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METHODS OF MEDIUM-RANGE FORECASTING 
Statistical Methods. Inasmuch asthe physics of large- 
scale weather phenomena has been so imperfectly un- 
derstood during the past half century, it seems natural 
that purely statistical approaches to the problem would 
be taken. These approaches have been many and varied. 
Some of them have been conducted with indiscriminate 
use of the correlation technique in the pious hope that 
the atmosphere would “speak for itself”’ and thus re- 
lieve man of the apparently superhuman task of work- 
ing out its physical behavior. For the most part such 
hopes have been consistently thwarted by an atmo- 
sphere which apparently resists such crude forms of 
regimentation represented by the strait-jacket tech- 
nique of simple lag correlation. 
Other statistical, or chiefly statistical, techniques 
which possess some background of physical reasoning 
have enjoyed more success. Among the most widely 
known and practiced of these, and those to which we 
shall refer, are methods involving trends, singularities, 
symmetry points, weather types, and weather ana- 
logues. A brief (though necessarily incomplete) de- 
scription of each of these methods will be given, followed 
by an attempt to evaluate and compare the various 
methods. 
Longer-period trends seem to infiltrate many systems 
of extended-range forecasting. In their simplest form, 
it is the purpose of these methods to estimate the rate 
of change of a state of the general circulation, regionally 
or for several regions, and from this rate and the initial 
state to extrapolate the circulation for desired periods 
of time. Precisely this sort of thing forms the basis of 
perhaps 80: per cent of short-range forecasts that are 
issued today. The problem has been rendered more 
tractable in short-range than in extended-range fore- 
casting by kinematic methods applied by Petterssen 
[16] and others, and more recently by the simple expe- 
dient of preparing synoptic charts every three or six 
hours. In this manner the tendencies are easily de- 
duced and from these and from the continuity, extra- 
polations are easily made. 
In extended-range forecasting, however, one is faced 
with the questions, first, What zs the initial state of the 
large-scale circulation? and second, What is the tend- 
ency interval desired? Various methods have been pro- 
posed for determining the initial large-scale state of 
the circulation. All of these essentially involve some 
form of smoothing, the effect of which is to damp out 
the smaller-scale and presumably secondary irregulari- 
ties of the circulation, chiefly migratory cyclones and 
anticyclones, and thereby bring into focus the great 
centers of action. Thus the Russian school plots com- 
posite charts on which are indicated singular features 
of the surface pressure distribution, particularly cy- 
clones, anticyclones, ridges, troughs, etc., for certain 
‘natural periods” during which the locations and tracks 
of these features are similar [15]. The areas persistently 
occupied or invaded by anticyclones or cyclones thereby 
become clear, and the composite chart gives a good 
clue to the dominating centers of action. In the U. 8. 
Weather Bureau the smoothing is achieved by the pro- 
WEATHER FORECASTING 
cedure of averaging over intervals of time. In this 
manner five-day (or other period) means are prepared. 
by averaging the pressures (or temperatures) inter- 
polated from a grid of latitude and longitude intersec- 
tions from twice-daily Northern Hemisphere charts at 
sea level and aloft. When isolines are drawn to these 
values, smooth patterns appear which usually leave no 
question as to the position and intensity of the centers 
of action. Other methods of smoothing are also possible 
and it may be that a simple arithmetic mean is not the 
best for the purposes of extended-range forecasting. 
Further research along these lines would appear to be 
desirable. 
Of late some have advocated that a sufficient degree 
of smoothing for ordinary medium-range forecasting 
work is achieved by merely resorting to charts for 
higher elevations, perhaps 10 to 13 km. While it cannot 
be denied that these charts appear simpler in form than 
those in the lowest layers of the troposphere (except at 
low latitudes), there is some question as to what extent 
the greater simplicity arises from fewer and less ac- 
curate data which give freer rein to the analyst’s im- 
agination. Besides, the slow evolution so characteristic 
of means taken over longer time intervals is easily lost 
when each snapshot of the circulation at any level is 
inspected from day to day. 
Having decided upon the initial state of the general 
circulation, the Grosswetterlagen, the next problem in 
the estimation of trends is to find the necessary “‘tend- 
ency interval” and methods of determining the tend- 
ency quantitatively. Here one rough method is to com- 
pare the last available daily chart with its preceding 
sequence, again using some integrating device like the _ 
mean or composite chart. The reason why such a 
method has some success in determining the trend of 
the large-scale features of the circulation is that there is 
appreciable serial correlation in meteorological data 
such as pressure. As a result, today’s chart will bear a 
maximum resemblance to the mean chart whose period 
centers on the current day—provided the period of 
averaging is not too large. Thus the comparison of daily 
charts with mean charts may throw light on the larger- 
scale trends. Because of its subjective nature, this pro- 
cedure is often not satisfactory and for this reason a 
more quantitative method of evaluating trends has been 
developed in the U. S. Weather Bureau. Inasmuch as 
this method is closely related to other statistical meth- 
ods to be compared, and perhaps clarifies these methods, 
it will be described in some detail. 
If we wish to treat the slow evolution of large-scale 
circulation patterns which, for example, appear at the 
700-mb level, it would be helpful to be able to construct 
a tendency field to serve the same function as does the 
3-hr tendency field of daily charts. The choice of a 
tendency interval, while somewhat arbitrary, must be 
small compared to the length of the period over which 
the means are taken and should preferably be centered 
around the mean. In the case of five-day means, for 
example, a tendency interval of two days might be a 
good choice. What is desired for each location, then, is 
the slope of a hypsogram representing a running five- 
