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.
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Derivation
First derived in 1978, Q-vector derivation can be simplified for the midlatitudes, using the midlatitude β-plane quasi-geostrophic prediction equations:
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D g u g D t − f 0 v a − β y v g = 0 (x component of quasi-geostrophic momentum equation) -
D g v g D t + f 0 u a + β y u g = 0 (y component of quasi-geostrophic momentum equation) -
D g T D t − σ p R ω = J c p
And the thermal wind equations:
where
From these equations we can get expressions for the Q-vector:
And in vector form:
Plugging these Q-vector equations into the quasi-geostrophic omega equation gives:
Which in an adiabatic setting gives:
Expanding the left-hand side of the quasi-geostrophic omega equation in a Fourier Series gives the
This expression shows that the divergence of the Q-vector (
Applications
Q-vectors can be determined wholly with: geopotential height (
In frontogenesis, temperature gradients need to tighten for initiation. For those situations Q-vectors point toward ascending air and the tightening thermal gradients. In areas of convergent Q-vectors, cyclonic vorticity is created, and in divergent areas, anticyclonic vorticity is created.