Skip to main content

Advertisement

SpringerLink
Log in

Spatial Wildfire Risk Modeling Using a Tree-Based Multivariate Generalized Pareto Mixture Model

  • Published:
Journal of Agricultural, Biological and Environmental Statistics Aims and scope Submit manuscript

Abstract

Wildfires pose a severe threat to the ecosystem and economy, and risk assessment is typically based on fire danger indices such as the McArthur Forest Fire Danger Index (FFDI) used in Australia. Studying the joint tail dependence structure of high-resolution spatial FFDI data is thus crucial for estimating current and future extreme wildfire risk. However, existing likelihood-based inference approaches are computationally prohibitive in high dimensions due to the need to censor observations in the bulk of the distribution. To address this, we construct models for spatial FFDI extremes by leveraging the sparse conditional independence structure of Hüsler–Reiss-type generalized Pareto processes defined on trees. These models allow for a simplified likelihood function that is computationally efficient. Our framework involves a mixture of tree-based multivariate generalized Pareto distributions with randomly generated tree structures, resulting in a flexible model that can capture nonstationary spatial dependence structures. We fit the model to summer FFDI data from different spatial clusters in Mainland Australia and 14 decadal windows between 1999 and 2022 to study local spatiotemporal variability with respect to the magnitude and extent of extreme wildfires. Our proposed method fits the margins and spatial tail dependence structure adequately and is helpful in providing extreme wildfire risk estimates. Our results identify a significant increase in spatially aggregated fire risk across a substantially large portion of Mainland Australia, which raises serious climatic concerns. Supplementary material to this paper is provided online.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Algorithm 1
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  • Andrews PL, Loftsgaarden DO, Bradshaw LS (2003) Evaluation of fire danger rating indexes using logistic regression and percentile analysis. Int J Wildland Fire 12(2):213–226

    Article  Google Scholar 

  • Asenova S, Mazo G, Segers J (2021) Inference on extremal dependence in the domain of attraction of a structured Hüsler–Reiss distribution motivated by a Markov tree with latent variables. Extremes 24:461–500

    Article  MathSciNet  Google Scholar 

  • Balkema AA, De Haan L (1974) Residual life time at great age. Ann Probab 2(5):792–804

    Article  MathSciNet  Google Scholar 

  • Beineke LW, Wilson RJ, Cameron PJ et al (2004) Topics in algebraic graph theory, vol 102. Cambridge University Press, Cambridge

    Google Scholar 

  • Bernard E, Naveau P, Vrac M, Mestre O (2013) Clustering of maxima: spatial dependencies among heavy rainfall in France. J Clim 26(20):7929–7937

    Article  ADS  Google Scholar 

  • Beyers JL, Neary DG, Ryan KC, DeBano LF (2005) Wildland fire in ecosystems: effects of fire on soil and water. United States Department of Agriculture, Forest Service, Rocky Mountain

  • Cisneros D, Gong Y, Yadav R, Hazra A, Huser R (2023) A combined statistical and machine learning approach for spatial prediction of extreme wildfire frequencies and sizes. Extremes 26(2):301–330

    Article  MathSciNet  Google Scholar 

  • Coles S, Bawa J, Trenner L, Dorazio P (2001) An introduction to statistical modeling of extreme values. Springer, London

    Book  Google Scholar 

  • Coles S, Heffernan J, Tawn J (1999) Dependence measures for extreme value analyses. Extremes 2(4):339–365

    Article  Google Scholar 

  • Cooley, D., Naveau, P., Poncet, P. (2006) Variograms for spatial max-stable random fields. In: Dependence in probability and statistics, pp. 373–390. Springer

  • Davison AC, Hinkley DV (1997) Bootstrap methods and their application. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Davison AC, Huser R (2015) Statistics of extremes. Ann Rev Stat Appl 2:203–235

  • Davison AC, Huser R, Thibaud E (2013) Geostatistics of dependent and asymptotically independent extremes. Math Geosci 45(5):511–529

    Article  MathSciNet  Google Scholar 

  • Davison AC, Huser R, Thibaud E (2019) Spatial extremes. In: Gelfand AE, Fuentes M, Hoeting JA, Smith RL (eds) Handbook of environmental and ecological statistics. CRC Press, Boca Raton

    Google Scholar 

  • Davison AC, Smith RL (1990) Models for exceedances over high thresholds. J Roy Stat Soc Ser B (Methodol) 52(3):393–425

    MathSciNet  Google Scholar 

  • de Fondeville R, Davison AC (2018) High-dimensional peaks-over-threshold inference. Biometrika 105(3):575–592

    Article  MathSciNet  Google Scholar 

  • Dowdy AJ, Mills GA, Finkele K, de Groot W (2010) Index sensitivity analysis applied to the Canadian forest fire weather index and the McArthur forest fire danger index. Meteorol Appl 17(3):298–312

    Article  Google Scholar 

  • Engelke S, Hitz AS (2020) Graphical models for extremes. J R Stat Soc Series B (Stat Methodol) 82(4):871–932

    Article  MathSciNet  Google Scholar 

  • Engelke S, Volgushev S (2022) Structure learning for extremal tree models. J R Stat Soc Ser B Stat Methodol 84(5):2055–2087

    Article  MathSciNet  Google Scholar 

  • Epskamp S, Waldorp LJ, Mõttus R, Borsboom D (2018) The Gaussian graphical model in cross-sectional and time-series data. Multivar Behav Res 53(4):453–480

    Article  Google Scholar 

  • Fiorucci P, Gaetani F, Minciardi R (2008) Development and application of a system for dynamic wildfire risk assessment in Italy. Environ Model Softw 23(6):690–702

    Article  Google Scholar 

  • Gissibl N, Klüppelberg C (2018) Max-linear models on directed acyclic graphs. Bernoulli 24(4A):2693–2720

    Article  MathSciNet  Google Scholar 

  • Godfree RC, Knerr N, Encinas-Viso F, Albrecht D, Bush D, Christine Cargill D, Clements M, Gueidan C, Guja LK, Harwood T et al (2021) Implications of the 2019–2020 megafires for the biogeography and conservation of Australian vegetation. Nat Commun 12(1):1–13

    Article  Google Scholar 

  • Griffiths D (1999) Improved formula for the drought factor in McArthur’s forest fire danger meter. Aust For 62(2):202–206

    Article  Google Scholar 

  • Hazra A, Huser R, Bolin D (2021) Realistic and fast modeling of spatial extremes over large geographical domains. arXiv:2112.10248

  • Hazra A, Reich BJ, Shaby BA, Staicu AM (2018) A semiparametric spatiotemporal Bayesian model for the bulk and extremes of the Fosberg Fire Weather Index. arXiv preprint arXiv:1812.11699

  • Hazra A, Reich BJ, Staicu A-M (2020) A multivariate spatial skew-t process for joint modeling of extreme precipitation indexes. Environmetrics 31(3):e2602

    Article  MathSciNet  Google Scholar 

  • Huang WK, Cooley DS, Ebert-Uphoff I, Chen C, Chatterjee S (2019) New exploratory tools for extremal dependence: \(\chi \) networks and annual extremal networks. J Agric Biol Environ Stat 24(3):484–501

    Article  MathSciNet  Google Scholar 

  • Huser R, Wadsworth JL (2019) Modeling spatial processes with unknown extremal dependence class. J Am Stat Assoc 114:434–444

    Article  MathSciNet  CAS  Google Scholar 

  • Huser R, Wadsworth JL (2022) Advances in statistical modeling of spatial extremes. Wiley Interdisciplinary Reviews (WIREs): Computational Statistics 14:e1537

  • Hüsler J, Reiss R-D (1989) Maxima of normal random vectors: between independence and complete dependence. Stat Prob Lett 7(4):283–286

    Article  MathSciNet  Google Scholar 

  • Jhariya MK, Raj A (2014) Effects of wildfires on flora, fauna and physico-chemical properties of soil-an overview. J Appl Nat Sci 6(2):887–897

    Google Scholar 

  • Klüppelberg C, Lauritzen S (2019) Bayesian networks for max-linear models. In: Network Science, pp. 79–97. Springer

  • Koller D, Friedman N (2009) Probabilistic graphical models: principles and techniques. MIT press, Cambridge

    Google Scholar 

  • Kreiss J-P, Paparoditis E (2011) Bootstrap methods for dependent data: a review. J Korean Stat Soc 40(4):357–378

    Article  MathSciNet  Google Scholar 

  • Lauritzen, S. (1996) Graphical models. Oxford Statistical Science: Series 17

  • Marlon JR, Bartlein PJ, Gavin DG, Long CJ, Anderson RS, Briles CE, Brown KJ, Colombaroli D, Hallett DJ, Power MJ et al (2012) Long-term perspective on wildfires in the western USA. Proc Natl Acad Sci 109(9):E535–E543

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  • Meilă M, Jaakkola T (2006) Tractable Bayesian learning of tree belief networks. Stat Comput 16(1):77–92

    Article  MathSciNet  Google Scholar 

  • Noble I, Gill A, Bary G (1980) McArthur’s fire-danger meters expressed as equations. Aust J Ecol 5(2):201–203

    Article  Google Scholar 

  • Papastathopoulos I, Strokorb K (2016) Conditional independence among max-stable laws. Stat Prob Lett 108:9–15

    Article  MathSciNet  Google Scholar 

  • Pickands J III (1975) Statistical inference using extreme order statistics. Ann Stat 3(1):119–131

    MathSciNet  Google Scholar 

  • Ren Z, Sun T, Zhang C-H, Zhou HH (2015) Asymptotic normality and optimalities in estimation of large Gaussian graphical models. Ann Stat 43(3):991–1026

    Article  MathSciNet  Google Scholar 

  • Resnick SI (2008) Extreme values, regular variation, and point processes, vol 4. Springer Science & Business Media, Berlin

    Google Scholar 

  • Rootzén H, Segers J, Wadsworth LJ (2018) Multivariate peaks over thresholds models. Extremes 21(1):115–145

    Article  MathSciNet  Google Scholar 

  • Rootzén H, Tajvidi N (2006) Multivariate generalized Pareto distributions. Bernoulli 12(5):917–930

    Article  MathSciNet  Google Scholar 

  • Sanabria L, Qin X, Li J, Cechet R, Lucas C (2013) Spatial interpolation of McArthur’s forest fire danger index across Australia: observational study. Environ Modell Softw 50:37–50

    Article  Google Scholar 

  • Sandberg DV (2003) Wildland fire in ecosystems: effects of fire on air. US Department of Agriculture, Forest Service, Rocky Mountain Research Station

  • Segers J (2020) One- versus multi-component regular variation and extremes of Markov trees. Adv Appl Probab 52(3):855–878

    Article  MathSciNet  Google Scholar 

  • Sirca C, Spano D, Pisanu P, Duce P, Delogu G, Cicalò GO (2006) Ichnusa fire index: development and preliminary evaluation at local scale. For Ecol Manage 234(S):250

    Article  Google Scholar 

  • Stephenson C, Handmer J, Betts R (2013) Estimating the economic, social and environmental impacts of wildfires in Australia. Environ Hazards 12(2):93–111

    Article  Google Scholar 

  • Thomas D, Butry D, Gilbert S, Webb D, Fung J et al (2017) The costs and losses of wildfires. NIST Special Publication 1215(11)

  • Van Wagner C, Forest P et al (1987) Development and structure of the Canadian forest fire weather index system. In Canadian forestry service, forestry technical report

  • Vettori S, Huser R, Segers J, Genton MG (2020) Bayesian model averaging over tree-based dependence structures for multivariate extremes. J Comput Graph Stat 29(1):174–190

    Article  MathSciNet  Google Scholar 

  • Westerling AL (2016) Increasing western US forest wildfire activity: sensitivity to changes in the timing of spring. Philos Trans R Soc B Biol Sci 371(1696):20150178

    Article  Google Scholar 

  • Yu H, Uy WIT, Dauwels J (2016) Modeling spatial extremes via ensemble-of-trees of pairwise copulas. IEEE Trans Signal Process 65(3):571–586

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors would like to gratefully thank the Editor, Associate Editor, and the anonymous reviewer for their constructive comments and suggestions that helped improve the quality of the manuscript.

Author information

Authors and Affiliations

  1. Statistics Program, Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, King Abdullah University of Science and Technology (KAUST), 23955-6900, Thuwal, Saudi Arabia

    Daniela Cisneros & Raphaël Huser

  2. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, 208016, India

    Arnab Hazra

Authors
  1. Daniela Cisneros
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Arnab Hazra
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Raphaël Huser
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Raphaël Huser.

Ethics declarations

Conflict of interest

The authors have no conflict of interest to declare.

Funding

This publication was supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Awards No. OSR-CRG2017-3434 and No. OSR-CRG2020-4394.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file 1 (pdf 5448 KB)

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cisneros, D., Hazra, A. & Huser, R. Spatial Wildfire Risk Modeling Using a Tree-Based Multivariate Generalized Pareto Mixture Model. JABES (2024). https://doi.org/10.1007/s13253-023-00596-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s13253-023-00596-5

Keywords

Search

Navigation