In concert with previous results, there is a surprisingly rich three-dimensional structure to the variance of the zonal wind field that is not (cannot be) captured by the covariance of lower tropospheric pressure, of flow variability in the zonal mean or, for that matter, of any variable on any planar surface. Correspondingly, many of the canonical variability patterns derived from lower tropospheric pressure or from the zonal mean exhibit considerable inconsistencies with respect to dynamically intuitive reorganizations of the subtropical and polar front jets and / or with respect to other forcing mechanisms. Different canonical variability patterns exhibit these inconsistencies to a greater or lesser degree. The three-dimensional covariance of the zonal wind field, by contrast, naturally exhibits structures that are both dynamically intuitive and have a surprisingly large amount of information in the vertical. The three-dimensional structures are related to canonical variability patterns, but they are not one and the same. These conclusions are robust in a variety of seasons and also in intraseasonal and interannual analyses. Similar results and conclusions are also derived using detrended data, other reanalyses, and state-of-the-art coupled climate model output. The results suggest not only a more focused perspective on atmospheric low frequency variability, but also the potential for clearer interpretations of the associated dynamics because of the intrinsic link between the three-dimensional zonal wind structures, their time evolution, and the requisite conservation of momentum (i.e. to the primitive equations and candidate forcing mechanisms).