The Azimuth Project
Climate model



This page offers a quick introduction to climate models: the physical, chemical and biological processes they model, the various types of models, and implementation issues. For more detailed information we refer to more specialized pages on the various types of models.

For a good understanding of climate models, it is necessary to known some basics of Earth science. A good place to start is the overview of the energy balance of the atmosphere: Radiation balance of the atmosphere.

On this page we will also explain the terms forcing and feedback and we will give a simple example of an energy balance model.

Classification of models

While all models strive to hold up the first law of thermodynamics, the conservation of energy, the role of the second law involving Entropy is not quite clear yet.

Climate models can be classified according to their dimensionality:

Zero-dimensional models

Energy balance models (EBM) try to predict the average surface temperature of the Earth depending on the energy flow. Energy comes in from the sun and is radiated to outer space by the Earth. What happens in between is modelled by averaged feedback equations. Box models may also be seen as zero-dimensional models.

One-dimensional models

One-dimensional radiative-convective models include one dimensional processes of heat transport.

Earth models of intermediate complexity

An Earth model of intermediate complexity or EMIC typically has a 3D atmosphere and a slab ocean, or a 3D ocean and an energy-moisture balance atmosphere.

General and regional circulation models

General circulation models (or GCMs) try to model global convection and feedback processes and are the most complex models known today. Feedback processes include biological and chemical processes that influence e.g. green gas emission and absorption.

Modern IPCC-class GCMs are not, or have not recently, been run at 10 km resolution for climate change purposes. In the AR4? report, the models tended to be around ~100-km resolution. Clouds can be started to be resolved at ~10 km or below.

General circulation models used to simulate weather and climate do not operate at fine enough grid resolutions to resolve many observed regional weather and climate features. Higher resolution regional climate models? can be used, embedded in a GCM domain, to do physical downscaling of GCM output over a selected region.

Regional circulation models? (or RCMs) or limited-area atmospheric models are run at higher resolution than the GCMs and are thus able to better represent mesoscale dynamics and thermodynamics, including processes resulting from finer-scale topographic and land-surface features. Typically the regional atmospheric model is run while receiving lateral boundary condition inputs from a relatively-coarse resolution atmospheric analysis model or from the output of a GCM.

Modelling basics: forcing and feedback

Climate scientists use the terms ‘forcing’ and ‘feedback’, which are related to cause and effect:

Forcing denotes an external influence on a characteristic of the climate system. Example: Increased emission from the sun leads to an increase of the temperature.

Feedback denotes the reaction of the (climate) system to the forcing which, in return, leads to a change in the forcings.

The following example of feedback comes from the Met Office:

Clouds could create positive or negative climate feedbacks and are an ongoing area of research. One example is low-level clouds, especially stratocumulus, which help reflect sunlight and keep the Earth cool. The more stratocumulus we get over the planet, the more cooling effect. If our warming climate creates more low cloud, this would be a negative feedback — helping to offset the heating by reflecting more sunlight away from Earth. If our current climate change means there will be less low cloud overall, then this would be a positive feedback — contributing further to the warming by allowing more sunlight in.

A system with an overall positive feedback is unstable: any forcing will be strengthened by the feedback indefinitely. Earth’s climate is currently not unstable in this sense, thanks to the crucial Planck feedback: the higher the temperature of a radiating body, the more energy it radiates. This ensures an overall negative feedback. In climate science, the Planck feedback is often not mentioned and explained explicitly. Other feedbacks are often defined relative to it: people call the Planck feedback λ 0\lambda_0, and they call the sum of the rest λ\lambda. Climatologists tend to take it for granted, and talk about just the non-Planck feedbacks, λ\lambda.

For more information, including a list of the major climatic feedback loops, see our page on Climate forcing and feedback.

Some examples

A very simple 0-dimensional model

We assume that the temperature T responds to a forcing F according to a linear differential equation

dT/dt=k(F+LT) d T/d t = k(F + L T)

Here LL is the total climate feedback, tt is the time, and kk is a constant controlling the rate at which the system responds. Furthermore, we assume that CO2 concentration increases to double the pre-industrial level and then stays there. (This would still require a large cut in emissions.) Now we can calculate the equilibrium state by setting dT/dt=0d T/d t = 0 and obtain

T=F/L T = -F/L

This does not tell us how quickly the system will approach equilibrium (which would require estimating kk), it just tells us where the system will eventually end up. For a doubling of CO 2CO_2 concentration over pre-industrial levels (from 285 ppm to 570 ppm) FF is about 4.0 Wm 2Wm^{-2}. A much larger uncertainty comes from estimating LL. As described above, L=λ 0+λL = \lambda_0 + \lambda. λ\lambda can be further decomposed into a sum of various feedbacks corresponding to different mechanisms. The four main ones are:

  • water vapor

  • lapse rate

  • surface albedo (including ice albedo)

  • clouds

For more details, including estimates of the numerical values of these feedbacks, see the page Climate feedback.

The graphs below show the total feedback LL and its uncertainty, modelled with a normal distribution with mean -1.5 and standard deviation 0.5, and the corresponding result in temperature rise for F=4.0Wm 2F = 4.0 Wm^{-2}. The colours change at the 5%, 17%, 83%, and 95% percentiles. The results are similar to those of Knutti and Hegerl, 2008 (see the bottom panel of Fig 3a).

You can obtain the R code for feedback and sensitivity graphs.

Note: these graphs are intended as demonstrations of the connection between feedback and temperature, not as authoritative predictions. The fourth IPCC assessment estimates a range of 2 to 4.5 °C for the overall climate sensitivity (the warming due to a doubling of CO2), compared to the 1.2 °C warming with no feedbacks except the Planck feedback. See Section 8.6 of the AR4 WG1 report for model estimates and Section 9.6 for observational estimates.

A simple general circulation model

Isaac Held has written about a simple reference model to help understand conceptual behavior:

For more, see Fruit Fly Climate Model.

A regional circulation model

For an example of an RCM, see:

Stochastic methods

Climate models may deterministic or stochastic. A stochastic model is one that contains random processes, perhaps described by stochastic differential equations.

Software Engineering

The branch of study that is concerned with the overall quality, structure and maintainability of big software systems is usually called “software engineering”. Since climate model implementations are rather big and complex software projects, the role of Software engineering in climate science has been and is discussed by scientists of different background.


Program for Climate Model Diagnosis and Intercomparison

The Program for Climate Model Diagnosis and Intercomparison is an organization that develops tools for the diagnosiing and comparing of general circulation models (GCMs) that simulate the global climate.

Clear Climate Code

The Climate Code Foundation is running a project called Clear Climate Code, which is currently focusing on a re-implementation of GISTEMP? in Python.



As usual, it’s good to start with Wikipedia:

Nathan Urban gave an overview of some aspects of climate modeling in this series of interviews on the Azimuth Blog:

Here are notes for a basic course on the Earth’s climate:

For a historical overview, see:

A vision of how climate and weather models should evolve in the 2010-2020-decade:

A good introduction to simple climate models:

A complete introductory textbook on climate modelling:


The Earth System Modeling Framework (ESMF) is software for building and coupling weather, climate, and related models:

For GCM software, see GCM.

A radiative transfer model, written in FORTRAN is SBDART which can be downloaded here:

Strictly speaking the SBDART software does not implement a real climate model. It can be used to calculate one-dimensional radiative transfer profiles.

There is a little model project to built a climate model here on Azimuth:


category: climate