Abstract
In a previous study, the authors studied a low order pressure gradient force (PGF) scheme referred to as the Primitive-Modified scheme, that appears to be equivalent to the Pressure-Jacobian PGF ( Lin, 1997). The scheme was successfully tested on the seamount experiment using a simplified equation of state (EOS). Yet, a complete equation of state, including compressibility effect, can raise a serious problem of accuracy. A new implementation is thus proposed in the present paper. The scheme is rewritten using a (numerically equivalent) geopotential formulation. The PGF truncation errors are removed by computing the EOS compressibility terms with potential temperature and salinity interpolated on a suitable geopotential level. The so-called Equivalent Geopotential Formulation (EGF) method is compared to the Finite-Volume approach proposed by Adcroft et al. (2008).
Highlights
Marsaleix et al (2009) present a low order pressure gradient force scheme referred to as the ‘‘Primitive Modified’’ scheme
We suggest an alternative geopotential formulation, numerically equivalent to the usual discretization, but offering a straightforward opportunity to solve the problem of the pressure gradient force (PGF) accuracy related to the compressibility terms of the equation of state
Even if the PGF scheme studied in M09 was the starting point of the present study, we may retain that the method proposed to remove the truncation error associated to the compressibility terms of the equation of state (EOS) is not limited to a particular PGF scheme
Summary
Marsaleix et al (2009) (hereafter M09) present a low order pressure gradient force (hereafter PGF) scheme referred to as the ‘‘Primitive Modified’’ (hereafter PM) scheme. First of all the discrete form used for the hydrostatic pressure is consistent with the conservation property of tracer advection and diffusion schemes, generally adopted by up-to-date ocean models. According to M09, the tracer conservation property naturally leads to consider that discrete values of potential temperature and salinity (hereafter h and S) represent averaged values of ‘‘true’’ (h, S) fields over the volume of cell boxes. Assuming this formulation of the discrete (h, S) fields and using a simplified equation of state (neglecting non-linearity and compressibility), M09 show that the discrete pressure at the upper and lower facets of the C-grid cell
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