EXTENDED-RANGE WEATHER FORECASTING 
correlation of the monthly means can be interpreted 
contrariwise: When the pressure over Iceland is very 
low, western Greenland lies within a cold northern 
flow, whereas to the west of the above-normal Azores 
High, warm air flows from the south to the north. 
In turn, with a strong air-mass exchange between 
high and low latitudes the temperature difference will 
diminish. The general circulation shows, after a certain 
duration of intensified air movement, “fatigue phenom- 
ena” which finally lead to a change im the circulation 
pattern (see Table II and [7]). 
In order to develop circulation methods so that they 
can be used as a basis for reliable extended forecasts; 
a transition is necessary from the statistics of averages, 
now predominantly in use, to statistics of selected cases 
which take into account especially the physical pro- 
cesses, and the special characteristics of the particular 
case. Examples of “selective statistics” are contained in 
Tables I and V, which, to some extent, form parts of a 
multiple-correlation table. Table VI also forms part of 
“selective statistics.” 
Long-Range Forecasting. Forecasts for more than 
five days are not possible on a synoptic basis. The 
multitude of all possible developments no longer per- 
mits consideration of the development in all physical 
details. Here, statistics must be employed if we are to 
make statements about the future. However, two pre- 
requisites must be fulfilled: (1) the choice of statistical 
methods must be guided by a physical formulation of 
the problems and by physical considerations, and (2) 
long-range forecasts should be given, at least publicly, 
only if better-than-chance statistical relationships are 
obtained that ensure the success of the forecast with 
a probability of over 92 per cent. It must be borne in 
mind that the damage which might result from an 
incorrect forecast is greater the longer the time interval 
for which the forecast is made. Therefore all demands 
for regular issues of monthly and seasonal forecasts 
must be declined in the present state of our knowledge. 
In order to be on the safe side, it is advisable to issue 
long-range weather forecasts only if at least two argu- 
ments are available that fulfill the above-mentioned 
prerequisites and lead to the same expected weather 
character without contradiction by any other statistical 
argument. 
Htrapolation of Periods. The extrapolation of periods 
is more helpful for long-range forecasts than for me- 
dium-range forecasts. Tests of over a thousand har- 
monic analyses at the Forschungsinstitut fiir langfristige 
Witterungsvorhersage over a number of years have 
shown, however, that the percentage of correct fore- 
casts is too small for these extrapolations to be used as a 
basis for long-range forecasts. Even the use of rigorous 
mathematical criteria permits only the decision as to 
whether the period has been persistent to date, but it 
does not yield any clues to its future behavior. Rhythm 
analyses cannot be used as the basis for any meteoro- 
logical forecasts as long as we have no physical, statis- 
tically sound criteria that would indicate the con- 
tinuation of the period with an expectancy of over 92 
per cent during the forecast period. 
831 
Symmetry Points. There are even stronger objections 
against the use of so-called symmetry points for the 
pressure curve. In the first place, it was shown that 
even in a model sample based on chance and persistence 
tendency only, symmetry points occur with the same 
degree of approximation as they do for the actual pres- 
sure curve [20, pp. 924-926 and 934-936]. In the second 
place, the existence of a symmetry point can be de- 
tected with some degree of certainty only if about 20 
days have elapsed. In the third place, even from a very 
good symmetry during 20-25 days, no sufficiently re- 
liable conclusion can be drawn as to whether and how 
long the reflected curve of the pressure or any other 
weather element will persist. As an example, the sym- 
metry poimt for the pressure curve of Potsdam on 
December 26, 1932, may be cited. The correlation co- 
efficient of corresponding days from the first to the 25th 
day before and after the symmetry pomt was +0.75; 
from the 26th to the 50th day it was —0.46. 
Regression Equations. It is necessary that regression 
equations which are to be used for long-range forecasts 
yield a multiple correlation coefficient greater than 
0.80, since only then will the standard error of estimate 
of the correlation be less than ®{9 of the standard 
deviation. Furthermore, the basic single correlations 
must be stable, that is, they must be approximately 
the same for subdivisions of the total period. 
Multiple Correlation Tables. Since most of the Gross- 
wetter correlations are not linear, it is very rare that 
noultiple-correlation coefficients are obtained for suffi- 
ciently long periods which are larger than 0.80. Selective 
statistics again appear much more promising in this 
case, since fundamentally they yield parts of multiple 
correlation tables. As long as their computation is 
guided by a physical approach to the problem, unequiv- 
ocal, better-than-chance results can be used as an 
empirical basis for the further development of the 
theory as well as a basis for long-range forecasts. 
REFERENCES 
1. Assot, C. G., Ann. astrophys. Obs. Smithson. Instn., Vol. 
6. Washington, D. C., 1942. (See Table 27) (Also, 
personal communications through December 1945.) 
2. —— and Fow tz, F. E., “Volcanoes and Climate.”? Smith- 
son. misc. Coll., Vol. 60, No. 29, 24 pp. (1913). 
3. Aurer, D., ‘Application of Schuster’s Periodogram to 
Long Rainfall Records, Beginning 1748.’ Mon. Wea. 
Rev. Wash., 52:479-483 (1924). 
4. Anesrrom, A., “Teleconnections of Climatic Changes in 
Present Time.’? Geogr. Ann., Stockh., 17:242-258 (1985). 
5. Baur, F., ‘‘The 11-Year Period of Temperature in the 
Northern Hemisphere in Relation to the 11-Year Sun- 
Spot Cycle.’ Mon. Wea. Rev. Wash., 53:204-207 (1925). 
6. —— “‘Statistische Untersuchungen tiber Auswirkungen 
und Bedingungen der grossen Stérungen der allgemeinen 
atmosphirischen Zirkulation, III.” Ann. Hydrogr., 
Hamb., 54:227-236 (1926). 
7. —— “Der gegenwirtige Stand der meteorologischen Kor- 
relationsforschung.’”? Meteor. Z., 47:42-52 (1930). 
8. —— “Die Formen der atmosphirischen Zirkulation in der 
gemiissigten Zone.’’ Beitr. Geophys., 34:264-309 (1931). 
. — “Schwankungen der Solarkonstante.”’ Z. Astrophys., 
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