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ROMS/TOMS Numerical Algorithms

ROMS/TOMS Numerical Algorithms. Hernan G. Arango IMCS, Rutgers University New Brunswick, NJ, USA. Developers and Collaborators. Hernan G. Arango Alexander F. Shchepetkin W. Paul Budgell Bruce D. Cornuelle Emanuele DiLorenzo Tal Ezer Mark Hadfield Kate Hedstrom Robert Hetland

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ROMS/TOMS Numerical Algorithms

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  1. ROMS/TOMS Numerical Algorithms Hernan G. Arango IMCS, Rutgers University New Brunswick, NJ, USA

  2. Developers and Collaborators Hernan G. Arango Alexander F. Shchepetkin W. Paul Budgell Bruce D. Cornuelle Emanuele DiLorenzo Tal Ezer Mark Hadfield Kate Hedstrom Robert Hetland John Klinck Arthur J. Miller Andrew M. Moore Christopher Sherwood Rich Signell John C. Warner John Wilkin Rutgers University UCLA IMR, Norway SIO SIO Princeton University NIWA, New Zealand University of Alaska, ARSC TAMU Old Dominion SIO University of Colorado USGS/WHOI SACLAND USGS/WHOI Rutgers University

  3. Universities • Government Agencies • Companies Our models are used in oceanographic studies in over 30 countries by: Totaling 280 registered users on six continents (Relief Image from NOAA Animation by Rutgers)

  4. KERNEL ATTRIBUTES • Free-surface, hydrostatic, primitive equation model • Generalized, terrain-following vertical coordinates • Boundary-fitted, orthogonal curvilinear, horizontal coordinates on an Arakawa C-grid • Non-homogeneous time-stepping algorithm • Accurate discretization of the baroclinic pressure gradient term • High-order advection schemes • Continuous, monotonic reconstruction of vertical gradients to maintain high-order accuracy

  5. Vieste (Italy) Dubrovnik (Croatia) Longitude Vertical Terrain-following Coordinates Depth (m)

  6. Curvilinear Transformation

  7. Model Grid Configuration Composed Nested

  8. ROMS/TOMS GOVERNING EQUATIONS

  9. Momentum Governing Equations

  10. Tracers Governing Equations

  11. Continuity Equation Vertical Velocity

  12. Deviatoric Transverse Stress Tensor

  13. Parabolic Splines Reconstruction

  14. Dispersive Properties of Advection 5/2 Parabolic Splines 2 10 Vs Finite Centered Differences 6 3/2 8 K(k) • x 4 1 2 1/2 /4 3/4 /2 kx

  15. Barotropic Filters

  16. Barotropic Power-Law Shape Functions

  17. Barotropic Power-Law Shape Functions

  18. Barotropic-Baroclinic Coupling

  19. ROMS/TOMS: MODULAR DESIGN

  20. CODE DESIGN • Modular, efficient, and portable Fortran code (F90/ F95) • C-preprocessing managing • Multiple levels of nesting and composed grids • Lateral boundary conditions options for closed, periodic, and radiation • Arbitrary number of tracers (active and passive) • Input and output NetCDF data structure • Support for parallel execution on both shared- and distributed -memory architectures

  21. PARALLEL DESIGN • Coarse-grained parallelization

  22. PARALLEL TILE PARTITIONS 8 x 8 Ny } } Nx

  23. PARALLEL DESIGN • Coarse-grained parallelization • Shared-memory, compiler depend directives MAIN (OpenMP standard) • Distributed-memory (MPI; SMS) • Optimized for cache-bound computers • ZIG-ZAG cycling sequence of tile partitions • Few synchronization points (around 6) • Serial and Parallel I/O (via NetCDF) • Efficiency 4-64 threads

  24. SUBGRID-SCALE PARAMETERIZATION • Horizontal mixing of tracers along level, geopotential, isopycnic surfaces • Transverse, isotropic stress tensor for momentum • General Length-Scale turbulence closure (GOTM) • Local, Mellor-Yamada, level 2.5, closure scheme • Non-local, K-profile, surface and bottom closure scheme

  25. BOUNDARY LAYERS • Air-Sea interaction boundary layer from COARE (Fairall et al., 1996) • Oceanic surface boundary layer (KPP; Large et al., 1994) • Oceanic bottom boundary layer (inverted KPP; Durski, 2001)

  26. Boundary Layer Schematic 1. ABL 2. SBL 3. BBL 4. WCBL L o n g w a v e Shortwave O E v a p H H O H H

  27. BOUNDARY LAYERS • Air-Sea interaction boundary layer from COARE (Fairall et al., 1996) • Oceanic surface boundary layer (KPP; Large et al., 1994) • Oceanic bottom boundary layer (inverted KPP; Durski et al., 2001) • Wave / Current / Sediment bed boundary layer (Styles and Glenn, 2000)

  28. Vertical Mixing and Sediment Models

  29. Turbulence Sub-Models(parameterization of <u’w’> = -ntdu/dz) • Zero equation models – Prescribe nt • One-equation models – nt ~ kl • Equation for k (advection/diffusion/production/dissipation) • Prescription for l • Two-equation models • Equation for k • Equation for l • Higher-order closures

  30. Generic Length Scale Turbulence Model Eq. 1: Eq. 2: MY25K-EK-W p 0.0 3.0 -1.0 m 1.0 1.5 0.5 n 1.0 -1.0 -1.0 Umlauf and Burchard (2002)

  31. Water 1 2 Sediment Bed 3 4 5 6 Suspended sediment transport model Transport Erosion Deposition Internal bed dynamics • - consolidation • bioturbation

  32. Estuary Test • Constant bed slope • Freshwater flow at east boundary • Tidal elevation and vertical salinity gradient at west boundary • Four turbulence models

  33. Estuary Test: Salinity Front MY 2.5 GLS - KKL GLS - KE GLS - KW Warner and Sherwood (USGS)

  34. Estuary Test: Suspended Sediment MY 2.5 GLS - KKL GLS - KE GLS - KW Warner and Sherwood (USGS)

  35. MODULES • Lagrangian Drifters (Klinck, Hadfield) • Tidal Forcing (Hetland, Signell) • River Runoff (Hetland, Signell, Geyer) • Sediment erosion, transport and deposition (Warner, Sherwood, Blaas) • Sea-Ice (Budgell, Hedstrom) • Biology Fasham-type Model (Moisan, Di Lorenzo, Shchepetkin) • EcoSim Bio-Optical Model (Bissett)

  36. Surface and sub-surface drifters Red: Surface Blue: Bottom Models predict that surface particles travel offshore and bottom particles travel onshore during upwelling events m e t e r s (Rutgers-LEO)

  37. The Coastal Gulf of Alaska Ocean currents transport fish larvae along the continental shelf in the Gulf of Alaska (PMEL/NOAA)

  38. Gulf of Maine M2 Tides 20 km Resolution Surface Elevation (m) (Hetland,Signell)

  39. Tidal currents around Martha's Vineyard and Nantucket Temperature (color) and currents (arrows) (Rutgers)

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