Modelling and parameterizing mesoscale eddies: a few remaining challenges Anne Marie Treguier (CNRS, Laboratoire de physique des océans, Brest) WGOMD meeting in Santa Fe, 5-6 march 2001

Rick Smith, ocean modeller ( ) Collins et al, The Community Climate System Model version 3 (CCSM3), JClim 2006 (225) Dukowicz and Smith, Implicit free-surface method for the Bryan-Cox-Semtner ocean model, JGR 1994 (190) Smith, RD, Maltrud, Bryan, Hecht, Numerical simulation of the North Atlantic ocean at 1/10°. JPO, 2000 (164) Smith et al, Parallel ocean general-circulation modeling, Physica D 1992 (133) Maltrud ME, Smith RD, Semtner AJ, et al: Global eddy-resolving ocean simulations driven by atmospheric winds, JGR 1998 (92) Griffies S.M. et al, Isoneutral diffusion in a z coordinate ocean model, JPO 1998 (87) Fu and Smith, Global ocean circulation from satellite altimetry and high-resolution computer simulation, BAMS 1996 (68) Dukowicz, Smith, Malone, A reformulation and implementation of the bryan-cox- semtner ocean model on the connection machine, JAOT 1993 (52) Treguier et al, The north Atlantic subpolar gyre in four high resolution ocean models, JPO 2005 (25) Best et al, Eddies in numerical models of the Antarctic circumpolar current and their influence on the mean flow, JPO 1999 (18)

Rick Smith, ocean modeller ( ) Bryan, Dukowicz, Smith: on the mixing coefficient in the parameterization of bolus velocity, JPO 1999 (32) Smith, The primitive equations in the stochastic theory of adiabatic stratified turbulence, JPO 1999 Dukowicz JK, Smith RD, Stochastic theory of compressible turbulent fluid transport, Phys. Fluids 1997 (12) Smith and Mc Williams, Anisotropic horizontal viscosity for ocean models, Ocean Modelling 2003 (29) Anisotropic Gent-McWilliams parameterization for ocean models: Smith RD, Gent PR, JPO 2004 (11)

Modelling and parameterizing mesoscale eddies: a few remaining challenges Questions (from a practioner point of view) - We all use the GM parameterization, what are we still unsure about? Spatial and temporal variation of coefficients? - Since the 80’s, we have improved our representation of tracers in ocean models: GM, isopycnal mixing, progress in advection schemes… What about the momentum equation? - What do we do about the anisotropy of eddy fluxes and nonloncal effects? - What about diabatic effects of eddies?

Outline 1 - Spatial structure of GM or isopycnal mixing coefficients. 2 - Large impacts of momentum parameterizations/numerics on the circulation 3 - Flow topography interaction, consequences for eddy fluxes 4 – Eddy fluxes in the submesoscale range (Levy et al) … other questions: Wind forcing and eddies: an issue to discuss (and settle?) What about diabatic effects of eddies?

1 - Spatial structure of eddy diffusivity Mixing coefficient for PV, tracer or buoyancy is positive; For tracer and PV it is maximum at mid-depth (stering level) PV mixing rather than GM Structure of the eddy fluxes in an unstable zonal jet (Treguier, jmr 1999) GM coefficient tracer PV

Spatial structure of eddy diffusivity Horizontal structure of mixing coefficients C Eden J. Marshall Posters by Tsujino… Riha et al, F. Bryan …

Spatial variation of diffusivity: isopycnal mixing of tracers Lee, Nurser, Coward and de Cuevas, jpo 2007 Coefficient for diffusion of T and S along isopycnals differ from GM coefficient.

Non homogeneous diffusion=advection Plumb and Mahlman 1987 GM velocity is not Lagrangian velocity Lagrangien velocity = eddy induced velocity + gradient of diffusivity

1- spatial structure of GM coefficient and diffusivity The mixing coefficient (and GM coefficient) vary in the vertical - Vertical structure varies according to location (J. Marshall) - We would like to mix PV but still don’t do it. The mixing coefficient (and GM coefficient) vary in the horizontal Two much emphasis on GM coefficient, not enough on isopycnal mixing coefficients?

Outline 1 - Spatial structure of GM or isopycnal mixing coefficients. 2 - Large impacts of momentum parameterizations/numerics on the circulation 3 - Flow topography interaction, consequences for eddy fluxes 4 – Eddy fluxes in the submesoscale range (Levy et al) … other questions: Wind forcing and eddies: an issue to discuss (and settle?) What about diabatic effects of eddies?

Position of main currents depends on viscosity Chassignet and Marshall 2009 Laplacian viscositybiharmonic viscosity

Do ocean circulation details matter for regional climate change? The path of the North Atlantic drift Top: Surface meridional currents in SODA and MPI-OM coupled runs. Bottom: Vertically integrated currents 0-750m. (Van Oldenborgh et al 2009)

Parameterizations in the momentum equation Laplacian, biharmonic? Smagorinsky? Anisotropic viscosity: Smith et al, NCAR model only. … do we know how to sort out effects of parameterizations from numerical effects?

Dependency on side wall boundary condition Free-slip, no-slip: it matters even for low resolution climate models (on a C grid) Two ORCA2 simulations, 500 years, CORE normal year (like Griffies et al, 2009). Weak salinity restoring.

ORCA2 free slip/ no slip Effects on transport over the sills (Denmark Strait) and on Labrador Sea convection Max mixed layer depth, years (top) and year (bottom) Free slip No slip

Side wall boundary condition Side wall boundary conditions have a strong effect on the circulation This is true even for low resolution climate models (at least on a C-grid). Changing the lateral boundary condition and modifying flow- topography interactions have similar effects (Penduff et al 2007, Ocean Science).

Flow-topography interactions Influence of bathymetry representation, momentum advection scheme and free-slip/no slip condition in a 0.25 degree model (Penduff et al, Ocean Science, 2007)

Outline 1 - Spatial structure of GM or isopycnal mixing coefficients. 2 - Large impacts of momentum parameterizations/numerics on the circulation 3 - Flow topography interaction, consequences for eddy fluxes 4 – Eddy fluxes in the submesoscale range (Levy et al) … other questions: Wind forcing and eddies: an issue to discuss (and settle?) What about diabatic effects of eddies?

Flow-topography interactions: local eddy fluxes The instability of the boundary currents leads to eddy shedding, controlling the exchange between the boundary currents and the interior. Example: eddy generation near Cape Desolation in the Labrador Sea

FLAME 1/12° (climatological forcing) z=1900 m U,V,T snapshots during austral winter Changes at depth z=2500 m G04G03G22 EEN + Full Steps ENS + Full Steps EEN + Partial Steps Solution resembles that of higher resolution models

Flow-topography interactions Flow instabilities often occur at specific locations constrained by the bathymetry. How do we represent/parameterize the exchange between the boundary currents and the interior in low resolution, eddy permitting, eddy resolving models?

Topography localizes/reinforces multiple jets When the baroclinic region is wide enough, multiple jets are created. The jets are modified by the presence of topography, even far away from the bathymetric feature itself. Streamfunction and kinetic energy (flat bottom wide channel), Treguier and Panetta 1994 Same with a meridional ridge across the channel

Momentum flux: generation of flow along f/h contours Zapiola anticyclone, Argentine basin, Barnier et al 2006

Flow-topography interactions - generation of localized instabilities leading to exchange between the boundary and the interior - rectification along f/h contours (Neptune effect)

Outline 1 - Spatial structure of GM or isopycnal mixing coefficients. 2 - Large impacts of momentum parameterizations/numerics on the circulation 3 - Flow topography interaction, consequences for eddy fluxes 4 – Eddy fluxes in the submesoscale range (Levy et al) … other questions: Wind forcing and eddies: an issue to discuss (and settle?) What about diabatic effects of eddies?

Effects of resolution on a subtropical gyre Levy, Klein, Treguier, Iovino, Madec, Masson, Takahashi, 2009, submitted: emergence of submesoscale dynamics in a double gyre primitive equation solution with full thermodynamics

Model configuration Simulations on the Earth Simulator  NEMO: z-coordinate free-surface primitive equation model.  Rotated double-gyre configuration, (3000  2000  4) km domain with uniform horizontal resolution on the  -plane and 30 vertical layers.  Analytical, zonal forcings (wind stress, heat and salt flux) which vary sinusoidally between winter and summer extrema.  4 simulations with increasing horizontal resolution: R1 = 1°R9 = 1/9°R27= 1/27°R54 = 1/54°  Simulations carried out for 100 years in order to reach equilibrium of intermediate waters. Model means are defined as time averages over the last 10 years.

Mean barotropic circulation As resolution is increased, the free jet gets stronger and the WBC separates earlier.

Emergence of zonal jets Zonal jets develop near the western boundary, between the latitude of jet separation and the 0 wind stress curl line

Eddies modify the stratification R1 to R9: destratification (Henning and Vallis). At higher resolution: opposite effect.

Amplification of eastward jet: consequence for the thickness of the warm water sphere How can we deal with this effect in eddy permitting and low resolution models?

Conclusion Progress of ocean models during the last 20 years: GM parameterization… but many other improvements in models (numerics: Griffies, etc). No consensus on the spatial structure of mixing coefficients? We need to develop/test parameterizations in the momentum equation, and/or for flow-topography interaction (Neptune effect, anisotropy, etc). A few surprises await us at higher resolution.