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Balanced and Unbalanced Components of Moist Atmospheric Flows with Phase Changes

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Chinese Annals of Mathematics,Series B 2019年第6期40卷 1005-1038页

作者： Alfredo N.WETZEL Leslie M.SMITH Samuel N.STECHMANN Jonathan E.MARTIN Department of Mathematics University of Wisconsin-MadisonMadisonWI 53706USA Department of Mathematics and Department of Engineering Physics University of Wisconsin-MadisonMadisonWI 53706USA Department of Mathematics and Department of Atmospheric and Oceanic Sciences University of Wisconsin-MadisonMadisonWI 53706USA Department of Atmospheric and Oceanic Sciences University of Wisconsin-MadisonMadisonWI 53706USA

Atmospheric variables(temperature, velocity, etc.) are often decomposed into balanced and unbalanced components that represent low-frequency and high-frequency waves, respectively. Such decompositions can be defined, for instance, in terms of eigenmodes of a linear operator. Traditionally these decompositions ignore phase changes of water since phase changes create a piecewise-linear operator that differs in different phases(cloudy versus non-cloudy). Here we investigate the following question: How can a balanced–unbalanced decomposition be performed in the presence of phase changes? A method is described here motivated by the case of small Froude and Rossby numbers,in which case the asymptotic limit yields precipitating quasi-geostrophic equations with phase changes. Facilitated by its zero-frequency eigenvalue, the balanced component can be found by potential vorticity(PV) inversion, by solving an elliptic partial differential equation(PDE), which includes Heaviside discontinuities due to phase changes. The method is also compared with two simpler methods: one which neglects phase changes, and one which simply treats the raw pressure data as a streamfunction. Tests are shown for both synthetic, idealized data and data from Weather Research and Forecasting(WRF) model simulations. In comparisons, the phase-change method and no-phase-change method produce substantial differences within cloudy regions, of approximately 5K in potential temperature, due to the presence of clouds and phase changes in the data. A theoretical justification is also derived in the form of a elliptic PDE for the differences in the two streamfunctions.

关键词： potential vorticity inversion Moist atmospheric dynamics Slow-fast systems Balanced-unbalanced decomposition Elliptic partial differential equations

A Survey of Unbalanced Flow Diagnostics and Their Application

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Advances in Atmospheric Sciences 2000年第2期17卷 165-183页

作者： Fuqing Zhang Steven E. Koch Christopher A. Davis and Michael L. Kaplan Department of Marine Earth and Atmospheric Sciences North Carolina State University Raleigh USA National Center for Atmospheric Research Boulder USA

This paper presents an extensive survey of the most commonly used tools for diagnosing unbalanced flow in the atmosphere, namely the Lagrangian Rossby number, Psi vector, divergence equation, nonlinear balance equation, generalized omega-equation, and departure from fields obtained by potential vorticity (PV) inversion. The basic thoery, assumptions as well as implementation and limitations for each of the tools are all discussed. These tools are applied to high—resolution mesoscale model data to assess the role of unbalanced dynamics in the generation of a mesoscale gravity wave event over the East Coast of the United States. Comparison of these tools in this case study shows that these various methods agree to a large extent with each other though they differ in details. Key words Unbalanced flow - Geostrophic adjustment - Gravity waves - Nonlinear balance equation - potential vorticity inversion - Omega equations - Rossby number This research was conducted under support from NSF grant ATM-9700626 of the United States. The numerical computations described herein were performed on the Cray T90 at the North Carolina Supercomputing Center and the Cray supercomputer at the NCAR Scientific Computing Division, which also provided the initialization fields for the MM5. Thanks are extended to Mark Stoelinga at University of Washington for the RIP post-processing package.

关键词： Unbalanced flow Geostrophic adjustment Gravity waves Nonlinear balance equation potential vorticity inversion Omega equations Rossby number

A Diagnostic and Numerical Study on a Rainstorm in South China Induced by a Northward-Propagating Tropical System

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Acta meteorologica Sinica 2008年第3期22卷 284-302页

作者：赵玉春李泽椿肖子牛 Wuhan Institute of Heavy Rain of CMA Wuhan Central Meteorological Observatory National Meteorological Center

A strong cyclonic wind perturbation generated in the northern South China Sea （SCS） moved northward quickly and developed into a mesoscale vortex in southwest Guangdong Province, and then merged with a southward-moving shear line from mid latitudes in the period of 21-22 May 2006, during which three strong mesoscale convective systems （MCSs） formed and brought about torrential rain or even cloudburst in South China. With the 1° ×1° NCEP （National Centers for Environment Prediction） reanalysis data and the Weather and Research Forecast （WRF） mesoscale model, a numerical simulation, a potential vorticity inversion analysis, and some sensitivity experiments are carried out to reveal the formation mechanism of this rainfall event. In the meantime, conventional observations, satellite images, and the WRF model outputs are also utilized to perform a preliminary dynamic and thermodynamic diagnostic analysis of the rainstorm systems. It is found that the torrential rain occurred in favorable synoptic conditions such as warm and moist environment, low lifting condensation level, and high convective instability. The moisture transport by strong southerly winds associated with the rapid northward advance of the cyclonic wind perturbation over the northern SCS provided the warm and moist condition for the formation of the excessive rain. Under the dynamic steering of a southwesterly flow ahead of a north trough and that on the southwest side of the West Pacific subtropical high, the mesoscale vortex （or the cyclonic wind perturbation）, after its genesis, moved northward and brought about enormous rain in most parts of Guangdong Province through providing certain lifting forcing for the triggering of mesoscale convection. During the development of the mesoscale vortex, heavy rainfall was to a certain extent enhanced by the mesoscale topography of the Yunwu Mountain in Guangdong. The effect of the Yunwu Mountain is found to vary under different prevailing wind directions and in

关键词： rainstorm in South China mesoscale vortex topography potential vorticity inversion mesoscale convective system (MCS)