Abstract
The generalized Lagrangian-mean (GLM) description extended by Noda (1988) is applied to mean meridional motions in the troposphere. A large number of air particles with different initial positions and initial times are traced for five days using a 30 day data set of velocities obtained from a perpetual January simulation of the MRI's tropospheric general circulation model. Meridional motions of the GLM are obtained by averaging the traced points over the initial times and over the Lagrangian longitudes with the fixed traced time. This GLM initially agrees with a conventional 25-day time averaged, zonal Eulerian mean. The initial hypersurfaces used for the space-time Lagrangian description are chosen as those determined by t0=constant, where t0 is the initial time, so that the averaging over the Lagrangian longitudes is equivalent to a zonal GLM but the averaging over the initial times is a time-ensemble GLM, in which the initial time is an ensemble parameter.
The well-known feature of the initial Eulerian mean meridional circulation with a three cell structure (in one hemisphere) disappears within a day in middle and high latitudes in the model troposphere, while Hadley circulations continue to dominate in the tropics. In each hemisphere, the GLM meridional circulation outside the tropics is characterized by the motions converging, along mean isentropes, to the periphery of the subtropical jet and to the storm track zone in the lower troposphere. The doubling time of the GLM density is about two days. The mean meridional velocity field of the GLM circulation is very different from both the Eulerian mean meridional circulation and the residual mean meridional circulation. The GLM circulation in the troposphere is not induced by a single eddy but by numerous eddies.
The eddy diffusion coefficients which are useful to the (zonally averaged) two-dimensional Eulerian models are approximated by the maximum values of the correlation coefficients between the velocity at traced points and the displacement from the GLM points. The diffusion along isentropes is dominant outside the tropics, resulting in the antisymmetric diffusion coefficient being proportional to the heat flux along the isentropes. This in turn results in the effective transport circulation being rather well approximated by the residual mean circulation, even in the troposphere. Particles need to be traced for more than five days in the tropics in order to evaluate the eddy diffusion coefficients by the present method.
