Space-time modelling of lightning-caused ignitions in the Blue Mountains, Oregon

Generalized linear mixed models (GLMM) were used to study the effect of vegetation cover, elevation, slope, and precipitation on the probability of ignition in the Blue Mountains, Oregon, and to estimate the probability of ignition occurrence at different locations in space and in time. Data on starting location of lightning-caused ignitions in the Blue Mountains between April 1986 and September 1993 constituted the base for the analysis. The study area was divided into a pixel-time array. For each pixel-time location we associated a value of 1 if at least one ignition oc - curred and 0 otherwise. Covariate information for each pixel was obtained using a geographic information system. The GLMMs were fitted in a Bayesian framework. Higher ignition probabilities were associated with the following cover types: subalpine herbaceous, alpine tundra, lodgepole pine (Pinus contorta Dougl. ex Loud.), whitebark pine (Pinus albicaulis Engelm.), Engelmann spruce (Picea engelmannii Parry ex Engelm.), subalpine fir (Abies lasiocarpa (Hook.) Nutt.), and grand fir (Abies grandis (Dougl.) Lindl.). Within each vegetation type, higher ignition probabilities occurred at lower elevations. Additionally, ignition probabilities are lower in the northern and southern extremes of the Blue Mountains. The GLMM procedure used here is suitable for analysing ignition occurrence in other forested regions where probabilities of ignition are highly variable because of a spatially complex biophysical environment. Resume : Des modeles lineaires generaux mixtes (GLMM) ont ete utilises pour etudier l'effet du couvert vegetal, de l'altitude, de la pente et des precipitations sur la probabilite d'allumage dans les Blue Mountains, en Oregon, et pour evaluer la probabilite qu'un allumage se produise a differents endroits dans l'espace et le temps. Des donnees sur la lo- calisation des allumages causes par la foudre dans les Blue Mountains entre les mois d'avril 1986 et septembre 1993 ont servi de base a l'analyse. L'aire d'etude a ete divisee en un reseau de pixel-temps. Une valeur de 1 ou 0 a ete at- tribuee a chaque endroit correspondant a un pixel-temps selon qu'au moins un allumage est survenu ou non. Les infor- mations associees a chaque pixel ont ete obtenues a l'aide d'un systeme d'information geographique. Les GLMM ont ete ajustes selon une structure bayesienne. De plus fortes probabilites d'allumage etaient associees aux types de cou- verts suivants : plantes herbacees subalpines, toundra alpine, pin lodgepole ( Pinus contorta Dougl. ex Loud.), pin a blanche ecorce (Pinus albicaulis Engelm.), epinette d'Engelmann (Picea engelmannii Parry ex Engelm.), sapin subalpin (Abies lasiocarpa (Hook.) Nutt.) et sapin grandissime (Abies grandis (Dougl.) Lindl.). Pour chaque type de couvert ve- getal, les probabilites d'allumage etaient plus elevees a plus faible altitude. De plus, les probabilites d'allumage etaient plus faibles aux extremites nord et sud des Blue Mountains. La procedure GLMM utilisee ici convient pour analyser l'occurrence des allumages dans d'autres regions couvertes de foret ou les probabilites d'allumage sont tres variables a cause d'un environnement biophysique dont la configuration spatiale est complexe.

[1]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[2]  David L. Martell,et al.  A Stochastic Model for the Occurrence of Man-caused Forest Fires , 1973 .

[3]  G. C. Tiao,et al.  Bayesian inference in statistical analysis , 1973 .

[4]  Romain M. Mees.  Computing arrival times of firefighting resources for initial attack , 1978 .

[5]  E. Krider,et al.  Lightning Direction-Finding Systems for Forest Fire Detection , 1980 .

[6]  P. McCullagh,et al.  Generalized Linear Models , 1984 .

[7]  Peter E. Rossi,et al.  Bayesian analysis of dichotomous quantal response models , 1984 .

[8]  P. Andrews.  BEHAVE : Fire Behavior Prediction and Fuel Modeling System - BURN Subsystem, Part 1 , 1986 .

[9]  D. Clayton,et al.  Empirical Bayes estimates of age-standardized relative risks for use in disease mapping. , 1987, Biometrics.

[10]  P. Quinby.  An index to fire incidence , 1987 .

[11]  Peter Breeze,et al.  Point Processes and Their Statistical Inference , 1991 .

[12]  William W. S. Wei,et al.  Time series analysis - univariate and multivariate methods , 1989 .

[13]  M. Finney,et al.  Forest fire history of Desolation Peak, Washington. , 1990 .

[14]  A. Agresti,et al.  Categorical Data Analysis , 1991, International Encyclopedia of Statistical Science.

[15]  J. Besag,et al.  Bayesian image restoration, with two applications in spatial statistics , 1991 .

[16]  D. Hosmer,et al.  Applied Logistic Regression , 1991 .

[17]  Alan F. Karr,et al.  Point Processes and Their Statistical Inference , 1991 .

[18]  Purushottam W. Laud,et al.  On Bayesian Analysis of Generalized Linear Models Using Jeffreys's Prior , 1991 .

[19]  D. Clayton.  Generalized Linear Mixed Models in Biostatistics , 1992 .

[20]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[21]  Edward A. Johnson,et al.  Wildfires in the southern Canadian Rocky Mountains and their relationship to mid-tropospheric anomalies , 1993 .

[22]  James K. Brown,et al.  Forest Health in the Blue Mountains: A Management Strategy for Fire-Adapted Ecosystems , 1993 .

[23]  Noel A Cressie,et al.  Statistics for Spatial Data. , 1992 .

[24]  T. Swetnam.  Fire History and Climate Change in Giant Sequoia Groves , 1993, Science.

[25]  Mike Rees,et al.  5. Statistics for Spatial Data , 1993 .

[26]  N. Breslow,et al.  Approximate inference in generalized linear mixed models , 1993 .

[27]  J. Agee.  Fire Ecology of Pacific Northwest Forests , 1993 .

[28]  R. G. Mitchell,et al.  Historical and current roles of insects and pathogens in eastern Oregon and Washington forested landscapes. Forest Service general technical report , 1994 .

[29]  C. Daly,et al.  A Statistical-Topographic Model for Mapping Climatological Precipitation over Mountainous Terrain , 1994 .

[30]  W. Reed.  Estimating the Historic Probability of Stand-Replacement Fire Using the Age-Class Distribution of Undisturbed Forest , 1994, Forest Science.

[31]  E. Johnson,et al.  Fire Frequency Models, Methods and Interpretations* , 1994 .

[32]  Kerrie Mengersen,et al.  [Bayesian Computation and Stochastic Systems]: Rejoinder , 1995 .

[33]  J. Besag,et al.  Bayesian Computation and Stochastic Systems , 1995 .

[34]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[35]  E. Johnson,et al.  The Relative Importance of Fuels and Weather on Fire Behavior in Subalpine Forests , 1995 .

[36]  Xiao-Li Meng,et al.  POSTERIOR PREDICTIVE ASSESSMENT OF MODEL FITNESS VIA REALIZED DISCREPANCIES , 1996 .

[37]  R. Keane,et al.  Simulating effects of fire on northern Rocky Mountain landscapes with the ecological process model FIRE-BGC. , 1996, Tree physiology.

[38]  C. D. Bevins,et al.  Simulating coarse-scale vegetation dynamics using the Columbia River Basin succession model-crbsum. Forest Service general technical report , 1996 .

[39]  Richard W. Haynes,et al.  Integrated scientific assessment for ecosystem management in the interior Columbia Basin and portions of the Klamath and Great Basins. , 1996 .

[40]  P. Rogers.  Disturbance Ecology and Forest Management: A Review of the Literature , 1996 .

[41]  K. Shaffer.  KEVIN S , 2000 .

[42]  S. Clarke,et al.  Hierarchical subdivisions of the Columbia Plateau and Blue Mountains ecoregions, Oregon and Washington. , 1997 .

[43]  Sylvia Richardson,et al.  Markov Chain Monte Carlo in Practice , 1997 .

[44]  Ajith H. Perera,et al.  Modelling the effect of spatial scale and correlated fire disturbances on forest age distribution , 1997 .

[45]  E. Heyerdahl.  Spatial and temporal variation in historical fire regimes of the Blue Mountains, Oregon and Washington: the influence of climate , 1997 .

[46]  R. Wolpert,et al.  Poisson/gamma random field models for spatial statistics , 1998 .

[47]  D. McKenzie.  Fire, vegetation, and scale: Toward optimal models for the Pacific Northwest , 1998 .

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

[49]  R. Fonda,et al.  Burning characteristics of western conifer needles , 1998 .

[50]  J. Agee.  The landscape ecology of western forest fire regimes , 1998 .

[51]  Thomas A. Spies,et al.  REGIONAL GRADIENT ANALYSIS AND SPATIAL PATTERN OF WOODY PLANT COMMUNITIES OF OREGON FORESTS , 1998 .

[52]  D. V. Sandberg,et al.  Assessing the effects of fire disturbances on ecosystems: A scientific agenda for research and management , 1999 .

[53]  Charles B. Halpern,et al.  Modeling the distributions of shrub species in Pacific northwest forests , 1999 .

[54]  J. Agee,et al.  FIRE FREQUENCY IN THE INTERIOR COLUMBIA RIVER BASIN: BUILDING REGIONAL MODELS FROM FIRE HISTORY DATA , 2000 .