THE FORECAST PROBLEM 
really significant correlations are found. It has been 
used widely by Baur [1] in Europe, by Wadsworth [16] 
to check contemporary and lag relationships between 
the positions and intensities of a number of the semi- 
permanent ‘‘centers of action” of the monthly mean 
Northern Hemisphere pressure maps, and most notably 
by Walker’ in his classical study of weather relationships 
over the globe and in particular of the forecasting of the 
seasonal monsoon rainfall in India. 
It is doubtful whether the highest degree of skill 
attained at the present time by forecasts based on the 
use of statistical extrapolation by correlation (as illus- 
trated perhaps by some of Walker’s seasonal forecasting 
by multiple regression equations derived from the 
Southern Oscillation) exceeds 60 per cent. This figure 
probably represents the best that is attamable by 
purely statistical extrapolation techniques in the ab- 
sence of any physical understanding of the underlying 
cause and effect relationships. 
Experience shows that without some real physical 
basis, the prognostic regression equations derived by 
random correlation almost invariably deteriorate sig- 
nificantly in their performance when applied to the 
forecasting of data other than that from which they 
were derived. This deterioration is doubtless caused in 
part by the fact that the few significant correlation 
coefficients which are used in the regression equations 
are usually selected from a relatively large number of 
predominantly insignificant coefficients computed on a 
random ‘trial and error” basis. Hence the selected 
coefficients do not possess the normal probability of 
significance. The deterioration is also partly caused by 
the fact, which is observed both statistically and synop- 
tically, that not only the general circulation pattern 
itself, but also its pattern of variation, is subject to 
considerable change over a long period of years. 
Tt is undoubtedly true that the area in which this 
technique of forecasting by statistical extrapolation 
may be applied can be extended by further statistical 
research, but it is doubtful if the present top level of 
performance will be exceeded appreciably. In other 
words, there is at present no reason to hope for any 
basic improvement of long-range weather forecasts by 
the routine statistical extrapolation technique under 
discussion. 
A second technique of long-range forecasting by sta- 
tistical extrapolation is based on the statistical analysis 
of long-term homogeneous records of pressure, and 
less frequently of temperature or precipitation, at sel- 
ected stations, in the effort to establish some type of 
periodicity or repetition in the variation that can be 
used for extrapolation. A large amount of harmonic 
analysis or other techniques of smoothing of such 
records has been done in order to resolve the variation 
into simple component periods. A great variety of such 
periods, ranging in length from a few days to at least 
forty-six years, have been rather dubiously established. 
In particular the longer periods have been tentatively 
established as fractional or integral multiples of the 
1. See Mon. Wea. Rev. Wash., Supp. No. 39, pp. 1-26, 1940. 
735 
sunspot period, notably by Abbot and Clayton. Another 
purported feature of the long-period pressure records at 
certain stations, first pointed out by Weickmann, is the 
occurrence at irregular intervals of so-called symmetry 
points, on either side of which the time graph of pressure 
varies In reverse sequence. 
There is considerable doubt as to the physical reality 
or statistical significance of most of these periodic or 
symmetry characteristics which are supposedly estab- 
lished in time series of meteorological data. It has been 
shown that in some cases smoothing techniques impose 
on the data periodicities which do not exist in reality. 
Forecasts based on the periodicity and symmetry tech- 
niques of statistical extrapolation have proved sig- 
nificantly even less successful than those based on the 
correlation techniques discussed above. There is no 
evidence to indicate that a skill verification of even as 
much as 55 per cent has been attained by the periodicity 
techniques. Baur [2] has made an extensive statistical 
study of the periodicity and symmetry techniques of 
extrapolating pressure and other weather data for ex- 
tended forecasting purposes. He came to the conclusion 
that these techniques do not merit the expenditure of 
additional effort. He produces statistical evidence that 
the great variety of periodicity and symmetry patterns 
which are derived statistically from time series of 
weather data probably are merely an incidental re- 
sult of serial correlation in the data, and as such are 
presumably of no greater prognostic significance than 
the persistence itself. Certainly it can be concluded that 
no important improvement of weather forecasting is to 
be expected from further development of this technique 
of statistical extrapolation. 
b. Synoptic techniques of extrapolation—based essen- 
tially on the extrapolation of synoptic weather patterns. 
The great bullx of weather-forecasting practice, both 
past and present, is of the daily, and more recently also 
of the short-range type. This common forecasting prac- 
tice is usually based on a combination of techniques, 
rarely on one exclusively. During the earlier years the 
forecasting procedures were almost exclusively those of 
synoptic extrapolation. Since World War I the physical 
techniques discussed below (p. 739) have come into ex- 
tensive use, and in recent years the techniques of 
mathematical extrapolation, discussed under c below, 
have also been utilized to a very limited extent to supple- 
ment other methods. But by and large it remains true 
today that common forecast practice is based primarily 
on methods of synoptic extrapolation, secondarily on 
physical considerations, and only slightly on purely 
statistical or mathematical extrapolation. It is this 
combination of synoptic-extrapolation techniques sup- 
plemented by certain physical considerations which 
currently effect a top skill verification of 90-95 per cent 
on short-range forecasting, for which extrapolation tech- 
niques are ideally suited, and of 70-90 per cent on the 
daily type of forecasting up to forty-eight hours in 
advance. 
Except for the occasional use of statistical probabil- 
ities to compensate a forecaster’s lack of practical 
experience, as mentioned previously, the entire short- 
