Phys 595 CL & Math 625

Mathematics and Physics of Climate Change

and

Low Dimensional Mathematical Models of Climate

Spring 2014

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 |

Grading |
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. |

Instructors |
Cristina
Cadavid Eucalyptus Hall, Room 2105 Phone: (818) 677- 2171 email: ana.cadavid@csun.edu Office Hours: MW 6:15 to 7:05 p.m.. & by Appointment David Klein Santa Susana Hall, Room 127 Phone: (818) 677-7792 email: david.klein@csun.edu, 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

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)

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: www.csun.edu/climate

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. http://www.aip.org/history/climate/index.htm

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: 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 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: Click here.

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

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