Each topic is accompanied by readings from the notes and other resources. There will be a problem set roughly every fortnight.

- Define what is meant by the term “general circulation”.
- Describe the basic thermal and dynamic structure of the atmosphere and its seasonal variations.
- List the equations required to solve for the large-scale atmospheric flow and describe the physical principles they are based upon.
- Distinguish the Lagrangian and Eulerian perspectives and mathematically describe the conversion between them.
- Explain why additional forces arise in rotating reference frames and describe each of them.
- Manipulate the equations when written in spherical coordinates and when using pressure as a vertical coordinate

- Lorenz, E. (1983), A history of prevailing ideas about the general circulation of the atmosphere,
*Bull. Amer. Met. Soc.*,**64**, 730-769.

- 1st March: Introduction & overview of the general circulation
- Chapter 1 of the class notes
- Slides

- 8th March: The governing equations
- Section 2.1 of the class notes
- Handwritten notes

- Describe the concepts of radiative equilibrium, radiative-convective equilibrium (RCE), and convective quasi-equilibrium and explain the differences between them.
- Recall Hide’s theorem and the conditions under which it applies
- Quantitatively evaluate whether a given RCE state is in violation of Hide’s theorem
- Give several independent reasons why the RCE solution is not observed on Earth
- Section 3.1.1 and 3.1.2 of the class notes.
- Manabe & Strickler (1964), Thermal Equilibrium of the Atmosphere with a Convective Adjustment,
*J. Atmos. Sci*,**21**, 361–385. - 15th March: Radiative-convective equilibrium
- Section 3.1 of the class notes
- Handwritten notes

- 22nd March: Hide's theorem
- Section 3.2 and 3.3 of the class notes
- Handwritten notes

- Describe the theoretical basis for the Held & Hou model of an axisymmetric Hadley Cell, including the application of angular-momentum conservation, the determination of the cell width, and the thermodynamics/energy transport of the cell.
- Apply the Held & Hou model to Earth's atmosphere and the atmosphere of hypothetical planets with different roation rates, sizes, etc..
- Identify the limitations of an axisymmetric description of the tropical circulation.
- Analyse atmospheric circulations using Reynold's decomposition to determing the role played by the mean circulation and transient and stationary eddies.
- Describe the problem of state estimation as it applied to the atmosphere, and explain methods to solve it including objective station-based analysis and reanalysis.
- Held & Hou (1980), Nonlinear Axially Symmetric Circulations in a Nearly Inviscid Atmosphere,
*J. Atmos. Sci*,**37**, 515–533. - 12th April: An axisymmetric Hadley circulaton
- Chapter 4 of the class notes
- Handwritten notes

- 12th April: Decomposing the circulation & state estimation
- Section 2.2 of the class notes
- Handwritten notes

- Describe the global angular momentum cycle and explain the role played by eddies and friction within it.
- Explain what is meant by the term form drag, and demonstrate how it arises.
- Qualitatively determine the structure of the meridional overturning circulation and mean surface winds given the angular momentum transports within the atmosphere using the concept of downward control.
- Quantitatively evaluate an atmopsheric budget (e.g., for angular momentum budget) from reanalysis data (Assignment 2)
- Get Ready for a Schooling in Angular Momentum, Wired Magazine, Nov 29, 2017.
- Explain the various uses of the terms barotropic and baroclinic.
- Describe the effect of localised stiring on the zonal wind distribution in a barotropic fluid.
- Demonstrate how the shape of eddies may contribute to fluxes of momentum.
- Apply the theory of linear Rossby waves to explain how their propagation leads to preferred regions of eddy momentum flux convergence and divergence.
- Use this theory to interpret and analyse phase speed spectra of eddy-momentum fluxes in the atmosphere
- Held (2000): General circulation of the atmosphere, Woods Hole Summer School, pp 1-8.
- Barotropic vs baroclinic.
- Describe the assumptions leading to the Quasi-geostrophic equations.
- Analyse and interpret distrubutons of QGPV and their expression in the wind and temperature field.
- Analyse and interpret the transformed Eulerian mean circualtion
- Analyse and interpret the Eliassen-Palm flux and its connection to wave propagation.
- Synthesise the above concepts into an explanation of jet formation in baroclinic atmospheres.
- Vallis (2018), Atmospheric and Oceanic Fluid Dynamics, Cambridge University Press, ch 10.1-10.4.
- Demonstrate the role played by the Rossby number in the dynamics of the Hadley Cell. Explain the limits of low Rossby number and angular-momentum conserving flow.
- Apply the subtropical angular-momentum budget to explain the influence of midlatitude eddies on the Hadley Cell
- Conrast the Solstitial and equinoctial Hadley Circulations in terms of their angular-momentum budgets.
- Describe how midlatitude eddies mediate regime transitions between the equinoctial and solsitital Hadley Cell, and explain the relevance to monsoons.
- Bordoni & Schneider (2008), Monsoons as eddy-mediated regime transitions of the tropical overturning circulation, doi:10.1038/ngeo248.