CSIRO PUBLISHING International Journal of Wildland Fire 2012, 21, 313–327 http://dx.doi.org/10.1071/WF11044 Spatial variability in wildfire probability across the western United States A,B,G C D Marc-Andre´ Parisien , Susan Snetsinger , Jonathan A. Greenberg , C E F Cara R. Nelson , Tania Schoennagel , Solomon Z. Dobrowski B and Max A. Moritz A Northern Forestry Centre, Canadian Forest Service, Natural Resources Canada, 5320 122nd Street, Edmonton, AB, T5H 3S5, Canada. B Department of Environmental Science, Policy and Management, University of California – Berkeley, 137 Mulford Hall 3114, Berkeley, CA 94720, USA. C Department of Ecosystem and Conservation Sciences, College of Forestry and Conservation, University of Montana, 32 Campus Drive, Missoula, MT 59812, USA. D Department of Geography, University of Illinois at Urbana-Champaign, 607 South Mathews Avenue, MC 150, Urbana, IL 61801, USA. E Department of Geography, University of Colorado, Boulder, Boulder, CO 80309, USA. F Department of Forest Management, College of Forestry and Conservation, University of Montana, Missoula, MT 59812,USA. G Corresponding author. Email: 314 Int. J. Wildland Fire M.-A. Parisien et al. North America. For instance, fire frequency metrics – computed far from true, as all but the most remote areas have some trace for large ecological or administrative areas from spatial fire of human influence (Cardille and Lambois 2010). The study atlases in the United States (Stephens 2005; Bartlein et al. 2008) of ‘natural’ fire regimes in areas – or time periods – of low and Canada (Stocks et al. 2002; Parisien et al. 2006) – have human influence is certainly pivotal to our understanding of provided a coarse estimate of subcontinental fire variability. fire–climate–vegetation interactions, but accurate estimates of There has also been an effort to classify fire regimes into a few current wildfire probability in North America require anthro- synthetic condition classes in order to evaluate the departure pogenic activities to be taken into account. For example, even from historical fire regimes (Hardy et al. 2001). Some investi- though much of the Great Plains was once fire-dominated gators have developed wildfire–climate relationships to map (Brown et al. 2005), widespread agriculture has rendered this monthly or annual predicted ignition probability (Balshi et al. area ill-suited for fire ignition and spread. 2009; Preisler et al. 2009), whereas others have linked long-term The purpose of this study is to build on previous investiga- climatology to decadal patterns in area burned (Skinner et al. tions of subcontinental fire activity to spatially evaluate the 1999; Gedalof et al. 2005). By developing fire–climate models likelihood of wildfire in the 11 westernmost states of the for ecological zones in the western USA, Littell et al. (2009) conterminous USA. This was achieved using a statistical frame- have implicitly accounted for the effect of dominant vegetation work that linked high-resolution patterns of area burned from type on annual area burned. Parisien and Moritz (2009) explic- 1984 to 2008 to a set of variables chosen to represent the ignition itly incorporated vegetation classes, in combination with patterns and vegetation, as well as climate normals, extremes mapped climate normals, to map relative wildfire likelihood and seasonality, that characterise this 25-year period. In addition across the USA. In contrast to these studies, which are statisti- to producing high-resolution estimates of wildfire probability, cally based, Finney et al. (2011) used a fire simulation model to we examined the influence of environmental factors on its produce wildfire probability estimates for 134 landscapes that spatial variability. In order to assess the anthropogenic imprint were composited to cover the entire conterminous USA (Finney on wildfire likelihood, we created a second model for which we et al. 2011). omitted all variables affected by human activities. Finally, we Despite recent progress in understanding continent-wide examined whether the exclusion of small fires, which burn a North American wildfire likelihood and wildfire–climate rela- minute fraction of the total area, is a reasonable simplification in tionships, studies to date often ignore ignition sources and the this type of modelling. presence of sufficient biomass for combustion (‘fuel’). Although three environmental factors must coincide for fire to Study area occur – available fuels, periods when weather conditions support combustion and ignitions – they rarely act indepen- The study area comprises the 11 westernmost states of the 6 2 dently of one another (Moritz et al. 2005). For instance, whereas conterminous USA (,310 km ) (Fig. 1). It covers a broad climate has a direct effect on fuel moisture and combustion, environmental spectrum that encompasses extreme variation in these same conditions also affect fire indirectly by controlling geology, landform, climate, vegetation and land use (Barbour patterns in vegetation (Krawchuk et al. 2009; Bradstock 2010). and Billings 2000). The climate of the area is controlled by two This dual influence of climate is best illustrated using the Sahara broad-scale gradients: a west–east ‘continentality’ gradient of desert: even though this area experiences some of the most decreasing moisture and increased temperature seasonality and extreme fire weather in the world, its climates are completely a north–south gradient of decreasing moisture and increasing unsuitable for the presence of flammable vegetation. temperature. Overall, most of the precipitation falls during the Realistic wildfire likelihood estimates require that models winter months, except for some dry areas of the south-west. The incorporate anthropogenic activities that shape our landscapes north-west, which experienceswarm summers andmildwinters, and disturbance regimes, but these anthropogenic drivers are receives themost precipitation, whereas the deserts of the south- seldom accounted for (but see Cardille et al. 2001; Syphard et al. west are the most arid. The terrain also plays a large role on 2008). Isolating the influence of people on fire regimes is not a climate, as temperature decreases and precipitation increases trivial task, as human activities often strongly covary with with elevation. There is a strong rain shadow effect on the lee changes in vegetation types or climatic factors (Girardin et al. side of largemountain ranges, notably the RockyMountains and 2009;Meyn et al. 2010). Nevertheless, every year humans ignite the Sierra Nevada, to the east of which lie the Great Basin and most wildfires in North America (Stocks et al. 2002; Stephens the Great Plains respectively, which are areas typified by dry 2005). Conversely, people may reduce wildfire activity through continental climates. fire suppression, but suppression effectiveness appears to be The climatic and geological gradients of the study area are highly variable among areas, ranging from a drastic reduction in reflected in the vegetation cover, as well as in the historical fire area burned in some areas to virtually no detectable long-term regimes (Hardy et al. 2001). The north-west boasts lush temper- effects in others (Stephens and Ruth 2005; Finney et al. 2009). ate rainforests that have infrequent wildfires. Southward, the Perhaps more significantly, humans may have modified fire area ranging from the coast to the SierraNevadaMountains has a regimes indirectly through land-use change. In fact, Marlon mix of forest, grassland and shrubland vegetation that varies et al. (2008) have reported a global decrease in fire activity considerably with respect to fire return interval and fire severity. during the last century, attributing this trend to a general The chaparral areas of southern California experience some reduction in fuel continuity in fire-prone areas as a result of of the highest fire frequencies of North America. To the east, land-use change. Althoughmuch ofNorthAmerica (particularly the Rocky Mountains are dominated by coniferous vegetation in the West) is viewed as largely undisturbed wildlands, this is that support a fire regime of frequent and fairly low-intensity Wildfire probability in the western US Int. J. Wildland Fire 315 Western United States Elevation Road density Canada Canada Canada Pacific Pacific Pacific Washington Ocean Ocean Ocean Montana Oregon Idaho Wyoming Nevada Utah Colorado California Arizona New Mexico Road density Elevation (m) ⫺1 (km km ) 4334 14.2 Mexico ⫺84 Mexico 0 Mexico Mean annual precipitation Mean annual temperature Generalised land cover Canada Canada Canada Pacific Pacific Pacific Ocean Ocean Ocean Precipitation Temperature (mm) (⬚C) 2100 24.9 Grassland Developed Shrubland Agriculture 20 Mexico ⫺2.6 Mexico Forest Sparse or barren Fig. 1. The study area showing the 11 western USA states, elevation, road density (computed using a 1000-ha circular window), mean annual precipitation, mean annual temperature and land cover that was generalised from the National Gap Analysis. wildfires at low elevations and periodic stand-renewing wild- software (Phillips et al. 2006), previously shown to be effective fires at high elevations. Between themore coastal Sierra Nevada in spatial modelling of environmental constraints on fire activity and Cascades Mountains and the more continental Rockies, the (Parisien and Moritz 2009). The climate variables were aver- vegetation is dominated by drought-adapted vegetation that aged for the study’s time period and captured spatial patterns in seldom burns; however, fires do occur within pockets with both climatic normals and extremes. The ignitions, vegetation fairly continuous biomass, including areas dominated by inva- and topography variables were also averaged among years when sive grasses (mainly Bromus tectorum). East of the Rocky appropriate (e.g. lightning) but most often used a single repre- Mountains, the Great Plains, which were historically fire-prone sentative year if they did not vary significantly from year to year grasslands, represent a fairly dry area that has undergone (e.g. road density, topographic roughness). Because it has been massive conversion to agriculture. shown that the neighbourhood information of the ignitions, vegetation and topography variables may be as important to area burned as the observation at a given location (Parisien et al. Methods 2011), four spatial scales of observation (1, 100, 1000 and Wildfire probability models were built by relating data points 10 000 ha) were computed for each variable using a ‘moving- sampled in burned areas from 1984 to 2008 (dependent variable) window’ approach. We deemed it unnecessary to compute to a set of explanatory variables that characterised ignition moving-window variables for the climate variables, because sources, flammable vegetation (i.e. fuels), climate and topog- using the neighbourhood of climate variables does not sub- raphy (Table 1). These models were built using the MaxEnt stantially improve fire predictions (Parisien et al. 2011). All data 316 Int. J. Wildland Fire M.-A. Parisien et al. Table 1. Variables selected for analysis and their description All climate variables were calculated on amonthly basis and annual averages were based onmean values of everymonth. Unless otherwise specified, all values were computed for the 1984–2008 time period. All citations for the sources are provided in the text Category Input name Source Description A 2 Ignitions Pop_Dens1 Gridded population of the world, Population density at the 1-ha scale (people km ) version 3 A 3 1 RdlsVol1 ESRI StreetMap Roadless volume metric (remoteness) at the 1-ha scale (km person ) A 3 1 RdlsVol10000 ESRI StreetMap Roadless volume metric (remoteness) at the 10 000-ha scale (km person ) Lgt_Dens10000 NASA Global Hydrology and Annual density of lightning strikes (1995–2005) at the 10 000-ha scale 2 1 Climate Centre (strikes km year ) Climate MeanTempWettest PRISM Temperature of the wettest month (8C) MeanTempDriest PRISM Temperature of the driest month (8C) DiurTempRange PRISM Diurnal range in temperature (8C) Isotherm PRISM Diurnal temperature range C temperature range (100) PcpColdest PRISM Precipitation of the coldest month (mm) PcpSeas PRISM Precipitation seasonality (coefficient of variation) WatDef_CV_Ann PRISM Coefficient of variation among annual water deficit values (%) MaxSPI PRISM Maximum monthly standardised precipitation index 1 WindDriest99 NOAA 99th percentile wind speed of the driest month (m s ) Topography SurfArea_Ratio1 USGS/EROS Ratio of surface to area at the 1-ha scale 2 1 Vegetation GPP100 MODIS (MOD17A3) Gross primary productivity at the 100-ha scale (gC km year ) A Fuel_Pct100 USA GAP Analysis Land cover Percentage land cover of fuels at the 100-ha scale (%) A Fuel_Pct10000 USA GAP Analysis Land cover Percentage land cover of fuels at the 10 000-ha scale (%) A Variables that were excluded from the Non-anthropogenic model. Large fires in the western US Large and small fires in subanalysis area 1984–2008 1999–2008 Canada Canada Pacific Ocean Small fires (<900 ha) Large fires Large fires (ⱖ364 ha) Pacific (ⱖ364 ha) Ocean Analysis area Analysis area Mexico Mexico Fig. 2. Location of fires used in the main analysis (left panel; only fires $364 ha) and the Small-fires analysis (right panel; both large and small fires) within their respective study areas. Note that the outlines of the fires were exaggerated for visualisation purposes. Wildfire probability in the western US Int. J. Wildland Fire 317 used an Albers NAD 1983 equal-area projection and were used: population density (Pop_Dens), road density (Rd_Dens), converted to a 1-km resolution. roadless volume (RdlsVol), and distance to the wildland–urban Two wildfire probability models were constructed in order interface (WUI_Dist). Whereas the computation of Pop_Dens to assess the effects of modelling assumptions. The main (Center for International Earth Science Information Network reference model, termed the ‘Full model’, was built for the (CIESIN), Columbia University, and Centro Internacional de entire western USA and the entire span of fire data (1984–2008), Agricultura Tropical (CIAT), Gridded Population of the World and used all of the selected exploratory variables. Because many Version 3 (GPWv3): Population Density Grids, see http://sedac. of the Full model’s ignitions and vegetation variables encom- ciesin.columbia.edu/gpw, accessed 12 June 2010) and Rd_Dens passed a high degree of anthropogenic influence, we sought to (ESRI 2008) is straightforward, RdlsVol is a transformation of examine the effect of these variables on wildfire probability by the distance to road that better characterises the degree of excluding them in the ‘Non-anthropogenic model’. To ensure isolation (Watts et al. 2007). WUI_Dist was obtained from a consistency among areas, only large fires ($364 ha or 900 acres) database of exurban residential development (Theobald and were used in the Full and Non-anthropogenic models, because Romme 2007). Note that these variables capture both the fires below this size threshold were not available for most of the potential for human ignitions and a measure of fire suppression study area. effectiveness, as fires are better detected and more readily We tested whether excluding small fires in our model accessed in areas of high population and road density respec- building substantially affected wildfire probability by conduct- tively (Syphard et al. 2007). ing an additional analysis, which was termed the ‘Small-fires In this study, vegetation was used to represent the biomass analysis.’ Small fires (,364 ha), which often suffer from available for burning. It was therefore desirable to capture the sporadic reporting in time and space, are assumed to have a continuous nature of the biomass spectrum, rather than using negligible effect wildfire probability (e.g. Parisien and Moritz vegetation classes. Parisien and Moritz (2009) have shown that 2009), but this claim has never been formally examined. using categorical vegetation variables can be problematic Although it is true that large wildfires are responsible for most because of overfitting and because each class is considered of the area burned in the western USA (Stephens 2005), small equally similar. The first vegetation variable, the percentage fires are numerous and may burn in areas that rarely experience land cover fuels (Fuel_Pct), was derived from a simple reclassi- large fires (Bartlein et al. 2008). Examining small fires also may fication of the US GAP Analysis Land Cover (US Geological bridge the gap between wildfire probability as influenced by Survey 2010), where all cover types in which wildland fire people and wildfire probability that could occur in the absence spread is unusual were termed ‘non-fuel’ and all others were of fire suppression. The Small-fires analysis consisted of a ‘fuel.’ All urban and agricultural areas were non-fuel, as were comparison of two types of wildfire probability models: one areas of sparse vegetation cover (e.g. deserts, alpine tundra) and createdwith only large fires and one createdwith small and large permanent wetlands. This fuel–non-fuel classification was fire observations. Small fires data were available for a shorter made continuous (i.e. percentage cover) by calculating the time period than large fires (1999 to 2008) and for a smaller moving-windows surfaces from its original 30-m resolution study area (Landfire 1.1.0 Events Geodatabase, US Department grid. The other vegetation variable used was gross primary of Interior, Geological Survey, see http://www.landfire.gov, productivity (GPP) (Zhao et al. 2005), which is the rate at which accessed 10 June 2010) (Fig. 2), but these were sufficient for plants store energy as biomass per unit time or, in other words, our comparative purposes. the capacity of ecosystems to produce flammable biomass. A major difference between Fuel_Pct and GPP is the degree of anthropogenic influence: the former is strongly affected by Data humans, whereas the latter is largely (but not entirely) a function The wildfire probability models’ dependent variable consisted of climate. of ‘presence’ points that were randomly sampled within recent Climate variables were chosen to represent both the effect of fire perimeters (see Spatial modelling section). Two datasets of climate on prevailing fuel moisture and its control on vegetation mapped fire perimeters were used for this purpose: one for patterns. Although climate exerts both a direct and an indirect the Full model and Non-anthropogenic model and one for influence on fire, it is difficult (if not impossible) to distinguish the two models of the Small-fires analysis. The Full and between these effects at the spatiotemporal frame of this study. Non-anthropogenic models used the recently compiled data The climate variables consisted of metrics describing various from the Monitoring Trends in Burn Severity (MTBS) project permutations of temperature and precipitation (Table 1) (Eidenshink et al. 2007). These data span the 1984–2008 period (PRISM Group 2004). In addition to mean annual measures and cover the entire western USA. They also include prescribed (Temp and PcpAnn), the extremes of monthly means of temper- burns, but for the fires $364 ha these only consist of ,7% of the ature and precipitation were computed. For example, the mean observations (and ,2% of the total area burned). The Small- temperature of the wettest month (MeanTempWettest) provides fires analysis combined the large fires from the MTBS for the an index of coincidence of a resource (moisture) and energy 1999 to 2008 time period with the small fires (,364 ha) com- (heat), whereas the minimum temperature of the coldest month piled for the Landfire project (http://www.landfire.gov). (MinTempColdest) quantifies stress to plants. Two variables Five variables were used to assess the role of ignitions on were also used to characterise the growing season: the length of wildfire probability (Table 1). The only natural ignition source the season in days, as defined in McKenney et al. (2007), considered is lightning (Ltg_Dens) (Christian et al. 2003), and the cumulative sum of degrees (growing degree days, whereas four proxies of anthropogenic ignition location were GrowDegDays) $58C. 318 Int. J. Wildland Fire M.-A. Parisien et al. Two water-balance metrics, annual evapotranspiration unburned areas. Fire presences, which represent the dependent (AET) andwater deficit (WatDef), were also used in themodels. variable, were point-based observations obtained by randomly Considered together, these variables were shown to correlate sampling point locations within fires perimeters. In a presence- well with ecosystem types of the western USA (Stephenson only framework, the lack of fire at a given location is not 1990) and individual tree species (Lutz et al. 2010). Reference interpreted as an ‘absence’ of fire by the model, as some of these evapotranspiration was calculated using the Penman–Monteith areas may in fact experience wildfire if they share environ- model (Allen et al. 1998), which uses temperature, radiation, mental characteristics with other wildfire-prone locations. precipitation and wind speed data. Water deficit was calculated At each fire presence point, MaxEnt estimates wildfire as the monthly sum of the difference between reference evapo- probability by fitting the probability distribution of maximum transpiration and precipitation such that no single month could entropy (the one that is most uniform) to the environmental have a water deficit less than zero. This technique generally variables. The algorithm iteratively evaluates the contrasts follows Stephenson (1990), except that it did not account for soil between the values of the fire presences and those of a back- water or carry-over from month to month. To assess fire spread ground.MaxEnt also has the flexibility to fit non-linear relation- potential, the 90th, 95th and 99th percentile wind speed were ships between the response variable and explanatory variables, calculated for the mean driest (WindDriest) and warmest so that resulting models have the ability to describe complex (WindWarmest) months, from Kalnay et al. (1996). Finally, relationships. However, environmental conditions that extreme values of the monthly standardised precipitation index exceeded the range of currently observed values were ‘clamped’ (MinSPI and MaxSPI) measured the departure from mean (i.e. held constant) at the maximum value of the range to avoid precipitation normals (McKee et al. 1993). unfounded extrapolations of wildfire probabilities. A single explanatory variable, the surface-area ratio The MaxEnt output represents an estimate of relative, rather (cf. Stambaugh and Guyette 2008), was used to characterise than absolute, wildfire probability. Because the models are the effect of topographic roughness on wildfire probability. At based on fire patterns and environmental data for a fairly long the spatial extent and resolution of the present study, the effect of time period (1984–2008), the mapped fire probabilities are not topography on fire activity is largely indirect: it exerts its effect designed to evaluate specific sets of conditions that lead to large on fire mainly by influencing patterns in ignitions, vegetation fires in a given year, but instead quantify the relative wildfire and weather. However, it can be used as a proxy for several likelihood over longer periods (Krawchuk et al. 2009; Parisien variables that may be missing from the model (Parisien et al. and Moritz 2009). The probability is relative in that a temporal 2011). The surface-area ratio variable (SurfArea_Ratio) was scale (e.g. 1 year) is not implied. Rather, the probabilities among calculated from a digital elevation model (US Geological pixels are relative to one another; that is, a pixel with a wildfire Survey 2000). Because the calculation of this measure is probability of 0.3 is estimated to be three times as likely to strongly scale-dependent, the moving-window approach was experience a fire as a pixel with a value of 0.1. used, as described for ignition and vegetation variables, whereby The entire pool of fire presences consisted of 10 000 points topographic roughness is measured at four spatial scales: 1, 100, that were randomly locatedwithin the burned areas from 1984 to 1000 and 10 000 ha. 2008, whereas 50 000 random points were used to characterise Many of the potential explanatory variables initially the background environment. The same presence points were considered for the modelling (Appendix 1) were similar and used for the Full model and Non-anthropogenic model; only the thus highly correlated. To avoid incorporating a large number of input set of explanatory variables differed between the two variables that have overlapping information, we selected a models. For the Small-fires analysis, 5000 and 20 000 points relatively parsimonious subset of variables for model building. were used as fire presences and background respectively. This was achieved in a heuristic manner by first cross- The effect of spatial autocorrelation in the fire data and the correlating the variables and identifying those that were explanatory variables was minimised through the following highly correlated (Spearman R.0.6). Within each of these steps. Only a small random fraction of the total fire presences groups, we retained the variable that performed the best in a was used to build individual wildfire probability models. This MaxEnt model that considered only that explanatory variable. was replicated for 25 bootstrap subsamples and the ensemble of As such, a limited set of fairly uncorrelated yet complementary resulting models was ultimately averaged for analysis. We used environmental variables were included in the model. In the Ripley’s K function with different-sized subsets to estimate the Non-anthropogenic model, the Pop_Dens, RdlsVol, Fuel_Pct sampling fraction at which the fire observations were spatially variables were excluded from the Full model to examine the independent. Last, we determined that 500 points sufficiently anthropogenic influence onwildfire likelihood, whereas the two captured fire–environment relationships while being only faintly models of the Small-fires analysis included the same variables clustered across the study area. The fraction of points unused for as the Full model. model building was instead used to calculate the evaluation metrics described below. The predictive accuracy of the wildfire probability model Spatial modelling output was evaluated using several metrics that were computed Wildfire probability models were computed in MaxEnt 3.3.3e and averaged for each of the 25 model replicates. The estimated (Phillips et al. 2006). MaxEnt is designed for presence-only fraction of the area suitable for fire (an approximation of the data. Presence-only models discern between the environment of false positive rate or 1 – specificity) and the omission (false burned areas (‘fire presence’) from that of the entire study area negative rate or 1 – sensitivity) were measured at the wildfire (‘background’), as opposed to discerning between burned and probability threshold that minimises the sum of these error Wildfire probability in the western US Int. J. Wildland Fire 319 measurements (Liu et al. 2005). Interpreted together, these fires only and large and small fires) were qualitatively compared measures give us the expected rate of false negatives for a given to visualise the effect of adding small fires to the wildfire predicted suitable area. probability map. In addition, the variable contributions (mean Amore comprehensive measure of model performance is the and s.d.) of these models were plotted and compared, and the area under the curve (AUC) of a plot of sensitivity (true rank-order correlation of the variable contributionswas assessed positives) v. 1 – specificity (false positives or 1 – true negatives). (Spearman correlation). In a presence–absence framework, the AUC computed with the Results points unused formodel building (i.e. the ‘test’ AUC)may range from 0.5, where prediction accuracy is no better than if samples There were a wide range of responses of wildfire probability to were randomly selected, to 1, which indicates perfect classifi- explanatory variables, as shown in six of the variables most cation accuracy. By contrast, in a presence-only framework, as influential in computing wildfire probability (see below) in this study, it is impossible to achieve unity in AUC because (Fig. 3). Although some responses were monotonic, notably that absences (hence false positives) are unknown. In fact, the of the top variable (Fuel_Pct100), this was not the norm. Many maximum achievable AUC is equal to 1 – a/2, where a is of the variables appeared to be unimodal, whereby the fire generally the fraction of the study area that the species (or response is maximised across intermediate values of the process) covers (i.e. the prevalence), a measure that is usually explanatory variable (e.g. MeanTempDriest, PcpColdest, unavailable. However, here, we considered a to be the percent- RdlsVol10000, GPP100). In general, weak variables had fire age of pixels where fire was observed. This provides a fair, yet responses that were highly complex and unintuitive (not shown). underestimated, approximation of prevalence. Model evaluation metrics show that the Full model and Finally, we computed the correlation between the wildfire Non-anthropogenic model performed similarly well (Table 2). probability predictions and 1–0 (i.e. fire–no fire) observations, Suitable area and omission error suggest that when approxi- which is known as the point-biserial correlation. Rather than mately one-third of the study area was considered ‘suitable’ for being based solely on rank, such as the AUC, the point-biserial fire, approximately one-quarter of the points were predicted to correlation uses the actual predictions to evaluate model perfor- be false positives. The uncorrected AUCs computed from the mance. To obtain this measure, the 50 000 random points used test portion of observations were 0.792 and 0.742 for the Full for the background were assigned a 1 or a 0 whether they were and Non-anthropogenic models respectively. However, when located in a fire pixel or a fire-free pixel respectively. These adjusted for wildfire prevalence (6.7% of the area), the AUCs values were then correlated with the predicted wildfire proba- were 0.836 and 0.810. AUCs are therefore somewhat larger for bility. Although the point-biserial correlation does not provide a the Full model, which suggests that anthropogenic variables are stand-alone interpretable value, it does provide a goodmetric for informative with respect to recent wildfire occurrence patterns. the comparison of the predictive ability among models. The slight superiority of the Full model is also reflected in the point-biserial correlation. Data analysis Patterns in modelled wildfire probability are highly hetero- The relative contribution of the explanatory variables to wildfire geneous throughout the study area (Fig. 4). Wildfire likelihood probability was assessed in MaxEnt by estimating the change in is at least moderately high (.0.3) in most areas, with the model gain associated with each variable. The mean and stan- exception of the south-west deserts, parts of the coastal north- dard deviation (s.d.) of the percentage contribution of each west and in the expansive agricultural areas, most of which were variable were compiled from the 25-model ensemble and were extensive grasslands in the past. plotted for both the Full model and the Non-anthropogenic Explanatory variables from each of the four main model. environmental factors, ignitions, climate, topography and To evaluate the relationship between fire activity and vegetation, appear to be important in predicting wildfire proba- environmental factors, the estimated wildfire probability was bility (Fig. 5). The Fuel_Pct100 variable explained nearly 25% plotted as a function of a selected explanatory variable. These of variation in the Full model. However, several other variables plots were produced from MaxEnt models where a single had important contributions (e.g. PcpColdest, RdlsVol10000, explanatory variable was used to predict wildfire probability. MeanTempDriest and SurfArea_Ratio1), whereas a few This said, these response curves were built to visualise bivariate had negligible contributions (e.g. Isotherm, MaxSPI and relationships and were not those used in the wildfire probability WindDriest99). Of the variables common to both models, those models, which are subject to complex interactions with other important for the Full model also contributed substantially to the variables. Twenty-five replicates of the bivariate models were Non-anthropogenic model, but some variables (SurfArea_ built and the mean and standard deviation of the 25 response Ratio1, GPP100) were disproportionately more important in curves were plotted. the latter model. Wildfire probability maps were produced for the Full and Wildfire probability patterns between the Full model and the Non-Anthropogenic models, as well as for the models of the Non-anthropogenic model are broadly similar across the study Small-fires analysis. The Full and the Non-anthropogenic area (Fig. 4a, b), but numerous differences are evident at local models were compared on a pixel-wise basis in two ways: first, scales. The absolute change (i.e. subtraction) in wildfire proba- through simple subtraction of the fire probabilities (absolute bility between the Full and Non-anthropogenic models shows change) and, second, by computing the relative change in that over the majority of the landscape, the anthropogenic probability, expressed as percentage change (relative change). variables included in the Full model served to reduce wildfire The mapped outputs of both Small-fires analysis models (large probability, with increases in wildfire probability concentrated 320 Int. J. Wildland Fire M.-A. Parisien et al. RdlsVol10000 MeanTempDriest PcpColdest 0.9 0.9 0.9 0.6 0.6 0.6 0.3 0.3 0.3 0.0 0.0 0.0 5 5 5 0 ⫻ 10 2 ⫻ 10 4 ⫻ 10 ⫺10 0 10 20 30 2 5 20 50 200 3 ⫺1 km person ⬚C mm SurfArea_Ratio1 GPP100 Fuel_Pct100 0.9 0.9 0.9 0.6 0.6 0.6 0.3 0.3 0.3 0.0 0.0 0.0 1.00 1.10 1.20 1.30 1000 5000 20 000 0 20 40 60 80 100 ⫺2 ⫺1 Unitless g C km year % Fig. 3. Predicted wildfire probability for a selected set of explanatory variables. The full variable names and descriptions are found in Table 1. These plots were obtained by buildingMaxEntmodels using only a single independent variable of interest. The line indicates themeanwildfire probability values, whereas the grey shading represents s.d., as calculated from 25 replicate runs using random subsets of the data. Note that the x-axis of the PcpColdest and GPP100 variables was logarithmically scaled. Table 2. Performance of MaxEnt models, including maximum test sensitivity plus specificity area The AUC is the area under the curve of the sensitivity v. predicted area (1 – specificity) plot; the ‘adjusted AUC’ adjusts these values according to geographic prevalence (seeMethods). The ‘suitable area’ represents the fraction of area predicted as suitable and the ‘omission error’ is the fraction of presence points found in areas predicted to be unsuitable. The probability threshold is minimised according to the sum of these values. The point-biserial correlation evaluates the correspondence between estimated wildfire probability of presence points (ones) and non-presence points (zeros) Western USA analysis Small-fire analysis Full model Non-anthropogenic model Large fires Largeþ small fires Suitable area (%) 30.5 32.9 30.0 29.7 Omission error (%) 23.3 25.7 24.2 26.1 AUC 0.792 0.742 0.806 0.795 Adjusted AUC 0.836 0.810 0.839 0.830 Point-biserial correlation 0.346 0.297 0.354 0.348 in large wilderness areas (Fig. 4c). Themap of relative change in the variable contributions were extremely similar, as the rank- wildfire probability amongmodels shows that most decreases in order correlation between variable ranks was R¼0.95 (Spear- wildfire probability in the Non-anthropogenic model compared man correlation). with the Full model occur in developed and agricultural areas, as expected (Fig. 4d). In fact, the most drastic decreases (.500%) Discussion almost always occur in and around urban areas. In contrast, only Fire–environment relationships in the western US minor relative increases in wildfire probability were observed over much of the study area when anthropogenic variables were This study brings us one step closer to understanding the sub- removed. continental controls on long-term (i.e. multi-decadal) wildfire The Small-fires analysis, which compared the wildfire prob- likelihood in North America. The results provide further support ability of models built with only the large fires and with both to the idea that large-scale assessments of wildfire likelihood are large and small fires, indicated strong similarities between best described using all of the necessary fire ingredients: an model outputs (Fig. 6). The spatial predictions were virtually ignition source, hot and dry weather, and sufficient biomass identical between models; differences were highly localised for sustained combustion. Fire universally requires the spatio- and, even so, relatively minor (e.g. coastal Oregon). Likewise, temporal coincidence of these same basic elements; however, Modelled fire probability Wildfire probability in the western US Int. J. Wildland Fire 321 (a) Full model (b) Non-anthropogenic model Fire probability 0–0.1 >0.1–0.2 >0.2–0.3 >0.3–0.4 >0.4–0.5 >0.5–0.6 >0.6–0.7 >0.7–1 N (c) Absolute change (d ) Relative change Absolute change in fire probability ⱖ1 s.d. increase <1 s.d. change ⱖ1 s.d. decrease Relative change in fire probability ⱖ100% increase <100% change ⱖ100% and <500% decrease ⱖ500% decrease Fig. 4. Mean predicted wildfire probability (based on 25 model replicates) for the Full model (a); the Non-anthropogenic model (b); the absolute change (c); and the relative change (d ) from the Full model to the Non-anthropogenicmodel, whereby green indicates an increase and blue represents a decrease inwildfire probability as a result of human-influenced variables. The wildfire probability maps produced in Fig. 4 and their projection information are available as supplementary material to this paper (see http://www.publish.csiro.au/?act=view_file&file_id=WF11044_AC.zip). understanding the specific effect of each of the variables chosen Our results suggest that gradients in topography, climate, is not straightforward. The degree to which elements limit fire biomass (i.e. GPP) and ignitions also play important roles in varies substantially across subcontinental extents, as shown in characterising wildfire likelihood across the study area. In fact, Australia (Russell-Smith et al. 2007) and subequatorial Africa when the percentage fuels variable was omitted from the model (Archibald et al. 2009). Although evaluating region-specific (i.e. in the Non-anthropogenic model), only a slight decrease in limits on fire activity was not the focus of the present study, our model performance was observed, suggesting that the percent- results are strongly coherent with those of previous studies age fuels information was reflected in a combination of other that show that fire–environment relationships are far from variables. These results are thus coherent with those of Russell- constant throughout the western US (McKenzie et al. 2004; Smith et al. (2007) in Australia and Parisien and Moritz (2009) Littell et al. 2009). in the conterminous USA, who found that, because they are It is not surprising that the strongest predictor of wildfire dependent on climate and human land use, measures of biomass likelihood in the western USA is the percentage cover of fuels. or flammable vegetation can be omitted from subcontinental However, this predictor only explains,25%ofmodel variation. models of fire activity. 322 Int. J. Wildland Fire M.-A. Parisien et al. 30 Non-anthropogenic model 40 20 30 10 20 0 Full model 10 0 Ignitions Climate Topo. Vegetation Fig. 5. Variable contributions, expressed as a percentage, of the Full model (bottom plot), and the Non-anthropogenic model (top plot). Large fires Large ⫹ small fires MaxSPI MeanTempWettest Isotherm WatDef_CV_Ann WindDriest99 RdlsVol1 Pop_Dens1 PcpColdest SurfArea_Ratio1 DiurTempRange PcpSeas GPP100 Fire probability MeanTempDriest 0–0.1 Fuel_Pct10000 >0.1–0.2 RdlsVol10000 >0.2–0.3 >0.3–0.4 Ltg_Dens10000 >0.4–0.5 Fuel_Pct100 >0.5–0.6 >0.6–0.7 30 20 10 0 0 10 20 30 >0.7–1 Contribution (%) Fig. 6. Wildfire probability maps of the Small-fires analysis study area using only large fire ($364 ha) data (left) and data from both small and large fires (right). The bar chart represents the comparison of variable contributions for both models. The wildfire probability maps represent the average of 25 model replicates. Contribution (%) Pop_Dens1 RdlsVol1 RdlsVol10000 Ltg_Dens10000 MeanTempWettest MeanTempDriest DiurTempRange Isotherm PcpColdest PcpSeas WatDef_CV_Ann MaxSPI WindDriest99 SurfArea_Ratio1 GPP100 Fuel_Pct100 Fuel_Pct10000