APPLICATION OF STATISTICAL METHODS TO WEATHER FORECASTING 
By GEORGE P. WADSWORTH 
Massachusetts Institute of Technology 
It must seem very odd to the layman and to the 
scientist who is not connected with the field of meteor- 
ology that so little practical progress has been made 
during the last decade in the all-important problem of 
weather forecasting. This defect is particularly con- 
spicuous when such phenomenal advances have been 
made in the field of nuclear physics and thermody- 
namics. However, it is necessary to spend only a 
moderate amount of time examining observational data 
of the meteorological elements to understand that the 
problem is much more difficult in many of its aspects 
than those considered in most allied fields. If we regard 
the atmosphere as a dynamic model, it soon becomes 
apparent that the whole process behaves as a compli- 
cated mechanism in which past and present values do 
not determine the future as in most linear processes, 
but they themselves have an effect upon the system 
which in turn produces nonlinearity of a very peculiar 
type. It is with this phenomenon that the meteorolo- 
gists must contend. 
There seem to be only two ways which are available 
to solve the problem of the motions of the weather 
systems and therefore the problem of weather fore- 
casting: one 1s the dynamical approach and the other 
is the statistical approach. Oftentimes one thinks of 
these two methods as conflicting programs but actually 
they are attempting to get at one and the same thing. 
In the dynamical approach the laws connecting various 
meteorological phenomena are investigated. These laws 
are considered to be precise in action even though the 
data are subject to fluctuations which are random and 
are thus necessarily incomplete. On the other hand, in 
the statistical approach the quantities are taken as 
they are found and the distributions examined both 
singly and in such combinations as one chooses for the 
purposes of investigation. In an ideal survey all possible 
statistical parameters would be considered and not 
merely a partial selection, but such an undertaking is 
impractical because of the sheer magnitude of the task. 
If, however, there exist among the statistical param- 
eters a few which are connected by sharp dynamic 
laws, then some of the parameters would be determined 
by a knowledge of the remainder, and the dynamics 
would be obvious as a Statistical fact. The failure to 
date of statistical methods to contribute markedly to 
the progress of meteorology may have been due to one 
or more of three facts: 
1. The parameters in the analyses to date are not 
the important ones. 
2. The parameters considered are insufficient in 
number to give us a true picture of the operation. 
3. These parameters have been observed so inac- 
curately that they are not in fact the significant para- 
meters of the dynamics. 
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It might however be said that it is impossible for 
dynamics to exist and be really significant and not be 
brought out by a proper statistical examination of the 
relevant quantities, and in fact, techniques available in 
the statistical category have the added advantage that 
it is unnecessary to make many simplifying assump- 
tions in order to yield relevant information concerning 
the meteorological phenomenon. 
At this point it cannot be too strongly emphasized 
that the use of statistical techniques for the solution of 
the behavior of the weather systems is equivalent to 
the setting up of equations of motion and obtaining 
the solution. The use of generalized harmonic analysis 
(discussed in a later paragraph) as a method of attack 
on the problem has the advantage that it automatically 
takes care of data which have superimposed a random 
component upon the dynamic motion. In other words, 
it is a technique which is especially designed to handle 
situations where, because of ignorance, there has to be 
omitted a certain number of factors which can be con- 
sidered in combination as a random phenomenon super- 
imposed on the dynamic movement. There is no doubt 
that the ideal way to solve any dynamical problem is 
to set up a physical model in terms of mathematical 
symbols and, after having solved the resulting mathe- 
matical model, to use statistical methods to solve for 
the basic parameters. However, if the mathematical 
model does not contain all of the variables which are 
actually important, the attempt to solve for the param- 
eters by statistical methods will give an unreliable 
result, and it is for this reason that a technique which 
takes account of this unknown group of variables is 
very appropriate for this problem. An example of such 
a situation would be one in which the phenomenon in 
which we were interested had a displacement y given 
by y = A sin kt. Superimposed upon this oscillation 
might be a group of frequencies which had periods 
entirely different from those of the phenomenon. This 
group of frequencies would have been reflected in our 
observations since they each enter the picture for short 
periods of time and more or less at random. It would 
be extremely difficult by observing a small section of 
the data to fit the parameters A and k, the constants 
in our equation. However, a statistical analysis would 
be much more successful in separating the basic signal 
from the random noise. 
It is perhaps during the last ten years that an added 
impetus has been given to this method of approach 
because of the growing conviction on the part of many 
investigators that the problems of the general circula- 
tion and of specific forecasting were not to be solved 
in the near future by the usual dynamic methods. 
This is reminiscent of other physical sciences wherein, 
at the beginning, a conceptual foundation was borrowed 
