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. M 2 Baroclinic Tides

6. K 1 Baroclinic Tides

7. Comparison to Observations: M 2 Major Axes

8. Comparison to Observations: K 1 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 R i 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 –N 2 )/2x10 -5 ] –Internal wave N dependent 10 -6 /N 2 (min N of 10 -7 ) –Double diffusion Only for tracers For R i < 0.8, the first dominates For R i > 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 - 3 rd order upstream differencing [McWilliams and Shchepetkin]  Explicit vertical advection  Laplacian lateral diffusion along sigma surfaces (1 m 2 s -1 )  LMD scheme for vertical mixing  Exact baroclinic pressure gradient  Density based on bulk modulus  Tidal Forcing – M 2, S 2, O 1, and K 1  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- M 2

32. Bathymetry- K 1

33. Horizontal Resolution – M 2

34. Horizontal Resolution – K 1

35. Comparison to Observations M 2

36. Comparison to Observations K 1

37. Comparison to Observations Mean Currents

38. Baroclinic Pressure Gradient

39. Simulations Case Num ber Purpose Horizontal Resolution (  x,  y) Vertical Resolution no. of levels) Vertical Resolution: Spacing (mixed layer,  S  B ) Baroclinic Pressure Gradient Vertical Mixing Horizont al Mixing Other 1Base Case2 km60uneven (100,2,.5) SDJLMD2 nd Order Laplacia n 2Horizontal Resolution 4 km30uneven (100,2,.5) SDJLMD2 nd Order Laplacia n 3Horizontal Resolution 1 km60uneven (100,2,.5) SDJLMD2 nd Order Laplacia n 4Bathymetry2 km60uneven (100,2,.5) SDJLMD2 nd Order Laplacia n Smith & Sandw ell 5Hydrography2 km60uneven (100,2,.5) SDJLMD2 nd Order Laplacia n Kunze 6Vertical Resolution 2 km30uneven (100,2,.5) SDJLMD2 nd Order Laplacia n 7Vertical Resolution 2 km90uneven (100,2,.5) SDJLMD2 nd Order Laplacia n 8Vertical Resolution 2 km60even (400, 1, 1) SDJLMD2 nd Order Laplacia n 9Vertical Resolution 2 km60even (100, 1, 1) SDJLMD2 nd Order Laplacia n 10Vertical Resolution 2 km60uneven (100, 2, 1) SDJLMD2 nd Order Laplacia n 11Vertical Resolution 2 km60uneven (100, 4, 1) SDJLMD2 nd Order Laplacia n 12Baroclinic Pressure Gradient 2 km60uneven (100,2,.5) Weighted Density Jacobian LMD2 nd Order Laplacia n 13Vertical Mixing 2 km60uneven (100,2,.5) SDJBrünt-Väisäla Frequency 2 nd Order Laplacia n 14Vertical Mixing 2 km60uneven (100,2,.5) SDJMellor- Yamada 2.5 Level Clos. 2 nd Order Laplacia n 15Vertical Mixing 2 km60uneven (100,2,.5) SDJPacanowski- Philander 2 nd Order Laplacia n 16Vertical Mixing 2 km60uneven (100,2,.5) SDJLOAM2 nd Order Laplacia n 17Vertical Mixing 2 km60uneven (100,2,.5) SDJLMD without BKPP 2 nd Order Laplacia n 18Vertical Mixing 2 km60uneven (100,2,.5) SDJLMD modified2 nd Order Laplacia n 19Vertical Mixing 2 km60uneven (100,2,.5) SDJGeneric Length Scale 2 nd Order Laplacia n 20Horizontal Mixing 2 km60uneven (100,2,.5) SDJLMD 1 m 2 s -1 21Horizontal Mixing 2 km60uneven (100,2,.5) SDJLMD1x10 -6 m 2 s -1 22Other2 km60uneven (100,2,.5) SDJLMD2 nd Order Laplacia n Latitud e Shift 5 o S

40. Inverse Richardson No.