Abstract
AbstractThere is a growing realization that the nonlinear nature of the equation of state has a deep impact on the global ocean circulation; however, the understanding of the global effects of these nonlinearities remains elusive. This is partly because of the complicated formulation of the seawater equation of state making it difficult to handle in theoretical studies. In this paper, a hierarchy of polynomial equations of state of increasing complexity, optimal in a least squares sense, is presented. These different simplified equations of state are then used to simulate the ocean circulation in a global 2°-resolution configuration. Comparisons between simulated ocean circulations confirm that nonlinear effects are of major importance, in particular influencing the circulation through determination of the static stability below the mixed layer, thus controlling rates of exchange between the atmosphere and the ocean interior. It is found that a simple polynomial equation of state, with a quadratic term in temperature (for cabbeling), a temperature–pressure product term (for thermobaricity), and a linear term in salinity, that is, only four tuning parameters, is enough to simulate a reasonably realistic global circulation. The best simulation is obtained when the simplified equation of state is forced to have an accurate thermal expansion coefficient near the freezing point, highlighting the importance of polar regions for the global stratification. It is argued that this simplified equation of state will be of great value for theoretical studies and pedagogical purposes.
Highlights
The equation of state (EOS) of seawater is a thermodynamic relationship whose definition derives from the first law of thermodynamics applied to a parcel of seawater, it is determined empirically in practice
Note that the Thermodynamic Equation of Seawater—2010 (TEOS-10) approximations proposed by Roquet et al (2015) are trivariate polynomials, but they differ from Eq (6) as they take a monotonic function of Absolute Salinity as an argument instead of the Absolute Salinity itself
Adding salinitydependent nonlinear terms only marginally improves the overall accuracy of the simplified EOS, albeit it has a major effect on the accuracy of the haline contribution on the horizontal density gradient (HDG)
Summary
The equation of state (EOS) of seawater is a thermodynamic relationship whose definition derives from the first law of thermodynamics applied to a parcel of seawater, it is determined empirically in practice. We consider the International Thermodynamic Equation of Seawater—2010 (TEOS-10) standard (IOC et al 2010), which defines seawater density r as a function of Absolute Salinity SA (see McDougall et al.2012), in situ temperature, and gauge pressure. The TEOS-10 variant, which is a function of Conservative Temperature Q (see McDougall 2003) instead of in situ temperature and geopotential depth instead of gauge pressure (defined as Z ’ p 3 1 m dbar21), will be preferred here (defined in Roquet et al 2015) because it is more suitable for ocean models, making the Boussinesq approximation (Young 2010):. The EOS is a nonlinear function of salinity, temperature, and pressure, which introduces considerable difficulty in the analysis of the ocean circulation, as it becomes impossible to define a truly conservative.
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