Parametric vertical coordinate formulation for multiscale, Boussinesq, and non-Boussinesq ocean modeling

Two physical parameters are introduced into the basic ocean equations to generalize numerical ocean models for various vertical coordinate systems and their hybrid features. The two parameters are formulated by combining three techniques: the arbitrary vertical coordinate system of Kasahara [Kasahara, A., 1974. Various vertical coordinate systems used for numerical weather prediction. Mon. Weather Rev. 102, 509–522], the Jacobian pressure gradient formulation of Song [Song, Y.T., 1998. A general pressure gradient formation for ocean models. Part I: Scheme design and diagnostic analysis. Mon. Weather Rev. 126 (12), 3213–3230], and a newly introduced parametric function that permits both Boussinesq (volume-conserving) and non-Boussinesq (mass-conserving) conditions. Based on this new formulation, a generalized modeling approach is proposed. Several representative oceanographic problems with different scales and characteristics––coastal canyon, seamount topography, non-Boussinesq Pacific Ocean with nested eastern Tropics, and a global ocean model––have been used to demonstrate the model s capabilities for multiscale applications. The inclusion of non-Boussinesq physics in the topography-following ocean model does not incur computational expense, but more faithfully represents satellite-observed oceanbottom-pressure data. Such a generalized modeling approach is expected to benefit oceanographers in solving multiscale ocean-related problems by using various coordinate systems on the same numerical platform. 2005 Elsevier Ltd. All rights reserved. 1463-5003/$ see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ocemod.2005.01.001 * Corresponding author. Tel.: +1 818 393 4876; fax: +1 818 393 6720. E-mail address: [email protected] (Y.T. Song). Y.T. Song, T.Y. Hou / Ocean Modelling 11 (2006) 298–332 299