Advertisement

Natural Hazards

, Volume 73, Issue 2, pp 597–612 | Cite as

A parametric Markov renewal model for predicting tropical cyclones in Bangladesh

  • Md. Asaduzzaman
  • A. H. M. Mahbub Latif
Original Paper
  • 174 Downloads

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.

Keywords

Cyclone prediction Marked Poisson process Poisson process Semi-Markov process Statistical estimation of Markov renewal process 

Notes

Acknowledgements

The authors would like to thank the Referees for their constructive comments and helpful suggestions for the improvement of this paper.

References

  1. Ali A (1996) Vulnerability of Bangladesh to climate change and sea level rise through tropical cyclones and storm surges. Water Air Soil Pollut 92(1):171–179Google Scholar
  2. Alvarez E (2005) Estimation in stationary Markov renewal processes, with application to earthquake forecasting in Turkey. Methodol Comput Appl Prob 7(1):119–130CrossRefGoogle Scholar
  3. Asaduzzaman M, Latif AHMM (2014) Computational intelligence techniques in earth and environmental sciences chap 7. Springer, New YorkGoogle Scholar
  4. Dube S, Sinha P, Roy G (1985) The numerical simulation of storm surges along the Bangladesh coast. Dyn Atmos Oceans 9(2):121–133CrossRefGoogle Scholar
  5. Dube S, Sinha P, Roy G (1986) Numerical simulation of storm surges in Bangladesh using a bay-river coupled model. Coast Eng 10(1):85–101CrossRefGoogle Scholar
  6. Fiorentino M, Versace P, Rossi F (1984) Two component extreme value distribution for flood frequency analysis. Water Resour Research 20(7):847–856CrossRefGoogle Scholar
  7. Garavaglia E, Pavani R (2011) About earthquake forecasting by Markov renewal processes. Methodol Comput Appl Prob 13(1):155–169CrossRefGoogle Scholar
  8. Gospodinov D, Rotondi R (2001) Exploratory analysis of marked Poisson processes applied to Balkan earthquake sequences. J Balkan Geophys Soc 4(3):61–68Google Scholar
  9. Gregory J, Wigley T, Jones P (1993) Application of Markov models to area-average daily precipitation series and interannual variability in seasonal totals. Clim Dyn 8(6):299–310CrossRefGoogle Scholar
  10. Gupta V, Duckstein L (1975) A stochastic analysis of extreme droughts. Water Resour Res 11(2):221–228CrossRefGoogle Scholar
  11. Haque C (1995) Climatic hazards warning process in Bangladesh: experience of, and lessons from, the 1991 April cyclone. Environ Manag 19(5):719–734CrossRefGoogle Scholar
  12. Haque C, Blair D (1992) Vulnerability to tropical cyclones: evidence from the April 1991 cyclone in coastal Bangladesh. Disasters 16(3):217–229CrossRefGoogle Scholar
  13. Islam T, Peterson R (2009) Climatology of landfalling tropical cyclones in Bangladesh 1877–2003. Nat Hazards 48(1):115–135CrossRefGoogle Scholar
  14. Jagger T, Niu X, Elsner J (2002) A space-time model for seasonal hurricane prediction. Int J Climatol 22(4):451–465CrossRefGoogle Scholar
  15. Janssen J, Manca R (2007) Semi-Markov risk models for finance, insurance and reliability. Springer, New YorkGoogle Scholar
  16. Khalil G (1992) Cyclones and storm surges in Bangladesh: some mitigative measures. Nat Hazards 6(1):11–24CrossRefGoogle Scholar
  17. Lardet P, Obled C (1994) Real-time flood forecasting using a stochastic rainfall generator. J Hydrol 162(3–4):391–408CrossRefGoogle Scholar
  18. Limnios N, Oprian G (2001) Semi-Markov processes and reliability. Springer, New YorkCrossRefGoogle Scholar
  19. Lu Y, Garrido J (2005) Doubly periodic non-homogeneous Poisson models for hurricane data. Stat Methodol 2(1):17–35CrossRefGoogle Scholar
  20. Masala G (2012a) Earthquakes occurrences estimation through a parametric semi-Markov approach. J Appl Stat 39(1):81–96CrossRefGoogle Scholar
  21. Masala G (2012b) Hurricane lifespan modeling through a semi-Markov parametric approach. J Forecast doi: 10.1002/for.2245
  22. Mooley D (1981) Applicability of the Poisson probability model to the severe cyclonic storms striking the coast around the Bay of Bengal. Sankhyā: Indian J Stat Series B 43(2):187–197Google Scholar
  23. Ogata Y (1988) Statistical models for earthquake occurrences and residual analysis for point processes. J Am Stat As 83(401):9–27CrossRefGoogle Scholar
  24. Ogata Y (1998) Space-time point-process models for earthquake occurrences. Ann Inst Stat Math 50(2):379–402CrossRefGoogle Scholar
  25. Pyke R (1961) Markov renewal processes: definitions and preliminary properties. Ann Math Stat 32(4):1231–1242CrossRefGoogle Scholar
  26. Rumpf J, Weindl H, Höppe P, Rauch E, Schmidt V (2007) Stochastic modelling of tropical cyclone tracks. Math Methods Oper Res 66(3):475–490CrossRefGoogle Scholar
  27. Sinha P, Dube S, Roy G, Jaggi S (1986) Numerical simulation of storm surges in Bangladesh using a multi-level model. Int J Numer Meth Fluids 6(5):305–311CrossRefGoogle Scholar
  28. Votsi I, Limnios N, Tsaklidis G, Papadimitriou E (2012) Estimation of the expected number of earthquake occurrences based on semi-Markov models. Methodol Comput Appl Prob 14(3):685–703CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Mathematics and Statistics Division, Faculty of Computing, Engineering and SciencesStaffordshire UniversityStoke-on-TrentUK
  2. 2.Institute of Statistical Research and Training (ISRT)University of DhakaDhakaBangladesh

Personalised recommendations