Future changes in climatic water balance determine potential for transformational shifts in Australian fire regimes

Most studies of climate change effects on fire regimes assume a gradual reorganization of pyrogeographic patterns and have not considered the potential for transformational changes in the climate-vegetation-fire relationships underlying continental-scale fire regimes. Here, we model current fire activity levels in Australia as a function of mean annual actual evapotranspiration (E) and potential evapotranspiration (E0), as proxies for fuel productivity and fuel drying potential. We distinguish two domains in E , E 0 space according to the dominant constraint on fire activity being either fuel productivity (PL-type fire) or fuel dryness (DL-type fire) and show that the affinity to these domains is related to fuel type. We propose to assess the potential for transformational shifts in fire type from the difference in the affinity to either domain under a baseline climate and projected future climate. Under the projected climate changes potential for a transformational shift from DL- to PL-type fire was predicted for mesic savanna woodland in the north and for eucalypt forests in coastal areas of the south–west and along the Continental Divide in the south–east of the continent. Potential for a shift from PL- to DL-type fire was predicted for a narrow zone of eucalypt savanna woodland in the north–east.


Introduction
Fire is a profound organizing force for ecosystems (Bowman et al 2009), a significant contributor to global biogeochemical cycles (van der Werf et al 2010) and a major influence on human populations in fireprone environments (Gibbons et al 2012, Chuvieco et al 2014. Projected changes in global fire patterns (Krawchuk et al 2009, Westerling et al 2011 in response to future climate, rising atmospheric [CO 2 ] and land use are highly uncertain, limiting our ability to predict the response of terrestrial ecosystems to global change. Fires occur across the continents with characteristic distributions of size, intensity, frequency and season, forming a small number of distinct 'pyromes', or broad syndromes of fire regimes (Archibald et al 2013). How these syndromes emerge from interactions of climate, vegetation, land use and human behaviour remains incompletely understood, hindering the predictions from dynamic global vegetation models (DGVMs) and other approaches that seek to predict land surface dynamics under global change (Kelley andHarrison 2014, Scheiter et al 2014). Incomplete knowledge about the biophysical relationships that control global patterns of fire increases uncertainty about the potential for widespread fire regime shifts under altered future climates. So far, most studies have focused on quantifying changes in the frequency of fire occurrence under future climate conditions (Krawchuk et al 2009, Pechony and Shindell 2010, whereas the potential for transformational changes in the processes underlying continental-scale fire regimes is less clearly understood (but see e.g., Lindenmayer et al 2011, Bowman et al 2014. Here, we propose a modelling framework for evaluating the potential for change in the average rate of burning (i.e. fire activity level) as well as for changes in fire type (i.e. transformational shifts) under altered future climates.
Fuel production and desiccation are the two fundamental processes underlying all fire regimes as fires will only burn across landscapes when there is sufficient fuel (i.e., combustible plant biomass) and when that fuel is dry enough to burn (Meyn et al 2007, Bradstock 2010. Frequencies of ignitions and favourable fire weather conditions also affect fire activity and behaviour once fuel load and fuel dryness constraints are overcome (Bradstock 2010). Thus fuel production and desiccation provide the functional platform on which potential fire activity is based and on which the influence of other factors, such as short term fluctuations in fire weather, variations in ignition and management activities, will be conditional. Thus an understanding of the relationship between fire activity and these two fundamental biophysical constraints on fire is necessary to delimit ecosystems where potential pathways of change under future climates may differ.
Essentially, fuel productivity and fuel dryness are a function of the local water and energy budgets available for the production and desiccation of plant biomass, and therefore a function of climate. Over annual or decadal time scales, the climatic water balance summarizes the simultaneous availability of biologically usable energy and water at a site (Budyko 1958, Stephenson 1998 where W is total precipitation infiltrating into the soil, E is actual evapotranspiration, and E 0 is potential evapotranspiration, while S and D are the mean annual climatic water surplus and deficit, respectively (all in mm yr −1 ). At annual timescales actual evapotranspiration (E) is a reliable predictor of continental patterns of annual primary productivity (Rosenzweig 1968, Yang et al 2013 and hence a reasonable proxy for fuel production rates. The potential evapotranspiration ( ) E 0 is an absolute measure of evaporative demand and proportional to energy available for desiccating live and dead fuels. Therefore, we hypothesized that continental variation in mean annual fire activity levels is well predicted by a combination of mean annual E and E 0 (Littell and Gwozdz 2011). If true this would provide an approach to evaluate the potential for incremental changes in mean annual fire activity levels under projected future climates. To evaluate potential for qualitative changes in the processes underlying continental-scale fire regimes ('transformational shifts', as developed in next paragraph) we focus on the relative importance of fuel productivity and fuel dryness constraints on fire activity levels.
As shown by Krawchuk and Moritz (2011), the relative importance of fuel productivity and fuel dryness constraints on global fire activity varies in a predictable way among the world's biomes according to their net primary productivity levels. Fuel productivity is the primary constraint on fire activity levels in lowproductivity ecosystems with discontinuous vegetation cover such as semiarid woodlands (O'Donnell et al 2011). Fuel dryness, in turn, limits fire activity in high-productivity ecosystems (e.g., temperate closed forests) where fuels are abundant year-round but too wet to burn for much of the time (Bradstock 2010, Caccamo et al 2012, Archibald et al 2013. Since fuels are a derivative of vegetation type, we hypothesized that fuels would differ qualitatively with the relative importance of productivity and dryness constraints. Grasses and herbaceous plants can be expected to be the main source of fuel where productivity limits fire, and litter, foliage and fine branches from woody shrubs and trees where dryness limits fire activity, but this remains to be demonstrated. The combination of vegetation/fuel type and dominant constraint on fire activity sets important boundary conditions for other key characteristics of continental-scale fire regimes, such as typical fire intervals, intensities and season of burning (Archibald et al 2013, Murphy et al 2013, Whitman et al 2015. Given these climate-vegetationfire relationships Paula 2012, Bowman et al 2014), a shift from one dominant climate constraint on fire activity to the other in response to altered climate conditions would represent a transformational shift in fire type and a qualitative change in ecological functioning. We hypothesized that environments characterized by either fuel productivity limitations on fire (PL-type fire) or fuel dryness limitations on fire (DL-type fire) occupy distinct climate domains that can be defined by a combination of mean annual E and E . 0 If true this would provide an approach to evaluate potential for transformational shifts in fire type (i.e., from PL-to DL-type fire or vice versa) under projected climate change.
To test these hypotheses we analysed Australian patterns of fire activity, climate water balance and fuel types. Australia is a highly fire-prone continent; on average 500 000 km 2 or 7% of its land area is burned annually (Russell-Smith et al 2007, Giglio et al 2013, representing a nationally significant source of carbon emissions (Haverd et al 2013). Australia's fire regimes are highly diverse (Archibald et al 2013, Murphy et al 2013 and many remain relatively unmodified compared with those of fire-prone environments on other continents . The paper first presents a modelling framework for quantification of the relative importance of fuel productivity (PL) and fuel dryness (DL) limitations on continental fire activity patterns and for the identification of the two corresponding climate domains, where either productivity-limited fire (PL) or dryness-limited fire (DL) prevails. We use quantile regression modelling to define how the upper limit of fire activity responds to fuel productivity and dryness and the corresponding domains of these controls on potential fire activity. We then demonstrate how this climate-fire model can be used with projections of future climate to assess the potential for incremental changes in fire activity levels and transformational shifts in fire type under projected climate conditions for the end of the 21st century.

Material and methods
2.1. Fire activity index Gridded, 0.01°×0.01°resolution (ca 1 km×1 km), fire frequency data for 1997-2010 covering the Australian continent were obtained from the AusCover remote sensing data portal (http://www.auscover. org.au/node/58) of Terrestrial Ecosystem Research Network (TERN). Here, fire frequency was defined as the number of times a pixel has been affected by fire in the observation period 1997-2010. The fire frequency estimate was derived from manual mapping of fire affected areas at fortnightly time steps using continental imagery from the Advanced Very High Resolution Radiometer (AVHRR) (Turner et al 2012). The 0.01°×0.01°resolution fire frequency data, with a range of 0 for unburned pixels to 14 for annually burned pixels, was used to calculate a fire activity index at 0.05°×0.05°resolution with a data range of 0 to 1 by: (i) aggregating and summing values of 25 (i.e., 5×5) 0.01°pixels, and (ii) dividing resulting values by 350 (i.e., 14 years×25 pixels). The resulting fire activity index, F, quantified the mean annual burn fraction of each 0.05°×0.05°grid cell.
2.2. Climatic water balance, mean annual E and E 0 Gridded, 0.05°×0.05°resolution (ca 5 km×5 km), climate data covering the Australian continent, including daily precipitation (P) and minimum and maximum air temperature, were obtained from the SILO data base (Jeffrey et al 2001). The Modified Hargreaves equation (Droogers and Allen 2002) was used to quantify mean monthly potential evapotranspiration (E 0 ) from extraterrestrial radiation, mean daily temperature range and mean monthly rainfall. The Modified Hargreaves equation is recommended for predicting E 0 , rather than the Penman-Monteith method, where accurate meteorological data are unavailable (Droogers and Allen 2002), such as in vast areas of inland Australia. Mean annual actual evapotranspiration (E) was estimated from mean annual P and E 0 using the semi-empirical model proposed by Budyko (1958): where AE is the aridity index computed from mean annual P and E 0 ( ) AE = E P 0 / . The Budyko curve was developed for predicting mean annual runoff (Q) and actual evapotranspiration ( ) = -E P Q from large catchments and is widely used in hydroclimatology and water balance studies (Potter andZhang 2009, Williams et al 2012).

Climate-fire model
The extent to which current fire activity is limited by fuel productivity or fuel dryness was quantified by modelling variation in the fire activity index as a function of mean annual E and E 0 over the same period (i.e., 1997-2010). A three-dimensional scatterplot of the data revealed strong increases of F with E and a humped relationship with E 0 (appendix S1 in supporting information). The limiting effect of E and E 0 on fire activity is best captured by the upper quantiles of F, because for those F observations we may assume that all other constraints that act on fire activity but are not explicitly included in the model (i.e. fire weather and ignitions) are non-limiting (Cade and Noon 2003). Lower quantiles of F may also show trends with E and E 0 and excellent fit to the data but do not provide the same level of inference about the fire-limiting effect of E and E 0 as for the upper quantiles (appendix S3). Importantly, prediction of future changes in the climatically determined fundamental domains of fire (i.e. fuel productivity versus fuel dryness) based on the upper limit of fire activity will be free of confounding influences, of for example, extant land use, fire management activities and ignition patterns. Use of a model for future projections of the changes to the climatically determined domain of fire, which implicitly incorporated these influences (i.e. at quantiles below the maximum) would require the unrealistic assumption that all other influences on fire would remain constant in the future. Our approach provides a pathway for a systematic, complementary exploration of the consequences for fire of changes in climate and other human influences.
The total data set for Australia consisted of 239 230 (0.05°×0.05°) grid cells representing the total continental land area under native vegetation cover. A randomly selected sample of 50% of the data (119 615 grid cells) was used for model fitting, leaving the other 50% of the data for model validation (appendix S2). Using the 'quantreg' package in R (R Development Core Team 2015) a nonlinear model was fitted to the 0.99 quantile of the fire activity index, F , 0.99 with mean annual E and E 0 as independent variables. A good fit was obtained for a model that combined two logistic terms: where, F 0.99 is the 0.99 quantile of the fire activity index, E and E 0 are mean annual actual and potential evapotranspiration in mm yr −1 , and = -D E E 0 or mean annual climatic water deficit (Stephenson 1998), and a, b, c and d are fitted coefficients (appendix S2, table S1).
To minimize bias towards arid and semiarid climates in the fitted climate-fire model, we used the following bootstrap procedure: (i) the continental E E , 0 space was divided into 100 mm×100 mm bins and all bins with a minimum of 10 grid cells identified (n=143), (ii) a random sample (with replacement) of 10 grid cells was drawn from these bins, and (iii) equation (2) was fitted to the sample data. This procedure was run 1000 times to generate 1000 response surfaces from which a mean response surface was calculated (figure 1(a)).
We hypothesized that there would be two distinct domains for the climate-fire relationship: (i) environments of PL-type fire characterized by F 0.99 increasing predominantly with E, and (ii) environments of DL-type fire characterized by F 0.99 increasing predominantly with E , 0 plus a narrow transition zone where F 0.99 was likely to be equally sensitive to both E and E . 0 We tested this hypothesis by graphing quantitative contours of F 0.99 in the two dimensional space defined by axes representing variation in mean annual E and E . 0 For the sake of simplicity, we ignored the transition zone and divided the E E , 0 space into two domains depending on the direction of the gradient of the fitted F 0.99 response surface. After rasterizing the F 0.99 response surface into 10 mm×10 mm E E , 0 grid cells the local slope direction (i.e. aspect) of every grid cell was decomposed into an E component, where a F is the aspect of the F 0.99 response surface in radians. All E E , 0 grid cells where > g g E E 0 were classified as being in the domain of PL-type fire and all others, where  g g , E E 0 as being in the domain of DL-type fire. This classification was applied to each of the 1000 fitted F 0.99 response surfaces yielding 1000 classifications from which a probability of being classified as PL-or DL-domain could be calculated for every E E , 0 grid cell (figure 2(a)). These probabilities were mapped to geographical space for the 1986-2005 baseline climate (figure 2(b)) and future climate using gridded mean annual E and E 0 for the corresponding period. Gradients and aspects of the F 0.99 response surface were computed using terrain analysis functions available in the 'raster' package for R (R Development Core Team 2015), while the 'intamap' package was used for spatial interpolation of PL-and DL-domain probabilities.

Fuel types and tree cover
The relationship between the dominant climate constraint on fire (i.e., fuel productivity or fuel dryness) and fuel type (i.e., grass versus litter from woody plants) was investigated in two steps. We first used an existing field data set of fuel loads and ground-based observations of tree cover for 113 sites across Australia (D M J S Bowman, B P Murphy and M A Cochrane, unpublished data, appendix S5, figure S7) to analyse the relationship between fuel composition and tree cover. We then used the moderate resolution imaging spectroradiometer (MODIS) data set of remotely sensed tree cover (MOD44B Collection 4 product, version 3, 500 m resolution) to analyse how continental tree cover varies with the modelled probability of being in the domain of PL-or DL-type fire as a test of our hypothesis that the relative strength of fuel productivity and fuel dryness constraints on fire is related to fuel composition. Tiled MOD44B data for the Australian continent was mosaicked to one layer and resampled to the 0.05°×0.05°grid used for the climate variables (appendix S5, figure S7). The relationship between MODIS tree cover percentage and probability of classification to the domain of DL-type fire was analysed by binning all Australian grid cells (n=239 230) in one of five probability classes (i.e. from 0 to 1 in 0.2 increments) and quantifying the distribution of MODIS tree cover percentage for each class ( figure 3(b)). The relationship between MODIS tree cover percentage and remotely sensed fire activity across Australia was analysed using nonparametric quantile regression with the 'quantreg' package in R (R Development Core Team 2015).

Projected climate
Projected changes in mean monthly precipitation and temperatures for 2080-2099 were obtained from the climate change in Australia data portal (CSIRO and  (2)) and the probability for being in the domains of fuel production limited fire (PL-type) or fuel dryness limited fire (DL-type), indicated by blue and pink tones respectively. Strictly, the colour scale indicates probability of DL-type, which equals 1 minus probability of PL-type. The white area and the dashed black line indicate the transition between the two domains (i.e., probability for either domain=0.5). The white dot (a 0 ) shows the current position of an arid environment, where fire activity would respond strongly to increasing E(a 2 ) but not to increasing E 0 (a 1 ). The black dot (b 0 ) shows the current position of a more humid temperate environment, where an increase in E 0 (b 1 ) would imply a strong increase in fire activity and create potential for a transformational fire regime shift, while an increase in E(b 2 ) would have a minor incremental effect on fire activity. Bureau of Meteorology 2015b). As our main goal was to demonstrate how our climate-fire model could be used to assess potential for incremental and transformational changes in fire activity and fire type, we selected projections from one CMIP5 (Coupled-Model Intercomparison Project) model and one representative concentration pathway (RCP). A full CMIP5 ensemble analysis was beyond the scope of the present paper.
The ACCESS1-0 model has been shown to simulate historical climate in Australia particularly well (CSIRO and Bureau of Meteorology 2015a). We obtained ACCESS1-0 projections of change with respect to 1986-2005 baseline in mean monthly precipitation and temperatures by 2080-2099 under RCP4.5. Under RCP4.5, radiative forcing of the global climate system is assumed to stabilize at ∼4.5 W m −2 after 2100, which is in the lower half of the range (CSIRO and Bureau of Meteorology 2015a). The projected change grids had been resampled by the data provider using bilinear interpolation from the native model resolution of 1.00°×1.00°to the 0.05°×0.05°grid used in this study. Future climatologies for mean monthly precipitation, and minimum and maximum air temperature were computed by adding the projected changes for 2080-2099 to gridded historical climate data (1986)(1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005) from the SILO data base (Jeffrey et al 2001). Projected mean annual E 0 and E for 2080-2099 was calculated from projected climate inputs as described above for the baseline climate.

Climate change impact assessment
The potential for future changes in fire activity and in the probability of falling in the domains of PL-or DLtype fire was assessed by comparing each grid cell's E E , 0 coordinates for the 20 year baseline period  with those projected for the future period (2080)(2081)(2082)(2083)(2084)(2085)(2086)(2087)(2088)(2089)(2090)(2091)(2092)(2093)(2094)(2095)(2096)(2097)(2098)(2099). Climate conditions during the 1986-2005 baseline period differed slightly from those during the climate-fire modelling period 1997-2010 (appendix S4, figure S6). Potential change in predicted F 0.99 was computed from the difference between the predicted F 0.99 for each grid cell's E E , 0 coordinates under 1986-2005 baseline climate and the projected 2080-2099 climate. Similarly, the potential for a shift from PL-to DL-type fire or vice versa was assessed for every grid cell from differences between baseline and future probabilities of being classified to the domain of PL-or DL-type fire, which in turn are a function of the uncertainty about the form of the fire response surface (as estimated from 1000 model fits) and baseline and future E E , 0 coordinates.

Climate-fire model
Current patterns of fire activity in Australia based on remote sensing of fire-affected areas were a nonlinear, yet highly predictable, function of mean annual E and E 0 ( figure 1(a)). The fitted model for F 0.99 (equation (2)) explained a large proportion of the continental variation in maximum fire activity levels for a given combination of mean annual E and ( E adj. 0 R 2 : 0.89, RMSE: 0.09) and model residuals were close to normally distributed (appendix S2). Low levels of F 0.99 were observed, as expected, in the driest and coldest environments of the continent characterized by low E and low E , 0 respectively. The highest levels of fire activity, with F 0.99 exceeding 0.8, was recorded in environments of intermediate to high E and very high E 0 corresponding to the tropical savannas of northern Australia, where the current fuel production and fuel desiccation potential supported (bi-) annual burning (Russell-Smith et al 2007). The form of the fitted F 0.99 response surface (figure 2(a)) supported the hypothesized dichotomy of two distinct domains of climate limitation on fire activity: (i) relatively hot and dry environments where F 0.99 was more sensitive to E than to ( E i.e., 0 PL-type fire), and (ii) relatively cool and humid environments where F 0.99 was more sensitive to E 0 than to E (i.e., DL-type fire). Interestingly, the transition between the domains of PL-and DL-type fire was predicted to fall at a nearly constant ratio of E 0 and E of about 1.46±0.03 (appendix S2, figure S3). This makes sense as the amount of energy required to dry out fuel to ignitable levels should be proportional to fuel productivity. When mapped to geographical space the two domains are sharply separated, with PL-type fire prevailing throughout the interior of the continent and DL-type fire restricted to the most humid coastal regions ( figure 2(b)).
3.2. Fuel type, tree cover and climate constraints on fire activity Field observations of fuel composition and continental patterns of tree cover fitted the hypothesized pattern: high proportions of grassy fuel were found in the domain of PL-type fire (appendix S5, figure S7(a)), while tree cover, which is inversely related to the maximum grass component of fuels ( figure 3(a)), was significantly higher in the domain of DL-type fire than in the domain of PL-type fire (appendix S5, figure  S7(b)), with a shift in the probability of being in the domain of DL-type fire observed at MODIS tree cover of circa 60% ( figure 3(b)). Tree cover was not only a predictor of fuel type but also strongly related to the maximum level of fire activity in the landscape. Across Australia fire activity was highest in ecosystems with less than 30% tree cover, decreased gradually for ecosystems with tree cover between 30% and 50%, and dropped to the lowest levels in ecosystems with tree cover exceeding about 55% ( figure 3(c)).

Impact of projected climate change
Under RCP4.5 the future climate in Australia was projected to become substantially drier in much of south-western Australia, the Kimberley, Tasmania, eastern Victoria and south-eastern Queensland, while substantial increases in mean annual precipitation were projected for Northern Queensland, and in parts of the arid interior and along the east coast of New South Wales ( figure 4(a)). By 2080-2099, mean annual potential evapotranspiration, was projected to increase in much of the continent, particularly in the southwest, and to decrease in Northern Queensland ( figure 4(b)). The projected changes in mean annual precipitation and potential evapotranspiration translated into proportionally strong changes in mean annual E ( figure 4(c)).
Combining the F 0.99 response surface ( figure 1(a)) with the projected change in mean annual E and E 0 yielded strong predicted increases in potential fire activity for Northern Queensland, parts of the northern interior, and the south-east of the continent, while decreases in the upper quantiles of fire activity were predicted for part of the south-west, southern Kimberley and Cape York ( figure 4(d)). Our analysis showed that under projected future climate conditions there were some areas with potential for transformational shifts in fire type, but that potential for such transformation was restricted to relatively small areas and to be predominantly from DL-to PL-type fire ( figure 5, table 1).
In tropical Northern Australia, potential for a shift from DL-to PL-type fire was predicted for relatively small areas (ca 7624 km 2 in total) of mesic eucalypt savanna woodland in the Northern Territory where the projected increases in E 0 would cause fuels to dryout earlier in the dry season and mean annual fire activity levels to increase ( figure 5(a), table 1). Potential for a shift from PL-to DL-type fire was predicted for a narrow band of eucalypt savanna woodland in the Cape York Peninsula and along the western slopes of the Great Dividing Range in Northern Queensland (ca 5646 km 2 in total) ( figure 5(a)). Potential mean annual fire activity in these areas is currently very high ( F 0.99 ≈0.7); future climate conditions were projected to become wetter and warmer (figure 4), creating potential for increased fuel production, an increase in fire activity and fuel dryness becoming the dominant climate constraint on fire ( figure 5(a), table 1).
In south-east Australia, transformational shifts from DL-to PL-type fire were projected for a scattering of small areas mostly along the Continental Divide (ca 18 380 km 2 in total) characterized by temperate eucalypt forest. In these areas climate conditions for 2080-2099 were projected to become warmer with significant increases in E , 0 creating potential for increasing mean annual levels of fire activity and for fuel productivity rather than fuel dryness becoming the main limiting factor for fire activity ( figure 5(b), table 1). In the coastal zone of south-west Western Australia an area of ca 3975 km 2 of predominantly temperate eucalypt forest was also projected to change from DL-to PL-type fire while mean annual fire activity levels were projected to increase slightly. These changes were predicted to result from drier future climate conditions caused by a decrease in mean annual precipitation and an increase in mean annual E 0 ( figure 4, table 1).

Discussion
The spatial pattern of the upper limit of mean annual fire activity was strongly related to mean annual climate conditions in Australia, consistent with previous studies of continental and global fire patterns (e.g., Krawchuk et al 2009, Archibald et al 2010. Significantly, 89% of the spatial variation in the 0.99 quantile of mean annual fire activity levels in Australia was explained by two components of the climatic water balance, mean annual actual evapotranspiration (E) and potential evapotranspiration ( ) E . 0 We proposed to model fire activity as a function of the climatic water balance terms E and E , 0 rather than the more commonly used mean annual or monthly precipitation and temperature (Spessa et al 2005, Daniau et al 2012, Batllori et al 2013, because E and E 0 are more directly related to a site's water and energy constraints on fuel production and fuel desiccation (Di Bella et al 2006, Littell and Gwozdz 2011, Parks et al 2014; the resulting climate-fire model, though statistical, has a sound biophysical basis (Bradstock 2010) and provided an excellent fit to the data.
As expected, fire activity was found to be lowest where either fuel productivity ( ) µE or fuel dryness constraints on fire ( ) µE 0 are strong and highest where favourable conditions for both fuel production and desiccation are met. Our hypothesis that the relative importance of fuel productivity and fuel dryness constraints on fire activity is correlated with continental variation in fuel composition and tree cover was also confirmed by our analyses. Environments with low tree cover and dominated by grassy fuels, which prevail in most of Australia (Murphy et al 2013), were shown to be associated with a predominance of fuel productivity constraints on fire activity (PL-type fire), while environments with high tree cover and litter fuels were associated with strong fuel dryness constraints on fire (DL-type fire). The finding that tree cover and fuel type in Australia varied consistently with E and E 0 supports Stephenson's (1998) proposed use of the climatic water balance as a biologically meaningful predictor of vegetation composition at (sub-)continental scales.
Our results demonstrated that the climatic water balance sets important boundary conditions for key aspects of fire regimes (e.g., fire activity levels and return intervals, intensity range, season) through its influence on the type of fuel and on the frequency/seasonality with which fuel load and dryness limitations on fire are overcome under a given climate. The consistency and predictability with which these fire and fuel characteristics vary with position in E E , 0 space provides a robust framework to objectively evaluate potential for incremental changes in upper quantiles of fire activity levels as well as for qualitative shifts in the processes that underlie fire regimes under altered future climate conditions. As noted, this provides potential for evaluation of the potential for changes in fire regimes as a function of climatic change that are largely independent of likely changes in human activity.
Though the concept of variable productivity and dryness constraints on fire activity has been quantified before (Meyn et al 2007, Littell et al 2009, Krawchuk and Moritz 2011, Batllori et al 2013, Pausas and Ribeiro 2013, Bistinas et al 2014, Bowman et al 2014, we provide the first quantitative evidence that the continental-scale dichotomy of PL-and DL-type fire may be determined by the climatic water balance. Importantly, the analysis demarcates clear climatic and geographical boundaries between these different fire types. Such boundaries also correspond, according to  2080-2099(RCP 4.5, 1986-2005 in Northern Australia (a), South-east Australia (b), and South-west Australia (c). In blue coloured areas there is potential for change from the domain of DL-to PL-type fire. In pink coloured areas there is potential for change from the domain of PL-to DL-type fire, while no domain change is projected for grey areas. Blue boxes in the inset map show approximate locations of the three regions of Australia. Numbers 1-4 are used to refer to areas of potential change in table 1. expectations based on inherent fuel type, with different Australian vegetation communities and associated fire regime syndromes , Murphy et al 2013. The proposed biophysical framework was built from first principles of how climatic energy and water balances interact at annual to decadal time scales to constrain fuel types and their flammability (Stephenson 1998). These principles should also hold for future environments in Australia and globally (e.g., Parks et al 2014) and therefore provide a robust model for assessing the potential for fire regime shifts under 21st century climate projections. Moreover, by modelling fire types as a function of the climatic water balance our framework is, in principle, well-suited to evaluating changes in fire that may come about through changes in fuel productivity per unit of water use (i.e., water use efficiency, WUE) under elevated atmospheric CO 2 concentrations (Leakey et al 2009). CO 2 -driven increases in ecosystem-level WUE could lower fuel-productivity constraints on fire activity in environments of PL-type fire, particularly in temperate Australia where C3 grasses prevail (Murphy and Bowman 2007), but concurrent warming and associated increases in atmospheric water demand could offset CO 2 -related fuel productivity gains (Morgan et al 2011). In environments of DL-type fire, CO 2 -driven increases in WUE are unlikely to affect fire activity levels via an increase in fuel productivity but could have an effect via changes in the timing and/or duration of periods of low canopy water content. The form of the F 0.99 response surface ( figure 1(a)) and therefore the climatic boundaries of the fire type domains (figure 2) could change if elevated atmospheric CO 2 would alter the competitive relations between grasses and woody plants in fire-prone ecosystems (e.g., Bond andMidgley 2012, Kelley and. Though our modelling framework has a biophysical basis, our assessment of potential fire regime shifts due to climate change is essentially a space-for-time substitution and has the associated limitations such as: (i) the inability to predict a response to novel future climates (Williams andJackson 2007, Blois et al 2013), (ii) the inability to account for the potentially very different time scales with which vegetation composition, tree cover, fuel type, fuel productivity and fuel dryness may respond to climate change across soil types (Krawchuk and Moritz 2014), or (iii) the inability to resolve transient ecosystem dynamics or novel outcomes of interacting ecosystem components (Bowman et al 2014). Our predictions of fire regime shifts therefore focused on evaluating whether projected changes in the climatic water balance would imply a move across the climatic boundary between DL-and PL-type fire. Where such a domain shift is climatically possible we assume that there is also potential for significant changes in fuel type and related fire regime characteristics (e.g., fire interval, intensity, size, season) to develop over long time scales (>>decades), but our modelling framework cannot resolve the actual trajectory or rate of change. These predictions could inform more complex modelling approaches such as DGVMs that do represent the transient dynamics of ecosystem change.
Our analysis suggested that under RCP4.5 projected changes in the climatic water balance by the end of the 21st century are of a magnitude and direction that could cause significant change in upper quantiles of fire activity levels ( ) F 0.99 in about a quarter of the continent (figure 4), with increases predicted for 20% of the continent and decreases for 6% of the land area. These findings are consistent with the nature and magnitude of changes in annually burnt area predicted by the LPX-Mv1 DGVM under RCP4.5 for the end of the 21st century (Kelley and Harrison 2014). Our analysis showed the potential for transformational fire regime shifts to be restricted to relatively small areas on steep environmental gradients (figure 5). Though the likelihood of these changes remains to be quantified by a full ensemble analysis, our results strongly indicate that even under a moderate RCP there may be substantial change in fire activity over vast areas with potential implications for continental carbon fluxes Our prediction of the locations in Australia where there is potential for transformational fire regime shifts (figure 5) is conditional on the specific climate projection used in this study. However, because the boundary between the domains of DL-and PL-type fire is very sharp and well-defined, both climatically and geographically (figure 2), we can have confidence that transformational fire regime shifts will most likely occur in areas located near or within the transition zone, irrespective of the climate change scenario. Since that transition zone falls on relatively steep sections of the continental gradients of E and E 0 (figure 2(b)) we infer that transformational fire regime shifts are unlikely in the vast majority of the continent. This insight is useful as it allows further research into transformational fire regime shifts to focus on a small number of sensitive environments.