The moist C-vector and its applications

The C-vector (C) is an extension of the Q-vector (Q) in the three-dimensional space, characterizing three-dimensional ageostrophic motion. However, C is derived from the geostrophic wind and adiabatic approximations, and the diabatic effect is excluded. Precipitation and its impact on weather systems in the atmosphere are frequently related to the diabatic effect produced by the release of latent heat. Based on the primitive equations in p-coordinate with the β-plane approximation and the diabatic effect, the moist C-vector (C^*) is proposed, and its physical interpretations are revealed. A Qingzang plateau vortex case is diagnosed by C^* using the fifth-generation European Center for Medium-Range Weather Forecasts atmospheric reanalysis data (ERA5) and the database of the Qingzang plateau vortex. Results are compared with the diagnostic results of C to prove the application value of C^*. It is found that compared with Q and C, C^* contains more comprehensive information of the ageostrophic motion and thus has more advantages in diagnosis. The horizontal component of C^* ( ${\mathit{C}}_{\text{hor}}^{\ast }$) depicts the secondary circulation caused by thermal wind imbalance and diabatic effect, better explaining the reason for the direction change of the Qingzang plateau vortex movement than that C. The vertical component of C^* ( $C_p^{\ast }$) restores the information of ageostrophic motion which is lost by Q, and depicts horizontal ageostrophic motion caused by geostrophic imbalance. The negative $C_p^{\ast }$ center represents the Qingzang plateau vortex center, and has a certain predictive effect on the development of the Qingzang plateau vortex. Besides, the relative sizes of ${\mathit{C}}_{\text{hor}}^{\ast }$ and $C_p^{\ast }$ indicate that the Qingzang plateau vortex has a significant baroclinic property.