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Climate models are systems of differential equations based on the basic laws of physics, fluid motion, and chemistry. To "run" a model, scientists divide the planet into a 3-dimensional grid, apply the basic equations, and evaluate the results. Atmospheric models calculate winds, heat transfer, radiation, relative humidity, and surface hydrology within each grid and evaluate interactions with neighboring points.[1]

A general circulation model (GCM) is a type of climate model. It employs a mathematical model of the general circulation of a planetary atmosphere or ocean. It uses the Navier–Stokes equations on a rotating sphere with thermodynamic terms for various energy sources (radiation, latent heat). These equations are the basis for computer programs used to simulate the Earth's atmosphere or oceans. Atmospheric and oceanic GCMs (AGCM and OGCM) are key components along with sea ice and land-surface components.

GCMs and global climate models are used for weather forecasting, understanding the climate, and forecasting climate change.

Atmospheric GCMs (AGCMs) model the atmosphere and impose sea surface temperatures as boundary conditions. Coupled atmosphere-ocean GCMs (AOGCMs, e.g. HadCM3, EdGCM, GFDL CM2.X, ARPEGE-Climat)[2] combine the two models. The first general circulation climate model that combined both oceanic and atmospheric processes was developed in the late 1960s at the NOAA Geophysical Fluid Dynamics Laboratory[3] AOGCMs represent the pinnacle of complexity in climate models and internalise as many processes as possible. However, they are still under development and uncertainties remain. They may be coupled to models of other processes, such as the carbon cycle, so as to better model feedback effects. Such integrated multi-system models are sometimes referred to as either "earth system models" or "global climate models."

Versions designed for decade to century time scale climate applications were created by Syukuro Manabe and Kirk Bryan at the Geophysical Fluid Dynamics Laboratory (GFDL) in Princeton, New Jersey.[1] These models are based on the integration of a variety of fluid dynamical, chemical and sometimes biological equations.

Terminology

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The acronym GCM originally stood for General Circulation Model. Recently, a second meaning came into use, namely Global Climate Model. While these do not refer to the same thing, General Circulation Models are typically the tools used for modeling climate, and hence the two terms are sometimes used interchangeably. However, the term "global climate model" is ambiguous and may refer to an integrated framework that incorporates multiple components including a general circulation model, or may refer to the general class of climate models that use a variety of means to represent the climate mathematically.

Atmospheric and oceanic models

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Further information: Atmospheric model and Oceanic model

Atmospheric (AGCMs) and oceanic GCMs (OGCMs) can be coupled to form an atmosphere-ocean coupled general circulation model (CGCM or AOGCM). With the addition of submodels such as a sea ice model or a model for evapotranspiration over land, AOGCMs become the basis for a full climate model.[4]

Structure

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General Circulation Models (GCMs) discretise the equations for fluid motion and energy transfer and integrate these over time. Unlike simpler models, GCMs divide the atmosphere and/or oceans into grids of discrete "cells", which represent computational units. Unlike simpler models which make mixing assumptions, processes internal to a cell—such as convection—that occur on scales too small to be resolved directly are parameterised at the cell level, while other functions govern the interface between cells.

Three-dimensional (more properly four-dimensional) GCMs apply discrete equations for fluid motion and integrate these forward in time. They contain parameterisations for processes such as convection that occur on scales too small to be resolved directly.

A simple general circulation model (SGCM) consists of a dynamic core that relates properties such as temperature to others such as pressure and velocity. Examples are programs that solve the primitive equations, given energy input and energy dissipation in the form of scale-dependent friction, so that atmospheric waves with the highest wavenumbers are most attenuated. Such models may be used to study atmospheric processes, but are not suitable for climate projections.

Atmospheric GCMs (AGCMs) model the atmosphere (and typically contain a land-surface model as well) using imposed sea surface temperatures (SSTs).[5] They may include atmospheric chemistry.

AGCMs consist of a dynamical core that integrates the equations of fluid motion, typically for:

  • surface pressure
  • horizontal components of velocity in layers
  • temperature and water vapor in layers
  • radiation, split into solar/short wave and terrestrial/infrared/long wave
  • parameters for:

A GCM contains prognostic equations that are a function of time (typically winds, temperature, moisture, and surface pressure) together with diagnostic equations that are evaluated from them for a specific time period. As an example, pressure at any height can be diagnosed by applying the hydrostatic equation to the predicted surface pressure and the predicted values of temperature between the surface and the height of interest. Pressure is used to compute the pressure gradient force in the time-dependent equation for the winds.

OGCMs model the ocean (with fluxes from the atmosphere imposed) and may contain a sea ice model. For example, the standard resolution of HadOM3 is 1.25 degrees in latitude and longitude, with 20 vertical levels, leading to approximately 1,500,000 variables.

AOGCMs (e.g. HadCM3, GFDL CM2.X) combine the two submodels. They remove the need to specify fluxes across the interface of the ocean surface. These models are the basis for model predictions of future climate, such as are discussed by the IPCC. AOGCMs internalise as many processes as possible. They have been used to provide predictions at a regional scale. While the simpler models are generally susceptible to analysis and their results are easier to understand, AOGCMs may be nearly as hard to analyse as the climate itself.

Grid

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The fluid equations for AGCMs are made discrete using either the finite difference method or the spectral method. For finite differences, a grid is imposed on the atmosphere. The simplest grid uses constant angular grid spacing (i.e., a latitude/longitude grid). However, non-rectangular grids (e.g., icosahedral) and grids of variable resolution [6] are more often used.[7] The LMDz model can be arranged to give high resolution over any given section of the planet. HadGEM1 (and other ocean models) use an ocean grid with higher resolution in the tropics to help resolve processes believed to be important for the El Niño Southern Oscillation (ENSO). Spectral models generally use a Gaussian grid, because of the mathematics of transformation between spectral and grid-point space. Typical AGCM resolutions are between 1 and 5 degrees in latitude or longitude: HadCM3, for example, uses 3.75 in longitude and 2.5 degrees in latitude, giving a grid of 96 by 73 points (96 x 72 for some variables); and has 19 vertical levels. This results in approximately 500,000 "basic" variables, since each grid point has four variables (u,v, T, Q), though a full count would give more (clouds; soil levels). HadGEM1 uses a grid of 1.875 degrees in longitude and 1.25 in latitude in the atmosphere; HiGEM, a high-resolution variant, uses 1.25 x 0.83 degrees respectively.[8] These resolutions are lower than is typically used for weather forecasting.[9] Ocean resolutions tend to be higher, for example, HadCM3 has 6 ocean grid points per atmospheric grid point in the horizontal.

For a standard finite difference model, uniform gridlines converge towards the poles. This would lead to computational instabilities (see CFL condition) and so the model variables must be filtered along lines of latitude close to the poles. Ocean models suffer from this problem too, unless a rotated grid is used in which the North Pole is shifted onto a nearby landmass. Spectral models do not suffer from this problem. Some experiments use geodesic grids[10] and icosahedral grids, which (being more uniform) do not have pole-problems. Another approach to solving the grid spacing problem is to deform a Cartesian cube such that it covers the surface of a sphere.[11]

Flux buffering

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Some early versions of AOGCMs required an ad hoc process of "flux correction" to achieve a stable climate. This resulted from separately prepared ocean and atmospheric models that each used an implicit flux from the other component different than that component could produce. Such a model failed to match observations. However, if the fluxes were 'corrected', the factors that led to these unrealistic fluxes might be unrecognised, which could affect model sensitivity. As a result, the vast majority of models used in the current round of IPCC reports do not use them. The model improvements that now make flux corrections unnecessary include improved ocean physics, improved resolution in both atmosphere and ocean, and more physically consistent coupling between the atmosphere and ocean submodels. Improved models now maintain stable, multi-century simulations of surface climate that are considered to be of sufficient quality to allow their use for climate projections.[12]

Convection

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Moist convection releases latent heat and is important to the Earth's energy budget. Convection occurs on too small a scale to be resolved by climate models, and hence it must be handled via parameters. This has been done since the 1950s. Akio Arakawa did much of the early work, and variants of his scheme are still used,[13] although a variety of different schemes are now in use.[14][15][16] Clouds are also typically handled with a parameter, for a similar lack of scale. Limited understanding of clouds has limited the success of this strategy, but not due to some inherent shortcomings of the method.[17]

Software

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Most models include software to diagnose a wide range of variables for comparison with observations or study of atmospheric processes. An example is the 2-metre temperature, which is the standard height for near-surface observations of air temperature. This temperature is not directly predicted from the model but is deduced from surface and lowest-model-layer temperatures. Other software is used for creating plots and animations.

Projections

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Main article: Global warming
Projected annual mean surface air temperature from 1970 to 2100, based on SRES emissions scenario A1B, using the NOAA GFDL CM2.1 climate model (credit: NOAA Geophysical Fluid Dynamics Laboratory)[18]

Coupled AOGCMs use transient climate simulations to project/predict climate changes under various scenarios. These can be idealised scenarios (most commonly, CO2 emissions increasing at 1%/yr) or based on recent history (usually the "IS92a" or more recently the SRES scenarios). Which scenarios are most realistic remains uncertain.

The 2001 IPCC Third Assessment Report Figure 9.3 shows the global mean response of 19 different coupled models to an idealised experiment in which emissions increased at 1% per year.[19] Figure 9.5 shows the response of a smaller number of models to more recent trends. For the 7 climate models shown there, the temperature change to 2100 varies from 2 to 4.5 °C with a median of about 3 °C.

Future scenarios do not include unknown events – for example, volcanic eruptions or changes in solar forcing. These effects are believed to be small in comparison to greenhouse gas (GHG) forcing in the long term, but large volcanic eruptions, for example, can exert a substantial temporary cooling effect.

Human GHG emissions are a model input, although it is possible to include an economic/technological submodel to provide these as well. Atmospheric GHG levels are usually supplied as an input, though it is possible to include a carbon cycle model that reflects vegetation and oceanic processes to calculate such levels.

Emissions scenarios

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See also: Economics of global warming: Scenarios
In the 21st century, changes in global mean temperature are projected to vary across the world
Projected change in annual mean surface air temperature from the late 20th century to the middle 21st century, based on SRES emissions scenario A1B (credit: NOAA Geophysical Fluid Dynamics Laboratory)[18]

For the six SRES marker scenarios, IPCC (2007:7–8) gave a "best estimate" of global mean temperature increase (2090–2099 relative to the period 1980–1999) of 1.8 °C to 4.0 °C.[20] Over the same time period, the "likely" range (greater than 66% probability, based on expert judgement) for these scenarios was for a global mean temperature increase of 1.1 to 6.4 °C.[20]

In 2008 a study made climate projections using several emission scenarios.[21] In a scenario where global emissions start to decrease by 2010 and then decline at a sustained rate of 3% per year, the likely global average temperature increase was predicted to be 1.7 °C above pre-industrial levels by 2050, rising to around 2 °C by 2100. In a projection designed to simulate a future where no efforts are made to reduce global emissions, the likely rise in global average temperature was predicted to be 5.5 °C by 2100. A rise as high as 7 °C was thought possible, although less likely.

Another no-reduction scenario resulted in a median warming over land (2090–99 relative to the period 1980–99) of 5.1 °C. Under the same emissions scenario but with a different model, the predicted median warming was 4.1 °C.[22]

Model accuracy

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SST errors in HadCM3
North American precipitation from various models
Temperature predictions from some climate models assuming the SRES A2 emissions scenario

AOGCMs internalise as many processes as are sufficiently understood. However, they are still under development and significant uncertainties remain. They may be coupled to models of other processes in Earth system models, such as the carbon cycle, so as to better model feedback. Most recent simulations show "plausible" agreement with the measured temperature anomalies over the past 150 years, when driven by observed changes in greenhouse gases and aerosols. Agreement improves by including both natural and anthropogenic forcings.[23][24][25]

Imperfect models may nevertheless produce useful results. GCMs are capable of reproducing the general features of the observed global temperature over the past century.[23]

A debate over how to reconcile climate model predictions that upper air (tropospheric) warming should be greater than observed surface warming, some of which appeared to show otherwise,[26] was resolved in favour of the models, following data revisions.

Cloud effects are a significant area of uncertainty in climate models. Clouds have competing effects on climate. They cool the surface by reflecting sunlight into space; they warm it by increasing the amount of infrared radiation transmitted from the atmosphere to the surface.[27] In the 2001 IPCC report possible changes in cloud cover were highlighted as a major uncertainty in predicting climate.[28][29]

Climate researchers around the world use climate models to understand the climate system. Thousands of papers have been published about model-based studies. Part of this research is to improve the models.

In 2000, a comparison between measurements and dozens of GCM simulations of ENSO-driven tropical precipitation, water vapor, temperature, and outgoing longwave radiation found similarity between measurements and simulation of most factors. However, the simulated change in precipitation was about one-fourth less than what was observed. Errors in simulated precipitation imply errors in other processes, such as errors in the evaporation rate that provides moisture to create precipitation. The other possibility is that the satellite-based measurements are in error. Either indicates progress is required in order to monitor and predict such changes.[30]

The precise magnitude of future changes in climate is still uncertain;[31] for the end of the 21st century (2071 to 2100), for SRES scenario A2, the change of global average SAT change from AOGCMs compared with 1961 to 1990 is +3.0 °C (5.4 °F) and the range is +1.3 to +4.5 °C (+2.3 to 8.1 °F).

The IPCC's Fifth Assessment Report asserted "very high confidence that models reproduce the general features of the global-scale annual mean surface temperature increase over the historical period". However, the report also observed that the rate of warming over the period 1998–2012 was lower than that predicted by 111 out of 114 Coupled Model Intercomparison Project climate models.[32]

Relation to weather forecasting

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The global climate models used for climate projections are similar in structure to (and often share computer code with) numerical models for weather prediction, but are nonetheless logically distinct.

Most weather forecasting is done on the basis of interpreting numerical model results. Since forecasts are typically a few days or a week and sea surface temperatures change relatively slowly, such models do not usually contain an ocean model but rely on imposed SSTs. They also require accurate initial conditions to begin the forecast – typically these are taken from the output of a previous forecast, blended with observations. Weather predictions are required at higher temporal resolutions than climate projections, often sub-hourly compared to monthly or yearly averages for climate. However, because weather forecasts only cover around 10 days the models can also be run at higher vertical and horizontal resolutions than climate mode. Currently the ECMWF runs at 9 km (5.6 mi) resolution[33] as opposed to the 100-to-200 km (62-to-124 mi) scale used by typical climate model runs. Often local models are run using global model results for boundary conditions, to achieve higher local resolution: for example, the Met Office runs a mesoscale model with an 11 km (6.8 mi) resolution[34] covering the UK, and various agencies in the US employ models such as the NGM and NAM models. Like most global numerical weather prediction models such as the GFS, global climate models are often spectral models[35] instead of grid models. Spectral models are often used for global models because some computations in modeling can be performed faster, thus reducing run times.

Computations

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This visualization shows early test renderings of a global computational model of Earth's atmosphere based on data from NASA's Goddard Earth Observing System Model, Version 5 (GEOS-5).

Climate models use quantitative methods to simulate the interactions of the atmosphere, oceans, land surface and ice.

All climate models take account of incoming energy as short wave electromagnetic radiation, chiefly visible and short-wave (near) infrared, as well as outgoing energy as long wave (far) infrared electromagnetic radiation from the earth. Any imbalance results in a change in temperature.

The most talked-about models of recent years relate temperature to emissions of greenhouse gases. These models project an upward trend in the surface temperature record, as well as a more rapid increase in temperature at higher altitudes.[36]

Three (or more properly, four since time is also considered) dimensional GCM's discretise the equations for fluid motion and energy transfer and integrate these over time. They also contain parametrisations for processes such as convection that occur on scales too small to be resolved directly.

Atmospheric GCMs (AGCMs) model the atmosphere and impose sea surface temperatures as boundary conditions. Coupled atmosphere-ocean GCMs (AOGCMs, e.g. HadCM3, EdGCM, GFDL CM2.X, ARPEGE-Climat[37]) combine the two models.

Models range in complexity:

  • A simple radiant heat transfer model treats the earth as a single point and averages outgoing energy
  • This can be expanded vertically (radiative-convective models), or horizontally
  • Finally, (coupled) atmosphere–ocean–sea ice global climate models discretise and solve the full equations for mass and energy transfer and radiant exchange.
  • Box models treat flows across and within ocean basins.

Other submodels can be interlinked, such as land use, allowing researchers to predict the interaction between climate and ecosystems.

Comparison with other climate models

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Main article: Climate model

Earth-system models of intermediate complexity (EMICs)

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Main article: Earth systems model of intermediate complexity

The Climber-3 model uses a 2.5-dimensional statistical-dynamical model with 7.5° × 22.5° resolution and time step of 1/2 a day. An oceanic submodel is MOM-3 (Modular Ocean Model) with a 3.75° × 3.75° grid and 24 vertical levels.[38]

Radiative-convective models (RCM)

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One-dimensional, radiative-convective models were used to verify basic climate assumptions in the 1980s and 1990s.[39]

Earth system models

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GCMs can form part of Earth system models, e.g. by coupling ice sheet models for the dynamics of the Greenland and Antarctic ice sheets, and one or more chemical transport models (CTMs) for species important to climate. Thus a carbon chemistry transport model may allow a GCM to better predict anthropogenic changes in carbon dioxide concentrations. In addition, this approach allows accounting for inter-system feedback: e.g. chemistry-climate models allow the effects of climate change on the ozone hole to be studied.[40]

History

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See also: Numerical weather prediction § History

In 1956, Norman Phillips developed a mathematical model that could realistically depict monthly and seasonal patterns in the troposphere. It became the first successful climate model.[41][42] Following Phillips's work, several groups began working to create GCMs.[43] The first to combine both oceanic and atmospheric processes was developed in the late 1960s at the NOAA Geophysical Fluid Dynamics Laboratory.[1] By the early 1980s, the United States' National Center for Atmospheric Research had developed the Community Atmosphere Model; this model has been continuously refined.[44] In 1996, efforts began to model soil and vegetation types.[45] Later the Hadley Centre for Climate Prediction and Research's HadCM3 model coupled ocean-atmosphere elements.[43] The role of gravity waves was added in the mid-1980s. Gravity waves are required to simulate regional and global scale circulations accurately.[46]

See also

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References

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Further reading

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

General circulation model

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from Grokipedia
A general circulation model (GCM) is a numerical framework that applies the fundamental equations of , , and to replicate the large-scale circulation patterns of a planetary atmosphere or . These models discretize continuous physical processes into a three-dimensional grid of computational cells, enabling the prediction of patterns over short timescales and states over decades or centuries by integrating conservation laws for , , , and moisture. Pioneered in 1956 by Norman Phillips, who demonstrated the feasibility of such simulations using a two-level quasi-geostrophic model on early computers, GCMs evolved from efforts to understand atmospheric dynamics and extend principles to global scales. Early models focused on atmospheric components alone, but coupled atmosphere-ocean GCMs emerged in the 1980s to capture interactions across Earth's , including land surface and processes. These advancements have supported projections of phenomena like global temperature changes and precipitation shifts, though empirical validation remains constrained by computational limits and observational gaps. Despite their foundational role in climate science, GCMs exhibit significant uncertainties arising from the parameterization of subgrid-scale processes—such as , , and —that cannot be explicitly resolved due to grid resolutions typically spanning tens to hundreds of kilometers. Structural differences across models lead to divergent simulations of key feedbacks, like tropical responses, contributing to wide ranges in equilibrium estimates. Peer-reviewed assessments highlight that while GCMs reproduce broad observed features, such as seasonal cycles, their long-term predictive skill is limited by incomplete representation of natural variability and effects, underscoring the need for ongoing empirical scrutiny over reliance on ensemble averages.

Definition and Fundamentals

Terminology and Scope

A general circulation model (GCM) is a numerical representation that approximates the three-dimensional, time-dependent solutions to the equations governing fluid motion in planetary atmospheres or oceans, discretized on a global grid to compute variables such as temperature, velocity components, pressure, and precipitation. These models incorporate physical laws derived from , , and , driven primarily by spatial gradients in solar insolation, planetary rotation via the Coriolis effect, and surface boundary conditions like and land-ocean contrasts. The terminology "general circulation" specifically denotes the simulation of large-scale, statistically steady patterns of , , and transport, as opposed to localized or transient phenomena. In scope, GCMs encompass global domains spanning from the surface to the upper atmosphere or depths, resolving explicit dynamics for grid-scale processes while parameterizing unresolved subgrid-scale phenomena such as , , and cloud microphysics. Atmospheric GCMs (AGCMs) focus solely on tropospheric and stratospheric circulation, often coupled to prescribed sea surface temperatures for climate studies; oceanic GCMs (OGCMs) analogously simulate currents, , and ; and coupled atmosphere-ocean GCMs integrate these with land surface and components to capture feedbacks in the full , emphasizing Earth's energy balance over multi-year to centennial timescales. Unlike models, which apply similar dynamical cores but prioritize high-resolution initial-value forecasts over days using real-time observations, GCMs generate ensemble statistics for long-term means, variability, and projections under forcing scenarios, such as altered concentrations. This distinction arises from computational constraints and the chaotic nature of atmospheric flows, where GCMs average over ensembles to isolate forced responses from internal variability. The foundational coupled GCM, developed at the Geophysical Fluid Dynamics Laboratory in the , marked the shift toward comprehensive Earth system simulations, enabling attribution of observed climate changes to natural versus anthropogenic drivers. Modern GCMs, as used in assessments like those from the , typically feature horizontal resolutions of 50– km and vertical layers numbering 20–100, balancing fidelity to observations with feasible computation on supercomputers.

Governing Physical Principles

General circulation models (GCMs) derive their foundational dynamics from the conservation laws of physics, including mass, momentum, and energy, applied to fluid motion on a rotating sphere. These principles are encapsulated in the primitive equations, a set of partial differential equations that approximate the compressible Navier-Stokes equations under the hydrostatic balance assumption, which holds for large-scale flows where vertical accelerations are negligible compared to gravitational forces. The primitive equations thus prioritize horizontal momentum balance influenced by Coriolis forces, pressure gradients, and frictional effects, while treating vertical structure through hydrostatic equilibrium: ∂p/∂z=−ρg\partial p / \partial z = -\rho g, where pp is pressure, ρ\rho is density, gg is gravity, and zz is height. The horizontal momentum equations in the primitive set are: DuDt+fk×u=−1ρ∇pϕ+F,\frac{D\mathbf{u}}{Dt} + f \mathbf{k} \times \mathbf{u} = -\frac{1}{\rho} \nabla_p \phi + \mathbf{F}, where u\mathbf{u} is the horizontal vector, D/DtD/Dt is the , f=2Ωsin⁡ϕf = 2\Omega \sin\phi is the Coriolis parameter (Ω\Omega being Earth's rotation rate and ϕ\phi ), ∇p\nabla_p is the horizontal gradient on pressure surfaces, ϕ\phi is , and F\mathbf{F} represents viscous and other forces. The ensures mass conservation: ∂ω∂p+∇⋅u=0\frac{\partial \omega}{\partial p} + \nabla \cdot \mathbf{u} = 0, with ω=dp/dt\omega = dp/dt as vertical velocity in pressure coordinates. The thermodynamic equation governs : DθDt=Q\frac{D\theta}{Dt} = Q, where θ\theta is potential temperature and QQ includes heating terms like release and , linked via the equation of state p=ρRTp = \rho R T (). These equations neglect sound waves through the anelastic or hydrostatic approximations, enabling efficient computation of synoptic-to-global scales without resolving acoustic timescales. For oceanic GCMs, analogous primitive equations apply, incorporating the Boussinesq approximation to filter gravity waves and treat density variations primarily through : DuDt+fk×u=−∇ϕ+bk+F\frac{D\mathbf{u}}{Dt} + f \mathbf{k} \times \mathbf{u} = -\nabla \phi + b \mathbf{k} + \mathbf{F}, where b=−gδρ/ρ0b = -g \delta \rho / \rho_0 is , alongside incompressibility ∇⋅u=0\nabla \cdot \mathbf{u} = 0 and a temperature-salinity equation for evolution. Radiation and phase changes enter as source terms, but their explicit resolution is limited by grid scales, necessitating parameterizations elsewhere; the primitive framework ensures dynamical consistency with observed circulations like Hadley cells or gyres when forced by realistic boundary conditions. Empirical validations, such as numerical convergence studies to resolutions below 10 km, confirm that solutions approach physical limits under dry adiabatic conditions, underscoring the robustness of these principles despite computational constraints.

Model Architecture

Spatial Discretization and Grids

Spatial in general circulation models (GCMs) involves approximating the continuous partial differential equations of atmospheric and oceanic dynamics on a discrete set of points, transforming the spherical domain of into a computational grid. This process is essential for , as it enables , finite volume, or methods to solve the governing equations while preserving key properties like and where possible. Horizontal discretization typically occurs on quasi-uniform or structured grids to handle the sphere's curvature, while vertical discretization uses coordinate transformations such as terrain-following levels or hybrid levels to resolve atmospheric layers from surface to upper . The most traditional horizontal grid is the latitude-longitude (lat-lon) system, where points are spaced uniformly in (e.g., 1° to 2.5° intervals) and at fixed latitudes, resulting in rectangular cells that converge toward the poles. This grid simplifies implementation for transform methods but introduces the "pole problem": grid cells shrink to zero size at the poles, violating the Courant-Friedrichs-Lewy (CFL) stability criterion due to excessively short time steps required near the poles, and causing numerical noise from grid-point singularities. To mitigate this, models apply semi-Lagrangian , polar filtering, or reduced Gaussian grids that omit points near the poles, allowing resolutions like T159 (approximately 125 km) in operational GCMs. Gaussian grids address some lat-lon limitations by selecting latitude points as roots of , enabling exact quadrature for spectral expansions in global GCMs and avoiding interpolation errors in transform methods. These grids pair with spherical harmonic basis functions for horizontal representation, computing derivatives analytically in space before transforming to grid space for nonlinear terms, which enhances accuracy for smooth large-scale flows but can suffer from that requires dealiasing techniques. Spectral methods on Gaussian grids have been foundational in models like those from ECMWF, supporting resolutions up to T799 (about 25 km) while maintaining computational efficiency through fast Fourier transforms. To overcome uniformity issues in lat-lon grids, quasi-uniform alternatives like icosahedral and cubed-sphere grids have gained adoption. Icosahedral grids subdivide the faces of a projected onto the sphere, yielding hexagonal or triangular cells with nearly equal areas (e.g., spacing of 100 km), which eliminate pole singularities and support scalable on Voronoi tessellations for finite-volume schemes. Cubed-sphere grids tile the sphere with six quadrilateral faces from a , providing quasi-uniform resolution (e.g., 0.25° effective spacing) and benefits for , as used in NASA's GEOS model and CESM, though they introduce seams requiring careful flux reconstruction. These grids improve conservation and reduce compared to lat-lon systems, particularly for high-resolution (sub-10 km) simulations, but demand more complex coding and higher memory for .

Parameterizations for Subgrid-Scale Processes

In general circulation models (GCMs), spatial resolutions of approximately 50–250 km horizontally preclude explicit resolution of subgrid-scale processes, necessitating parameterizations to approximate their aggregate effects on resolved variables such as , , and fluxes. These processes, including deep , boundary-layer , and formation, operate on scales of 1–10 km or smaller and exert critical influences on large-scale dynamics, yet their representation relies on empirical or closures rather than direct . Traditional parameterizations introduce structural uncertainties, as evidenced by inter-model spreads in and feedbacks, often requiring tuning to observational datasets for realism. Convection parameterizations predominantly adopt the mass-flux approach, decomposing subgrid updrafts and downdrafts into organized transports with prescribed entrainment, detrainment, and closure assumptions like convective quasi-equilibrium, where is rapidly relieved. Schemes such as the original Arakawa-Schubert formulation or its derivatives, including Tiedtke's bulk mass-flux variant, compute cloud-base based on and inhibition, thereby simulating vertical redistribution of heat and moisture. These methods capture essential features of organized but struggle with scale transitions in higher-resolution "gray-zone" simulations (around 10 km), where partial resolution of plumes leads to double-counting or underestimation of transports, prompting scale-aware modifications that reduce as grid spacing decreases. Turbulence in the and free is parameterized via diffusion closures, with first-order schemes applying eddy viscosities for vertical mixing, often augmented by nonlocal terms for convective boundary layers. Higher-order closures, such as those prognosticating turbulent or using probability density functions (PDFs) for subgrid variability, provide more comprehensive representations; for instance, the Cloud Layers Unified By Binormals (CLUBB) scheme unifies treatment of , shallow , and boundary-layer clouds by modeling joint PDFs of velocity and buoyancy. These approaches address non-local mixing but remain computationally intensive and sensitive to stability functions, contributing to biases in surface fluxes and low-level winds when validated against large-eddy simulations. Cloud and microphysics parameterizations handle subgrid condensate formation, often diagnostically linking cloud fraction to relative humidity exceedance or convectively detrained moisture, with overlap assumptions (e.g., random or maximum) affecting . Prognostic schemes track water/ice paths, incorporating autoconversion and sedimentation for , but their coupling to and schemes frequently underpredicts low- cover and , exacerbating shortwave biases in midlatitudes. Overall, these parameterizations' foundations—relying on bulk assumptions rather than scale-invariant physics—underscore persistent challenges in faithfully reproducing observed variability, with ongoing refinements targeting improved process interactions for coupled atmosphere-ocean GCMs.

Numerical Methods and Flux Conservation

Finite difference methods, pioneered in early atmospheric models such as those developed by Phillips in 1956, approximate spatial derivatives via expansions on structured grids like latitude-longitude or cubed-sphere configurations, enabling straightforward implementation but prone to issues like the pole problem in polar regions where grid points converge. Finite volume methods, as implemented in dynamical cores like GFDL's, integrate the governing equations over discrete control volumes, computing fluxes across cell faces to inherently enforce local , , and , which is essential for long-term stability in climate simulations. Spectral methods transform variables into global basis functions, such as or , offering high accuracy for smooth flows and efficient handling of spherical geometry but requiring dealiasing techniques to mitigate Gibbs oscillations and ensure . Flux conservation in GCMs prevents artificial accumulation or depletion of conserved quantities, such as dry mass and total , which could otherwise induce spurious trends over multi-decadal runs; for instance, non-conservative schemes have been shown to cause energy drifts exceeding observational uncertainties in atmospheric models. In finite volume and finite difference approaches, conservation is achieved by designing monotonic, positivity-preserving flux limiters (e.g., van Leer or PPM schemes) that reconstruct variables at interfaces while satisfying the telescoping property of integrated fluxes, as demonstrated in operational models like ECMWF's IFS. Spectral models enforce global conservation through quadrature rules that integrate exactly over the sphere and post-processing adjustments, though they may violate local conservation, necessitating hybrid schemes for coupled systems where ocean-atmosphere interfaces demand precise flux matching. Advanced techniques, including discontinuous Galerkin methods, further enhance flux conservation by using flux integrals along element boundaries, reducing errors in high-resolution simulations. Time-stepping schemes, typically explicit or semi-implicit, must couple with spatial to maintain overall conservation; for example, schemes with Asselin filters control computational modes in GCMs, while implicit treatments of gravity waves in models (e.g., via the ECMWF semi-implicit scheme since 1975) allow larger time steps without violating flux balances. Validation of these methods against benchmarks, such as Held-Suarez tests, confirms that conservative formulations yield statistically steady circulations with minimal drift, whereas non-conservative variants exhibit unphysical warming or cooling rates. In coupled GCMs, interfacial flux conservation is often enforced via adjustments like those in OASIS coupling software, mitigating biases from mismatched grids and ensuring consistency with empirical energy budgets derived from satellite observations.

Types and Configurations

Atmospheric-Only GCMs

Atmospheric-only general circulation models (AGCMs) simulate the dynamics and physics of the Earth's atmosphere by numerically solving the Navier-Stokes equations in spherical coordinates, along with equations for , continuity, and , while prescribing time-varying lower boundary conditions such as observed or modeled sea surface temperatures (SSTs) and sea ice concentrations. These models typically operate on global grids with horizontal resolutions ranging from 50 to 250 km and vertical levels extending from the surface to the or lower , incorporating parameterizations for sub-grid processes like , cloud formation, and turbulence. By excluding interactive ocean and land components, AGCMs enable controlled experiments to isolate atmospheric responses to specified forcings, such as SST anomalies associated with El Niño-Southern Oscillation (ENSO). AGCMs trace their origins to early numerical weather prediction models developed in the 1950s, evolving into comprehensive atmospheric simulations by the 1960s through efforts at institutions like the and the Geophysical Fluid Dynamics Laboratory (GFDL). Notable early examples include the GFDL spectral models, which advanced from barotropic to primitive equation formulations, enabling the first multi-year integrations of global in the late 1960s. Modern implementations, such as NASA's GEOS-5 AGCM, build on these foundations with enhanced resolution and physics, supporting configurations for both free-running and nudged simulations aligned to reanalysis data. Key examples of operational AGCMs include the Australian Community Climate and Earth-System Simulator (ACCESS) version 1.0 atmosphere-only configuration, which uses prescribed SSTs to constrain 70% of the surface temperature field to observations, and the UCLA AGCM, employed in coupled and uncoupled modes for ENSO prediction experiments since the 1990s. These models often employ finite-volume or spectral dynamical cores to ensure conservation of mass, momentum, and energy, with horizontal resolutions as fine as 25 km in high-resolution variants for studying phenomena like tropical cyclones. AGCMs are applied in seasonal-to-interannual forecasting by forcing ensembles with predicted or observed SSTs, revealing atmospheric teleconnections such as the Pacific-North American pattern during ENSO events, and in paleoclimate studies by imposing proxy-reconstructed SSTs to assess shifts. They also facilitate attribution studies, such as evaluating the atmospheric impact of volcanic aerosols or forcings under fixed oceanic boundaries. Despite their utility, AGCMs exhibit limitations due to the absence of ocean-atmosphere , resulting in unrealistic flux biases in midlatitudes and inadequate representation of coupled modes like the Madden-Julian Oscillation's full variability. For instance, AGCM predictions of midlatitude oceanic fluxes diverge from coupled general circulation models (CGCMs) by up to 20 W/m² in seasonal means, underscoring the need for coupled systems in long-term climate projections. Validation against satellite-derived fields and reanalyses often highlights systematic errors in tropical and stratospheric circulation, attributable to parameterization uncertainties.

Oceanic GCMs


Oceanic general circulation models (OGCMs) numerically simulate the three-dimensional movement of , including fields, , and distributions, to represent basin-scale to global dynamics. These models solve the of motion, comprising prognostic equations for horizontal , tracer conservation ( and ), and a diagnostic for hydrostatic , typically under the Boussinesq that treats as constant except in terms. The hydrostatic assumes vertical accelerations are negligible compared to gravity, simplifying the vertical to a balance between and weight. OGCMs discretize the ocean domain on structured grids, such as latitude-longitude or , with vertical levels using z-coordinates (fixed depth), terrain-following sigma coordinates, or hybrid schemes to resolve and stratification. Sub-grid-scale processes, including turbulent mixing, mesoscale eddies, and air-sea fluxes, are parameterized due to resolution limits that prevent explicit ; for instance, eddy viscosities and diffusivities are applied to mimic unresolved lateral and vertical transports. Initial spin-up integrates the model from rest under climatological forcing to achieve quasi-equilibrium circulation, often requiring decades of simulated time. Key implementations include the Modular Ocean Model (MOM), a flexible hydrostatic primitive code supporting generalized vertical coordinates and mass-conserving formulations, developed at NOAA's Laboratory for process to planetary-scale studies. The Parallel Ocean Program (POP) version 2 uses a z-level grid with an implicit , optimized for in global simulations. NEMO (Nucleus for European Modelling of the Ocean) provides a primitive framework configurable for regional or global domains, incorporating advanced options for biogeochemical tracers and sea-ice coupling. These models have evolved since early global efforts in the late 1970s, with refinements in resolution and physics enabling hindcasts of observed circulations like the thermohaline conveyor.

Coupled Atmosphere-Ocean GCMs

Coupled atmosphere-ocean general circulation models (AOGCMs) integrate an atmospheric general circulation model with an oceanic general circulation model, enabling bidirectional exchanges of , heat, freshwater, and radiative fluxes at the air-sea interface. These interactions simulate the coupled dynamics essential for phenomena like El Niño-Southern Oscillation (ENSO) and decadal climate variability, which cannot be adequately captured by uncoupled models using prescribed s (SSTs). Initial efforts to develop AOGCMs occurred in the late 1960s and early 1970s, with pioneering work by Manabe and Bryan in demonstrating basic coupled simulations, though limited by coarse resolutions and computational constraints. By the mid-1980s, coupled models supplanted atmospheric-only GCMs as the standard for studies, incorporating dynamics to address deficiencies in SST variability representation. Development accelerated in the , with models run synchronously to produce multi-century integrations for equilibrium states. A primary challenge in early AOGCMs was climate drift, arising from mismatches in simulated meridional heat and freshwater transports between the atmosphere and components, leading to unrealistic SST trends. To mitigate this, flux adjustments—artificial corrective fluxes derived from uncoupled model differences—were introduced in models like those from the Hadley Centre and GFDL, ensuring stable pre-industrial despite underlying parameterization errors. Critics argue flux adjustments obscure physical deficiencies rather than resolving them, prompting later generations to prioritize improved subgrid-scale parameterizations and higher resolutions for drift-free . Prominent examples include HadCM3, developed by the UK Met Office in the late , which operates without flux adjustments at 2.75°×3.75° atmospheric and 1.25°×1.25° oceanic resolutions, simulating realistic tropical SST biases and ENSO variability. GFDL's CM3, introduced around 2006, couples the AM3 atmosphere with MOM4 ocean, emphasizing refined physics for ocean circulation and , contributing to CMIP5 assessments. These models participate in frameworks like the (CMIP), standardizing evaluations across institutions for projections and variability studies. Ongoing advancements focus on resolving coupled feedbacks, such as air-sea interactions in the Maritime Continent, using nested regional models or enhanced global resolutions to reduce biases in and circulation. Despite progress, persistent issues include high computational demands—requiring supercomputers for simulations—and incomplete representation of ocean mesoscale eddies, which influence global uptake. AOGCMs thus provide a hierarchical tool for dissecting system responses, though validation against paleoclimate proxies reveals limitations in capturing low-frequency variability without additional forcings.

Computational Framework

Software and Algorithms

General circulation models (GCMs) are predominantly coded in , valued for its efficiency in handling large-scale numerical arrays and vectorized operations essential for simulating over global grids. This choice stems from the field's origins in the mid-20th century, when enabled early computational experiments, leading to extensive legacy codebases that prioritize and performance on systems over modern language features. Complementary languages include or C++ for low-level optimizations, such as in parallel environments, and Python for scripting, data I/O, and post-processing tasks. Key software frameworks orchestrate GCM components, such as the Community Earth System Model (CESM), an open-source system that couples atmospheric, oceanic, land, sea ice, and biogeochemical modules through the CPL7 flux coupler. CPL7 manages asynchronous data exchanges, interpolates fluxes (e.g., heat, momentum, freshwater) between disparate grids using methods like bilinear or conservative remapping, and enforces conservation laws to prevent spurious energy drifts in long simulations. Similarly, the NOAA Laboratory (GFDL) employs the Flexible Modeling System (FMS), which supports modular assembly of GCMs with built-in parallelism via (MPI) for distributed-memory architectures. For European models, the OASIS3-MCT coupler enables parallel, conservative interpolation across model domains, reducing interpolation errors in coupled atmosphere-ocean simulations by up to 10-20% compared to non-conservative schemes. These frameworks abstract low-level I/O and communication, allowing scientists to focus on physics while leveraging libraries like for gridded data storage. Core algorithms emphasize numerical stability and efficiency. Time-stepping routines often employ explicit schemes, such as the leapfrog method for prognostic variables in atmospheric GCMs, which alternates between time levels to damp computational modes while advancing solutions with time steps on the order of 10-30 minutes for typical resolutions. Implicit or semi-implicit solvers handle stiff terms like or oceanic baroclinic modes, enabling larger effective time steps via techniques like distorted physics, where horizontal is amplified to relax stability constraints without altering long-term equilibria. Coupling algorithms in frameworks like OASIS prioritize flux conservation through Schwarz or great-circle mappings, minimizing artificial sources/sinks that could bias budgets by 0.1-1 W/m². Emerging hybrid approaches, such as NeuralGCM, integrate surrogates for subgrid processes within traditional dynamical cores, accelerating simulations by factors of 10-100 while preserving skill in mid-latitude weather patterns. However, these remain experimental, as core GCMs rely on deterministic physics-based solvers verified against observational benchmarks.

Hardware Requirements and Parallel Computing

General circulation models demand substantial hardware resources due to the computational intensity of solving coupled partial differential equations for atmospheric, oceanic, and other components over global three-dimensional grids, often involving billions of grid cells and millions of time steps per . High-resolution configurations, such as those targeting sub-100 km horizontal spacing and dozens of vertical levels, typically require supercomputers with peak performances exceeding 1 petaflop (10^15 floating-point operations per second) and memory capacities in the petabyte range to handle the data volume from prognostic variables like , , and . For context, a single century-long at moderate resolution (e.g., 1° grid) can consume 10^5 to 10^6 core-hours on multi-core clusters, scaling to months of wall-clock time on dedicated partitions of national facilities like those in the list. Parallel computing frameworks are essential for feasibility, leveraging domain decomposition to partition the spatial grid into subdomains assigned to individual processors or nodes, minimizing communication overhead while maximizing load balance. In distributed-memory systems, the (MPI) standard facilitates data exchange across nodes for boundary updates and global reductions, with hybrid MPI plus approaches combining distributed and shared-memory parallelism for intra-node efficiency on multi-core CPUs. Spectral transform methods, common in atmospheric GCMs, exhibit strong scalability due to their separable computations in and grid spaces, achieving near-linear speedup up to thousands of processors in models like those used for CMIP. Grid-point formulations, prevalent in oceanic components, employ similar 1D or 2D decompositions but require careful halo exchanges to maintain locality. Advancements in hardware, including graphics processing units (GPUs) for accelerating parameterizations and linear solvers, offer potential speedups of 2-10x over CPU-only runs for certain kernels, though full model porting remains challenged by irregular memory access patterns in dynamical cores. Coupled atmosphere-ocean GCMs amplify requirements, with between components necessitating asynchronous strategies to sustain parallelism across heterogeneous architectures. For CMIP6, aggregate computational demands across participating models totaled over 10^9 core-hours for core experiments, underscoring reliance on exascale-capable systems for future higher-fidelity ensembles.

Simulation Timescales and Resolution Limits

Spatial resolutions in general circulation models (GCMs) are constrained by computational resources, with typical horizontal grid spacings in Coupled Model Intercomparison Project phase 6 (CMIP6) atmospheric components ranging from 25 km in high-resolution variants to 250 km in coarser configurations. Vertical resolutions commonly feature 30 to 100 levels to represent atmospheric layers from the surface to the or higher. These choices balance fidelity in resolving large-scale dynamics against the exponential growth in computational demands; finer grids increase the number of grid points cubically for three-dimensional domains, scaling roughly as (Δx)−3(\Delta x)^{-3} for fixed vertical extent. Temporal resolution, dictated by numerical stability criteria such as the Courant-Friedrichs-Lewy condition, requires time steps on the order of minutes (typically 10-30 minutes) to prevent instability in explicit schemes for advection-dominated processes. Doubling spatial resolution not only multiplies grid points but also halves allowable time steps, yielding an overall computational cost increase of approximately one order of magnitude per simulation unit time. This scaling precludes routine global simulations below 10-25 km horizontal resolution for extended periods, as such efforts demand supercomputing resources equivalent to thousands of CPU-years, often limiting applications to short-term weather-like forecasts or regional domains rather than century-scale climate integrations. Simulation timescales in GCMs prioritize long-term averages for climate statistics, with standard runs spanning 150 years for historical hindcasts (e.g., 1850-2000) and projections extending to 2100 or 2300 under emission scenarios. At coarser resolutions (e.g., 100-250 km), multi-century or millennial simulations are feasible on modern supercomputers, enabling equilibrium assessments, though they rely heavily on parameterizations for unresolved sub-grid phenomena like deep , which require resolutions below 5-10 km for explicit resolution. Higher-resolution models, while improving representation of mesoscale features such as storm tracks, face trade-offs: extended runs become impractical, restricting ensemble sizes (often to 1-5 members versus dozens at low resolution) and hindering robust . For paleoclimate or very long-term studies, coarser grids or hybrid approaches (e.g., emulators) are employed to circumvent these limits.

Validation Against Empirical Data

Observational Benchmarks

General circulation models (GCMs) are benchmarked against observational data to evaluate their fidelity in simulating Earth's , focusing on climatological means, variability, and spatial patterns from instrumental records spanning decades to centuries. Empirical datasets include surface station measurements from networks like the Global Historical Climatology Network (GHCN), satellite-derived products such as those from NASA's CERES for radiation budgets, ARGO floats for , and reanalyses like ERA5 for upper-air fields. Validation typically involves control runs (equilibrium simulations under constant forcing) or historical simulations driven by observed forcings, assessing metrics like root-mean-square error (RMSE) and pattern correlations against these observations. Near-surface air serves as a primary benchmark, where multi-model ensembles from phases like CMIP5 and CMIP6 reproduce the observed global mean warming of approximately 0.85°C from 1880 to 2012, but with regional discrepancies; for instance, models often overestimate mid-tropospheric warming in the compared to radiosonde and records showing slower rates. Precipitation patterns reveal persistent biases, including the double-ITCZ problem, where CMIP6 models still simulate spurious equatorial rainfall maxima in both hemispheres, contrasting with asymmetric observations dominated by a single ITCZ shifted northward. GCMs perform better on large-scale fields (pattern correlations often exceeding 0.9 globally) than on , where wet biases over oceans and dry biases in subtropical lands yield lower skills, with RMSE values for annual means typically 20-50% higher relative to errors. Upper-air and circulation benchmarks highlight additional challenges; for example, GCMs underpredict observed stratospheric cooling trends post-1979, linked to , and exhibit errors in jet stream positions, such as weakened over the mid-latitudes. Ocean surface temperatures (SSTs) show good agreement in annual cycles but discrepancies in variability, with models like those in CMIP5 failing to capture the observed slowdown in global warming rates during the early 2000s hiatus period. Sea ice extent validations indicate overestimation of summer minima in historical runs, while trends are mismatched, with models projecting decline against observed expansion until 2014. These benchmarks underscore that while GCMs capture first-order and energy balances, subgrid-scale processes like clouds and drive systematic errors, necessitating ongoing refinements.

Historical Hindcasting Performance

General circulation models (GCMs) undergo hindcasting by simulating historical conditions using observed forcings such as concentrations, solar variability, volcanic aerosols, and anthropogenic emissions, typically spanning the instrumental record from 1850 onward or the . These simulations are validated against empirical datasets like HadCRUT for surface temperatures or GPCP for to assess fidelity in reproducing observed trends, variability, and spatial patterns. Multi-model ensembles, such as those from the (CMIP), aggregate outputs from dozens of GCMs to evaluate collective performance, revealing improvements over successive phases (e.g., CMIP3 to CMIP5) in capturing large-scale features while highlighting persistent systematic errors. In global mean surface temperature (GMST), CMIP5 ensembles demonstrate high skill, with the multi-model mean aligning closely with observations over the —tracking within 0.5°C and achieving pattern correlations exceeding 0.95 for large-scale fields—and effectively reproducing post-1950 warming, volcanic cooling episodes, and interannual variability linked to phenomena like El Niño-Southern Oscillation (ENSO). Earlier individual GCMs from 1970–2007 also exhibit skillful hindcasts of multidecadal GMST trends, with an average skill score of 0.69 when adjusted for forcing uncertainties, showing no systematic over- or underestimation across 17 models evaluated against post-publication observations. CMIP6 models similarly capture decadal trends, such as 1901–1940 warming and 1941–1970 cooling, but display greater spread and overestimation of post-1998 warming in 90% of simulations, with the ensemble mean implying trends ~0.1–0.2°C per decade higher than observed rates of ~0.18°C per decade. Regional biases persist across phases, including cold anomalies of 1–2°C in zones (e.g., eastern Pacific), overestimation of seasonal cycle amplitude over land, and errors in high-topography areas like the and . Precipitation hindcasts show moderate skill at large scales, with CMIP5 pattern correlations improving to 0.82 (from 0.77 in CMIP3) for features like tropical maxima, subtropical dry zones, and monsoon systems, alongside better representation of intense extremes in higher-resolution variants. However, systematic errors include a spurious double (ITCZ), overestimation of tropical rainfall (e.g., western Pacific), underestimation of heavy sensitivity to warming, and regional discrepancies exceeding 20% for return values in many areas. CMIP6 simulations exacerbate some issues, such as overestimating historical trends relative to observations, which propagates into projections. Other variables reveal mixed results: ocean heat content changes from 1961–2005 fall within observational ranges, seasonal cycles match with <10% error (though Arctic summer decline is underestimated in ~75% of models), and top-of-atmosphere radiative fluxes align within 2.5 W/m² of satellite data. Cloud and moisture biases remain prominent, contributing to radiative imbalances of tens of W/m² regionally and dry lower-troposphere errors up to 25%, while tropical cyclone intensity is underestimated in standard resolutions. Overall, while GCM hindcasts robustly simulate global-scale historical evolution—bolstered by ensemble averaging—their regional and process-level fidelity is limited by parameterization uncertainties, with CMIP6 introducing hotter baselines that challenge attribution of recent trends.

Identified Biases and Systematic Errors

General circulation models (GCMs) exhibit persistent systematic biases in simulating the mean climate state, including a double intertropical convergence zone (ITCZ) bias characterized by excessive precipitation in the southern equatorial Pacific alongside the observed northern ITCZ, observed across CMIP3, CMIP5, and CMIP6 ensembles based on annual mean precipitation metrics. This error stems from deficiencies in representing ocean-atmosphere interactions and convection parameterization, leading to unrealistic equatorial asymmetry that propagates into variability simulations like ENSO. Models without this bias, such as those refined for better Pacific SST gradients, show improved tropical circulation fidelity. Temperature biases include a widespread cold bias in the equatorial Pacific sea surface temperatures (SSTs), with models producing excessively cool and narrow cold tongues due to overestimated trade winds and insufficient warming feedbacks. Polar regions often display a "cold pole" bias, where stratospheric temperatures are underestimated, linked to overly strong polar vortices and errors in gravity wave drag parameterization. CMIP5 models consistently underpredict surface air, ground, and soil temperatures globally, with deviations of several degrees in high-latitude continental areas. Precipitation simulations suffer from overfrequent light rain events, or "drizzling bias," arising from inadequate resolution of subgrid convective processes, which contributes to the double-ITCZ and excessive tropical wetness. Cloud-related errors include misrepresented diurnal cycles, with models failing to capture peak afternoon convection and instead producing nocturnal maxima, tied to boundary layer and microphysics shortcomings. Warm precipitation biases in midlatitudes reflect rapid droplet formation and fallout, exacerbating mean-state errors in vertical structure. These biases accumulate from approximations in unresolved physics, such as convection and clouds, and persist despite tuning to historical observations, indicating structural limitations rather than mere calibration issues. Downscaling amplifies them unless corrected, often resulting in overly wet and cold regional projections. Efforts like quantile mapping address statistical mismatches but do not resolve underlying causal errors in dynamics.

Applications in Prediction

Relation to Numerical Weather Prediction

General circulation models (GCMs) and numerical weather prediction (NWP) models share a foundational reliance on the numerical solution of the same primitive equations governing atmospheric dynamics, including the Navier-Stokes equations for momentum, thermodynamic equations for energy, and continuity equations for mass and water vapor. These shared physical principles enable both approaches to simulate fluid motions in the atmosphere, but they diverge in application: NWP focuses on deterministic short-term forecasts from hours to about two weeks by assimilating current observational data into high-resolution initial conditions, whereas GCMs emphasize statistical long-term climate behavior over months to centuries. Historically, GCMs emerged directly from advancements in NWP during the mid-20th century, as computational capabilities allowed extension of short-range weather simulation techniques to global, multi-year integrations. Early NWP efforts, pioneered by figures like Lewis Fry Richardson in the 1920s and realized computationally in the 1950s at institutions such as the Swedish Meteorological and Hydrological Institute and the U.S. Joint Numerical Weather Prediction Unit, provided the algorithmic basis for GCM development; by 1955, Joseph Smagorinsky at Princeton adapted NWP barotropic models into the first three-dimensional GCM, running simulations lasting days on early computers like the IBM 701. This evolution reflected a shift from initial-value problems in NWP—highly sensitive to precise starting states due to chaos in nonlinear dynamics—to boundary-value problems in GCMs, where external forcings like solar radiation and greenhouse gases drive ensemble-averaged outcomes insensitive to exact initial conditions after weeks. Key operational differences include spatial and temporal resolution: NWP models typically employ grids of 1–10 km horizontally with frequent data assimilation from satellites, radars, and surface stations to correct errors, enabling skillful predictions up to 10 days for mid-latitudes, whereas GCMs use coarser 50–200 km grids optimized for computational efficiency over decades, relying less on real-time observations and more on prescribed boundary conditions. Despite these distinctions, hybrid applications bridge the gap, such as seasonal-to-subseasonal forecasting models that extend NWP frameworks with GCM-like coupling to oceans and land, as seen in systems like the European Centre for Medium-Range Weather Forecasts' Integrated Forecasting System, which supports predictions from days to months. Modern unified modeling frameworks, exemplified by Germany's ICON model introduced in 2015, further blur boundaries by configuring the same core equations for both NWP (high-resolution, short-term) and climate simulations (lower-resolution, long-term).

Climate Projections and Scenario Modeling

General circulation models (GCMs) generate climate projections by simulating future atmospheric, oceanic, and land surface responses to prescribed radiative forcing scenarios, primarily through coordinated experiments under the Coupled Model Intercomparison Project (CMIP). In CMIP6, contributing GCMs from approximately 49 modeling groups produced runs under Shared Socioeconomic Pathways (SSPs) that incorporate varying greenhouse gas concentrations, aerosol levels, and land use changes, such as SSP1-2.6 for sustainable development with low emissions and SSP5-8.5 for fossil-fueled development with high emissions. These scenarios enable assessment of equilibrium climate sensitivity (ECS), estimated in CMIP6 models to range from 1.8°C to 5.6°C for doubled CO2, wider than the 2.1–4.7°C in prior phases due to inclusion of models with higher sensitivity. Projections from CMIP6 GCM ensembles, as synthesized in IPCC AR6, indicate global mean surface temperature (GMST) increases of 1.5°C (likely range 1.0–1.8°C) under SSP1-2.6 and 4.4°C (3.3–5.7°C) under SSP5-8.5 by 2081–2100 relative to 1850–1900, with scenario uncertainty dominating long-term projections alongside model structural differences. Regional patterns show amplified warming over land and polar regions, with precipitation increases in high latitudes and decreases in subtropical zones, though GCMs exhibit substantial spread in monsoon circulation changes influenced by internal variability like the Atlantic Multidecadal Variability (AMV). Extreme event projections, such as intensified heavy precipitation, rely on multi-model means to mitigate individual biases, yet uncertainties persist from unresolved cloud feedbacks and ocean heat uptake. Historical evaluations of GCM projections demonstrate skill in capturing observed global warming trends since the 1970s, with 10 of 17 models from 1970–2007 closely matching subsequent observations after publication, though adjustments for volcanic aerosols and internal variability improve alignment. However, CMIP5 models simulated surface warming about 16% faster than observations from 1970 onward, partly attributable to overestimated tropical tropospheric warming and aerosol effects, highlighting systematic hot biases in some ensembles. These discrepancies underscore the need for ongoing validation against empirical data, as GCM projections inform policy but remain subject to epistemic uncertainties in parameterizations of sub-grid processes like convection and ice-cloud interactions.

Role in Paleoclimate and Regional Studies

General circulation models (GCMs) facilitate paleoclimate investigations by integrating physical equations to simulate equilibrium climates under altered boundary conditions, such as reduced greenhouse gas concentrations, expanded continental ice sheets, and modified orbital forcings. These simulations test hypotheses about causal mechanisms driving past climate shifts, including the amplification of cooling via ice-albedo feedbacks during glacial periods. For the Last Glacial Maximum (LGM), dated to approximately 21,000 years before present, multi-model ensembles from the Paleoclimate Modelling Intercomparison Project (PMIP) indicate a global mean surface temperature anomaly of -4.5°C to -6.5°C relative to pre-industrial levels, with greater cooling over landmasses (up to 10°C in mid-latitudes) and polar amplification exceeding 15°C in some cases. Proxy validations against ice core δ¹⁸O records and pollen assemblages confirm broad patterns like equatorward shifts in westerly jets and expanded subtropical aridity, though tropical sea surface temperature discrepancies highlight ongoing model-proxy tensions. GCM paleosimulations extend to interglacial periods, such as the Eemian (ca. 130,000–115,000 years ago), where increased Northern Hemisphere insolation drives simulated warming of 1–2°C globally, modulated by vegetation and ocean circulation feedbacks that alter regional moisture transport. By isolating forcings, these models quantify sensitivities, such as CO₂'s radiative role in deglaciation, supporting estimates of equilibrium climate sensitivity around 3°C per CO₂ doubling derived from LGM cooling patterns. Limitations arise from idealized boundary conditions and coarse resolution, which underrepresent mesoscale dynamics, prompting integration with proxy data assimilation for refined reconstructions. In regional studies, GCMs provide boundary forcings for downscaling techniques that enhance spatial detail for impact assessments, as global grids (typically 100–250 km) inadequately resolve orographic precipitation, land-sea breezes, and convective extremes influenced by local geography. Dynamical downscaling via nested regional climate models (RCMs) at 10–50 km resolution refines GCM outputs, reducing biases in present-day climatologies by 20–50% for variables like summer precipitation in complex terrains. Applied to paleoregions, such methods simulate LGM hydroclimate variability, revealing enhanced aridity in the American Southwest due to strengthened subtropical highs and reduced winter storm tracks. Statistical downscaling empirically maps GCM large-scale fields to local observations using transfer functions, assuming relative stability in statistical relationships, and has been validated for regional paleoprecipitation proxies like speleothem δ¹⁸O, though non-stationarities under forcings like ice sheet melt challenge long-term applicability. These approaches enable sector-specific analyses, such as agricultural vulnerability in Mediterranean-like paleoregions during pluvial events, by linking global forcings to localized responses in evapotranspiration and runoff. Overall, GCM-driven regional frameworks bridge scales, informing evidence-based projections while exposing gaps in representing unresolved processes like aerosol-cloud interactions.

Criticisms and Limitations

Issues with Model Tuning and Overfitting

General circulation models (GCMs) incorporate numerous uncertain parameters in subgrid-scale parameterizations for processes such as clouds, convection, and aerosols, which are adjusted during tuning to align simulated outputs with observational targets like global mean surface temperature trends and top-of-atmosphere radiation balance. This process, often manual and iterative, involves selecting parameter values that minimize discrepancies with historical data, typically spanning the instrumental record from the late 19th or 20th century. However, tuning introduces risks of overfitting, where models achieve spurious agreement with training data by compensating for structural deficiencies in physics representations rather than resolving underlying errors, potentially inflating apparent skill on tuned metrics while impairing generalization to novel conditions like future forcings or paleoclimates. The degrees of freedom in tuning—often exceeding 10-20 adjustable parameters per model—exacerbate overfitting concerns, as limited and noisy observational datasets allow multiple parameter combinations to fit global aggregates, masking regional or process-level biases. For instance, U.S. modeling centers report tuning to targets with structural uncertainties, such as cloud radiative effects, which can lead to over-reliance on imperfect data and reduced out-of-sample performance, as evidenced by persistent errors in tropical precipitation or stratospheric dynamics post-tuning. Critics highlight that this practice lacks standardization and transparency, with documentation often inadequate to distinguish legitimate calibration from data assimilation-like fitting, fostering circular validation where models are deemed skillful primarily against the data used for adjustment. Empirical assessments show that tuned frequently exhibit degraded hindcast fidelity for pre-industrial or glacial periods, suggesting overfitting to anthropogenic-era signals rather than robust physical emulation. Efforts to mitigate overfitting include objective methods like perturbed parameter ensembles or machine learning-assisted calibration, but these remain nascent and do not eliminate the fundamental challenge of high-dimensional parameter spaces relative to sparse, heterogeneous observations. Over-tuning can also entrench compensatory errors, such as inflating cloud feedback parameters to offset convection scheme flaws, leading to unreliable equilibrium climate sensitivity estimates that diverge from independent constraints like those from volcanic eruptions or satellite radiances. Consequently, while tuning enhances mean-state realism for control simulations, it compromises causal inference in attribution studies, as adjusted parameters may implicitly encode unobserved forcings or feedbacks without first-principles justification.

Discrepancies with Observations

General circulation models (GCMs) frequently exhibit systematic biases when compared to observational records, particularly in vertical temperature profiles, precipitation distributions, and cloud properties, which can amplify projected climate sensitivities beyond empirical evidence. For instance, in the tropical upper troposphere (200-300 hPa), GCMs predict amplified warming rates relative to the surface—termed the "hotspot"—driven by moist convective processes, yet radiosonde and satellite datasets such as those from the (UAH) show observed trends of approximately 0.09 K/decade from 1979-2014, compared to model ensemble means exceeding 0.15 K/decade over similar periods. This discrepancy persists across CMIP5 and CMIP6 ensembles, with high-equilibrium climate sensitivity (ECS > 4°C) models showing the largest inconsistencies against reanalyzed data like ERA5. Surface and tropospheric trends also reveal overestimation in many GCMs; CMIP6 simulations, evaluated against HadCRUT5 observations, display an warming rate of 0.24 K/decade from 1970-2020, surpassing the observed 0.18 K/decade, particularly in "hot" models with ECS above 4.5°C that contribute disproportionately to projections. These models often run warmer over land and mid-latitudes, with amplification ratios in CMIP6 averaging 3-4 times polar vs. global warming since 1990, exceeding observed ratios closer to 2.5 in reanalysis products. patterns show analogous issues, including a "double intertropical convergence zone" (ITCZ) bias in the tropics, where models overestimate zonal rainfall by 1-2 mm/day compared to GPCP observations, linked to errors in ocean-atmosphere and convective parameterization. Extreme daily events exhibit wet biases of up to 14% in global land domains against ERA5 reanalysis, complicating regional projections. Cloud representation remains a core source of error, with GCMs underestimating low-cloud coverage over subtropical oceans by 10-20% relative to MODIS and observations, leading to overstated shortwave cloud radiative effects and positive feedbacks that inflate ECS estimates. Mixed-phase feedbacks in high latitudes show opposing errors—overly reflective clouds in some models reduce simulated warming, while others amplify it—resulting in net uncertainties of ±0.5 W/m²/K in feedback strength against CERES satellite flux data. Ocean circulation discrepancies further compound these, as mid-tropospheric flows in models diverge from float and altimetry observations in intensity and direction, particularly in the where upwelling biases alter heat uptake by 0.1-0.2 PW. These persistent mismatches, evident across model generations despite tuning to historical data, underscore limitations in resolving sub-grid processes like and aerosols, with peer-reviewed evaluations indicating that no single GCM fully reconciles with all observational benchmarks.

Challenges from Natural Variability and Feedbacks

General circulation models (GCMs) face significant challenges in accurately simulating internal climate variability, such as oscillations driven by ocean-atmosphere interactions, which can obscure the detection and attribution of anthropogenic forcing. Modes like the El Niño-Southern Oscillation (ENSO), (PDO), and (AMO) exhibit amplitudes and teleconnections in observations that many GCMs fail to reproduce faithfully, often underestimating their strength or periodicity in control simulations without external forcing. For instance, Phase 5 (CMIP5) models largely lack robust internal multidecadal and bidecadal oscillations akin to the observed PDO and AMO, leading to inflated signal-to-noise ratios in projections where natural fluctuations are downplayed relative to forced trends. This underrepresentation contributes to biases in regional and patterns, as seen in persistent errors in North Atlantic winter variability across millennial simulations. Natural variability also exacerbates discrepancies between model ensembles and satellite observations, particularly in tropospheric warming rates, where multidecadal internal fluctuations can account for much of the observed-model over recent decades. GCMs' coarse resolution and parameterized subgrid processes limit their ability to capture , nonlinear interactions underlying these modes, resulting in reduced ensemble spread that masks true uncertainty in decadal predictions. Consequently, projections may overestimate the emergence of forced signals in regions dominated by variability, such as the tropical Pacific, where ENSO modulation by decadal modes like the PDO remains poorly hindcast. Feedback mechanisms introduce further uncertainties, as GCMs rely on parameterizations for unresolved processes like cloud formation and phase transitions, leading to divergent estimates of (ECS) across models. Cloud feedbacks, in particular, dominate the intermodel spread, with low-altitude liquid clouds potentially providing stronger than simulated, while high-latitude mixed-phase clouds yield opposing signs in some configurations. and lapse-rate feedbacks amplify warming but are intertwined with schemes that exhibit systematic biases, such as overestimating moist static transport in the . Ice-albedo feedbacks are another source of asymmetric uncertainty, where models may miss nonlinear responses to sea ice retreat, including open-water formation and deposition effects not fully resolved at typical grid scales. In the , GCMs often produce unrealistic negative longwave feedbacks due to underestimated cloud and influences, contributing to excessive simulated cooling in polar amplification scenarios. These parameterization dependencies propagate into projections, where feedback uncertainties explain regional ECS variations, such as stronger ice-albedo effects at poles versus dominance in . Overall, the interplay between unresolved feedbacks and natural variability amplifies structural errors, underscoring the need for emergent constraints from observations to narrow parameter ranges without .

Comparisons with Alternative Models

Simplified Models like Radiative-Convective and EMICs

Radiative-convective models (RCMs) represent a class of one-dimensional simplified models that compute vertical profiles of , , and radiative fluxes in a single atmospheric column, assuming hydrostatic balance and moist convective adjustment to prevent superadiabatic . These models balance incoming solar radiation with , incorporating as a parameterization to redistribute heat vertically, as developed in the seminal work by Manabe and Wetherald in 1967, which demonstrated a global surface warming of approximately 2.3 K for a doubling of atmospheric CO2 concentration due to and feedbacks. RCMs serve as foundational tools for understanding equilibrium climate sensitivity (ECS), typically yielding estimates between 2.0 and 3.0 K per CO2 doubling, depending on assumptions about relative and effects, but they exclude horizontal , dynamics, and land-atmosphere interactions present in full general circulation models (GCMs). Compared to GCMs, RCMs offer significant computational efficiency, enabling rapid exploration of radiative-convective processes and sensitivity to parameters like aerosol optical depth or concentrations without the need for three-dimensional grid resolutions. Their simplicity allows isolation of key feedbacks, such as the positive feedback amplifying warming by 50-100% over pure radiative models, providing a benchmark for validating GCM parameterizations of subgrid-scale . However, limitations include an inability to capture zonal asymmetries, tracks, or teleconnections, leading to overestimation of tropical uniformity and underrepresentation of dynamical cooling effects that moderate in GCMs. Earth system models of intermediate complexity (EMICs) extend beyond RCMs by incorporating reduced-form representations of multiple Earth system components, such as zonally or hemispherically averaged ocean circulation, simplified atmospheric dynamics, and biogeochemical cycles, while maintaining computational costs orders of magnitude lower than GCMs—for instance, the JUMP-LCM EMIC executes 63,000 times faster than the high-resolution GCM MIROC4h. EMICs often employ statistical-dynamical approaches, like diffusive closures for and transport, to emulate large-scale circulation without resolving eddies, enabling simulations over millennial timescales to study phenomena like evolution or feedbacks under paleoclimate forcings. In intercomparisons, EMICs reproduce GCM-like global mean and responses to CO2 forcing, with ensemble spreads comparable to those in comprehensive models, though regional patterns exhibit greater divergence due to simplified and resolution. Relative to GCMs, EMICs facilitate through large ensembles and perturbed physics experiments, as demonstrated in studies using models like LOVECLIM to assess sensitivity to ocean parameters, revealing that EMIC ECS ranges (around 2-4 ) align with GCM multimodel means but with reduced from unresolved mesoscale processes. Their advantages include tractability for exploring long-term feedbacks, such as permafrost carbon release or heat uptake, which GCMs struggle with due to high resource demands, but they sacrifice fidelity in simulating transient variability, extreme events, and fine-scale features like El Niño-Southern Oscillation. EMICs thus complement GCMs by providing efficient scoping tools and theoretical insights, though their reliance on tuned can introduce systematic errors in meridional energy transport, underscoring the need for GCM validation of intermediate approximations.

Comprehensive Earth System Models

Comprehensive Earth System Models (ESMs) integrate simulations of the atmosphere, oceans, land surface, , and , incorporating physical, chemical, and biological processes to capture interactions across the system. These models extend beyond atmosphere-ocean general circulation models (AOGCMs) by including dynamic representations of biogeochemical cycles, such as carbon, , and aerosols, which enable the simulation of feedbacks like responses to and their effects on atmospheric composition. ESMs typically operate on global grids with resolutions ranging from 25 to 100 km horizontally and multiple vertical levels, relying on coupled component models linked via flux exchanges for , , , and tracers. Core components encompass atmospheric dynamics via modules like the Community Atmosphere Model (CAM), oceanic circulation through models such as the Parallel Ocean Program version 2 (POP2), land surface processes including hydrology and vegetation dynamics in the Community Land Model (CLM), sea ice evolution with the CICE model, and biogeochemical modules for terrestrial and marine ecosystems. For instance, ESMs simulate nutrient-limited in oceans and soils, aerosol-cloud interactions, and from wetlands, which influence and . Equilibrium in ESMs varies but has increased in recent generations; CESM2, for example, yields 5.1–5.3 °C, attributed to refinements in cloud microphysics and land carbon feedbacks. Prominent ESMs include the Community Earth System Model version 2 (CESM2), released in 2020 by the , which supports simulations from paleoclimate to future scenarios and has been used in CMIP6 intercomparisons. Other examples are NOAA's Laboratory (GFDL) ESMs, such as ESM4, which emphasize high-resolution ocean , and the European Centre for Medium-Range Weather Forecasts' Integrated Forecasting System extended to Earth system components. These models demand , with CESM2 runs requiring thousands of processor hours for century-scale simulations on platforms like supercomputers. In comparison to atmospheric-only GCMs or simplified energy balance models, ESMs provide more realistic projections of transient responses by accounting for slow feedbacks like thaw releasing gases, though their parameterizations for sub-grid processes introduce uncertainties that require empirical tuning against observations. Validation involves hindcasts against data, paleoproxies, and in-situ measurements, revealing strengths in large-scale circulation but gaps in regional extremes and biosphere-atmosphere . Despite computational costs, ESMs underpin IPCC projections, with advancements like CESM2 improving historical biases compared to predecessors.

Emerging Machine Learning and Neural GCMs

Neural general circulation models (Neural GCMs) represent a hybrid paradigm that integrates machine learning components, particularly neural networks, into the framework of traditional physics-based GCMs to enhance simulation efficiency and accuracy. These models retain a differentiable solver for large-scale atmospheric dynamics while replacing or augmenting subgrid-scale parameterizations—such as convection, clouds, and turbulence—with data-driven neural networks trained on reanalysis datasets like ERA5. This approach addresses longstanding challenges in traditional GCMs, where hand-tuned parameterizations often introduce biases and computational bottlenecks. A prominent example is NeuralGCM, developed by Research in collaboration with ECMWF and MIT, which achieves state-of-the-art performance in medium-range up to 10 days while simulating realistic variability, including phenomena like El Niño-Southern (ENSO). NeuralGCM outperforms operational physics-based models like ECMWF's IFS in global forecast skill metrics and surpasses pure emulators, such as GraphCast, in physical consistency due to its hybrid structure. The model's differentiability enables end-to-end optimization, allowing joint training of dynamics and parameterizations to minimize errors against observations, which reduces computational costs by factors of 10-100 compared to fully numerical GCMs for equivalent resolutions. Advantages of Neural GCMs include accelerated simulations suitable for ensemble predictions and experiments, as demonstrated by NeuralGCM's ability to generate multi-decadal runs with equilibrium climate states aligning closely with observations in metrics like global energy balance and tropical precipitation patterns. For instance, in 2024 applications, variants of NeuralGCM improved forecasting accuracy for Indian agriculture by incorporating regional data biases. However, limitations persist: reliance on historical training data risks poor extrapolation to novel climates, such as high-emission scenarios beyond 2100, and neural components can amplify uncertainties in extreme events if not constrained by physics. Unlike traditional GCMs, which derive from first-principles equations, Neural GCMs exhibit reduced interpretability, necessitating rigorous validation against independent datasets to mitigate . Ongoing developments, including extensions for radiance assimilation as of December 2024, aim to enhance constraint and realism.

Historical Evolution

Pioneering Efforts (1950s-1960s)

The foundations of general circulation models (GCMs) emerged from early efforts in (NWP) during the 1950s, building on the vision of simulating atmospheric dynamics using computational methods. In 1950, Jule Charney led a team that performed the first successful numerical weather forecasts using the computer, applying barotropic equations to predict large-scale flow patterns over 24 hours, which demonstrated the feasibility of integrating the of motion for short-term predictions. These experiments, conducted at the Institute for Advanced Study under John von Neumann's influence, marked a shift from manual graphical methods to digital computation, though limited to simplified, two-dimensional models without full three-dimensional circulation. A pivotal advance came in 1956 with Norman Phillips' development of the first rudimentary GCM, a two-level quasi-geostrophic model simulating hemispheric on the IAS computer. Starting from an initial state of relative rest, Phillips' numerical experiment integrated the model over extended periods, producing realistic features such as mid-latitude , jet streams, and zonal-mean meridional circulations driven by differential solar heating, thereby validating the potential for computers to replicate observed general circulation patterns without external forcing beyond . This work, detailed in Phillips' paper "The General Circulation of the Atmosphere: A Numerical Experiment," highlighted the roles of synoptic eddies and mean flows in maintaining thermal balance, though the model's coarse resolution (about 1,000 km grid spacing) and lack of or constrained its realism. In parallel, Joseph Smagorinsky established the General Circulation Research Section at the U.S. Weather Bureau in 1955, initiating systematic development of three-dimensional primitive equation models aimed at global simulations. Smagorinsky's group advanced beyond quasi-geostrophic approximations by incorporating full hydrostatic and primitive equations, achieving early integrations of baroclinic global atmospheres by the late 1950s, which included realistic pressure gradients and vertical structure but struggled with computational instability and required manual adjustments for long-term stability. These efforts culminated in the first operational three-level global models by the early 1960s, setting the stage for coupled atmosphere-ocean representations, though initial runs revealed challenges in resolving small-scale processes like convection without excessive diffusion. Independent work, such as Cecil Leith's primitive equation model at Lawrence Livermore National Laboratory around 1960-1965, further explored energy-conserving formulations for sustained simulations, emphasizing spectral methods to mitigate grid-scale errors. Collectively, these pioneering models underscored the computational barriers of the era—limited to hours of integration on vacuum-tube machines—yet proved that first-principles fluid dynamics could yield emergent circulation resembling observations.

Expansion and Refinement (1970s-1990s)

During the 1970s, atmospheric general circulation models (AGCMs) advanced through increased vertical resolution and incorporation of physical processes such as the hydrologic cycle and , enabling more realistic simulations of global climate dynamics. and colleagues at the Geophysical Fluid Dynamics Laboratory (GFDL) published a seminal 1970 study using a nine-level AGCM that included moist convection, cloud formation, and interactions between , , and in radiation calculations, producing equilibrium climates comparable to observations. This model demonstrated seasonal variations in and temperature, highlighting the role of land-sea contrasts in driving circulation patterns. Concurrently, the UK developed its first AGCM in 1972, employing grid-point methods to simulate tropospheric flows with improved parameterizations. The 1979 Charney Report, commissioned by the , endorsed GCMs as reliable tools for predicting greenhouse gas-induced warming, estimating a 1.5–4.5°C global temperature rise for doubled CO₂ based on early model ensembles, though it noted uncertainties in cloud feedbacks. By the late , spectral transform methods emerged as a dominant numerical approach, allowing efficient handling of and reducing computational costs for higher resolutions, as implemented in models like the NCAR Community Climate Model (CCM). In the 1980s, efforts shifted toward coupled atmosphere-ocean GCMs (AOGCMs) to capture air-sea interactions without artificial flux corrections, though initial versions suffered from climate drift requiring adjustments. GFDL's R15-resolution AOGCM, coupled in 1985, simulated El Niño-Southern Oscillation (ENSO) variability but exhibited systematic errors in tropical mean states. James Hansen's GISS model II, updated in 1988, incorporated historical forcings and sulfate aerosols, projecting 0.7–1.3°C warming by 2019 under business-as-usual scenarios, with emphasis on stratospheric cooling and . The 1990s saw refinements in model resolution, parameterizations for and surface processes, and ensemble simulations for the inaugural IPCC assessment, where nine AGCMs and early AOGCMs provided equilibrium estimates averaging 2.5°C for doubled CO₂. HadCM3, released by the UK Met Office in 1998, featured a 2.75°×3.75° atmosphere and 1.25° grid, demonstrating stable coupled behavior without flux adjustments and improved ENSO hindcasts. These advances enabled projections of regional patterns, such as enhanced warming over and precipitation shifts, though discrepancies persisted in simulating observed cooling.

Contemporary Advances (2000s-2025)

The 2000s marked a shift toward fully coupled atmosphere-ocean general circulation models (AOGCMs) as the standard for long-term climate simulations, with improvements in representing ocean-atmosphere interactions and initial integrations of biogeochemical cycles in Earth system models (ESMs). The Climate Model Intercomparison Project Phase 3 (CMIP3), launched in 2005, enabled multi-model ensembles that quantified uncertainties in projections for the IPCC Fourth Assessment Report, demonstrating better skill in simulating historical temperature trends compared to prior phases. Physical parameterizations advanced, particularly for convection and large-scale dynamics, though persistent biases in cloud feedbacks remained evident across models. In the 2010s, CMIP5 models featured atmospheric resolutions typically around 100-250 km horizontally, incorporating refined representations of aerosols, land surface processes, and dynamics, which enhanced simulations of phenomena like El Niño-Southern Oscillation (ENSO) variability. These developments supported Representative Concentration Pathways (RCPs) for scenario-based forecasting, with ensembles showing reduced spread in global mean temperature projections relative to CMIP3. Computational advances, including parallel processing on supercomputers, allowed for longer integrations and higher ensemble sizes, improving statistical robustness despite ongoing challenges in tropical precipitation biases. The 2020s brought CMIP6, with participating models exhibiting higher average spatial resolutions—often 50-100 km horizontally—and enhanced parameterizations for cloud-aerosol interactions and stratospheric processes, leading to better alignment with observed precipitation patterns in some regions. Shared Socioeconomic Pathways (SSPs) expanded scenario diversity, while incremental gains in simulating extreme events were noted, though equilibrium climate sensitivity ranges widened compared to CMIP5 due to diverse model physics. By 2025, experimental high-resolution simulations reached 9 km global grids, enabling finer depiction of regional variability and extreme weather, facilitated by exascale computing capabilities. These advances, while improving overall fidelity, have been characterized as evolutionary rather than transformative, with persistent structural uncertainties in unresolved subgrid processes.

References

  1. https://www.ipcc-data.org/guidelines/pages/gcm_guide.html
  2. https://www.e-education.psu.edu/meteo469/node/140
  3. https://gmd.copernicus.org/articles/15/3923/2022/
  4. https://journals.ametsoc.org/view/journals/bams/79/1/1520-0477_1998_079_0039_ctdotg_2_0_co_2.pdf
  5. https://history.aip.org/climate/GCM.htm
  6. https://www.researchgate.net/publication/337363210_Coupled_Atmosphere-Ocean_Models_in_Climate_Science_a_critical_review
  7. https://www.pnas.org/doi/10.1073/pnas.2202075119
  8. https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/GL017i012p02173
  9. https://www.wcrp-climate.org/images/modelling/WGCM/publications/sap3-climate-models.pdf
  10. https://www.sciencedirect.com/science/article/abs/pii/S0169809525003928
  11. https://wjarr.com/sites/default/files/WJARR-2024-1235.pdf
  12. https://psl.noaa.gov/enso/glossary.html
  13. https://www.gfdl.noaa.gov/climate-modeling/
  14. https://pmc.ncbi.nlm.nih.gov/articles/PMC11357988/
  15. https://math.nyu.edu/~gerber/pages/climod/the_models.html
  16. https://staff.cgd.ucar.edu/islas/teaching/2_Equations.pdf
  17. https://journals.ametsoc.org/view/journals/mwre/128/7/1520-0493_2000_128_2471_mtagcu_2.0.co_2.pdf
  18. https://www.gfdl.noaa.gov/wp-content/uploads/files/user_files/pjp/polvani_etal-mwr-2004.pdf
  19. https://repository.library.noaa.gov/view/noaa/20342/noaa_20342_DS1.pdf
  20. https://link.springer.com/content/pdf/10.1007/978-3-642-13574-3_20.pdf
  21. https://cdn.intechopen.com/pdfs/43438/InTech-Grids_in_numerical_weather_and_climate_models.pdf
  22. https://www.gfdl.noaa.gov/bibliography/related_files/jlh7301.pdf
  23. https://indico.ictp.it/event/7619/session/65/contribution/274/material/0/0.pdf
  24. https://gmd.copernicus.org/articles/7/909/2014/gmd-7-909-2014.pdf
  25. https://ntrs.nasa.gov/citations/20030020781
  26. https://www.ecmwf.int/sites/default/files/elibrary/1998/76045-non-standard-grids_0.pdf
  27. https://www.nature.com/articles/s41467-020-17142-3
  28. https://www.ecmwf.int/sites/default/files/elibrary/2002/16956-mass-flux-approach-parametrization-deep-convection.pdf
  29. https://web.lmd.jussieu.fr/~crio/EXT/Convection_1.pdf
  30. https://www.nature.com/articles/s41612-018-0021-0
  31. https://journals.ametsoc.org/view/journals/clim/26/23/jcli-d-13-00075.1.xml
  32. https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2022MS003127
  33. https://journals.ametsoc.org/view/journals/clim/25/14/jcli-d-11-00399.1.xml
  34. https://atmos.uw.edu/~dargan/591/591_1.pdf
  35. https://www.ess.uci.edu/~yu/PDF/YU.2000.MCS.pdf
  36. https://gmd.copernicus.org/articles/13/685/2020/
  37. https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2020GL089764
  38. https://www.researchgate.net/publication/226537881_Emerging_Numerical_Methods_for_Atmospheric_Modeling
  39. https://gmao.gsfc.nasa.gov/geos-systems/
  40. https://gmao.gsfc.nasa.gov/pubs/docs/Molod484.pdf
  41. https://repository.library.noaa.gov/view/noaa/28420
  42. https://www.gfdl.noaa.gov/bibliography/related_files/xqy9801.pdf
  43. https://ntrs.nasa.gov/citations/20120011790
  44. https://gmd.copernicus.org/articles/9/2077/
  45. https://esto.nasa.gov/conferences/estc2005/papers/a7p1.pdf
  46. https://ntrs.nasa.gov/citations/19950043426
  47. https://data.coaps.fsu.edu/eric_pub/papers_html/Chassignet_et_al_19.pdf
  48. https://www.mri-jma.go.jp/Publish/Technical/DATA/VOL_59/tec_rep_mri_59_2.pdf
  49. https://www.sciencedirect.com/topics/physics-and-astronomy/primitive-equation
  50. https://frouingroup.ucsd.edu/0_PPARR5_NEMO_ORCA2_v3_4/Appendix_A/Doc_OPA8.1.pdf
  51. https://www.gfdl.noaa.gov/mom-ocean-model/
  52. https://mom-ocean.github.io/assets/pdfs/MOM5_manual.pdf
  53. https://uskess.whoi.edu/components/gcm-modeling/
  54. https://frouingroup.ucsd.edu/Most_recent_figs/Refs/NEMO_book_v3_3.pdf
  55. https://link.springer.com/chapter/10.1007/978-94-017-0627-8_3
  56. https://geo.libretexts.org/Bookshelves/Oceanography/Introduction_to_Physical_Oceanography_%28Stewart%29/15%253A_Numerical_Models/15.6%253A_Coupled_Ocean_and_Atmosphere_Models
  57. https://archive.ipcc.ch/publications_and_data/ar4/wg1/en/ch1s1-5-3.html
  58. https://link.springer.com/article/10.1007/BF00195851
  59. https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/2017ms000947
  60. https://gmd.copernicus.org/articles/10/3715/2017/gmd-10-3715-2017.pdf
  61. https://www.gfdl.noaa.gov/wp-content/uploads/files/user_files/mw/cm3-ocean-ice.pdf
  62. https://pcmdi.llnl.gov/mips/cmip5/history.html
  63. https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2019JC014978
  64. https://www.sciencedirect.com/science/article/pii/S2666592125000952
  65. https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2020PA003959
  66. https://partee.io/2021/02/21/climate-model-response/
  67. https://fortran-lang.discourse.group/t/why-are-climate-models-written-in-programming-languages-from-1950/832
  68. https://www.quora.com/What-coding-languages-do-you-use-for-writing-climate-models
  69. https://news.ycombinator.com/item?id=38381867
  70. https://www.cesm.ucar.edu/models/cpl
  71. https://journals.ametsoc.org/view/journals/bams/94/9/bams-d-12-00121.1.xml
  72. https://climate-dynamics.org/software/
  73. https://gmd.copernicus.org/articles/6/373/2013/gmd-6-373-2013.pdf
  74. https://journals.ametsoc.org/view/journals/atot/15/2/1520-0426_1998_015_0482_tssaas_2_0_co_2.xml
  75. https://research.google/blog/fast-accurate-climate-modeling-with-neuralgcm/
  76. https://www.nature.com/articles/s41586-024-07744-y
  77. https://gmd.copernicus.org/articles/17/3081/2024/
  78. https://theconversation.com/supercomputers-can-take-months-to-simulate-the-climate-but-my-new-algorithm-can-do-it-ten-times-faster-229041
  79. https://journals.ametsoc.org/view/journals/mwre/120/5/1520-0493_1992_120_0835_tpsots_2_0_co_2.xml
  80. https://www.sciencedirect.com/science/article/abs/pii/S0167739X17302017
  81. https://www.quora.com/Is-it-possible-to-run-a-general-circulation-model-GCM-of-the-atmosphere-on-a-PC-or-laptop
  82. https://www.sciencedirect.com/science/article/pii/S1674927821001477
  83. https://theclimatedatafactory.com/blog/high-resolution-cmip6-projections-now-available/
  84. https://acp.copernicus.org/articles/24/7041/2024/
  85. https://www.carbonbrief.org/qa-how-do-climate-models-work/
  86. https://climate.sustainability-directory.com/question/what-are-the-limitations-of-high-resolution-climate-models/
  87. https://journals.ametsoc.org/view/journals/clim/38/10/JCLI-D-24-0303.1.xml
  88. https://www.frontiersin.org/journals/earth-science/articles/10.3389/feart.2023.1245815/full
  89. https://gmao.gsfc.nasa.gov/gmao-products/aogcm/
  90. https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/JD095iD01p00829
  91. https://pubmed.ncbi.nlm.nih.gov/28401886/
  92. https://espo.nasa.gov/tc4/content/The_Double%25E2%2580%2590ITCZ_Bias_in_CMIP3_CMIP5_and_CMIP6_Models_Based_on_Annual_Mean_Precipitation
  93. https://iwaponline.com/jwcc/article/14/5/1585/94988/Evaluation-of-global-climate-models-for-the
  94. https://journals.ametsoc.org/view/journals/clim/5/4/1520-0442_1992_005_0343_cogcma_2_0_co_2.xml
  95. https://pmc.ncbi.nlm.nih.gov/articles/PMC5394343/
  96. https://pubs.usgs.gov/publication/ofr20221062/full
  97. https://www.ipcc.ch/site/assets/uploads/2018/02/WG1AR5_Chapter09_FINAL.pdf
  98. https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2019GL085378
  99. https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2020EF001667
  100. https://iopscience.iop.org/article/10.1088/1748-9326/abb051
  101. https://www.nature.com/articles/s41467-022-31782-7
  102. https://esd.copernicus.org/articles/12/545/2021/
  103. https://repository.library.noaa.gov/view/noaa/67421/noaa_67421_DS1.pdf
  104. https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2020GL087232
  105. https://journals.ametsoc.org/view/journals/clim/aop/JCLI-D-22-0336.1/JCLI-D-22-0336.1.xml
  106. https://ui.adsabs.harvard.edu/abs/2025EGUGA..2717292J/abstract
  107. https://journals.ametsoc.org/view/journals/clim/36/24/JCLI-D-22-0874.1.xml
  108. https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2024MS004232
  109. https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2025JD043507?af=R
  110. https://journals.ametsoc.org/view/journals/clim/35/24/JCLI-D-22-0336.1.xml
  111. https://www.nature.com/articles/s41467-017-02369-4
  112. https://repository.library.noaa.gov/view/noaa/28249/noaa_28249_DS1.pdf
  113. https://glisa.umich.edu/wp-content/uploads/2021/03/Global-Climate-Model-Bias-and-Bias-Correction.pdf
  114. https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2023GL106264
  115. https://ascmo.copernicus.org/articles/9/1/2023/
  116. https://journals.ametsoc.org/view/journals/bams/106/6/BAMS-D-24-0042.1.xml
  117. https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2018GL080704
  118. https://www.sciencedirect.com/science/article/pii/S0065268708601703
  119. https://wcrp-cmip.org/
  120. https://www.carbonbrief.org/cmip6-the-next-generation-of-climate-models-explained/
  121. https://www.ipcc.ch/report/ar6/wg1/downloads/report/IPCC_AR6_WGI_Chapter04.pdf
  122. https://www.ipcc.ch/report/ar6/wg1/chapter/chapter-4/
  123. https://www.sciencedirect.com/science/article/pii/S2212094722000238
  124. https://www.giss.nasa.gov/research/features/202001_accuracy/
  125. https://www.carbonbrief.org/analysis-how-well-have-climate-models-projected-global-warming/
  126. https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0129037
  127. https://cp.copernicus.org/articles/17/1065/2021/cp-17-1065-2021.pdf
  128. https://pastglobalchanges.org/publications/pages-magazines/pages-magazine/128655
  129. https://www.sciencedirect.com/science/article/pii/104061829190055S
  130. https://www.gfdl.noaa.gov/bibliography/related_files/bush9901.pdf
  131. https://nap.nationalacademies.org/read/11798/chapter/4
  132. https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2007GL032849
  133. https://www.sciencedirect.com/science/article/abs/pii/S0169809519308403
  134. http://www.diva-portal.org/smash/get/diva2:1054715/FULLTEXT01.pdf
  135. https://pmc.ncbi.nlm.nih.gov/articles/PMC3261962/
  136. https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2019GL085127
  137. https://journals.ametsoc.org/view/journals/bams/98/3/bams-d-15-00135.1.xml
  138. https://pmc.ncbi.nlm.nih.gov/articles/PMC6309528/
  139. https://judithcurry.com/2018/09/17/a-test-of-the-tropical-200-300-mb-warming-rate-in-climate-models/
  140. https://www.jstor.org/stable/43735178
  141. https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2022GL097716
  142. https://www.science.org/content/article/use-too-hot-climate-models-exaggerates-impacts-global-warming
  143. https://www.heritage.org/environment/report/global-warming-observations-vs-climate-models
  144. https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2023JD039269
  145. https://eesm.science.energy.gov/research-highlights/understanding-origin-tropical-precipitation-bias-climate-models
  146. https://link.springer.com/article/10.1007/s00382-024-07355-3
  147. https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2024GL114507
  148. https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2025GL116330
  149. https://www.nature.com/articles/s41612-025-00948-7
  150. https://pmc.ncbi.nlm.nih.gov/articles/PMC10097707/
  151. https://journals.ametsoc.org/view/journals/clim/10/8/1520-0442_1997_010_1909_dgcmut_2.0.co_2.pdf
  152. https://www.nature.com/articles/s41467-019-13823-w
  153. https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2023GL105231
  154. https://pmc.ncbi.nlm.nih.gov/articles/PMC8020635/
  155. https://ui.adsabs.harvard.edu/abs/2017AGUFMGC21E0984M/abstract
  156. https://journals.ametsoc.org/view/journals/clim/33/11/jcli-d-19-0740.1.pdf
  157. https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2005GL025540
  158. https://journals.ametsoc.org/view/journals/clim/22/17/2009jcli2885.1.xml
  159. https://pmc.ncbi.nlm.nih.gov/articles/PMC7479110/
  160. https://journals.ametsoc.org/view/journals/clim/32/23/jcli-d-18-0774.1.xml
  161. https://pubs.aip.org/aapt/ajp/article/91/9/731/2906666/Climate-sensitivity-from-radiative-convective
  162. https://geo.libretexts.org/Bookshelves/Meteorology_and_Climate_Science/Introduction_to_Climate_Science_%28Schmittner_2021%29/01%253A_Chapters/1.07%253A_Models
  163. https://www.global-climate-change.org.uk/4-4-2.php
  164. https://cs3.mit.edu/publication/13918
  165. https://ui.adsabs.harvard.edu/abs/2010WIRCC...1..243W/abstract
  166. https://progearthplanetsci.springeropen.com/articles/10.1186/s40645-019-0294-x
  167. https://archive.ipcc.ch/publications_and_data/ar4/wg1/en/ch8s8-8-3.html
  168. https://www.climateurope.eu/earth-system-modeling-a-definition/
  169. https://www.gfdl.noaa.gov/earth-system-model/
  170. https://www.energy.gov/science/doe-explainsearth-system-and-climate-models
  171. https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2019ms001916
  172. https://www.cesm.ucar.edu/models/cesm2
  173. https://www.cesm.ucar.edu/
  174. https://www.ecmwf.int/en/about/media-centre/focus/2021/fact-sheet-earth-system-modelling-ecmwf
  175. https://gmd.copernicus.org/articles/16/3123/2023/
  176. https://arxiv.org/abs/2311.07222
  177. https://blog.google/technology/research/indian-farmers-monsoon-prediction/
  178. https://news.mit.edu/2025/simpler-models-can-outperform-deep-learning-climate-prediction-0826
  179. https://arxiv.org/abs/2412.11973
  180. https://www.vos.noaa.gov/MWL/dec_07/weatherprediction.shtml
  181. https://journals.ametsoc.org/view/journals/bams/60/4/1520-0477_1979_060_0302_tecotn_2_0_co_2.xml
  182. https://rmets.onlinelibrary.wiley.com/doi/10.1002/qj.49708235202
  183. https://journals.ametsoc.org/view/journals/bams/79/1/1520-0477_1998_079_0039_ctdotg_2_0_co_2.xml
  184. http://pne.people.si.umich.edu/sloan/1955_65.html
  185. https://earthobservatory.nasa.gov/blogs/earthmatters/2015/05/21/see-one-of-the-first-climate-models/
  186. https://www.gfdl.noaa.gov/bibliography/results.php?author=1070
  187. https://www.carbonbrief.org/timeline-history-climate-modelling/
  188. https://journals.ametsoc.org/view/journals/clim/21/1/2007jcli1412.1.xml
  189. https://www.climatechangeinaustralia.gov.au/overview/cmip6-comparison-cmip5
  190. https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2021EF001995
  191. https://journals.ametsoc.org/view/journals/clim/36/17/JCLI-D-22-0375.1.xml
  192. https://www.sciencedirect.com/science/article/pii/S2214581822000489
  193. https://esd.copernicus.org/articles/16/1103/2025/
  194. https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2021MS002781
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