Method 1, EOF
We employ a method proposed by KM to distinguish the 2-D and 3-D regimes by using an Empirical Orthogonal Function (EOF), which is usually called as principal component analysis in the field of multivariate analysis. In the EOF expression used in the present study, the vertical velocities are given as the superposition of orthogonal modes in the vertical direction as,
,
(1)
where and
are the horizontal coordinates,
is the vertical coordinate,
the time,
the vertical velocity, and
the mode number,
the vertical structure of the nth mode amplitudes,
the spatial distribution of the mode. According
to KM, an experiment for which the first
EOF mode explains more than (less than) 60%
of the total energy of the vertical velocities
is classified into the 2-D (3-D) regime.
EOF calculations are repeatedly conducted
for each experiment, and the average of explained
variances from 80 to 144 hours is adopted
as the variance for the experiment. If we
change the threshold from KM's 60% to another
possible value, i.e., 50%, the conclusions
of the present papers are essentially unchanged.