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. 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. First derived in 1978, Q-vector derivation can be simplified for the midlatitudes, using the midlatitude β-plane quasi-geostrophic prediction equations: 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) f 0 ∂ v g ∂ p = − R p ∂ T ∂ x {displaystyle f_{0}{frac {partial v_{g}}{partial p}}=-{frac {R}{p}}{frac {partial T}{partial x}}} (y component of thermal wind equation) where f 0 {displaystyle f_{0}} is the Coriolis parameter, approximated by the constant 1e−4 s−1; R {displaystyle R} is the atmospheric ideal gas constant; β {displaystyle eta } is the latitudinal change in the Coriolis parameter β = ∂ f ∂ y {displaystyle eta ={frac {partial f}{partial y}}} ; σ {displaystyle sigma } is a static stability parameter; c p {displaystyle c_{p}} is the specific heat at constant pressure; p {displaystyle p} is pressure; T {displaystyle T} is temperature; anything with a subscript g {displaystyle g} indicates geostrophic; anything with a subscript a {displaystyle a} indicates ageostrophic; J {displaystyle J} is a diabatic heating rate; and ω {displaystyle omega } is the Lagrangian rate change of pressure with time. ω = D p D t {displaystyle omega ={frac {Dp}{Dt}}} . Note that because pressure decreases with height in the atmosphere, a − ω {displaystyle -omega } is upward vertical motion, analogous to + w = D z D t {displaystyle +w={frac {Dz}{Dt}}} .