Abstract: Having investingated into the general concept of potential vorticity inversion (hereafter, referred to as PV inversion) and its properties as well as its recent progress, the authors point out that this technology has deficiency in meso-scale systems research and, the higher-order PV inversion operator needs to be developed for these issues. The PV inversion operator depends on how to proper establish a balance equation to a great extent. However, the spontaneous emission of inertiagravity waves makes the exact balanced flow be hardly to exist and is potentially related to the fuzziness of the socalled slow manifold. A series of problems with the slow manifold were introduced and discussed, including how to overcome the fuzzy property. From the basic characters of slow manifold, a new definition was given and the corresponding higherorder balance equations were deduced. The characteristics of this higherorder balance equation and its application in the PV inversion for mesoscale research are investigated. Finally, the technology was used to the diagnostic study of the rainfall event in the Yangtzi RiverHuaihe River area caused by a low vortex moving eastward between July 21 and 24 2008. The analysis results demonstrate that the higherorder PV inversion operator is better than the old one satisfying the nonlinear balance equation. In addition, some meaningful conclusions were drawn based on the analyses of the balanced flow, vertical velocity field and nonbalanced flow.