average i and l_max values from the Wet Sclerophyll Forests (shrubby subform) formation, but I subtracted 0.5 and 1.0 from these numbers under the assumption that Eucalyptus spp. are not as abundant in these systems.

Heathlands used i and l_max from the Western Slopes Dry Sclerophyll Forests class. I left this unedited. This had a low set of values, which I chose because I suspect Eucalypts are uncommon but still present in Heathlands.

Semi-arid woodlands (Shrubby subformation) used the average i and l_max from the Dry Sclerophyll Forests (shrubby subform) formation.

Semi-arid woodlands (Grassy subformation) used the average i and l_max from the Dry Sclerophyll Forests (grassy subform) formation.