Editing General circulation model (section)

==Structure==
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 wave]]s with the highest [[wavenumber]]s 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 temperature]]s (SSTs).<ref>{{cite web |url=http://www-pcmdi.llnl.gov/projects/amip/index.php |title=Atmospheric Model Intercomparison Project |publisher=The Program for Climate Model Diagnosis and Intercomparison, Lawrence Livermore National Laboratory |access-date=21 April 2010 |archive-date=22 August 2017 |archive-url=https://web.archive.org/web/20170822235226/http://www-pcmdi.llnl.gov/projects/amip/index.php |url-status=dead }}</ref> 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
* [[Parametrization (climate)|parameters]] for:
** convection
** land surface processes
** [[albedo]] 
** [[hydrology]]
** [[cloud cover]]

A GCM contains [[prognostic equation]]s that are a function of time (typically winds, temperature, moisture, and surface pressure) together with [[diagnostic equation]]s 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 [[HadCM3#Ocean model (HadOM3)|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 [[Intergovernmental Panel on Climate Change|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===
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{{nnbsp}}<ref name="jablonowski-etal-2004">
{{cite report
 | last1 = Jablonowski | first1 = Christiane
 | last2 = Herzog | first2 = M
 | last3 = Penner | first3 = JE
 | last4 = Oehmke | first4 = RC
 | last5 = Stout | first5 = QF
 | last6 = van Leer | first6 = B
 | title = Adaptive grids for weather and climate models
 | date = 2004
 | publisher = National Center for Atmospheric Research (NCAR)
 | location = Boulder, Colorado, United States
 | url = https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=3919a358564b1533666e55cb1ebda7180cb245d6
 | access-date = 2024-10-13
}}  PDF create date 2004-10-28. See also {{cite web |first=Christiane |last=Jablonowski |url=http://www-personal.umich.edu/~cjablono/amr.html |title=Adaptive Mesh Refinement (AMR) for Weather and Climate Models |archive-url=https://web.archive.org/web/20160828124836/http://www-personal.umich.edu/~cjablono/amr.html |archive-date=28 August 2016 |access-date=24 July 2010 |url-status=live}}</ref> are more often used.<ref>NCAR Command Language documentation: [http://www.ncl.ucar.edu/Document/Graphics/contour_grids.shtml Non-uniform grids that NCL can contour] {{webarchive |url=https://web.archive.org/web/20160303171034/http://www.ncl.ucar.edu/Document/Graphics/contour_grids.shtml |date=3 March 2016 }} (Retrieved 24 July 2010)</ref> 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|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 ([[Wind speed|''u'',''v'']], [[Temperature|''T'']], [[Humidity|''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.<ref>{{cite web 
|url=http://higem.nerc.ac.uk/ 
|title=High Resolution Global Environmental Modelling (HiGEM) home page 
|publisher=Natural Environment Research Council and Met Office 
|date= 18 May 2004}}</ref> These resolutions are lower than is typically used for weather forecasting.<ref>{{cite web|title=Mesoscale modelling |url=http://www.metoffice.gov.uk/science/creating/hoursahead/mesoscale.html |access-date=5 October 2010 |url-status=dead |archive-url=https://web.archive.org/web/20101229170731/http://www.metoffice.gov.uk/science/creating/hoursahead/mesoscale.html |archive-date=29 December 2010 }}</ref> 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 [[Courant–Friedrichs–Lewy condition|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 grid]]s<ref>{{cite web 
|url=http://www.unisci.com/stories/20013/0924011.htm 
|title=Climate Model Will Be First To Use A Geodesic Grid 
|publisher=Daly University Science News 
|date=24 September 2001}}</ref> 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 coordinate system|Cartesian]] [[cube]] such that it covers the surface of a sphere.<ref>{{cite web|title=Gridding the sphere|url=http://mitgcm.org/projects/cubedsphere/|work=MIT GCM|access-date=9 September 2010}}</ref>

===Flux buffering===
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.<ref>{{cite web|title=IPCC Third Assessment Report - Climate Change 2001 - Complete online versions|url=http://www.grida.no/publications/other/ipcc_tar/?src=/climate/ipcc_tar/wg1/309.htm|publisher=IPCC|access-date=12 January 2014|url-status=dead|archive-url=https://web.archive.org/web/20140112230927/http://www.grida.no/publications/other/ipcc_tar/?src=%2Fclimate%2Fipcc_tar%2Fwg1%2F309.htm|archive-date=12 January 2014}}</ref>

===Convection===
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,<ref>{{cite web |url=http://www.aip.org/history/climate/arakawa.htm |title=Arakawa's Computation Device |publisher=Aip.org |access-date=2012-02-18 |archive-date=15 June 2006 |archive-url=https://web.archive.org/web/20060615032539/http://www.aip.org/history/climate/arakawa.htm |url-status=dead }}</ref> although a variety of different schemes are now in use.<ref>{{cite web |url=http://grads.iges.org/reps/rep27/colarep27.html |title=COLA Report 27 |publisher=Grads.iges.org |date=1996-07-01 |access-date=2012-02-18 |url-status=dead |archive-url=https://web.archive.org/web/20120206085956/http://grads.iges.org/reps/rep27/colarep27.html |archive-date=6 February 2012}}</ref><ref>{{cite web|url=http://www-pcmdi.llnl.gov/projects/modeldoc/amip/10Tbl2.10.html |title=Table 2-10 |publisher=Pcmdi.llnl.gov |access-date=2012-02-18}}</ref><ref>{{cite web |url=http://rainbow.llnl.gov/projects/modeldoc/cmip/table4.html |title=Table of Rudimentary CMIP Model Features |publisher=Rainbow.llnl.gov |date=2004-12-02 |access-date=2012-02-18 |archive-date=15 May 2006 |archive-url=https://web.archive.org/web/20060515195016/http://rainbow.llnl.gov/projects/modeldoc/cmip/table4.html |url-status=dead }}</ref> 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.<ref>{{cite web |url=http://www.aip.org/history/climate/GCM.htm |title=General Circulation Models of the Atmosphere |publisher=Aip.org |access-date=2012-02-18 |archive-date=30 July 2012 |archive-url=https://web.archive.org/web/20120730192534/http://www.aip.org/history/climate/GCM.htm |url-status=dead }}</ref>

===Software===
Most models include software to diagnose a wide range of variables for comparison with observations or [[process study|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.