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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 the TEM 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 TEM formulation 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. Th...

A Statistical Generalization of the Transformed Eulerian-Mean Circulation for an Arbitrary Vertical Coordinate System