Accurate Boussinesq oceanic modeling with a practical, “Stiffened” Equation of State

The Equation of State of seawater (EOS) relates in situ density to temperature, salinity and pressure. Most of the effort in the EOS-related literature is to ensure an accurate fit of density measurements under the conditions of different temperature, salinity, and pressure. In situ density is not of interest by itself in oceanic models, but rather plays the role of an intermediate variable linking temperature and salinity fields with the pressure-gradient force in the momentum equations, as well as providing various stability functions needed for parameterization of mixing processes. This shifts the role of EOS away from representation of in situ density toward accurate translation of temperature and salinity gradients into adiabatic derivatives of density.In this study we propose and assess the accuracy of a simplified, computationally-efficient algorithm for EOS suitable for a free-surface, Boussinesq-approximation model. This EOS is optimized to address all the needs of the model: notably, computation of pressure gradient – it is compatible with the monotonized interpolation of density needed for the pressure gradient scheme in sigma-coordinates of Shchepetkin and McWilliams (2003), while more accurately representing the pressure dependency of the thermal expansion and saline contraction coefficients as well as the stability of stratification; it facilitates mixing parameterizations for both vertical and lateral (along neutral surfaces) mixing; and it leads to a simpler, more robust, numerically stable barotropic–baroclinic mode splitting without the need of excessive temporal filtering of fast mode. In doing so we also explore the implications of EOS compressibility for mode splitting in non-Boussinesq free-surface models with the intent to design a comparatively accurate algorithm applicable there.

Research highlights
► Examine the role of compressibility in Boussinesq and non-Boussinesq ocean modeling.
► Simplified, yet accurate EOS for Boussinesq modeling with free-surface.
► Emphasis of pressure-dependency of thermal expansion and saline contraction in EOS.
► Barotropic–baroclinic splitting algorithms derived using incremental variables.
► Mode-splitting algorithm for non-Boussinesq ocean model with fully-compressible EOS.