EXTENDED-RANGE WEATHER FORECASTING 
days. However, even the more than one thousand 
analyses are not sufficient to permit the definite state- 
ment that the frequency of a single wave exceeds the 
maximum limit of chance [20, pp. 933-934]. 
Periods of Several Years. Of the many oscillations 
with periods of several years that have been claimed 
in the past, only a small number have proved to be 
“probably real.’’ They are a 2.2-yr period, a 3- to 3%-yr 
period, and an approximately 7-yr period. All these 
periods, however, are nonpersistent, in other words, 
they cease intermittently. With respect to temperature 
and pressure, the 3- to 314-yr period is most marked 
in the region of the Malayan Archipelago and northern 
Australia. This period is probably a ‘free oscillation” 
(in a broader sense) between a tropical low-pressure 
area (India-northern Australia) and a subtropical high 
(South Pacific anticyclone near Easter Island), caused 
by the lagging of the temperature anomalies with re- 
spect to the pressure anomalies as a consequence of the 
inertia of the participating ocean currents. According 
to Berlage [25], this oscillation is propagated from the 
Malayan region over both hemispheres to the sub- 
polar pressure troughs. The cause for the excitation of 
the Indian-Pacific oscillation has not yet been deter- 
mined. 
The oscillations with periods of 2.2 yr and 7 yr are 
probably free oscillations of the atmospheric circulation 
over the North Atlantic. These oscillations are similar 
to the 3-yr period found in the Malayan region. Whereas 
the 2.2-yr fluctuation is restricted to the North Atlantic 
and Europe, the 7-yr period has a world-wide distribu- 
tion [20, pp. 937-940]. 
The 3-yr fluctuation in the Malayan region occurs 
so clearly at times that it can be obtained directly 
from the curve of the semiannual pressure averages. 
However, on the whole, these fluctuations of several 
years’ period have such a small amplitude that they 
can be extracted from the observations only by means 
of mathematical processes (e.g., periodogram analysis). 
From periodogram analyses, a widespread 5- to 514- 
yr oscillation has been found [17, pp. 93-96]. In reality, 
however, this oscillation has a variable period which 
only on the average amounts to 544 yr and is identical 
with the double oscillation of the large-scale weather 
during a sunspot cycle (see section on cosmic influ- 
ences). 
Periodic Fluctuations of Climate. Rhythmic fluctua- 
tions of the meteorological elements having a period 
of more than 30 yr are called “climatic periods.”’ For 
many decades, the existence of a 35-yr period was pre- 
sented in all meteorological textbooks, and was known 
as the “Briickner cycle.”’ This period is a classic ex- 
ample of the deceptions to which one may succumb by 
determining periods with primitive research methods 
and without adequate statistical tests for significance. 
It is to Wagner’s credit that he proved [54] that the 
30-yr period does not exist as a natural phenomenon, 
but was introduced by the methods of computation 
and smoothing used by Briickner. 
For the demonstration of still longer periods, the 
data available today are insufficient. 
817 
Correlations between Consecutive Weather Anoma- 
lies. Persistence and Repetition Tendencies. The per- 
sistence tendency of the weather is caused by the fact 
that, for physical reasons, certam weather anomalies 
(e.g., very high pressure or cold air) extending over 
wide regions, cannot disappear from one day to the next. 
However, this persistence tendency in its proper sense 
extends over a period of only a few days. When a cer- 
tain anomaly in ten-day or monthly averages is found 
to be generally followed by one of the same sign more 
frequently than by one of opposite sign, it exhibits, 
fundamentally, not a persistence tendency but rather 
a repetition tendency, that is, the tendency of a situa- 
tion which has existed for several days to be reinstated 
after a brief mterruption. Important as the repetition 
tendency may be for the explanation of some phe- 
nomena, its importance must not be overrated. In 
the temperate zone, the repetition tendency is subject 
to strong local and seasonal differences. The dependence 
of the repetition tendency on the seasons is shown in 
Fig. 1. 
Statistical determination of the local and seasonal 
differences of persistence and repetition tendencies and 
their physical explanation are indirectly of importance 
for extended-range weather forecasting. In the past, 
the persistence tendency of certain weather elements, 
such as pressure or temperature, was usually investi- 
gated by counting the frequency of sequences of the 
same sign or by computing correlation coefficients. 
Instead, the persistence and repetition tendencies of 
Grosswetterlagen should be subject to imvestigations im 
which statistics and synoptics supplement each other. 
During certain parts of the year and in some regions, 
the probability of weather changes is, under certain pre- 
mises, greater than is the persistence tendency during 
other seasons. As can be seen from Fig. 1a, such a ten- 
dency toward a major change in the synoptic situation 
exists in Europe in the last third of June. Connected 
with this tendency is the fact that for fourteen years 
(of the 102-yr period 1848-1949), in which the tem- 
perature of the first half of June in Berlin was more than 
2C above normal, the following midsummer (July and 
August) was for the most part abnormally cool in cen- 
tral Europe, and that in thirteen (93 per cent) of these 
years the precipitation was more than 15 mm above 
normal (Table I). Since the fundamental probability 
of a positive precipitation departure of more than 15 
mm in midsummer is 38 per cent, the maximal chance 
limit of the relative frequency of such midsummers for 
a random choice of 14 cases is 81 per cent if, as is cus- 
tomary, the limit of the range of chance is so chosen 
that the probability of exceeding this limit is e = 0.0027. 
The observed relative frequency of 93 per cent of wet 
midsummers is, therefore, significantly above chance. 
On the other hand, when the temperature during 
the first half of July is 2C above normal in central 
Europe, there follows in about three-fourths of the cases 
a warm and dry late summer (August and September). 
This varying repetition tendency can probably be ex- 
plained physically as follows: In June, when the sub- 
tropical high-pressure belt over the North Atlantic 
