Extreme value analysis of wildfires in Canadian boreal forest ecosystems

Large fires are a major disturbance in Canadian forests and exert significant effects on both the climate system and ecosystems. During the last century, extremely large fires accounted for the majority of Canadian burned area. By mak- ing an instaneous change over a vast area of ecosystems, extreme fires often have significant social, economic, and ecologi- cal consequences. Since extreme values of fire size always situate in the upper tail of a cumulative probability distribution, the mean and variance alone are not sufficient to fully characterize those extreme events. To characterize the large fire be- haviors in the upper tail, the authors in this study applied three extreme value distribution functions: (i) the generalized ex- treme value (GEV) distribution, (ii) the generalized Pareto distribution (GPD), and (iii) the GEV distribution with a Poisson point process (PP) representation to fit the Canadian historical fire data of the period 1959-2010. The analysis was con- ducted with the whole data set and different portions of the data set according to ignition sources (lightning-caused or hu- man-caused) and ecozone classification. It is found that (i) all three extreme statistical models perform well to characterize extreme fire events, but the GPD and PP models need extra care to fit the nonstationary fire data, (ii) anthropogenic and natural extreme fires have significantly different extreme statistics, and (iii) fires in different ecozones exhibit very different characteristics in the view of statistics. Further, estimated fire return levels are comparable with observations in terms of the magnitude and frequency of an extreme event. These statistics of extreme values provide valuable information for future quantification of large fire risks and forest management in the region. Resume : Les grands feux constituent une perturbation majeure dans les forets canadiennes et ont des effets importants tant sur le systeme climatique que sur les ecosystemes. Au cours du dernier siecle, la majorite des superficies brulees au Canada l'ont ete lors de feux extremement importants. En provoquant des changements instantanes sur de vastes superficies des eco- systemes, les feux extremes ont souvent d'importantes consequences sociales, economiques et ecologiques. Etant donne que les valeurs extremes de la dimension des feux se situent toujours a l'extremite superieure d'une distribution de probabilite cumulative, la moyenne et la variance seules ne suffisent pas pour caracteriser pleinement ces evenements extremes. Pour caracteriser le comportement des grands feux dans l'extremite superieure de la distribution, les auteurs de cette etude ont ap- plique trois fonctions de distribution de valeurs extremes : (i) la distribution generalisee de valeurs extremes (DGVE), (ii )l a distribution Pareto generalisee (DPG) et (iii) la DGVE avec une representation par le processus ponctuel de Poisson (PP) pour decrire les donnees canadiennes de l'historique des feux durant la periode 1959 a 2010. L'analyse a ete realisee avec le jeu de donnees au complet et avec differentes portions selon la source d'allumage (feu cause par la foudre ou par l'homme) et la classification de l'ecozone. On constate que (i) les trois modeles de statistiques extremes sont capables de bien caracteriser les episodes de feu extreme mais les modeles DPG et PP necessitent une attention particuliere pour ajuster les donnees de feu evolutif, (ii) les feux extremes d'origine humaine et naturelle ont des statistiques extremes significative- ment differentes et (iii) compte tenu des statistiques, les caracteristiques des feux sont tres differentes selon l'ecozone. De plus, les niveaux estimes de retour du feu sont comparables aux observations en termes d'ampleur et de frequence d'un eve- nement extreme. Ces statistiques de valeurs extremes fournissent une information precieuse pour la quantification future des risques de grand feu et pour l'amenagement forestier dans la region. (Traduit par la Redaction)

[1]  Xin Zhao,et al.  GARCH dependence in extreme value models with Bayesian inference , 2011, Math. Comput. Simul..

[2]  D. Gamerman,et al.  Bayesian analysis of extreme events with threshold estimation , 2004 .

[3]  David Weinbaum,et al.  A Conditional Extreme Value Volatility Estimator Based on High-Frequency Returns , 2007 .

[4]  Johan Segers,et al.  Inference for clusters of extreme values , 2003 .

[5]  M. Krawchuk,et al.  Disturbance history affects lightning fire initiation in the mixedwood boreal forest: Observations and simulations , 2009 .

[6]  David V. Sandberg,et al.  Modeling Large Forest Fires as Extreme Events , 1998 .

[7]  Brian J. Stocks,et al.  The extent and impact of forest fires in northern circumpolar countries , 1991 .

[8]  Francesco Pauli,et al.  Penalized likelihood inference in extreme value analyses , 2001 .

[9]  Marcus C. Sarofim,et al.  CO2 and CH4 exchanges between land ecosystems and the atmosphere in northern high latitudes over the 21st century , 2006 .

[10]  Max A. Moritz,et al.  ANALYZING EXTREME DISTURBANCE EVENTS: FIRE IN LOS PADRES NATIONAL FOREST , 1997 .

[11]  Richard L. Smith,et al.  Models for exceedances over high thresholds , 1990 .

[12]  S. García-Marco,et al.  Impact of fire and post-fire management techniques on soil chemical properties , 2013 .

[13]  R. Guyette,et al.  Dynamics of an Anthropogenic Fire Regime , 2003, Ecosystems.

[14]  Steven G. Cumming,et al.  A parametric model of the fire-size distribution , 2001 .

[15]  Jean Palutikof,et al.  Tests of the Generalized Pareto Distribution for Predicting Extreme Wind Speeds , 2000 .

[16]  R. Rigby,et al.  Generalized additive models for location, scale and shape , 2005 .

[17]  A. Weaver,et al.  Detecting the effect of climate change on Canadian forest fires , 2004 .

[18]  A. O'Hagan,et al.  Accounting for threshold uncertainty in extreme value estimation , 2006 .

[19]  Joel S. Levine,et al.  The Extent and Impact of Forest Fires in Northern Circumpolar Countries , 1991 .

[20]  David L. Martell,et al.  Characterizing extreme fire and weather events in the Boreal Shield ecozone of Ontario , 2005 .

[21]  Qianlai Zhuang,et al.  Drought effects on large fire activity in Canadian and Alaskan forests , 2007 .

[22]  R. Koenker.  Quantile Regression: Name Index , 2005 .

[23]  Characterization of wildfire regimes in Canadian boreal terrestrial ecosystems , 2009 .

[24]  R. Engle.  GARCH 101: The Use of ARCH/GARCH Models in Applied Econometrics , 2001 .

[25]  Ramazan Gençay,et al.  EVIM: A Software Package for Extreme Value Analysis in MATLAB , 2001 .

[26]  William J. Reed,et al.  Power-law behaviour and parametric models for the size-distribution of forest fires , 2002 .

[27]  William J. Ripple,et al.  The role of terrain in a fire mosaic of a temperate coniferous forest , 1997 .

[28]  Martijn Gough.  Climate change , 2009, Canadian Medical Association Journal.

[29]  Richard L. Smith.  Extreme Value Analysis of Environmental Time Series: An Application to Trend Detection in Ground-Level Ozone , 1989 .

[30]  C. E. Van Wagner,et al.  Development and structure of the Canadian Forest Fire Weather Index System , 1987 .

[31]  J. Levine.  Global biomass burning - Atmospheric, climatic, and biospheric implications , 1990 .

[32]  B. M. Wotton,et al.  Climate Change and People-Caused Forest Fire Occurrence in Ontario , 2003 .

[33]  Synoptic Climatology , 1958, Nature.

[34]  Douglas G. Woolford,et al.  Characterizing temporal changes in forest fire ignitions: looking for climate change signals in a region of the Canadian boreal forest , 2010 .

[35]  K. Hirsch,et al.  Large forest fires in Canada, 1959–1997 , 2002 .

[36]  E. Kasischke,et al.  Recent changes in the fire regime across the North American boreal region—Spatial and temporal patterns of burning across Canada and Alaska , 2006 .

[37]  B. Malamud,et al.  Characterizing wildfire regimes in the United States. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[38]  P. Naveau,et al.  Statistical methods for the analysis of climate extremes , 2005 .

[39]  M. Flannigan,et al.  Future wildfire in circumboreal forests in relation to global warming , 1998 .

[40]  Marcus C. Sarofim,et al.  CO 2 and CH 4 exchanges between land ecosystems and the atmosphere in northern high latitudes over the 21 st century , 2006 .

[41]  S. Sitch,et al.  Uncertainty analysis of vegetation distribution in the northern high latitudes during the 21st century with a dynamic vegetation model , 2012, Ecology and evolution.

[42]  Eric P. Smith,et al.  An Introduction to Statistical Modeling of Extreme Values , 2002, Technometrics.

[43]  Edward A. Johnson,et al.  Synoptic climatology of lightning-caused forest fires in subalpine and boreal forests , 1996 .

[44]  Michel M. Verstraete,et al.  Remote sensing and climate modeling : synergies and limitations , 2001 .

[45]  Michael Lehning,et al.  Extreme value statistics of snowfall in the Swiss Alpine region , 2009 .

[46]  Johann G. Goldammer,et al.  Boreal Forest Fire Regimes And Climate Change , 2001 .

[47]  Roger D. Peng,et al.  Detection of non-linearities in the dependence of burn area on fuel age and climatic variables , 2003 .

[48]  R. Wein,et al.  Biotic and abiotic regulation of lightning fire initiation in the mixedwood boreal forest. , 2006, Ecology.

[49]  R. Guyette,et al.  Anthropogenic fire history and red oak forests in south-central Ontario , 2000 .

[50]  Marc B. Parlange,et al.  STATISTICS OF EXTREMES: MODELING ECOLOGICAL DISTURBANCES , 2005 .

[51]  Ronald J. Hall,et al.  Large fires as agents of ecological diversity in the North American boreal forest , 2008 .

[52]  Arctic Monitoring,et al.  Impacts of a warming Arctic : Arctic Climate Impact Assessment , 2004 .

[53]  David L. Martell,et al.  Statistical quality control analysis of forest fire activity in Canada , 2002 .

[54]  S. Coles,et al.  An Introduction to Statistical Modeling of Extreme Values , 2001 .

[55]  Richard Wilson.  Risk analysis , 1986, Nature.

[56]  L. Mearns,et al.  Climate Change and Forest Fire Potential in Russian and Canadian Boreal Forests , 1998 .

[57]  Qianlai Zhuang,et al.  Modeling Large Fire Frequency and Burned Area in Canadian Terrestrial Ecosystems with Poisson Models , 2012, Environmental Modeling & Assessment.

[58]  M. R. Leadbetter,et al.  Extremes and Related Properties of Random Sequences and Processes: Springer Series in Statistics , 1983 .

[59]  M. Flannigan,et al.  Future Area Burned in Canada , 2005 .

[60]  B. Stocks,et al.  Risk Analysis in Strategic Planning: Fire and Climate Change in the Boreal Forest , 1996 .

[61]  Acia.  Impacts of a Warming Arctic: Arctic Climate Impact Assessment , 2004 .

[62]  R. Koenker.  Quantile Regression: Fundamentals of Quantile Regression , 2005 .

[63]  S. Coles,et al.  Likelihood-Based Inference for Extreme Value Models , 1999 .