Advertisement

Journal of Statistical Theory and Practice

, Volume 8, Issue 3, pp 534–545 | Cite as

Explaining Return Times for Wildfires

  • Alan E. Gelfand
  • Joao V. D. Monteiro
Article

Abstract

Our interest is in analyzing fire regimes in the Mediterranean ecosystem in the Cape Floristic Region of South Africa (CFR). With this objective, we consider an extensive database of observed fires with high-resolution meteorological data during the period 1980–2000 to build a novel survival model. The model is constructed as a time-to-event specification incorporating space- and time-varying covariates along with spatial random effects. With data at grid cell level, conditionally autoregressive (CAR) modeling is used for the spatial random effects. However, areal sampling is very irregular, yielding disjoint sets of areal units. Hence, disappointingly, the spatial model does not improve upon the nonspatial version. Results regarding the covariates reveal an important influence of seasonally anomalous weather on fire probability, with increased probability of fire in seasons that are warmer and drier than average. In addition to these local-scale influences, the Antarctic Ocean Oscillation (AAO) is identified as a potentially important large-scale influence on precipitation and moisture transport. Fire probability increases in seasons during positive AAO phases, when the subtropical jet moves northward and low-level moisture transport decreases. We conclude that fire occurrence in the CFR is strongly affected by climatic variability at both local and global scales. Thus, there is the suggestion that fire risk is likely to respond sensitively to future climate change. Comparison of the modeled fire risk/probability across four 12-year periods (1951–1963, 1963–1975, 1975–1987, 1987–1999) provides some supporting evidence. If, as currently forecast, climate change in the region continues to produce higher temperatures, more frequent heat waves, and/or lower rainfall, our model thus indicates that fire frequency is likely to increase substantially. This article extends earlier work by Wilson etal. (2010).

Keywords

CAR model Hierarchical model Markov-chain Monte Carlo Probit link Time-to-event model 

AMS Subject Classification

62F15 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Albert, J. H., and S. Chib. 1993. Bayesian analysis of binary and polychotomous response data. J. Am. Stat. Assoc., 88(422), 669–679.MathSciNetCrossRefGoogle Scholar
  2. Banerjee, S., B. P. Carlin, and A. E. Gelfand. 2004. Hierarchical modeling and analysis for spatial data. Boca Raton, FL: Chapman & Hall/CRC.zbMATHGoogle Scholar
  3. Berkson, J., and R. P. Gage. 1952. Survival curve for cancer patients following treatment. J. Am. Stat. Assoc., 47, 501–515.CrossRefGoogle Scholar
  4. Besag, J. 1974. Spatial interaction and the statistical analysis of lattice systems. J. R. Stat. Soc. Ser. B, 36(2), 192–236.MathSciNetzbMATHGoogle Scholar
  5. Bond, W. J., G. F. Midgley, and F. I. Woodward. 2003. What controls South African vegetation climate or fire? South Afr. J. Bot., 69(1), 79–91.CrossRefGoogle Scholar
  6. Bond, W. J., and B. W. van Wilgen. 1995. Fire and plants. London, UK: Chapman & Hall.Google Scholar
  7. Cowling, R. M., and A. T. Lombard. 2002. Heterogeneity, speciation/extinction history and climate: Explaining regional plant diversity patterns in the Cape Floristic Region. Diversity Distrib., 8(3), 163–179.CrossRefGoogle Scholar
  8. Epstein, E. S. 1969. A scoring system for probability forecasts of ranked categories. J. Appl. Meteorol., 6, 985–987.CrossRefGoogle Scholar
  9. Hewitson, B. C., and R. G. Crane. 2002. Consensus between gcm climate change projections with empirical downscaling: Precipitation downscaling over south africa. Global Ecol. Biogeogr., 26, 1315–1337.Google Scholar
  10. Hodges, J. S., B. P. Carlin, and Q. Fan. 2003. On the precision of the conditionally autoregressive prior in spatial models. Biometrics, 59(2), 317–322.MathSciNetCrossRefGoogle Scholar
  11. Latimer, A. M., J. A. Silander, Jr., and R. M. Cowling. 2005. Neutral ecological theory reveals isolation and rapid speciation in a biodiversity hot spot. Science, 309(5741), 1722–1725.CrossRefGoogle Scholar
  12. Maller, R., and X. Zhou. 1996. Survival analysis with long-term survivors. New York, NY: Wiley.zbMATHGoogle Scholar
  13. Markham, C. G., 1970. Seasonality of precipitation in the United States. Ann. Assoc. Am. Geogr., 60, 593–597.CrossRefGoogle Scholar
  14. Marshall, G. J. 2003. Trends in the southern annular mode from observations and reanalyses. J. Climate, 16, 4134–4143.CrossRefGoogle Scholar
  15. McKenzie, D., Z. Gedalof, D. L. Peterson, and P. Mote. 2004. Climatic change, wildfire, and conservation. Conserv. Biol., 18(4), 890–902.CrossRefGoogle Scholar
  16. Midgley, G. F., L. Hannah, D. Millar, M. C. Rutherford, and L. W. Powrie. 2002. Assessing the vulnerability of species richness to anthropogenic climate change in a biodiversity hotspot. Global Ecol. Biogeogr., 11, 445–451.CrossRefGoogle Scholar
  17. Schulze, R. E. 1997. South African atlas of agrohydrology and climatology. Technical report TT82/96, Water Resource Commission, Pretoria, South Africa.Google Scholar
  18. Schurr, F. M., G. F. Midgley, A. G. Rebelo, G. Reeves, P. Poschlod, and S. I. Higgins. 2007. Colonization and persistence ability explain the extent to which plant species their potential range. Global Ecol. Biogeogr., 16, 449–459.CrossRefGoogle Scholar
  19. Shlisky A., J. Waugh, P. Gonzalez, M. Gonzalez, M. Manta, H. Santoso, E. Alvarado, A. A. Nuruddin, D. A. Rodrguez-Trejo, R. Swaty, D. Schmidt, M. Kaufmann, R. Myers, A. Alencar, F. Kearns, D. Johnson, J. Smith, and D. Zollner. 2007. Fire, ecosystems and people: Threats and strategies for global biodiversity conservation. In 4th International Wildland Fire Conference, Seville, Spain, May 14–17.Google Scholar
  20. Spiegelhalter, D. J., N. G. Best, B. P. Carlin, and A. van der Linde. 2002. Bayesian measures of model complexity and t. J. R. Stat. Soc. Ser. B, 64, 583–639.MathSciNetCrossRefGoogle Scholar
  21. Terres, M., A. E. Gelfand, J. Allen, J. A. Silander, Jr. 2013. Analyzing first flowering event data using survival models with space and time-varying covariates. Environmetrics, 24(5), 317–331.MathSciNetCrossRefGoogle Scholar
  22. von Holstein, C. A. S. S. 1970. A family of strictly proper scoring rules which are sensitive to distance. J. Appl. Meteorol., 9(3), 360–364.CrossRefGoogle Scholar
  23. Wilson A. M., J. A. Silander, Jr., A. E. Gelfand, and J. Glenn. 2011. Scaling up: Linking field data and remote sensing with a hierarchical model. J. Geogr. Information Sci., 25, 509–521.CrossRefGoogle Scholar
  24. Wilson, A. M., A. M. Latimer, J. A. Silander, Jr., A. E. Gelfand, and H. de Klerk. 2010. A hierarchical Bayesian model of wildfire in a Mediterranean biodiversity hotspot: Implications of weather variability and global circulation. Ecol. Model., 221(1), 106–112.CrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2014

Authors and Affiliations

  1. 1.Department of Statistical ScienceDuke UniversityDurhamUSA

Personalised recommendations