A Study On Theory, Algorithm And Application Of Potential Vorticity Inversion

Long-term observation and research indicate that slow and fast variations which are mainly corresponding to the vortical and divergent motions coexist at middle-high latitude. Potential vorticity inversion (hereafter, referred as PV inversion) technology is regarded to be successful in distinguishing the above two modes of motion. However, the super-gradient flows often makes it difficulty to separate the above two modes accurately. How to accurately separate the slow motion from all the other forms of motion becomes a major problem of the PV inversion research. The understanding and further research on these issues are involved in related theory of balanced flow, slow manifold and other important concepts. Therefore, the study on higher-order operator is one of the important aspects of PV inversion. This paper is focused on deducing higher-order balanced equations and the corresponding inversion operator. Idealistic test is designed to test this higher-order operator. And its superiority is demonstrated through the analysis of a rainfall event.Firstly, the relations among the PV inversions, balanced flow and slow- manifold are investigated. The author points out the theoretical limitation to the construction of higher-order operator of PV inversion. Such limitation is due to the spontaneous emission of inertia-gravity waves, which makes the exact balanced flow can not exist and is related to the fuzziness the slow manifold. In order to overcome this fuzzy property of the slow manifold, this article gives a new definition of slow manifold and deduces the corresponding higher-order balance equations and PV inversion operator.Secondly, in order to study the properties of the higher-order PV inversions operator, small vortex disturbance experiments are designed to confirm the validity of this higher-order PV inversion operator. Vortex experiments with different intensities, scales and resolutions are designed to study the properties of the higher-order PV inversion. Furthermore, we analysis the vertical velocity fields, which are produced by the higher-order PV inversions.Finally, we demonstrate the application of the higher-order PV inversion by the rainfall event in Yangtzi-Huai area rising from a low vortex that moves eastward between July 21th and 24th,2008. This work is divided into two parts:â‘ the application of higher-order PV inversion, including analysis of the balanced flow, its vertical velocity field and the evolution of imbalanced flowâ‘¡the application of the piecewise potential vorticity inversion, including analysis of the roles of disturbances at different layers and comparison between the nonlinear balanced (Charney balance)inversion and higher-order PV inversion.