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 latex version of this
lecture is available
which has Figure
1, Figure2
and Figure
3.
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 latex version of this lecture is available
which has Figure
1 and Figure
2.
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 latex version of this lecture is available
which has Figure
1, Figure
2, Figure
3, Figure
4 and Figure
5.
Equatorial
ocean adjustment I:
Adjustment
of the equatorial shallow water equations to a variety of forcing will
be derived and illustrated using the modal framework derived in the previous
topic. Subjects addressed will include the Sverdrup balance; the Yoshida
jet, boundary reflections and the effect of dissipation. Reference:
Philander Chapter 3. A latex version of this lecture is available
which has Figure
1, Figure
2, Figure
3, Figure
4, Figure
5 and Figure
6.
Equatorial
ocean adjustment II:
Adjustment
of the full three-dimensional ocean will be examined using the vertical
mode framework. Topics covered will include the equatorial current system;
time dependent forcing; the role of varying dissipation on vertical modes;
remote versus local responses and the relative importance of non-linearity
to equatorial currents. Reference: Philander Chapter 4. A latex
version of this lecture is available
which has Figure
1, Figure
2, Figure
3, Figure
4, Figure
5 and Figure
6
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 latex version of this lecture is available
which has Figure
1, Figure
2, Figure
3, Figure
4, Figure
5 and Figure
6
Tropical
atmosphere-ocean coupling:
The
significance of wind stress, SST and heat flux will be described. A positive
feedback loop for the maintenance of El Nino will be covered in detail.
A more general framework for coupled instability will also be introduced.
It will be related to the concepts introduced in topic 3. References:
Philander Chapter 6 and article by Neelin et. al. in TOGA Decade Volume.
A latex version of this lecture is available
which has Figure
1, Figure
2, Figure
3, and Figure
4
Models
of the El Nino/Southern Oscillation (ENSO):
A
typical simple ENSO mathematical model will be described in detail. Its
behavior will be analyzed and the concept of the delayed action oscillator
as a paradigm for ENSO introduced. The model behavior will also be compared
to observations. Causes of the irregularity of ENSO will be discussed with
supporting model results. References: A selection of papers from
the climate literature. A latex version of this lecture is available
which has Figure
1, Figure
2a, Figure
2b, and Figure
3
The
effects of ENSO:
An
observational survey and commentary on the economic significance of this
phenomenon will be undertaken. Canonical atmospheric and oceanic teleconnections
will be presented. The mid-latitude atmospheric response to ENSO will be
examined with the help of barotropic framework. References: Philander
Chapters 1 and 2; article by Trenberth et. al. in TOGA Decade Volume. A
latex version of this lecture is available
which has Figure
1, Figure
2, Figure
3, Figure
4, Figure
5, Figure
6 and Figure
7.
Prediction
of ENSO:
The
types of models used will be described and the reason for the continuing
success of simple models explained. Factors currently limiting prediction
will be detailed. Observations needed for prediction will be described
and various methods of data assimilation briefly introduced. Finally fundamental
limitation to predictability will be reviewed as well theories for the
strong variations in prediction skill. A stochastic framework will be introduced
to unify these results as well as to explain the irregularity of ENSO.
References:
Article by Latif et. al. in TOGA Decade Volume; selected recent papers.
A latex version of this lecture is available
which has Figure
1, Figure
2, Figure
3, Figure
4, and Figure
5
