Decomposition and Application of the Modified Moist Potential Vorticity Tendency Equation

In this study, the modified moist potential vorticity tendency equation is theoretically analyzed, discussed, and verified in a typhoon process. The main conclusions are as follows: The modified moist potential vorticity tendency equation can be decomposed into dry and moist component tendency equations. Without regard to the moisture species and friction, the dry component of the modified moist potential vorticity tendency equation is conservative, and it is the same as the Ertel potential vorticity tendency equation. The moisture gradient term has an obvious effect on the variation of the modified moist potential vorticity; thus, the tendency equation is more suitable for diagnosing and analyzing some mesoscale and microscale weather systems. With the same decomposition method, the upgraded virtual potential vorticity tendency equation and the upgraded equivalent moist potential vorticity tendency equation can be derived. After this upgrade, these equations now include the moisture gradient term, which potentially makes the potential vorticity diagnosis more precise. By analyzing the latent heat of condensation in various potential vorticity tendency equations, we determined that the Ertel potential vorticity tendency equation overestimates the effect of the latent heat of condensation, whereas the modified moist potential vorticity tendency equation can deduct some of the latent heat of condensation; thus, it should have a better diagnostic effect. The result of subtracting the modified moist potential vorticity tendency equation and the equivalent moist potential vorticity tendency equation can reasonably reflect the effect of the latent heat of condensation. Therefore, it can have a better diagnostic effect for the Meiyu front rainstorm and tropical cyclones, where the latent heat of condensation plays a major role.