OBSERVATIONAL STUDIES OF GENERAL CIRCULATION PATTERNS 
trough is greater than that to the east, the trough will 
tend to move faster than expected from the empirical 
wave formula. The opposite result is often obtained 
if the amplitude to the east is greater. 
Studies of trough motion similar to those above have 
been made with the aid of constant absolute vorticity 
trajectories [42]. The theory, which gives an estimate 
of the paths of individual air parcels, is based on the 
conservation of absolute vorticity just as in the wave 
theory, but avoids many of the latter’s assumptions. 
For example, local wind speeds are used in place of a 
fictitious uniform zonal wind, and the assumption of 
small perturbations is avoided, so that estimates of wave 
amplitude may be obtained. However, a new assump- 
tion that the speeds of individual air parcels remain 
constant is introduced. 
Using this theory, Bortman [6] obtained empirical 
corrections (for each season and several geographical 
areas) to the “first characteristic points.”’ These are the 
first trough or ridge points following the inflection point 
of the vorticity path at which the computation is made. 
The results were quite similar to those using the wave 
formula in that large eastward empirical corrections 
were found for the theoretical trough points over east- 
ern North America, indicating that the theoretical 
trough speeds are too low. Also, there is a positive corre- 
lation between theoretical and observed wave speeds. 
Corrections are generally less over ocean than over land 
areas. Of special interest are the corrections in the 
western Rocky Mountain area, where both trough and 
ridge points give evidence of strong divergence as a 
result of lifting. The study thereby emphasizes the 
importance of geographical and climatological features 
on the behavior of long waves. 
Another unpublished empirical study of wave motion 
on five-day mean 700-mb charts [7] over North America 
attempts to make use both of the theory of planetary 
waves and that of constant vorticity trajectories. Thus, 
followmg a suggestion by Cressman [14], the wave 
length and wind speed of observed waves were measured 
along the streamlines (or isobars) rather than along 
fixed latitude circles. Amplitudes were measured in the 
same manner. These three parameters were then re- 
lated by graphical correlation methods to the observed 
trough displacements at 45°N. Such a procedure is an 
empirical attempt to take cognizance of the jet stream, 
which tends to follow the streamline flow. The results 
show not only the expected relationship between wave 
length and displacement, but indicate that amplitude 
and to a certain extent wind speed are also significant 
parameters. The most interesting result was the signifi- 
cant positive correlations found among all three in- 
dependent parameters. The relationships among wave 
length, amplitude, and wind speed for small and inter- 
mediate values of wave length were found to be quali- 
tatively the same as those to be expected from the 
theory of constant vorticity trajectories, while for larger 
wave lengths the agreement was poor (Fig. 12). The 
explanation for this discrepancy has not yet been found 
but when found it should aid in seeking an understand- 
ing of the observed behavior of planetary waves. Studies 
563 
of a similar nature should be made for other levels and 
areas besides North America, to which the above study 
applies. 
S 
lu 
S5 
=a OBSERVED WINTER 
2 50 
= 
+4500 10 20 30 40 50 60 70 80 90 100 110 120130 
(e) 1/2 WAVE LENGTH (° LONGITUDE) 
ANI 
LATE 
a 
iC 
10 20 30 40 50 60 70 80 90 100 II0 120 130 
1/2 WAVE LENGTH (° LONGITUDE) 
Om On 
(b) 
Fie. 12—(a) Observed relationship between wave length, 
amplitude, and wind speed for waves whose minimum latitude 
is 45°N, from five-day mean 700-mb charts for the years 
1941-47. (b) Theoretical relationship between wave length, 
amplitude, and wind speed for waves whose minimum latitude 
is 45°N, using the Bellamy vorticity slide rule. (From Bortman 
I7].) 
One of the basic difficulties of all studies treated so 
far is that they require the identification from map to 
map of various characteristic points or lines (highs, 
lows, troughs, or ridges). Because of the complexity of 
atmospheric behavior this is not always easy. This 
suggests that a more profitable empirical (or theoreti- 
cal) approach is to study local changes in various 
meteorological quantities, since this does not involve 
the troublesome problem of continuity. To a certain 
extent the vorticity paths are designed to do this, and 
such use has been made of them by Dorsey and Brier 
{19] and by Fultz [23]. 
Dorsey and Brier, using selected trajectories made on 
daily synoptic 10,000-ft charts, compared the theoreti- 
cally computed wind speeds and directions with those 
observed at the same points at intervals of 24 hr up to 
seven days in advance. Among their interesting results 
is the finding that trajectories are likely to be more 
successful when made in a well-defined fast flow. It was 
also found that if the trajectory verified well for the 
