850 
from physics and mathematics, but it was only after 
extended programs of experimental work had been 
carried out that the subjects progressed independently 
and produced the astounding developments which have 
occurred in the last century. A continual succession of 
experimentation, followed by new theory to explain 
the results obtained, and then a new period of experi- 
mentation, has characterized the development of most 
of the physical sciences. Unfortunately, meteorology is 
not in the same position because it is impossible to 
conduct experiments with controlled variables since no 
formal method for the inclusion of all the pertinent 
variables into a single mathematical system has yet 
been found as a substitute for experimental control. 
Thus the most powerful techniques which have been 
used in the development of other physical sciences are 
not available to the meteorologist at the present time 
and he must search elsewhere for his method of attack 
upon this formidable problem. 
According to a prevalent misconception, statistical 
methods mean the neglect of root causes and the sub- 
stitution of shadow for substance. To be sure, statistical 
methods often lead to useful rules of thumb even when 
qualitative understanding is absent, but these rules 
should never be regarded as anything but makeshift. 
Doubtless the facility with which empirical recipes can 
be invented, together with a natural human tendency 
to let well enough alone, has engendered a willingness 
on the part of some statistical practitioners to content 
themselves with ersatz. But we do not hold medicine 
in contempt because of quackery, and it would be 
fallacious to condemn statistics on account of super- 
ficiality. It is perfectly true that at the present time 
too many meteorologists and statisticians attempt to 
indulge in an orgy of correlation analysis. Because the 
processes which they are examining lack the property 
of being stationary, results are obtained which are 
inconsistent from one period of time to the next. This 
difficulty becomes less and less important if a certain 
amount of physical reasoning is the basis for the cor- 
relation; and as time goes on and more is understood 
about the phenomenon, this operational approach of 
examining the physics of the situation will correct much 
of the condemnation which is now directed at statisti- 
cal studies. Thus the future of meteorology depends 
decisively upon an enlightened and energetic use of 
this important tool. 
The meteorologist is primarily interested in the be- 
havior of his phenomenon as a function of time, and 
all his observations are either taken continuously in 
terms of this variable or are taken at discrete points 
along the time axis. Each one of the series, therefore, 
which are considered in the problem of prediction of 
single meteorological elements or combinations of them 
can be looked at from the time-series point of view. 
Since the beginning of World War II, considerable 
impetus has been given to the development of general- 
ized harmonic analysis because of its importance in 
the analysis of time series which occur not only in the 
weather problem but also in all fields where prediction 
is important. Unfortunately, most of the work has been 
WEATHER FORECASTING 
done in the field of what might be termed stationary 
time series. In this type of series the actual dynamics 
which motivate the series itself is assumed constant 
from one period of time to the next. 
Considering the characteristics of these time series 
by themselves, we note that the sequence of observa- 
tions has certain inherent dynamic properties as well 
aS a superimposed random component. This random 
component may well be due to other variables not 
considered. The actual statistical problem is to sepa- 
rate the dynamics from the random element so that 
the dynamics can be studied and classified. This situa- 
tion is entirely analogous to a similar one encountered 
when information is transmitted by mechanical or elec- 
trical methods. In this case, the signal frequently 
becomes distorted and when this distortion phenom- 
enon is of a purely random statistical nature it is called 
‘moise.”” Hence, as also in weather phenomena, the 
thing that we observe, or the message, contains the 
original signal plus a random noise, and the problem 
is to isolate the signal from the message. 
In the case of pressure, if we consider the sequence 
of values as a continuous function, the behavior is 
analogous to the response of a sluggish oscillator to a 
series of impulses, where the dynamics are represented 
by the parameters of the oscillator. Because the oscil- 
lator is sluggish, the effect of the impulse at any one 
time is not immediately worn off but is carried over to 
affect the pressure at a future time. Even the random 
components, introduced probably by the variables not 
considered, affect the future value of the pressure vari- 
able since they are equivalent to an additional impulse 
on the oscillator. 
The problem of weather forecasting can therefore be 
thought of in the following terms: In Fig. 1 the solid 
Fie. 1.—Schematic time series. 
line represents the past performance of some meteor- 
ological phenomenon a. For example, it might be past 
values of the pressure at a single station or even a 
characteristic of an entire synoptic map. By analyzing 
this sequence from some period of time in the distant 
past up to the present time to, the predictable part of 
this sequence is to be determined. This predictable part 
represents the true dynamical component, and it is 
this component which permits one to extrapolate the 
solid line into the future to give a prediction (dotted 
line). Naturally, the further one extends this prediction 
