EXTENDED-RANGE WEATHER FORECASTING 
Instead of counting the frequency of the occurrence 
in each series consisting of s tests, 1t is possible to de- 
termine the frequency of the occurrence in the first 
n tests, in the second n tests, etc., of all series, thus 
obtaining the standard deviation cy, as well as Q. = 
ox/op and Dy = ox/owy, from the resulting distribu- 
tion. If the probability p of the occurrence of a phe- 
nomenon varies systematically from test to test such 
that, for instance, the probability p of the third and 
tenth tests in each series is larger than that of the other 
tests, which would, meteorologically, correspond to an 
existence of true “‘singularities”’ according to Schmauss 
[50], then Q:/Q2 = Di/D2 < 1. 
A study has been undertaken [20, pp. 924-928] in- 
volving nineteen series of meteorological observations 
of various elements, made at different locations (in 
different countries of the temperate zone) and during 
different seasons. Observations from January 1 to Feb- 
ruary 19 and from July 1 to August 19 for the fifty 
years from 1888 to 1937 (where s = n = 50) were 
used. The results showed that Di > 1 for all these 
series without exception (D is considerably greater 
than 1 in most cases) and Q;/Q»2 was much larger than 1, 
the maximum of this ratio bemg 3.46. Two theorems 
follow unequivocally: 
First EmprricAL THrorem: A Grosswetter exzsts, 
im which there are governing complexes comprising vari- 
able conditions; because of these complexes, the probabil- 
aties of the occurrence of certain indices that characterize 
the weather for longer periods vary from year to year. 
Sreconp HEpirican THnorem: These fluctuations of 
the weather-forming probabilities are, apart from the large 
annual trend, much more significant for the weather char- 
acter than are the calendar probabilities. 
The first of these two theorems, that concerning the 
existence of Grosswetter, forms the logical foundation 
for the exploration of the problem of extended-range 
weather forecasting. If there were no governing com- 
plexes comprising variable conditions, and the Gross- 
wetter evolved by chance and by a persistence tendency, 
then a reliable extended-range weather forecast would 
be impossible for all time, and a detailed study of this 
problem would be senseless. 
The Second Basic Problem of Macrometeorology. Sta- 
tistical evidence has been obtained that the fundamen- 
tal probabilities of the meteorological elements change 
from year to year, and that there must be governing 
complexes comprising variable conditions which pro- 
duce these variations of the fundamental probabilities. 
This evidence leads to the second problem: What are 
these governing complexes? Are they of terrestrial or 
extraterrestrial origin? 
Whereas we shall see the various terrestrial influ- 
ences on Grosswetter, we shall find that these influences 
are not sufficient to explain the large fluctuations of 
the probabilities of the occurrence of the indices that 
characterize the weather for longer periods of time. 
‘Therefore, we must look outside the earth for the gov- 
erning complexes comprising variable conditions. This 
is now only an assumption. Evidence of the correctness 
815 
of this assumption is found in the section on cosmic 
influences (p. 819). 
Terrestrial Influences on Grosswetter. Volcanic Erup- 
tions. The investigations by Abbot and Fowle [2], Hum- 
phreys [34], and Angstrom [4] have shown conclusively 
that after violent volcanic eruptions the atmospheric 
transparency for solar radiation is decreased over wide 
regions. After the Katmai eruption in 1912, the direct 
solar radiation reaching the earth’s surface was reduced 
by more than 10 per cent for several months. Further- 
more, there is no doubt that, as a consequence of the 
decrease of insolation, the mean temperature for large 
regions is decreased by 0.5-1.0 centigrade degrees; and 
by as much as 2-3 centigrade degrees after especially 
violent eruptions. 
According to Defant [31], the atmospheric circulation 
over the North Atlantic is disturbed through violent 
volcanic eruptions to an oscillation with a period of 
approximately 314 yr, with a decrease of the meridional 
pressure gradient after the eruption, and an increase in 
the following two years. The disturbance, however, 
is rapidly damped. 
These and similar examples cannot be considered the 
basis for extended-range forecasting. At best, they serve 
as a warning against the application of statistical re- 
sults obtained in years without eruptions to a year 
during which there will be an eruption. At any rate, 
major volcanic eruptions that imfluence the general 
weather are too rare to provide an explanation for the 
fluctuations of the fundamental probabilities of the 
weather elements, mentioned in the opening section. 
Ocean Currents and Ice Conditions. The number of 
investigations that have been made regarding the rela- 
tionship between Grosswetter and preceding anomalies! 
of ocean currents and ice conditions is so great that 
it is impossible to mention all of them here. Most of 
these investigations were made in Kurope; the reason 
for this is that the Gulf Stream, owing to the orienta- 
tion of the west coast of Europe (from southwest to 
northeast), is much more important for the climate of 
western Europe than is the Kuroshio for North Amer- 
ica. Furthermore, it is evident that the occurrence of 
ice in the North Atlantic plays an important role in 
the climate of Europe, since a large portion of the 
ocean ice of the north polar basin melts in the summer 
and is transported into the North Atlantic through the 
region between the northeastern tip of Greenland and 
Spitsbergen, as well as through the Davis Strait. By 
contrast, according to Schott [51], no ice passes from 
the polar basin through the Bering Strait into the 
Pacific Ocean. 
It was initially hoped that a study of the influences of 
temperature and velocity anomalies in the Gulf Stream 
on Kuropean weather, as well as of the occurrence of 
ice near Iceland, might yield clues for extended-range 
weather forecasting. However, these hopes were not 
fulfilled. This statement is corroborated by the follow- 
1. The term ‘‘anomaly,”’ as used in this article, refers to 
departure from a long-term average over time and has nothing 
to do with departures from means computed for latitude circles. 
