Q-Vectors

Q-vectors are used in atmospheric dynamics to understand physical processes such as vertical motion and frontogenesis. Q-vectors are not physical quantities that can be measured in the atmosphere but are derived from the quasi-geostrophic equations and can be used in the previous diagnostic situations. On meteorological charts, Q-vectors point toward upward motion and away from downward motion. Q-vectors are an alternative to the omega equation for diagnosing vertical motion in the quasi-geostrophic equations.

==Derivation== First derived in 1978, Q-vector derivation can be simplified for the midlatitudes, using the midlatitude β-plane quasi-geostrophic prediction equations: \frac{D_g u_g}{Dt} - f_{0}v_a - \beta y v_g = 0 (x component of quasi-geostrophic momentum equation) \frac{D_g v_g}{Dt} + f_{0}u_a + \beta y u_g = 0 (y component of quasi-geostrophic momentum equation) \frac{D_g T}{Dt} - \frac{\sigma p}{R} \omega = \frac{J}{c_p} (quasi-geostrophic thermodynamic equation)