where d is the potential temperature, defined later in Section 5.3.1. This quantity may be calculated from temperature and pressure maps fitted to measured data and since qE is conserved (under frictionless, non-diabatic heating cases) maps of this quantity may also be used as a tracer for atmospheric motion. However, recent observations of Jupiter's atmosphere by Cassini have shown that Ertel's potential vorticity is not actually conserved in Jovian atmospheres (Gierasch et al., 2004) due to variations in the water vapor abundance and the ortho-hydrogen:para-hydrogen ratio, which mean that the potential temperature is no longer a function of just pressure and temperature. Gierasch et al. (2004) note that it is likely that a modified form of potential vorticity is conserved in these cases.

Another more approximate expression for potential vorticity is the quasi-geostrophic expression described, for example, by Andrews (2000).

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