Math 2.0

Geophysics Definition

Climate model

Builds on Navier–Stokes equationsRadiative transfer equationPartial differential equationOrdinary differential equation

Definition

A climate model is a mathematical model of the climate system, given by:

  1. state variables, such as temperature, velocity, humidity, salinity and ice cover, for one or more components (atmosphere, ocean, land, ice, biosphere);
  2. ordinary or partial differential equations for these variables, from conservation of mass, momentum and energy, with radiation to space;
  3. prescribed external forcings, such as the incoming solar radiation and the atmospheric concentrations of greenhouse gases, or equations for them.

The climate predicted by the model is the statistics of its solutions over long times, rather than a single trajectory.

Remarks

Example: a general circulation model of the atmosphere solves the primitive equations on a grid over the globe. These approximate the Navier–Stokes equations for a thin layer on a rotating sphere, and are coupled with the radiative transfer equation. It meets clause 1 with fields on the grid, clause 2 with the primitive equations and the energy equation, and clause 3 with the solar input and the gas concentrations.

Non-example: a statistical fit of observed temperatures against time is not a climate model, since it has no evolution equations derived from conservation laws (clause 2 fails).

Processes too small for the grid, such as clouds and turbulence, enter through parameterisations, which express their average effect in terms of the resolved variables.

Reading path

To understand this page from the ground up, read these 5 pages in order. The foundations come first.

Show the path as a graph
Navier–Stokes equations, concept, no evidence levelNavier–Stokes equatio…conceptOrdinary differential equation, concept, no evidence levelOrdinary differential…conceptPartial differential equation, concept, no evidence levelPartial differential …conceptRadiative transfer equation, example, no evidence levelRadiative transfer eq…exampleClimate model, definition, no evidence levelClimate modeldefinition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Navier–Stokes equations concept
  2. Ordinary differential equation concept
  3. Partial differential equation concept
  4. Radiative transfer equation example
  5. Climate model definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Climate_model
About this page
Tag54FR8EYWZ6
URIm2://54FR8EYWZ6
Kinddefinition
WritingW0 stub
MSC86A08, 86A10, 35Q86
DefinesClimate model
UsesNavier–Stokes equations, Radiative transfer equation, Partial differential equation, Ordinary differential equation
Changed3 November 2026

Markdown · JSON · Edit on GitHub

What this page needs for W1

  • an inventory row: the row of the inventory that the node accounts for (0 of 1)
  • a source with a locator (0 of 1)

The writing levels say how complete the text of a page is. They do not measure its truth.

What links here

No page links to this page yet.