Orthobaric Density: A Thermodynamic Variable for Ocean Circulation Studies

A new density variable, empirically corrected for pressure, is constructed. This is done by first fitting compressibility (or sound speed) computed from global ocean datasets to an empirical function of pressure and in situ density (or specific volume). Then, by replacing true compressibility by this best-fit virtual compressibility in the thermodynamic density equation, an exact integral of a Pfaffian differential form can be found; this is called orthobaric density. The compressibility anomaly (true minus best-fit) is not neglected, but used to develop a gain factor on the irreversible processes that contribute to the density equation and drive diapycnal motion. The complement of the gain factor, 1, multiplies the reversible motion of orthobaric density surfaces to make a second contribution to diapycnal motion. The gain factor is a diagnostic of the materiality of orthobaric density: gain factors of 1 would indicate that orthobaric density surfaces are as material as potential density surfaces. Calculations of the gain factor for extensive north-south ocean sections in the Atlantic and Pacific show that it generally lies between 0.8 and 1.2.