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1

Horizontal divergence is expressed mathematically as

2

When thedivergence is positive, the air parcel 

grows (i.e., its area increases)

3

If the divergence is negative, it is called 

convergence, then the air parcel shrinks (i.e., area decreases).

4

The relationship between horizontal divergence and the change in a parcel’s area
(A) can be expressed as:

The above equation states that the fractional change in the area is equal to the
horizontal divergence.

5

The relationship between horizontal divergence and the vertical velocity can be
obtained from

the continuity equation as:

6

In the troposphere, the vertical velocity is

close to zero (w~0) at two altitudes

7

In the troposphere, the vertical velocity is close to zero (ݓ~0) at two altitudes.

The first is Earth’s surface, which forms a solid boundary.
• The second is the tropopause, above which the rapid increase in stratospheric potential temperature strongly inhibits vertical motion.

8

Divergence aloft is associated with

 air throughout the troposphere

9

Divergence aloft is associated with air throughout the troposphere, which
is associated with

 pressure and at the surface

10

Convergence aloft is associated with 

sinking air throughout the troposphere

11

Convergence aloft is associated with sinking air throughout the troposphere,
which is associated with

high pressure and divergence at the surface

12

So, starting at the surface, the vertical velocity becomes 

more with height when there is surface convergence, reaches some maximum vertical velocity, and then becomes positive with height becoming divergence aloft

13

Similarly, starting again at the surface, the vertical velocity becomes more negative
with height when there is

surface divergence, reaches some maximum negative velocity, and then becomes less negative with height again near convergence aloft.

14

When the surface divergence (or convergence) with height changes into

upper air convergence (or divergence)

15

When the surface divergence (or convergence) with height changes into upper air
convergence (or divergence), at some level in the troposphere (called 

the level of non-divergence, LND), the divergence becomes zero.