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

Gour Chandra Paul; Md. Emran Ali

doi:10.1007/s13131-019-1385-7

Volume 38 Issue 6

Turn off MathJax

Article Contents

Article Navigation > Acta Oceanologica Sinica > 2019 > 38(6): 100-116

Gour Chandra Paul, Md. Emran Ali. Numerical storm surge model with higher order finite difference method of lines for the coast of Bangladesh[J]. Acta Oceanologica Sinica, 2019, 38(6): 100-116. doi: 10.1007/s13131-019-1385-7

Citation:

Gour Chandra Paul, Md. Emran Ali. Numerical storm surge model with higher order finite difference method of lines for the coast of Bangladesh[J]. Acta Oceanologica Sinica, 2019, 38(6): 100-116. doi: 10.1007/s13131-019-1385-7

Citation:

PDF( 4880 KB)

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

doi: 10.1007/s13131-019-1385-7

Gour Chandra Paul^{1
,
,},
Md. Emran Ali²

1.
Department of Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh
2.
Department of Textile Engineering, Northern University Bangladesh, Dhaka 1230, Bangladesh

More Information

Corresponding author: E-mail: pcgour2001@yahoo.com
Received Date: 2018-01-31
Accepted Date: 2018-05-11

Available Online: 2020-04-21

Publish Date: 2019-06-01

Abstract

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.
- shallow water equations,
- method of lines,
- higher order finite difference approximation method,
- surge,
- nested scheme

FullText(HTML)

References(42)

References

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

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

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

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

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

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

Flather R A. 1994. A storm surge prediction model for the northern Bay of Bengal with application to the cyclone disaster in April 1991. Journal of Physical Oceanography, 24(1): 172–190. doi: 10.1175/1520-0485(1994)024<0172:ASSPMF>2.0.CO;2

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

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

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)093<0343:ANCOS>2.3.CO;2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Relative Articles

Supplements(0)

Cited By

Proportional views