In this Brewer seminar, I will discuss why the Transformed Eulerian Mean is unsuited to approximate the moist meridional overturning circulation. I will show possible fixes from different studies but will ultimately introduce a new solution: the Statistical Transformed Eulerian Mean. I will show that this approach makes it possible to obtain an accurate approximation to the moist overturning circulation by emphasizing the role of large moisture variances. I will then illustrate how the relative simplicity of the Statistical TEM formulation can be used to split the moist circulation into its sensible heat and latent heat components. Finally, I will explain what this approximation tells us about the effective moist stratification in the midlatitudes and give heuristic arguments to how it could be affected by warming surface temperatures.