ROMS Embedded Gridding,

1. ROMS Embedded Gridding, Test and Application for the Simulation of the Central Upwelling of the Pacific Coast of the United States Aim: to obtain high resolution local coastal solutions, at reasonable computational cost, while preserving the large scale circulation Contributors: James C Mc Williams, Institute of Geophysics and Planetary Physics, UCLA, USA Laurent Debreu, Institut d’Informatique et Mathematiques Appliquees de Grenoble, France Patrick Marchesiello, Institute of Geophysics and Planetary Physics, UCLA, USA Pierrick Penven, Institute of Geophysics and Planetary Physics, UCLA, USA Approach: Local refinement via nested grids – family of fixed high resolution local models embedded in larger coarse-grid models.

2. Plan • Embedding method • The 1 way, 15 + 5, Central Upwelling model • 1 way nesting evaluation – comparisons with other models • Another application: the Southern California Bight • Conclusion

3. 1 - Embedding method • AGRIF (Adaptive Grid Refinement in Fortran) package [Debreu & Blayo 1999]: • Fortran 90 library for the integration of adaptive mesh refinement (AMR) features in a finite difference model. • Arbitrary number of embedded levels. • Solution-adaptive grid refinement (not used). • Based on the use of pointers  minimizes the changes in the original model • CFL criterion: child time step equal the parent time step divided by the coefficient of refinement • (3 for 5 km resolution grid embedded in a 15 km resolution grid) • Recursive procedure for the temporal coupling between parent and child grids • Advance parent by one parent time step • Interpole parent variables in space and time to get the boundary conditions for the child grid • Advance the child grid • Update point by point the parent model by the child model variables

4. Embedding in ROMS • Time splitting for barotropic and baroclinic modes: • Parent-child coupling only at each baroclinic time step. • Local preservation of the volume fluxes across the parent-child boundaries via the use of the parent volume fluxes to get the child barotropic boundary conditions. • Parallelization • S-coordinate: difference of topography between the parent and child grid. Can create inconsistencies when updating parent variables (2-way nesting). Positions of the parent (o) and child (.) “rho-points” for refinement coefficient of 3

5. 2 – The 1 way, 15 + 5, Central Upwelling model • Central Upwelling of the Pacific Coast: • From Point Conception to Cape Mendocino • Year long upwelling favorable winds • Maximum eddy energy in Northern California • Topographic particularities: Cape Mendocino – Point Arena – Monterey Bay Canyon • 1 Level embedding: • 1-way nesting • Parent model: • 15 km resolution • 84 X 169 X 20 grid points • dt = 40 min • Derived from the US-West Coast model [Marchesiello et al., 2001b] • 3 open boundaries [Marchesiello et al., 2001a] – oblique radiation condition – if direction inward: nudging towards Levitus (1994) monthly climatology – sponge layers (width = 150 km , max = 300 m2.s-1) – global volume conservation enforcement • Child model: • 5 km resolution • From north of Cape Mendocino to Point Conception • 94 X 190 X 20 grid points ( ~ 500 km cross shore X 1000 km along shore) • dt ~ 15 min • weak sponge layers (width = 50 km , max = 30 m2.s-1) • Both models: same forcing (COADS) – same initial condition (Levitus) – same topography

6. Results of the 15+5 model • Solution stable (10 years) – statistical equilibrium • No discontinuities at the parent – child boundary • Vigorous eddy activity in the child grid SST (°C) and surface currents 6 August 10 SST (°C) – 15 July 6

7. Parent – Child comparison: SST 15 July 6 (°C) Parent Child • Similitude of the solutions – filament general location does not appear to be affected by the resolution • Child grid: • longer filaments • stronger upwelling • intrusion of off shore warm water closer to the shore • narrower upwelling front

8. 15 December 9 15 January 10 15 February 10 15 March 10 15 April 10 15 May 10 15 June 10 15 July 10 Illustration of the parent-child boundary behavior: SSH time series (m)

9. Annual Mean SSH (m) Parent Child Preservation of the large scale mean circulation, but stronger meanders for the child model

10. RMS SSH (m) Parent Child RMS of SSH off shore in the child model more than 2 times stronger than the parent: Effects of eddy variability or variations induced by the boundary ?

11. Summer mean EKE (cm2.s-2) Parent Child More than 2 times more eddy activity in the child model

12. 3 – 1 way nesting evaluation – comparisons with other models • 3 other simulations used to evaluate the capabilities of 1 way nesting: • Whole pacific coast model at 5 km resolution [Marchesiello et al, 2001] used as a reference (WPC) . • 2 models using the child grid alone and active open boundaries: • 1 using the Levitus (1994) monthly climatology to force the boundaries (LEV). • 1 using a monthly climatology derived from the solution of the whole pacific at 5 km resolution (MCLM).

13. SST 15 July 6 for the 4 experiments (°C) • Strong similarities in the upwelling structure. • Filaments at approximately the same location and with the same lengths. • Smoother field offshore for LEV.

14. Mean SSH for the 4 experiments (m) • Stronger differences • Stronger gradient for LEV • The 15+5 model is very close to WPC (3 meanders with the correct values at the correct locations)

15. Annual RMS SSH for the 4 experiments (m) • LEV and MCLM around 2 times smaller than WPC. • Few differences between LEV and MCLM: the mean state does not affect much the variance of SSH. • 15+5 close to WPC : SSH variance appears to be forced by the large scale. • Stronger values ( ~ 10%) in the north-west corner: sign of blocking.

16. Annual Surface EKE for the 4 experiments (cm2.s-2 ) • LEV 2 time smaller than WPC • MCLM perform well away from the boundaries • The eddy kinetic energy is locally produced and is controlled by the mean large scale. • 15+5 is slightly lower to MCLM near the coast (mean state induced by the parent less accurate than the climatology used in MCLM). • Better values in the middle of the domain. • Blocking at the offshore boundary and in the north-west corner

17. Summer intra-seasonal surface EKE for the 4 experiments (cm2.s-2 ) • During the period of strongest eddy activity: • 15+5 closest to WPC • Good off shore • 25 % lower in the coastal transition zone • Some eddy activity, coming from North, is not resolved by the 15+5 (extension of the child domain a bit North ?)

18. 4 – Another application: the Southern California Bight • From Point Conception to the US-Mexico border • Complex bathymetric region (Islands, shallow banks, basins and trough) • Sheltered from the upwelling favorable winds •  Circulation driven by interactions between bathymetry and remotely forced currents • 2 levels of embedding – parent: 20 km resolution – 1st child: ~ 6 km resolution – 2nd child: ~ 2 km resolution • Bottom topography different between the parent and the Childs (connection at the boundaries)

19. Southern California Bight - SST - 1 October 3 (°C) • New type of instabilities at high resolution

20. Southern California Bight – Chlorophyll-a - 1 October 3 (mg.m-3)

21. 5 -Conclusion • Using the 1-way embedding method, we obtained a high resolution local solution, at reasonable computational cost, while preserving the large scale circulation. • (It requires about 19 wall-clock hours on 16 processors of SGI Origin 2000 to compute 1 year of simulation, against 16 hours for the child grid alone and 120 hours for the whole pacific coast at high resolution) • The solution compares well to the whole pacific coast model, but • there are some blocking near the off shore boundary • the level of EKE is slightly smaller at the coast. • In the near future, we propose to radiate the variables at the child boundaries, to develop and test the 2-way nesting, and to extend the child grid of the 15+5 slightly to the North. • The new pressure gradient scheme will allow the use of closer topographies between parent and child grids. • For the Central Upwelling of California, in case of smooth climatological atmospheric forcing, the variance in SSH is mostly produced by variations in the large scale circulation, while most of the eddy activity is locally generated (a part is also coming from the north).