Skip to main content
Log in

A parametric Markov renewal model for predicting tropical cyclones in Bangladesh

  • Original Paper
  • Published:
Natural Hazards Aims and scope Submit manuscript


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.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others


  • 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):171–179

    Google Scholar 

  • Alvarez E (2005) Estimation in stationary Markov renewal processes, with application to earthquake forecasting in Turkey. Methodol Comput Appl Prob 7(1):119–130

    Article  Google Scholar 

  • Asaduzzaman M, Latif AHMM (2014) Computational intelligence techniques in earth and environmental sciences chap 7. Springer, New York

    Google Scholar 

  • Dube S, Sinha P, Roy G (1985) The numerical simulation of storm surges along the Bangladesh coast. Dyn Atmos Oceans 9(2):121–133

    Article  Google Scholar 

  • Dube S, Sinha P, Roy G (1986) Numerical simulation of storm surges in Bangladesh using a bay-river coupled model. Coast Eng 10(1):85–101

    Article  Google Scholar 

  • Fiorentino M, Versace P, Rossi F (1984) Two component extreme value distribution for flood frequency analysis. Water Resour Research 20(7):847–856

    Article  Google Scholar 

  • Garavaglia E, Pavani R (2011) About earthquake forecasting by Markov renewal processes. Methodol Comput Appl Prob 13(1):155–169

    Article  Google Scholar 

  • Gospodinov D, Rotondi R (2001) Exploratory analysis of marked Poisson processes applied to Balkan earthquake sequences. J Balkan Geophys Soc 4(3):61–68

    Google Scholar 

  • 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):299–310

    Article  Google Scholar 

  • Gupta V, Duckstein L (1975) A stochastic analysis of extreme droughts. Water Resour Res 11(2):221–228

    Article  Google Scholar 

  • Haque C (1995) Climatic hazards warning process in Bangladesh: experience of, and lessons from, the 1991 April cyclone. Environ Manag 19(5):719–734

    Article  Google Scholar 

  • Haque C, Blair D (1992) Vulnerability to tropical cyclones: evidence from the April 1991 cyclone in coastal Bangladesh. Disasters 16(3):217–229

    Article  Google Scholar 

  • Islam T, Peterson R (2009) Climatology of landfalling tropical cyclones in Bangladesh 1877–2003. Nat Hazards 48(1):115–135

    Article  Google Scholar 

  • Jagger T, Niu X, Elsner J (2002) A space-time model for seasonal hurricane prediction. Int J Climatol 22(4):451–465

    Article  Google Scholar 

  • Janssen J, Manca R (2007) Semi-Markov risk models for finance, insurance and reliability. Springer, New York

    Google Scholar 

  • Khalil G (1992) Cyclones and storm surges in Bangladesh: some mitigative measures. Nat Hazards 6(1):11–24

    Article  Google Scholar 

  • Lardet P, Obled C (1994) Real-time flood forecasting using a stochastic rainfall generator. J Hydrol 162(3–4):391–408

    Article  Google Scholar 

  • Limnios N, Oprian G (2001) Semi-Markov processes and reliability. Springer, New York

    Book  Google Scholar 

  • Lu Y, Garrido J (2005) Doubly periodic non-homogeneous Poisson models for hurricane data. Stat Methodol 2(1):17–35

    Article  Google Scholar 

  • Masala G (2012a) Earthquakes occurrences estimation through a parametric semi-Markov approach. J Appl Stat 39(1):81–96

    Article  Google Scholar 

  • Masala G (2012b) Hurricane lifespan modeling through a semi-Markov parametric approach. J Forecast doi:10.1002/for.2245

  • 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):187–197

    Google Scholar 

  • Ogata Y (1988) Statistical models for earthquake occurrences and residual analysis for point processes. J Am Stat As 83(401):9–27

    Article  Google Scholar 

  • Ogata Y (1998) Space-time point-process models for earthquake occurrences. Ann Inst Stat Math 50(2):379–402

    Article  Google Scholar 

  • Pyke R (1961) Markov renewal processes: definitions and preliminary properties. Ann Math Stat 32(4):1231–1242

    Article  Google Scholar 

  • Rumpf J, Weindl H, Höppe P, Rauch E, Schmidt V (2007) Stochastic modelling of tropical cyclone tracks. Math Methods Oper Res 66(3):475–490

    Article  Google Scholar 

  • 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):305–311

    Article  Google Scholar 

  • 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):685–703

    Article  Google Scholar 

Download references


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

Author information

Authors and Affiliations


Corresponding author

Correspondence to Md. Asaduzzaman.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Asaduzzaman, M., Latif, A.H.M.M. A parametric Markov renewal model for predicting tropical cyclones in Bangladesh. Nat Hazards 73, 597–612 (2014).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: