Skip to main content
SpringerLink
Log in

Numerical storm surge model with higher order finite difference method of lines for the coast of Bangladesh

  • Published:
Acta Oceanologica Sinica Aims and scope Submit manuscript

Abstract

In this study, the method of lines (MOLs) with higher order central difference approximation method coupled with the classical fourth order Runge-Kutta (RK(4,4)) method is used in solving shallow water equations (SWEs) in Cartesian coordinates to foresee water levels associated with a storm accurately along the coast of Bangladesh. In doing so, the partial derivatives of the SWEs with respect to the space variables were discretized with 5-point central difference, as a test case, to obtain a system of ordinary differential equations with time as an independent variable for every spatial grid point, which with initial conditions were solved by the RK(4,4) method. The complex land-sea interface and bottom topographic details were incorporated closely using nested schemes. The coastal and island boundaries were rectangularized through proper stair step representation, and the storing positions of the scalar and momentum variables were specified according to the rules of structured C-grid. A stable tidal regime was made over the model domain considering the effect of the major tidal constituent, M2 along the southern open boundary of the outermost parent scheme. The Meghna River fresh water discharge was taken into account for the inner most child scheme. To take into account the dynamic interaction of tide and surge, the generated tidal regime was introduced as the initial state of the sea, and the surge was then made to come over it through computer simulation. Numerical experiments were performed with the cyclone April 1991 to simulate water levels due to tide, surge, and their interaction at different stations along the coast of Bangladesh. Our computed results were found to compare reasonable well with the limited observed data obtained from Bangladesh Inland Water Transport Authority (BIWTA) and were found to be better in comparison with the results obtained through the regular finite difference method and the 3-point central difference MOLs coupled with the RK(4,4) method with regard to the root mean square error values.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Ali A, Choudhury, G A. 2014. Storm Surges in Bangladesh: An Introduction to CEGIS Storm Surge Model. Dhaka, Bangladesh: The University Press Limited

    Google Scholar 

  • Bakodah, H O. 2011. Non-central 7-point formula in the method of lines for parabolic and Burgers’ equations. International Journal of Research and Reviews in Applied Sciences, 8(3): 328–336

    Google Scholar 

  • Chapra, S C, Canale, R P. 2015. Numerical Methods for Engineers. 7th ed. New York, USA: McGraw-Hill, Inc

    Google Scholar 

  • Das, P K. 1972. Prediction model for storm surges in the Bay of Bengal. Nature, 239(5369): 211–213, doi: 10.1038/239211a0

    Article  Google Scholar 

  • Das, P K, Sinha, M C, Balasubramanyam, V. 1974. Storm surges in the Bay of Bengal. Quarterly Journal of the Royal Meteorological Society, 100(425): 437–449

    Google Scholar 

  • Debsarma, S K. 2009. Simulations of storm surges in the Bay of Bengal. Marine Geodesy, 32(2): 178–198, doi: 10.1080/01490410902869458

    Article  Google Scholar 

  • Flather, R A. 1994. A storm surge prediction model for the northern Bay of Bengal with application to the cyclone disaster in Apri. 1991. Journal of Physical Oceanography, 24(1): 172–190, doi: 10.1175/1520-0485(1994)0240172:ASSPMF2.0.CO;2

    Article  Google Scholar 

  • Hossain, M Z, Islam, M T, Sakai, T, et al. 2008. Impact of tropical cyclones on rural infrastructures in Bangladesh. Agricultural Engineering International: the CIGR Ejournal, 2: 1–13

    Google Scholar 

  • Ismail A, I M, Karim, F, Roy, G D, et al. 2007. Numerical modelling of tsunami via the method of lines. World Academy of Science, Engineering and Technology, 32: 177–185

    Google Scholar 

  • Jelesnianski, C P. 1965. A numerical calculation of storm tides induced by a tropical storm impinging on a continental shelf. Monthly Weather Review, 93(6): 343–358, doi: 10.1175/1520-0493(1993)0930343:ANCOS2.3.CO;2

    Article  Google Scholar 

  • Johns B, Ali, M A. 1980. The numerical modelling of storm surges in the Bay of Bengal. Quarterly Journal of the Royal Meteorological Society, 106(447): 1–18, doi: 10.1002/(ISSN)1477–870X

    Article  Google Scholar 

  • Johns B, Rao, A D, Dube, S K, et al. 1985. Numerical modelling of tidesurge interaction in the Bay of Bengal. Philosophical Transactions of the Royal Society A, 313(1526): 507–535, doi: 10.1098/rsta.1985.0002

    Article  Google Scholar 

  • Khalil, G M. 1992. Cyclones and storm surges in Bangladesh: some mitigative measures. Natural Hazards, 6(1): 11–24, doi: 10.1007/BF00162096

    Article  Google Scholar 

  • Khalil, G M. 1993. The catastrophic cyclone of Apri. 1991. its impact on the economy of Bangladesh. Natural Hazards, 8(3): 263–281, doi: 10.1007/BF00690911

    Article  Google Scholar 

  • Lewis M, Bates, P, Horsburgh K, et al. 2013. A storm surge inundation model of the northern Bay of Bengal using publicly available data. Quarterly Journal of the Royal Meteorological Society, 139(671): 358–369, doi: 10.1002/qj.2040

    Article  Google Scholar 

  • Lewis M, Horsburgh, K, Bates, P. 2014. Bay of Bengal cyclone extreme water level estimate uncertainty. Natural Hazards, 72(2): 983–996, doi: 10.1007/s11069-014-1046-2

    Article  Google Scholar 

  • Loy, K C, Sinha, P C, Liew, J, et al. 2014. Modeling storm surges associated with super typhoon durian in South China Sea. Natural Hazards, 70(1): 23–37, doi: 10.1007/s11069-010-9674-7

    Article  Google Scholar 

  • Madsen H, Jakobsen, F. 2004. Cyclone induced storm surge and flood forecasting in the northern Bay of Bengal. Coastal Engineering, 51(4): 277–296, doi: 10.1016/j.coastaleng.2004.03.001

    Article  Google Scholar 

  • McCammon C, Wunsch, C. 1977. Tidal charts of the Indian Ocean North of 15°S. Journal of Geophysical Research, 82(37): 5993–5998, doi: 10.1029/JC082i037p05993

    Article  Google Scholar 

  • Mills, D A. 1985. A numerical hydrodynamic model applied to tidal dynamics in the Dampier Archipelago. Bulletin No. 190. Western Australia: Department of Conservation and Environment

    Google Scholar 

  • Paul, G C, Ismail A, I M. 2012a. Numerical modeling of storm surges with air bubble effects along the coast of Bangladesh. Ocean Engineering, 42: 188–194, doi: 10.1016/j.oceaneng.2012.01.006

    Article  Google Scholar 

  • Paul, G C, Ismail A, I M. 2012b. Tide-surge interaction model including air bubble effects for the coast of Bangladesh. Journal of the Franklin Institute, 349(8): 2530–2546, doi: 10.1016/j.jfranklin. 2012.08.003

    Article  Google Scholar 

  • Paul, G C, Ismail A, I M. 2013. Contribution of offshore islands in the prediction of water levels due to tide–surge interaction for the coastal region of Bangladesh. Natural Hazards, 65(1): 13–25, doi: 10.1007/s11069-012-0341-z

    Article  Google Scholar 

  • Paul, G C, Ismail A, I M, Karim, M F. 2014. Implementation of method of lines to predict water levels due to a storm along the coastal region of Bangladesh. Journal of Oceanography, 70(3): 199–210, doi: 10.1007/s10872–014–0224-x

    Article  Google Scholar 

  • Paul, G C, Ismail A I M, Rahman, A, et al. 2016. Development of tide–surge interaction model for the coastal region of Bangladesh. Estuaries and Coasts, 39(6): 1582–1599, doi: 10.1007/s12237-016-0110-4

    Article  Google Scholar 

  • Paul, G C, Murshed, M M, Haque, M R, et al. 2017. Development of a cylindrical polar coordinates shallow water storm surge model for the coast of Bangladesh. Journal of Coastal Conservation, 21(6): 951–966, doi: 10.1007/s11852-017-0565-x

    Article  Google Scholar 

  • Paul, G C, Senthilkumar, S, Pria, R. 2018a. Storm surge simulation along the Meghna estuarine area: an alternative approach. Acta Oceanologica Sinica, 37(1): 40–49, doi: 10.1007/s13131-018-1157-9

    Article  Google Scholar 

  • Paul, G C, Senthilkumar, S, Pria, R. 2018b. An efficient approach to forecast water levels owing to the interaction of tide and surge associated with a storm along the coast of Bangladesh. Ocean Engineering, 148: 516–529, doi: 10.1016/j.oceaneng.2017.10.031

    Article  Google Scholar 

  • Pregla R. 1987. About the nature of the method of lines. Archiv für Elektronik und Übertragungstechnik, 41(6): 368–370

    Google Scholar 

  • Pregla R, Pascher, W. 1989. The method of lines. In: Itoh T, ed. Numerical Techniques for Microwave and Millimeter-Wave Passive Structures. New York: John Wiley, 381–446

    Google Scholar 

  • Rahman, M M, Paul, G C, Hoque, A. 2017. A shallow water model for computing water level due to tide and surge along the coast of Bangladesh using nested numerical schemes. Mathematics and Computers in Simulation, 132: 257–276, doi: 10.1016/j.matcom.2016.08.007

    Article  Google Scholar 

  • Rehman, M A, Taj M S A. 2009. Fourth-order method for non-homogeneous heat equation with nonlocal boundary conditions. Applied Mathematical Sciences, 3(37): 1811–1821

    Google Scholar 

  • Rehman, M A, Taj M S A. 2011. A numerical technique for heat equation subject to integral specifications. Science International (Lahore), 24(1): 1–6

    Google Scholar 

  • Rehman, M A, Taj M S A, Mardan, S A. 2014. Fifth order numerical method for heat equation with nonlocal boundary conditions. Journal of Mathematical and Computational Science, 4(6): 1044–1054

    Google Scholar 

  • Roy, G D. 1995. Estimation of expected maximum possible water level along the Meghna estuary using a tide and surge interaction model. Environment International, 21(5): 671–677, doi: 10.1016/0160-4120(95)00078-Y

    Article  Google Scholar 

  • Roy, G D. 1999a. Inclusion of off-shore islands in a transformed coordinates shallow water model along the coast of Bangladesh. Environment International, 25(1): 67–74, doi: 10.1016/S0160-4120(98)00094–4

    Article  Google Scholar 

  • Roy, G D. 1999b. Sensitivity of water level associated with tropical storms along the Meghna estuary in Bangladesh. Environment International, 25(1): 109–116, doi: 10.1016/S0160-4120(98) 00095-6

    Article  Google Scholar 

  • Roy, G D, Kabir A B M H, Mandal, M M, et al. 1999. Polar coordinates shallow water storm surge model for the coast of Bangladesh. Dynamics of Atmospheres and Oceans, 29(2–4): 397–413, doi: 10.1016/S0377-0265(99)00012-3

    Article  Google Scholar 

  • Sadiku M N O, Garcia, R C. 2000. Method of lines solution of axisymmetric problems. In: Proceedings of 2000 IEEE Southeastcon. Nashville, TN, USA: IEEE, 527–530

    Google Scholar 

  • Schiesser, W E, Griffiths, G W. 2009. A Compendium of Partial Differential Equation Models: Method of Lines Analysis with Matlab. Cambridge: Cambridge University Press

    Book  Google Scholar 

  • Sinha, P C, Dube, S K, Roy, G D, et al. 1986. Numerical simulation of storm surges in Bangladesh using a multi-level model. International Journal for Numerical Methods in Fluids, 6(5): 305–311, doi: 10.1002/(ISSN)1097–0363

    Article  Google Scholar 

  • Zhang Wenzhou, Hong Huasheng, Shang Shaoping, et al. 2007. A two-way nested coupled tide-surge model for the Taiwan Strait. Continental Shelf Research, 27(10–11): 1548–1567, doi: 10.1016/j.csr.2007.01.018

    Article  Google Scholar 

Download references

Acknowledgements

The first author thanks Sujit Kumar Debsarma for his valuable discussion about the data sources. We thank Mizanur Rahman from Sylhet University of Science and Technology for providing necessary data. The second author thanks Aslam Hossain, lecturer, Department of Applied Mathematics, Gono University, Savar, Dhaka, Bangladesh for his kind help during editing the manuscript.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Rajshahi, Rajshahi, 6205, Bangladesh

    Gour Chandra Paul

  2. Department of Textile Engineering, Northern University Bangladesh, Dhaka, 1230, Bangladesh

    Md. Emran Ali

Authors
  1. Gour Chandra Paul
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Md. Emran Ali
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gour Chandra Paul.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Paul, G.C., Ali, M.E. Numerical storm surge model with higher order finite difference method of lines for the coast of Bangladesh. Acta Oceanol. Sin. 38, 100–116 (2019). https://doi.org/10.1007/s13131-019-1385-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13131-019-1385-7

Key words

Search

Navigation