The Mesoscale Balance and Imbalance and the Corresponding Potential Vorticity Inversion from the View of Helicity

The static balance and the geostrophic balance are the common balances in meteorology. All the synop-tic systems and most of the mesoscale systems satisfy the above two balances. However, due to the strong convection and non-geostrophic feature, many mesoscale systems usually present as static imbalance, and the quasi-geostrophic approximation is no longer attainable. This paper tried to find out a kind of balance that exists for mesoscale convective system. To do this, the concrete mathematics definitions for balance and imbalance equations were defined. Then, it is proposed that the new balance equation should include the divergence, vorticity, and vertical motion simultaneously, and the helicity equation was a good choice for the basis. Finally, the mesoscale balance and imbalance equations were constructed, as well as a new balance model that was based on the helicity, horizontal divergence, vertical vorticity, continuity, and ther-mal dynamic equations under same approximations. Moreover, the corresponding potential vorticity (PV) inversion technique was introduced. It was pointed out that by using the PV conservation and the potential temperature conservation, the flows of the mesoscale balance model can be deduced, and their comparison with the real fields would give the degree of the imbalance.