Use of artificial landscapes to isolate controls on burn probability
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- Parisien, M., Miller, C., Ager, A.A. et al. Landscape Ecol (2010) 25: 79. doi:10.1007/s10980-009-9398-9
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Techniques for modeling burn probability (BP) combine the stochastic components of fire regimes (ignitions and weather) with sophisticated fire growth algorithms to produce high-resolution spatial estimates of the relative likelihood of burning. Despite the numerous investigations of fire patterns from either observed or simulated sources, the specific influence of environmental factors on BP patterns is not well understood. This study examined the relative effects of ignitions, fuels, and weather on mean BP and spatial patterns in BP (i.e., BP variability) using highly simplified artificial landscapes and wildfire simulation methods. Our results showed that a limited set of inputs yielded a wide range of responses in the mean and spatial patterning of BP. The input factors contributed unequally to mean BP and to BP variability: so-called top-down controls (weather) primarily influenced mean BP, whereas bottom-up influences (ignitions and fuels) were mainly responsible for the spatial patterns of BP. However, confounding effects and interactions among factors suggest that fully separating top-down and bottom-up controls may be impossible. Furthermore, interactions among input variables produced unanticipated but explainable BP patterns, hinting at complex topological dependencies among the main determinants of fire spread and the resulting BP. The results will improve our understanding of the spatial ecology of fire regimes and help in the interpretation of patterns of fire likelihood on real landscapes as part of future wildfire risk assessments.
KeywordsBurn probabilityBurn-P3 simulation modelIgnitionsFuelsFire weather
Fire is a natural ecosystem process affecting landscapes worldwide (Bond and van Wilgen 1996; Krawchuk et al. 2009) and an integral part of one of the most important pattern-process feedbacks on natural landscapes (Turner et al. 1989; Peterson 2002). Although fire regimes have been described for many areas of the globe (e.g., Niklasson and Granström 2000; Rollins et al. 2002; Russell-Smith et al. 2003), we are only beginning to develop a mechanistic understanding of how biophysical and anthropogenic factors affect the spatio-temporal distribution of fires. Because an understanding of where and when fires occur is necessary for our successful coexistence with fire, either “wild” or prescribed, land managers have developed numerous tools for assessing the spatially-explicit likelihood of fire—also known as burn probability (BP)—in a risk analysis framework (Miller 2003; Ager et al. 2006; Finney 2006).
Fires require the co-occurrence in time and space of three main factors: fire-conducive weather, ignitions, and flammable vegetation (i.e., fuels) (Moritz et al. 2005; Parisien and Moritz 2009). Weather has often been called a ‘top-down’ control on fire behavior because of its mesoscale impact, whereas ignitions and fuels are considered ‘bottom-up’ (Heyerdahl et al. 2001). Weather affects the occurrence, size, and shape of fires through the frequency of consecutive days of fire-conducive weather, the severity of fire weather conditions, and the constancy of wind direction (Moritz 1997; Beverly and Martell 2005). Ignitions are seldom random on the landscape (Krawchuk et al. 2006). High ignition densities, which tend to be near urban areas and roads, may translate into high concentrations of fires (Parisien et al. 2004; Badia-Perpinyà and Pallares-Barbera 2006), but not necessarily the greatest area burned (Sturtevant and Cleland 2007; Syphard et al. 2007). Fuels affect the spread of fires according to the relative proportions of fuel types on the landscape (Finney 2003; Leohle 2004) and their spatial configuration (Finney 2001; Parisien et al. 2007).
Although ignitions, fuels, and fire-conducive weather are necessary ingredients for fire, their respective influence on the manifestation of fire patterns appears to vary enormously among landscapes, as well as across temporal and spatial scales (Falk et al. 2007). Fire ignition and spread respond sequentially to a complex suite of environmental factors (including weather variables) that vary in both time and space. The complexity of fire-environment relationships thus makes it intrinsically difficult to disentangle the relative influence of these factors, especially on landscapes where topography acts as a modifier (Taylor and Skinner 2003; van Wagtendonk and Cayan 2008). Moreover, determining the relative influence of environmental factors can be further complicated by a certain dichotomy between so-called “normal” and “extreme” fire-conducive conditions. For example, in some environments (e.g., Mediterranean), the influence of fuel type on fire spread is greatly diminished under extreme weather conditions (Moritz 2003; Nunes et al. 2005).
Computer simulation models that explicitly ignite and spread fires across a landscape provide an opportunity for significant advancement in our understanding of the factors driving fire likelihood, because variables can be controlled and fire occurrence patterns can be more easily interpreted. We used a spatially explicit simulation model to investigate the relative influence of key environmental factors on BP. We designed heuristic artificial landscapes and three simulation experiments focusing on how ignitions, fuels, and weather influence mean BP and BP variability. We developed scenarios to crudely represent archetypal fire regimes from around the globe and to discern the influences of so-called top-down (weather) and bottom-up (fuels and ignitions). A factorial design allowed us to reveal effects of interactions among factors. In an effort to simplify our experimental design, we did not consider topography in this study. Although topography can influence spatio-temporal patterns of fires (Rollins et al. 2002; Stambaugh and Guyette 2008), it does so indirectly, by influencing ignition and fuel patterns, as well as weather conditions (wind vectoring).
Experimental factors in the three burn probability experiments
Mean fire size
1/20 of study area
1/100 of study area
Fire size distribution
16 h of burning
8–24 h (mean = 16) of burning
Negative exponential (Exp)
8–40 h (mean = 16) of burning
Direction of burning
One direction; perpendicular to rectangular fuel feature
One direction; parallel to rectangular fuel feature
Spatial pattern of features of higher relative ignition density for two relative density levels
All cells have equal likelihood of ignition
Linear, high density (LinHi)
Ignitability ratio 10:1
Clustered, high density (CluHi)
Linear, low density (LinLo)
Ignitability ratio 2:1
Clustered, low density (CluLo)
Configuration and composition of spatial fuel features
Uniform fast-burning fuels
All cells have equal rate of spread
Rectangular slow-fuel features; 25% slow fuel (Rec25)
Rate of spread for slow fuel is half that of fast fuel
Circular slow-fuel features; 25% slow fuel (Cir25)
Rectangular fast-fuel features; 75% slow fuel (matrix) (Rec75)
Circular fast-fuel features; 75% slow fuel (matrix) (Cir75)
Characteristics of burn probability (BP) experiments
Factors and levels
BP = IGNIT + SIZE + DIR
BP = SIZE + FUELS + IGNIT
BP = DIST + FUELS + DIR
Burn-P3 simulation model
Burn-P3 simulates fire growth based on the physical factors that control fire spread and the larger-scale probabilistic components of fire regimes (e.g., ignitions and fire weather) on a landscape of known fuels and topography. The model simulates the ignition and spread of a very large number of fires on a rasterized landscape to calculate spatially explicit BP for each cell for a snapshot in time (e.g., year). It does not account for vegetation succession. Monte Carlo methods are used to draw the locations of ignitions from a probability density grid. A fire growth model (Tymstra et al. 2009) is then used to calculate fire spread through complex terrain and fuels, as described by the Canadian Fire Behavior Prediction (FBP) System (Forestry Canada Fire Danger Group 1992). Within the FBP System, flammable vegetation is categorized into fuel types, which are used to calculate quantitative fire behavior outputs for a given set of fire weather inputs. Fire weather conditions drive fire spread and the length of the fire-conducive burning period are modeled stochastically from user-supplied distributions. Although fire weather conditions may change hourly, here they were set as constant for 7- or 8-h periods, which would be analogous to a daily burning period.
Inputs to the model
Fuels were also integrated as gridded inputs, whereby cells were classified as one of two fuel types, fast or slow, for which the rate-of-spread ratio was 2:1. To achieve this ratio, the fast fuel type was the FBP System’s Boreal Spruce and the slow fuel type was a mix of coniferous and leafed-out deciduous (Boreal Mixedwood with a 45% coniferous component). The FUELS factor comprised five levels. The first level consisted of uniform fast fuels. The second level, Rec25, consisted of five rows of staggered rectangular features having a 2:1 ratio of length to width, laid out lengthwise in an east–west orientation (Fig. 2). The rectangular features represented slow fuels (accounting for 25% of the total area) embedded in a matrix of fast fuels (75%). The third level was the same as the second, but the features were circular (Cir25). The fourth and fifth levels (Rec75 and Cir75, respectively) had the same spatial configurations as the second and third levels, but the slow and fast fuels were inverted, with the features containing fast fuels (25%) embedded in a matrix of slow fuels (75%). The fuel features were designed to be analogous to distinct vegetation stands or fuel treatments across a landscape.
Fire weather conditions were selected to produce a range of fire sizes and shapes described by the factorial levels of the SIZE, DIST, and DIR experimental factors. In Burn-P3, fire weather is input as daily weather observations (temperature, relative humidity, wind speed, wind direction, and 24-h precipitation) at noon local standard time and the associated fuel moisture codes and fire behavior indexes from the Canadian Forest Fire Weather Index System (Van Wagner 1987). All of these variables except wind direction were held constant among simulation scenarios. A wind speed of 15 km/h was used to approximate a 2:1 length-to-breadth ratio for the perimeter of an elliptical fire. Different fire sizes were achieved by altering the duration of the burning period.
To assess the effect of the mean duration of fire-conducive weather, two levels were developed for the SIZE factor: small (Sm) and large (Lg), corresponding to fire sizes of 1/100 and 1/20 of the area of the study landscape, respectively (FUELS = Uniform) (Table 1). Under the specified weather conditions, these sizes represent 7 (Sm) and 16 h (Lg) of burning.
The DIR factor was used to examine the effect of the constancy of wind direction on BP, as well as effect of the orientation relative to rectangular fuel features. Three levels were devised for the DIR factor: fires burning exclusively from the south (S), fires burning exclusively from the west (W), and fires burning from random directions (Rnd), where wind direction varies randomly among 8-h burning periods.
Effects of combinations of inputs on BPmean and BPvar
Relative importance of environmental factors
The relative importance of the factors affecting BPmean and in BPvar, as well as their second-order interactions, was assessed for each experiment using generalized linear models (GLM). The experimental factors were treated as independent categorical predictor variables with multiple levels (Table 2). The contribution of each factor and their interactions was determined by leaving the term of interest out of the model and calculating to what extent this omission reduced model performance in comparison with the full model. To enable computation and to limit spatial autocorrelation in the model, a subset of cells was systematically sampled from the BP maps at equal intervals. Heuristic explorations showed that a grid of 36 × 36 points (total 1296 points; distance of 20 cells between samples) provided a good compromise between depicting the spatial BP patterns of interest and minimizing spatial autocorrelation with a fairly low number of points relative to a random sampling scheme.
The contribution to BPmean of environmental factors was measured with generalized linear models for a binomial response (logit link function), where the dependent variable was arranged as the number of times selected cell i burned, bi, and bi minus the total number of fires simulated, N. The models of BPvar, which was defined as the relative difference in BP (absolute values) from the BPmean of each scenario, were structured like those for BPmean, but modeled a Gaussian response (identity link function). The natural log of BPvar values was used because of asymmetry in the data distribution, as well as in model residuals.
Two performance measures were used to evaluate relative contribution of each predictor variable. The first consisted of an adjusted R2 computed for regression models using maximum likelihood estimates (Nagelkerke 1991), which could be interpreted as “explained variation”. The second was the Akaike Information Criterion (AIC), a measure of goodness of fit in which models are penalized for each free parameter. Reported here was the change in AIC (∆AIC) between reduced models (those omitting the variable of interest) and the full models. The importance of model terms is proportional to their relative ∆AIC values. Here, the predictor variables or interactions that resulted in a model with ∆AIC < 4 were considered poor predictors of BP (Burnham and Anderson 1998). Because some autocorrelation remained in the model residuals, it was necessary to adjust the ∆AIC according to the effective sample size (Dutilleul 1993). Very conservative sample sizes of 25 and 81 points were deemed suitable for the BPmean and BPvar models, respectively, by identifying the number of data points corresponding to the spacing dictated by the start of a sill in the semivariograms of model residuals.
Local examination of BP patterns
BP within and surrounding ignition and fuel features were examined for selected combinations of factors and levels in order to adequately describe the fine-scale spatial patterns in BP. BP “profiles” were created by sampling BP values at every cell spanning a north–south transect at the center of the study landscape for selected scenarios in each of the three experiments (Fig. 2) and plotting them as a function of location (i.e., northness). In the ignitions experiment, BP was sampled across an area containing a high-density cluster feature (IGNIT = CluHi) for two levels of DIR (S and Rnd). In the fuels experiment, BP was sampled across an area containing a rectangular feature of slow fuels in a fast fuel matrix and one of fast fuels in a slow matrix (FUELS = Rec25 and Rec75, respectively) for scenarios using small and large fires (SIZE = Sm and Lg, respectively). In the weather experiment, the BP values of the three fire size distributions (DIST = Cst, Reg, and Exp) were sampled across the Rec25 FUELS feature with fires burning from random directions (DIR = Rnd).
Effects of combinations of inputs on BPmean and BPvar
In the fuels experiment, the NBPDmean and NBPDstd varied mainly as a function of the overall flammability of the landscape, but apparent interactions with ignition patterns produced rather erratic patterns in BP (Fig. 3b). The inclusion of both spatially variable fuels and ignitions dramatically increased the NBPDstd, especially for the scenarios with clustered high-density ignitions. The NBPDmean within the fuel features (Fig. 3b, x’s) differed substantially from overall NBPDmean, but the relative difference was moderated when the ignitions patterns were nonrandom.
In the weather experiment, NBPDmean and NBPDstd varied slightly with the DIST factor (Fig. 3c): the departure in NBPDmean decreased as fire size distribution became more variable. The DIR factor affected NBPDstd, with fires burning in westerly and random directions resulting in the highest and lowest NBPDstd, respectively. The overall and within-feature NBPDmean in scenarios using rectangular slow fuel features (FUELS = Rec25) was slightly lower for simulations with southerly winds than for those with westerly winds because the less flammable features were wider relative to the frontal fire spread of southerly winds. That the rectangular slow fuel features were more effective than round ones when the wind direction was random is somewhat surprising and suggests that this feature yielded a disproportionate reduction in fire size when it was oriented perpendicular to fire spread. The east–west alignment of fuel features (Fig. 2) resulted in small discrepancies in NBPDmean for circular fuels between southerly and westerly wind directions (Fig. 3c).
Relative importance of environmental factors
Partitioning of variation (R2) and change in model AIC for mean and variability of burn probability (BP) between groups of factors in each experiment
% Variation explaineda
% Variation explained
IGNIT × SIZE
IGNIT × DIR
DIR × SIZE
FUELS × IGNIT
FUELS × SIZE
IGNIT × SIZE
DIST × DIR
DIST × FUELS
DIR × FUELS
In the ignitions experiment, SIZE explained almost all (97.4%) of the model variation for BPmean. The small contribution of the IGNIT factor (2.4%) was due to the imbalance in ignitions between the study landscape and its buffer for the clustered and linear IGNIT inputs. Although the importance of SIZE dwarfed that of other factors, the ∆AIC suggests that all model terms but one (IGNIT × DIR) improved the BPmean model. The IGNIT factor explained almost all of the variation in the BPvar model, with SIZE and DIR contributing minimally. According to ∆AIC, the interaction terms including IGNIT marginally improved model fit, whereas DIR × SIZE did not.
In the fuels experiment, the SIZE and FUELS factors explained most of the variation in BPmean, but ∆AIC values suggest that all factors and interactions improved the model. Both the IGNIT and FUELS factors and, to a lesser extent, SIZE made strong contributions to the BPvar model. In addition, this model had a highly-significant contribution from the interaction term between FUELS and IGNIT, as exemplified in the following section, and a moderate interaction between IGNIT and SIZE.
In the weather experiment, the DIST and FUELS factors contributed most to the explained variation in the BPmean model. The DIR factor was also more important here than in the ignitions experiment because some combinations of DIR and FUELS had noticeable effects on BP (e.g., south-burning fires and rectangular fuel features). All interactions improved the model according to the ∆AIC values. The FUELS factor made by far the largest contribution to the BPvar model, but all other terms except DIST × DIR contributed to the model of spatial BP patterns.
Local examination of BP patterns
The BP profiles from the selected fuels experiment scenarios indicate a complex relationship between the duration of fire-conducive weather (SIZE) and fuel patterns. The high- (Rec25) and low-flammability (Rec75) levels of the FUELS factor yielded seemingly reciprocal patterns, but they were not perfect mirror images (Fig. 4b). Although large fires produced much large BP shadows than small fires, the relative contrasts in BP patterns produced in fuels of opposite flammability appeared to be far greater with small fires than with large ones.
The three levels of the DIST factor produced similar forms of BP shadows in and around a rectangular fuel feature (Rec25) (Fig. 4c). However, the absolute BP values varied substantially among levels, despite burning for the same period of time, on average. In fact, the lowest BP values of the Rnd DIST level (those in the center of the fuel feature) were higher than the highest BP of the Cst level. In addition, these results show that high variability in the duration of fire-conducive weather (DIST = Exp) produced only about a 25% reduction in BP within the fuel feature compared to a 40% reduction for the low variability level (Cst) (Fig. 4c).
Interactions between fuel and ignition patterns were amplified when the simulated fires were large. Notably, the efficacy of fuel features at reducing BP was highly variable throughout the landscape (Fig. 5d). At one extreme, high BP values resulting from the confluence of the two linear ignition features overwhelmed any mitigating effect of the central fuel feature, whereas fuel features on the leeward side of ignition features appeared to produce a large BP shadow (Fig. 5e). The overlay of fuel and ignition features lead to the creation of an intriguing lenticular pattern in BP on the lee side of the fuel features (Fig. 5f). This pattern can be explained by the combined effects of fires successfully spreading through and beyond the fuel feature and fires flanking from the right side of the feature. The relative decrease in BP to the left of this pattern is a result of fewer ignitions, because of the diagonality of the ignition feature and the greater time traveled by fires ignited at the southernmost part of the fuel feature, which significantly reduced frontal fire spread.
Our results show that a limited set of simplistic ignitions, fuels, and weather inputs can yield complex responses in the mean and spatial patterning of BP. The model output were usually consistent with our understanding of controls on BP (Fig. 1), but this was not always the case, affirming that fire regimes are a manifestation of highly-intertwined and complex relationships among a set of environmental drivers (Peterson 2002). Furthermore, although weather-related factors had a greater effect on mean BP, and ignition and fuels chiefly influenced BP variability, our results did not fully support the assertion that environmental factors could be cleanly partitioned into ‘top-down’ and ‘bottom-up’ controls on these two BP measurements.
Characterizing a control on BP as either top-down or bottom-up is problematic. For example, weather-induced temporal synchrony of fire events over large areas clearly exerts a top-down influence (McKenzie et al. 2006; Gavin et al. 2006), but the extent to which fuels amplify or mute the impact of weather may be difficult to assess. Similarly, the dependence of ignitions on weather for ignition sources (lightning) and suitable dryness of the fuelbed suggests that ignitions obscure the top-down–bottom-up categorization; lightning-caused ignitions may appear to be more top-down, whereas distinct patterns of human-caused ignitions may be considered more—but not entirely—bottom-up.
This study highlights the complex role played by ignitions in defining fire likelihood. Simple interactions with other environmental factors may considerably affect the spatial patterns in BP in and around an ignition feature. For example, our results show that varying the constancy of wind direction and the mean duration of fire-conducive weather (fire size) may not alter the overall likelihood of fire, but effectively modulate a tradeoff between the relative BP contrast (i.e., between high- and low-BP areas) and its spatial dispersion (extent). This has practical implications for wildfire-risk analysis in which fire likelihood is estimate from a single set of mean or median conditions, including a single wind direction. However, in areas where large fires predominate, as in boreal biomes, and wind direction is fairly constant, the impact of ignition location on BP patterns is strongly diluted (Barclay et al. 2006).
As with ignitions, the results of a few simplistic manipulations of fuels—which have long been considered the most “controllable” aspect of fire risk—hint at its multi-faceted relationships with other factors. Our results are consistent with those of Finney (2001), who reported a nonlinear response of area burned to the ratio of fuel treatment (i.e., feature) and fire size for individual fires. This phenomenon was observed here as a reduced fuel treatment effect on BP when fires were relatively large (Fig. 4). This is due to the nonlinear (power function) increase in area burned according to the rate of spread. Interpreting BP patterns resulting from varying mean fire sizes and fuel configurations is thus not straightforward. For example, a fuel patch with a rate of spread that is half that of the matrix, which represents a substantial discrepancy in real landscapes, may do little to reduce landscape BP if the fire size is large compared to the patch size.
Given its overarching influence on the fire environment, it is difficult—and perhaps even impossible—to discuss the role of weather without implicitly considering fuels and ignitions. As such, the characterization of fire regimes as weather- or fuels-dominated seems overly categorical. There are fire-prone systems where weather is the dominant cross-scale factor affecting fire likelihood, such as the shrublands of some Mediterranean climate areas (Moritz 2003; Nunes et al. 2005). However, these systems represent an extreme in fuels homogeneity (from a fire spread standpoint) and fire weather severity; fuel and fire weather conditions are more variable in most fire-prone systems (Keane et al. 2009). Nevertheless, our results suggest that large weather-driven fire events exert a disproportionate influence on BP patterns and are consistent with the idea that very large fires periodically homogenize landscapes (in terms of age class distribution) and diminish the influence of fuels on BP (Baker 1994; Kerby et al. 2007).
The peculiar localized spatial patterns seen in our results exemplify how emergent properties result from a set of simple inputs. The interaction between ignition density and the relative flammability of fuels can create an array of BP patterns by compensation or competing effects on fire spread. On the one extreme, when two linear ignition features intersected, an area of disproportionately high BP (a “fire concourse”) created conditions largely overwhelmed the potential effect of the slow fuel feature. By contrast, under certain environmental conditions (e.g., small mean fire size) and a particular placement, the 10-fold increase of the ignition features was largely muffled by the same fuel features. This phenomenon is relevant to the placement and configuration of fuel treatments. Although fuel treatments are often effective at limiting the rate of spread (and hence the size) of large wildfires, their perceived benefits could be reduced if the number of ignitions increase (LaCroix et al. 2006) because of, for example, increased road access (Syphard et al. 2007).
The use of heuristic artificial landscapes, rather than stochastically derived neutral or fractal landscapes, allowed us to refine our understanding of the relative contribution of each factor because the resulting BP patterns could be attributed to one or more causal factors. Although this approach offers tremendous opportunity to learn, the current computational demand for models such as Burn-P3 poses a challenge to the use of a very large factorial design (e.g., Clark et al. 2008), or inter-model comparisons (e.g., Cary et al. 2006). Furthermore, because vegetation succession was not addressed, it was not possible to evaluate potential feedbacks over a temporal horizon. Rather, the strength of the Burn-P3 model is rooted in the accuracy of fire spread. A highly-accurate fire spread module further enhanced our ability to detect very subtle changes in BP. Furthermore, an accurate depiction of emergent spatial fire patterns is essential to our understanding of, and ability to predict, key ecological interactions, such as landscape-scale changes in species composition (Wimberly 2004).
The potential challenge of isolating the effects of the environmental factors that control patterns in BP were partly overcome by studying a set of simplistic artificial landscapes. The results reaffirm the importance of explicitly modeling fire spread in order to account for topological dependencies on the landscape. In many of the simulation scenarios, neighborhood effects coupled with interactions among a small number input variables generated unpredictable outcomes that, despite the simplistic inputs, required further examination of the BP patterns in order to be fully understood. These results reinforce the claims that injecting variability into simple controls of fire-prone systems results in significantly altered fire patterns (Lertzman et al. 1998). Although it was useful to separate fire susceptibility into its mean and variability components—something that appears to be a source of confusion and debate in the fire patterns literature—our results suggest that, in light of natural complexity, it would be extremely difficult to successfully partition the relative contribution of environmental factors in real landscapes. Rather, a more realistic goal may be to describe the manner in which the combinations of factors generate landscape fire patterns.
This work was supported by a Joint Fire Sciences Program grant to the authors. We are grateful to Brett Davis for assistance with geographic information systems and to Meg Krawchuk, Max Moritz, Erica Newman, and Diana Stralberg and two anonymous reviewers for providing constructive comments.