A pair of millennium (1000 yr) integrations with a simple global circulation model under the same conditions as in Part I of this paper are performed for further statistical analyses on internal intraseasonal and interannual variations of the troposphere-stratosphere coupled system. According to the previous parameter sweep experiment of Part I, in which topographic amplitude h(0) is changed, the two runs of h(0) = 500 and 1000 m correspond, respectively, to the real Southern and Northern Hemispheres in stratospheric interannual variation. The 1000-yr datasets reveal detailed features of frequency distributions of stratospheric interannual variation in the two runs. The frequency distributions of the monthly mean temperature in the polar upper stratosphere are positively skewed from autumn to spring for h(0) = 500 m. On the other hand, the distributions are positively skewed in autumn and bimodal in winter for h(0) =1000 m.
It is shown statistically that warm winters (springs) for h0 5 1000 m (500 m) in the stratosphere related to stratospheric sudden warming (SSW) events occur at random from year to year, as described by Poisson processes. The power spectrum of the stratospheric interannual variation is close to a red noise spectrum. The multiple empirical orthogonal function (EOF) analysis applied to the polar temperature in the upper stratosphere shows different sequences of low-frequency variability through a year between the two runs. The primary EOFs for h(0) =500 m represent variations of timing of the seasonal march from winter to spring. For h0 5 1000 m, on the other hand, variation of the minimum temperature in winter is extracted as the leading EOF, and variations appearing in winter or early spring at shorter timescales are also significant.
A sequence of low-frequency variability associated with SSW events in January, which are defined as when the January mean temperature at the polar upper stratosphere is among the 200 highest in the 1000 yr, is examined in the framework of frequency distributions for h0 5 1000 m. The association of variability with SSW events emerges as a bias of frequency distributions; the subset of distributions of the 200 SSW events is occasionally biased in the whole 1000-yr distributions. The bias of the preconditioning or the aftereffect in the troposphere related to SSW events is emphasized. For example, there are 130 yr in the whole 1000 yr for which planetary wave amplitude in the high-latitude troposphere is smaller than its climatology minus 1 standard deviation in February; 62 of the 130 appear one month after the 200 SSW events in January. On the basis of the present results, discussion will include (i) the difference of the randomness obtained in this study from the biennial oscillation of Scott and Haynes for stratospheric interannual variation, and (ii) implications for numerical experiments and statistical analyses on atmospheric variability and so forth.