Prévoir pour mieux s’adapter : sensibilité de
l’activité des incendies de forêt aux
changements climatiques et de couverture terrestre
Thèse
Jean Marchal
Doctorat en sciences forestières
Philosophiae doctor (Ph. D.)
Québec, Canada
© Jean Marchal, 2017
Résumé
Le feu de forêt est une perturbation naturelle extrêmement répandue sur la planète. Au Québec, les incendies de forêt ont affecté entre 1990 et 2013 une moyenne de 330 000 hectares par année contre une moyenne de 2,3 millions d’hectares pour le Canada. À l’heure des changements climatiques, dont les conséquences sont annoncées comme très coûteuses pour les sociétés humaines, il est important de développer des stratégies d’adaptations aux changements climatiques le plus tôt possible afin de minimiser les coûts, les impacts environnementaux et les impacts sur nos sociétés. Le climat et la météo influencent fortement les patrons spatiaux et temporels de l’activité des incendies de forêt. La couverture terrestre joue également un rôle important à court terme en modulant l’influence des conditions climatiques sur l’activité des feux et à plus long terme par des changements de composition dans la matrice forestière, graduels (succession forestière, changements climatiques) ou rapides (perturbations). Ainsi, il devient urgent de développer des projections fiables de l’activité future des incendies de forêt tout en réduisant l’incertitude autour de ces projections. Malgré le fait que ces besoins ont été identifiés depuis plus d’une décennie, les méthodes nécessaires à l’élaboration de ces projections restaient à être développées. La capacité de prédire ou de prévoir comment un système peut se comporter à l'avenir a toujours représenté un formidable défi pour la communauté scientifique. Dans mes deux premiers chapitres, j’ai modélisé l’influence des changements climatiques et de végétation sur la fréquence et la distribution des tailles des incendies de forêt à l’aide de modèles statistiques. Mon troisième et dernier chapitre utilise les modèles développés dans les deux premiers pour projeter de quelle manière l’activité des incendies de forêt évoluera dans un contexte où le climat (ou la météo) et la végétation (ou la couverture terrestre) sont
dynamiques. Grâce à ces travaux on peut aujourd’hui projeter quelle sera l’activité future des incendies de forêt dans un contexte de changements dans la matrice forestière et climatiques.
Abstract
Wildfire is an extremely widespread natural disturbance on the planet. In Quebec, forest fires have affected between 1990 and 2013 an average of 330,000 hectares per year against an average of 2.3 million hectares for Canada. In these times of climate change, whose effects are reported as very costly to human societies, it is important to develop adaptation strategies to climate change as soon as possible to minimize costs, environmental impacts and impacts on our societies. Climate and weather strongly influence the spatial and temporal patterns of forest fires activity. Land-cover plays an important role in the short term by modulating the effect of weather on fire activity and longer-term changes in forest composition matrix, gradual (forest succession, climate change), or rapid (disturbances). Thus, it is urgent to develop reliable projections of future activity of forest fires while reducing the uncertainty surrounding these projections. Despite the fact that these requirements have been identified for more than a decade, the methods for the preparation of these projections remained to be developed. The ability to forecast or predict how a system might behave in the future has always been a formidable challenge for the scientific community. In my first two chapters, I modeled the influence of climate change and vegetation on the frequency and size distribution of forest fires using statistical models. My third and final chapter uses models developed in the first two to project how the activity of forest fires will evolve in a context where the climate (or weather) and vegetation (or land-cover) are dynamic. Thanks to this work, we can now project what will be the future activity of forest fires in the context of climate and forest changes.
Table des matières
Résumé ... iii
Abstract ... v
Table des matières ... vi
List of tables ... ix
List of figures ... x
Remerciements ... xvi
Avant-propos ... xix
Introduction générale ... 1
Les incendies de forêt au Canada : un aperçu ... 2
Le feu de forêt : un processus écologique complexe ... 2
Contrôles environnementaux de l’activité des incendies de forêt ... 3
Changements climatiques, vulnérabilité, exposition et adaptation ... 4
Quels outils pour la prévision du futur dans un contexte de changements climatiques ? ... 5
Objectifs de la thèse ... 6
Chapitre 1 – Exploiting Poisson additivity to predict fire frequency from maps of fire weather and land cover in boreal forests of Québec, Canada ... 8 Résumé ... 9 Abstract ... 11 Introduction ... 12 Methods ... 15 Study area ... 15
Data and exploratory analysis... 15
Counts and Poisson additivity ... 19
Model specification ... 21
Parameter estimation, model selection and model evaluation ... 24
Results ... 25
Discussion ... 27
Acknowledgements ... 31
References ... 32
Chapitre 2 – Land cover, more than monthly fire weather, drives fire-size distribution in Southern Québec forests: implications for fire risk
management ... 59 Résumé ... 60 Abstract ... 62 Introduction ... 63 Methods ... 65 Study area ... 65 Data ... 66
Tapered Pareto Distribution ... 67
Regression analysis ... 68 Results ... 70 Discussion ... 73 Acknowledgements ... 76 References ... 77 Appendix 2 ... 91
Chapitre 3 – Turning down the heat: vegetation feedbacks limit fire regime responses to global warming ... 99
Résumé ... 100 Abstract ... 102 Introduction ... 103 Methods ... 106 Study area ... 106 Data ... 106
Dynamic vegetation model ... 107
Landscape fire model ... 108
Ignition ... 109 Escape ... 109 Spread ... 110 Simulation experiments ... 112 Results ... 114 Discussion ... 116 Acknowledgements ... 119 References ... 120
Appendix 3 ... 131
Conclusion générale ... 153
Implications des résultats ... 156
Limites ... 158
Perspectives ... 159
Liste des tableaux
Table 1.1: Selection and diagnostics for fire frequency models ... 37 Table 1.2: Maximum-likelihood estimates and 95% confidence intervals
for each term in top models for lightning-caused and human-caused fires Piecewise 4 and 2 of Table 1.1. ... 39
Table 1.A.1: Habitat types classed as “Open areas” with their
proportional areas within that class. Proportions are calculated over all voxels. ... 44
Table 1.A.2: Proportional contribution of disturbance agents to the
“Recently Disturbed” vegetation class. Proportions are calculated over all voxels. ... 45
Table 1.A.3: Functional forms of piecewise regression models. ... 46 Table 2.1: Alternate statistical models of fire size distribution ordered by
AICc. The best fit for each criteria is shown in bold. ... 82
Table 2.2: Maximum-likelihood estimates and 95% confidence intervals
for each term in top models for lightning- and human-caused fires: models WV_WV and WV_WV of Table 2.1. ... 84
Table 3.A.1: Details on the General Circulation Models used in this study.
... 131
Table 3.A.2: Selection and diagnostics for logistic regression models of
initial fire spread accounting only for fire weather (here the MDC of June), land-cover or both. ... 132
Table 3.A.3: Selection and diagnostics for logistic regression models of
initial fire spread accounting for both fire weather and land cover. .... 133
Table 3.A.4: Alternative formulation of the 𝑥 term from Eq. 3.4 (see main
text). ... 134
Table 3.A.5: Fuel-type trajectories for flammable cover-types in
Scenario 2. ... 135
Table 3.A.6: Fuel-type trajectories for flammable cover-types in
Scenario 3. ... 136
Table 3.A.7: Fuel-type trajectories for flammable cover-types in
Liste des figures
Figure 1.1: Location of the study area relative to the vegetation zones in
Québec. Boreal zone and hemiboreal zone as defined by Brandt (2009), hardwood forest by Robitaille and Saucier (1998). ... 40
Figure 1.2: Predicted annual number of (a) lightning- and (c)
human-caused fire counts plotted against the observations. Observations are represented by the line with breakpoints. Shaded polygon represents the range of variability between 10,000 simulations (parametric bootstrap) for the Piecewise 4 (lightning-caused) and Piecewise 2 (human-caused) models. (b) and (d) correlation between observations and the median of 10,000 simulations. The regression line (solid) and null hypothesis (intercept 0, slope 1; dashed line) are also shown, with regression coefficients and their associated p-values obtained by testing if the regression coefficients differ from expectations at the 5% significance level. ... 41
Figure 1.3: Expected fire frequencies for (a) Piecewise 4
(lightning-caused) and (b, c) Piecewise 2 (human-(lightning-caused) models (Table 1.1). Low and high road density scenarios are described in the Methods. ... 42
Figure 1.A.1: Annual variations in the number of fires and Monthly
Drought Code (MDC) of July. Error bars represent one standard deviation of MDC of July (across pixels). ... 48
Figure 1.A.2: Spatial distribution of Monthly Drought Code (MDC)
interpolated to 100km2 pixels, seen in the years of minimum (a) and maximum (b) regional means. ... 49
Figure 1.A.3: Spatial variation in the proportional abundance of the two
most common forest vegetation classes (a) coniferous dominated forest, (b) recently disturbed (≤ 15 years) dominated forest. ... 50
Figure 1.A.4: Road density (km km-2) within pixel was calculated as the
total length of roads divided by pixel area (100km2). ... 51
Figure 1.A.5: Piecewise regression models variants. Solid and dotted
lines represent the expected fire frequency for two hypothetical cover types. (a) and (b) the slope of the first segment is constrained to 0 so that no fires can occur below the breakpoint (Piecewise 1 and 2), unlike (c) and (d) cases (Piecewise 3 and 4). (a) and (c) describe models where all cover types have an identical breakpoints value (Piecewise 1 and 3) while for (b) and (d) these vary between cover types (Piecewise 2 and 4). β1, β2, β1', β2' and γ, γ1, γ2 are respectively slopes and breakpoints parameters to be estimated. ... 52
Figure 1.A.6: Spatial distribution of human- (a) and lightning- (b) caused
Figure 1.A.7: Maps of the mean deviance residuals for (a) lightning-
(Piecewise 4, Table 1.A.3) and (b) human-caused (Piecewise 2, Table 1.A.3) fire frequency and 2000 – 2010 period. ... 54
Figure 1.A.8: Local Moran’s I map of deviance residuals for lightning-
(Piecewise 4, Table 1.A.3) and human-caused (Piecewise 2, Table 1.A.3) fire frequency. Z score values are displayed only in areas with significant spatial autocorrelation at the 5% level after Bonferroni correction. ... 55
Figure 1.A.9: Predicted annual lightning-caused fire frequency for all
alternative models evaluated. See caption of Table 1.1 for description of model acronyms. Model with the best support is in boldface. ... 56
Figure 1.A.10: Predicted annual human-caused fire frequency for all
alternative models evaluated. See caption of Table 1.1 for description of model acronyms. Model with the best support is in boldface. ... 57
Figure 2.1: Land-cover map with the five classes used in this study. . 86 Figure 2.2: Empirical survival functions of (a) lightning- and (b)
human-caused fire sizes) with 95% confidence intervals (shaded polygons), and empirical distributions (black lines). ... 87
Figure 2.3: Influence of landscape fuel composition on the shape of the
predicted distribution of lightning-caused fires sizes under the best supported model (full model where β and θ are both function of fire weather and land cover, see Tables 2.1 and 2.2). Predicted FSDs for hypothetical landscapes from 100% conifer to 100% deciduous in 10% increments, under means of fire weather covariates. ... 88
Figure 2.4: Influence of fire weather on the shape of the expected
distribution of the lightning-caused fires sizes (full model where β and θ are both function of fire weather and land cover, see Tables 2.1 and 2.2). Predicted FSDs for fire weather conditions in 10 percentiles increments from the most extreme to lowest Monthly Drought Code (MDC) recorded in our data. For illustrative purposes, all lines are for landscapes with 50% hardwoods and 50% conifer-dominated stands. ... 89
Figure 2.5: Expected fire sizes, conditional on the fitted tapered Pareto
distributions of (a) lightning- and (b) human-caused fires along with the location and sizes of recorded fires (black circles). ... 90
Figure 2.A.1: Influence of (a) 𝛽 and (b) 𝜃 parameters on the shape of
the tapered Pareto survival function. For illustrative purposes, we fixed 𝜃 to 100 000 in (a) and 𝛽 at 0.5 in (b). ... 91
Figure 2.A.2: Spatial variation in the proportional abundance of the
conifer-dominated forest (%). ... 92
Figure 2.A.3: Influence of landscape fuel composition on the shape of
the predicted distribution of lightning-caused fires sizes under the best supported model (full model where β and θ are both function of fire weather and land cover, see Tables 2.1 and 2.2). Predicted FSDs for hypothetical landscapes from 100% conifer to 100% deciduous in 10%
increments, under extreme fire weather: 90th percentiles of fire weather covariates. ... 93
Figure 2.A.4: Estimated survival functions for all competitive hypotheses
tested (black lines) with their 95% confidence intervals (grey lines) along with empirical survival function for the distribution of lightning-caused fires sizes (blue lines). 𝛽0 and 𝛾0, intercepts; W, fire weather and V, land-cover terms. ... 94
Figure 2.A.5: Estimated survival functions for all competitive hypotheses
tested (black lines) with their 95% confidence intervals (grey lines) along with empirical survival function for the distribution of human-caused fires sizes (red lines). 𝛽0 and 𝛾0, intercepts; W, fire weather and V, land-cover terms. ... 95
Figure 2.A.6: Influence of landscape fuel composition on the shape of
the predicted distribution of lightning-caused fires sizes under the best supported model (full model where β and θ are both function of fire weather and land cover, see Tables 2.1 and 2.2). Predicted FSDs for hypothetical landscapes from 100% conifer to 100% disturbed in 10% increments, under means of fire weather covariates. ... 96
Figure 2.A.7: Histogram of the starting date (month) of lightning- (blue
bars) and human- (red bars) caused fires during the 2000 – 2010 period. ... 97
Figure 3.1: Location of the study area relative to the vegetation domains
in Québec. We defined the mixed forest as the aggregate of both yellow birch – balsam fir and white birch – balsam fir domains. Vegetation domains are defined in Robitaille and Saucier (1998). ... 126
Figure 3.2: Fuel-type trajectories: (a) southern hardwoods, (b)
mixedwood, (c) coniferous and (d) open, and transition rules for flammable cover-types in Scenario 4. Trajectories are also described in Table 3.A.5 to 3.A.7. The “mixedwood” trajectory regenerates as hardwoods post-fire, but transitions to conifer dominance after 80 years post-fire. ... 127
Figure 3.3: Historical annual variations of the burn rate for the 2000 –
2010 period (black lines) and (a) the entire study area, (b) the hardwood forest and (c) the mixed forest. These are compared to the simulated burn rates under the four scenarios described in the Simulation experiments section (see Methods), i.e. climate change only (red lines), climate change along with the refractory period of 15 years (orange lines), climate change along with fuel dynamics (green lines), and climate change along with the refractory period and fuel dynamics (blue lines). ... 128
Figure 3.4: Empirical survival functions of historical fire sizes (black line)
and simulated fire sizes for the 2089 – 2099 period under the four scenarios described in the Simulation experiments section (see Method), i.e. climate change only (red line), climate change along with the refractory period of 15 years (orange line), climate change along with fuel
dynamics (green line), and climate change along with the refractory period and fuel dynamics (blue line). ... 129
Figure 3.5: Simulated annual variations in the burn rate (blue lines) and
in the relative abundances of the flammable cover-types under the fourth scenario (climate change + refractory period + fuel dynamics) in (a) the entire study area, (b) the hardwood forest and (c) the mixed forest (Fig. 3.1). Flammable cover-types are: hardwoods-dominated stands (light-green lines), conifer-dominated stands (dark-(light-green lines), recently disturbed areas (gray lines) and open areas (orange lines). ... 130
Figure 3.A.1: Set of rules used to assign fuel-type trajectories to forest
stands. We obtained land-cover maps from the Ministère des Ressources naturelles (2013). We derived the hardwoods, conifers and open types from the original cover-types following the rules described in Marchal et al. (2017a). Locations of the “hardwood forest” and “spruce-moss domain” geographic areas are illustrated in Fig. 3.1. ... 139
Figure 3.A.2: Expected lightning-caused fire frequencies for the various
cover-types. Adapted from Marchal et al. (2017a). Legend labels: HW, hardwood; CN, conifer; D, disturbed; O, open. ... 140
Figure 3.A.3: Predicted probabilities that fires escape for a hypothetical
landscape of 50% hardwood and 50% conifer, as function of Monthly Drought Code of June along with the histograms of fire counts (escaped fires at the top). Gray bars represent individual fires. ... 141
Figure 3.A.4: Shape and rational functions of the various functional
forms evaluated. ... 142
Figure 3.A.5: Simulated fire sizes for a homogeneous landscape of
spread probabilities. Loess line (red) is included. ... 143
Figure 3.A.6: Empirical survival function of observed fire sizes (black
lines) with the survival functions of the simulated fires (orange lines) and their 95% prediction intervals, under alternative formulations of the 𝑥 term of the 5-parameter logistic model (see Eq. 3.4 in main text). 𝛽 and 𝜃 are the shape and taper parameters of tapered Pareto distributions used to model the empirical fire size distribution. We selected the model described in panel (a). ... 144
Figure 3.A.7: Estimated relation between fire spread probability
(y-axis), the shape (𝛽, x-axis) and taper (𝜃) parameters of a tapered Pareto fire size distribution model for the range of observed data (see Eq. 3.5). ... 145
Figure 3.A.8: Probability of fire spread calculated from Eq. 3.5 along with
locations and sizes of recorded fires (black circles). ... 146
Figure 3.A.9: Historical mean annual variations of the Monthly Drought
Code (MDC) of May-June (blue), June (green) and July (red) for the 2000 – 2010 period, and (a) the entire study area, (b) the hardwood forest and (c) the mixed forest (Fig. 3.1). Plain lines from 2011 to 2099 are yearly
means of an ensemble of 23 projections (see Table S1). Shaded areas represent one standard deviation around the mean. ... 147
Figure 3.A.10: Historical annual variations of the escape probability for
the 2000 – 2010 period (black line). These are compared to the simulated escape probability under the four scenarios described in the Simulation experiments section (see Methods), i.e. climate change only (red lines), climate change along with the refractory period of 15 years (orange lines), climate change along with fuel dynamics (green lines), and climate change along with the refractory period and fuel dynamics (blue lines). ... 148
Figure 3.A.11: Historical annual variations of the number of fires for the
2000 – 2010 period (black lines) and (a) the entire study area, (b) the hardwood forest and (c) the mixed forest (Fig. 3.1). These are compared to the simulated number of fires under the four scenarios described in the Simulation experiments section (see Methods), i.e. climate change only (red lines), climate change along with the refractory period of 15 years (orange lines), climate change along with fuel dynamics (green lines), and climate change along with the refractory period and fuel dynamics (blue lines). ... 149
Figure 3.A.12: Historical annual variations of the mean fire size for the
2000 – 2010 period (black lines) and (a) the entire study area, (b) the hardwood forest and (c) the mixed forest (Fig. 3.1). These are compared to the simulated mean fire sizes under the four scenarios described in the Simulation experiments section (see Methods), i.e. climate change only (red lines), climate change along with the refractory period of 15 years (orange lines), climate change along with fuel dynamics (green lines), and climate change along with the refractory period and fuel dynamics (blue lines). ... 150
Figure 3.A.13: Simulated annual variations in the burn rate (purple
lines) and in the relative abundances of the flammable cover-types under the second scenario (climate change + refractory period) for (a) the entire study area, (b) the hardwood forest and (c) the mixed forest (Fig. 3.1). Flammable cover-types are: hardwoods-dominated stands (light-green lines), conifer-dominated stands (dark-green lines), recently disturbed areas (gray lines), and open areas (orange lines). Points represent the historical or initial conditions in 2010. ... 151
Figure 3.A.14: Simulated annual variations in the burn rate (purple
lines) and in the relative abundances of the flammable cover-types under the third scenario (climate change + fuel dynamics) for (a) the entire study area, (b) the hardwood forest and (c) the mixed forest (Fig. 3.1). Flammable cover-types are: hardwoods-dominated stands (light-green lines), conifer-dominated stands (dark-green lines), and open areas (orange lines). Points represent the historical or initial conditions in 2010. ... 152
Remerciements
Je tiens tout d’abord à remercier les différents partenaires qui ont contribué au financement de cette recherche à savoir le consortium sur les changements climatiques Ouranos, le Fonds vert, Le Programme des chaires de recherche du Canada et le Centre d’étude de la forêt.
Un merci particulier pour Cumming, mon directeur de recherche, pour m’avoir accueilli au sein de son laboratoire, pour sa disponibilité, pour la confiance qu’il m’a accordée, pour ses précieux conseils et pour la liberté d’action dont j’ai disposé pendant toute la durée de mon doctorat ainsi que pour son soutien financier. Merci pour tout !
Je tenais également à remercier Eliot McIntire, mon co-directeur, pour sa disponibilité, sa réactivité, son sens de l’accueil, les discussions stimulantes, les heures passées devant le tableau blanc et les sessions
brainstorming ainsi que pour son soutien financier. Ce séjour à Victoria
aura largement contribué à faire avancer cette thèse et sans ton aide je n’aurais jamais pu mener à bien ce doctorat, un grand merci !
Je tiens à remercier toutes les personnes avec qui j’ai pu avoir des discussions stimulantes : Louis Bélanger et François Brassard pour leurs conseils avisés. Louis et François ont été source de nombreuses discussions stimulantes sur des sujets variés comme la foresterie, les aires protégées, la conservation ou encore le sujet de cette thèse : les incendies de forêt. Je remercie Sylvie Gauthier et Yan Boulanger pour des discussions stimulantes sur les effets des changements climatiques sur l’activité des incendies de forêt, ainsi que pour les infos sur les objectifs
de la SOPFEU en ce qui concerne l’extinction des feux au Québec. Je remercie également Claude Samson pour notre discussion sur le grand écosystème du Parc national du Canada de la Mauricie.
Ce travail n’aurait pas été possible sans le soutien technique dont j’ai disposé tout au long de ma thèse. Je tiens à remercier Pierre Racine pour m’avoir initié aux joies de PostGIS, Stefano Biondo pour m’avoir permis d’accéder aux données écoforestières, Travis Logan pour l’accès aux données climatiques, Alex Chubaty pour le soutien logistique à Victoria. Je souhaite également remercier Calcul Québec et Calcul Canada pour les ressources qui ont été mises à ma disposition et sans lesquelles je n’aurais pu mener à bien cette thèse.
Je remercie également les collègues du labo pour la bonne ambiance de travail, les moments de détentes et les sorties. Certains pour m’avoir supporté pendant de longues années et pour les discussions sur les statistiques, d’autres pour m’avoir tant de fois recentré sur mon doctorat notamment avec des « Fais ton doc ! », m’avoir fait découvrir de nouveaux horizons (paradoxalement) et ton soutien sans failles ! Un merci spécial à Yong pour les sorties, ta bonne humeur au quotidien et ton aménité. Je tiens également à remercier chaleureusement les Beavers et leur désormais fameux cousin congolais pour tous ces moments inoubliables ! Ce fût et ce sera toujours un plaisir de vous côtoyer.
Je tiens à remercier particulièrement Yan Boulanger, Martin Simard et Francis Zwiers pour avoir accepté d’être membres du jury.
Un merci particulier aux habitants de la maison bon-accueil pour ces moments inoubliables ainsi qu’à Gilles pour ton accessibilité, les
Je remercie du plus profond de mon cœur ma famille et en particulier mes parents pour leur soutien et leur patience tout au long de ces années.
Finalement, je tiens à remercier toutes les personnes que je n’ai pas citées et qui ont contribué de près ou de loin à cette thèse. Merci !
Avant-propos
Cette thèse est articulée en trois chapitres rédigés sous la forme d’articles scientifiques pour être ensuite publiés et sont rédigés en anglais. Je suis l’auteur principal de chaque article et Steve Cumming mon directeur de recherche ainsi que Eliot McIntire mon co-directeur en sont co-auteurs pour avoir contribués à la formulation des objectifs et hypothèses, à l’interprétation des résultats et à la révision des articles. Les objectifs et méthodes utilisées pour chaque chapitre sont présentés succinctement dans l’introduction générale. De même un résumé court des résultats et conclusions principales de chaque article est présenté dans la conclusion générale. La version des articles inclus dans cette thèse est la version acceptée pour publication, ou qui sera soumise prochainement.
Chapitre 1
Le premier article est intitulé « Exploiting Poisson additivity to predict fire
frequency from maps of fire weather and land cover in boreal forests of Québec, Canada ». Ecography, 40, 200–209.
Chapitre 2
Le deuxième article s’intitule « Land cover, more than monthly fire weather, drives fire-size distribution in Southern Québec forests: implications for fire risk management ». L’article a été soumis à la revue Plos One et est actuellement en révision.
Chapitre 3
Le troisième article s’intitule « Turning down the heat: vegetation feedbacks limit fire regime responses to global warming ». L’article sera prochainement soumis à la revue Global Change Biology.
Co-auteurs
Steve Cumming
Département des Sciences du Bois et de la Forêt, Pavillon Abitibi-Price, Université Laval, Québec, QC G1V 0A6, Canada.
stevec@sbf.ulaval.ca
Eliot McIntire
Canadian Forest Service, Natural Resources Canada, 506 Burnside Rd W, Victoria, BC, Canada, V8Z 1M5
“The world in which you were born is just one model of reality.” -Wade Davis
Introduction générale
Les changements climatiques sont aujourd’hui une réalité et constituent une menace grandissante aussi bien pour la biodiversité que pour l’humanité. On s’attend à ce que les changements climatiques affectent de manière prononcée le fonctionnement des écosystèmes et notamment les processus écologiques qui sont au cœur de leur fonctionnement (IPCC 2014). Le feu est l’un de ces processus écologiques clés dans les écosystèmes boréaux et permet par exemple à de nouvelles espèces de coloniser les zones récemment brûlées et opère ainsi un changement dans la trajectoire de succession de ces forêts. Au cours des deux dernières décennies, les incendies de forêt ont reçu une attention considérable en raison de leurs impacts écologiques et socio-économiques (Barlow et al. 2003, Krawchuk & Moritz 2014, Appenzeller 2015). En outre, les récents événements à Fort McMurray, AB ont souligné à quel point les sociétés humaines peuvent être exposées aux risques que représentent les incendies de forêt aussi bien pour les installations que les activités humaines. Ces événements nous rappellent également qu’il est important de bien se préparer à ce type d’événements extrêmes dans leur rareté et dans leur intensité, et plus largement de s’adapter aux changements climatiques. Dans le processus d’adaptation aux changements climatiques, l’utilisation de modèles de simulation et de projections futures est un élément central. Ces informations permettront par la suite de potentiellement prendre des décisions éclairées, pertinentes et en temps opportun dans le but de maximiser notre résilience face aux effets des changements climatiques (IPCC 2014). Par conséquent, la qualité de ces informations est déterminante et les projections futures doivent viser à être les plus exactes possible.
Les incendies de forêt au Canada : un aperçu
Les incendies de forêt sont présents dans de nombreuses régions du globe, influençant la distribution globale de la végétation et des écosystèmes autour du globe (Bond et al. 2005). Le feu de forêt est un processus écologique central dans la dynamique de nombreux écosystèmes à travers le monde (Bowman et al. 2009), et notamment dans la forêt boréale (Gauthier et al. 2015), et peut faciliter (Johnstone
et al. 2010, Fletcher et al. 2014) ou au contraire empêcher (Jasinski &
Payette 2005, Staver et al. 2011) la transition entre différents états alternatifs stables. Les incendies de forêt créent une mosaïque de peuplements de différents âges, structures et compositions (Payette 1992, Turner et al. 1997) mais peuvent également agir comme agents d’homogénéisation lorsque de grandes superficies sont affectées. Au Canada, les feux sont principalement causés par la foudre dans le nord du pays alors que les feux d’origine anthropique sont beaucoup plus fréquents dans le sud du pays, où se concentre la population humaine (Stocks et al. 2002). Les feux causés par la foudre contribuent pour la majeure partie des superficies incendiées. Une large majorité des incendies de forêt sont de petites superficies (inférieures à quelques hectares), mais les grands incendies (> 1 000 ha) qui comptent pour moins de 1% des incendies contribuent pour la plus grande partie des superficies incendiées (Strauss et al. 1989, Chabot et al. 2009).
Le feu de forêt : un processus écologique complexe
Le feu de forêt est un processus écologique complexe présentant un comportement non linéaire, résultant des interactions multi-échelles et des rétroactions positives ou négatives entre les différents composants du système. Face à cette complexité, le processus de propagation du feu de forêt peut être décomposé en trois processus stochastiques :
l’initiation, la propagation à l’échelle locale puis à l’échelle du paysage. Par la suite, on peut utiliser des modèles statistiques pour approximer comment ces processus et les contrôles environnementaux interagissent et mènent à l’émergence des patrons de brûlage que l’on observe. Cette décomposition permet de décrire et de représenter plus finement comment les différents éléments du système interagissent entre eux malgré le fait qu’ils soient associés à différentes échelles temporelles et spatiales. Finalement, cette dissociation permettra de mieux comprendre comment chacun des processus contribue à l’activité des incendies de forêt. En effet, l’influence des contrôles environnementaux varie à la fois qualitativement et quantitativement avec l’échelle spatio-temporelle d’observation, mais aussi selon le processus étudié.
Contrôles environnementaux de l’activité des incendies de forêt
Le climat (ou la météo), le type de couverture terrestre (ou de combustible) et la topographie sont les principaux contrôles de l’activité des feux au Canada (Johnson 1992). L'activité des feux est un terme général utilisé pour décrire le nombre d'incendies, leurs comportements et/ou l'empreinte qui résulte des brûlages (M. Krawchuk comm. pers. 2016). Les variations temporelles et spatiales dans l’activité des feux sont directement influencées par ces trois contrôles, mais aussi par les interactions entre ces contrôles. Par exemple, le risque d’initiation d’incendie est non seulement plus élevé dans un peuplement à dominance coniférienne que dans un peuplement feuillu pour des conditions météorologiques identiques (Krawchuk et al. 2006), mais augmentera également plus vite avec des conditions de sécheresse croissantes (Marchal et al. 2017). En outre, un feu ne pourra prendre si les conditions météorologiques sont trop humides, et ce quel que soit le type de couverture terrestre.
Au Québec, le taux annuel de brûlage, c’est-à-dire la proportion du territoire qui est brûlée en moyenne annuellement, s’accroît d’est en ouest sous l’effet du gradient de précipitations et les périodes de sécheresse sont généralement plus longues et plus sévères à l’ouest qu’à l’est (Gauthier et al. 2001, 2008). De même, au Canada on observe que les feux se propagent plus facilement dans le nord que le sud notamment à cause du gradient de végétation (Wang et al. 2014). La proportion des peuplements forestiers à dominance feuillue diminue dans le paysage avec la latitude, de même que la proportion moyenne de feuillus dans les peuplements. Or, les peuplements feuillus sont beaucoup moins susceptibles de brûler que les peuplements résineux (Hély et al. 2000) et ce particulièrement pendant la saison de végétation. Outre le fait que l’activité des feux soit contrôlée par des facteurs environnementaux, elle dépend également de l’historique passé des perturbations et notamment de l’activité des feux (Parks et al. 2015). Plusieurs études ont apporté des éléments de preuve qui suggèrent que les zones récemment brûlées sont moins susceptibles de brûler à nouveau, et ce pour une période allant jusqu’à quelques décennies (Cumming 2001, Krawchuk & Cumming 2011, Parks et al. 2015).
Changements climatiques, vulnérabilité, exposition et adaptation
Le climat exerce un contrôle important sur l’activité des incendies de forêt qui sont de fait très sensibles aux changements climatiques, qui vont les affecter à de multiples échelles spatio-temporelles (Bowman et
al. 2009) ; par exemple, en modifiant directement les conditions
météorologiques qui contrôlent les régimes de feux et indirectement en modifiant l’abondance et la distribution de la composante feuillue dans le paysage et la structure d’âge des forêts. Étant donné l’ubiquité et la
magnitude des changements climatiques récents et futurs (IPCC 2013), il est devenu urgent de pouvoir prédire de quoi le futur sera fait. En effet, s’adapter tôt dans le processus de changement offrirait plus d’opportunités pour évaluer les options possibles et les risques qui leurs sont associés afin de maximiser notre résilience face aux changements climatiques (IPCC 2014) et limiteraient les coûts liés à l’adaptation (Hallegatte 2009). Malgré le fait que des changements dans l’activité des feux sont largement anticipés, il reste une grande part d’incertitude quant à la grandeur de ces changements et la vitesse à laquelle ils vont se produire (Moritz et al. 2012). Notre capacité à pouvoir prédire avec précision et exactitude quels seront ces changements influence directement notre aptitude à identifier nos vulnérabilités face à ces changements et par la suite mettre en place des stratégies d’adaptation pertinentes et maximiser la résilience des sociétés humaines face à ces changements.
Quels outils pour la prévision du futur dans un contexte de changements climatiques ?
La prévision du futur a probablement toujours été l’un des plus grands défis pour les scientifiques et présente un intérêt certain pour l’humanité tout entière. Afin de mieux se préparer face aux défis futurs, il est nécessaire d’avoir des projections fiables, mais aussi de limiter l’incertitude autour de telles projections. Les modèles statistiques sont fortement utilisés dans la prévision du futur. Malgré la complexité des systèmes écologiques, les modèles statistiques, bien formulés, peuvent décrire raisonnablement bien la dynamique passée d’un système au travers des relations entre observations et variables environnementales. Néanmoins, leur capacité à prédire comment un système va se comporter dans des conditions encore jamais observées est limitée (Evans 2012).
Contrairement aux modèles statistiques, les modèles mécanistes capturent les principaux mécanismes sous-jacents qui gouvernent les systèmes écologiques et les patrons simulés émergent alors des interactions entre les différentes composantes du système. Dans un contexte de changements climatiques où il n’y aura pas forcément d’analogues aux conditions abiotiques et biotiques observées dans le passé (Williams & Jackson 2007; Williams et al. 2007), les modèles mécanistes semblent tout indiqués pour faire des prédictions plus fiables (Cuddington et al. 2013). Toutefois, ces modèles ne viennent pas sans limitations, ils demandent par exemple de nombreux paramètres, une connaissance approfondie des mécanismes principaux du système écologique étudié et des données écologiques qui ne sont pas toujours disponibles. Par conséquent, les deux approches sont souvent combinées (Gustafson 2013) et les modèles statistiques peuvent servir à informer les parties plus mécanistes du modèle global.
Objectifs de la thèse
L’objectif de ma thèse était de développer des méthodes pour quantifier puis intégrer dans des modèles de simulations la sensibilité de l’activité des feux à deux de ces principaux contrôles environnementaux : la météo (ou le climat) et la couverture terrestre (ou la végétation). Malgré le fait que la végétation soit un contrôle important de l’activité des feux (Krawchuk et al. 2006, Pausas & Paula 2012, Wang et al. 2014), elle n’a été que rarement intégrée dans les modèles statistiques qui décrivent les relations entre le feu et la météo. En outre, les interactions et rétroactions entre le feu, les conditions climatiques et la couverture terrestre sont rarement représentées dans ces modèles. Par conséquent, la fiabilité des projections produites par ces modèles est discutable dans le sens où elles pourraient largement sous-estimer ou surestimer les
conséquences des changements climatiques sur l’activité des feux comme nous le montrerons par la suite, et par le fait induire en erreur. Étant donné que les projections issues des modèles de simulation sont au cœur du processus d’évaluation des risques liés aux changements climatiques et subséquemment du développement de stratégies d’adaptation pertinentes, il apparait essentiel de produire des projections valides.
Dans les deux premiers chapitres je cherchais à mieux comprendre quelles étaient la nature et la force des liens qui existaient entre les incendies de forêt et les processus biophysiques qui contrôlent leur activité. Étant donné que l’activité des incendies émerge des interactions entre les processus d’allumage et de propagation des feux avec les conditions environnementales, j’ai d’abord scindé l’activité des feux en ses deux grandes composantes. Cela a constitué les deux premiers axes de ma thèse. J’ai modélisé la réponse de la fréquence d’allumage puis de la distribution de la taille des feux aux variations spatio-temporelles des conditions météorologiques et de type de couvert. La fréquence d’allumage peut être décrite comme étant le nombre d’incendies par unités de temps et de surface tandis que la distribution de la taille de ces feux reflète quant à elle la facilité de ces feux à se propager dans le paysage. Pour le troisième et dernier axe je me suis intéressé à l’aspect dynamique du système climat-feux-végétation. J’ai simulé l’activité des feux dans un contexte de changements climatiques, en intégrant la sensibilité aux changements de conditions climatiques et d’abondance relative des types de couverts dans le paysage ainsi que deux rétroactions négatives clés liées aux processus de régénération et de succession après feu.
Chapitre 1 – Exploiting Poisson additivity to predict fire
frequency from maps of fire weather and land cover in
boreal forests of Québec, Canada
Résumé
Les modèles prédictifs de la fréquence des incendies de forêt conditionnelle aux conditions météorologiques et de couverture terrestre sont indispensables pour évaluer comment la future distribution spatiale des types de couvert et des conditions météorologiques va influencer les régimes de feu. Nous avons modélisé l’effet des variables bottom-up (par exemple la couverture terrestre) et top-down (par exemple la météo) simultanément avec des données agrégées ou interpolées à des unités spatiales de 100 km2 et temporelles de 1 an dans la forêt boréale du Québec, Canada. Dans le cas des modèles d’incendies d’origine anthropique, nous avons utilisé la densité des routes comme substitut de la facilité d’accès aux territoires. Nous avons exploité la propriété d’additivité des distributions de Poisson pour estimer la fréquence des incendies de forêt pour chaque type de couvert, ce qui ne serait normalement pas possible avec des données ayant la présente résolution spatiale. Nous avons utilisé des modèles dits en « bâton de hockey » pour modéliser la relation non linéaire entre la météo et la fréquence des incendies, et ce simultanément pour chaque type de couvert. Les taux estimés peuvent être considérés comme la moyenne du nombre de feux attendus par unité de surface et de temps. Il en résulte que ces taux peuvent être recalculés à des résolution spatiales et temporelles arbitraires. Nos résultats montraient que la fréquence des incendies de forêt augmentait de façon non linéaire avec des niveaux de sécheresse croissants et plus rapidement dans les zones récemment perturbées que les autres types de couvert. La densité des routes exerçait la plus forte influence sur la fréquence des incendies d’origine anthropique, qui était positivement corrélée avec la densité des routes. Les estimés peuvent être utilisés pour paramétrer le module d’allumage des feux dans les modèles de simulation, qui ont souvent une résolution différente de celle
essentielle dans l'intégration des rétroactions biotiques et abiotiques, de l’aspect dynamique de la couverture terrestre, et des projections climatiques dans les prévisions écologiques. L’idée d’utiliser la propriété d’additivité des distributions de Poisson pour dévoiler des processus écologiques se produisant à haute résolution à partir de données de faible résolution pourrait avoir des applications dans d'autres domaines de l'écologie.
Abstract
Predictive models of fire frequency conditional on weather and land cover are essential to assess how future cover-type distributions and weather conditions may influence fire regimes. We modeled the effects of bottom-up variables (e.g. land cover) and top-down variables (e.g. fire weather) simultaneously with data aggregated or interpolated to spatial and temporal units of 100 km2 and 1yr in the boreal forest of Québec, Canada. For models of human-caused fires, we used road density as a surrogate for human access and behaviour. We exploited the additive property of Poisson distributions to estimate cover-type specific fire count rates, which would normally not be possible with data of this spatial resolution. We used piecewise linear functions to model nonlinear relations between fire weather and fire frequency for each cover-type simultaneously. The estimated conditional rates may be considered as expected mean counts per unit area and time. It follows that these rates can be rescaled to arbitrary spatial and temporal extents. Our results showed fire frequency increased nonlinearly as aridity increased and more quickly in disturbed areas than other types. Road density exerted the strongest influence on the frequency of human-caused fires, which were positively correlated with road density. The estimates may be used to parameterize the fire ignition component of spatial simulation models, which often have a resolution different from that at which the data were collected. This is an essential step in incorporating biotic and abiotic feedbacks, land-cover dynamics, and climate projections into ecological forecasting. The insight into the power of Poisson additivity to reveal high-resolution ecological processes from low-high-resolution data could have applications in other areas of ecology.
Introduction
Wildfire is the predominant natural disturbance in the boreal forests of North America (Gauthier et al. 2015). A fire regime is a quantitative description of the characteristics of fires that occur in a given region, including their number, size, intensity, severity, seasonality, and cause (Whelan 1995). In boreal forests, these attributes are affected by climate and fire weather (Johnson 1992), land cover (Krawchuk et al. 2006, Parks
et al. 2012), and human activities (Gralewicz et al. 2012). Here, we focus
on counts per unit area and time. This quantity is a rate or, equivalently, a frequency. “Frequency” has also been used to refer to the expected proportion of a given region that will burn each year (Johnson and Wagner 1985). The proportional annual area burned is simply the sum of the area burned by all the fires that occurred within a year, divided by the size of the study area. Thus, in this second sense, fire frequency is a function of the number and size of fires. In other words, fire frequency conflates at least two processes: fire count frequency and fire spread. We are concerned here with the first of these two processes.
Models based on historical relations between fire and fire weather predict steadily increasing wildfire activity in Canada by the end of the 21st century, due to more frequent and longer periods of low fuel moisture (e.g. Wotton et al. 2010). Fire activity is a general term used to describe fire events, their behaviour, and/or the footprint that results from burning (M. Krawchuk pers. comm. 2016). However, weather alone is not sufficient to explain present patterns (Krawchuk et al. 2006) or to predict future trends of wildfire activity (Higuera et al. 2009, Girardin et al. 2013). Vegetation, or fuel type, also plays a role (Krawchuk et al. 2006). Climate change will directly alter some of the factors driving fire regimes (e.g. temperature, precipitation, wind), but will also act indirectly by shifting
tree species distributions (Terrier et al. 2013). In the boreal forest of Canada, deciduous species are expected to increase in abundance at the current northern limits of their ranges, and to expand their ranges northward (Morin and Thuiller 2009, Zhu et al. 2014). Stands dominated by deciduous trees are less fire-prone than those dominated by coniferous trees (Hély et al. 2000), which would tend to partially counteract the effects of warming (Girardin et al. 2013) if deciduous stands were to become more abundant in the landscape. Under some conditions, cover-type shifts might completely override the influence of fire weather by altering landscape flammability (Higuera et al. 2009). Likewise, there is some evidence that areas recently burned may be less likely to burn again for some years or decades (Cumming 2001, Krawchuk and Cumming 2011). These indirect effects imply a form of self-organization (Malamud 1998, Krawchuk et al. 2006), which would tend to moderate the direct effects of climate warming on fire activity. To predict and model fire regimes under future conditions, it is necessary to disentangle these effects.
The spatial patterns of fire activity result from interactions among land cover, climate or fire weather, and topography, which act at different scales (Heyerdahl et al. 2001, Parks et al. 2012). Climate and fire weather are considered top-down controls, acting at large spatial scales (Falk et
al. 2011). Cover types or fuels are usually considered bottom-up controls,
with high spatial heterogeneity at small scales (Parks et al. 2012). In understanding interactions among these factors, the scales of observation and data aggregation are crucial (Levin 1992, McIntire and Fajardo 2009). The integration of top-down with bottom-up controls poses challenges for statistical modeling of fire regime attributes. On the one hand, models built at low spatial resolution may be unable to detect the effect of
interest. For example, regional models of annual area burned may not capture the heterogeneity present at small scales (Parisien et al. 2011), and the effects of fuels and weather may be confounded. On the other hand, standard approaches to modeling spatial point processes such as fire counts may require data of higher spatial or temporal resolution than are available. When land-cover varies at scales finer than the spatial resolution of fire count data, the cover-type associated with a given fire count cannot always be determined. We present methods to overcome these challenges.
Our primary objective was to develop predictive statistical models of fire frequency as a function of fire weather and land cover, as represented by categorical data such as vegetation or land-cover types. As a secondary objective, we sought parameter estimates that were independent of the spatial units of analysis. Scalable rate estimates could be used, for example, in spatial simulations of ecosystem dynamics under land use and climate change, without constraining the spatial resolution of the simulation model to that of the statistical analysis.
We present a new method for scale-independent estimation of cover- or fuel-type specific count rates from the records of fire management agencies. The method exploits the additive property of Poisson distributions to permit estimates of type-specific count rates even when the cover-types associated with individual fires are not known. We illustrate the approach with fire counts from a large number of landscapes with contrasting abundances of the various land-cover types in the boreal forest of Québec, Canada. We extend our analysis to approximate type-specific, nonlinear relations between annual fire weather and count rates with piecewise linear models. We conducted separate analyses for
lightning- and human-caused fires, which to our knowledge few previous studies have done. In the latter case, we use local road density as a surrogate for human use intensity. We evaluated alternate hypotheses on the associations between count rates and land cover, fire weather, and roads by comparing models including individual factors and all combinations of factors.
Methods
Study area
The study area (Fig. 1.1) covers approximately 197,000 km2 of southern Québec, Canada, encompassing the transition between the northern boreal and southern hardwood forest. The latter is dominated by sugar maple (Acer saccharum Marsh.), red maple (Acer rubrum), and yellow birch (Betula alleghaniensis Britt.). The main species in the coniferous forest are black spruce (Picea mariana (Mill.) B.S.P.), balsam fir (Abies balsamea (L.) Mill), jack pine (Pinus banksiana Lamb), paper birch (Betula papyrifera Marsh.), and trembling aspen (Populus
tremuloides). The climate is humid continental (Gouvernement du Québec
2014a). Regional mean temperatures range from −15°C in winter (December, January, February) to +18°C in summer (June, July, August). Mean seasonal precipitation ranges from 88 to 407 mm in winter and from 153 to 547 mm in summer.
Data and exploratory analysis
We retrieved fire weather, land cover and fire count data for the period 2000 – 2010. The temporal breadth of our analysis was constrained by the availability of digital data necessary to derive a time series of land-cover maps. All data were registered to a 10 km grid land-covering the study area. There were 1,969 pixels x 11 years = 21,659 voxels. The grid
resolution was consistent with that used for downscaling climate projections (McKenney et al. 2011) and the spatial resolution of many past studies (e.g. Krawchuk et al. 2006).
Fire counts
Our source of fire count information was the forest fire database maintained by the Ministère des Resources Naturelles du Québec. Fire attributes include location, date of detection, and cause. We assumed a constant and high level of fire detection efficiency over the study region and period given the high capabilities of the fire protection agency (Société de protection des forêts contre le feu 2014). Whenever two or more fires with the same date of initiation were reported, we used other recorded attributes (e.g. location and final size) to verify that a single fire had not been reported more than once. Annual counts, for human-caused and for lightning-caused fires, were determined for each pixel and year by registering the recorded locations to the 10 km grid in a Geographical Information System.
Fire weather
We obtained spatially interpolated monthly means of daily mean, minimum, and maximum temperature (°C) and total monthly precipitation (mm) from Natural Resources Canada (McKenney et al. 2011). We estimated Monthly Drought Code (MDC) as in Bergeron et al. (2010) for April through October in each year. The MDC is a monthly version of the daily Drought Code (Girardin and Wotton 2009), an indicator of the moisture content of deep, compact soil organic layers (Van Wagner 1987). MDC was positively correlated with annual area burned (Girardin and Wotton 2009, Bergeron et al. 2010). A systematic variable-selection process (see methods in appendix A) identified July MDC
(hereafter MDC) as a covariate for human- and lightning-caused fire frequency at the scale of our voxels. Annual variations in regional aggregates of these variables are shown in Fig. 1.A.1 MDC varied widely both in time and space, but was consistently higher in the west, reflecting regional gradients in precipitation (Grondin et al. 1996, Fig. 1.A.2).
Land cover
We derived land-cover composition data from digital maps of the Québec 4th inventory (Ministère des Ressources naturelles 2013). The inventory produced polygons interpreted from 1:20,000 aerial photographs flown between 2000 and 2010 for 97% of the area, with the remaining area covered by photographs from the preceding inventory, which was flown in the 1990s. Inventory attributes include tree species composition, stand age and date of origin, disturbance history, and various categorical fields for non-forested areas. From these, we classified land cover as hardwoods (HW), conifers (CN), disturbed (D), open (O), and open water. Forested stands were classified as HW when >50% of total basal area was deciduous, and as CN otherwise. Polygons that had been disturbed within 15 years preceding the fire count date were designated as D, and accounted for 8% of the study region. Of this 8%, 71% were logging, and another 21%, plantations Table 1.A.2. Open areas, which covered 8% of the region, primarily were wetlands (Table 1.A.1). Another 10% of the study region was open water.
Two versions of the 4th inventory exist: the original interpretation, and a version that includes updates of cumulative annual disturbance. We created our land-cover-composition time series from the updated versus backdated disturbed areas to the pre-disturbance cover for years prior to the disturbance. However, roughly 5% by area of the original inventory
was classified as disturbed before the year in which the photograph was taken. For those areas, no digital information about pre-disturbance cover was available. We filled in these areas with the MODIS land-cover product (MCD12Q1, Collection 5.1; Friedl et al. 2010). We reclassified the Plant Functional Type legend into our types and then used the classified images to fill gaps in the annualised inventory maps.
For each voxel, indexed by location i and year t, we calculated the proportional areas 𝑉𝑘,𝑖,𝑡, 𝑘 = 1, … ,5 of the five cover types in units of 100 km2. Areas where cover type could not be determined (roughly 1% of total area) were aggregated with open areas under the assumption that closed-crown forests would have been identified as such when the photographs were interpreted. We excluded areas covered in open water, as clearly no fires can start there. Accordingly, the sum of the areas of the other four cover-types is the total flammable area in each pixel. Regional variations in the cover of CN and D types are shown in Fig. 1.A.3. The distribution of HW is nearly the inverse of CN, because hardwoods are most abundant in the south. The O type was most abundant in the northwestern part of the study area.
Road density
Most of the study region is rural with low population density, or nearly uninhabited tracts of forest. The frequency of human-caused fires is less related to the human settlement than to human resource extraction and recreational activities which are restricted to the proximity of roads (Martell et al. 1989). Road density (km km-2) has been found to be correlated with the human-caused fire counts (Cardille et al. 2001), acting as a surrogate for human access to forests. We used publicly available road-network data (Gouvernement du Québec 2014b) to derive road
density by summing the length of all roads for each pixel and dividing by the pixel area (Fig. 1.A.4). Road densities were assumed to be constant over the study interval. Voxel road densities ranged from 0 to 3.79 km km-2 (mean = 0.15, sd = 0.32).
Counts and Poisson additivity
Fire count data are counts of events (Cunningham and Martell 1973) and should therefore be modeled by a discrete probability distribution, such as the Poisson (Wotton et al. 2010) or Negative Binomial distribution (Arienti et al. 2009). The parameter that determines the expected value, or mean, of these distributions is a rate, which must be greater than 0. Thus, we wished to express that rate as a function of land cover and fire weather. Because we used categorical land-cover data, the procedure is equivalent to fitting a unique model for each cover type. In inferential terms, this means we are testing whether the mean fire frequency varies among cover types. Perhaps the most obvious modeling approach is to fit a Generalized Linear Model, with logarithmic link to enforce non-negativity. However, the resultant parameter estimates would not be interpretable as type-specific rates because individual model terms are multiplicative on the response scale. In contrast, the property that would allow for scale-insensitive parameter estimates is additivity: other things being equal, doubling the area of given a cover-type should double the expected number of fires. A consequence of the more standard logarithmic link is that the true, scale-independent relation between the response variable and the underlying factors cannot be determined. Modeling at scales where local homogeneity of land cover can be assumed, say 1 ha, would not only require precise count locations, but would greatly inflate the proportion of zeroes in the data, leading to analytical difficulties, and the results would remain scale-dependent.
The locations of individual counts are associated with 10x10 km cells, not homogeneous land-cover patches. How, then, may cover-type specific rates be estimated? To estimate cover-specific rates, we assumed that the number of counts per unit area of cover-type 𝑖 = 1,2 is a random variable 𝑿𝑖 ~ Poisson(𝜆𝑖) where 𝜆𝑖 are the type-specific rate parameters to be estimated (the relational symbol ~ means “is distributed as”). To illustrate, suppose that the annual counts per unit area were Poisson, conditional only on land cover, and there were only two cover types. Suppose the cover types were geographically separated, such that type 1 was found only in the north and type 2 only in the south of the study region, with areas 𝑎1 and 𝑎2, respectively. Suppose further that each fire could be assigned accurately to the north or south such that the counts for each subregion, 𝑛1 and 𝑛2, were known with negligible error. Then, the maximum likelihood estimates of the rate parameters are:
𝜆̂𝑖 =𝑛𝑖
𝑎𝑖 (1.1) The same would be true no matter how the areas 𝑎1 and 𝑎2 were spatially arranged, provided the cover type of each fire were known. Now suppose the study region is partitioned into 𝑁 spatial units indexed by 𝑗 = 1, … , 𝑁, and that for each unit, the areas of the two cover types 𝑎𝑗,1 and 𝑎𝑗,2 are known. We can derive the expected number of fires in unit j from the property of Poisson additivity: if 𝑋𝑖 are Poisson random variables with parameters 𝜆𝑖 then the sum 𝑿1+ 𝑿2 ~ Poisson(𝜆1+ 𝜆2) (Forbes et al. 2010, p. 153–154), from which can be deduced the scaling rule 𝑎𝑿1~Poisson(𝑎𝜆1), 𝑎 > 0. It follows that the number of fires in spatial unit
j is a random variable:
𝑋𝑗~Poisson(𝑎𝑗,1𝜆1+ 𝑎𝑗,2𝜆2) (1.2) If we relax our assumption of locational precision to require only that the spatial unit of each fire count can be accurately determined, then we can
assume that the number of counts within each unit 𝑛𝑗 ≥ 0 is known, even though the cover type where any particular fire started is not known. It may seem impossible to estimate the λis because even though the denominator of Eq. 1.1, the total area of a given cover type, can be calculated, the numerator, or total number of counts in each type, cannot be. Suppose, however, that λ1 > λ2. In that case, units with a high proportion of cover type 1 should have more fires than units with a lower proportion. Thus, provided the spatial units have differing proportions of the two cover types, variation among the 𝑛𝑖 provides information about variation among the 𝜆𝑖, which may be estimated from Eq. 1.2 by the method of maximum likelihood. This can be generalised to more than two cover types, and to the case where the 𝜆𝑖 are functions of space- and time-varying factors such as fire weather, and to certain forms of overdispersion by use of the negative binomial in place of the Poisson distribution.
Model specification
We conducted separate analyses for lightning- and human-caused fire counts because their spatial and temporal patterns differ markedly (Stocks et al. 2002, Wang and Anderson 2010). Starting with lightning-caused fires, we initially assumed that counts 𝑦𝑖,𝑡 at pixel i in year t were generated by a Poisson process with intensity or rate 𝜆𝑖,𝑡. The exact locations, and hence cover types of fire start, are unknown, but each fire must have started in one of the four types. We assumed that the number of fires per unit area of each type is also Poisson but that the intensity parameter may vary among types. We made use of the additive property of Poisson processes (Forbes et al. 2010, p. 153–154) to decompose the voxel-level intensity as a mixture of n = 4 cover-type specific Poisson processes, as follows:
𝜆𝑖,𝑡 = ∑(𝜆𝑘 𝑉𝑘,𝑖,𝑡) 𝑛
𝑘=1
(1.3)
where 𝜆𝑘 are the Poisson intensities for the area of cover type k; 𝑉𝑘,𝑖,𝑡 is the area of cover type k in pixel i in year t, in units of 100km2.
We next considered how the intensity of the fire count process may vary as a function of fire weather. We first assessed the functional response to fire weather, independent of land cover, by graphical analysis. This revealed a positive and nonlinear relation between frequency and MDC, where the slope increased sharply above a certain threshold value or breakpoint. There was also some indication that the process may saturate at high MDC levels. We explored this possibility with Holling type III and IV (Bolker 2008) sigmoidal forms, but we were not able to verify the apparent effect due to lack of data at the upper end of the MDC range (results not shown).
To incorporate the effects of fire weather, we begin with a linear model with unique intercept and slope for each cover type. We then rewrote voxel-level intensity as:
𝜆𝑖,𝑡 = ∑ 𝑉𝑘,𝑖,𝑡 𝑛
𝑘=1
(𝜆𝑘+ 𝛽𝑤,𝑘𝑊𝑖,𝑡) (1.4)
where the fire-weather covariate 𝑊𝑖,𝑡 is the MDC of July in pixel i in year
t. We approximated the observed nonlinear relation with piecewise linear
regression models, where two or more lines are linked at breakpoints (Toms and Lesperance 2003). We then introduced the assumption that no fires can start when MDC = 0, a situation that corresponds to the full saturation of large woody debris and deep soil organic matter (Wotton
and Beverly 2007). It follows that the intercept terms of Eq. 1.5 are 0. Accordingly, the full piecewise linear regression model for lightning-caused fires is:
𝜆𝑖,𝑡 = ∑ 𝑉𝑘,𝑖,𝑡(𝛽𝑤,𝑘𝑊𝑖,𝑡+ 𝛽𝑤,𝑘′ ∙ 𝑔(𝑊 𝑖,𝑡, 𝛾𝑘)) 𝑛 𝑘=1 (1.5) where: 𝑔(𝑎, 𝑏) = {0 if 𝑎 ≤ b𝑎 − 𝑏 if 𝑎 > b (1.6)
𝑊𝑖,𝑡 is as in Eq. 1.4 and 𝛾𝑘 are breakpoint locations to be estimated. Inherent variation in vegetation characteristics such as moisture content, vertical foliage profiles, understory composition, and fuel load (Hély et al. 2000, Krawchuk et al. 2006) may result in differences in flammability (Beverly and Wotton 2007, Wotton and Beverly 2007). Accordingly, we allowed the location of breakpoints and both slopes to vary among cover types. Starting from the full model (Piecewise 4; Eq. 1.5, Fig. 1.A.5d), we built nested alternatives by imposing two restrictions: (a) Common breakpoint, i.e., 𝛾𝑘 are identical for all cover types (Piecewise 1 and 3; see Fig. 1.A.5a and 1.A.5c) and (b) No fires under wet conditions: i.e., there are no counts when 𝑊𝑖,𝑡 ≤ 𝛾𝑘 (Piecewise 1 and 2; see Fig. 1.A.5a and 1.A.5b). All alternative models are presented fully in Table 1.A.3.
For the case of human-caused fires, we considered road density in addition to the covariates already used. We introduced an interaction term between land cover, fire weather and road density representing the additional number of fires that occur as road density increases while preserving the structure of dependency on land cover and fire weather. Thus Eq. 1.4 becomes:
