Reappraising the appropriate calculation of a common meteorological quantity: Potential Temperature

The potential temperature is a widely used quantity in atmospheric science since it is conserved for dry air's adiabatic changes of state. Its definition involves the specific heat capacity of dry air, which is traditionally assumed as constant. However, the literature provides different values of this allegedly constant parameter, which are reviewed and discussed in this study. Furthermore, we derive the potential temperature for a temperature-dependent parameterisation of the specific heat capacity of dry air, thus providing a new reference potential temperature with a more rigorous basis. This new reference shows different values and vertical gradients, in particular in the stratosphere and above, compared to the potential temperature that assumes constant heat capacity. The application of the new reference potential temperature is discussed for computations of the Brunt-Väisälä frequency, Ertel's potential vorticity, diabatic heating rates, and for the vertical sorting of observational data.