Abstract
Storm surge simulation models require certain parameters for evaluating the worst possible event that could occur at a site with respect to a certain return period. The most significant probable maximum tropical cyclone parameters are pressure deficiency at the centre (ΔP) and maximum wind speed (Vmax) during the cyclone. In this study, the probable maximum tropical cyclone parameters that would yield the maximum probable storm surge along the Indian coasts of Arabian Sea and Bay of Bengal are estimated. Datasets are created based on various existing data archives for each basin. The datasets are subjected to extreme value analysis for determining the ΔP and Vmax parameters. The data are fitted to various probability distributions (Gumbel, Fréchet, Weibull and Log-normal) whose parameters (scale, shape, and location parameters) are estimated using graphical (least square fit) and numerical (order statistics approach) methods. A mean recurrence interval of 1000 and 10,000 years is considered for strategic structures. The best fit distribution and its parameters are obtained based on goodness of fit criteria. The resulting ΔP and Vmax are compared with theoretical maximum cyclone parameter values of each basin and revised till an optimal set of values are reached. The analysis shows that ΔP and Vmax values for Arabian Sea and Bay of Bengal are best represented by Weibull distribution. The estimated parameters are useful input to a storm surge model to determine the design basis flood level for the strategic coastal sites.
Similar content being viewed by others
References
Abramowitz M, Irene S (1964) Handbook of mathematical functions
AERB (Atomic Energy Regulatory Board - India) (1998) Design basis flood for nuclear power plants on inland sites (AERB SG/S-6A). Mumbai 400094
AERB (Atomic Energy Regulatory Board - India) (2002) Design basis flood for nuclear power plants at coastal sites (AERB/SG/S-6B). Mumbai 400094
AERB (Atomic Energy Regulatory Board - India) (2008) Extreme values of meteorological parameters (AERB/NF/SG/S-3). Mumbai 400094
AERB (Atomic Energy Regulatory Board - India) (2014) Site evaluation of nuclear facilities (AERB/NF/SC/S Rev.1). Mumbai 400094
Benjamin JR, Cornell CA (2014) Probability, statistics, and decision for civil engineers. Dover Books on Engineering, Mineola
BMPTC (Building Materials and Technology Promotion Council) (2018) Hazard maps of India—cyclone occurrence map. https://bmtpc.org/DataFiles/CMS/file/VAI2019/MAP/cymap/06_INDIA_CYCLONE_OCCURRENCE_DEC_2018.jpg Accessed 4 Mar 2022
Bury K (1999) Statistical distributions in engineering. Cambridge University Press, New York
Coles S, Bawa J, Trenner L, Dorazio P (2001) An introduction to statistical modeling of extreme values. Springer, London
CWPRS (Central water and power research station – Pune, India) (2007) Storm wave hindcasting and storm surge analysis for BARC at Trombay, Mumbai, Technical Report no. 4501
Demaria M, Kaplan J (1994a) Sea surface temperature and the maximum intensity of Atlantic tropical cyclones. J Clim 7(9):1324–1334. https://doi.org/10.1175/1520-0442(1994)007%3c1324:SSTATM%3e2.0.CO;2
Demaria M, Kaplan J (1994b) A statistical hurricane intensity prediction scheme (ships) for the Atlantic basin. Weather Forecast 9(2):209–220. https://doi.org/10.1175/1520-0434(1994)009%3c0209:ASHIPS%3e2.0.CO;2
Emanuel KA (1987) The dependence of hurricane intensity on climate. Nature 326(6112):483–485. https://doi.org/10.1038/326483a0
Emanuel KA (1988) The maximum intensity of hurricanes. J Atmos Sci 45(7):1143–1155
Emanuel KA (1995) Sensitivity of tropical cyclones to surface exchange coefficients and revised steady-state model incorporating eye dynamics. J Atmos Sci 52(22):3969–3976. https://doi.org/10.1175/1520-0469(1995)052%3c3969:SOTCTS%3e2.0.CO;2
Filliben JJ (1975) The probability plot correlation coefficient test for normality. Technometrics 17(1):111–117. https://doi.org/10.1080/00401706.1975.10489279
Fisher RA, Tippett LHC (1928) Limiting forms of the frequency distribution of the largest or smallest member of a sample. Math Proc Camb Philos Soc 24(2):180–190. https://doi.org/10.1017/S0305004100015681
Goda Y (1990) Distribution of sea state parameters and data fitting. Handb Coast Ocean Eng 1:371–408
Gringorten II (1963) A plotting rule for extreme probability paper. J Geophys Res 68(3):813–814. https://doi.org/10.1029/JZ068i003p00813
GSDMA (Gujarat State Disaster Management Authority) (2014) Cyclone preparedness and response plan. Government of Gujarat Publication
Gumbel EJ (1942) On the frequency distribution of extreme values in meteorological data. Bull Am Meteorol Soc 23(3):95–105
Gumbel EJ (1958) Statistics of extremes. Columbia University Press, New York. https://doi.org/10.7312/gumb92958
Gumbel EJ (1954) Statistical theory of extreme values and some practical applications. NBS applied mathematics series 33
Gupta A, Dauji S, Srivastava PK, Bhargava K (2018) Extreme value analysis by graphical and Lieblein techniques for rainfall on western coast of India. IWRA (india) J (half Yearly Tech J Indian Geogr Comm IWRA) 7(2):1–21
Hosmer DW, Hosmer T, Le Cessie S, Lemeshow S (1997) A comparison of goodness-of-fit tests for the logistic regression model. Stat Med 16(9):965–980. https://doi.org/10.1002/(SICI)1097-0258(19970515)16:9%3c965::AID-SIM509%3e3.0.CO;2-O
IAEA (International Atomic Energy Agency) (2011) Meteorological and hydrological hazards in site evaluation for nuclear installations (Specific Safety Guide No. SSG-18)
IMD (India Meteorological Department) (2003) Cyclone manual
Kessler E, Neas B (1994) On correlation, with applications to the radar and raingage measurement of rainfall. Atmos Res 34(1–4):217–229. https://doi.org/10.1016/0169-8095(94)90093-0
Khokiattiwong S, Yu W (2012) Note on the occurrence of high sea surface temperatures in the Andaman Sea, in 2010. Phuket Mar Biol Cent Res Bull 71:1–9
Kotal SD, Kundu PK, Roy Bhowmik SK (2009) An analysis of sea surface temperature and maximum potential intensity of tropical cyclones over the Bay of Bengal between 1981 and 2000. Meteorol Appl J Forecast Pract Appl Train Tech Model 16(2):169–177. https://doi.org/10.1002/met.96
Kudale MD (2010) Design wave prediction and storm surge analysis. National Water Academy (NWA), Central Water Commission (CWC), Pune
Lieblein J (1974) Efficient methods of extreme-value methodology (NEA-CSNI-R—1976-10). Nuclear energy agency of the OECD (NEA), Washington DC. https://inis.iaea.org/collection/NCLCollectionStore/_Public/41/073/41073093.pdf?r=1
Makkonen L (2006) Plotting positions in extreme value analysis. J Appl Meteorol Climatol 45(3):334–340. https://doi.org/10.1175/JAM2349.1
Miller BI (1958) On the maximum intensity of hurricanes. J Meteorol 15(2):184–195. https://doi.org/10.1175/1520-0469(1958)015%3c0184:OTMIOH%3e2.0.CO;2
NCEP (US National Centers for Environmental Prediction – National Weather Service) Maximum Potential Hurricane Intensity. http://wxmaps.org/pix/hurpot#NIND Accessed 3 Mar 2022
Ologhadien I (2021) Study of unbiased plotting position formulae for the generalized extreme value (GEV) distribution. Eur J Eng Technol Res 6(4):94–99. https://doi.org/10.24018/ejeng.2021.6.4.2468
Palutikof JP, Brabson BB, Lister DH, Adcock ST (1999) A review of methods to calculate extreme wind speeds. Meteorol Appl 6(2):119–132. https://doi.org/10.1017/S1350482799001103
Pandey S (2020) Numerical modeling of coastal inundation in response to a tropical cyclone along the east coast of India. Dissertation, Indian Institute of Technology Delhi (IITD).
Petruaskas C, Aagaard PM (1970) Extrapolation of historical storm data for estimating design wave heights. In: Proceedings of the annual offshore technology conference, 1970-April. https://doi.org/10.2118/3127-PA
Poulose J, Rao AD, Dube SK (2020) Mapping of cyclone induced extreme water levels along Gujarat and Maharashtra coasts: a climate change perspective. Clim Dyn 55(11–12):3565–3581. https://doi.org/10.1007/s00382-020-05463-4
Rajalakshmi PR, Achyuthan H (2021) Climate change as observed in the Bay of Bengal. J Clim Change 7(3):69–82. https://doi.org/10.3233/JCC210020
Rao AD, Jain I, Venkatesan R (2010) Estimation of extreme water levels due to cyclonic storms: a case study for Kalpakkam coast. Int J Ocean Clim Syst 1(1):1–14. https://doi.org/10.1260/1759-3131.1.1.1
RSMC (Regional Specialised Meteorological Centre - India Meteorological Department) (2011a) Cyclone e-Atlas. http://14.139.191.203/ Accessed 3 Mar 2022
RSMC (Regional Specialised Meteorological Centre – Indian Meteorological Department) (2018) Best Track. https://rsmcnewdelhi.imd.gov.in/report.php?internal_menu=MzM=. Accessed 9 Feb 2022
RSMC (Regional Specialised Meteorological Centre - India Meteorological Department) (2011b) Cyclone eAtlas—IMD Technical Note. Chennai
Subramanya K (2008) Floods. In: Mukherjee S, Chandrasekhar S, Mukherjee S (eds) Engineering Hydrology, Third edit. Tata McGraw-Hill Publishing Company Limited, West Patel Nagar, New Delhi, pp 245–279
Tai J, Chu A, Zhang J (2014) Determination of the probable maximum tropical cyclone for the Chinese coast: case of Nansha, Guangzhou. Proc Int Offshore Polar Eng Conf 3:457–462
USNRC, (United States Nuclear Regulatory Commission -USA) (2011) Design-basis flood estimation for site characterization at nuclear power plants in the United States of America (NUREG/CR-7046)
Vivekanandan N (2017) Rainfall intensity-duration-frequency analysis using order statistics approach of gumbel and frechet distributions. Int J Emerg Eng Res Technol 5(9):13–19
Vivekanandan N, Ramesh C (2017) Statistical analysis of rainfall data for estimation of peak flood discharge using rational formula. Int J Emerg Eng Res Technol 5(5):1–6
Vivekanandan E, Hermes R, O’Brien C (2016) Climate change effects in the Bay of Bengal large marine ecosystem. Environmental Development 17:46–56. https://doi.org/10.1016/j.envdev.2015.09.005
Wang XN (1982) The value of some parameters on typhoons. Storm Surge 2:97–103
Weibull W (1939) A statistical theory of strength of materials. Ing Vetensk Akad Handl 151:1–45
Weibull W (1951) A Statistical distribution function of wide applicability. J Appl Mech 18:293–297
Whitney LD, Hobgood JS (1997) The relationship between sea surface temperatures and maximum intensities of tropical cyclones in the eastern North Pacific Ocean. J Clim 10(11):2921–2930. https://doi.org/10.1175/1520-0442(1997)010%3C2921:TRBSST%3E2.0.CO;2
Yin QJ, Wang XN (1991) The possible maximum typhoon storm surge of Hangzhou Bay calculation. Mar Forecast 8(4):41–44
Yin QJ, Wang XN, Wu SH (1995) The calculation of possible maximum storm surge of Zhenhai. Acta Oceanol Sin 2:97–103
Zeng Z, Wang Y, Wu CC (2007) Environmental dynamical control of tropical cyclone intensity—an observational study. Mon Weather Rev 135(1):38–59. https://doi.org/10.1175/MWR3278.1
Zhao X (2009) Study on the storm-high tide level raised by probable maximum tropical cyclone in the north shore of Qian tang River. Dissertation, Zhejiang University
Acknowledgements
We acknowledge the technical support of Mr. Pankaj Kumar Srivastava, Nuclear Recycle Board (NRB), Bhabha Atomic Research Center (BARC), India in this investigation. We are grateful to the Ocean Engineering Lab, Department of Civil Engineering, IIT Bombay for providing the computational resources. The data resources of India Meteorological Department (IMD) has been a valuable asset in completing this research. We thank the Editor and anonymous reviewers for their constructive comments and corrections which contributed to improving this manuscript.
Funding
The authors did not receive any financial support to conduct the research work.
Author information
Authors and Affiliations
Contributions
All authors contributed to the study. The first draft of the manuscript was written by DSK and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
Corresponding author
Ethics declarations
Conflict of interest
No potential conflict of interest was reported by the author(s).
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Information
Below is the link to the electronic supplementary material.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Kumar, D.S., Behera, M.R., Nadella, S. et al. Probable maximum tropical cyclone parameters for east and west coast of India. Nat Hazards 116, 2437–2455 (2023). https://doi.org/10.1007/s11069-022-05773-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11069-022-05773-2