AbstractPrecipitating 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.
Journal of the Atmospheric Sciences – American Meteorological Society
Published: Oct 24, 2017
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.
All for just $49/month
Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.
Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.
It’s easy to organize your research with our built-in tools.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera