642 
motion, the equation of continuity requires horizontal 
convergence at the surface (Fig. 4). Quantitative com- 
putations [8] show that divergence in and above the 
tropopause almost exactly compensates the surface con- 
vergence. The same is true for surface divergence and 
stratospheric convergence. The observations are too 
crude to permit the exact location of a level of “‘non- 
divergence” in the upper troposphere. 
For several months, synoptic vertical velocity charts 
were constructed at New York University at 10,000 
ft or 700 mb along with the regular analysis of standard 
maps. Aside from the correlation between vertical veloc- 
ities and meridional flow at the same levels, the follow- 
height km 
15 
h_line _ 
wedge line 
—— ee 
troug 
PPI | 
CONVERGENCE 
\ 
\\ DIVERGENCE 
N 
high 
pressure. 
center 
\\. CONVERGENCE 
“XN 
MECHANICS OF PRESSURE SYSTEMS 
duces convergence in the northward flow, and (2) the 
curvature term in the gradient wind equation produces 
faster motions at the wedge than at the trough lines, 
hence, for sinusoidal isobars, there is convergence with 
flow from the north. The curvature term depends on 
the square of the wind speed, the latitude term on the 
first power. Thus the curvature term is relatively more 
important at high than at low levels. Quantitative 
computations show that near the surface the latitude 
term determines the distribution of divergence, and 
that above a critical level the curvature term takes the 
upper hand. This theory, again, leads to qualitative 
agreement with Fig. 4. Quantitatively, however, the 
el bel 
DIVERGENCE 
level of nondivergence 
HTT 
\ DIVERGENCE 
N 
low high 
pressure pressure 
center center 
Fig. 4.—Schematic distribution of divergence and vertical velocity in an east-west cross section. Full drawn vertical lines are 
lines of zero vertical velocity and divergence. 
ing qualitative relations between the features of the 
surface charts and the vertical velocity charts were 
noted: 
1. Upward motion in cloud and precipitation areas. 
2. Upward motion above low-pressure centers and 
fronts. 
3. Downward motion above polar high-pressure re- 
gions. 
4. Upward motion to the west of wedge lines in strong 
southerly flow. 
In agreement with these results, Petterssen [23] found 
anticyclonic curvature of surface isobars generally asso- 
ciated with subsidence. 
Theoretical Explanations of the Distribution of Vertical 
Velocity and Divergence 
Bjerknes and Holmboe [3] arrived at a distribution 
of divergence for finite motions under the assumption 
of the gradient-wind equation. Essentially, there are 
two contributions to the divergence of the gradient 
wind: (1) the variation of the Coriolis parameter pro- 
Bjerknes-Holmboe theory predicts smaller divergence 
and vertical motion than are actually observed. Part 
of the discrepancy may be due to the fact that the 
Bjerknes-Holmboe theory applies to a slightly larger 
scale than the observations. 
Charney [4] arrived at a similar distribution of verti- 
cal velocity and divergence from the complete mete- 
orological equations; his work, however, was done by 
the perturbation method, so it does not permit a quan- 
titative comparison between theoretical and observed 
vertical velocity and divergence. 
Surface friction, which is neglected in these studies, 
may account for the discrepancy between theory and 
observations. A simplified treatment based on constant 
eddy viscosity [16] shows a relationship between V’p, 
surface divergence, and vertical velocity above the 
friction layer; pressure minima are associated with 
convergence and upward vertical motion. 
A simple derivation with no assumption regarding 
the distribution of eddy viscosity with height shows 
