Eliassen-Palm Cross Sections for the Troposphere

Abstract

“Eliassen-Palm (EP) cross sections” are meridional cross sections showing the Eliassen-Palm flux F by arrows and its divergence by contours. For large-scale, quasi-geostrophic motion F is defined to have ϕ and ρ components r0 cosϕ[−u′v′, fv′θ′/θp] where ϕ is latitude, ρ pressure, θ potential temperature, r0 the radius of the earth, bars and primes denote zonal means and deviations and (u,v) is horizontal velocity. The theoretical reasons for using EP cross sections diagnostically are reviewed. The divergence of F reflects the magnitude of transient and irreversible eddy processes at each height and latitude, and is proportional to the northward flux of quasi-geostrophic (not Ertel's) potential vorticity. It is a direct measure of the total forcing of the zonal-mean state by the eddies. The direction of F indicates the relative importance of the principal eddy fluxes of heat and momentum. If the eddy dynamics is Rossby wavelike, then F is also a measure of net wave propagation from one height and latitude to another. Observational and theoretical EP cross sections are presented for the layer 1000–50 mb, and discussed in terms of the abovementioned properties. The observational cross sections for transient eddies are more reliably determined than for stationary eddies, and resemble to a significant degree the cross sections given by nonlinear baroclinic instability simulations. They do not resemble those given by linear instability theory for a realistic mean state (verifying the inappropriateness of linear theory as a basis for eddy parameterizations). They provide a direct view of the latitudinal planetary-wave propagation mechanism whereby midlatitudinal instabilities influence the high-tropospheric subtropics. A similar dynamical linkage appears to be depicted by the EP cross sections for stationary eddies in winter. The cross sections for stationary eddies in summer are strikingly different, but not very well determined by the data. Nevertheless, there are reasons why some of the differences might be real, with possible implications for theories of stationary planetary waves. The “residual meridional circulations” associated with the observed EP cross sections are presented and discussed.