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Phys 595 CL & Math 625 Mathematics and Physics of Climate Change and Low

Dimensional Mathematical Models of Climate Spring 2014

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 effect, atmospheric 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.


Class Meetings 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 100 points. Plus 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 presentation attended.

Final Exam: Wednesday, May 14, 2014, 5:30 PM - 7:30 PM

Textbook An 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.


Cristina Cadavid
Eucalyptus Hall, Room 2105
Phone: (818) 677- 2171
Office Hours: MW 6:15 to 7:05 p.m. & by Appointment

David Klein
Santa Susana Hall, Room 127
Phone: (818) 677-7792
web page:
Office Hours: MW 4:00 to 4:50 p.m. & by Appointment

Global Warming Overview, powerpoint from first lecture

Other Reference Books

Elementary 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)

Online Resources

CSUN Climate Science Program:

Intergovernmental Panel on Climate Change

Real Climate

Radiative Transfer in the Earth, by Charlie Zender, UC Irvine

The Discovery of Global Warming, by Spencer Weart, director of the Center for History of Physics at the American Institute of Physics.

Differentiation under the integral sign, by H. Flanders, American Mathematical Monthly, vol. 80, 615-627, 1973

Perpetual Ocean: NASA simulation of worldwide ocean currents

Review 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

  • Part 1 – The mathematics of planet Earth.
  • Part 2 – Simple estimates of the Earth’s temperature.
  • Part 3 – The greenhouse effect.
  • Part 4 – History of the Earth’s climate.
  • Part 5 – A model showing bistability of the Earth’s climate due to the ice albedo effect: statics.
  • Part 6 – A model showing bistability of the Earth’s climate due to the ice albedo effect: dynamics.
  • Part 7 – Stochastic differential equations and stochastic resonance.
  • Part 8 – A stochastic energy balance model and Milankovitch cycles.
  • Part 9 – Changes in insolation due to changes in the eccentricity of the Earth’s orbit.
  • Part 10 – Didier Paillard’s model of the glacial cycles.
  • Exam Dates and Homework Assignments from Spring 2014

    Assignment 1: download Assignment 1, due Feb 10

    Assignment 2: download Assignment 2, due Feb 19

    Assignment 3: download Assignment 3, due March 5

    Exam 1: Monday, March 17 on atmospheric thermodynamics and zero dimensional climate models

    Assignment 4: download Assignment 4, due March 26

    Assignment 5: download Assignment 5, due April 21

    To help strengthen your intution about Coriolis forces for Assignment 5 watch:
    Laboratory Demonstrations of Planetary-Style Fluid Dynamics, from Spin-Lab at UCLA

    Exam 2: Wed, April 23 on radiative transfer in the atmosphere

    Assignment 6: download Assignment 6.

    Some Homework Assignments from Previous Offerings of the Course
    Spring 2011 Assignment (includes exercise on derivation of Stephan-Boltzmann Law)
    Spring 2012 Assignment 1, includes exercises on equilibrium energy balance models
    Assignment 2, thermodynamics exercises
    Assignment 3, exercises for derivation of Planck's formula for Blackbody radiance and GRACE satellite gravity field mapping
    Assignment 4, radiative transfer exercises
    Assignment 5, remote sensing exercises (mathematical)
    Assignment 6, Claussius Clapeyron, stress tensor

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