Numerical storm surge model with higher order finite difference method of lines for the coast of Bangladesh Gour Chandra Paul 1 *, Md. Emran Ali 2 1 Department of Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh 2 Department of Textile Engineering, Northern University Bangladesh, Dhaka 1230, Bangladesh Received 31 January 2018; accepted 11 May 2018 © Chinese Society for Oceanography and Springer-Verlag GmbH Germany, part of Springer Nature 2019 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, M 2 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. Key words: shallow water equations, method of lines, higher order finite difference approximation method, surge, nested scheme Citation: Paul Gour Chandra, Ali Md. Emran. 2019. Numerical storm surge model with higher order finite difference method of lines for the coast of Bangladesh. Acta Oceanologica Sinica, 38(6): 100–116, doi: 10.1007/s13131-019-1385-7 1  Introduction Geographically, Bangladesh is situated at the interface of two important relatively opposite geographical constituents, namely ocean and hills (Ali and Choudhury, 2014). For such a type of junction, this area is highly favorable for different natural calam- ities, such as cyclones, storm surges, earthquakes, floods, droughts, etc. The Himalayas and Kashi-Jaintia hills, situated at the north and east of the country, respectively, are responsible for inland flooding by making monsoon rain and melting snow and ice through numerous rivers produced from their waterfall what make erosion of the river bank, create sedimentation and river migration, etc. On the other hand, the Bay of Bengal (BOB) is the source of various disasters, namely tropical cyclones (TCs) and associated surges, floods, salinity intrusion, coastal erosion, etc. Among the disasters, TCs and associated surges cause major dev- astation. It is documented that about five to six storms form every year in the BOB region but with about 80% of the global casual- ties (Debsarma, 2009). For making understand the ferocity of these storm surges along this region, Fig. 1 having different storm tracks and Table 1 with the corresponding losses are included. From Table 1 and Fig. 1, one can figure out the extent of losses made by the surges associated with some notable tropical storms over the years and its impact on socioeconomic sectors. The coast of Bangladesh, located at the northern tip of the BOB, is re- cognized globally as the most vulnerable to cyclones and associ- ated surges (Paul et al., 2017). The reasons behind the vulnerabil- ity are the complex coastline, thickly populated offshore islands of different shapes, shallow bathymetry, huge discharge through the Meghna River and other rivers, high tidal range, etc. We can- not prevent storm surges, but we can better be prepared for it. However, this can best be done by increasing awareness among the coastal people through a proper warning system and such a system is highly dependent on an accurate storm surge predic- tion model. Bangladesh Meteorological Department (BMD) has a warning system based on a numerical model brought from the IIT Kharagpur, India, which is a surge model and can predict the landfall time, sea level rising as well as the storm track in a cer- tain accuracy (Debsarma, 2009). But the predictions by the storm warning center meteorologists of the BMD in terms of the pre- cise location of cyclones, landfall timing, precise estimation of surge height, etc. have often been criticized (Hossain et al., 2008). Thus an appeal is emerged to the research community for the de-   *Corresponding author, E-mail: pcgour2001@yahoo.com   Acta Oceanol. Sin., 2019, Vol. 38, No. 6, P. 100–116 https://doi.org/10.1007/s13131-019-1385-7 http://www.hyxb.org.cn E-mail: hyxbe@263.net