Such a database that combines vital information is necessary to investigate options to develop a bushfire severity scale so that better fire management processes, including community information and warnings, can be put in place. The aim of this paper is to develop a measure of fire severity, or potential destructive force, focused on community impact, either by improving current FDRS by accounting for fuel and slope variability , or as a standalone scale. Therefore, a new methodology was established to assess how various measures of fire severity impact on community loss. South-eastern Australia experiences relatively frequent major fires with the bushfire danger becoming serious in some parts of Victoria every two to three years Luke and McArthur This is because of the regular occurrence of extreme weather Long , the steep topography and the accumulation of flammable vegetation as well as occasional severe droughts all of which influence fire behaviour.
Eucalypts are the dominant forest type McArthur , but there are a range of other flammable vegetation types such as mallee heath and coastal heathland Billing Due to the natural climate variability in Australia, and specifically in Victoria, large areas are prone to bushfires. Long periods of hot weather, coupled with low rainfall affect vegetation dryness and often cause drought and tinder conditions throughout the state Bureau of Meteorology Additionally, if these drought conditions are preceded by high spring rains, the summer bushfires in more grassy communities can be intense due to high grass curing and additional fuel load on the surface Bureau of Meteorology To assess the relationship between loss and the destructive power of the fires studied, several data sets were required.
Fire weather, fire behaviour, vegetation type, fuel loading, topography, community loss and house and population density information were collected for each fire. The data sets were compiled from a range of sources and each data set is discussed separately. The spatial layers and the tabular data were linked spatially so that where possible spatial information could be extracted for analysis.
Several fires were included for which no community loss was recorded so that the risk of loss could be assessed for given weather conditions. A Victorian fire history database created by the Country Fire Authority CFA and the Department of Sustainability and Environment DSE containing a digital perimeter for many fires was used; however, for some older fires pres and fires from other states, perimeters were only available as paper maps so they were scanned, digitised, geometrically rectified and then added to the geographical information systems GIS spatial database.
Many of the fires occurred over several days or were several fires that eventually coalesced. Where it was known, the fire perimeter on the day the damage was incurred was used in the analysis. Isochrones, or the locations of the fire perimeter at known times, were obtained where possible for each fire.
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Such detailed information is essential for understanding how the fire propagated pre- and post-frontal change, as well as quantifying the rate of spread at various points across the fire. The level of detail for each fire varied depending on the source and age of the fire, and unfortunately, very few fires had highly detailed isochrone information such as those available for the fires.
These data included temperature, relative humidity, rainfall and wind speed and direction. Therefore, the distance between the fire and the weather station was calculated so that this could be incorporated into the analysis. Best estimates of fuel load were taken from the literature including case study reports, journal articles and government agency documents , although some areas lacked any estimate, so modelled fuel loads were used.
Modelled fuel loads were created using fuel types, fire history and accumulation curves. Information about the grouping of fuel types and the fuel accumulation rates can be found in Tolhurst and McCarthy et al. These data were used to produce estimates of the bark load, surface load and elevated load. For consistency with the literature data, only surface fuel loads estimates from the modelled data were incorporated into the analysis.
Where there were no estimates for fuel load in the literature or modelled data, estimates were taken from Gellie et al. Community loss data were collected from a range of sources many of which were already compiled by the CFA. Estimates of economic loss were also used in the analyses.
Economic data for the fires were acquired from a recent economic loss assessment Stephenson , which is based on methods developed by the OESC These economic figures were also converted to Australian dollars. This framework was also used to calculate simple economic costs for fires other than those in Victoria. To assess the community loss in relation to the community affected, house and population density information were required. In order to be more representative in describing the impact of house loss, fatalities and economic loss in fire-affected communities, average densities were calculated over the fire-affected area only.
For house density, where possible, aerial photography obtained over a fire-affected region around the time of the fire was collected. These images were georectified, collated as a mosaic, and then each property was digitised to establish the housing density.
Aerial photography was not available for all regions and was not always feasible for ascertaining house density and for estimating the population density; consequently, Australian Bureau of Statistics ABS population and housing census data were incorporated. This was achieved by using statistical local boundaries, local government or census districts to provide the best available estimate of broad population and housing densities using the proportion of area burnt and proximity to towns.
The ABS data set at the closest time to the fire event was used. Fuel load inferred from vegetation type and fuel age Gellie et al.
Fire behaviour—rate of spread ROS. The data were taken when the FFDI was highest for the day. The DF is a function of the Keetch—Byram Drought Index KBDI , which estimates the cumulative moisture deficiency in the upper soil layers, and it also incorporates information about the rainfall record Keetch and Byram Because the indices are used for broad scale applications, both forms of the indices assume standard fuel loadings, being 4. Note that this assumes that the heat yield and available fuel remain constant around the fire, whereas recent studies e.
Linn and Cunningham suggest that the combustion processes are different for heading, flanking and backing fires, thus h and w a would vary somewhat around the perimeter. The use of the whole fire was necessary as the position of losses for older fires was unknown. However, as stated in Wade and Ward , fires are a function of fire size and the rate at which they spread since this drives the convective phases of the fire. This process draws energy from all sides of the fire perimeter.
Having a better account of fire intensity along the total fire perimeter and therefore the total energy output better describes the potential of increased convective energy.
Project Vesta- fire in dry eucalypt forest: fuel structure, fuel dynamics, and fire behaviour
Blow-outs in this study are defined as the rapid spread of fire following a major wind change when the flank turns into the head fire. The methods used to calculate the power of the fire from these blow-outs can be found in the Appendix of Harris et al. The equations are just variations on the equation for an ellipse and cover square, rectangular and triangular blow-outs. This is explained further in the next section.
One example of applying shapes to actual fire events, in this case the Murrindindi fire: B is breadth of ellipse, L is length of ellipse, B B is the breadth of the blow-out in this case a rectangle , and L B is the length of the blow-out. The average fine fuel load w was extracted from either the literature or the modelled data for the fire-affected area and assumed to equal the available fuel. The power and intensity values were then calculated using the various dimension measurements, rate of spread, fuel load estimates and heat yield.
Finally, the average slope was calculated by taking the mean slope within the fire perimeter in a GIS. Average values over the fire were used because the position of the losses was largely unknown. For the power variables, the total power from ellipse and blow-out was used. However, for fires with triangular blow-outs, PWR1 was not applicable, as a characteristic distance for a triangular blow-out is hard to determine. As PWR1 could not be calculated for triangular blow-outs, only data with PWR1 values were used for comparison of variables.
These classifications were based on previous studies such as Cheney et al. The numerical weights associated with each category were estimates of the relative reliability determined when setting up the database. These weights were used in the statistical analysis of the relationships, as described in the statistical methods section.
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The aim was to establish whether there was a relationship between any of the FDIs raw or adjusted or any of the measures of the strength of the fire the independent variable x and community loss the dependent variable Y , and if so, which measure of strength or FDI gave the strongest relationship. The data were analysed using generalised linear models McCullagh and Nelder To deal with the overly large variation overdispersion often found in count data, a quasi-Poisson was assumed.
Another possible model that can cope with overdispersion is the negative binomial model, but as pointed out by Ver Hoef and Boveng , the quasi-Poisson model gives more weight to larger losses. Since it is critical to model high losses accurately, the quasi-Poisson model was considered to be preferable.
In addition to overly large variation, count data may contain more zeros than would be allowed for by the standard distributions, and there is also a possibility of underrepresentation of zeros because of the bias towards including fires with some losses in the database.
Scientific and social challenges for the management of fire-prone wildland–urban interfaces
To deal with these situations, a hurdle model Mullahy ; Zeileis et al. In the hurdle model, there are two component models: a truncated count model that is used for the positive counts and a hurdle component that models zero versus positive counts. In the case of fatalities, for example, the hurdle model may be interpreted as there being one process that determines whether there was a fatality on a fire and another process that determines how many fatalities there were, given that there was at least one fatality.
The software did not allow a quasi-Poisson hurdle model. However, the estimates of the coefficients from the quasi-Poisson model are the same as those for the Poisson model, but the standard errors are larger Agresti Thus, the hurdle Poisson model was used to fit the data, and the standard errors were calculated using the sandwich covariance matrix estimator White , to test for the significance of the coefficients. The models were fitted using the software R R Development Core Team with the extra packages pscl Jackman , lmtest Zeileis and Hothorn and sandwich Zeileis , included for analysis of the hurdle model and for the sandwich covariance estimator.
The economic loss data were continuous and highly skewed to the right. One method of analysing this type of data is to use a generalised linear model with a Gaussian distribution and a log link which essentially assumes a Gaussian distribution of the logarithm of the data. On the other hand, economic loss is highly correlated with house loss and fatalities. As an approximation, the economic loss was rounded to the nearest million dollars and hurdle Poisson models were fitted, as the Gaussian model gave poor regression diagnostics.
The models were assessed using three goodness of fit statistics: the root mean squared error RMSE , the mean bias error MBE Willmott , and for a non-dimensional standardised measure of goodness of fit, the correlation, r , between the observed values and the fitted model predictions, as recommended by Agresti Untransformed regressor variables were fitted as this provided better error statistics than using a logarithmic transformation.
The logarithm of house or population exposure fire area multiplied by density was used as a covariate regressor variable depending on whether the independent variable was house loss, fatalities or economic loss. For comparison of models, the regressions were unweighted apart for economic loss that had different reliabilities in the Y variable , but in the final model development, the regressions were weighted.
If spread rate was estimated from the McArthur equations, or if one of the FDIs raw or adjusted was the regressor variable, the weather reliability weighting was included in the weighting. Sensitivity to the weighting was examined by fitting a non-weighted model and comparing the results. The analyses were supplemented by residual plots: residuals against fitted values, normal quantile plots of the standardised deviance residuals, square root standardised deviance residuals against fitted values and standardised Pearson residuals against leverage see Davison and Snell for details.
Correlation r , RMSE and MBE between observed and predicted values for models predicting house loss from house exposure and fire-related variables unweighted. In the following analyses for house loss, the best models for the combined data set are developed using weighted data, as appropriate, and the terms in the zero-hurdle model are tested for significance. Predicted values plotted against observed values for the prediction equation for house loss in terms of PWR1 0. Fire reliability is shown by shading in the symbols: black filled circles weight greater or equal to 0.
Goodness of fit statistics for the fitted regression models in Eqs. Coefficients and standard errors for fitted regression models in Eqs.
Standard errors are given in parenthesis. Standard errors for the hurdle Poisson count model are sandwich standard errors.