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4. Analysis I: Downward propagation in the stratosphere
The downward propagation of upcm variations in the stratosphere is analyzed by considering the temporal dependence of the different terms of the polar cap mean quasigeostrophic zonal momentum equation (Peixoto and Oort, 1992), neglecting friction:
The upcm tendency directly calculated from upcm [hereafter ('upcm/'t)d] closely resembles the residual upcm tendency [hereafter ('upcm/'t)r], which is the sum of the computed Fm and Fc, giving confidence in the accuracy of the computed Fm and Fc (see Figure 6).
Figure 4: The low-pass filtered time series of Fm at different levels.
Figure 5: Correlation coefficient between the low-pass filtered Fm time series at 10 hPa and the low-pass filtered time series at all levels, with different time lags.
Figure 4 and 5 show that ultra-low frequency variations of Fm propagate downward from 10 hPa to 200 hPa in about 20 days, like the upcm variations in Figures 1 and 2, and consistent with the hypothesized mechanism.