Effective Isentropic Diffusivity of Tropospheric Transport

Tropospheric transport can be described qualitatively by the slow mean diabatic circulation and rapid isentropic mixing, yet a quantitative understanding of the transport circulation is complicated, as nearly half of the isentropic surfaces in the troposphere frequently intersect the ground. A theoretical framework for the effective isentropic diffusivity of tropospheric transport is presented. Compared with previous isentropic analysis of effective diffusivity, a new diagnostic is introduced to quantify the eddy diffusivity of the near-surface isentropic flow. This diagnostic also links the effective eddy diffusivity directly to a diffusive closure of eddy fluxes through a finite-amplitude wave activity equation. The theory is examined in a dry primitive equation model on the sphere. It is found that the upper troposphere is characterized by a diffusivity minimum at the jet's center with enhanced mixing at the jet's flanks and that the lower troposphere is dominated by stronger mixing throughout the baroclinic zone. This structure of isentropic diffusivity is generally consistent with the diffusivity obtained from the geostrophic component of the flow. Furthermore, the isentropic diffusivity agrees broadly with the tracer equivalent length obtained from either a spectral diffusion scheme or a semi-Lagrangian advection scheme, indicating that the effective diffusivity of tropospheric transport is largely dictated by large-scale stirring rather than details of the small-scale diffusion acting on the tracers.