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The MOM Manual
Contents
Contents
List of Figures
Introduction to MOM and its use
II.
Introduction to MOM and its use
1. Introduction
1.1 What is MOM?
1.2 Accessing the manual, code, and database
1.3 Minimum computational requirements
1.4 How this manual is organized
1.5 Special acknowledgments and disclaimers
1.5.1 Acknowledgments
1.5.2 Disclaimer
1.5.3 Software license
2. A brief history of ocean model development at GFDL
2.1 Bryan-Cox-Semtner: 1965-1989
2.2 The GFDL Modular Ocean Models: MOM 1 and MOM 2: 1990-1995
2.3 MOM 3: 1996-1999
2.4 Documentation
2.4.1 Main differences between MOM 2 and MOM 3
2.4.2 Parallelization and Fortran 90
2.4.3 Model physics and numerics
2.5 Main differences between MOM 1 and MOM 2
2.5.1 Architecture
2.5.2 Physics and analysis tools
3. Getting Started
3.1 How to find things in MOM
3.2 Directory Structure
3.3 The MOM Test Cases
3.3.1 The run_mom script
3.4 Sample printout files
3.5 How to set up a model
3.6 Executing the model
3.7 Analyzing solutions
3.8 Executing on 32 bit workstations
3.9 NetCDF and time averaged data
3.10 Using Ferret
3.11 Upgrading from MOM 1
3.12 Upgrading to the latest version of MOM
3.12.1 The recommended method to incorporate personal changes
3.12.2 An alternative recommended method
3.13 Finding all differences between two versions of MOM
3.14 Applying bug fixes
Basic formulation
IV.
Basic formulation
4. Fundamental equations
4.1 Assumptions
4.2 The primitive equations
4.2.1 Basic constants and parameters
4.2.2 Hydrostatic pressure and the equation of state
4.2.3 Horizontal momentum equations
4.2.4 Tracer equations
4.3 Boundary and initial conditions
4.3.1 Bottom kinematic boundary condition
4.3.2 Surface kinematic boundary condition
4.3.3 Dynamic boundary conditions
4.3.4 Tracer fluxes through the model boundaries
4.3.5 Open boundaries and sponges
4.3.6 Initial conditions
4.4 Comments on volume versus mass conservation
4.4.1 Volume conservation
4.4.2 Mass conservation
4.4.3 Surface kinematic boundary conditions revisited
4.5 Flux form and finite volumes
4.6 Some basic formulae and notation
4.6.1 Differential operators
4.6.2 Leibnitz's Rule
4.6.3 Cross-products and the Levi-Civita symbol
4.6.4 Area element and volume element on a sphere
4.6.5 Vertical grid levels
5. Momentum equation methods
5.1 Separation into vertical modes
5.1.1 Vertical modes in MOM and their relation to eigenmodes
5.1.2 Motivation for separating the modes
5.2 Methods for solving the separated equations
5.2.1 The fixed surface / rigid lid method in brief
5.2.2 The free surface / non-rigid lid method in brief
6. Rigid lid streamfunction method
6.1 The barotropic streamfunction
6.2 Streamfunction and volume transport
6.3 Hydrostatic pressure with the rigid lid
6.4 The barotropic vorticity equation
6.4.1 Tendencies for the vertically averaged velocities
6.4.2 The barotropic vorticity equation
6.4.3 Caveat: inversions with steep topography
6.5 Boundary conditions and island integrals
6.5.1 Dirichlet boundary condition on the streamfunction
6.5.2 Separating the streamfunction's boundary value problem
6.5.3 Island integrals for the volume transport
6.6 The baroclinic mode
6.7 Summary of the rigid lid streamfunction method
6.8 Rigid lid surface pressure method
7. Free surface method
7.1 Hydrostatic pressure with the free surface
7.2 The barotropic system
7.2.1 Vertically integrated transport
7.2.2 Bottom and surface kinematic boundary conditions
7.2.3 Free surface height equation
7.2.4 Vertically integrated momentum equations
7.2.5 Global water budget
7.3 A linearized barotropic system
7.3.1 The barotropic system
7.3.2 The shallow water limit
7.3.3 The linearized free surface height equation
7.3.4 Summary of the linear barotropic system
7.4 Stresses at the ocean surface and bottom
7.4.1 Bottom stress
7.4.2 Surface stress
7.4.3 Revisiting the surface stress
7.5 A comment about atmospheric pressure
7.6 Vertically integrated transport
7.6.1 General considerations
7.6.2 An approximate streamfunction
8. The tracer budget
8.1 The continuum tracer concentration budget
8.2 Finite volume budget for the total tracer
8.3 Surface tracer flux
8.4 Comments on the surface tracer fluxes
8.4.1 Fresh water flux into the free surface model
8.4.2 Heat flux into the free surface model
8.5 River runoff
9. Momentum friction
9.1 History of friction in MOM
9.2 Basic properties of the stress tensor
9.2.1 The deformation or rate of strain tensor
9.2.2 Relating strain to stress
9.2.3 Angular momentum and symmetry of the stress tensor
9.3 The stress tensor in Cartesian coordinates
9.3.1 Generalized Hooke's law form
9.3.2 Angular momentum
9.3.3 Dissipation of total kinetic energy
9.3.4 Transverse isotropy
9.3.5 Trace-free frictional stress
9.3.6 Summary of the frictional stress tensor
9.3.7 Quasi-hydrostatic assumption
9.3.8 Cartesian form of the friction vector
9.3.9 The case of nonconstant viscosity
9.4 Orthogonal curvilinear coordinates
9.4.1 Some rules of tensor analysis on manifolds
9.4.2 Orthogonal coordinates
9.4.3 Physical components of tensors
9.4.4 General form of the frictional stress tensor
9.4.5 Horizontal tension and shearing rate of strain
9.4.6 The friction vector
9.4.7 Effects on kinetic energy
9.4.8 Summary of second order friction
9.5 Biharmonic friction
9.5.1 General formulation
9.5.2 Effects on kinetic energy
9.6 Comments on frictional and advective metric terms
9.6.1 Motion on an infinite plane
9.6.2 Conservation of angular momentum about the north pole
9.6.3 The advective and frictional metric terms
9.7 Functional formalism
9.7.1 Continuum formulation
9.7.2 Discrete formulation
9.8 Old friction implementation
9.8.1 Spherical form of second order friction
9.8.2 Zonal friction
9.8.3 Meridional friction
9.8.4 Old biharmonic algorithm
Code design
VI.
Code design
10. Design Philosophy
10.1 Objective
10.1.1 Speed
10.1.2 Flexibility
10.1.3 Modularity
10.1.4 Documentation
10.1.5 Coding efficiency.
10.1.6 Ability to upgrade.
11. Uni-tasking
11.1 Why memory management is important
11.2 Minimizing the memory requirement
11.2.1 Slicing through the 3-D prognostic data
11.3 The Memory Window
11.3.1 Detailed anatomy
11.3.2 Solving prognostic equations within the MW.
11.3.3 Moving the memory window
11.3.4 Questions and Answers
12. Multi-tasking
12.1 Scalability
12.2 When to multi-task
12.3 Approaches to multi-tasking
12.4 The distributed memory paradigm
12.5 Domain Decomposition
12.5.1 Calculating row boundaries on processors
12.5.2 Communications
12.5.3 The barotropic solution
13. Database
13.1 Data files
14. Variables
14.1 Naming convention for variables
14.2 The main variables
14.2.1 Relating indices j and jrow
14.2.2 Cell faces
14.2.3 Model size parameters
14.2.4 T cells
14.2.5 U cells
14.2.6 Vertical spacing
14.2.7 Time level indices
14.2.8 3-D Prognostic variables
14.2.9 2-D Prognostic variables
14.2.10 3-D Workspace variables
14.2.11 3-D Masks
14.2.12 Surface Boundary Condition variables
14.2.13 2-D Workspace variables
14.3 Operators
14.3.1 Tracer Operators
14.3.2 Momentum Operators
14.4 Input Namelist variables
14.4.1 Time and date
14.4.2 Integration control
14.4.3 Surface boundary conditions
14.4.4 Time steps
14.4.5 External mode
14.4.6 Mixing
14.4.7 Diagnostic intervals
14.4.8 Directing output
14.4.9 Isoneutral diffusion
14.4.10 Nonconstant isoneutral diffusivities
14.4.11 Pacanowski/Philander mixing
14.4.12 Smagorinsky mixing
14.4.13 Bryan/Lewis mixing
15. Modules and Modularity
15.1 List of Modules
15.1.1 convect.F
15.1.2 denscoef.F and MOM's density
15.1.3 grids.F
15.1.4 iomngr.F
15.1.5 poisson.F
15.1.6 vmix1d.F
15.1.7 timeinterp.F
15.1.8 timer.F
15.1.9 Time manager
15.1.10 topog.F
15.1.11 util.F
Grids, Geometry, and Topography
VIII.
Grids, Geometry, and Topography
16. Grids
16.1 Domain and Resolution
16.1.1 Regions
16.1.2 Resolution
16.1.3 Describing a domain and resolution
16.2 Grid cell arrangement
16.2.1 Relation between T and U cells
16.2.2 Regional and domain boundaries
16.2.3 Non-uniform resolution
16.3 Constructing a grid
16.3.1 Grids in two dimensions
16.4 Summary of options
17. Grid Rotation
17.1 Defining the rotation
17.2 Rotating Scalars and Vectors
17.3 Considerations
18. Topography and geometry
18.1 Designing topography and geometry
18.2 Options for constructing the KMT field
18.3 Meta land masses
18.4 Modifications to KMT
18.4.1 Altering the code
18.4.2 Directly editing the KMT field
18.5 Topographic instability
18.6 Viewing results
18.7 Summary of options for topography
Boundary Conditions
X.
Boundary Conditions
19. Generalized Surface Boundary Condition Interface
19.1 Coupling to atmospheric models
19.1.1 GASBC
19.1.2 GOSBC
19.2 Coupling to datasets
19.2.1 Bulk parameterizations
19.3 Surface boundary conditions
19.3.1 Default Surface boundary conditions
19.3.2 Adding or removing surface boundary conditions
20. Stevens Open Boundary Conditions
20.1 Boundary specifications
20.2 Options
20.3 New Files
20.4 Important changes to existing subroutines
20.5 Data Preparation Routines
20.6 TO-DO List (How to set up open boundaries)
Finite Difference Equations
XII.
Finite Difference Equations
21. The Discrete Equations
21.1 Time and Space discretizations
21.1.1 Averaging operators
21.1.2 Derivative operators
21.2 Key to understanding finite difference equations
21.2.1 Rules for manipulating operators
21.2.2 Rules involving summations
21.2.3 Other rules
21.3 Primitive finite difference equations
21.3.1 Momentum equations
21.3.2 Tracer equations
21.4 Time Stepping Schemes
21.4.1 Leapfrog
21.4.2 Forward
21.4.3 Euler Backward
21.4.4 Robert time filter
22. Solving the Discrete equations
22.1
Start of computation within Memory Window
22.2 loadmw (load the memory window)
22.2.1 Land/Sea masks
22.2.2 Reading latitude rows into the Memory window
22.2.3 Constructing the total velocity
22.2.4 Computing quantities within the memory window
22.3 adv_vel (computes advective velocities)
22.3.1 Advective velocities for T cells
22.3.2 Advective velocities for U cells
22.3.3 Vertical velocity on the ocean bottom
22.4 isopyc (computes isoneutral mixing tensor components)
22.5 vmixc (computes vertical mixing coefficients)
22.6 hmixc (computes horizontal mixing coefficients)
22.7 setvbc (set vertical boundary conditions)
22.8 tracer (computes tracers)
22.8.1 Tracer components
22.8.2 Advective and Diffusive fluxes
22.8.3 Isoneutral fluxes
22.8.4 Source terms
22.8.5 Sponge boundaries
22.8.6 Shortwave solar penetration
22.8.7 Tracer operators
22.8.8 Solving for the tracer
22.8.9 Diagnostics
22.8.10 End of tracer components
22.8.11 Explicit Convection
22.8.12 Filtering
22.8.13 Accumulating
22.9 baroclinic (computes internal mode velocities)
22.9.1 Hydrostatic pressure gradient terms
22.9.2 Momentum components
22.9.3 Advective and Diffusive fluxes
22.9.4 Source terms
22.9.5 Momentum operators
22.9.6 Solving for the time derivative of velocity
22.9.7 Diagnostics
22.9.8 Vertically averaged time derivatives of velocity
22.9.9 End of momentum components
22.9.10 Computing the internal modes of velocity
22.9.11 Filtering
22.9.12 Accumulating
22.10
End of computation within Memory Window
22.11 barotropic (computes external mode velocities)
22.12 diago
General model options
XIV.
General model options
23. Options for testing modules
23.1 test_convect
23.2 drive_denscoef
23.3 drive_grids
23.4 test_iomngr
23.5 test_poisson
23.6 test_vmix
23.7 test_rotation
23.8 test_timeinterp
23.9 test_timer
23.10 test_tmngr
23.11 drive_topog
23.12 test_util
24. Options for the computational environment
24.1 Computer platform
24.1.1 cray_ymp
24.1.2 cray_c90
24.1.3 cray_t90
24.1.4 cray_t3e
24.1.5 sgi
24.2 Compilers
24.3 Dataflow I/O Options
24.3.1 ramdrive
24.3.2 crayio
24.3.3 ssread_sswrite
24.3.4 fio
24.4 Parallelization
24.4.1 parallel_1d
25. Options for grid, geometry and topography
25.1 Grid generation
25.1.1 drive_grids
25.1.2 generate_a_grid
25.1.3 read_my_grid
25.1.4 write_my_grid
25.1.5 centered_t
25.2 Grid Transformations
25.2.1 rot_grid
25.3 Topography and geometry generation
25.3.1 rectangular_box
25.3.2 idealized_kmt
25.3.3 gaussian_kmt
25.3.4 scripps_kmt
25.3.5 etopo_kmt
25.3.6 read_my_kmt
25.3.7 write_my_kmt
25.3.8 flat_bottom
25.3.9 fill_isolated_cells
25.3.10 fill_shallow
25.3.11 deepen_shallow
25.3.12 round_shallow
25.3.13 fill_perimeter_violations
25.3.14 widen_perimeter_violations
26. Partial Bottom Cells
26.1 Motivation
26.2 Discrete Equations
26.2.1 Momentum equations
26.2.2 Pressure gradient
26.2.3 Tracer equations
26.3 Conservation of energy
26.3.1 Changes in Kinetic energy due to partial bottom cells
26.3.2 Additional kinetic energy change due to boundary effects
26.3.3 Changes in Potential energy due to partial bottom cells
27. Filtering
27.1 Convergence of meridians
27.1.1 fourfil
27.1.2 firfil
27.1.3 An analysis of polar filtering
27.1.4 Recommendation for tuning the polar filter
27.2 Inertial period
27.2.1 damp_inertial_oscillation
28. Initial and boundary conditions
28.1 Initial Conditions
28.1.1 ideal_thermocline
28.1.2 ideal_pycnocline
28.1.3 idealized_ic
28.1.4 levitus_ic
28.2 Surface Boundary Conditions
28.2.1 simple_sbc
28.2.2 constant_taux
28.2.3 constant_tauy
28.2.4 analytic_zonal_winds
28.2.5 linear_tstar
28.2.6 time_mean_sbc_data
28.2.7 time_varying_sbc_data
28.2.8 coupled
28.2.9 restorst
28.2.10 shortwave
28.2.11 minimize_sbc_memory
28.3 Lateral Boundary Conditions
28.3.1 cyclic
28.3.2 solid_walls
28.3.3 symmetry
28.3.4 sponges
28.3.5 obc
29. Options for the external mode
29.1 Concerning which external mode option to use
29.1.1 Wave processes
29.1.2 Surface tracer fluxes
29.1.3 Killworth topographic instability
29.1.4 Wave speed considerations
29.1.5 Polar filtering
29.1.6 Parallelization
29.2 stream_function
29.2.1 The equation
29.2.2 The coefficient matrices
29.2.3 Solving the equation
29.2.4 Island equations
29.2.5 Symmetry in the stream function equation
29.2.6 zero_island_flow
29.3 rigid_lid_surface_pressure
29.3.1 The equations
29.3.2 Remarks
29.4 implicit_free_surface
29.4.1 The equations
29.4.2 Remarks
29.5 The Killworth
et al
explicit_free_surface
29.5.1 The numerical implementation
29.5.2 Energy analysis
29.5.3 Options
29.5.4 Compatibility with other model options
29.5.5 Test cases
29.5.6 Open boundary conditions and river inflow
29.6 MOM's standard explicit_free_surface
29.6.1 Options
29.6.2 Momentum equations
29.6.3 Time stepping algorithm
29.6.4 Vertical velocities
29.6.5 Comments on the algorithm
29.6.6 Discrete tracer budgets
29.6.7 Time discretization of the tracer budgets
29.6.8 Further comments on surface fluxes and the case of salt
29.6.9 Discrete conservation properties
29.6.10 Checkerboard null mode
29.6.11 Polar filtering
30. Options for solving elliptic equations
30.1 conjugate gradient
30.2 sf_9_point
30.3 sf_5_point
31. Options for advecting tracers
31.1 Considerations of accuracy in one-dimension
31.1.1 Lattice and continuum operators
31.1.2 Leap frog in time and centered in space
31.1.3 A critique of upwind advection
31.2 second_order_tracer_advection
31.3 linearized_advection
31.4 fourth_order_tracer_advection
31.5 quicker
31.6 fct
31.6.1 Sub-options fct_dlm1 and fct_dlm2
31.6.2 Sub-option fct_3d
31.7 bottom_upwind
32. Vertical SGS options
32.1 Vertical convection
33. Vertical SGS options
33.1 Vertical convection
33.1.1 Summary of the vertical convection options
33.1.2 Explicit convection
33.2 Vertical SGS mixing schemes
33.2.1 constvmix
33.2.2 bryan_lewis_vertical
33.2.3 kppvmix
33.2.4 ppvmix
33.2.5 tcvmix
34. Horizontal SGS options
34.1 Summary of the options
34.1.1 Horizontal tracer mixing options
34.1.2 Horizontal velocity mixing options
34.2 Some numerical constraints
34.2.1 Balance between advection and diffusion
34.2.2 Linear stability of the diffusion equation
34.2.3 Western boundary currents
34.2.4 Summary: viscosity on the sphere
34.3 A comment on mixing and finite impulse filtering
34.4 Comparing Laplacian and biharmonic mixing
34.5 bryan_lewis_horizontal
34.6 Variable horizontal mixing coefficients
34.6.1 Discretization of the new metric terms
34.6.2 am_cosine
34.6.3 am_taper_highlats
34.7 The Smagorinsky scheme
34.7.1 General ideas
34.7.2 Choosing the scaling coefficient
34.7.3 Scaling coefficient conventions
34.7.4 Smagorinsky and isoneutral mixing together
34.7.5 Biharmonic Smagorinsky
34.7.6 Discretization of the Smagorinsky viscosity coefficient
34.7.7 Diffusive terms for the tracer equation
34.8 tracer_horz_laplacian
34.9 tracer_horz_biharmonic
34.10 velocity_horz_laplacian
34.11 velocity_horz_biharmonic
34.12 velocity_horz_friction_operator
35. Isoneutral SGS options
35.1 Basic isoneutral schemes
35.1.1 A note about MOM3 updates
35.1.2 Summary of the isoneutral mixing schemes
35.1.3 Summary of the options and namelist parameters
35.1.4 Some caveats and comments
35.1.5 redi_diffusion
35.1.6 gent_mcwilliams
35.1.7 Linear numerical stability for Redi and GM
35.1.8 biharmonic_rm
35.1.9 Isoneutral mixing and steep sloped regions
35.2 Schemes with nonconstant diffusivities
35.2.1 hl_diffusivity
35.2.2 vmhs_diffusivity
35.2.3 Held and Larichev combined with Visbeck
et al.
35.2.4 Netcdf information for nonconstant diffusivities
36. Miscellaneous SGS options
36.1 Eddy-topography interactions and neptune
36.2 xlandmix
36.2.1 Formulation
36.2.2 Considerations
36.2.3 xlandmix_eta
37. Bottom Boundary Layer
38. Miscellaneous options
38.1 max_window
38.2 knudsen
38.3 pressure_gradient_average
38.4 fourth_order_memory_window
38.5 implicitvmix
38.6 beta_plane
38.7 f_plane
38.8 source_term
38.9 readrmsk
38.10 show_details
38.11 timing
38.12 equivalence_mw
Diagnostic options
XVI.
Diagnostic options
38. Design of diagnostic options
38.1 Ferret
38.2 Naming Diagnostic files
38.3 Format of diagnostic data files
38.4 Sampling data
38.5 Regional masks
38.6 A note about areas on the sphere
39. Diagnostics for physical analysis
39.1 cross_flow_netcdf
39.1.1 Continuous formulation
39.1.2 Discretization
39.2 density_netcdf
39.3 diagnostic_surf_height
39.4 energy_analysis
39.5 fct_netcdf
39.6 gyre_components
39.7 local_potential_density_terms
39.7.1 Locally referenced potential density equation
39.7.2 Discretization
39.7.3 Output
39.8 matrix_sections
39.9 meridional_overturning
39.9.1 Thickness equation
39.9.2 Zonally integrated circulation and its streamfunction
39.9.3 Overturning streamfunction
39.9.4 Comments on the free surface overturning streamfunction
39.9.5 Overturning streamfunction in the plane
39.9.6 Overturning streamfunction in the plane
39.9.7 Overturning streamfunction in the plane
39.9.8 Overturning streamfunction in the plane
39.9.9 Overturning streamfunction in the plane
39.9.10 Discrete vertical-meridional streamfunction
39.9.11 Discrete density-meridional streamfunction
39.9.12 Option
merid_by_basin
39.9.13 Output
39.10 meridional_tracer_budget
39.11 monthly_averages
39.12 save_convection
39.13 save_mixing_coeff
39.14 show_external_mode
39.15 show_zonal_mean_of_sbc
39.16 snapshots
39.17 term_balances
39.17.1 Momentum Equations
39.17.2 Tracer Equations
39.18 time_averages
39.19 time_step_monitor
39.20 topog_diagnostic
39.21 tracer_averages
39.22 tracer_yz
39.23 trajectories
39.24 save_xbts
39.24.1 Momentum Equations
39.24.2 Tracer Equations
40. Diagnostics for numerical analysis
40.1 General debug options
40.2 stability_tests
40.3 trace_coupled_fluxes
40.4 trace_indices
Appendices and references
XVIII.
Appendices and references
41. Kinetic energy budget
41.1 Continuum version of the kinetic energy budget
41.1.1 The kinetic energy density
41.1.2 External and internal mode kinetic energies
41.1.3 Budget for the local kinetic energy
41.1.4 Budget for the volume averaged kinetic energy and kinetic energy density
41.1.5 External mode kinetic energy budget
41.1.6 Internal mode global kinetic energy density budget
41.1.7 Concerning the diagnostic option
energy_analysis
41.2 Energetics on the discrete grid
41.2.1 Conservative advection: part I
41.2.2 Conservative advection: part II
41.2.3 Zero work by the Coriolis force
41.2.4 Work done by pressure terms
41.2.5 Work done by Buoyancy
42. Tracer mixing kinematics
42.1 Basic properties
42.1.1 Kinematics of an anti-symmetric tensor
42.1.2 Tracer moments
42.2 Horizontal-vertical diffusion
42.3 Isopycnal diffusion
42.4 Symmetric and anti-symmetric tensors
42.5 Summary
43. Isoneutral diffusion discretization
43.0.1 Summary and Caveats
43.0.2 Functional formalism
43.0.3 Neutral directions
43.0.4 Full isoneutral diffusion tensor
43.0.5 Active tracers versus passive tracers
44. Horizontal friction discretization
44.1 Motivation and summary
45. A note about computational modes
46. References
RC Pacanowski and SM Griffies, GFDL, Jan 2000
