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.
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.
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.