Summer Semester 2025

Summary

This class covers the fundamentals of modeling weather and climate for undergraduate students of Mathematics and Data Science. It has the following main themes:

  • Simple models that illustrate the difference between weather and climate from a dynamical systems viewpoint (Lorenz model) and simple models of climate (energy balance models),
  • Fundamental equations of geophysical fluid dynamics and basic phenomenology,
  • Depending on time and interest: focus more in-depth on selected aspects, and/or do simple practical experiments with a toy climate model.

Textbooks

  • Shen, Somerville, Climate Mathematics: Theory and Applications, Cambridge University Press, 2019
  • Engler, Kaper, Mathematics of Climate, SIAM, 2013
  • Warner, Numerical Weather and Climate Prediction, Cambridge University Press, 2010

Grading

  • Regular exercise assignments
  • The grade for this class is determined by a final oral exam
  • Successful submission of exercises will add a grade bonus of 2/3 of a grade step to your final grade. Note that the pass/fail decision is not affected by the bonus, and the top grade can be achieved without the bonus.

Topics

Apr 24, 2025

Introduction; The Lorenz equations as a paradigm (selected topics from Kaper/Engler, Chapter 7

Apr 28, 2025

Some basic notions from dynamical systems: flow, attractor (cf. Kaper/Engler, Chapter 4), Lyapunov exponents (see, e.g., these lecture notes from BYU)

May 5, 2025

No class due to MIDS event

May 8, 2025

Background knowledge for completing Problem Sheet 1: writing a determinant as a Laplace expansion, change of variables for multiple variables, Computing the leading Lyapunov exponent in practice; Tangent propagator

May 12, 2025

Discussion of Problem Sheet 1

May 15, 2025

No class due to conference

May 19, 2025

Discussion and review

May 22, 2025

Introduction to linear response theory

May 26, 2025

A simple energy balance model for the earth (Kaper/Engler, Chapter 2)

May 30, 2025

Discussion of implementation issues for the linear response calculation on Problem Sheet 2

June 3, 2025

2-box model for the thermohaline circulation (Kaper/Engler, Chapter 3)

June 12, 2025

2-box model for the thermohaline circulation (finish); introduction to the Euler and Navier-Stokes equations