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.
Quick Links
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 Engler/Kaper, Chapter 7
- Apr 28, 2025
-
Some basic notions from dynamical systems: flow, attractor
(cf. Engler/Kaper, Chapter 3), 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 Exercise 1: writing a determinant
as a Laplace
expansion, change
of variables for multiple variables, Computing the leading Lyapunov
exponent in practice; Tangent propagator