Positive vorticity advection
Positive vorticity advection, or PVA, is the result of more cyclonic values of vorticity advecting into lower values of vorticity. It is more generally referred to as "Cyclonic Vorticity Advection" (CVA). In the Northern Hemisphere this is positive, whilst in the Southern Hemisphere it is negative.
Vorticity in the atmosphere is created in three different ways, which are named in their resultant vorticity. These are; Coriolis vorticity, curvature vorticity, and shear vorticity. For example, at the base of a trough, there is curvature and shear vorticity. Air entering the base of the trough does not have this vorticity and so there is anticyclonic vorticity advection (AVA). This produces convergence because of the way the air gains cyclonic vorticity while entering the base of the trough. The opposite happens when air is exiting the base of a trough. This air has more cyclonic vorticity than the air it is entering and therefore produces CVA. CVA produces divergence as a result of how there is a loss of cyclonic vorticity. Coriolis vorticity in this situation is ignored because it acts about the same on all the air flowing through the base of the trough.
Significance in forecasting
The divergence with CVA is significant because it creates forced lift in the atmosphere. This forced lift, in the presence of conditions favorable for atmospheric convection, can cause clouds or precipitation. AVA will do the opposite and lead to a stable atmosphere. In combination with a jet streak, CVA can lead to the amplification of a trough which is significant for forecasting many conditions of the atmosphere.