852 
stations and using the entire group as predictors for 
an individual station. Correlations as high as 0.97 for 
24 hr and remaining between 0.80 and 0.90 for 48- and 
72-hr intervals show that a certain degree of statistical 
regularity is demonstrably present. Despite these high 
correlations, the forecasts leave much to be desired, 
for the lmear operator seems incapable of detecting 
sudden changes in weather regime. Unfortunately, non- 
linear techniques, in the elementary sense, have not 
yet succeeded so that it is impossible to improve the 
forecasts without some form of subjective analysis, such 
as a synoptic classification of the regime. Unquestion- 
ably there exist additional variables which, if clearly 
understood, would change the linear dynamics slightly 
from year to year and permit better predictions. 
Equivalent studies have been made on pressure, 
including daily mean pressures, nonoverlapping five- 
day means, and running averages taken over five, 
fifteen, and thirty-one days. No long-term predictable 
components in any one of these time series taken at 
many localities over the Northern Hemisphere ever 
produced spectra which would indicate any long-term 
periods. Once again, networks involving a group of 
stations surrounding the one to be predicted give the 
best daily predictions. Correlations in the neighborhood 
of 0.70, which remain stable from year to year, indicate 
the order of the linear component, while four or five 
stations surrounding a given station at a distance of 
about 500 mi seem to produce all of the dynamics of a 
linear type which is in the network. Thus, increasing 
the network of stations either in number or in radius 
seems in no way to increase this predictability. Studies 
of this nature seem to afford ample proof that the 
synoptic situation expressed in terms of present tem- 
perature, pressure, humidity, etc., does not uniquely 
determine the future distribution and that the behavior 
of the pressure distribution outside this ring of 500 mi 
does not have much influence upon the future of the 
pressure at the center of the ring. Furthermore, if a 
forecast is made for 24 or 48 hr in advance by predict- 
ing a group of stations individually (considering each 
one as made up of an individual network), the correla- 
tion of the actual predicted map with the observed 
conditions is not much better than the correlation that 
one would obtain between predicted and observed pres- 
sures at an individual station. This indicates that the 
errors of forecast are correlated over the entire country 
and that we are not making a series of individual ran- 
dom predictions. The fact that the errors prove to be 
highly correlated means, of course, that an outside 
influence has moved into the picture and that all of 
the mechanisms fail to predict simultaneously. This 
brings out rather clearly the concept of changes in 
regimes in the entire weather pattern, followed again 
by a stabilization of whatever linear component exists. 
Once the regime has established itself, pressure changes 
of considerable magnitude can be forecast quite accu- 
rately, but the physical bases for the changes must 
already exist within the network. Six principal con- 
clusions can be arrived at through a close analysis of 
WEATHER FORECASTING 
pressure forecasting utilizing straightforward statistical 
techniques: (1) The performance of the linear forecast 
from year to year is stable in that the mean errors of 
prediction show no significant difference between years 
and the root-mean-square errors are homogeneous, (2) 
a small network is adequate, (8) errors cannot be 
ascribed to improper weighting of the predictors, (4) 
it is extremely doubtful that lear prediction can be 
improved upon by using fixed functions of higher de- 
gree, and therefore additional variables not considered 
at the present time are important, (5) the errors in the 
forecast are not caused primarily by a failure to indicate 
pressure changes as such, but rather by an inability to 
predict extreme values whether they represent changes 
from the initial situation or not, and (6) statistical 
forecasts fail under the same circumstances that syn- 
optic forecasts fail and apparently for the same reasons. 
In order to give a little more background to the 
direction that future research should follow, let us 
consider for a moment the combined motion of the 
four major centers of action for the North American 
continent, namely, the semipermanent highs and lows— 
the Atlantic high, the Pacific high, the Icelandic low, 
and the Aleutian low. It is in the motion of these centers 
of action that one can first observe the fact that 
considerable dynamics exists in the atmosphere and 
that it is not a random phenomenon nor anywhere 
near random. If we consider any one of these cells as 
the one to be predicted and utilize its past and the 
present and past of the other three cells as predictors, 
prediction for a considerable time in advance is pos- 
sible for any particular year. One can think of this 
prediction process, of course, merely as a reproduction 
of the data after the fact, but nevertheless the repro- 
duction of the data by means of the operator is so 
startling that it deserves notice. Both the spectra 
obtained from the autocorrelation functions and those 
obtained from the cross-correlation functions are ex- 
tremely active, showing that the density of frequency 
is located in rather narrow bands. The graphs of these 
spectra are, however, quite different from year to year, 
indicating that we are dealing with a phenomenon 
which has certain specific characteristics at any one 
time but that these characteristics vary from year to 
year because of some outside influence. The sharp 
spectral characteristics which occur in these control 
cells unquestionably lead oftentimes to the wrong con- 
clusions, namely, that periodicities exist in the atmos- 
phere in the sense of being true line spectra. For 
periods of time, therefore, one can observe certain 
fluctuations of these meteorological elements and 
erroneously conclude that there is a law, perfectly 
determined, which is influencing their behavior. This 
is the clearest indication of why it is possible to tie 
up cycle theory with weather phenomena of various 
types, particularly for specific short periods of time. 
Although a large amount of work has been done by 
many investigators in computing correlations of 
pressure at one point in the atmosphere with that at 
another point, correlations of precipitation and tem- 
