Abstract
Wildfires have been studied in many ways, for instance as a spatial point pattern or through modeling the size of fires or the relative risk of big fires. Lately a large variety of complex statistical models can be fitted routinely to complex data sets, in particular wildfires, as a result of widely accessible high-level statistical software, such as R. The objective in this paper is to model the occurrence of big wildfires (greater than a given extension of hectares) using an adapted two-part econometric model, specifically a hurdle model. The methodology used in this paper is useful to determine those factors that help any fire to become a big wildfire. Our proposal and methodology can be routinely used to contribute to the management of big wildfires.
This is a preview of subscription content, access via your institution.









References
Amaral-Turkman MA, Turkman KF, Le PY, Pereira JMC (2011) Hierarchical space-time models for fire ignition and percentage of land burned by wildfires. Environ Ecol Stat 18:601–617
Bachmann A, Allgower B (2001) A consistent wildland fire risk terminology is needed. Fire Manag Today 61(4):28–33
Baddeley A, Turner R (2005) Spatstat: an R package for analyzing spatial point patterns. J Stat Softw 12:1–42
Berman M, Turner, TR (1992) Approximating point process likelihoods with GLIM. J Appl Stat 41:31–38
Blangiardo M, Cameletti M, Baio G, Rue H (2013) Spatial and spatio-temporal models with R-INLA. Spatial Spatio-temporal Epidemiol 4:33–49
Bremaud P (1981) Point processes and queues: martingale dynamics. Springer, New York
Chuvieco E (2009) Earth observation of wildland fires in Mediterranean ecosystems. Springer, Berlin
Comas C, Palahi M, Pukkala T, Mateu J (2009) Characterising forest spatial structure through inhomogeneous second order characteristics. Stoch Environ Res Risk Assess 23:387–397
Comas C, Mateu J (2011) Statistical inference for Gibbs point processes based on field observations. Stoch Environ Res Risk Assess 25:287–300
Cressie NAC (1993) Statistics for spatial data (revised ed). Wiley, New York
Daley D, Vere-Jones D (2003) An introduction to the theory of point processes, 2nd edn, vol I. Springer, New York
Deb DP, Trivedi PK (2002) The structure of demand for health care: latent class versus two-part models. J Health Econ 21:601–625
Diggle PJ (2003) Statistical analysis of spatial point patterns, 2nd edn. Arnold, London
Dillon GK, Holden ZA, Morgan P, Crimmins MA, Heyerdahl EK, Luce CH (2011) Both topography and climate affected forest and woodland burn severity in two regions of the western US, 1984 to 2006. Ecosphere 2(12):1–33
Fernandes PM, Botelho HS (2003) A review of prescribed burning effectiveness in fire hazard reduction. Int J Wildl Fire 12(2):117–128
García M, Chuvieco E, Nieto H, Aguado I (2008) Combining AVHRR and meteorological data for estimating live fuel moisture. Remote Sens Environ 112(9):3618–3627
Gneiting T, Kleiber W, Schlather M (2010) Matérn cross-covariance functions for multivariate random fields. J Am Stat Assoc 105(491):1167–1177
Gonzalez JR, Pukkala T (2007) Characterization of forest fires in Catalonia (north-east Spain). Eur J For Res 126(3):421–429
Harvill JL (2010) Spatio-temporal processes. WIREs Comput Stat 2:375–382
Hirsch RE, Lewis BD, Spalding EP, Sussman MR (1998) A role for the AKT1 potassium channel in plant nutrition. Science 8:918–921
Illian JB, Hendrichsen DK (2010) Gibbs point process models with mixed effects. Environmetrics 21:341–353
Illian JB, Sorbye SH, Rue H (2012) A toolbox for fitting complex spatial point processes models using integreted nested Laplace approximations (INLA). Ann Appl Stat 6(4):1499–1530
Juan P, Mateu J, Saez M (2012) Pinpointing spatio-temporal interactions in wildfire patterns. Stoch Environ Res Risk Assess 26(8):1131–1150
Lindgren F, Rue H, Lindström J (2011) An explicit link between Gaussian fields and Gaussian Markov random fields the SPDE approach. J R Stat Soc Ser B 73:423–498
Møller J, Díaz-Avalos C (2010) Structured spatio-temporal shot-noise Cox point process models, with a view to modelling forest fires. Scand J Stat 37:2–15
Mullahy J (1986) Specification and testing of some modified count data models. J Econometri 33:341–365
Neelon B, Ghosh P, LoebsMullahy PF (2013) A spatial Poisson hurdle model for exploring geographic variation in emergency department visits. J R Stat Soc Ser A 176(2):389–413
Ordóñez C, Saavedra A, Rodríguez-Pérez JR, Castedo-Dorado F, Covin E (2012) Using model-based geostatistics to predict lightning-caused wildfires. Environ Modell Softw 29(1):44–50
Piñol J, Terradas J, Lloret R (1998) Climate warming, wildfire hazard, and wildfire occurrence in coastal eastern Spain. Clim Change 38:345–357
Plummer M, Penalized L (2008) Functions for Bayesian model Comparation. Biostatistics 9(3):523–539
R Development Core Team (2011) R: a language and environment for statistical computing. R Foundation for Statistical Computing, http://www.r-project.org/
R-INLA project. http://www.r-inla.org/home. Accessed 13 Aug 2012
Reus Dolz ML, Irastorza F (2003) Estado del Conocimiento de causas sobre los incendios forestales en Espana. APAS and IDEM Estudio sociologico sobre la percepcion de la poblacion espanola hacia los incendios forestales. http://www.idem21.com/descargas/pdfs/IncediosForestales.pdf
Røder A, Hill J, Duguy B, Alloza JA, Vallejo R (2008) Using long time series of landsat data to monitor fire events and post-fire dynamics and identify driving factors. A case study in the Ayora region (eastern Spain). Remote Sens Environ 112(1):259–273
Rue H, Martino S, Chopin N (2009) Approximate Bayesian inference for latent Gaussian models using integrated nested Laplace approximations (with discussion). J R Stat Soc Ser B 71:319–392
Saez M, Barcelo MA, Tobias A, Varga D, Ocaña-Riola R, Juan P, Mateu J (2012) Space–time interpolation of daily air temperatures. J Environ Stat 3(5)
San-Miguel-Ayanza J, Rodrigues M, Santos de Oliveira S, Kemper Pacheco C, Moreira F, Duguy B, Camia A (2012) Land cover change and fire regime in the European Mediterranean region. In: Moreira F, Arianoustsou M, Corona P, de las Heras J (eds) Post-fire mangement and restoration of southern European forests managing forest ecosystems. Springer, Berlin, pp 21–43
San-Miguel-Ayanza J, Moreno JM, Camia A (2013) Analysis of large fires in European Mediterranean landscapes: lessons learned and perspectives. For Ecol Manag 294:11–22
Simpson D, Illian J, Lindgren F, Sorbye SH, Rue H (2011) Going off grid: computationally efficient inference for log-Gaussian Cox processes. Technical Report, Trondheim University
Serra L, Juan P, Varga D, Mateu J, Saez M (2012) Spatial pattern modelling of wildfires in Catalonia, Spain 2004–2008. Environ Modell Softw 40:235–244
Tiernery L, Kadane JB (1986) Accurate approximations for posterior moments and marginal densities. J Am Stat Assoc 81:82–86
Turner R (2009) Point patterns of forest fire locations. Environ Ecol Stat 16:197–223
Wang Z, Ma R, Li S (2012) Assessing area-specific relative risks from large forest fire in Canada. Environ Ecol Stat 20(2):285–296
Wisdom M, Dlamini A (2010) Bayesian belief network analysis of factor influencing wildfire occurrence in Swaziland. Environ Modell Softw 25(2):199–208
Acknowledgments
This work was partially funded by Grant MTM2010-14961 from the Spanish Ministry of Science and Education.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Serra, L., Saez, M., Juan, P. et al. A spatio-temporal Poisson hurdle point process to model wildfires. Stoch Environ Res Risk Assess 28, 1671–1684 (2014). https://doi.org/10.1007/s00477-013-0823-x
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00477-013-0823-x
Keywords
- Hurdle model
- INLA
- Spatio-temporal point processes
- SPDE
- Wildfire