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A Technical Guide to MOM4

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A Technical Guide to MOM4 A Technical Guide to MOM4 GFDL OCEAN GROUP TECHNICAL REPORT NO. 5 AUTHORS FOR MOM4.0 STEPHEN M. GRIFFIES,MATTHEW J. HARRISON, RONALD C. PACANOWSKI, AND ANTHONY ROSATI ADDITIONAL CONTRIBUTIONS FROM ZHI LIANG,MARTIN SCHMIDT, HARPER SIMMONS, AND RICHARD SLATER This document is being freely distributed by S.M. Griffies, M.J. Harrison, R.C. Pacanowski, and A. Rosati [email protected] [email protected] [email protected] [email protected] It should be referenced as ATECHNICAL GUIDE TO MOM4 GFDL OCEAN GROUP TECHNICAL REPORT NO. 5 S.M. Griffies, M.J. Harrison, R.C. Pacanowski, and A. Rosati NOAA/Geophysical Fluid Dynamics Laboratory Version prepared on August 23, 2004 Available online at www.gfdl.noaa.gov Information about how to download and run MOM4 can be found at the GFDL Flexible Modeling System (FMS) web site accessible from www.gfdl.noaa.gov. This document was prepared using LATEX as described by [561994Lamport] and [291994Goosens et al.Goosens, Mittelbach, and Samarin]. CONTENTS I Basics of MOM4 11 1 An introduction to MOM 15 1.1 What is MOM? ............................... 16 1.2 Release of MOM4.0 October 2003 ..................... 17 1.3 MOM4 documentation ........................... 17 1.4 Modeling frameworks ........................... 17 1.5 Some characteristics of MOM4 ...................... 19 1.6 Reproducing older results using MOM4.0 ................ 24 1.7 Planned ocean model development .................... 25 2 MOM4 QuickStart Guide 27 2.1 Derived types used in MOM4.0 ...................... 28 2.2 Code organization .............................. 29 2.3 How boundary conditions are handled ................. 31 2.4 Grid and topography generation ..................... 32 2.5 Initial conditions and boundary conditions ............... 33 2.6 Managing multiple tracers ......................... 34 2.7 Static memory for optimizing on SGI machines ............. 45 2.8 SHMEM versus MPI ............................ 46 2.9 MOM4 printout ............................... 47 2.10 Test cases ................................... 47 2.11 Reproducibility across processors and restarts ............. 48 II Fundamentals of MOM4 51 3 Ocean primitive equations 55 3.1 Orthogonal coordinates and the Traditional Approximation ..... 55 3.2 Ocean primitive equations ......................... 58 3.3 Ensemble averaged ocean primitive equations ............. 60 3.4 Mapping to ocean model variables .................... 64 4 Grids and halos 67 4.1 The B-grid used in MOM4 ......................... 67 4.2 The Murray (1996) tripolar grid ...................... 71 4.3 Specifying fields and grid distances within halos ............ 77 3 4 CONTENTS 5 Advection velocity components and remapping operators 87 5.1 General considerations ........................... 87 5.2 Remapping operators for horizontal fluxes ............... 89 5.3 Remapping operator for vertical fluxes .................. 90 5.4 Remapping error .............................. 95 5.5 Subtleties at the southern-most row ................... 96 6 Energetics on the B-grid lattice 97 6.1 Introduction ................................. 98 6.2 Pressure work conversions ......................... 101 6.3 Kinetic energy advection .......................... 109 6.4 Kinetic energy in the external and internal modes ........... 113 6.5 A caveat regarding the tripolar grid ................... 114 7 Total ocean mass and tracer content 115 7.1 Introduction ................................. 115 7.2 Continuum model budget ......................... 116 7.3 Discrete Boussinesq rigid lid budget ................... 116 7.4 Discrete non-Boussinesq free surface budget .............. 118 7.5 Global adjustments to recover conservation ............... 122 7.6 Comments on three versus two time level schemes ........... 127 III Vertical physics and transport 129 8 Shortwave heating 133 8.1 General considerations and model implementation .......... 133 8.2 The Paulson and Simpson (1977) irradiance function .......... 134 8.3 Shortwave penetration based on chlorophyll-a ............. 135 9 Vertical adjustment schemes 137 9.1 Introduction ................................. 137 9.2 Summary of the vertical adjustment options ............... 138 9.3 Concerning a double application of vertical adjustment ........ 138 9.4 Boussinesq and non-Boussinesq cases .................. 139 9.5 Implicit vertical mixing ........................... 139 9.6 Convective adjustment ........................... 143 10 Vertical advection 145 10.1 Vertical transport equation ......................... 145 10.2 Vertical CFL violations ........................... 146 10.3 Integer and non-integer advection .................... 146 10.4 Implicit second order vertical advection ................. 148 10.5 Implicit first order upwind advection .................. 151 CONTENTS 5 IV Some coupled modeling issues 153 11 Considerations for ice-ocean modeling 157 11.1 Introduction ................................. 157 11.2 Ocean heating due to frazil formation .................. 158 11.3 Ice with a free surface in a z-model .................... 159 11.4 Steady state mass budget .......................... 159 11.5 Dynamical budgets ............................. 160 11.6 The problem for z-coordinate ocean models ............... 161 11.7 The alternatives ............................... 162 11.8 Heat budget in coupled models ...................... 164 11.9 Some comments on suppressing a leap-frog mode ........... 165 12 River discharge into the ocean model 167 12.1 Introduction ................................. 167 12.2 General considerations ........................... 168 12.3 Steps in the algorithm ........................... 169 V Quasi-physical Parameterizations 173 13 Cross-land mixing 177 13.1 Introduction ................................. 177 13.2 Tracer and mass/volume compatibility ................. 178 13.3 Tracer mixing in a Boussinesq fluid with fixed boxes .......... 178 13.4 Mixing of mass/volume .......................... 179 13.5 Tracer and mass mixing .......................... 182 13.6 Formulation with multiple depths .................... 182 13.7 Implementation in MOM4 ......................... 185 13.8 Suppression of B-grid null mode ..................... 187 14 Cross-land insertion 189 14.1 Introduction ................................. 189 14.2 Algorithm details .............................. 190 14.3 An example: insertion to three cells .................... 192 14.4 An example: insertion to just the top cell ................. 194 15 Sigma tracer diffusion 197 15.1 Motivation for the scheme ......................... 197 15.2 Diffusivities ................................. 198 15.3 Implementation ............................... 198 16 Discharging overflow waters into the deep 201 16.1 The ubiquitous cliffs in coarse z-models ................. 201 16.2 The Campin and Goosse (1999) algorithm ................ 202 16.3 Implementation in MOM4 ......................... 205 16.4 Comments on the two overflow schemes in MOM4 .......... 207 6 CONTENTS VI Some diagnostics 209 17 Streamfunctions 213 17.1 Meridional-overturning streamfunction ................. 213 17.2 Vertically integrated transport ....................... 218 18 Diagnosing tracer transport 221 18.1 Introduction ................................. 221 18.2 Integrated mass budget .......................... 222 18.3 Integrated tracer budget .......................... 223 18.4 Northward tracer transport ........................ 224 19 Effective dianeutral diffusivity 227 19.1 Potential energy and APE in Boussinesq fluids ............. 228 19.2 Effective dianeutral mixing ........................ 229 19.3 An example with vertical density gradients ............... 233 19.4 An example with vertical and horizontal gradients ........... 239 20 Age tracers 249 20.1 Fundamental considerations ........................ 249 20.2 Age tracers .................................. 250 VII Miscellaneous Topics 253 21 Equation of state considerations 257 21.1 Introduction ................................. 257 21.2 Comments on highly accurate equations of state ............ 258 21.3 Linear equation of state ........................... 258 21.4 McDougall, Jackett, Wright, and Feistel’s EOS .............. 259 22 Open boundary conditions 263 22.1 Introduction ................................. 265 22.2 One-dimensional, linear, non-rotating waves .............. 267 22.3 Two dimensional Sommerfeld radiation condition for sea level .... 284 22.4 The rotating and stratified case ...................... 285 22.5 A radiation condition for tracers ..................... 290 22.6 The implementation of open boundaries for MOM4 .......... 292 22.7 Code Design ................................. 300 22.8 Configuration of the open boundary condition via a namelist ..... 305 22.9 Open problems ............................... 307 22.10Ocean test cases ............................... 307 23 Tidal forcing from the moon and sun 309 23.1 Tidal consituents and tidal forcing .................... 309 23.2 Implementation in MOM4 ......................... 310 CONTENTS 7 24 Eddy-topography interaction via Neptune 313 24.1 Introduction ................................. 313 24.2 Basics of the parameterization ....................... 313 24.3 As implemented in MOM4 ......................... 314 25 Temporal treatment of the Coriolis force 315 25.1 Inertial oscillations ............................. 315 25.2 Explicit temporal discretization ...................... 316 25.3 Semi-implicit temporal discretization ..................
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