The Slowly Varying Background State of the Atmosphere

A notion of an atmospheric background state is involved frequently in theories of atmospheric behaviour, or in the diagnosis of models and data. For example, linear wave and stability theories describe the evolution of disturbances to a background state. The behaviour of weather phenomena, such as extratropical and tropical cyclones, is often described with reference to their "background environment". The role of background state is central to wave-mean flow interaction theory and notions of wave activity density and flux. Such concepts are often used to describe the behaviour of stormtracks and their interaction with the "climate state". However, the deductions regarding disturbances (waves or eddies) are dependent on the partition of the full flow between a background and disturbance, especially when the disturbances have large amplitude.

Here, the behaviour and utility of a particular definition of background state is explored. It is defined by the modified Lagrangian mean (MLM) obtained by re-arranging the observed 3-D atmospheric state to be zonally symmetric while conserving both mass and circulation enclosed by potential vorticity (PV) contours in isentropic layers. The simultaneous constraint of mass and circulation requires consistency between the density and vorticity fields. The solution procedure starts with a first guess of the background PV distribution and position of the lower boundary obtained assuming uniform density in each isentropic layer. The zonally symmetric background PV is inverted to obtain Montgomery potential, density and zonal wind. These are integrated to provide estimates of mass and circulation integrals from the 2-D state that differ from the results obtained from the analysed 3-D state. The differences are used to shift the positions of background PV contours, the result is inverted and an iteration proceeds in this manner until both mass and circulation are consistent. The position of the ground in isentropic coordinates is obtained as part of the solution procedure.

This state would be steady if the full flow were adiabatic and frictionless. Since non-conservative processes are weak on average, the MLM state is found to be inherently slowly varying. The background state is also a solution to the primitive equations. This is a necessary property to apply large-amplitude wave activity conservation laws that are valid for the primitive equations on the sphere. The pseudomomentum flux in the large-amplitude theory has a similar form to the Eliassen-Palm flux and the vertical component is the same (form-drag in isentropic coordinates). However, crucially E-P flux is calculated relative to the Eulerian zonal mean state which often fluctuates rapidly, and consequently the E-P flux vectors change direction and magnitude rapidly due to the changing "background". In contrast, here the background state is slowly varying and so the wave activity fluxes are also less variable.

Both the background state and the wave activity on it are calculated from ERA-Interim data. Illustrations are given of jet migration at tropopause level associated with vortex erosion by baroclinic waves and wave activity fluxes from the troposphere to stratosphere in stratospheric sudden warmings.