EXTENDED-RANGE FORECASTING 
day mean of the 700-mb surface. The two-day tendency 
would then be the slope of the hypsogram from one day 
preceding to one day following the mean on the day the 
tendency was desired. 
The use of the persistence correlation (or the short- 
range, 24-hr prognosis) makes it possible to estimate 
the values of the predictors for the tendency interval. 
The statistical method of doing this, described in more 
detail elsewhere [11], involves the computation of re- 
gression equations which express unknown (subsequent) 
values as a function of the last-known quantities and 
the normal values for the particular time and place. 
The basis of these computations rests in the observed 
approximately exponential behavior of the autocorre- 
lation coefficient for pressure (and other continuous 
meteorological elements) as expressed by the equation: 
Py Ss PIE, 
where 7; is the simple linear one-day lag autocorrela- 
tion coefficient for the departure from normal of pres- 
sure, and n refers to the number of days between 
values being correlated. While 7; varies with season, 
elevation, and geographical location, its value at mid- 
troposphere levels is surprisingly uniform (around 0.7). 
This uniformity makes tendency computations by this 
method practicable in routine forecasting procedure. 
These height tendencies are computed for a desired 
grid of points, and from them a field of isallohypses 
(corresponding to isallobars) may be constructed. From 
the tendencies and mean contour fields it is possible to 
make kinematic computations of the movement and 
development of the principal singular features of the 
mean maps such as troughs, ridges, centers, and so on, 
for desired periods of time. 
In short, the particular method just described, called 
the trend method, utilizes both the persistence of pres- 
sure and its tendency to be restored to certain normal 
values which vary from place to place and from month 
to month. It makes use of these two factors together 
with the past performance characteristics of the at- 
mosphere in an attempt to evaluate longer-period trends 
of large-scale circulation features and results in tend- 
ency fields which apply to moving and developing 
centers of action. The use of climatological normals and 
extremes as a qualitative guide in projecting thickness 
patterns for extended-range forecasting work has re- 
cently been started by Suteliffe and his colleagues in 
England [20]. It appears that the trend technique just 
described might be applied with advantage to thickness 
patterns as well as to.contour patterns. 
Another statistical method using a related technique 
is currently being used by German meteorologists. This 
method, credited to Baur, involves correlation tables. 
The ultimate purpose is to arrive at a forecast of the 
pressure distribution three days in advance. The 
method relies upon multiple correlations computed from 
a number of variables, important among which are the 
current day’s pressure, pressure tendencies for different 
time periods, and the cloudiness. Tables giving the 
expected three-day changes in pressure are worked out 
for several stations in Europe. The grid of stations per- 
805 
mits the construction of a prognostic chart of three-day 
isallobars. An attempt is then made to decide subjec- 
tively how the prognostic changes might come about 
from the initial state. 
Clearly, this method has some features in common 
with the trend method of the U. 8. Weather Bureau, 
described previously. The latest daily pressure and 
certain pressure tendencies used in the formulation of re- 
gression equations undoubtedly enter, though not neces- 
sarily explicitly, mto both methods. But in the use of the 
multiple correlation technique it is of some importance 
to evaluate the contribution of each of the participating 
terms to the final correlation. To the knowledge of the 
present author, no figures on this point are available, 
and it seems quite possible, if not probable, that some 
of the terms used are not contributing to the goodness 
of the final correlation. The trend method, utilizing only 
autocorrelation and the normal restoring force, suffers 
from no such ambiguity. The contributions of its com- 
ponents are known through many statistical works [22]. 
Besides, the computed tendencies can be applied in an » 
objective manner to the initial large-scale pressure pat- 
terns as reflected in the mean states. 
Still another allied statistical procedure used in ex- 
tended-range forecasting is the method of singularities. 
The primary contention of this method is that certain 
characteristic circulations and weather tend to recur in 
certain areas at almost the same time of the year, year 
in and year out. One might in this connection refer to 
the many papers of Schmauss (see, for example, [19]) 
which have appeared in German meteorological publi- 
cations, and a summarization of some allied work by 
Brooks [4]. In the practical use of this method in the 
French Meteorological Service, normal curves of sea- 
level pressure for periods of five days are computed for a 
number of stations in Europe and the eastern Atlantic. 
In spite of the long periods of record from which they 
are constructed, these curves show certain irregular 
convolutions which are superimposed upon gradual sea- 
sonal trends. It is the contention of the followers of the 
school of singularities that many of these irregularities 
are genuine and would not be smoothed out by adding 
more years of record to the data. Hundreds of papers 
have appeared in the literature of the past twenty years 
in which attempts were made to endow these singulari- 
ties with statistical significance. The arguments pro 
and con are still reverberating in the meteorological 
world, and in all probability it is safe to say that the 
last word on singularities has not been said nor will be 
for many years to come. 
Returning to the practical use of the method, at 
least as the author saw it practiced in France, a plot is 
made of the observed five-day mean pressures for the 
past several months. This plot is made on a tissue and 
then superimposed on a normal curve with the same 
time scale. An approximate match is chosen chiefly by 
the positions of troughs and ridges in the curves, little 
consideration being given to amplitude or general mean 
level. In other words, parallelism is used as the prin- 
cipal indicator of singularity, and a slight sliding of the 
time scale generally becomes necessary to find the singu- 
