What Can Mathematicians Do About Climate Change?

For my Fields Institute project on Mathematics of Climate Change, I’m trying to compile a list of ways that mathematicians can help the human response to climate change.

Here’s a short list, with reading material for each one. I threw it together quite quickly. I’m sure I left out some big important topics, and I probably haven’t found the best reading material for many topics. Can you help out?

Before you try:

Note that right now I’m looking for topics that are abstract and general enough that they will resonate with mathematicians. I’m imagining that mathematicians could get interested in these topics and then go to workshops where they talk to those experts and get clued in to the details, and the applications to climate change.

Also note that I’m not including climate modeling—for example, solving nonlinear PDE to model the behavior of the oceans and atmosphere. The big question I’m interested in here is not what will the Earth do? but what should we do?

Finally, note that I’m looking for fairly broad topics, not individual problems within these topics. You should imagine these as possible topics for workshops or conferences.

Okay, here we go. The Wikipedia articles here are okay for a quick overview, but you’ll need to dig into their bibliographies to go further.

Parameter estimation

How can we improve methods for estimating parameters from data in complex models?

• Wikipedia, Estimation theory.

• William Broniec, Sungeun An, Spencer Rugabera and Ashok Goel, Guiding parameter estimation of agent-based modeling through knowledge-based function approximation.

Optimization

How can we optimize decisions when our models of these situations are complex and uncertain?

• Wikipedia, Mathematical optimization.

• Hoai An Le Thi, Hoai Minh Le and Tao Pham Dinh, Optimization of Complex Systems: Theory, Models, Algorithms and Applications. (Not open access, but available at LibGen.)

• Marco Janssen, Jan Rotmans, Kooze Vrieze, Climate change: optimization of response strategies. (Not open access, but available at LibGen and SciHub.)

General systems theory

How can existing work using modern mathematics to study general dynamical systems be leveraged to create better simulation software for improving the human response to climate change?

• David Jaz Myers, Categorical Systems Theory.

• Brendan Fong, The Algebra of Open and Interconnected Systems.

• Matteo Capucci, Bruno Gavranović, Jules Hedges and Eigil Fjeldgren Rischel, Towards foundations of categorical cybernetics.

• John Baez, Xiaoyan Li, Sophie Libkind, Nathaniel D. Osgood and Eric Redekopp, A categorical framework for modeling with stock and flow diagrams.

Agent-based models

What is a good general mathematical framework for agent-based models, that would allow them to be built in a transparent, unified yet flexible, and composable manner?

• Wikipedia, Agent-based model.

• Wikipedia, Agent-based computational economics.

• Wikipedia, Agent-based social simulation.

• Sharan S. Agrawal, Scalable Agent-Based Models for Optimized Policy Design: Applications to the Economics of Biodiversity and Carbon.

Uncertainty quantification

How should we measure the level of confidence or reliability of predictions?

• Wikipedia, Uncertainty quantification.

• Ralph C. Smith, Uncertainty Quantification: Theory, Implementation, and Applications. (Not open access, but see LibGen.)

Extreme events

How should we quantify the risks associated to low-probability but high-impact events?

• Wikipedia, Heavy tailed distribution.

• Wikipedia, Fat-tailed distribution.

• Wikipedia, Extreme value theory.

• Wikipedia, Tail risk.

Causal inference and attribution

How can we improve our frameworks for determining what causes what?

• Wikipedia, Causal inference.

• Wikipedia, Extreme event attribution.

• Judea Pearl, Causal inference in statistics: an overview, and other papers and books here.

Tipping points

How can we improve our ability to detect the approach to ‘tipping points’, where a system dramatically changes its behavior?

• Wikipedia, Tipping points in the climate system.

• Valerie Livina, Tipping Point Analysis and Applications.

• Valerie Livinia and Tim M. Lenton, A modified method for detecting incipient bifurcations in a dynamical system.

• T. M. Bury, C. T. Bauch and M. Anand, Detecting and distinguishing tipping points using spectral early warning signals.