562 
Studies of General Circulation Patterns,” it would ap- 
pear that the principal treatment of this vast subject 
belongs elsewhere in this Compendium.® 
Before we leave the subject, however, a few pertinent 
remarks are in order. First, it appears from actual stud- 
ies that the choice of the length of period does not essen- 
tially change the character of the problem of 
fundamental oscillations of circulations from high- to 
low-index states. In fact, there is evidence to suggest 
(Willett [57], Tannehill [49]) that the longer the period, 
the correspondingly greater the interperiod variability 
compared with what might be expected if the variations 
were random in character. Secondly, experience with 
monthly mean charts over the past eight years suggests 
an evolution which is not entirely chaotic and which 
indeed appears capable of kinematic and possibly physi- 
cal rationalization [31, 34]. The kmematic aspects were 
pointed out as early as 1926 by Brooks [8]. 
In short, the problem of the index cycle and its evo- 
lution would appear to be an integral part of any theory 
of secular, climatic, and geological (7.e., ice-age) varia- 
tions of world weather—a fact repeatedly stressed by 
Willett [58]. 
Quantitative Empirical Studies. The qualitative be- 
havior of large-scale circulation patterns described 
above is obviously of sufficient interest to justify more 
objective quantitative studies. Such studies have two 
basic purposes: to provide empirical formulas for pre- 
dicting the motion and development of large-scale cir- 
culation features, and to furnish the theoretical meteor- 
ologist with quantitative evidence for supporting or 
extending his theories. Since the forecasting aspects of 
these studies are treated elsewhere,® we shall treat here 
only the theoretical implications. 
One investigation of this sort, involving the motion 
of long waves at different latitudes, was made by the 
authors with the aid of two-and-a-half years of five-day 
mean 700-mb charts [36]. This study was an attempt to 
verify and make use of the simple theory of planetary 
wave motion based on the principle of conservation 
of absolute vorticity [44]. 
From this material it was found that while there is 
positive (but far from perfect) correlation between ob- 
served and theoretically computed displacements of 
selected trough systems, observed waves usually travel 
much faster than the speed given by the vorticity the- 
ory, thereby making necessary large empirical correc- 
tions. The reason for this discrepancy seems to lie in 
part in the fields of divergence accompanying observed 
waves, whereas the theoretical formula is based on the 
assumption of no divergence. This problem, as it affects 
the stationary wave length, was discussed in the section 
of this article dealing with physical climatology. 
Of considerable importance is the empirical finding 
that when wave length and zonal wind speed are con- 
sidered separately there appears no significant relation- 
ship between wind speed and displacement. This was 
6. See, for example, the discussion in ‘‘Solar Energy Vari- 
ations as a Possible Cause of Anomalous Weather Changes”’ 
by R. A. Craig and H. C. Willett, pp. 379-390. 
THE GENERAL CIRCULATION 
certainly not expected from theory. While no satis- 
factory explanation for this discrepancy has yet been 
found, it may be due in part to a possible interdepend- 
ence of wave length and zonal index [13] or, as Cressman 
[14] indicates, to the small variability of the zonal index 
which cannot produce changes in displacement larger 
than the errors of measurement. 
Because of this finding, empirical formulas were de- 
rived by considering that displacement is a simple linear 
function of wave length. This is equivalent to substi- 
tuting the average or normal value for zonal wind speed 
in the theoretical displacement formula and then as- 
suming that the range in wave length is small in com- 
parison to its average magnitude. 
The latest unpublished studies of this kind show that 
the stationary wave lengths (the wave lengths observed 
when trough displacement is zero) for North America 
are roughly the same as the normal wave lengths ob- 
tained from normal upper-level charts. This means that 
when the wave lengths found on individual five-day 
mean charts exceed the normal value, the waves will 
tend to retrograde (move westward) while they will 
be progressive (move eastward) if the observed wave 
lengths are smaller. 
It was previously suggested that seasonal variations 
of the normal wave lengths could be accounted for by 
seasonal changes in the zonal index. But there are also 
pronounced geographical variations. Thus the station- 
ary wave lengths for the Atlantic are found to be shorter 
than those for North America, suggesting that for the 
same wave length, displacements in an easterly direc- 
tion are slower over the Atlantic. This better agreement 
with the theoretical wave formula indicates that waves 
over flat ocean areas more closely approximate free 
perturbations. 
The empirical studies also show a systematic decrease 
of wave speed with time. This may be a purely statis- 
tical result, but a possible physical explanation may lie 
in the Rossby wave formula in which a decrease in wave 
speed may result from a systematically increasing wave 
length. It has been suggested [86] that such an increase 
in wave length as troughs move eastward may be due 
to the tendency for certain troughs and ridges to be 
fixed because of topographical or solenoidal effects. 
For example, the length between a trough moving 
eastward over the Mississippi Valley and a ridge fixed 
to the Rocky Mountain area must continually increase, 
resulting in a deceleration. 
Perhaps a more universal explanation for systematic 
changes in wave length has been offered by Cressman 
[15], who has adapted the theory of group velocity to 
changes in wave length of individual systems. Synoptic 
evidence, on both daily and five-day mean charts, ap- 
pears to support his conclusion that if the wave length — 
increases in an upstream direction the easternmost wave 
will slow down, while the opposite distribution of wave 
length will lead to acceleration. 
In investigating other parameters besides wave length 
which might be related to displacement, it was found 
that the shape of the wave was often quite important 
[13]. Thus, if the wave amplitude to the west of a given 
