Climate modelling is the use of mathematical equations, physical laws, numerical methods and computer simulations to represent the behaviour of Earth's climate system and investigate how it responds to different conditions. A climate model represents interacting components such as the atmosphere, ocean, land surface, sea ice, glaciers, vegetation and sometimes chemical and carbon cycle processes.
Models divide the Earth or its atmosphere and ocean into computational grids and calculate how physical quantities such as temperature, pressure, humidity, wind, radiation, water and energy change through time. Different models vary in complexity, spatial resolution and the processes they represent explicitly. Climate models are not intended to reproduce every individual weather event decades in advance. Instead, they are designed to investigate statistics, large scale patterns, energy balances, physical mechanisms and long term responses to specified forcings. They are important tools for understanding past climate, interpreting observations, testing physical hypotheses and exploring possible future climate trajectories.
The foundations of climate modelling come from physical principles including conservation of energy, conservation of mass, conservation of momentum and the laws governing radiation, fluid dynamics, thermodynamics and phase changes. Atmospheric models solve equations describing the motion and thermodynamic state of air, while ocean models represent fluid circulation, temperature, salinity and mixing. Radiation schemes calculate how solar and infrared energy interacts with gases, clouds and surfaces. Land models represent processes such as soil moisture, evaporation, vegetation and snow.
Sea ice models simulate ice growth, melting, movement and interactions with the ocean and atmosphere. The coupled interaction of these components is essential because the climate system is interconnected. For example, atmospheric warming affects ocean temperature, ocean temperature influences evaporation and circulation, and changes in snow or sea ice alter surface reflectivity. A climate model therefore consists of many interacting physical representations rather than a single temperature equation.
Climate models use parameterisations for processes that occur at spatial or temporal scales too small to resolve directly. Clouds are a major example because individual cloud structures can be much smaller than the grid cells of many global climate models. Models therefore use mathematical relationships to represent the statistical effects of unresolved cloud formation, convection, turbulence and precipitation. Similar parameterisations may represent boundary layer processes, soil interactions, ocean mixing and other subgrid scale phenomena.
Parameterisations are based on observations, laboratory experiments, theory and higher resolution simulations, but they introduce uncertainty because no simplified representation captures every detail. Increasing computational power allows some processes to be represented at finer resolution, while specialised high resolution models can explicitly simulate phenomena that coarser models must parameterise. Model development therefore involves continual comparison between computational feasibility, physical realism and observational evidence.
General circulation models and Earth system models represent different levels of climate system complexity. A physical climate model may simulate the atmosphere, ocean, land and sea ice, while an Earth system model additionally represents components such as the carbon cycle, vegetation dynamics, atmospheric chemistry or other biogeochemical processes. Coupled models allow changes in one component to affect others.
For example, an Earth system model can simulate how vegetation responds to changing carbon dioxide and temperature, how those changes affect carbon storage and how the resulting atmospheric carbon dioxide concentration influences climate. Climate models can also be run at regional or global scales. Regional climate models use finer spatial resolution over limited areas and can provide information about local climate patterns, often driven at their boundaries by global model simulations or observations.
Climate models are evaluated against observations and historical climate records. Scientists may run a model using known historical greenhouse gas concentrations, volcanic forcing, solar changes, land use and other influences and compare the resulting climate statistics with observed temperature, precipitation, sea ice, ocean heat content and other variables. This process is called model evaluation or validation, although validation should not imply that a model becomes permanently proven correct. Models inevitably contain approximations and uncertainties.
Ensembles of multiple simulations help scientists examine the range of outcomes associated with model structural differences, internal climate variability and uncertain parameters. Hindcasts and historical simulations can test whether models reproduce broad observed patterns, while idealised experiments can isolate particular mechanisms. A model that performs well in one variable or region is not automatically accurate in every aspect of the climate system.
Climate projections are conditional on assumptions about future greenhouse gas emissions, land use, aerosols, socioeconomic development and other external influences. Scientists therefore use scenarios or pathways describing different possible future forcing trajectories. A projection is not necessarily a prediction that a particular socioeconomic pathway will occur; it is an internally consistent conditional estimate of what climate could look like under specified assumptions.
This distinction is important because future climate depends partly on human decisions that cannot be known with certainty decades in advance. Model ensembles can therefore produce multiple future trajectories corresponding to different forcing scenarios. The further into the future the simulation extends, the more the result depends on both physical climate response and assumptions about future emissions and other human influences.
Climate modelling is particularly useful for studying processes that cannot be isolated easily in observations. Scientists can conduct numerical experiments in which individual forcings are switched on or off, allowing investigation of the effects of greenhouse gases, volcanic aerosols, solar variability, land use and other factors. Models can also test feedback mechanisms such as water vapour, ice albedo, clouds, carbon cycle responses and ocean heat uptake.
They can simulate hypothetical climates that have no direct modern analogue and examine how changing boundary conditions affect circulation, precipitation and ecosystems. Model experiments are therefore analogous in some respects to controlled laboratory experiments, although they depend on the accuracy of the mathematical representation. Comparison between models, observations, theory and paleoclimate evidence provides multiple lines of evidence for assessing the robustness of conclusions.
Climate models have limitations and uncertainties that must be interpreted rather than ignored. Internal variability means that even a perfect model could produce different short term climate trajectories from different initial conditions. Model structural uncertainty arises because different models represent processes differently. Parameter uncertainty concerns values used within particular physical schemes. Scenario uncertainty results from uncertainty about future human activities. Some phenomena, especially regional precipitation, clouds, ice sheet dynamics and extreme events, remain particularly challenging to simulate.
These limitations do not mean that climate models are useless or that all outcomes are equally uncertain. Model skill varies by variable, location, timescale and process. Climate modelling is best understood as a quantitative framework grounded in physical laws and constrained by observations, used to estimate conditional climate responses and explore mechanisms. Its reliability comes from the combination of theory, observations, repeated testing, multiple models and physical consistency rather than from any assumption that a computer simulation can reproduce every detail of future weather.
