1. Model Comparison and Evaluation Studies Tal Ezer (with H. Arango & A. Shchepetkin) TOMS Inaugural Meeting, NCAR, Aug. 23, 2001

2. Goal: to evaluate and test new numerical elements in terrain-following ocean models. Goal: to evaluate and test new numerical elements in terrain-following ocean models. Why: to help developers in improving codes and users in selecting options and parameterizations. Why: to help developers in improving codes and users in selecting options and parameterizations. How: by comparing different schemes and parameterizations in POM and ROMS/TOMS. How: by comparing different schemes and parameterizations in POM and ROMS/TOMS. Criteria: numerical errors, accuracy, stability, compatibility between schemes, computational cost. Criteria: numerical errors, accuracy, stability, compatibility between schemes, computational cost.

3. Tested Elements Advection schemes Advection schemes Time stepping algorithms Time stepping algorithms Pressure gradient schemes Pressure gradient schemes Others Others

4. Seamount configuration test Very steep case h=4050m, w=50km s=0.36, r=14.2 moderately steep h=2700m, w=100km s=0.07, r=2.7 S=max(  H/2H) r=max(  grid=(64x64x20),  x=8km

5. Zonal flow Topography Sea surface height Topography Sea surface height -50cm 0 +50cm

6. Effect of advection scheme on model: Surface elevation anomaly ADV4- 4 th ord. cnt. ADV2- 2 nd ord. cnt. ADV3- 3rd ord. upst. POMROMS

7. Time-stepping schemes (split mode: baroclinic/internal and barotropic/external) POMROMS schemeLeap-FrogPredictor-Corrector Time-splitting filter Weights: (n-1, n, n+1) Asselin (  Adams-Moulton (-1/12, 2/3, 5/12) Internal-externalCoupling Once every internal time step Weighted, every external time step

8. Coupling of barotropic (external) and baroclinic (internal) modes in ROMS DTI  U n+1 =   a m  U m  U n+½ =  b m’  U m’ DTE weights 1<m<N, N=DTI/DTE

9. Sensitivity to internal (DTI) & external (DTE) time steps DTI DTIDTE180s360s540s720s900s1080s 8s22456790112 12s1530456075 16s22344556 20s18273645 24s15223037 26s192532 32s172228 DTE180s360s540s720s900s1080s8s22456790 12s15304560 16s11223445 20s9182736 ROMS POM UNSTABLE STABLE TDI/DTE CFL=13s

10. Computational cost for different models & parameterizations model modelfeatures CPU (ms)/ (Im*Jm*Km*n) CPU (s)/ 1 day 2 nd order cent. advection 12.521.3 2 nd order upstream adv. Lin et al. (1994) 13.2 POM 3 rd order upstream adv. Smolarkiewicz (1984) 17.1 6 th order PG (CPP) Chu & Fan (1998) 207.4 Z-lev. Interp. PG scheme Kliem & Pietrzak (1999) 40.0 2 nd order cent. Adv. 17.321.6 ROMS 4 th order cent. Adv. 19.2 3 rd order upstream adv. 20.0

11. The adjustment process in POM and ROMS: forced case (zonal flow)

12. Roms- sensitivity of adjustment proces to time step choices DTE=12s DTE=24s DTI=360s DTI=720s

13. Pressure Gradient Schemes SchemeTypeReference POM-DJ Standard Density Jacobian scheme Mellor et al. (1998) POM-CCD Combined Compact Difference scheme (6 th ) Chu & Fan (1997) ROMS-FPJ Finite-Volume Pressure Jacobian scheme Lin (1997) ROMS-DJ Weighted Density Jacobian scheme (  0) Song (1998) ROMS-WDJ Weighted Density Jacobian scheme (  0.125) Song (1998) ROMS-PJQ Pressure Jacobian scheme with Quadratic Polynomial fit Shchepetkin & McWilliams (2001) ROMS-DJC Density Jacobian scheme with Cubic Polynomial fit Shchepetkin & McWilliams (2001)

14. Structure of  V (cm/s) in ROMS for different PG schemes (medium seamount case) R-DJ (Vmax=3.7) R-WDJ (Vmax=0.3) R-FPJ (Vmax=30) R-PJQ (Vmax=0.03) R-DJC (Vmax=0.06)

15. PG errors- moderately steep seamount

16. More model elements and schemes need to be tested Boundary conditions Boundary conditions Data assimilation Data assimilation Nesting and air-sea coupling Nesting and air-sea coupling Horizontal and vertical mixing schemes Horizontal and vertical mixing schemes Generalized coordinate system: comparisons between sigma, z-level & isopycnal grids. Generalized coordinate system: comparisons between sigma, z-level & isopycnal grids.