ORIGINAL ARTICLE Implementation of method of lines to predict water levels due to a storm along the coastal region of Bangladesh Gour Chandra Paul • Ahmad Izani Md. Ismail • Md. Fazlul Karim Received: 7 January 2013 / Revised: 10 February 2014 / Accepted: 11 February 2014 / Published online: 7 March 2014 Ó The Oceanographic Society of Japan and Springer Japan 2014 Abstract In this study, the method of lines (MOL) has been applied to solve two-dimensional vertically integrated shallow water equations in Cartesian coordinates for the prediction of water levels due to a storm surge along the coast of Bangladesh. In doing so, the partial derivatives with respect to the space variables were discretized by the finite difference (central) method to obtain a system of ordinary differential equations (ODEs) with time as inde- pendent variable. The classical fourth-order Runge–Kutta method was used to solve the obtained system of the ODEs. We used a nested finite difference scheme, where a high resolution fine grid model (FGM) capable of incorporating all major islands along the coastal region of Bangladesh was nested into a coarse grid model (CGM) covering up to 15°N latitude of the Bay of Bengal. The boundaries of the coast and islands were approximated through proper stair step. Appropriate tidal condition over the model domain was generated by forcing the sea level to be oscillatory with the constituent M 2 along the southern open boundary of the CGM omitting wind stress. Along the northeast corner of the FGM, the Meghna River discharge was taken into account. The developed model was applied to estimate water levels along the coast of Bangladesh due to the interaction of tide and surge associated with the April 1991 storm. We also computed our results employing the stan- dard finite difference method (FDM). Simulated results show the MOL performs well in comparison with the FDM with regard to CPU time and stability, and ensures con- formity with observations. Keywords Method of lines  Tropical cyclone  Storm surge  Nested grid  Finite difference method  Runge– Kutta method 1 Introduction Storm surge prediction with various numerical models has proved to be useful for disaster planning, mitigations, and coastal management, and research is still being carried out into discovering more accurate storm surge prediction models. The method of lines (MOL) is an important tool for the treatment of boundary value problems arising in mathematics, engineering, and physical sciences, and can be applied to all major classes of partial differential equations (PDEs). The basic idea of the MOL for solving PDE is to discretize all dimensions leaving one continuous (Schiesser and Griffiths 2009). This method most often replaces the spatial derivatives in which these derivatives are discretized with respect to the spatial variables by means of FDM and enables us to apply any sophisticated time integrators for solving the resulting system of ODEs (Van der Houwen and Wubs 1987). The semi-analytical character of the formulation leads to a simple and compact algorithm, which yields accurate results with less compu- tational effort than the FDM (Sadiku and Gorcia 2000). It G. C. Paul (&)  A. I. Md. Ismail School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Georgetown, Pulau Pinang, Malaysia e-mail: pcgour2001@yahoo.com A. I. Md. Ismail e-mail: izani@cs.usm.my G. C. Paul Department of Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh Md. F. Karim Faculty of Engineering, Institute Technology Brunei, Gadong BE 1410, Brunei e-mail: mdfazlulkk@yahoo.com 123 J Oceanogr (2014) 70:199–210 DOI 10.1007/s10872-014-0224-x