STATISTICAL METHODS AND WEATHER FORECASTING 
perature with the forward movement of ice in the North 
Pole region, etc., the illustrations set forth m the 
preceding paragraphs give a picture of about the order 
of magnitude of the results which one can expect to 
find in setting up lmear hypotheses involving pressure, 
temperature, humidity, ete., either singly or m com- 
bination and at one station or in the network. With 
this background, I should like to discuss possible future 
courses which statistical analysis can follow toward 
the solution of this complicated situation involving 
dynamics and thermodynamics. 
Perhaps one of the greatest contributions which 
statistical methods can, at the moment, make to the 
field of meteorology is in the classification of climato- 
logical information. It is well known, for example, that 
the forecasters in the short-range verification program 
during World War II greatly improved their accuracy 
by being given the probability of the occurrence of the 
events for which they were forecasting. This climato- 
logical information, however, is only part of that which 
is available to the forecasters to improve their forecast- 
ing techniques. There exist certain statistical laws 
which hold individually for all climatological elements 
and for all possible locations. These relationships have 
very profound effects upon the distribution of these 
elements for a given week or a given month and are 
entirely different from the over-all distributions that 
are at present given as the climatological expression of 
the variability. It is the peculiar behavior of these 
daily, weekly, monthly, and seasonal distributions at 
various localities which are the real characteristics of 
the climatology and could be extremely useful in 
understanding better the weather processes themselves 
and also m improving the forecasts at a particular 
location. Thus a re-evaluation of the whole method of 
presenting the climatology of various localities and the 
individual behavior of climate during reasonably short 
periods of time at a particular locality might do much 
to imcrease our knowledge concerning the general 
behavior of the circulation. In fact, it might be stated 
that if the basic characteristics of the climatology were 
plotted on a Northern Hemisphere map, obvious 
simultaneous relationships could be studied and the 
whole forecasting problem could be reduced to a group 
of much more specific questions. 
A great deal of thought has been given by many 
meteorologists to the use of analogues as a method of 
forecasting. The basic argument against the use of 
analogues is, of course, that the weather never follows 
exactly the same pattern. However, in the light of 
past experience in forecasting by statistical methods, 
it is obvious that in order to progress much further it 
is going to be necessary to find a way of classifying the 
dynamics. Dynamic classification might be achieved 
through the use of analogues, and in that event it should 
be possible to utilize the correct statistical operator 
for the prediction mechanism. Many attempts have 
been made by various people to express the dynamics 
of a present system in terms of some linear combination 
853 
of the dynamics of past experience or similar situations. 
This seems to be extremely logical. 
One can set up a practical analogy. An engineer 
wishes to determine the dynamics of a particular 
machine which, for some reason, he is unable to analyze 
completely. It might, however, be possible for him to 
analyze three or four machines which are similar to the 
original machine but differ in some minor details. It is 
then quite possible that by observing the dynamics of 
the similar machines he may infer how the machine in 
question will behave and operate. Actually if the dy- 
namics are changing, in the sense of the series’ being 
nonstationary, about the only way that one can judge 
what these dynamics might be in the future is through 
the use of such a technique. Our failure up to this 
time to extrapolate the dynamics properly from the 
known situations is probably due to the fact that the 
parameters used to express the synoptic picture are 
not dynamic in themselves. It is therefore necessary 
for us to solve more completely the following problems: 
1. Parameters must be found that will adequately 
classify the static picture of the weather situation over 
a large area. They should represent the general features, 
particularly the flow patterns, over a region even 
though they might not bring out every individual 
detail. The analogue technique calls for a classification 
in terms of a general flow pattern, and such a classifi- 
cation would tend to eliminate the influence of 
extremely random fluctuations which hinder progress 
in fathoming the dynamics. Whatever parameters are 
used should maximize the discrimination between dif- 
ferent synoptic situations. 
2. Parameters should be found which actually clas- 
sify the dynamic features of large areas. Having real 
physical significance, they would have some chance of 
being associated with both the static picture and the 
dynamic processes of the weather elements over an 
area. 
3. The relationship between the static and dynamic 
properties of the parameters should be distinguishable 
so that it would be possible to go from one to the other 
and realize what is important from both points of view. 
Because the entire Northern Hemisphere affects the 
weather patterns at one single locality, it would seem 
advisable to attempt to make these parameters of a 
Northern Hemisphere character. If the characteristics 
of the general flow could be determined by examining 
the dynamics of past situations and extrapolating them 
in order to obtain the dynamics of the present one in 
the correct manner, then it is entirely possible that the 
network theory of simple linear hypothesis would be 
sufficient to predict the individual weather at various 
localities by the use of an operator fitted to a correct 
dynamic model. 
Although none of the problems mentioned above 
have to my knowledge been solved as yet, there are 
certain specific conclusions about analogues in general 
which seem to indicate that the method holds some 
hope for future development: (1) When the correlations 
between the sequence of past and current maps main- 
