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A parametric Markov renewal model for predicting tropical cyclones in Bangladesh

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  • Md. Asaduzzaman
  • A. Latif

Abstract

In this paper, we consider a Markov renewal process (MRP) to model tropical cyclones occurred in Bangladesh during 1877–2009. The model takes into account both the occurrence history and some physical constraints to capture the main physical characteristics of the storm surge process. We assume that the sequence of cyclones constitutes a Markov chain, and sojourn times follow a Weibull distribution. The parameters of the Weibull MRP jointly with transition probabilities are estimated using the maximum likelihood method. The model shows a good fit with the real events, and probabilities of occurrence of different types of cyclones are calculated for various lengths of time interval using the model. Stationary probabilities and mean recurrence times are also calculated. A brief comparison with a Poisson model and a marked Poisson model has also been demonstrated. Copyright Springer Science+Business Media Dordrecht 2014

Suggested Citation

  • Md. Asaduzzaman & A. Latif, 2014. "A parametric Markov renewal model for predicting tropical cyclones in Bangladesh," 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. 73(2), pages 597-612, September.
    • Handle: RePEc:spr:nathaz:v:73:y:2014:i:2:p:597-612
    DOI: 10.1007/s11069-014-1101-z
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    References listed on IDEAS

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    1. Enrique E. Alvarez, 2005. "Estimation in Stationary Markov Renewal Processes, with Application to Earthquake Forecasting in Turkey," Methodology and Computing in Applied Probability, Springer, vol. 7(1), pages 119-130, March.
    2. Yosihiko Ogata, 1998. "Space-Time Point-Process Models for Earthquake Occurrences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 379-402, June.
    3. Tanveerul Islam & Richard Peterson, 2009. "Climatology of landfalling tropical cyclones in Bangladesh 1877–2003," 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. 48(1), pages 115-135, January.
    4. Elsa Garavaglia & Raffaella Pavani, 2011. "About Earthquake Forecasting by Markov Renewal Processes," Methodology and Computing in Applied Probability, Springer, vol. 13(1), pages 155-169, March.
    5. Irene Votsi & Nikolaos Limnios & George Tsaklidis & Eleftheria Papadimitriou, 2012. "Estimation of the Expected Number of Earthquake Occurrences Based on Semi-Markov Models," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 685-703, September.
    6. Jonas Rumpf & Helga Weindl & Peter Höppe & Ernst Rauch & Volker Schmidt, 2007. "Stochastic modelling of tropical cyclone tracks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 475-490, December.
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