An estimation of water levels associated with a storm along the coast of Bangladesh using a non-central difference method of lines

Abstract

In this paper, depth-averaged shallow water equations were solved using a non-central difference method of lines together with the classical RK(4,4) method to estimate water levels associated with a cyclone along the coast of Bangladesh. A 4-point backward finite difference method was adopted in discretizing spatial derivatives retaining time derivatives as continuous. Thus, the shallow water equations together with the boundary conditions were transformed into a system of initial value problems, which was solved using the RK(4,4) method. A nesting approach was employed to incorporate the land-sea interface and bottom topography effectively with economic cost. A stable tidal oscillation was generated in the domain applying the M2 tidal constituent along the southern boundary of the parent model and the surge model was then run to get water levels owing to dynamic tide-surge interaction. Numerical experiments were performed to simulate water levels due to tide, surge, and nonlinear tide-surge interactions associated with the cyclonic storm, AILA. The obtained results were in good agreement with those attained in some previous studies and observations and the WLs due to the nonlinear tide-surge interaction were in a reasonable agreement with respect to the root mean square error values and predictive skills.