EXTENDED-RANGE WEATHER FORECASTING 
radiation. The irregularity of the rhythm probably has 
its cause in the irregular distribution of land and water 
and in the variation of the period of the possible free 
oscillations. This latter variability results from the con- 
tinuous change of temperature in the course of the 
year. The occurrence or nonoccurrence of the atmos- 
pheric phenomena pertaining to the weather key-days 
of the year is therefore the expression of the circula- 
tion character of the season or year in question. It is 
therefore probable that the weather on weather key- 
days is connected with the later weather development. 
In fact, in Europe series of better-than-chance con- 
nections have been found between characteristic 
weather anomalies occurring around weather key-days 
and the subsequent or later meteorological situation ~ 
{15; 17, p. 133]. For example, September 29 is a weather 
key-day for Europe. On this day, as well as on the 
preceding and the following day, certain European 
anticyclonic situations within the period from 1881 to 
1943 reach a better-than-chance frequency [16]. From 
September 23 to October 1, central Hurope has in 65 
per cent of all years a so-called Altwezbersommer with 
little cloudiness, infrequent precipitation, and relatively 
high midday temperatures. Weather of this character 
occurs in high-pressure regions, stretching from west to 
east, with a zonal circulation over northern Europe, as 
well as in the region of high pressure with the center 
over eastern Europe accompanied by a meridional cir- 
culation. In the latter case, the pressure at Moscow is 
considerably above normal. As is shown in Table V, 
Taste V. Pressure ANOMALIES DURING THE HUROPEAN 
‘CAL TWEIBERSOMMER’’? AND TEMPERATURE CHARACTER 
OF THE SUBSEQUENT WINTER 
(Example of an unequivocal, significant relation) 
Pressure departure (in mb) Temperature 
departure of 
Year Sept. 21 to 30 Sept. 1 to 30 fhe jsubsequent 
= tral Europe 
Moscow Berlin Moscow (cent. deg.) 
1884 +5.3 +3.7 +3.5 +0.9 
1901 +8.3 +2.4 +4.7 +1.4 
1902 $2.3 —+9°3 +0.9 +0.7 
1904 +16.7 —-l.5 +8.8 +1.1 
1909 +5.6 +2.0 5.5 +2.2 
1912 +7.2 +9.7 +2.8 +1.5 
1913 +4.8 +6.0 ae llo3 +0.8 
1920 +12.3 +5.1 +3.2 +2.4 
1926 +4.3 Sree! +0.1 Srl 6) 
1929 +6.3 +95.9 Srl.3 +2.0 
1937 oat +2.3 +0.9 +1.2 
1938 +12.4 +3.9 +5.9 Srl 
1947 $5.7 +0.4 Stalls +2.2 
in all the years of the period from 1881 to 1948 during 
which the mean pressure between September 21 and 
September 30 at Moscow was 2.0 mb above normal 
and, furthermore, the mean pressure departure was 
positive for Berlin from September 21 to 30 and for 
Moscow from September 1 to 30, the average tem- 
perature of the subsequent winter in central Europe 
was, without exception, greater than 0.6C above nor- 
mal. Since the basic probability of such winters is 41.8 
per cent, the upper limit of the scope of chance, within 
which the relative frequency can fluctuate by chance 
827 
alone (if one defines the chance limit as on p. 817) lies 
at 86.5 per cent for n = 13. We can therefore conclude 
from the 13 cases (100 per cent) of mild winters shown 
in Table V that a physical relationship exists between 
the given pressure anomalies in September and the 
temperature character of the following winter in cen- 
tral Europe. This relationship is founded on the laws 
followed by the change between meridional and zonal 
circulation in the North Atlantic and European circu- 
lation regions. 
Ninta EmprricAn THroremM: Unequivocal relation- 
ships which lie outside the scope of chance exist between 
the weather anomalies about the time of the weather key- 
days and the subsequent Grosswetter. 
The Change between Meridional and Zonal Circula- 
tion. The persistence of each of the seven types of 
special circulation, described on page 826 is limited. 
For example, if with low pressure over the North 
Atlantic and high pressure over Hurope and North 
America, subtropical meridional flow (Type IV) prevails 
for a relatively long period over western Hurope and 
polar meridional flow (Type V) over eastern North 
America, then over western EKurope and the eastern 
Atlantic, warm subtropical air is contmuously trans- 
ported toward the polar regions, while over eastern 
North America and the western Atlantic, cold polar air 
is transported toward the subtropical regions. Thereby 
the temperature contrast between subtropical and polar 
regions is diminished and with it the fundamental 
cause of the meridional circulation, so that eventually 
a zonal circulation replaces the meridional circulation. 
On the other hand, in the absence of a meridional ex- 
change the temperature difference between subtropical 
and polar regions is re-established by the radiation dif- 
ference between these two regions. With purely zonal 
circulation the temperature contrast between low and 
high latitudes eventually becomes so great that it 
forces the establishment of a meridional circulation. 
This re-establishment of a meridional circulation is ex- 
plained as follows: The increase in the meridional tem- 
perature gradient causes a strong concentration of iso- 
therms connected with a strengthening of the jet stream 
aloft. The large-scale lateral mixing processes (and 
frictional forces) on both sides of the vigorous westerly 
flow cause the formation of cyclonic vortices on the 
equatorial side and of anticyclonic vortices on the 
polar side of the band of west winds [44, 53]. Thus 
pressure troughs and ridges are formed, and a meridi- 
onal circulation is again started. 
In this manner, a continuous change between in- 
creased and diminished, and between predominantly 
zonal and predominantly meridional circulation, takes 
place. However, this change in circulation types does 
not occur in the same manner over the entire tem- 
perate zone of the Northern Hemisphere and, in gen- 
eral, not simultaneously either. This follows from the 
fact that, aside from the very rare case of a zonal cir- 
culation over all meridians, one and the same circula- 
tion type never exists in all special circulation regions 
(see seventh empirical theorem). The significant corre- 
lation coefficients in Table II confirm the fact that 
