A statistical generalization of the transformed Eulerian-mean circulation for an arbitrary vertical coordinate system

A new method is derived for approximating the mean meridional circulation in an arbitrary vertical coordinate system using only the time-mean and zonally averaged meridional velocity, meridional eddy transport, and eddy variance. The method is called the statistical transformed Eulerian mean (STEM) and can be viewed as a generalization of the transformed Eulerian mean (TEM) formulation. It is shown that theTEM circulation can be obtained from the STEM circulation in the limit of small eddy variance. The main advantage of the STEM formulation is that it can be applied to nonmonotonic coordinate systems such as the equivalent potential temperature. In contrast, the TEMformulation can only be applied to stratified variables. Reanalysis data are used to compare the STEM circulation to an explicit calculation of the mean meridional circulation on dry and moist isentropic surfaces based on daily data. It is shown that the STEM formulation accurately captures all the key features of the circulation. The error in the streamfunction is less than 10%. The STEM formulation is subsequently used to analyze the circulation induced by latent heat transport and to understand the processes responsible for setting the effective stratification in the troposphere. The eddy sensible heat transport dominates in the midlatitudes and in the winter hemisphere, while the eddy latent heat transport dominates in the subtropical regions and in the summer hemisphere. For the dry isentropic circulation, the approximate effective stratification is dominated by the vertical stratification, whereas for the moist isentropic circulation it is dominated by the eddy variance contribution. The importance of the eddy variance in setting the stratification is in agreement with previous work.