East Asia and Western Pacific METEOROLOGY AND CLIMATE

509
To investigate the statistical property of the quasi-stationary
solutions, we take a monthly running mean with a 20-day overlap and
regard it as a sample of monthly-mean model climate. Traveling waves
are almost averaged out in the monthly means, with locked waves
remaining. To examine the distribution of their probability density
functions, we evenly divide a range of each monthly-mean variable
into twenty intervals and count the frequency of appearance for the
variable in each interval. The number of frequency divided by two
hundred is the probability of this variable in each interval. Fig. 6
shows the contours of the probability distributions for monthly-mean
AT, 4>£i' anc * ^W2" There are two well-separated peaks in the probability
distribution, i.e., it is distinct bimodal distribution. The
well-defined bimodal distribution demonstrates that the system has
two preferred states for winter which resulted from two different
attractor basins pulling the solutions toward them.
In an attempt to understand how the system is attracted by
Branch B and Branch C throughout the__seasons, we traced the annual
cycles of the two sub-ensemble mean AT (starting from summer in the
AT) vs. AT diagram of statistical Equilibria (Fig. 7). During
summer the two mean AT are very close and lower than AT for Branch B.
During early fall, the system has two possible ways to go: one is to
follow a branch possessing a larger AT, and the other is to follow a
branch possessing a smaller AT. In the later part of the year (i.e.,
winter), the smaller AT solution stays near Branch B, while the
larger AT solution can no longer be maintained in late fall and is
attracted into Branch C. We interpret the split routes for the
system solutions are due to transition behavior of Branch B solutions
around AT = 40°K (not shown) . One type of the present solutions
follows the upper AT branch of the transition solution, and the other
type of solutions follows the lower AT branch of the transition
solution. As we have found in the fixed AT timeintegrations that
the lower AT branch of the transition solutions remain in Branch B
as AT increases, the smaller AT solutions are stable and__stay near
Branch B. On the other hand, as AT increases the upper AT Branch of
the transition solutions cannot be maintained and thus the solutions
attracted into Branch C in the following season. The self-transition
from Branch B to Branch C are found in fixed AT integrations which
indicates that Branch C is more stable than Branch B, Therefore, the
system is attracted into Branch C rather than Branch_J3 when it is
unstable. Whether the system will follow the upper AT branch or
the lower SF branch in the transition range determines the system
behavior in the following fall, winter and early spring seasons. We
consider that the choice by the system to follow one of those two
branches during the transition range is stochastic. However, the
predictability of different winter types is at least one season
earlier as the zone mean flow of the two type solutions is distinctly
separated in fall (see Fig. 6).