A global climate model typically contains enough computer code to fill 18,000 pages of printed text; it will have taken hundreds of scientists many years to build and improve; and it can require a supercomputer the size of a tennis court to run. ¹

Climate modelling is similar to weather forecasting but at a timescale of decades instead of hours. Some metereological services use climate models for both.

At their most basic level, climate models use equations to represent the processes and interactions that drive the Earth’s climate. These cover the atmosphere, oceans, land and ice-covered regions of the planet.

A number of fundamental physics principals go into models:

• The first law of thermodynamics. i.e "in a closed system, energy cannot be lost or created, only changed from one form to another".
• The Stefan–Boltzmann law, i.e. that greenhouse gases naturally keep the earth about 33°C warmer than it would be.
• The Clausius-Clapeyron equation which "characterises the relationship between the temperature of the air and its maximum water vapour pressure".
• The Navier-Stokes equations of fluid motion, which "capture the speed, pressure, temperature and density of the gases in the atmosphere and the water in the ocean."

Climate models are typically written using Fortran!

The energy balance model

• Earth gets ALL energy from the sun. In turn, it returns energy to space. In general:
• Energy from sun that hits the earth is called a "solar flux", measured as watts/m².
• Energy in can roughly be calculated as , where S is a solar flux.
• "Albedo" is the reflectivity of the earth.
• Reflected energy is calculated as , where is the albedo
• The remaining energy is absorbed, either into the atmosphere or into Earth's surface. It's then converted to infrared energy and emitted from Earth to space as infrared radiation.
• A "black body" is a perfect absorber and emitter of radiation. Earth is not a black body, but it's relatively close to being one.
• Radiated energy is calculated as , where is the temperature of Earth and is the Stefan–Boltzmann constant.
• Therefore:

Statistics in climate science

The correlation between temperature and carbon dioxide levels does not necessarily imply a “causal” relationship. Before human activity became a dominant force affecting the climate, warmer temperatures from natural planetary cycles led to more ocean mixing and CO₂ release from oceans, leading to an increase in atmospheric CO₂, which then caused more warming as CO₂ trapped heat in the atmosphere. So in that long-ago time, an increase in temperatures caused an increase in CO₂ levels!

With statistical analysis of how temperature and CO₂ trends relate and an understanding of [radiative forcing](/notes/climate#Radiative forcing) we can have confidence there's a causal connection between CO2 and temperature.

How climate models work

Two important inputs are "spatial resolution" (i.e. the area looked at in individual parts of a model) and "time step" (i.e. how often a model calculates the climate).

Mathematically speaking, the correct approach [to choosing a time step] would be to keep decreasing the time step until the simulations are converged and the results stop changing. However, we normally lack the computational resources to run the models with a time step this small. Therefore, we are forced to tolerate a larger time step than we would ideally like. ²

Climate models generate a nearly complete picture of the Earth’s climate, including thousands of different variables across hourly, daily and monthly timeframes.

The main inputs of a climate model are:

• Sun output
• Greenhouse gases (carbon dioxide, methane, halocarbons, etc.)
• Aerosols

The main outputs are:

• Temperature and humidity of different layers of the atmosphere from the surface to the upper stratosphere, as well as temperatures, salinity and acidity (pH) of the oceans from the surface down to the sea floor.
• Estimates of rainfall, snow fall and cover, and the extent of glaciers, ice sheets, and sea ice.
• Wind speed, strength, and direction, and other similar climate phenomena like jet streams and ocean currents.

More unusual model outputs include cloud cover and height, along with more technical variables, such as surface upwelling longwave radiation – how much energy is emitted by the surface back up to the atmosphere – or how much sea salt comes off the ocean during evaporation and is accumulated on land.

Climate models also produce an estimate of “climate sensitivity”. That is, they calculate how sensitive the Earth is to increases in greenhouse gas concentrations, taking into account various climate feedbacks, such as water vapour and changes in reflectivity, or “albedo”, of the Earth surface associated with ice loss.

Today, most model projections use one or more of the “Representative Concentration Pathways” (RCPs), which provide plausible descriptions of the future, based on socio-economic scenarios of how global society grows and develops. ²

Notably, this technology continues to improve thanks to advances in a standard framework for climate modeling called CMIP, which stands for Coupled Model Intercomparison Project. ²

Uncertainty in climate models

Scientist Stephan Rasp summarizes the types of model uncertainties as follows:

Climate model uncertainty can be partitioned into three components: 1) model uncertainty (models are bad), 2) scenario uncertainty (we don't know how emissions will evolve) and 3) internal variability (random chaotic noise aka butterfly effect).

There's evidence that we're potentially underestimating greenhouse gas impacts in climate models.

A big reason for the uncertainty of models is the unpredictable behaviour of humans.

Models also currently underestimate extreme weather events. As an example, the 2022 heatwaves in Europe should have been "statistically impossible" under current climate models. ³

References

1. Q&A: How do climate models work? - Carbon Brief ↩

2. Terra.do coursework ↩ ↩² ↩³

3. Zeke Hausfather on Twitter ↩