Further Study of theQ-Vector Based on the Quasi-Geostrophic Omega Equation

Q-vector is an important physical quantity in diagnosing the vertical velocity based on the quasi-geostrophic ω-equation. Generally, Q-vector and its extension expressions, such as the semi-geostrophic-, ageostrophic- and moist Q-vectors, can be derived from the primitive equation set on the approximated f-plane. However, the atmospheric quasi-geostropic feature can not be considered in the traditional method. In this paper, the Q-vector and its extension expressions were derived from the quasi-geostrophic ω-equation directly in terms of the mathematical-physical transformation. Then, the deficiency of the traditional Q-vector derivation in physics was discussed.