General circulation of the atmosphere

Semester 1 2024



Lectures

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

Topic 1: Overview & tools

Learning outcomes

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

Background reading

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

Lectures

  • 1st March: Introduction & overview of the general circulation
  • 8th March: The governing equations

  • Topic 2: Radiative-convective equilibrium & Hide's theorem

    Learning outcomes

    1. Describe the concepts of radiative equilibrium, radiative-convective equilibrium (RCE), and convective quasi-equilibrium and explain the differences between them.
    2. Recall Hide’s theorem and the conditions under which it applies
    3. Quantitatively evaluate whether a given RCE state is in violation of Hide’s theorem
    4. Give several independent reasons why the RCE solution is not observed on Earth

    Background reading

    Lectures

    • 15th March: Radiative-convective equilibrium


    • Topic 3: Axisymmetric & non-axisymmetric circulations

      Learning outcomes

      1. 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.
      2. Apply the Held & Hou model to Earth's atmosphere and the atmosphere of hypothetical planets with different roation rates, sizes, etc..
      3. Identify the limitations of an axisymmetric description of the tropical circulation.
      4. Analyse atmospheric circulations using Reynold's decomposition to determing the role played by the mean circulation and transient and stationary eddies.
      5. 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.

      Background reading

      • Held & Hou (1980), Nonlinear Axially Symmetric Circulations in a Nearly Inviscid Atmosphere, J. Atmos. Sci, 37, 515–533.

      Lectures


      Topic 4: The angular momentum budget of the atmosphere

      Learning outcomes

      1. Describe the global angular momentum cycle and explain the role played by eddies and friction within it.
      2. Explain what is meant by the term form drag, and demonstrate how it arises.
      3. 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.
      4. Quantitatively evaluate an atmopsheric budget (e.g., for angular momentum budget) from reanalysis data (Assignment 2)

      Background reading

      Lectures


      Topic 5: Jet formation & maintenance: the barotropic case

      Learning outcomes

      1. Explain the various uses of the terms barotropic and baroclinic.
      2. Describe the effect of localised stiring on the zonal wind distribution in a barotropic fluid.
      3. Demonstrate how the shape of eddies may contribute to fluxes of momentum.
      4. Apply the theory of linear Rossby waves to explain how their propagation leads to preferred regions of eddy momentum flux convergence and divergence.
      5. Use this theory to interpret and analyse phase speed spectra of eddy-momentum fluxes in the atmosphere

      Background reading

      Lectures


      Topic 6: Quasigeostrophic theory and forcing of the zonal mean

      Learning outcomes

      1. Describe the assumptions leading to the Quasi-geostrophic equations.
      2. Analyse and interpret distrubutons of QGPV and their expression in the wind and temperature field.
      3. Analyse and interpret the transformed Eulerian mean circualtion
      4. Analyse and interpret the Eliassen-Palm flux and its connection to wave propagation.
      5. Synthesise the above concepts into an explanation of jet formation in baroclinic atmospheres.

      Background reading

      • Vallis (2018), Atmospheric and Oceanic Fluid Dynamics, Cambridge University Press, ch 10.1-10.4.

      Lectures


      Topic 7: Non-axisymmetric tropical circulations

      Learning outcomes

      1. 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.
      2. Apply the subtropical angular-momentum budget to explain the influence of midlatitude eddies on the Hadley Cell
      3. Conrast the Solstitial and equinoctial Hadley Circulations in terms of their angular-momentum budgets.
      4. Describe how midlatitude eddies mediate regime transitions between the equinoctial and solsitital Hadley Cell, and explain the relevance to monsoons.

      Background reading

      • Bordoni & Schneider (2008), Monsoons as eddy-mediated regime transitions of the tropical overturning circulation, doi:10.1038/ngeo248.

      Lectures


      Topic 8: Paper discussions