An accurate implementation of the compressibility terms in the equation of state in a low order pressure gradient scheme for sigma coordinate ocean models

Patrick Marsaleix (1) , Francis Auclair (1) , Claude Estournel (1) , Cyril Nguyen (2) , Caroline Ulses (1)

1 LAERO - Laboratoire d'aérologie
2 ECOLA - Echanges Côte-Large

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).

Mots clés: Seamount; Pressure Jacobian; Equation of state; Compressibility; Sigma coordinate; Pressure gradient

Domaines: Océan, Atmosphère

Patrick Marsaleix, Francis Auclair, Claude Estournel, Cyril Nguyen, Caroline Ulses. An accurate implementation of the compressibility terms in the equation of state in a low order pressure gradient scheme for sigma coordinate ocean models. Ocean Modelling, 2011, 40 (1), pp.1-13. ⟨10.1016/j.ocemod.2011.07.004⟩. ⟨hal-02110128⟩