Vertical Mixing Parameterizations and their effects on the skill of Baroclinic Tidal Modeling

1. Vertical Mixing Parameterizations and their effects on the skill of Baroclinic Tidal Modeling Robin Robertson Lamont-Doherty Earth Observatory of Columbia University Palisades, NY

2. Domain

3. Internal Wave Theory • Internal wave generation criteria according to linear theory •  - slope of internal wave rays •  =1 – critical • Most generation • resonant •  < 1 – subcritical • Less generation • Propagates both on and offslope •  > 1 – supercritical • Less generation • Propagates offslope

4. Internal Tide Generation according to linear theory

5. M2 Baroclinic Tides

6. K1 Baroclinic Tides

7. Comparison to Observations:M2 Major Axes

8. Comparison to Observations:K1 Major Axes

9. Comparison to Observations:Mean Currents

10. Vertical Mixing Parameterizations • Large-McWilliams-Doney (LMD) Kp profile • Mellor-Yamada 2.5 level turbulence closure (MY2.5) • Brunt-Väisälä frequency (BVF) • Pacanowski-Philander (PP) • Generic Length Scale (GLS) • Lamont Ocean Atmosphere Mixed Layer Model (LOAM ) • LMD - modified

11. Large-McWilliams-Doney Kp profile • Primary processes • Local Ri instabilities due to resolvable vertical shear • If (1-Ri/0.7) > 0 10-3 (1-Ri/0.7)3 • Convection • N dependent 0.1 * [1.-(2x10-5 –N2)/2x10-5] • Internal wave • N dependent 10-6/N2 (min N of 10-7) • Double diffusion • Only for tracers • For Ri< 0.8, the first dominates • For Ri> 0.8, the third dominates • Modified • Non-local fluxes, Langmuir, Stokes drift • Changes two of the Kp profile values

12. Mellor-Yamada 2.5 level turbulence closure • Designed for boundary layer flows • Based on turbulent kinetic energy and length scale which are time stepped through the simulation • Matched laboratory turbulence • Logarithmic law of the wall • Not designed for internal wave mixing • Fails in the presence of stratification

13. Brunt-Väisälä frequency • Diffusivity is a function of N • If N < 0 Kv = 1 • If N = 0 Kv = background value • If N > 0 Kv = 10-7/N • Min of 3x10-5 • Max of 4x10-4 • Background values is input (10-6)

14. Pacanowski-Philander • Designed for the tropics • Gradient Ri dependent • If Ri > .2 Kv = 0.01/(1-5Ri)2+background max = 0.01 • Otherwise Kv = 0.01 • LOAM – version modified for use outside the tropics • If Ri > .2 Kv = 0.05/(1-5Ri)2+background max = 0.05 • Otherwise Kv = background

15. Generic Length Scale • Two generic equations • D - turbulent and viscous transport • P - KE production by shear • G - KE production by buoyancy •  - Dissipation • c - model constants • Based on turbulent kinetic energy and length scale which are time stepped through the simulation • MY2.5 is a special case • p=0, m=1, n=1

16. Major Axis Errors Red indicated absolute error values lower than those of the base case.

17. Comparisons to Observations (velocities)

18. Vertical Diffusivity Observations From Kunze et al. [1991]

19. Vertical Diffusivity (Temperature)

20. Vertical Diffusivity (Temperature) (cont)

21. Vertical Diffusivity Observations

22. Vertical Diffuxivity (Temperature)

23. Vertical Diffusivity (Temperature)

24. Summary • Baroclinic tides were simulated using ROMS • Semidiurnal tides were reproduced successfully • Diurnal tides were not reproduced • Critical latitude effects • Mean currents insufficiently simulated • Generic Length Scale (GLS) produced the most realistic vertical diffusivities • Acknowledgments – Data from Brink, Toole, Kunze, Noble, and Eriksen

25. Model Description  Regional Ocean Modeling System (ROMS) ·  Primitive equation model; non-linear  Split 2-D and 3-D modes ·  Boussinesq and hydrostatic approximations ·  Horizontal advection - 3rd order upstream differencing [McWilliams and Shchepetkin] ·  Explicit vertical advection ·  Laplacian lateral diffusion along sigma surfaces (1 m2 s-1) ·  LMD scheme for vertical mixing  Exact baroclinic pressure gradient ·  Density based on bulk modulus ·  Tidal Forcing – M2, S2, O1, and K1  Elevations - set at boundaries ·  2-D velocities – radiation [Flather] ·  3-D velocities – flow relaxation scheme ·   tracers – flow relaxation scheme ·   Time Step - 4 s barotropic, 120 s baroclinc mode ·   Simulation Duration: 30 days

26. Hydrography

27. Evaluation of Operational Considerations and Parameterizations • Horizontal Resolution: • Improving resolution improves agreement • 1 km shows best agreement • Vertical Resolution: • No. of Levels: • Doubling the number of levels from 30 to 60 slightly improved the agreement • Increasing the number of levels to 90, showed no improvement • Spacing: • Uneven spacing with more levels near the surface and bottom improves agreement with observations • Best match - shallow mixed layer, S = 2, and B = .5 • Bathymetry: • Improvement with the finer scale Eriksen bathymetry • Increased generation of internal tides on a small scale • Hydrography: • Improvement with the finer scale Kunze hydrography • Baroclinic Pressure Gradient: • Weighted Density Jacobian performed more poorly than Spline Density Jacobian • Vertical Mixing: • GLS showed the best agreement • Horizontal Mixing: No appreciable effect

28. Sensitivity Study • Bathymetry • Hydrography • Horizontal Resolution • Vertical Resolution and Spacing • Baroclinic Pressure Gradient Parameterization • Vertical Mixing Parameterization • Horizontal Mixing

29. Major Axis Errors Red indicated absolute error values lower than those of the base case.

30. Bathymetry

31. Bathymetry- M2

32. Bathymetry- K1

33. Horizontal Resolution – M2

34. Horizontal Resolution – K1

35. Comparison to Observations M2

36. Comparison to Observations K1

37. Comparison to Observations Mean Currents

38. Baroclinic Pressure Gradient

39. Case Number Purpose Horizontal Resolution (x, y) Vertical Resolution no. of levels) Vertical Resolution: Spacing (mixed layer, S B) Baroclinic Pressure Gradient Vertical Mixing Horizontal Mixing Other 1 Base Case 2 km 60 uneven (100,2,.5) SDJ LMD 2nd Order Laplacian 2 Horizontal Resolution 4 km 30 uneven (100,2,.5) SDJ LMD 2nd Order Laplacian 3 Horizontal Resolution 1 km 60 uneven (100,2,.5) SDJ LMD 2nd Order Laplacian 4 Bathymetry 2 km 60 uneven (100,2,.5) SDJ LMD 2nd Order Laplacian Smith & Sandwell 5 Hydrography 2 km 60 uneven (100,2,.5) SDJ LMD 2nd Order Laplacian Kunze 6 Vertical Resolution 2 km 30 uneven (100,2,.5) SDJ LMD 2nd Order Laplacian 7 Vertical Resolution 2 km 90 uneven (100,2,.5) SDJ LMD 2nd Order Laplacian 8 Vertical Resolution 2 km 60 even (400, 1, 1) SDJ LMD 2nd Order Laplacian 9 Vertical Resolution 2 km 60 even (100, 1, 1) SDJ LMD 2nd Order Laplacian 10 Vertical Resolution 2 km 60 uneven (100, 2, 1) SDJ LMD 2nd Order Laplacian 11 Vertical Resolution 2 km 60 uneven (100, 4, 1) SDJ LMD 2nd Order Laplacian 12 Baroclinic Pressure Gradient 2 km 60 uneven (100,2,.5) Weighted Density Jacobian LMD 2nd Order Laplacian 13 Vertical Mixing 2 km 60 uneven (100,2,.5) SDJ Brünt-Väisäla Frequency 2nd Order Laplacian 14 Vertical Mixing 2 km 60 uneven (100,2,.5) SDJ Mellor-Yamada 2.5 Level Clos. 2nd Order Laplacian 15 Vertical Mixing 2 km 60 uneven (100,2,.5) SDJ Pacanowski-Philander 2nd Order Laplacian 16 Vertical Mixing 2 km 60 uneven (100,2,.5) SDJ LOAM 2nd Order Laplacian 17 Vertical Mixing 2 km 60 uneven (100,2,.5) SDJ LMD without BKPP 2nd Order Laplacian 18 Vertical Mixing 2 km 60 uneven (100,2,.5) SDJ LMD modified 2nd Order Laplacian 19 Vertical Mixing 2 km 60 uneven (100,2,.5) SDJ Generic Length Scale 2nd Order Laplacian 20 Horizontal Mixing 2 km 60 uneven (100,2,.5) SDJ LMD 1 m2 s-1 21 Horizontal Mixing 2 km 60 uneven (100,2,.5) SDJ LMD 1x10-6 m2 s-1 22 Other 2 km 60 uneven (100,2,.5) SDJ LMD 2nd Order Laplacian Latitude Shift 5oS Simulations

40. Inverse Richardson No.