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Modelling Sub-daily Precipitation Extremes with the Blended Generalised Extreme Value Distribution

Author

Listed:
  • Silius M. Vandeskog

    (Norwegian University of Science and Technology (NTNU))

  • Sara Martino

    (Norwegian University of Science and Technology (NTNU))

  • Daniela Castro-Camilo

    (University of Glasgow)

  • Håvard Rue

    (King Abdullah University of Science and Technology (KAUST))

Abstract

A new method is proposed for modelling the yearly maxima of sub-daily precipitation, with the aim of producing spatial maps of return level estimates. Yearly precipitation maxima are modelled using a Bayesian hierarchical model with a latent Gaussian field, with the blended generalised extreme value (bGEV) distribution used as a substitute for the more standard generalised extreme value (GEV) distribution. Inference is made less wasteful with a novel two-step procedure that performs separate modelling of the scale parameter of the bGEV distribution using peaks over threshold data. Fast inference is performed using integrated nested Laplace approximations (INLA) together with the stochastic partial differential equation approach, both implemented in R-INLA. Heuristics for improving the numerical stability of R-INLA with the GEV and bGEV distributions are also presented. The model is fitted to yearly maxima of sub-daily precipitation from the south of Norway and is able to quickly produce high-resolution return level maps with uncertainty. The proposed two-step procedure provides an improved model fit over standard inference techniques when modelling the yearly maxima of sub-daily precipitation with the bGEV distribution. Supplementary materials accompanying this paper appear on-line.

Suggested Citation

  • Silius M. Vandeskog & Sara Martino & Daniela Castro-Camilo & Håvard Rue, 2022. "Modelling Sub-daily Precipitation Extremes with the Blended Generalised Extreme Value Distribution," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(4), pages 598-621, December.
    • Handle: RePEc:spr:jagbes:v:27:y:2022:i:4:d:10.1007_s13253-022-00500-7
    DOI: 10.1007/s13253-022-00500-7
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    as
    1. Peter Guttorp & Tilmann Gneiting, 2006. "Studies in the history of probability and statistics XLIX On the Matern correlation family," Biometrika, Biometrika Trust, vol. 93(4), pages 989-995, December.
    2. James E. Matheson & Robert L. Winkler, 1976. "Scoring Rules for Continuous Probability Distributions," Management Science, INFORMS, vol. 22(10), pages 1087-1096, June.
    3. Eric A. Lehmann & Aloke Phatak & Alec Stephenson & Rex Lau, 2016. "Spatial modelling framework for the characterisation of rainfall extremes at different durations and under climate change," Environmetrics, John Wiley & Sons, Ltd., vol. 27(4), pages 239-251, June.
    4. Petra Friederichs & Thordis L. Thorarinsdottir, 2012. "Forecast verification for extreme value distributions with an application to probabilistic peak wind prediction," Environmetrics, John Wiley & Sons, Ltd., vol. 23(7), pages 579-594, November.
    5. Daniela Castro-Camilo & Raphaël Huser & Håvard Rue, 2019. "A Spliced Gamma-Generalized Pareto Model for Short-Term Extreme Wind Speed Probabilistic Forecasting," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(3), pages 517-534, September.
    6. M. E. Robinson & J. A. Tawn, 2000. "Extremal analysis of processes sampled at different frequencies," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 117-135.
    7. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    8. Bivand, Roger & Gómez-Rubio, Virgilio & Rue, Håvard, 2015. "Spatial Data Analysis with R-INLA with Some Extensions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i20).
    9. Cooley, Daniel & Nychka, Douglas & Naveau, Philippe, 2007. "Bayesian Spatial Modeling of Extreme Precipitation Return Levels," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 824-840, September.
    10. Finn Lindgren & Håvard Rue & Johan Lindström, 2011. "An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(4), pages 423-498, September.
    11. Anita Verpe Dyrrdal & Alex Lenkoski & Thordis L. Thorarinsdottir & Frode Stordal, 2015. "Bayesian hierarchical modeling of extreme hourly precipitation in Norway," Environmetrics, John Wiley & Sons, Ltd., vol. 26(2), pages 89-106, March.
    12. Bucher, Axel & Segers, Johan, 2017. "On the maximum likelihood estimator for the Generalized Extreme-Value distribution," LIDAM Reprints ISBA 2017039, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    13. Tilmann Gneiting & Roopesh Ranjan, 2011. "Comparing Density Forecasts Using Threshold- and Quantile-Weighted Scoring Rules," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 411-422, July.
    14. Bucher, Axel & Segers, Johan, 2018. "Inference for heavy tailed stationary time series based on sliding blocks," LIDAM Reprints ISBA 2018007, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    15. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    16. Daniela Castro-Camilo & Raphaël Huser, 2020. "Local Likelihood Estimation of Complex Tail Dependence Structures, Applied to U.S. Precipitation Extremes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(531), pages 1037-1054, July.
    17. Lindgren, Finn & Rue, Håvard, 2015. "Bayesian Spatial Modelling with R-INLA," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i19).
    18. Geir-Arne Fuglstad & Daniel Simpson & Finn Lindgren & Håvard Rue, 2019. "Constructing Priors that Penalize the Complexity of Gaussian Random Fields," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 445-452, January.
    19. Gneiting, Tilmann & Ranjan, Roopesh, 2011. "Comparing Density Forecasts Using Threshold- and Quantile-Weighted Scoring Rules," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(3), pages 411-422.
    20. Wang, Yixin & So, Mike K.P., 2016. "A Bayesian hierarchical model for spatial extremes with multiple durations," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 39-56.
    21. Óli P. Geirsson & Birgir Hrafnkelsson & Daniel Simpson, 2015. "Computationally efficient spatial modeling of annual maximum 24‐h precipitation on a fine grid," Environmetrics, John Wiley & Sons, Ltd., vol. 26(5), pages 339-353, August.
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