798 
usually important matter because of previous extremely 
wet weather or extremely dry weather or because of an 
approaching national holiday, the forecaster will have 
to reach a decision not alone on the basis of the prob- 
ability of occurrence of rain but in large measure on the 
anticipated public reaction to a rain (or no-rain) fore- 
cast. This type of situation is well typified in Gulf and 
Atlantic coastal areas when a hurricane is approaching. 
An objective forecasting system obviously cannot take 
into account these nonmeteorological factors. However, 
progress toward a rational solution from the standpoint 
of meteorology has been made by expressing the objec- 
tive forecast in terms of the probability of occurrence 
of the specified event. 
Another serious deficiency of objective forecasting 
systems which have been developed thus far is that the 
selected weather element is forecast only for individual 
times and places. Aviation forecasts in particular must 
usually cover a route of hundreds or perhaps thousands 
of miles, and forecasts generally must portray the ex- 
pected weather trends through time intervals up to 
several days. These requirements impose a severe limi- 
tation on the extent to which objective forecasts have 
been applicable, although some progress has been made 
in solving this problem. New developments in the field 
of air traffic control suggest that probability forecasts 
may eventually be required for essentially all aviation 
purposes. 
TYPES OF OBJECTIVE FORECASTS 
A review of the literature on forecasting suggests 
three different methods of approach to the development 
of systems of objective forecasting. Although it is the 
purpose of this paper to discuss only one of these ap- 
proaches, the other two are mentioned briefly in order 
to indicate in what way they offer the possibility of im- 
proved forecasts. 
Numerical Calculation. The method of numerical cal- 
culation which was first attempted by Richardson [19] 
has recently become of practical importance through 
the work of Charney and Eliassen [6] and the develop- 
ment of high-speed electronic computers. This method 
of producing a forecast, based solely on the solution of 
simplified equations of the atmosphere, showed little 
promise of practical value so long as hand computation 
was required to obtain the solution. The value of the 
equations of motion for applied forecasting was limited 
to their ability to suggest variables which might then 
be found, empirically, to be of forecasting significance. 
The possibility now exists, however, that a prediction 
of the contour pattern at an upper level can be com- 
pleted by a high-speed computer in time to be of use in 
preparing the weather forecast. This development re- 
quires careful consideration by those engaged in 
research on objective forecasting to msure that the 
information in such prognostic contour charts can be 
fully incorporated in objective techniques for preparing 
the weather forecast. Relatively little work has been 
done on the use of prognostic charts, and few forecast- 
ing systems can be evaluated in a way that would show 
the increase in accuracy to be had with a perfect prog- 
WEATHER FORECASTING 
nostic chart or that give any hint of the possibility of 
using information from a prognostic chart in preparing 
the forecast. Studies of this kind have been made by 
Mook and Price [13] and by Klein [11]. 
Statistical Methods. Although all forecasting except 
that done by numerical calculation is in reality based 
on the statistical processing of data, there are differ- 
ences in the extent to which a logical foundation of 
meteorological and physical principles is built up prior 
to the application of statistics. One possibility is to use 
statistical methods exclusively in the search for vari- 
ables, retaining for prediction purposes only those vari- 
ables which have a statistically significant relation to 
the element being forecast. In the field of long-range 
forecasting particularly, this approach has been appeal- 
ing and to some extent perhaps necessary because of 
the absence of enough knowledge of the causes of long- 
term fluctuations in the general circulation to provide a 
useful mathematical-physical foundation. Among those 
leading in such studies have been Walker and Bliss (for 
a critique and bibliography of Walker’s work up to 
1936, see [16]). 
More recently in the field of short-range forecasting, 
the statistical approach has been investigated at some 
length by Schumann [21] and Wadsworth [28]. Me- 
teorologists have criticized this type of study on the 
basis that the statistical selection of variables for pre- 
diction without resort to prior meteorological knowledge 
is basically unsound [23], and this has led in some cases 
to rather sharp differences of opinion between meteorol- 
ogists and statisticians. Sutcliffe, for example, takes the 
extreme view that meteorologists, by developing a phys- 
ical foundation for all relationships used in forecasting, 
should drive statisticians out of meteorology. On the 
other hand, Professor Norbert Wiener discusses this 
question in an unpublished note [29], in which he points 
out that in meteorology the role of dynamics is to sug- 
gest what quantities one should expect to find inter- 
related, and that the role of statistics is to verify the 
correctness of the dynamics. Although this may be a 
somewhat oversimplified statement of the situation, 
it seems clear that any meteorological hypothesis which 
is claimed to be of use in forecasting must be tested 
statistically before its value will have been demon- 
strated, even though it may express a theoretical re- 
lationship based on what seem to be reasonable 
assumptions. Conversely, of course, relationships which 
are derived solely from empirical considerations, even 
though supported by a large number of cases, cannot be 
safely adopted as real (?.e., practically certain to exist 
in future data) unless they can be shown to have a 
rational physical basis. 
To the extent that the goal of a study is to increase 
the accuracy of forecasts, the proof of success will rest 
in the verification of the forecasts, and this is largely a 
statistical matter. In order that the interplay between 
the physical and statistical approaches can be effective, 
somewhat greater recognition needs to be given to the 
place of modern statistical methods in meteorology. At 
the same time, it must be recognized that statistical 
tools, for example, correlation or regression, can easily 
