Math 595 MP
Special Topics in Math/Physics
Topic for Spring Semester2020:
Climate Modeling

The global climate crisis is the greatest threat humanity has ever faced. At the current rate of greenhouse gas emissions, climate models predict a global average temperature rise of 4˚C to 7˚C beyond pre-industrial averages by the year 2100.  Climate scientists warn that a temperature rise within this range would likely lead to the collapse of civilization, and may even pose an existential threat to humanity and other life on this planet.  In 2018, the Intergovernmental Panel on Climate Change (IPCC) released a report to all governments of the world warning that drastic cuts in emissions of greenhouse gases must occur within the next eleven years to avoid irreversible consequences to Earth’s climate system. 

In this context, climate science has emerged as a leading scientific discipline at universities all around the world, and mathematics plays a key role (see for example, Mathematics of Planet Earth, 2013).  This semester, Math 595 MP will be devoted to the mathematical modeling of Earth’s climate with an emphasis on low dimensional models of the atmosphere and oceans. Topics include Energy Balance Models, Oceans and Climate, Introduction to Dynamical Systems, Radiative transfer, Hydrodynamics, Elementary Thermodynamics, and other topics as time permits.

Class Meetings              Mondays and Wednesdays, 5 to 6:15 pm, in CR 5117

Math 250, Math 351 (or Math 280), Math 462, or permission of the instructor

There will be two midterm exams, each worth 20%, and a final exam worth 40% of the grade.  Homework  will constitute 20% of the grade.  Plus (+) and minus (–) grades will be assigned for this course.  The date of the midterms will be announced in class. 

Primary: Mathematics & Climate, Hans Kaper, Hans Engler, SIAM 2013
Coverage: Chapters 1-5, 12-15, and 19 as time permits.

Secondary: Capitalism & Climate Change: The Science and Politics of Global Warming, David Klein, illustrated by Stephanie McMillan (free pdf download from link)

Instructor Information

David Klein
Santa Susana Hall,  Room 127  
Phone: (818) 677-7792
email:, web page:
Office Hours: MW 4:30 to 4:55 & by appointment

Additional References

Global Warming: Understanding the Forcast, by David Archer

Global Physical Climatology,
by Dennis Hartman
Fundamentals of Atmospheric Physics, by M.L. Salby

Atmospheric Science: An Introductory Survey, by Wallace and Hobbs

An Introduction to Atmospheric Physics, by D. G. Andrews

Elementary Climate Physics, by F.W. Taylor

Entropy Production of the Earth System, CSUN M.S. Thesis by Suanne Oh

General atmospheric circulation in an energy balance model, CSUN M.S. Thesis by Cord Perillo

Online Resources

Climate Overview: Powerpoint from first class meeting

CSUN Climate Science Program:

Intergovernmental Panel on Climate Change

Real Climate

    Dynamics sites (for Chap 14)

    Laboratory Demonstrations of Planetary-Style Fluid Dynamics, from Spin-Lab at UCLA

    Perpetual Ocean: NASA simulation of worldwide ocean currents

Exam dates and Homework Assignments

Assignment 1: Read Part 1 of Capitalism & Climate Change: The Science and Politics of Global Warming
and be able to explain clearly and concisely the green house effect (without equations).  Understand how the
carbon cycle works, and know which planet, Mercury or Venus, has the higher global average temperature and why.

Assignment 2: Read and understand Chapter 1 of Mathematics & Climate. 

Assignment 3.  Do these problems and turn in your solutions Wed Feb 5 in class.

Assignment 4.  Do these problems and turn in your solutions Wed Feb 12 in class.

Assignment 5.  Read Chapter 2 of Mathematics & Climate.  Read only: Exercises 1, 2, 3 (you essentially did these already
for Assignment 2).  Do Exercises 8, 11, 12, 14, and turn in your solutions to Excercises 8, 12, 14 Wed Feb 26 in class.  Don't
turn in your solution to Excercise 11, but be prepared to discuss it in class.

Assignment 6.  Do these problems and turn in your solutions Wed March 4 in class.

Exam 1 based on material covered since the beginning of the semester through Assignment 6, Wed, March 11

Assignment 7.  Do these problems and turn in your solutions Wed April 1 via email. 
Be sure to use black ink if you scan and email handwritten solutions.

Assignment 8. Do these problems and turn in your solutions Wed April 8 via email. 
Be sure to use black ink if you scan and email handwritten solutions.

Assignment 9. Do these problems.  Due Mon April 20.

Assignment 10. Do these problems.  Due Wed April 29.

Assignment 11.   Topics for last week of class: climate sensitivity, feedbacks, and geo-engineering.  Read or watch:

Reference for Climate Feedbacks

Thomas Stocker, Introduction to Climate Modelling, 2020 (revised), University of Bern. Download pdf from here:, Reference pages 38 to 49.

Geoengineering Overview

Watch Video: Geoengineering May Be the Answer to Climate Change:

Overview of Climate Crisis, Possible Solutions, and False Solutions

Skim: James Hansen et al, Young People's Burden: Requirement of Negative CO2 Emissions,

Read: David Klein, The Limits of Green Energy Under Capitalism,

Combined Midterm 2 and Final Exam to be available last day of class. Instructions: open book, open notes, open internet,
but NO discussions with other humans.
Due Thursday, May 14, 9 a.m.