A Two-level Scheme, Primitive Equation, Three-dimensional Ocean Circulation Model (MASNUM) And Its Validation

A finite-difference, primitive equation, three-dimensional ocean circulation model (MASNUM circulation model) was established. This model is characterized by its Boussinesq approximation, free-surface, mode-splitting, terrain-following features, and temporally discretized with a two-level scheme.The mathematical model of the oceanic motions is based on the terrain-following, Reynolds-averaged ocean governing equations, which are derived from the complete geophysical fluid dynamical equations under the hydrostatic and Boussinesq approximations. As the numerical techniques, a simplest two-level, single-step algorithm, Eulerian forward and backward difference method (FB), is adopted for the temporal difference. The staggered Arakawa-C stencil is used for spatial arrangements of the model variables. A volume-conserved spatial smoothing method is devised to surppress the growing of the short perturbations due to nonlinear terms.The spline interpolated density Jacobian algorithm is cited in calculating the internal pressure gradient force. However, certain correction has to be made to the harmonic mean in the original algorithm to reduce the error. The error analysis and correction has been made to the diagnostic computation of the vertical velocity. The problem that the kinetic boundary conditions at the surface and the bottom cannot be strictly satisfied simultaneously in the original algorithm has been fixed.The algorithms of some main thermodynamic variables, such as in-situ density and static stability have been reviewed and updated with up-to-date and stable computation methods. The detailed numerical forms are derived for three categories,18kinds of open boundary condtions for the kinetic variables prevelant in current ocean models. Most of these conditions have been included in the MASNUM circulation model, to be invoked in all kinds of numerical experiments.To verify the performance of the MASNUM circulation model, the coastal tide of the China Seas is first simulated, and MASNUM circulation model appears improvements in the phase lag. Secondly, MASNUM circulation model could simulate the main features and seasonal evolutions of the Yellow-Sea Cold Water Mass, a typical baroclinic phenomenon. Thirdly, the MASNUM circulation model has been setup to compute the Northwest Pacific with horizontal resolution of1/6degrees and vertically16layers. The3-year time series of four prognostic variables has been compared with those of the POM model. The comparisons show farily good consistent in both amplitude and phase between the two models. These experiments and comparisons verified the reliablity and applicability of the newly-built circulation model to a large extent.