Advantages of a conservative coordinate system

Observations of middle atmospheric circulation and planetary wave amplitudes in equivalent latitude coordinates provide insights about non-conservative forcing and the resulting dynamical consequences. Novel diagnostics of circulation and finite wave amplitudes calculated in conserved isentropic-potential vorticity coordinates are applied to thirty years of reanalysis data, bringing to light dramatic trends which are not apparent in the zonal mean. Conventional, linear theory relies upon the zonal mean as a reference state as well as a diagnostic of atmospheric dynamics. The zonal mean is an intrinsically Eulerian average which varies due to wave transience as well as non-adiabatic forcing and mixes the material properties of distinct air-masses. The circulation diagnostic introduced here is a Lagrangian mean, which is conserved for adiabatic, inviscid flow. This use of a conserved diagnostic restricts attention irreversible processes and improves the signal-to-noise ratio, elucidating long-term trends, which could not be detected by conventional means.