12.831 Dynamics and Transport in the Stratosphere
Fall 2013

Alan Plumb

TR 11 - 1230, 54-1623


There is no set text -- I'll be handing out notes and posting them below -- but some of the material we'll cover can be found in Andrews, Holton, and Leovy, Middle Atmospheric Dynamics, Academic Press, 1987. (Referred to as AHL in the following.)

Some useful sites

The latest stratospheric analyses and forecasts out to 10 days can be found on the Stratosphere Home Page of the Climate Prediction Center.

Class notes (pdf)

0: Introduction - quick tour of the observed stratosphere (slide show)

1: Climatological balances of heat, mass, and angular momentum (and the role of eddies).
Here we establish that the observed departures of the zonal-mean stratosphere from radiative equilibrium could not be sustained without the presence of eddies.

2: Transport of heat, momentum, and PV
(Some additional notes on the Lagrangian theory of eddy transport can be found here).
Discussion of "Modified Lagrangian Mean" theory for the barotropic case can be found in Nakamura & Zhu (2010) (through the end of Section 2c; we'll talk about effective diffusivity later).
Problem Set 1 (due Wed Oct 2).

3: Stratospheric Rossby waves
Here we'll talk about conditions for wave propagation; Rossby wave EP fluxes; and wave breaking.
The classic paper on baroclinic Rossby wave propagation on a beta-plane is Charney & Drazin, J. Geophys. Res. (1961); analysis on a sphere and "refractive index" was presented by Matsuno, J. Atmos. Sci. (1970). Propagation up a vortex with a discrete PV edge is discussed in Esler & Scott, J. Atmos. Sci. (2005) (and references therein).
Problem "Set" 2 (due Wed Oct 22): Based on Esler & Scott's paper, present your own analysis of wave propagation up a vortex with a discrete edge (i.e., with a single PV jump at the edge).

4: The impact of large-scale waves on the stratosphere.
Solution of the mean state problem, given divF. "Downward control"; the Kuo-Eliassen problem for the transient case. Variability of the winter stratosphere; major warmings.

5: Gravity waves and their role in the middle atmosphere circulation. (N.B.: This is a *.xps file.)
Here we'll talk about how upward propagating internal gravity waves: their propagation characteristics, how they break and thereby drive the pole-to-pole mesospheric circulation (the "Murgatroyd-Singleton" circulation). A fairly recent review is Fritts & Alexander, Rev. Geophys. (2003).

Homework #3 (due Mon 24 Nov): Access climatological data for the stratosphere (multiple years or a single month) and thereby calculate the EP flux (using the QG representation) and its divergence. Express the latter (actually (1/rho)*divF) in units of m/s/day. Plot the winter (or January) mean for the N Hem for all levels available above 100hPa.

6: Quantifying stratospheric transport
Here we talk about effective diffusivity and age.
Effective diffusivity, in this context and for the purely 2D case, was introduced by Nakamura, J. Atmos. Sci. (1996). It was applied to stratospheric data by Haynes & Shuckburgh, J. Geophys. Res. (2000) and Allen & Nakamura, J. Geophys. Res. (2001). The 3D case, in which ultimate mixing is accomplished by vertical diffusion (and the result that it does not matter much how variance is ultimately destroyed, as long as it is done at small scales), is discussed in Liebensperger & Plumb, J. Atmos. Sci. (2004)

Homework #4: Read the following papers. (The first two are about age observations and the search for trends; the 3rd about modeling trends in the residual circulation and age.)
Engel et al., Nature Geoscience, 2008.
Stiller et al., Atmos. Chem. Phys., 2012.
Garcia et al., J. Atmos. Sci., 2011.
Prepare a summary of these papers to present to class on Wednesday, Nov 26.

7: The Quasi-biennial oscillation
We'll discuss the theory of the QBO driven by 2 internal gravity waves. Movies of the QBO experiment in the lab can be found on the Kyoto Uni. GFD web site (click on "QBO" and then explore). (Description of the original experiment can be found in: Plumb & McEwan, J. Atmos. Sci. (1978).)

8: Stratospheric trace species: distribution and inter-relationships
Here we apply what we have learned about stratospheric transport -- in particular, the dominance of isentropic mixing in the wintertime extratropical stratosphere -- to understand how tracer distributions are controlled, and the significance of "equilibrium slopes" and compact tracer-tracer relationships. A more complete exposition is in Plumb, Rev. Geophys. (2007).

2 Dec 2014