Climate Dynamics (G63.2830.002)

Course given Fall 2001 in Room 1013 Warren Weaver Hall. Wednesday 1.25pm-3.15pm

Office Hours: Thursday 1.30pm-3.00pm.
Assignment 1 (due November 21) is here .
Examination (due Decmber 14) is here.
 
 
 

Texts

A.E. Gill, Atmosphere-Ocean Dynamics, Academic Press, 1982: Main Reference


S.G.H. Philander, El Nino, La Nina and the Southern Oscillation, Academic Press, 1990.


J. Holton, An Introduction to Dynamic Meteorology, Academic Press, 1992.




Syllabus

The following topics will be covered in the Fall 2001 term. A summary of material for each topic is also provided. Please keep checking this page for updates relevant to the course (e.g. Lecture notes).

The primitive equations for atmosphere and ocean

The fundamental equations used to model the climate system will be derived. This will include the equations for momentum, density, temperature, salinity and moisture. Special attention will be paid to the coriolis force and various conservation laws. Approximations often made in the climate context will be introduced including hydrostatic, Boussinesq and incompressibility. References: Gill Chapter 4 (and parts of Chapter3). A postscript version of this lecture is available .


Sources of forcing and the process of parameterization

The forcing terms for the primitive equations will be introduced. These include those in the media interior such as diabatic heating (caused by atmosphere and ocean convection and radiation transfer) and turbulent mixing. Also discussed will be forcing at the media boundary often called interfacial fluxes. These are related to the interior turbulent fluxes. We will look at the effects of the important tropical forcings of wind stress and heat flux. Reference : Gill Chapters 2 and 9. A postscript version of this lecture is available .


 

Linearization of the equations

Linearization about a state of rest will be first considered. The concept of stratification and the Brunt-Vasailla frequency introduced. The separation of vertical and horizontal variables will be performed and the resulting Sturm-Loiuville eigensystem in the vertical derived. This will introduce vertical modes. The equations satisfied by the separated horizontal part of the flow will be then examined. These are the shallow water equations. The projection of forcing onto modes will be detailed. Secondly linearization about a state of motion will be considered and this will serve to introduce concepts of instability theory such as normal modes and singular vectors. References : Parts of Gill Chapter 6 and Philander Chapter 4. A postscript version of this lecture is available .

 

Shallow water equations

The Sturm-Loiuville eigensystem in the horizontal in an equatorial channel will be introduced following separation of variables in the latitudinal and longitudinal directions. The dispersion relation will be solved and the Kelvin, Rossby and gravity waves introduced. The propagation of these waves in the equatorial wave guide will be derived. Reflection of the waves from eastern and western boundaries will also be analyzed. Reference: Gill Chapter 11. A postscript version of this lecture is available .


 

Tropical atmospheric dynamics

The effects of diabatic heating due to convection will be described and the so-called Gill model solved. The significance of convection in general will be closely analyzed. Atmospheric transients such as the Madden Julian Oscillation and easterly waves will be briefly described. The Walker and Hadley circulations will be introduced and the effects of non-linearity examined. References : Philander Chapter 5, Gill Chapter 11 and Holton. A postscript version of this lecture is available .

Equatorial ocean adjustment
The equatorial ocean and its dynamics is crucial to explaining climatic variability. Adjustment of the equatorial ocean to a variety of forcing will be derived and illustrated using the modal framework derived in the linearization and shallow water equation Lectures. A postscript version of this lecture is available .
The quasi-geostrophic approximation
The primitive equations are generally very difficult to analyze 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 ocean and atmosphere. Postscript Lecture notes are available here .
The general circulation
Basic latitudinal flows characterize the mean atmospheric and oceanic circulations. In the atmosphere the Hadley Cell is directly forced by diabatic heating while the Ferrel Cell is driven mainly by transient eddies. Models of these fundamental circulations are considered. Postscript Lecture notes are available here 

 

Coupled Ocean Atmosphere models of the El Nino phenomenon

El Nino is the dominant cause of short term climate variability and is a coupled ocean atmosphere phenomena. A typical simple mathematical model will be described in detail. Its behavior will be analyzed and the concept of the delayed action oscillator as a paradigm for El Nino introduced. Causes of the irregularity of El Nino will be discussed with supporting model results. Postscript Lecture notes are available here .


 

Predictability Theory
Geophysical (including climatic) systems are chaotic dynamical systems. This implies limits to their intrinsic predictability. Recent developments at the Courant in predictability theory are introduced and discussed.  Postscript Lecture notes are available here .