This class covers the fundamentals of modeling weather and climate for undergraduate students of Mathematics and Data Science. It has the following main themes:
Introduction; The Lorenz equations as a paradigm (selected topics from Kaper/Engler, Chapter 7
Some basic notions from dynamical systems: flow, attractor (cf. Kaper/Engler, Chapter 4), Lyapunov exponents (see, e.g., these lecture notes from BYU)
No class due to MIDS event
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
Discussion of Problem Sheet 1
No class due to conference
Discussion and review
Introduction to linear response theory
A simple energy balance model for the earth (Kaper/Engler, Chapter 2)
Discussion of implementation issues for the linear response calculation on Problem Sheet 2
2-box model for the thermohaline circulation (Kaper/Engler, Chapter 3)
2-box model for the thermohaline circulation (finish); introduction to the Euler and Navier-Stokes equations