828 
circulation changes within limited regions—of the size 
of perhaps a continent or an ocean—actually exist and 
are caused to a large extent, though not exclusively, 
by the distribution of pressure and temperature within 
these regions and those immediately adjacent to them. 
CRITIQUE OF THE METHODS OF EXTENDED- 
RANGE FORECASTING 
Medium-Range Forecasts. It is useful to distinguish 
between medium-range forecasts (for two to five days) 
and extended-range forecasts (for six to ten days, for 
months, or for seasons). The methods of synoptic mete- 
orology play a decisive role in medium-range forecasts. 
This is possible today, since weather maps of the entire 
Northern Hemisphere are available every day owing 
to the improvement of the communication system. 
However, it is necessary to supplement synoptics by 
meaningful statistics, partly to enlarge and consolidate 
our experience, and partly to create objective bases 
which could be of direct aid to forecasting. The appli- 
cation of rhythm analyses and symmetry points is of 
little use for the medium-range forecast, since the 
shorter pressure waves are mostly nonpersistent [20, 
pp. 933-934]. These methods are therefore discussed 
in the section on long-range forecasting. 
Analogue Methods. An aid for the medium-range 
forecast can be found in the study of the subsequent 
development of past cases with both similar pressure 
distributions and similar preceding Grosswetter devel- 
opments. It is to be noted, however, that such subse- 
quent developments have a definite seasonal trend with 
frequency maxima in certain rather narrowly limited 
portions of the year, just as have the types of Gross- 
weiterlagen and the repetition tendency. Therefore, only 
those days of previous years should be used for com- 
parison whose date is not more than five days removed 
from the day in question. As a consequence of this 
restriction, really useful and significantly similar cases 
can be found only on rare occasions. This method can 
be used regularly only when weather map series for 
150 yr are available. 
Combination of Synoptics and Statistics. The only 
hopeful method of obtaining reliable medium-range 
weather forecasts is the combination of synoptics and 
statistics. By synoptics we mean here not only the 
chartwise representation and analysis of weather and 
Grosswetterlagen, but also the thorough consideration 
of subsequent developments from a physical viewpoint. 
For this purpose, it is necessary to develop the present 
synoptics, from which forecasts can be made only up 
to 36 hr in advance, to Grosswetter synoptics. Such 
Grosswetter synoptics deal with the physical aspects of 
the sequence of Grosswetterlagen, the forms of transition 
from one type to another, and the mutual influence of 
Grosswetterlagen in neighboring circulation regions. With 
such Grosswetter synoptics, the preceding development 
which has led to a certain Grosswetterlage must be 
taken into account to a much greater extent than has 
been the case with daily synoptics. 
The multitude of the phenomena and problems that 
must be taken into account make it absolutely neces- 
WEATHER FORECASTING 
sary that statistics be used as a broad empirical basis. 
What a theoretically designed experiment is to the 
physicist, clear statistics are to the Grosswetter investi- 
gator. Investigations of special situations which are 
favored in the usual synoptics give results which only 
appear to be proofs and have no value in promoting 
knowledge of macrometeorology. Such investigations 
can be compared to experiments in physics in which 
uncontrollable secondary effects are not eliminated. 
Clean-cut statistics must be preceded by definite physi- 
cal or theoretical formulations of the problems; these 
statistics must comprise all available observations per- 
taiming to the problem and they must be compared 
with suitable control samples to show whether or not 
the correlations are statistically significant. Such inves- 
tigations can serve a double purpose: furthering our 
knowledge in a manner similar to a well-designed ex- 
periment as well as serving as a basis for forecasting, 
provided their results are unequivocal and significant 
(with a significance level of 0.27 per cent). 
Forecasting the Sea-Level Pressure Distribution for 
Two to Three Days. The combination of synoptics and 
statistics makes it possible today to predict in many 
cases the approximate pressure distribution for the 
second and third day in those regions for which the 
necessary data are available. Scherhag [49] has shown 
how to determine the sea-level pressure distribution for 
the following day from the movement and intensity 
change of 3-hr and 24-hr isallobars, from the direction 
of the isopleths of geopotential, and finally from the 
divergence and convergence of the isopleths on the 500- 
and 225-mb charts. Furthermore, one can compute 
approximately the change in thickness of the layer 
between the 500- and 1000-mb surfaces from the sur- 
face pressure distribution; by adding the prognostic 
thickness chart to the prognostic surface pressure chart, 
the prognostic 500-mb chart for the following day can 
be obtained. In turn, from this 500-mb chart a fore- 
cast of the surface pressure distribution can be obtained 
for the second consecutive day. Finally, a prognostic 
chart of the surface pressure for the third consecutive 
day can be obtained by repeating this procedure with 
a consideration of the “steering” of the isallobaric 
maxima and minima in the upper troposphere by means 
of the 96-mb chart [17, p. 126]. Of course, the forecast 
becomes more uncertain with each successive day be- 
cause of the propagation of errors. For this reason, it 
is necessary to supplement the prognosis statistically. 
If we transform the hydrodynamic equation of mo- 
tion so that it includes surface friction, and add to it 
the equation of continuity, the first law of thermody- 
namics, and the equation of state, a system of equa- 
tions is obtained from which the following equation for 
the pressure change can be derived, as shown in [24]: 
Gp fe dy ( =) 
a oe 1 — xoz 
dv p i 
+0(@+0)| Tae 
where the symbol dive v stands for the horizontal diver- 
gence of the velocity v, x = R/cp = 0.2884, dq/dt is 
