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Sun, S., R. Bleck, C. Rooth, J. Dukowicz, E. Chassignet, and P. Killworth, 1999: Inclusion of thermobaricity in isopycnis-coordinate ocean models. J. Phys. Oceanog., 29, 2719-2729, doi:10.1175/1520-0485(1999)029<2719:IOTIIC>2.0.CO;2.
Buoyancy anomalies caused by thermobaricity, that is, the modulation of seawater compressibility by potential temperature anomalies, underlie a long-standing argument against the use of potential-density-framed numerical models for realistic circulation studies. The authors show that this problem can be overcome by relaxing the strict correspondence between buoyancy and potential density in isopycnic-coordinate models. A parametric representation of the difference between the two variables is introduced in the form of a "virtual potential density," which can be viewed as the potential density that would be computed from the in situ conditions using the compressibility coefficient for seawater of a fixed (but representative) salinity and potential temperature. This variable is used as a basis for effective dynamic height computations in the dynamic equations, while the traditionally defined potential density may be retained as model coordinate. The conservation properties of the latter assure that adiabatic transport processes in a compressibility-compliant model can still be represented as exactly two-dimensional. Consistent with its dynamic significance, the distribution of virtual potential density is found to determine both the local static stability and, to a lesser degree, the orientation of neutrally buoyant mixing surfaces. The paper closes with a brief discussion of the pros and cons of replacing potential density by virtual potential density as vertical model coordinate.
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