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A non‐homogeneous hidden Markov model for precipitation occurrence

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  • J. P. Hughes
  • P Guttorp
  • S. P. Charles

Abstract

A non‐homogeneous hidden Markov model is proposed for relating precipitation occurrences at multiple rain‐gauge stations to broad scale atmospheric circulation patterns (the so‐called ‘downscaling problem’). We model a 15‐year sequence of winter data from 30 rain stations in south‐western Australia. The first 10 years of data are used for model development and the remaining 5 years are used for model evaluation. The fitted model accurately reproduces the observed rainfall statistics in the reserved data despite a shift in atmospheric circulation (and, consequently, rainfall) between the two periods. The fitted model also provides some useful insights into the processes driving rainfall in this region.

Suggested Citation

  • J. P. Hughes & P Guttorp & S. P. Charles, 1999. "A non‐homogeneous hidden Markov model for precipitation occurrence," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(1), pages 15-30.
    • Handle: RePEc:bla:jorssc:v:48:y:1999:i:1:p:15-30
    DOI: 10.1111/1467-9876.00136
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    3. David J. Allcroft & Chris A. Glasbey, 2003. "A latent Gaussian Markov random‐field model for spatiotemporal rainfall disaggregation," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(4), pages 487-498, October.
    4. Gallego, C. & Pinson, P. & Madsen, H. & Costa, A. & Cuerva, A., 2011. "Influence of local wind speed and direction on wind power dynamics – Application to offshore very short-term forecasting," Applied Energy, Elsevier, vol. 88(11), pages 4087-4096.
    5. Pierre Ailliot & Craig Thompson & Peter Thomson, 2009. "Space–time modelling of precipitation by using a hidden Markov model and censored Gaussian distributions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(3), pages 405-426, July.
    6. M. Ritter & O. Mußhoff & M. Odening, 2014. "Minimizing Geographical Basis Risk of Weather Derivatives Using A Multi-Site Rainfall Model," Computational Economics, Springer;Society for Computational Economics, vol. 44(1), pages 67-86, June.
    7. Abhay Srivastava & Mrinal Mishra & Manoj Kumar, 2015. "Lightning alarm system using stochastic modelling," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 75(1), pages 1-11, January.
    8. Francesca Bassi & Jacques A. Hagenaars & Marcel A. Croon & Jeroen K. Vermunt, 2000. "Estimating True Changes when Categorical Panel Data are Affected by Uncorrelated and Correlated Classification Errors," Sociological Methods & Research, , vol. 29(2), pages 230-268, November.
    9. Monbet, Valérie & Ailliot, Pierre, 2017. "Sparse vector Markov switching autoregressive models. Application to multivariate time series of temperature," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 40-51.
    10. Regnier, Eva, 2008. "Doing something about the weather," Omega, Elsevier, vol. 36(1), pages 22-32, February.
    11. Spezia, Luigi, 2020. "Bayesian variable selection in non-homogeneous hidden Markov models through an evolutionary Monte Carlo method," Computational Statistics & Data Analysis, Elsevier, vol. 143(C).
    12. Guillermo Ferreira & Jorge Mateu & Emilio Porcu, 2018. "Spatio-temporal analysis with short- and long-memory dependence: a state-space approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 221-245, March.
    13. Avanzi, Benjamin & Taylor, Greg & Wong, Bernard & Xian, Alan, 2021. "Modelling and understanding count processes through a Markov-modulated non-homogeneous Poisson process framework," European Journal of Operational Research, Elsevier, vol. 290(1), pages 177-195.
    14. Jonsson, Robert, 2011. "A Markov Chain Model for Analysing the Progression of Patient’s Health States," Research Reports 2011:6, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    15. Benjamin Avanzi & Greg Taylor & Bernard Wong & Alan Xian, 2020. "Modelling and understanding count processes through a Markov-modulated non-homogeneous Poisson process framework," Papers 2003.13888, arXiv.org, revised May 2020.
    16. K. Shuvo Bakar, 2020. "Interpolation of daily rainfall data using censored Bayesian spatially varying model," Computational Statistics, Springer, vol. 35(1), pages 135-152, March.
    17. Paroli, Roberta & Spezia, Luigi, 2008. "Bayesian inference in non-homogeneous Markov mixtures of periodic autoregressions with state-dependent exogenous variables," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2311-2330, January.
    18. Francesca Bassi, 1997. "Identification of latent class Markov models with multiple indicators and correlated measurement errors," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 6(3), pages 201-211, December.
    19. Savannah Wei Shi & Hai Che & Lang Jin, 2021. "Strategic Product Displays Across Different Assortment Levels," Customer Needs and Solutions, Springer;Institute for Sustainable Innovation and Growth (iSIG), vol. 8(3), pages 84-101, September.
    20. Andriyas, Sanyogita & McKee, Mac, 2014. "Exploring irrigation behavior at Delta, Utah using hidden Markov models," Agricultural Water Management, Elsevier, vol. 143(C), pages 48-58.
    21. Jonsson, Robert, 2011. "Tests of Markov Order and Homogeneity in a Markov Chain," Research Reports 2011:7, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.

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