LARGE-SCALE VERTICAL VELOCITY AND DIVERGENCE 
operator applied in the horizontal direction. If tempera- 
ture changes are adiabatic, dT’ /dt is given by —wyaa 
where Yaa is the adiabatic lapse rate. Then 
+ Val = 
w= — =— ; (7) 
Yad — Y Yad — 
where 67'/ét is the change of temperature along a hori- 
zontal trajectory and y is the existing lapse rate. 
Air trajectories constructed from observations of 
either geostrophic or observed winds are not very ac- 
curate due to the large time lapse between observations, 
and the eddy fluctuations of the wind. The inaccuracy 
of the air trajectories presumably causes errors in the 
vertical velocities determined by the adiabatic method. 
Therefore the results could be greatly improved if 
constant-level balloons [26] were in regular use. Other 
errors arise from nonadiabatic temperature changes 
which cannot readily be evaluated. The adiabatic method 
can be applied in many different forms [10, 11, 14, 
20, 23]. Basically, however, all these procedures are 
subject to similar assumptions and similar errors. 
Vertical velocities computed by the adiabatic method 
are average values over a considerable length of time 
(usually twelve hours) and over a considerable distance 
(the length of the trajectory). They are relatively 
inaccurate at low levels due to nonadiabatic tempera- 
ture changes there. Furthermore, when the atmospheric 
stability is nearly neutral, the method does not lead to 
dependable results. 
Unlike the kinematic method, the adiabatic method 
is not restricted to observed winds; geostrophic winds 
may be used instead. Since geostrophic winds can be 
computed even in areas of bad weather, and at high 
levels, the adiabatic method is useful for drawing daily 
charts of vertical velocities covering a given region. 
Moreover, the method has been applied successfully 
to levels as high as 16 km. 
Figure 3, taken from the paper by Panofsky [20] 
shows a comparison between vertical velocities obtained 
by the two methods. Both methods yield values of the 
order of 1 em sect. The figure shows considerable 
scattering which might be ascribed to maccuracy of 
trajectories, small eddies in the wind field, nonadia- 
batie temperature changes, etc. 
Several other methods have been suggested for the 
determination of vertical velocities. For example, the 
rainfall intensity is proportional to the mean vertical 
velocity in a saturated layer [1, 12, 17]. Hence rain- 
fall intensities could be converted into average vertical 
velocities. Such vertical velocities, however, have some 
essentially different properties from those computed 
by the other two methods. For example, if convection 
produces equal amounts of upward and downward 
motion, considerable precipitation may fall. Yet the 
kinematic method would yield a value of zero for the 
mean vertical motion. This example is important, since 
occurrence of moderate rainfall without considerable 
convective activity is not common. Bannon [1] applied 
this technigue and obtained vertical velocities greater 
641 
than 10 em sec. This large order of magnitude is 
probably due to the effect of turbulence, or possibly to 
a somewhat smaller horizontal scale. 
Another method of computing vertical velocities is 
based on determination of divergence from the vorticity 
equation and integration of the divergence. This tech- 
nique has been applied by Sawyer [25] to a limited 
degree. His results agree qualitatively with those ob- 
tamed by the other methods. 
VERTICAL VELOCITY 
ADIABATIC METHOD 
cM. SEc.! 
LEGEND +4 
e---- LAPSE RATE <8C KM 'e ° do 
> 
en--= LAPSE RATE >8C KM +5) 
° 
+2} 
oH 
° 
é VERTICAL VELOCITY 
KINEMATIC METHOD 
cM. SEC.! 
+ 
-5) 0-46 -3 43. #+4°~«=+5 
Fic. 3.—Vertical velocity by adiabatic method plotted as 
function of vertical velocity by kinematic method. 
Distribution of Large-Scale Vertical Motion and Di- 
vergence 
Considerable information is available regarding the 
distribution of vertical motion in the United States east 
of the Rocky Mountains at 10,000 ft (700 mb) and toa 
somewhat smaller extent at 5000 ft [15, 16, 17]. In 
three selected weather situations, computations were 
carried out up to 16 km [7]. Similar studies of more 
limited vertical extent were made in Kurope by Hewson 
{11] and Petterssen [23]. 
Figure 4 shows a schematic picture of the distribu- 
tion of divergence and vertical velocity in relation to 
the pressure distribution. Generally, above 5000 ft the 
wedge and trough lines coincide with the lines of zero 
vertical motion, with downward motion east of the 
wedge line and upward motion east of the trough lines. 
In other words, above 5000 ft upward vertical motion 
is associated with geostrophic winds (and observed 
winds) which have components from the south, and 
downward vertical motions with winds which have com- 
ponents from the north. Moreover, since pressure sys- 
tems normally move from west to east, local pressure 
changes are negatively correlated with vertical veloci- 
ties. The degree of correlation between vertical velocity 
on the one hand and meridional velocity and pressure 
tendency on the other varies from level to level. From 
10,000 ft to the tropopause the correlation coefficients 
vary in magnitude in the range from 0.58 to 0.72. 
In the stratosphere, the vertical velocities are gen- 
erally smaller than they are in the troposphere and 
are of the same sign, resulting in strong vertical con- 
vergence (horizontal divergence) near the tropopause 
in regions of upward motion. Also, in regions of upward 
