Phys 595 CL & Math 625
Mathematics and Physics of
Low Dimensional Mathematical Models of Climate
During the past decade, the study of global climate change has emerged
as one of the most pressing and important scientific disciplines of the
current era. This interdisciplinary course for math and physics
students is an introduction to the scientific and mathematical
foundations of climate science. Topics include the green house
thermodynamics, radiative transfer, and fluid dynamics. Simple
mathematical models will be developed for various coupled components of
the climate system, such as plane parallel models of the atmosphere and
radiative transfer, one-dimensional ice-albedo models, models of heat
transfer between ocean and atmosphere, and possibly models
incorporating two horizontal dimensions. Because of the
interdisciplinary nature of the course, it will be largely
self-contained; physical principles and mathematical techniques will be
carefully explained. Students may enroll for this course either
through Math 625 or Phys 595 CL.
||Mondays & Wednesdays, 5:00
to 6:15 p.m., Chaparral Hall 5117
|There will be
two midterm exams, each worth100 points, and a final exam worth 200
points. Collected homework, cumulatively, will contribute up to
grades (+) and minus grades (–) will be assigned for this
course. The dates of the midterms will be announced in
class. 5 bonus points may be earned for each Climate Seminar
Final Exam: Wednesday, May 14, 2014, 5:30 PM -
Introduction to Atmospheric Physics, Second Edition (2010) by David
G. Andrews. This will serve primarily as a reference for the
lectures. Additional references will be made available.
Eucalyptus Hall, Room 2105
(818) 677- 2171
Office Hours: MW 6:15 to 7:05 p.m.. & by Appointment
Santa Susana Hall, Room 127
web page: www.csun.edu/~vcmth00m
Office Hours: MW 4:00 to 4:50 p.m. & by Appointment
Global Warming Overview,
powerpoint from first lecture
Other Reference Books
Climate Physics, by F.W. Taylor
Fundamentals of Atmospheric Physics,
by M.L. Salby
An Introduction to Atmospheric
Radiation Dynamics, by K.N. Liou
A course in mathematics for students
of physics 2, by P. Bamberg & S. Sternberg
(for the Caratheodory-Born development of Thermodynamics)
CSUN Climate Science Program: www.csun.edu/climate
Intergovernmental Panel on
Transfer in the Earth, by Charlie Zender, UC Irvine
Discovery of Global Warming, by Spencer Weart, director of the
Center for History of Physics at the American Institute of Physics.
under the integral sign, by H. Flanders, American Mathematical
Monthly, vol. 80, 615-627, 1973
Ocean: NASA simulation of worldwide ocean currents
of Vector Calculus: Chapters 2 and 3 of this CSUN masters thesis,
by Rena Petrollo
Mathematics of the Environment,
a topic developed on Azimuth, by Prof. John
Baez, UC Riverside
1 – The mathematics of planet Earth.
2 – Simple estimates of the Earth’s temperature.
3 – The greenhouse effect.
4 – History of the Earth’s climate.
5 – A model showing bistability of the Earth’s climate due to the
ice albedo effect: statics.
6 – A model showing bistability of the Earth’s climate due to the
ice albedo effect: dynamics.
7 – Stochastic differential equations and stochastic resonance.
8 – A stochastic energy balance model and Milankovitch cycles.
9 – Changes in insolation due to changes in the eccentricity of the
10 – Didier Paillard’s model of the glacial cycles.
Exam Dates and Homework Assignments from Spring 2014
Assignment 1: Click here,
due Feb 10
Assignment 2: Click here,
due Feb 19
Assignment 3: Click here,
due March 5
Exam 1: Monday, March 17 on
atmospheric thermodynamics and zero dimensional climate models
Assignment 4: Click here,
due March 26
Assignment 5: Click here,
due April 21
To help strengthen your intution about Coriolis forces for Assignment 5
Demonstrations of Planetary-Style Fluid Dynamics, from Spin-Lab
Exam 2: Wed, April 23 on
radiative transfer in the atmosphere
Assignment 6: Click here.
Some Homework Assignments from Previous Offerings of the Course
(includes exercise on
derivation of Stephan-Boltzmann Law)
, includes exercises on equilibrium energy balance models
, exercises for
derivation of Planck's formula for Blackbody radiance and GRACE
satellite gravity field mapping
, remote sensing
Clapeyron, stress tensor