644 
is near 5 X 10-* sect. Hence, the term averages around 
5 & 10- cm sec in magnitude, about half as large 
as the other acceleration terms. Neglecting the vertical 
advection terms may lead to considerable errors. 
Vertical Advection of Temperature and Potential Tem- 
perature. Vertical advection of temperature and po- 
tential temperature is also important, as was shown 
by the fact that reasonable values of w have been ob- 
tained by the effect of vertical motion on the tempera- 
ture field. Again, the effect of vertical motion on local 
temperature changes averages about half the effect 
of horizontal advection [7, 19]. 
Vertical Motion and Pressure Changes. Since the verti- 
cal velocity has an important effect on the tempera- 
ture field, and since changes in the temperature field 
are associated with pressure changes, Raethjen [24] 
first suggested a pressure-tendency equation in which 
the pressure tendency is expressed in terms of an inte- 
gral with respect to height of local density changes. 
The density changes in turn are computed from hori- 
zontal advection and the effect of vertical motion. 
The equation can be written 
MECHANICS OF PRESSURE SYSTEMS 
where g is the acceleration of gravity, i, and he are 
arbitrary levels, k is the ratio of the gas constant to 
the specific heat at constant pressure, and # is the 
stability (yaa — y)/T. This equation avoids the low- 
level, high-level compensation of the Margules-Bjerknes 
tendency equation. However, the vertical velocity is 
not known sufficiently well to permit forecasts of pres- 
sure tendencies from (11) or a modification of it; on 
the contrary, Panofsky [19] used this equation to com- 
pute the vertical velocity from the pressure tendency. 
Later Fleagle [8] discussed the relative importance of 
vertical and horizontal motion on pressure changes in 
selected situations, and Godson [9] considered the con- 
ditions favorable for cyclogenesis, on the basis of a 
similar equation. These studies indicated that vertical 
motion has effects on local pressure changes of the same 
order of magnitude as horizontal motion. 
Vertical Velocities and Changes in Cloudiness. Large- 
scale vertical velocities have their most conspicuous 
effect in the production of cloudiness. Since air cools 
when it rises, increasing cloudiness should be associated 
with positive vertical velocities. Panofsky and Dickey 
[22] and Miller and others [17] showed that middle 
cloudiness tends to increase along the trajectories of 
ho 
() Op 5 ope : ¢ : fae 
(2 saa esa) aa) V-Vup dz rising air and decrease along the trajectories of sinking 
h ho h . . ond 3 Deno 
a a? a (11) air. However, vertical velocities do not seem to discrimi- 
h rhe 5 : G0 3 
4. Pe Bade 4: | 2 @op2 Op a nate between overcast with or without precipitation. 
7 ee et AY, Eehuasy? . . . 
g oi g ie pot ” Figure 5, taken from Miller [15], shows this effect 
© to ®@ to = ® to P to 
w 
e) ® B ie) ® ® cm/sec 2 2 z 2 2 E 
° ana 
° — 
fo) 
° ° 
: op : 8 
eee Nay & = 
8 ©0990 99 0) ow oo 
as oBo Ze 2 ee 2 
g So 0500 SE. 000 
0000 009: ie) 9 = 
000 (} ° fete} 
Gas) 00 8 000 098 els) 
Q0000 898 fefo) el ceye) oO 
& 888 re a> 6 m 8 . 
000 osoreo ° g 
0000 2. 8 
}OOO ° 
Ee oto 
OPO 00 090 
0000 ce} 
°88° ° 8 =, 
fefe) 00 ° 
eS ° 
° 8 —}) —— 
Fic. 5.—Changes of weather following 24-hr isobaric trajectory at 700 mb as function of vertical velocity. The circled D means 
clear with relative humidity 30 per cent or less, the circled M clear with relative humidity greater than 30 per cent, © clear ir- 
respective of relative humidity, @ overcast, and P precipitation. The slanting lines connect mean vertical velocities corre- 
sponding to the weather changes indicated at the heads of the columns. 
