Sec. 5 A brief primer on climate modelling
Last update: Mon Jan 23 22:03:22 2023 -0500 (d07d3c4)
In Lab 1, we learned how to acquire data for the past, and perform a basic baseline analysis. In Lab 2 (Sec. 6), we will be looking the other direction, towards the future. Before we begin, this chapter serves as a primer on basic climate modelling.
Since we scientists do not have a crystal ball to tell the future of our climate system, we rely on models to provide us with one of many “possible futures”. Unlike fortune telling, climate modelling is based on our scientific understanding of the Earth’s climate system. Indeed, the most important point to be made for climate modelling is that, in principle, all climate models are based in the laws of physics: conservation of energy, conservation of mass, and conservation of momentum. As such, climate models provide a mathematical representation of the interactions among the distinct components of the Earth’s climate system.
5.1 Types of climate models
Climate models vary in complexity. The complexity of a model can depend on the number of dimensions represented in the model and/or the number of climate system components (e.g., atmosphere, ocean, land and sea ice) that the model examines.
5.1.1 Lower-dimensional models
Let’s first take a look at some examples of models of varying dimensionality. As we will see, models can have between zero to three dimensions (four it we include the time dimension).
5.1.1.1 0-D models
Among the earliest climate models were the zero-dimensional models, which only model the conservation of energy. A famous 0-D model is the Daisyworld model by Watson and Lovelock (1983) The Daisyworld model considered the manipulation of albedo, and its impact on temperature on the fictional planet of Daisyworld. While, by all considerations, a fairly simple model, Daisyworld represents many of the processes of climate change here on Earth, such as the ice-albedo feedback involved in arctic warming.
If you would like to see the output of a Daisyworld model, you can check out this implementation for Python, or this implementation for R.
5.1.2 3-D models and model components
Chances are, if you consider a climate model today, you are probably thinking about a 3-D model, specifically about a General Circulation Model or Global Climate Model (GCM). Three-dimensional models are based on important laws of physics, such as the conservation of energy, the conservation of momentum (atmospheric and oceanic flows), and the conservation of mass (atmospheric gasses, water vapour, and salt in the oceans), as well as many other theoretical and empirical physical relationships. These models require, at a minimum, a system of governing mathematical equations that represent our understanding of the Earth’s climate system, methods for solving these equations, good observational data of the boundary conditions (e.g. GHGs, aerosols, insolation, orography, etc.), and (without fail) considerable computing resources.
You may have noticed that we left out 2-D models, above. A two-dimensional climate model starts out as a 3-D model, but removes one of the dimensions (often longitude). By removing a dimension, we reduce the resources needed to compute the model. While 2-D models can be efficient for modelling simple processes, they have become less relevant as the cost of computing resources continues to decline.
3-D models can consist of a single climate system component, such as atmosphere-only GCMs or ocean-only GCMs. However, the term “GCM” most often refers to Coupled Global Climate Models (CGCMs) or Earth System Models (ESMs), which comprise several of these individual component models coupled together. These components exchange heat, water, and other variables, and thus, influence one another, making up the larger overall CGCM or ESM. State-of-the-art ESMs consist of all the main climate system components, atmosphere, ocean, land and sea ice, and also include some representation of biogeochemistry, atmospheric chemistry and/or the carbon cycle.
Throughout the lab exercises, we will make use of model output from the models that participated in the Coupled Model Intercomparison Project Phase 6 (CMIP6). CMIP6 is an international effort, involving 49 modelling teams and up to 72 individual models. CMIP6 model output were used to inform the IPCC Sixth Assessment Report. You can find more information about CMIP6 here.
The energy-balance model can be summarized by the following equation: \[ \textrm{Absorbed Solar Radiation} - \textrm{Outgoing Longwave Radiation} = \textrm{Energy Transport}\\ S(x,\alpha(T_s)) - F(x, T_s) = D(x, T_s)\\ \] Where \(x = \sin\phi\), \(\phi\) is the latitude, and \(\alpha\) is albedo. \(D\) represents the divergence of the horizontal energy flux, often approximated by downgradient diffusive horizontal heat transport.