Precipitating Quasigeostrophic Equations and Potential Vorticity Inversion with Phase Changes

Author:

Smith Leslie M.1,Stechmann Samuel N.2

Affiliation:

1. Department of Mathematics, and Department of Engineering Physics, University of Wisconsin–Madison, Madison, Wisconsin

2. Department of Mathematics, and Department of Atmospheric and Oceanic Sciences, University of Wisconsin–Madison, Madison, Wisconsin

Abstract

Abstract Precipitating versions of the quasigeostrophic (QG) equations are derived systematically, starting from the equations of a cloud-resolving model. The presence of phase changes of water from vapor to liquid and vice versa leads to important differences from the dry QG case. The precipitating QG (PQG) equations, in their simplest form, have two variables to describe the full system: a potential vorticity (PV) variable and a variable M including moisture effects. A PV-and-M inversion allows the determination of all other variables, and it involves an elliptic partial differential equation (PDE) that is nonlinear because of phase changes between saturated and unsaturated regions. An example PV-and-M inversion is provided for an idealized cold-core cyclone with two vertical levels. A key point illustrated by this example is that the phase interface location is unknown a priori from PV and M, and it is discovered as part of the inversion process. Several choices of a moist PV variable are discussed, including subtleties that arise because of phase changes. Boussinesq and anelastic versions of the PQG equations are described, as well as moderate and asymptotically large rainfall speeds. An energy conservation principle suggests that the model has firm physical and mathematical underpinnings. Finally, an asymptotic analysis provides a systematic derivation of the PQG equations, which arise as the limiting dynamics of a moist atmosphere with phase changes, in the limit of rapid rotation and strong stratification in terms of both potential temperature and equivalent potential temperature.

Funder

Division of Atmospheric and Geospace Sciences

Alfred P. Sloan Foundation

Publisher

American Meteorological Society

Subject

Atmospheric Science

Cited by 26 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3