830 
order to include these valuable investigations in the 
total structure of macrometeorology. 
The most important aspect of these investigations 
is the world-wide pomt of view of the general circula- 
tion, on which they are based. This is Grosswetter 
synoptics in the true sense of the term. This method of 
consideration, comprising the entire Northern Hemi- 
sphere, is also applied in Rossby’s formula [45]: 
BL’ 
air fe, Aa? 
where c is the eastward velocity of the perturbation 
(trough or ridge), L is the wave length, U is the zonal 
velocity of the westerlies, and 6 is the rate of change of 
the Coriolis parameter with latitude. This formula (as 
derived from simplifying assumptions) is of such funda- 
mental importance for the mean circulation methods 
that it is necessary to conduct rigorous statistical in- 
vestigations to determine the extent to which it is con- 
firmed by observation, and the conditions under which 
systematic deviations occur which can be eliminated 
by computation. 
Clapp [41] made such an investigation using five- 
day mean 10,000-ft charts covering the period from 
January 1941 to April 1943. He computed the correla- 
tion coefficients between the observed displacements 
(for half a week and for a full week) of troughs and 
ridges at 45°N and those computed from Rossby’s 
formula. Clapp used as a representative value of U, the 
zonal westerlies, the mean west to east geostrophic wind 
between 40°N and 50°N over the entire range of longi- 
tudes from about 130°W to 30°W, known as the 10,000- 
ft mdex J;. He furthermore defined the wave length DL 
as twice the difference in longitude between a given 
trough and the ridge to the west of it. Hliminating cases 
of new trough development, Clapp obtained the fol- 
lowing correlation coefficients r in N cases: 
Full week "Half week 
r N r N 
Winter 0.66 37 0.67 36 
Spring 0.44 35 0.51 35 
Summer 0.35 29 0.42 29 
Fall 0.42 35 0.63 35 
For the displacements during a full week the correla- 
tion is better than chance (with a significance level of 
0.27 per cent) only in winter; however, for displace- 
ments during half a week, three of the four correlation 
coefficients are significant. We can conclude from this, 
that the Rossby formula, in spite of the simplifications 
made in its derivation, furnished an approximation of 
actual conditions. However, the correlations are too 
small to permit predictions of the displacement of 
troughs and ridges on the basis of this formula. For 
this reason, Namias [40] employed additional criteria 
and methods for the forecasting of circulation patterns. 
According to Rossby’s formula, a westward displace- 
ment (retrogression) of a trough or a ridge occurs when 
the wave length, that is, the distance between troughs, 
exceeds a certain value depending on the season and 
the geographical latitude; in other words, when an in- 
ereased zonal circulation exists. This result is in appar- 
WEATHER FORECASTING 
ent contradiction with the concept prevailing among 
central European investigators, according to which a 
westward displacement of steering centers, particu- 
larly high-pressure centers, at the 5-km level is to be 
expected for physical reasons, notably when a pro- 
nounced meridional circulation prevails on both sides 
of the steering center [47]. Nevertheless, both concepts 
are mutually consistent. It is entirely possible that a 
strong meridional circulation on both sides of a ridge 
at high altitudes is associated with a large distance 
between pressure ridges (Fig. 12a), whereas for a shorter 
Fig. 12—Schematic representation of the 500-mb contour 
lines with (a) alternating strong zonal and strong meridional 
circulation on both sides of a ridge, and large distance be- 
tween ridges, and (6) prevailing meridional circulation, but 
not so concentrated locally and not so strong as in (a) and 
small distance between ridges. 
distance the strong meridional circulation will, per- 
haps, occur less frequently or not at all (Fig. 126). 
Further investigations are needed to establish the rela- 
tive frequency with which a strong meridional cir- 
culation on both sides of a steermg center in the upper 
troposphere is associated with an intensified zonal cir- 
culation at a relatively large distance from this steering 
center. 
Observation of the large-scale meridional and zonal 
temperature centrasts is of great importance for the 
theory as well as for the practice of extended-range 
forecasting. Namias [39] has called attention to the 
very high correlation between the meridional tempera- 
ture difference (85°N-55°N) and the west-east com- 
ponent of the wind speed at the 3-km level. Scherhag 
[48] has shown by a selected example that, even for 
monthly means, a strong negative pressure anomaly 
near Iceland corresponds to a strong meridional tem- 
perature gradient over the Great Lakes region of North 
America. Both these results are in agreement with the 
high correlation obtained by Baur [6] of the monthly 
mean temperature difference between New England 
and eastern Greenland with the simultaneous monthly 
mean pressure difference between the Azores and Ice- 
land, for nearly all months of the year. For January, 
the correlation coefficient for the mean monthly tem- 
perature difference between New Haven and 44 (Ja- 
cobshavn + Upernivik) and the simultaneous mean 
monthly pressure difference between Ponta Delgada 
and Stykkisholm amounts to +0.61. However, this 
