Energy balance models
16
EBM with latitude IV
MA30287: Mathematics of Planet Earth
Preface
Lecture plan
Introduction
1
What does Mathematics of Planet Earth mean?
2
Conservation laws
3
Dimensional scaling analysis
4
Basic energy models
Practical applied mathematics
5
Asymptotic approximations I
6
Asymptotic approximations II
7
Numerical solutions of IVPs
8
Asymptotic approximations III
9
Nonlinear root finding
10
Numerical solutions of PDEs
11
The wine cellar problem
Energy balance models
12
EBM with nonlinear albedo
13
EBM with latitude I
14
EBM with latitude II
15
EBM with latitude III
16
EBM with latitude IV
Fast-slow dynamics
17
Ice ages I: an introduction
18
Ice ages II: a model for fast-slow dynamics
19
Ice ages III: analysis of the van der Pol equation
20
Fast-slow dynamics for higher-order systems
Box models of the ocean and environment
21
Basic models of the ocean
22
Stommel’s box model
23
Box models for flood estimation
Exercises
24
Problem set 1
25
Problem set 2
26
Problem set 3
27
Problem set 4
28
Problem set 5
29
Problem set 6
30
Problem set 7
31
Problem set 1 solutions
32
Problem set 2 solutions
33
Problem set 3 solutions
34
Problem set 4 solutions
35
Problem set 5 solutions
36
Problem set 6 solutions
37
Problem set 7 solutions
Problem classes
38
Problem class 1: an introduction to Noteable
39
Problem class 2: dimensional analysis
40
Problem class 3: BVPs
41
Problem class on PDEs and the CFL condition
Appendices
42
Differential equations
43
Dynamical systems
44
Vector calculus
45
Modelling
46
Finite difference approximations
47
Coding
48
An example of ChatGPT going wrong
References
Energy balance models
16
EBM with latitude IV
16
EBM with latitude IV
This chapter is currently kept free.
15
EBM with latitude III
Fast-slow dynamics