This document provides the reader with the information necessary to carry out numerical experiments using MITgcm. It gives a comprehensive description of the continuous equations on which the model is based, the numerical algorithms the model employs and a description of the associated program code. Along with the hydrodynamical kernel, physical and biogeochemical parameterizations of key atmospheric and oceanic processes are available. A number of examples illustrating the use of the model in both process and general circulation studies of the atmosphere and ocean are also presented.
MITgcm has a number of novel aspects:
- it can be used to study both atmospheric and oceanic phenomena; one hydrodynamical kernel is used to drive forward both atmospheric and oceanic models - see
onemodel
MITgcm has a single dynamical kernel that can drive forward either oceanic or atmospheric simulations.
- it has a non-hydrostatic capability and so can be used to study both small-scale and large scale processes - see
all-scales
MITgcm has non-hydrostatic capabilities, allowing the model to address a wide range of phenomenon - from convection on the left, all the way through to global circulation patterns on the right.
- finite volume techniques are employed yielding an intuitive discretization and support for the treatment of irregular geometries using orthogonal curvilinear grids and shaved cells - see
fvol
Finite volume techniques (bottom panel) are used, permitting a treatment of topography that rivals σ (terrain following) coordinates.
- tangent linear and adjoint counterparts are automatically maintained along with the forward model, permitting sensitivity and optimization studies.
- the model is developed to perform efficiently on a wide variety of computational platforms.
Key publications reporting on and charting the development of the model are Hill and Marshall (1995), Marshall et al. (1997a), Marshall et al. (1997b), Adcroft and Marshall (1997), Marshall et al. (1998), Adcroft and Marshall (1999), Hill et al. (1999), Marotzke et al. (1999), Adcroft and Campin (2004), Adcroft et al. (2004b), Marshall et al. (2004) (an overview on the model formulation can also be found in Adcroft et al. (2004c)):
Hill, C. and J. Marshall, (1995) Application of a Parallel Navier-Stokes Model to Ocean Circulation in Parallel Computational Fluid Dynamics, In Proceedings of Parallel Computational Fluid Dynamics: Implementations and Results Using Parallel Computers, 545-552. Elsevier Science B.V.: New York hill:95
Marshall, J., C. Hill, L. Perelman, and A. Adcroft, (1997a) Hydrostatic, quasi-hydrostatic, and nonhydrostatic ocean modeling, J. Geophysical Res., 102(C3), 5733-5752 marshall:97a
Marshall, J., A. Adcroft, C. Hill, L. Perelman, and C. Heisey, (1997b) A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers, J. Geophysical Res., 102(C3), 5753-5766 marshall:97b
Adcroft, A.J., Hill, C.N. and J. Marshall, (1997) Representation of topography by shaved cells in a height coordinate ocean model, Mon Wea Rev, 125, 2293-2315 adcroft:97
Marshall, J., Jones, H. and C. Hill, (1998) Efficient ocean modeling using non-hydrostatic algorithms, Journal of Marine Systems, 18, 115-134 mars-eta:98
Adcroft, A., Hill C. and J. Marshall: (1999) A new treatment of the Coriolis terms in C-grid models at both high and low resolutions, Mon. Wea. Rev., 127, 1928-1936 adcroft:99
Hill, C, Adcroft,A., Jamous,D., and J. Marshall, (1999) A Strategy for Terascale Climate Modeling, In Proceedings of the Eighth ECMWF Workshop on the Use of Parallel Processors in Meteorology, 406-425 World Scientific Publishing Co: UK hill:99
Marotzke, J, Giering,R., Zhang, K.Q., Stammer,D., Hill,C., and T.Lee, (1999) Construction of the adjoint MIT ocean general circulation model and application to Atlantic heat transport variability, J. Geophysical Res., 104(C12), 29,529-29,547 maro-eta:99
A. Adcroft and J.-M. Campin, (2004a) Re-scaled height coordinates for accurate representation of free-surface flows in ocean circulation models, Ocean Modelling, 7, 269–284 adcroft:04a
A. Adcroft, J.-M. Campin, C. Hill, and J. Marshall, (2004b) Implementation of an atmosphere-ocean general circulation model on the expanded spherical cube, Mon Wea Rev , 132, 2845–2863 adcroft:04b
J. Marshall, A. Adcroft, J.-M. Campin, C. Hill, and A. White, (2004) Atmosphere-ocean modeling exploiting fluid isomorphisms, Mon. Wea. Rev., 132, 2882–2894 marshall:04
A. Adcroft, C. Hill, J.-M. Campin, J. Marshall, and P. Heimbach, (2004c) Overview of the formulation and numerics of the MITgcm, In Proceedings of the ECMWF seminar series on Numerical Methods, Recent developments in numerical methods for atmosphere and ocean modelling, 139–149. URL: http://mitgcm.org/pdfs/ECMWF2004-Adcroft.pdf adcroft:04c
We begin by briefly showing some of the results of the model in action to give a feel for the wide range of problems that can be addressed using it.
MITgcm has been designed and used to model a wide range of phenomena, from convection on the scale of meters in the ocean to the global pattern of atmospheric winds - see all-scales
. To give a flavor of the kinds of problems the model has been used to study, we briefly describe some of them here. A more detailed description of the underlying formulation, numerical algorithm and implementation that lie behind these calculations is given later. Indeed many of the illustrative examples shown below can be easily reproduced: simply download the model (the minimum you need is a PC running Linux, together with a FORTRAN77 compiler) and follow the examples described in detail in the documentation.
global_atmos_hs.rst ocean_gyres.rst global_ocean_circ.rst cvct_mixing_topo.rst bound_forc_inter_waves.rst parm_sens.rst global_state_est.rst ocean_biogeo_cyc.rst sim_lab_exp.rst
To render atmosphere and ocean models from one dynamical core we exploit ‘isomorphisms’ between equation sets that govern the evolution of the respective fluids - see isomorphic-equations
. 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, if we are modeling the atmosphere (right hand side of isomorphic-equations
) and height, z, if we are modeling the ocean (left hand side of isomorphic-equations
).
Isomorphic equation sets used for atmosphere (right) and ocean (left).
The state of the fluid at any time is characterized by the distribution of velocity zandp-vert-coord
.
Vertical coordinates and kinematic boundary conditions for atmosphere (top) and ocean (bottom).
b = b(θ, S, r) equation of state
Here:
r is the vertical coordinate
text{ is the ‘grad’ operator}
with ∇h operating in the horizontal and
t is time
ϕ is the ‘pressure’/‘geopotential’
b is the ‘buoyancy’
θ is potential temperature
S is specific humidity in the atmosphere; salinity in the ocean
𝒬θ are forcing and dissipation of θ
𝒬S are forcing and dissipation of S
The terms
kinematic_bound.rst atmosphere.rst ocean.rst hydrostatic.rst soln_strategy.rst finding_pressure.rst forcing_dissip.rst vector_invar.rst adjoint.rst
hydro_prim_eqn.rst
eqn_motion_ocn.rst
coordinate_sys.rst