Atmospheric Dynamics
(G63.2840.003)

Instructor: Prof. Richard Kleeman (Office: 901 Warren Weaver)
Location: 1013 Warren Weaver
Time: Tuesday 1:25-3:15pm, Spring 2008.
Basic Text:  J.R. Holton, “An Introduction to Dynamic Meteorology”, Academic Press, 1992.
Secondary Text: A.E. Gill, “Atmosphere-Ocean Dynamics”, Academic Press, 1982.

Assessment: 40% Assignments (3); 40% Final Examination (Take Home) and 20% Class Attendance.

Assignment 1

Assignment 2

Syllabus

There will be 13 lectures. The contents are described approximately below. Latex versions of the lectures will appear during the term and will be linked below.

Lecture 1: The basic equations for the atmospheric fluid.
The fundamental equations governing atmospheric flow will be derived and carefully explained. Approximations commonly used such as the hydrostatic and  incompressibility will be introduced and evaluated. Conservation laws for mass, energy and moisture will be derived and discussed.

Lecture 2: The forcing terms for the primitive equations.
External and internal forcings of the atmosphere are responsible fundamentally for the setting up of the observed mean circulations. The processes causing this forcing are primarily radiation, moist convection and turbulent transport. These are commonly described as physical processes and are modeled using physical parameterization. The nature of these forcings will be introduced and their importance for the atmospheric circulation motivated.

Lecture 3: Circulation and Vorticity.
Circulation and vorticity are the primary measures of rotation in a fluid such as the atmosphere. Understanding these concepts is basic to dynamical theories of geophysical flows. We derive the circulation theorems and the conservation equations for potential vorticity. Potential vorticity is explored in both a vertically uniform and non-uniform context. The latter form is referred to as Ertel's potential vorticity.

Lecture 4: The Planetary Boundary Layer.
The layer of the atmosphere close to the surface (within 1km) is subject to vigorous turbulent motion. Understanding how momentum is dissipated from the atmosphere by this process and how heat is acquired from the surface is crucial for an analysis of the mean atmospheric circulation is. The nature of the boundary layer and its effects on the interior of the atmosphere are examined.

Lecture 5: Quasi-geostrophic analysis.
The primitive equations are generally very difficult to analyse in a transparent way so various approximations are usually resorted to in order to further understanding. In the extratropics a particularly useful approximation is the quasi-geostrophic. The mathematics of this are carefully introduced and applied to understanding the mid-latitude atmosphere.

Lecture 6: Linearization Part I.
Another particularly useful methodology for the analysis of the atmospheric circulation are the linearized solutions of the primitive equations. Various wave-like disturbances may be derived and these play a basic role in our current understanding of the atmosphere. In this lecture we consider linearization about a state of rest. We shall assume solutions are separable between the vertical and horizontal and derive equations for so called barotropic and baroclinic waves.

Latex Version

Lecture 7: Linearization Part II
The horizontal equations of the separable linearization about a state of rest are analyzed. Gravity and Rossby waves are discussed and the implications of the quasigeostrophic approximation explored. Finally the thermal wind relations are derived and their implications discussed.

Lecture 8: Linearization Part III (Baroclinic Instability)

Differential radiative forcing and the thermal wind relations imply that the mean state of the atmosphere is very far from rest. In this lecture we examine the consequences of the vertical shear of this mean flow. When the equations are linearized about such a flow exponentially growing solution can arise. The most unstable of such solutions have a horizontal structure strong resembling mid-latitude storms.

Lecture 9: The General Circulation: The zonally averaged circulations.
Basic latitudinal flows characterize the mean atmospheric circulation. The Hadley Cell is thermally forced while the Ferrel Cell is driven mainly by the perturbations discussed in Lecture 8. Models of these fundamental circulations are considered.

Lecture 10: Tropical Dynamics.
In the vicinity of the equator, atmospheric dynamics are different to the mid-latitudes due to the vanishing of the Coriolis force and the dominance of moist convection. A survey of the appropriate dynamical machinery will be given.

Lectures 11: Predictability.
The concept of chaos was first introduced by a meteorologist (E. Lorenz of MIT) because the turbulent nature of the atmosphere means that detailed weather predictions are highly inaccurate beyond a certain time scale. The problem of prediction is thus a statisitical one due to this rapid growth of errors. A survey of approaches to statistical predictability are outlined. These range from those currently used in practical weather forecasting through to more theoretical/fundamental approaches studied by the Lecturer in recent years.