Editing General circulation model (section)

===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>