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view on githubraw file Latest commit 0bad585a on 2022-02-16 18:55:09 UTCf67abf1ee3 Jeff*0001 Overview 0002 ******** 0003 0004 This document provides the reader with the information necessary to 0005 carry out numerical experiments using MITgcm. It gives a comprehensive 0006 description of the continuous equations on which the model is based, the 0007 numerical algorithms the model employs and a description of the associated 0008 program code. Along with the hydrodynamical kernel, physical and 0009 biogeochemical parameterizations of key atmospheric and oceanic processes 0010 are available. A number of examples illustrating the use of the model in 0011 both process and general circulation studies of the atmosphere and ocean are 0012 also presented. 0013 0014 Introduction 0015 ============ 0016 0017 MITgcm has a number of novel aspects: 0018 0019 - 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 :numref:`onemodel` 0020 0021 .. figure:: figs/onemodel.* 0022 :width: 80% 0023 :align: center 0024 :alt: One model for atmospheric and oceanic simulations 0025 :name: onemodel 0026 0027 MITgcm has a single dynamical kernel that can drive forward either oceanic or atmospheric simulations. 0028 0029 0030 - it has a non-hydrostatic capability and so can be used to study both small-scale and large scale processes - see :numref:`all-scales` 0031 0032 .. figure:: figs/scales.png 0033 :width: 90% 0034 :align: center 0035 :alt: MITgcm can simulate a wide range of scales 0036 :name: all-scales 0037 0038 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. 0039 0040 - 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 :numref:`fvol` 0041 0042 .. figure:: figs/fvol.* 0043 :width: 80% 0044 :align: center 0045 :alt: Finit volume techniques 0046 :name: fvol 0047 0048 Finite volume techniques (bottom panel) are used, permitting a treatment of topography that rivals :math:`\sigma` (terrain following) coordinates. 0049 0050 - tangent linear and adjoint counterparts are automatically maintained along with the forward model, permitting sensitivity and optimization studies. 0051 0052 - the model is developed to perform efficiently on a wide variety of computational platforms. 0053 0054 0055 Key publications reporting on and charting the development of the model are Hill and Marshall (1995), Marshall et al. (1997a), 0056 Marshall et al. (1997b), Adcroft and Marshall (1997), Marshall et al. (1998), Adcroft and Marshall (1999), Hill et al. (1999), 0057 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)): 0058 0059 Hill, C. and J. Marshall, (1995) 0060 Application of a Parallel Navier-Stokes Model to Ocean Circulation in 0061 Parallel Computational Fluid Dynamics, 0062 In Proceedings of Parallel Computational Fluid Dynamics: Implementations 0063 and Results Using Parallel Computers, 545-552. 0064 Elsevier Science B.V.: New York :cite:`hill:95` 0065 0066 Marshall, J., C. Hill, L. Perelman, and A. Adcroft, (1997a) 0067 Hydrostatic, quasi-hydrostatic, and nonhydrostatic ocean modeling, 0068 J. Geophysical Res., **102(C3)**, 5733-5752 :cite:`marshall:97a` 0069 0070 Marshall, J., A. Adcroft, C. Hill, L. Perelman, and C. Heisey, (1997b) 0071 A finite-volume, incompressible Navier Stokes model for studies of the ocean 0072 on parallel computers, J. Geophysical Res., **102(C3)**, 5753-5766 :cite:`marshall:97b` 0073 0074 Adcroft, A.J., Hill, C.N. and J. Marshall, (1997) 0075 Representation of topography by shaved cells in a height coordinate ocean 0076 model, Mon Wea Rev, **125**, 2293-2315 :cite:`adcroft:97` 0077 0078 Marshall, J., Jones, H. and C. Hill, (1998) 0079 Efficient ocean modeling using non-hydrostatic algorithms, 0080 Journal of Marine Systems, **18**, 115-134 :cite:`mars-eta:98` 0081 0082 Adcroft, A., Hill C. and J. Marshall: (1999) 0083 A new treatment of the Coriolis terms in C-grid models at both high and low 0084 resolutions, 0085 Mon. Wea. Rev., **127**, 1928-1936 :cite:`adcroft:99` 0086 0087 Hill, C, Adcroft,A., Jamous,D., and J. Marshall, (1999) 0088 A Strategy for Terascale Climate Modeling, 0089 In Proceedings of the Eighth ECMWF Workshop on the Use of Parallel Processors 0090 in Meteorology, 406-425 0091 World Scientific Publishing Co: UK :cite:`hill:99` 0092 0093 Marotzke, J, Giering,R., Zhang, K.Q., Stammer,D., Hill,C., and T.Lee, (1999) 0094 Construction of the adjoint MIT ocean general circulation model and 0095 application to Atlantic heat transport variability, 0096 J. Geophysical Res., **104(C12)**, 29,529-29,547 :cite:`maro-eta:99` 0097 0098 A. Adcroft and J.-M. Campin, (2004a) 0099 Re-scaled height coordinates for accurate representation of free-surface flows in ocean circulation models,** Warning **
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0100 Ocean Modelling, **7**, 269–284 :cite:`adcroft:04a` 0101 0102 A. Adcroft, J.-M. Campin, C. Hill, and J. Marshall, (2004b) 0103 Implementation of an atmosphere-ocean general circulation model on the expanded 0104 spherical cube,** Warning **
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0105 Mon Wea Rev , **132**, 2845–2863 :cite:`adcroft:04b` 0106 0107 J. Marshall, A. Adcroft, J.-M. Campin, C. Hill, and A. White, (2004)** Warning **
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0108 Atmosphere-ocean modeling exploiting fluid isomorphisms, Mon. Wea. Rev., **132**, 2882–2894 :cite:`marshall:04` 0109 0110 A. Adcroft, C. Hill, J.-M. Campin, J. Marshall, and P. Heimbach, (2004c)** Warning **
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0111 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 :cite:`adcroft:04c` 0112 0113 We begin by briefly showing some of the results of the model in action to 0114 give a feel for the wide range of problems that can be addressed using it. 0115 0116 0117 Illustrations of the model in action 0118 ==================================== 0119 MITgcm has been designed and used to model a wide range of phenomena, 0120 from convection on the scale of meters in the ocean to the global pattern of 0121 atmospheric winds - see :numref:`all-scales`. To give a flavor of the 0122 kinds of problems the model has been used to study, we briefly describe some 0123 of them here. A more detailed description of the underlying formulation, 0124 numerical algorithm and implementation that lie behind these calculations is 0125 given later. Indeed many of the illustrative examples shown below can be 0126 easily reproduced: simply download the model (the minimum you need is a PC 0127 running Linux, together with a FORTRAN\ 77 compiler) and follow the examples 0128 described in detail in the documentation. 0129 0130 0131 .. toctree:: 0132 :maxdepth: 3 0133 0134 global_atmos_hs.rst 0135 ocean_gyres.rst 0136 global_ocean_circ.rst 0137 cvct_mixing_topo.rst 0138 bound_forc_inter_waves.rst 0139 parm_sens.rst 0140 global_state_est.rst 0141 ocean_biogeo_cyc.rst 0142 sim_lab_exp.rst 0143 0144** Warning **
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0145 Continuous equations in ‘r’ coordinates 0146 ======================================= 0147 To render atmosphere and ocean models from one dynamical core we exploit** Warning **
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0148 ‘isomorphisms’ between equation sets that govern the evolution of the 0149 respective fluids - see :numref:`isomorphic-equations`. One system of 0150 hydrodynamical equations is written down and encoded. The model 0151 variables have different interpretations depending on whether the 0152 atmosphere or ocean is being studied. Thus, for example, the vertical** Warning **
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0153 coordinate ‘:math:`r`’ is interpreted as pressure, :math:`p`, if we are 0154 modeling the atmosphere (right hand side of :numref:`isomorphic-equations`) and height, :math:`z`, if we are modeling 0155 the ocean (left hand side of :numref:`isomorphic-equations`). 0156 0157 0158 .. figure:: figs/zandpcoord.png 0159 :width: 80% 0160 :align: center 0161 :alt: isomorphic-equations 0162 :name: isomorphic-equations 0163 0164 Isomorphic equation sets used for atmosphere (right) and ocean (left). 0165 0166 0167 The state of the fluid at any time is characterized by the distribution 0168 of velocity :math:`\vec{\mathbf{v}}`, active tracers :math:`\theta` and** Warning **
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0169 :math:`S`, a ‘geopotential’ :math:`\phi` and density 0170 :math:`\rho =\rho (\theta ,S,p)` which may depend on :math:`\theta`, 0171 :math:`S`, and :math:`p`. The equations that govern the evolution of 0172 these fields, obtained by applying the laws of classical mechanics and 0173 thermodynamics to a Boussinesq, Navier-Stokes fluid are, written in 0174 terms of a generic vertical coordinate, :math:`r`, so that the 0175 appropriate kinematic boundary conditions can be applied isomorphically 0176 see :numref:`zandp-vert-coord`. 0177 0178 0179 .. figure:: figs/vertcoord.* 0180 :width: 60% 0181 :align: center 0182 :alt: zandp-vert-coord 0183 :name: zandp-vert-coord 0184 0185 Vertical coordinates and kinematic boundary conditions for atmosphere (top) and ocean (bottom). 0186 0187 .. math:: 0bad585a21 Navi*0188 \frac{D\vec{\mathbf{v}}_{h}}{Dt}+\left( 2\vec{\boldsymbol{\Omega}}\times \vec{\mathbf{v}} 0189 \right) _{h}+ \nabla _{h}\phi = \vec{\boldsymbol{\mathcal{F}}}_h\text{ horizontal momentum} f67abf1ee3 Jeff*0190 :label: horiz-mtm 0191 0192 .. math:: 0bad585a21 Navi*0193 \frac{D\dot{r}}{Dt}+\hat{\boldsymbol{k}}\cdot \left( 2\vec{\boldsymbol{\Omega}}\times \vec{\mathbf{ f67abf1ee3 Jeff*0194 v}}\right) +\frac{\partial \phi }{\partial r}+b=\mathcal{F}_{\dot{r}}\text{ vertical momentum} 0195 :label: vert-mtm 0196 0197 .. math:: 0bad585a21 Navi*0198 \nabla _{h}\cdot \vec{\mathbf{v}}_{h}+\frac{\partial \dot{r}}{ f67abf1ee3 Jeff*0199 \partial r}=0\text{ continuity} 0200 :label: continuity 0201 0202 .. math:: 0203 b=b(\theta ,S,r)\text{ equation of state} 0204 :label: eos 0205 0206 .. math:: 0207 \frac{D\theta }{Dt}=\mathcal{Q}_{\theta }\text{ potential temperature} 0208 :label: pot-temp 0209 0210 .. math:: 0211 \frac{DS}{Dt}=\mathcal{Q}_{S}\text{ humidity/salinity} 0212 :label: humidity-salt 0213 0214 Here: 0215 0216 .. math:: r\text{ is the vertical coordinate} 0217 0218 .. math:: 0219 0bad585a21 Navi*0220 \frac{D}{Dt}=\frac{\partial }{\partial t}+\vec{\mathbf{v}}\cdot \nabla \text{ is the total derivative} f67abf1ee3 Jeff*0221 0222 .. math:: 0223 0bad585a21 Navi*0224 \nabla = \nabla _{h}+\hat{\boldsymbol{k}}\frac{\partial }{\partial r} f67abf1ee3 Jeff*** Warning **
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0225 \text{ is the ‘grad’ operator} 0226 0bad585a21 Navi*0227 with :math:`\nabla _{h}` operating in the horizontal and 0228 :math:`\hat{\boldsymbol{k}} f67abf1ee3 Jeff*0229 \frac{\partial }{\partial r}` operating in the vertical, where 0bad585a21 Navi*0230 :math:`\hat{\boldsymbol{k}}` is a unit vector in the vertical f67abf1ee3 Jeff*0231 0232 .. math:: t\text{ is time} 0233 0234 .. math:: 0235 0236 \vec{\mathbf{v}}=(u,v,\dot{r})=(\vec{\mathbf{v}}_{h},\dot{r})\text{ is the velocity} 0237** Warning **
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0238 .. math:: \phi \text{ is the ‘pressure’/‘geopotential’} 0239 0bad585a21 Navi*0240 .. math:: \vec{\boldsymbol{\Omega}}\text{ is the Earth's rotation} f67abf1ee3 Jeff*0241** Warning **
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0242 .. math:: b\text{ is the ‘buoyancy’} 0243 0244 .. math:: \theta \text{ is potential temperature} 0245 0246 .. math:: S\text{ is specific humidity in the atmosphere; salinity in the ocean} 0247 0248 .. math:: 0249 0bad585a21 Navi*0250 \vec{\boldsymbol{\mathcal{F}}}\text{ are forcing and dissipation of }\vec{ f67abf1ee3 Jeff*0251 \mathbf{v}} 0252 0253 .. math:: \mathcal{Q}_{\theta }\mathcal{\ }\text{ are forcing and dissipation of }\theta 0254 0255 .. math:: \mathcal{Q}_{S}\mathcal{\ }\text{are forcing and dissipation of }S 0256 0bad585a21 Navi*0257 The terms :math:`\vec{\boldsymbol{\mathcal{F}}}` and :math:`\mathcal{Q}` f67abf1ee3 Jeff*** Warning **
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0258 are provided by ‘physics’ and forcing packages for atmosphere and ocean. 0259 These are described in later chapters. 0260 0261 0262 .. toctree:: 0263 :maxdepth: 3 0264 0265 kinematic_bound.rst 0266 atmosphere.rst 0267 ocean.rst 0268 hydrostatic.rst 0269 soln_strategy.rst 0270 finding_pressure.rst 0271 forcing_dissip.rst 0272 vector_invar.rst 0273 adjoint.rst 0274 0275 0276 Appendix ATMOSPHERE 0277 =================== 0278 0279 .. toctree:: 0280 :maxdepth: 3 0281 0282 hydro_prim_eqn.rst 0283 0284 0285 Appendix OCEAN 0286 ============== 0287 0288 .. toctree:: 0289 :maxdepth: 3 0290 0291 eqn_motion_ocn.rst 0292 0293 0294 Appendix OPERATORS 0295 ================== 0296 0297 .. toctree:: 0298 :maxdepth: 3 0299 0300 coordinate_sys.rst
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