782 
would be advectively advanced to the right of the 
upper low (see Fig. 7), the anterior ascent of air in 
the low and posterior descent alone could maintain a 
concentric system of relative and absolute isohypses, 
HORIZONTAL PROJECTION 
SS aS ~ S “es 
Ww E 
Fic. 7.—Three-dimensional motion in a nondeveloping upper 
low concentric with its island of cold air. In the lower part, 
the continuous concentric circles are the absolute isohypses 
of an upper low at, say, fo. The dashed circle congruent with an 
absolute isohypse is a relative isohypse, also for to, of an upper 
island of cold air. The double-stroked arrow is the subsequent 
displacement of the nondeveloping cold low from L to C, while 
the two curved single-stroked arrows give the resulting trajec- 
tories of two selected points on the relative isohypse, accord- 
ing to the field of gradient motion of the propagating cold low. 
When continuous, the single-stroked: arrows also indicate up- 
ward motion; when dashed, downward motion (cf. upper part 
of figure). The displacements and trajectories during four 
successive 6-hourly periods are indicated by the numbers (1, 2, 
3, and 4) along all three arrows. With C as its center, the circle 
indicated by the shaded areas is the position of the relative 
isohypse at to + 24". The eccentric, dashed closed curve is the 
advected position of the relative isohypse also at to + 245. The 
shaded areas therefore indicate the nonadvective displacement 
of the relative isohypse—light-shaded for nonadvective in- 
crease in relative height, dark-shaded for nonadvective de- 
crease. The letters A and B are references to the upper part of 
the figure. 
(even disregarding the contributing diabatic effects). 
The thermal low thus appears as a sort of cold-air 
source region, mainly in the middle tropopause just 
above the cold-front surface. Most important in upper- 
air map prognosis, this conservatism of the cold-air 
islands allows for their geometrical extrapolation. In 
WEATHER FORECASTING 
fact, the forecaster, at least in the beginning, devotes 
considerable attention to the thermal lows, treating 
the prediction of them as a mainstay around which the 
map prognosis can be built. 
The Prognosis of the Relative Hypsography by Ad- 
vective-Adiabatic Extrapolation. Local changes in the 
relative height may be considered as being associated 
mainly with the isobaric transport—into the locality— 
of an air column with a height different from that of 
the initial column. As a semi-Lagrangian method of 
predicting this advective change in the relative height, 
the relative isohypses for t) are considered as conserva- 
tive mean-isentropes of their mandatory layer embedded 
im its wsobaric flow; and, as the fourth prognostic stage, 
they are displaced passively with the estimated future 
flow of the same layer, for the period, say, from to to 
t) + 24”. The transport of the relative isohypses should 
melude not only that part of the advection which is 
due to the gradient wind at either boundary surface of 
their mandatory layer, but also the advection by the 
gradient wind shear between these boundary surfaces. 
(The advection effect of the gradient wind shear is 
zero only if, along the vertical, the horizontal gradient 
of the virtual temperature maintains the same direc- 
tion throughout the layer.) 
The most accurate procedure, therefore, is to trans- 
port the relative isohypses according to the vector 
mean of the gradient flow at the boundary surfaces of 
their mandatory layer. This. vector mean is deter- 
mined approximately by the mean absolute hypsog- 
raphy of the bounding surfaces, obtained by the 
graphical addition of the two absolute hypsographies 
with only every second pessible line being drawn. Since 
the mean absolute isohypses form a greater angle of 
intersection with the relative isohypses than do the 
absolute isohypses of either bounding surface, the mean 
absolute hypsography is more useful than either of 
the absolute hypsographies for estimating the trans- 
port of the relative isohypses due to gradient advection. 
On a hitherto unused map (printed on vellum tracing 
paper), superimposed on the constant-pressure map 
for t, a rough draft of the prognostic relative hypsog- 
raphy for tf) + 24> is, in this way, completed for each 
mandatory layer under the prelimmary assumptions 
that advection is perfectly isobaric and that the field 
of horizontal motion at ¢) is constant during the prog- 
nostic period. But, after having first found the prog- 
nostic absolute hypsographies for t + 24>, we may 
then apply—as a correction to stage four—an average 
field of motion during the 24-hr prognostic period and 
arrive at better-advected positions of the prognostic 
relative isohypses. A method of successive approxima- 
tions can thus be introduced for finding the varying 
field of horizontal motion during the 24-hr prognostic 
period, thereby improving the advective-adiabatic ex- 
trapolation of the relative hypsography. 
We shall now proceed to consider the nonadvective 
and diabatic extrapolations of the relative hypsog- 
raphy. This prognostic operation takes into account 
the changes occurring in the quasi-conservative aspects 
of relative height and neglected in stage four. These 
