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

2. Domain

3. 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

4. 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
Propagates offslope

5. Internal Tide Generation according to linear theory

6. M2 Baroclinic Tides

7. K1 Baroclinic Tides

8. Comparison to Observations: M2 Major Axes

9. Comparison to Observations: K1 Major Axes

10. Comparison to Observations: Mean Currents

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

12. 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

13. 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 * [1.-(2x10-5 –N2)/2x10-5]
Internal wave
N dependent /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 (Smyth, Skyllingstad, Crawford, Wijesekera)
Non-local fluxes, Langmuir, Stokes drift
Changes two of the Kp profile values

14. 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

15. 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)

16. 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
Kv = 0.05/(1-5Ri)2+background
max = 0.05
Otherwise Kv = background

17. 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

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

19. Comparisons to Observations (velocities)

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

21. Vertical Diffusivity (Temperature)

22. Vertical Diffusivity (Temperature) (cont)

23. Vertical Diffusivity Observations

24. Vertical Diffuxivity (Temperature)

25. Vertical Diffusivity (Temperature)

26. 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

27. Hydrography

28. 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

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. Simulations Case Number Purpose Horizontal Resolution (x, y)
Simulations
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 3
1 km 4
Bathymetry
Smith & Sandwell 5
Hydrography
Kunze 6
Vertical Resolution 7 90 8
even
(400, 1, 1) 9
(100, 1, 1) 10
uneven (100, 2, 1) 11
uneven (100, 4, 1) 12
Weighted Density Jacobian 13
Brünt-Väisäla Frequency 14
Mellor-Yamada 2.5 Level Clos. 15
Pacanowski-Philander 16
LOAM 17
LMD without BKPP 18
LMD modified 19
Generic Length Scale 20
1 m2 s-1 21
1x10-6 m2 s-1 22
Latitude Shift 5oS

40. Inverse Richardson No.