# Q vector

From AMS Glossary

## Q vector

A horizontal vector, arising in quasigeostrophic and semigeostrophic theory, the divergence of which appears on the right-hand side of the omega equation.

In the context of ''f''-plane (i.e., the Coriolis parameter where

*f*is assumed constant) quasigeostrophic theory, the**Q**vector is defined as*g*is the acceleration of gravity, θ_{0}a constant reference value of the potential temperature,**v**_{g}the horizontal geostrophic wind,**∇**_{p}the horizontal gradient operator on a constant-pressure surface, and θ the potential temperature. In the context of*f*-plane semigeostrophic theory, the definition of the**Q**vector is identical except that the physical coordinates (*x, y*) are replaced by the geostrophic coordinates (*X, Y*). The**Q**vector tends to point in the direction of rising air. If**Q**points toward warm air, the geostrophic flow is frontogenetic. If**Q**points toward cold air, the geostrophic flow is frontolytic.