In the past decade, we have studied the dynamical coupling between the stratosphere and the troposphere with mechanistic circulation models (MCMs); the term of MCM was introduced by Byron, I think, as a medium class of numerical models between complex and realistic GCMs and simple and idealistic low-order models. We have investigated the internal interannual variability of the troposphere-stratosphere coupled system (Taguchi et al., 2001; Taguchi and Yoden, 2002a,b), the effect of the equatorial quasi-biennial oscillation (QBO) on the global circulation (Naito et al., 2003; Naito and Yoden, 2006), and the detectability of a linear trend in a finite-length dataset with natural internal variability (Nishizawa and Yoden, 2005; Nishizawa et al., 2007).
Recently, we have used an MCM to study a possible downward influence of temperature variations around the stratopause that mimic the 11-year modulations of solar effect. A relationship of the occurrence frequency of stratospheric sudden warmings and modulation of the polar vortex is obtained for the combination of the equatorial QBO and the stratopause temperature variations, consistent with the observed relationship (Labitzke, 1987; Labitzke and van Loon, 1988). However, the statistical significance is much lower than that for the difference between westerly and easterly phase of the QBO for the same data length. A possible explanation of the relationship can be given by the dynamics of planetary waves.