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

Domain

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

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

Internal Tide Generation according to linear theory

M2 Baroclinic Tides

K1 Baroclinic Tides

Comparison to Observations: M2 Major Axes

Comparison to Observations: K1 Major Axes

Comparison to Observations: Mean Currents

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

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

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 (Smyth, Skyllingstad, Crawford, Wijesekera) Non-local fluxes, Langmuir, Stokes drift Changes two of the Kp profile values

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

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)

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

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

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

Comparisons to Observations (velocities)

Vertical Diffusivity Observations From Kunze et al. [1991]

Vertical Diffusivity (Temperature)

Vertical Diffusivity (Temperature) (cont)

Vertical Diffusivity Observations

Vertical Diffuxivity (Temperature)

Vertical Diffusivity (Temperature)

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

Hydrography

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

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

Bathymetry

Bathymetry- M2

Bathymetry- K1

Horizontal Resolution – M2

Horizontal Resolution – K1

Comparison to Observations M2

Comparison to Observations K1

Comparison to Observations Mean Currents

Baroclinic Pressure Gradient

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

Inverse Richardson No.