To render atmosphere and ocean models from one dynamical core MITGCM exploit `isomorphisms' between equation sets that govern the evolution of the respective fluids. One system of hydrodynamical equations is written down and encoded. The model variables have different interpretations depending on whether the atmosphere or ocean is being studied. Thus, for example, the vertical coordinate `r' is interpreted as pressure, `p', in the atmosphere and height, `z', in the ocean. From a numerical implementation point of view there is no fundamental difference between atmosphere and ocean in the MITGCM model.
To know more about the way MITGCM exploit `isomorphisms' between atmosphere and ocean governing equations see : <a href="../../../paoc/papers/atmosphere_ocean_modeling.pdf" target="_blank">
Marshall, J. A. Adcroft, J-M Campin and C. Hill (2004) Atmosphere-ocean
modeling exploiting fluid isomorphisms.</a>  Mon. Wea. Rev., 132 (12),
<p> The horizontal and vertical representation, resolution and other important characteristics of the <a href="http://mitgcm.org/public/docs.html">" MITgcm "</a>
hydrodynamical kernel used for the study of the circulation of atmosphere and ocean are as follows (2011):</p>
<p> </p><h2> A. Atmosphere </h2>
<p> The model has run using different grids. The coarsest resolution grid used was C32 (the cubic grid of Rancic and Purser
with 32 points across a tile) which is equivalent to G64 (128×64 points in spherical polar coordinates) in equatorial resolution. Other grid resolutions are C46, C64 and C96 all using the conformal cubic grid of Rancic et al. (1996).
<br />More on model grid resolution: <a href="http://paoc.mit.edu//paoc/papers/adcroft_et_al_MWR_2004.pdf" target="_blank">Adcroft,
A., J-M Campin, C. Hill and J. Marshall (2004) Implementation of
an atmosphere-ocean general circulation model on the expanded
spherical cube.</a>  Mon. Wea. Rev., 132 (12), 2845-2863
<li> numerical scheme/grid
<p> o Grid - Arakawa C grid. The basic algorithm employed for stepping forward the momentum equations is based on retaining non-divergence of the flow at all times. This is most naturally done if the components of flow are staggered in space in the form of an Arakawa C grid.
The finite volume method is used to discretize the equations in space.
<br align="left" />More on the finite volume implementation: Adcroft, A.J., Hill, C.N. and J. Marshall, (1997) Representation of topography by shaved cells in a height coordinate ocean model  <em>Mon Wea Rev</em>, vol 125, 2293-2315
</p><p> o Time-stepping - The algorithm for each of the 5 basic formulations in which the model comes is:
<li> the semi-implicit pressure method for hydrostatic equations with a rigid-lid, variables co-located in time and with Adams-Bashforth time-stepping,</li>
<li> as 1 but with an implicit linear free-surface,</li>
<li> as 1 or 2 but with variables staggered in time,</li>
<li> as 1 or 2 but with non-hydrostatic terms included,</li>
<li> as 1 or 3 but with non-linear free-surface.</li>
<p><br align="left" />More on discretization and time-stepping: <a href="http://mitgcm.org/public/r2_manual/latest/online_documents/node30.html"> " here "</a>
</p></li><li> list of prognostic variables :
<p> The equations of motion integrated by the model involve four prognostic equations for flow: the two horizontal components of velocity, temperature, potential temperature and salt/moisture, and three diagnostic equations for vertical flow, density/buoyancy, and pressure/geo-potential.
<br /> In addition, the surface pressure or height may by described by either a prognostic or diagnostic equation and if non-hydrostatics terms are included then a diagnostic equation for non-hydrostatic pressure is also solved. </p></li>
<li> Major atmospheric parameterizations.
The atmospheric parameterizations are based on the Atmospheric Intermediate Physics aim_v23 package that is based on the version v23 of the SPEEDY code described in: Molteni, F., Atmospheric simulations using a GCM with simplified physical parametrization, I: Model climatology and variability in multidecadal experiments, Clim. Dynamics, 20, 175-191, 2003. The parameters are:
<-Name->|Levs|<-parsing code->|<-- Units -->|<- Tile (max=80c)
DIABT | 5 |SM ML |K/s |Pot. Temp. Tendency (Mass-Weighted) from Diabatic Processes
DIABQ | 5 |SM ML |g/kg/s |Spec.Humid. Tendency (Mass-Weighted) from Diabatic Processes
RADSW | 5 |SM ML |K/s |Temperature Tendency due to Shortwave Radiation (TT_RSW)
RADLW | 5 |SM ML |K/s |Temperature Tendency due to Longwave Radiation (TT_RLW)
DTCONV | 5 |SM MR |K/s |Temperature Tendency due to Convection (TT_CNV)
TURBT | 5 |SM ML |K/s |Temperature Tendency due to Turbulence in PBL (TT_PBL)
DTLS | 5 |SM ML |K/s |Temperature Tendency due to Large-scale condens. (TT_LSC)
DQCONV | 5 |SM MR |g/kg/s |Spec. Humidity Tendency due to Convection (QT_CNV)
TURBQ | 5 |SM ML |g/kg/s |Spec. Humidity Tendency due to Turbulence in PBL (QT_PBL)
DQLS | 5 |SM ML |g/kg/s |Spec. Humidity Tendency due to Large-Scale Condens. (QT_LSC)
TSR | 1 |SM P U1 |W/m^2 |Top-of-atm. net Shortwave Radiation (+=dw)
OLR | 1 |SM P U1 |W/m^2 |Outgoing Longwave Radiation (+=up)
RADSWG | 1 |SM P L1 |W/m^2 |Net Shortwave Radiation at the Ground (+=dw)
RADLWG | 1 |SM L1 |W/m^2 |Net Longwave Radiation at the Ground (+=up)
HFLUX | 1 |SM L1 |W/m^2 |Sensible Heat Flux (+=up)
EVAP | 1 |SM L1 |g/m^2/s |Surface Evaporation (g/m2/s)
PRECON | 1 |SM P L1 |g/m^2/s |Convective Precipitation (g/m2/s)
PRECLS | 1 |SM M1 |g/m^2/s |Large Scale Precipitation (g/m2/s)
CLDFRC | 1 |SM P M1 |0-1 |Total Cloud Fraction (0-1)
CLDPRS | 1 |SM PC167M1 |0-1 |Cloud Top Pressure (normalized)
CLDMAS | 5 |SM P LL |kg/m^2/s |Cloud-base Mass Flux (kg/m^2/s)
DRAG | 5 |SM P LL |kg/m^2/s |Surface Drag Coefficient (kg/m^2/s)
WINDS | 1 |SM P L1 |m/s |Surface Wind Speed (m/s)
TS | 1 |SM L1 |K |near Surface Air Temperature (K)
QS | 1 |SM P L1 |g/kg |near Surface Specific Humidity (g/kg)
ENPREC | 1 |SM M1 |W/m^2 |Energy flux associated with precip. (snow, rain Temp)
ALBVISDF| 1 |SM P L1 |0-1 |Surface Albedo (Visible band) (0-1)
DWNLWG | 1 |SM P L1 |W/m^2 |Downward Component of Longwave Flux at the Ground (+=dw)
SWCLR | 5 |SM ML |K/s |Clear Sky Temp. Tendency due to Shortwave Radiation
LWCLR | 5 |SM ML |K/s |Clear Sky Temp. Tendency due to Longwave Radiation
TSRCLR | 1 |SM P U1 |W/m^2 |Clear Sky Top-of-atm. net Shortwave Radiation (+=dw)
OLRCLR | 1 |SM P U1 |W/m^2 |Clear Sky Outgoing Longwave Radiation (+=up)
SWGCLR | 1 |SM P L1 |W/m^2 |Clear Sky Net Shortwave Radiation at the Ground (+=dw)
LWGCLR | 1 |SM L1 |W/m^2 |Clear Sky Net Longwave Radiation at the Ground (+=up)
UFLUX | 1 |UM 184L1 |N/m^2 |Zonal Wind Surface Stress (N/m^2)
VFLUX | 1 |VM 183L1 |N/m^2 |Meridional Wind Surface Stress (N/m^2)
DTSIMPL | 1 |SM P L1 |K |Surf. Temp Change after 1 implicit time step
</p><h2> B. Ocean </h2>
<li> List of prognostic variables and tracers:
<p> Velocities U and V, Temperature and Salinity. </p></li>
<li> Main parametrisations.
<p> Gent/McWiliams/Redi SGS Eddy Parameterization scheme and Nonlocal K-Profile Parameterization for Vertical Mixing of Large et al.  describe in Large, W., J. McWilliams, and S. Doney, Oceanic vertical mixing: A review and a model with nonlocal boundary layer parameterization, Rev. Geophys., 32, 363-403, 1994. </p></li>
<p> <br align="left" />More on Ocean Parametrization packages in MITgcm: <a href="http://mitgcm.org/public/r2_manual/latest/online_documents/node239.html"> " here "</a>
</p><li> Model top
<p>The upper surface of the ocean is a free surface which is driven by the divergence of volume flux (Boussinesq) in the interior. There are three treatments of the upper boundary available in MITgcm:
</p><p> a. Rigid-lid approximation in which the upper surface is imagined to be an impermeable boundary
which exerts a pressure on the fluid.
</p><p> b. The linear free-surface which ignores some small terms in the depth integrated continuity equation,
that permits surface gravity waves to propagate with finite phase speed and introduces a Helmholtz term in the surface pressure equation when treated implicitly in time.
This is a very good approximation in deep water for whic.
</p><p> c. The non-linear free-surface an un-approximated treatment of the upper surface </p></li>
<p> </p><h2> C. sea ice </h2>
<p>The MITgcm sea ice model (MITgcm/sim) is based on a variant of the viscous-plastic (VP) dynamic-thermodynamic sea ice model [Zhang and Hibler, 1997] first introduced by Hibler [1980,1979]. In order to adapt this model to the requirements of coupled ice-ocean state estimation, many important aspects of the original code have been modified and improved: </p>
</p><pre> * the code has been rewritten for an Arakawa C-grid, both B- and C-grid variants are available; the C-grid code allows for no-slip and free-slip lateral boundary conditions;
* two different solution methods for solving the nonlinear momentum equations have been adopted: LSOR [Zhang and Hibler, 1997], and EVP [Hunke and Dukowicz, 1997];
* ice-ocean stress can be formulated as in Hibler and Bryan  or as in Campin et al. ;
* ice variables are advected by sophisticated, conservative advection schemes with flux limiting;
* growth and melt parameterizations have been refined and extended in order to allow for more stable automatic differentiation of the code.
<p>The sea ice model requires the following input fields: 10-m winds, 2-m air temperature and specific humidity, downward longwave and shortwave radiations, precipitation, evaporation, and river and glacier runoff. The sea ice model also requires surface temperature from the ocean model and the top level horizontal velocity. Output fields are surface wind stress, evaporation minus precipitation minus runoff, net surface heat flux, and net shortwave flux. The sea-ice model is global: in ice-free regions bulk formulae are used to estimate oceanic forcing from the atmospheric fields. </p>
<p> <br align="left" />More on Sea Ice packages in MITgcm: <a href="http://mitgcm.org/public/r2_manual/latest/online_documents/node251.html"> " here "</a>
</p><h2> D. Land / ice sheets </h2>
<p> The land model is a simple two-layer model with prognostics temperature, liquid groundwater and snow height. There is no continental ice.
</p><p> <br align="left" />More on the land model package in MITgcm: <a href="http://mitgcm.org/public/r2_manual/latest/online_documents/node249.html"> " here "</a>
</p><h2> E. coupling details </h2>
<p>1. frequency of coupling
</p><p> Every ocean time step.
</p><p>2. Are heat and water conserved by coupling scheme?
</p><p>3. list of variables passed between components:
<br align="left" />More on the coupling package in MITgcm: <a href="http://mitgcm.org/public/r2_manual/latest/online_documents/node256.html"> " here "</a>#
Data availability and file format
Documentation and Links to further information and references
Who to contact
For comments and suggestion:
" here ".
Earth, Atmospheric and Planetary Sciences,
Massachusetts Institute of Technology