A PROCEDURE OF SHORT-RANGE WEATHER FORECASTING 
to which he can predict the acceleration of propagation 
of the long waves depends on how well he can predict 
the changes in their wave length. 
In an intense westerly jet stream (and also in the 
cases with waves of large amplitude), representative 
values of v,,; cannot be determined; the evaluation of 
c by Byers’ nomogram should therefore not be at- 
tempted for such waves. The motion of the long waves 
in a narrow jet stream can be determined instead by 
averaging the speed profile from several cross sections, 
each eight degrees of latitude in width, and centered 
at the maximum speed of the jet stream. Next, a; , 
the average direction, measured from the east-west 
axis (east = 0), of the isohypses at their inflection 
points, and ¢; , the corresponding average latitude are 
found directly from the 500-mb map. Then, the con- 
stant absolute vorticity path is evaluated; the wave 
length of this constant absolute vorticity path is equal to 
L’,, the stationary-wave length. Therefore, for L’/L’,<1, 
the long wave under consideration will progress east- 
ward during the prognostic period; and for L’/L’,= 1, 
the wave will be quasi-stationary. When L’/L’, > 1, 
L’ will soon decrease; the decrease occurs first as a 
retrogression of the long waves and then as an increase 
in their wave number n. 
The westward movement of the long waves is seldom 
a real phenomenon, but only an apparent, discontinu- 
ous one. It results from the fact that the major trough 
is transformed into a vanishing minor trough accelerat- 
ing eastward simultaneously as a new major trough 
forms westward of the former position of the old major 
trough. After the retrogression, the final position of 
the major trough is at the distance of L’, from the next 
major trough to the west. In the hemispheric chain 
of long waves, successive retrogressions of the major 
troughs generally occur downstream at short intervals 
of time. 
At the end of this retrogression cycle, a new major 
trough often forms as an adjustment of Z’ in response 
to a change in L’,, this adjustment appearing as an 
increase in n. It has been generally observed that an 
increase in a hemispheric chain of previously retrograd- 
ing long waves leads to progression. 
Tf the considerations outlined above could lead to a 
prognosis, three to six days m advance, of the major 
waves in the upper westerlies, it would establish the 
basic framework, so to speak, of the predicted future 
atmospheric state. But many assumptions still are in- 
volved in passing over from this more or less abstract 
prediction (“‘analysis-prognostic process”) to the more 
detailed forecasting of the various weather constitu- 
~ ents (“‘prognosis-forecast process’’). These mental oper- 
ations do, however, fall naturally mto three straight- 
forward parts: conjecturing qualitatively the most 
probable future (1) development of the minor waves in 
the upper westerlies, (2) sea-level paths of the cyclones, 
(3) anomaly patterns of precipitation and ground- 
surface temperature for the forecast period, or large 
intervals thereof, rather than for certain days, or par- 
ticular times of the period. 
Fultz [80] has suggested a certain life cycle for the 
787 
minor waves in their conjunction with the major waves. 
These minor waves are associated with the cyclones. 
According to Klein [48] two of the prevailing sea-level 
paths of the cyclones converge in a region of confluence 
in the major wave. In this region, heavy precipitation 
is generally observed. In fact, from his investigation 
and from the experiences of others, Klein [48] has 
developed a schematic model of the precipitation anom- 
aly pattern probably associated with a major wave. 
The ground-surface temperature anomaly pattern asso- 
ciated with the major wave has been studied by several 
investigators, whose results are reported by Bund- 
gaard [33, Fig. 18-61-2]. 
THE PREDICTION OF VARIOUS 
WEATHER CONSTITUENTS 
Introduction. The prediction of the interrelated 
weather constituents—temperature, cloud, precipita- 
tion—is naturally a composite process and should there- 
fore be based mainly on the synoptic system of weather 
maps, actual and prognostic. But the map-made pre- 
dictions of the weather cannot express the details of 
the local effects, since the map systems are intended 
to describe only in a coarse way the atmospheric state 
for the future—or even for the present. However, such 
effects can sometimes be applied locally for predicting 
an explicit weather constituent. In the first subsection 
we shall mention briefly and in a general way how 
objective techniques can be developed by methods of 
statistico-graphical integration. We then illustrate in a 
few words how temperature, cloudiness, precipitation, 
wind, ete., can be predicted by objective methods as 
well as by various physico-empirical considerations and 
synoptic rules of experience. 
The Objective Method. The method of graphical 
integration provides a graphical solution of the form: 
WW COS 5 Ah oo), a, EOS AG) (4) 
where W is the value of the weather constituent, 
(e.g., rainfall, temperature) which is to be predicted 
and X; are variables, measured at the initial time, 
which are believed to be related to W at some later 
period. The X; are combined in successive pairs, each 
set of two variables being plotted on a scatter diagram 
with the X; as coordinates and the values of the de- 
pendent variate, W, indicated beside each plotted point 
(see Fig. 9). Here, the small frequency charts represent 
the distribution of W in a small area on the graph. 
The data are analyzed by constructing W ;-isograms of 
a, b,---,n. 
Hach pair of X,; is analyzed in this manner, result- 
ing in an equation of the form: 
W = F(Wi, Wo, --:, Wi, °°, Wap), (5) 
where each of the W; is now a function of two X;. 
The number of the new, W;-variables in (5) is about 
half the number of original X,-variables in (4). This 
process is repeated, now using pairs of W, as coordinate 
variables and, as before, analyzing each scatter diagram 
by considering the distribution of W itself. Obviously 
