786 
ciated physical extrapolations, also provides for the 
acquisition of forecasting experience concerning such 
processes and extrapolations. Later verification will 
indicate the extent to which the nonadvective, diabatic 
processes have been correctly anticipated in the 24-hr 
prognosis: this verification is automatically accom- 
plished at t + 24>, at which time is made the actual 
nonadvective relative allohypsography for the period 
from to to to + 24h. 
The final 24-hr prognosis of the relative hypsography 
is now obtained simply by adding graphically the prog- 
nosis of the advective relative hypsography for t) + 24", 
which has been just obtained by stage four, and the 
prognostic pattern of the nonadvective relative allo- 
hypsography for the period (f) + 24") — to. 
With the completion of stages four and five, we can 
now proceed to utilize the temperature field for the 
prognosis of the surface map in a way not possible 
before the development of synoptic aerology, owing 
to the unrepresentativeness of the surface air-tempera- 
ture observations. As stage six, then, we exploit the 
prognostic relative hypsography for obtaining the prog- 
nosis of the surface map. For example, as shown in 
Fig. 8b, frontal waves on the surface map should be 
associated with a warm tongue, or ridge, in the rela- 
tive hypsography. An open frontal wave should be 
fitted to a broad and flat tongue (e.g., Florida). A 
large spread between the prognostic relative isohypses 
describes a homogeneous air mass, which should be 
associated with the warm sector of an open wave 
(e.g., Lake Ontario). The packing of the prognostic 
relative isohypses must occur in the frontal strip (e.g., 
Gulf of Alaska, Mississippi Basin, Atlantic Ocean). 
An occluded frontal disturbance should be chosen for 
a narrow ridge with large amplitude in the prognostic 
relative hypsography (e.g., the west coast). 
Stage seven is the prognosis of the absolute hypsography, 
obtained by a simple routine procedure. The 24-hr 
prognosis of the relative hypsography is superimposed 
upon the prognostic surface map, upon which is now 
placed a hitherto unused transparent map overlay. 
By graphically adding these two prognoses, the prog- 
nostic absolute hypsography is drawn on the overlay. 
Prognosis Beyond Thirty-Six Hours, Based on Extra- 
polation of Individual Upper Long Waves. The im- 
portance of the latitudinal variation of the Coriolis 
parameter for the explanation of the large-scale motions 
has been incorporated by Rossby [68] mto a barotropic, 
approximately nondivergent, wave model. This physical 
model became a very simple instrument for the ex- 
tended-period extrapolation of the baroclinic long waves 
in the upper westerlies. This extrapolation is based upon 
parameters determined at the ‘“‘equivalent barotropic 
level.” At this level it is then assumed that the extra- 
polation is governed primarily by the quasi-conserva- 
tion of the vertical component of absolute vorticity. 
In spite of this somewhat unrealistic assumption, the 
simple prognostic rules developed from the application 
of this autobarotropic model have achieved partial 
success in predicting the propagation speed of the 
individual long waves in the upper westerlies and, to 
WEATHER FORECASTING 
a lesser extent, their development. (This partial suc- 
cess initiated the use of such a model in making the 
mathematico-physical prognosis discussed in this vol- 
ume by Charney on pp. 470-482 and by Fjgrtoft on 
pp. 454-463.) In this subsection we very briefly con- 
sider the application of these rules, particularly those 
which have been rather well substantiated by synoptic 
experience. 
Let us first consider the individual 500-mb maps, 
selected because they are, according to Charney [16, 
p. 147] approximately at the level of nondivergence. 
In the 500-mb westerlies one often finds long waves 
consisting of slowly moving cold troughs and warm 
ridges. Being often obscured on the surface map, they 
represent a family of major waves quite distinct from 
the rapidly moving minor waves or warm troughs and 
cold ridges which have their greatest amplitudes at 
the lowest level of the atmosphere and diminish with 
height. 
The eastward velocity of propagation of the long 
waves is computed by means of Rossby’s wave formula 
in the form 
sg he — 1° 
@ 2Qa cos’ o (60)? ” 
where L’ is the observed angular wave-length (ex- 
pressed in degrees), and UL’, is the theoretical angular 
length which a wave should have in the atmospheric 
situation under consideration in order to be stationary. 
(The earth’s parameters are represented by the usual 
notation, vz., angular speed ©, radius a, and mean 
latitude ¢ of the waves.) Rossby’s wave formula in the 
form 
(2) 
20aL” cos® é 
(3860)2 
shows that, on the 500-mb map, a change in ¢ can 
occur from a change in L’ or from a change in ¢ (the 
latitudinal position of the maximum zonal wind) or 
Vz,5 (the geostrophic west-wind component), that is, 
in L’, according to (2). In practice, the hemispheric 
chain of maximum westerlies is divided up into three 
parts, approximately 120° of longitude im length, such 
that waves within each part are roughly at the same 
latitude. Then v,,; , which is measured at various lati- 
tudes across the maximum westerlies, and ¢ are space- 
averaged along each 120°-length of the maximum wes- 
terlies. To facilitate the application of equations (2) 
and (8), Byers has designed a nomogram [17] into 
which L’, vz,;, and ¢ can be entered for finding c. 
The short-range (e.g., 48-hr) variations in these aver- 
aged values v,; and ¢ of the maximum zonal wind- 
stream over its 120°-length are so small that they cause 
no significant change in L’,, which is a function only 
of vis; and ¢. A forecast of persistence for L’, is therefore 
usually a good forecast. Hence, ¢ varies primarily ac- 
cording to L’. However, it is generally difficult to pre- 
dict the future changes in L’, so that the forecaster 
must be content with using just the .mstantaneous 
to-value of c, over a third of the hemisphere, for the 
prognostic extrapolation of the long waves. The extent 
(3) 
G= tba = 
