Vorticity forecast information, the thermal wind and the omega equation

 Relative vorticity is a measure of the rotation of fluids about a vertical axis relative to the earth's surface. Colors indicate the strength of relative vorticity, red for positive (counterclockwise rotation) and blue for negative (clockwise rotation) vorticity, respectively.

Positive Vorticity develops in a wind field with counterclockwise curvature and/or due to shear with higher velocities on the right, as seen in flow direction.

positive Vorticity due to curvature
positive Vorticity due to shear
 
Positive vorticity at the 500 hPa level are often associated with cyclones and troughs in the 500 hPa topography.

Negative Vorticity develops in a wind field with clockwise curvature and/or due to shear with higher velocities on the left, as seen in flow direction.

negative Vorticity due to curvature
negative Vorticity due to shear
 
Negative vorticity at the 500 hPa level is often associated with fair weather and ridges in the 500 hPa topography.

Vorticity is an important measure and used to locate dynamically active zones and  fronts. The omega-equation, an equation used to diagnose vertical motion (or the so called omega, in pressure units) links vorticity and vertical motion. It says that:

greater upward velocity occurs where there is greater advection of positive vorticity by the thermal wind

The geostrophic vorticity at the 700 hPa level is often used as a representative value for the omega equation.  Now the thermal wind is only a mathematical construct (vector difference between geostrophic winds at two different heights or pressures) and not an actual wind. To examine the thermal wind, thickness maps are needed:


Thickness map (colors) with thermal wind (arrows) and surface pressure (black contours).

A thickness map between two different pressures (e.g 1000 and 500 hPa) is a measure of the average virtual potential temperature within that layer, where blue is cold and red is warm. As can be seen the thermal wind is parallel to the thickness contours, with cold air to the left in the northern hemisphere. Closer packing of thickness colors indicates a stronger horizontal temperature gradient and thus a stronger thermal wind. By the thermal wind relationship, the horizontal temperature gradient causes the geostrophic wind to change with altitude (how much is shown by a thermal wind vector).

Note that if thickness lines (layer temperature) cross pressure lines, there is a temperature advection (a transport of temperature by the wind. The wind is parallel to pressure lines and stronger if isobars [lines of constant pressure] are closer together). In the thickness map shown above, there is cold air advection over Great Britain.

 
Greater upward velocity favors clouds and heavier precipitation and that's another good reason to look for vorticity. It may be complicated to evaluate vertical motion from vorticity, but this has historical reasons. If you like it simple examine the plots of vertical velocity.