12.810 (Spring): Dynamics of the Atmosphere

Class description

This class discusses the dynamics of the atmosphere, with emphasis on the large scale. Topics include internal gravity waves in the atmosphere; potential vorticity conservation and Rossby waves; baroclinic instability and extratropical storms; the tropical Hadley and Walker circulations and equatorial waves; the general circulation, annular modes, and the response to climate change. (Pre-req: 12:800 or instructor's permission)


• Meets in 54-824 on Tuesdays and Thursdays from 10:30am-12pm
• Office hour in 54-1712 on Fridays 11am-12pm
• Download the class syllabus


1) An Introduction to Dynamic Meteorology, 5th edition (Holton and Hakim)
2) Atmospheric and Oceanic Fluid Dynamics (Vallis)


Class presentations will be in class on May 8th, 10th, and 15th.
Project reports are due on May 17th

Problem sets

Lecture slides and additional reading

1. Introduction (pdf)
ERA-40 reanalysis: Uppala et al, Quart. J. Roy. Met. Soc., 131, 2961-3012, 2005

2. Hadley circulation (pdf)
Theory: Vallis sections 11.2-11.4 (1st edition) and 14.2-14.4 (2nd edition); Held and Hou, J. Atmos. Sci., 37, 515-533, 1980
Superrotation: Caballero and Huber, Geophys. Res. Lett., 37, L11701, 2010

3. Internal gravity waves (pdf)
Introductory notes for the Boussinesq case (pdf)
Internal gravity waves and mountain waves: Holton sections 5.4 and 9.4
Log-pressure coordinates: Vallis section 2.6.3; Holton section 7.4.1

4. Large-scale rotating and stratified dynamics (pdf)
Shallow water dynamics: Holton 4.5; Vallis 3.1
Quasigeostrophy: Holton chapter 6; Vallis 5.4
Potential vorticity song: lyrics

5. Vertical motion and the omega equation (pdf)
Variants of the omega equation: Holton chapter 6

6. Vertically propagating and stationary Rossby waves (pdf)
Stationary waves: overview chapter by Isaac Held
Ray tracing: Vallis 14.2 (1st ed.) or 16.2 (2nd ed.)

7. E-P fluxes and instability in midlatitudes (pdf)
E-P fluxes: QG theory and observations Edmon et al, J. Atmos. Sci., 37, 1980
Models of baroclinic instability: Holton chapter 7 and Vallis chapter 6 (1st ed.) or 9 (2nd ed.)

8. Available potential energy of the atmosphere (pdf)
Dry available potential energy: Lorenz, Tellus, 2, 1955; Vallis section 3.10 (1st ed.) or 3.11 (2nd ed.)
Energetics under climate change: O'Gorman, PNAS, 107, 2010

9. General circulation (pdf)
Eddy forcing of the mean circulation and the transformed Eulerian mean: Holton 10.2 and 10.3
Effect of eddies on the Hadley cells: Sections 3.2 & 3.4 of Schneider et al, Rev. Geophysics, 48, RG3001, 2010
Stratospheric circulation and downward control: Holton 12.2