Introduction

Although the governing equations of the evolution of the oceanic system are not very different from the atmospheric system, there are a few examples of ocean models that do not have a similar or equivalent atmospheric model. Furthermore, there are distinct differences between ocean and atmospheric models, for example, ocean models require larger computer resources in terms of the CPU time, core memory, as well as disk storage. As the eddies in the ocean are much smaller than the atmospheric weather systems, the grid resolution needed in ocean modeling is therefore much finer as compared to atmospheric models. Owing to considerations of stability in terms of CFL condition, fine grid resolution in ocean models also translates into smaller time steps while using explicit finite difference schemes. The time step is determined by the speed of the fast moving surface gravity waves while solving an ocean free surface model using explicit finite difference scheme. The smaller time step in the free surface ocean models while employing explicit finite difference scheme necessitates larger number of time marchings and, hence, longer CPU time to integrate over the specified integration or the forecast duration. Utilizing an implicit/semiimplicit method of finite difference will take care of the stability requirements as these schemes are unconditionally stable; however, the CPU time required for such schemes would depend on the rate of convergence of the iterative method used to solve the matrix equation (for fully implicit schemes) and the rate of convergence of the iterative method used to solve the resulting elliptic partial differential equation (for semi-implicit schemes).

It is well known that unlike the atmospheric system, the ocean system is poorly observed. The only information that satellites provide are about ocean bathymetry, sea surface temperature, sea surface salinity, ocean color, coral reefs, and sea and lake ice. Data assimilation is a technique whereby observational data are combined with output from a numerical model to produce an optimal estimate of the evolving state of the atmospheric or the oceanic system. Owing to the lack of ocean observations, data assimilation methods are inherently more difficult to implement for ocean models.