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:
D g u g D t − f 0 v a − β y v g = 0 {\displaystyle {\frac {D_{g}u_{g}}{Dt}}-f_{0}v_{a}-\beta yv_{g}=0} (x component of quasi-geostrophic momentum equation)
D g v g D t + f 0 u a + β y u g = 0 {\displaystyle {\frac {D_{g}v_{g}}{Dt}}+f_{0}u_{a}+\beta yu_{g}=0} (y component of quasi-geostrophic momentum equation)
D g T D t − σ p R ω = J c p {\displaystyle {\frac {D_{g}T}{Dt}}-{\frac {\sigma p}{R}}\omega ={\frac {J}{c_{p}}}} (quasi-geostrophic thermodynamic equation) And the thermal wind equations:
f 0 ∂ u g ∂ p = R p ∂ T ∂ y {\displaystyle f_{0}{\frac {\partial u_{g}}{\partial p}}={\frac {R}{p}}{\frac {\partial T}{\partial y}}} (x component of thermal wind equation)
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