J Coast Conserv https://doi.org/10.1007/s11852-017-0565-x Development of a cylindrical polar coordinates shallow water storm surge model for the coast of Bangladesh G. C. Paul 1 · M. M. Murshed 1 · M. R. Haque 1 · M. M. Rahman 2 · A. Hoque 1 Received: 11 May 2016 / Revised: 18 September 2017 / Accepted: 20 September 2017 © Springer Science+Business Media B.V. 2017 Abstract The coast of Bangladesh is funnel shaped. The narrowing of the Meghna estuary along with its peculiar topography creates a funneling effect that has a large impact on surge response. In order to have an accurate estimation of surge levels, the impacts of the estuary should be treated with due importance. To represent in detail the real com- plexities of the estuary, a very high resolution is required, which in turn necessitates more computational cost. Con- sidering the facts into account, a location specific vertically integrated shallow water model in cylindrical polar coor- dinates is developed in this study to foresee water levels associated with a storm. A one-way nested grid technique is used to incorporate coastal complicities with minimum cost. In specific, a fine mesh scheme (FMS) capable of incor- porating coastal complexities with acceptable accuracy is  G. C. Paul pcgour2001@yahoo.com M. M. Murshed mmmurshed82@gmail.com M. R. Haque mrhaque09@gmail.com M. M. Rahman mizanmath sust@yahoo.com A. Hoque ashabulh@yahoo.com 1 Department of Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh 2 Department of Mathematics, Shahjalal University of Science & Technology, Sylhet 3114, Bangladesh nested into a coarse mesh scheme (CMS) covering up to 15 ◦ N latitude in the Bay of Bengal. The coastal and island boundaries are approximated through appropriate stair step representation and the model equations are solved by a con- ditionally stable semi-implicit finite difference technique using a structured C-grid. Numerical experiments are per- formed using the model to estimate water levels due to surge associated with the April 1991 and AILA, 2009 cyclones, which struck the coast of Bangladesh. Time series of tidal level is generated from an available tide table through a cubic spline interpolation method. The computed surge response is superimposed linearly with the generated time series of tidal oscillation to obtain the time series of total water levels. The model results exhibit a good agreement with observation and reported data. Keywords Bay of Bengal · Finite difference method · Cylindrical polar coordinates · Meghna estuary · Tropical storm · Water levels Introduction Tropical cyclones along with associated tidal surges often cause considerable devastation along the coast of Bangladesh (Paul and Ismail 2012a). Paul et al. (2014) note that on an average 5–6 storms form in the Bay of Bengal every year, but with 80% of the global casualties. The coast of Bangladesh, located at the northern tip of the Bay of Ben- gal, is recognized globally as most vulnerable to cyclones and storm surges. A list of major factors behind the vul- nerability can be found in Paul and Ismail (2013). But the area is insufficiently studied (Paul et al. 2016). Therefore,