Community Ocean Vertical Mixing (CVMix) Parameterizations M. Levy 1, G. Danabasoglu 1, S. Griffies 2, T. Ringler 3, A. Adcroft 2, R. Hallberg 2, and D. Jacobsen 3 1 National Center for Atmospheric Research Boulder, CO 2 Geophysical Fluid Dynamics Laboratory Princeton, NJ 3 Los Alamos National Laboratory Los Alamos, NM OMWG Meeting Breckenridge, CO June 18, 2013 M. Levy (mlevy@ucar.edu) Vertical Mixing June 18, 2013 1 / 15
Outline 1 Vertical Mixing Overview Current State of Mixing What CVMix Brings to the Table Types of Mixing 2 Results (CVMix in Stand-alone Mode) 3 Final Remarks Progress / Timeline Summary References M. Levy (mlevy@ucar.edu) Vertical Mixing June 18, 2013 2 / 15
Why is Vertical Mixing Important to Ocean Models? Basics http://weather.unisys.com/surface/sst.gif (Oct 14, 2012) Sea surface temperature (SST) has a major role in atmosphere ocean energy exchange Vertical mixing is one of many processes affecting SST Occurs on scales that are not resolved by current ocean models, need to use parameterization instead Other physical quantities (tracers, salinity, etc) also affected by mixing M. Levy (mlevy@ucar.edu) Vertical Mixing June 18, 2013 3 / 15
Mixing in Ocean Models Current State Numerous techniques for parameterizing the mixing process Currently, model developers choose their favorite parameterization(s) and code them up as part of the ocean model CVMix Project Our goal: produce an easy-to-use library containing a range of parameterizations Secondary goal: provide a stand-alone driver to test the library on its own M. Levy (mlevy@ucar.edu) Vertical Mixing June 18, 2013 4 / 15
Why CVMix? Driving Force MPAS-O does not have a KPP module yet and MOM5 is using an outdated implementation. CVMix will be used by MPAS-O and MOM6. Other Benefits 1 Reduce duplicate code for example, static mixing occurs as a step in many parameterizations 2 CSEG is working to include non-pop / non-data ocean models in CESM Vertical mixing library allows [some] physics to stay the same even if dynamics change Allow more detailed model inter-comparisons M. Levy (mlevy@ucar.edu) Vertical Mixing June 18, 2013 5 / 15
Vertical Mixing Overview kw=1 z=η(x, y, t) Divide column into nlevs levels dzw(kw=1) kt=1 dzt(kt=1) Data on cell centers and interfaces Center index kt = 1... nlevs z dzw(kw=2) dzw(kw=3) kw=2 kt=2 kw=3 dzt(kt=2) zw(kw=4) zt(kt=3) Interface index kw = 1... nlevs+1 Depth z η at surface 0 at average sea level H(x,y) at bottom (positive up!) kt,kw dzw(kw=4) dzw(kw=5) kt=3 kw=4 kt=4 dzt(kt=3) dzt(kt=4) zw(kw=nlevs+1) kw=5 z= H(x, y) What Does a Vertical Mixing Parameterization Look Like? Inputs: combination of parameters and physical values in column Outputs: viscosity (ν) and tracer diffusivity (κ) coefficients on cell interfaces M. Levy (mlevy@ucar.edu) Vertical Mixing June 18, 2013 6 / 15
Blue indicates method is already in package. M. Levy (mlevy@ucar.edu) Vertical Mixing June 18, 2013 7 / 15 [Some] Mixing Parameterizations 1 Static background mixing Constant mixing Bryan-Lewis (1979) Henyey et al. (1986) 2 Shear-induced mixing ( Richardson number mixing ) Pacanowski and Philander (1981) Large et al. (1994) Jackson et al. (2008) 3 Tidal mixing Simmons et al. 2004 Polzin (2009) / Melet et al. (2013) 4 Double diffusion mixing (Schmitt, 1994 / Large et al., 1994 / Danabasoglu et al., 2006) 5 K-profile parameterization (KPP; Large et al., 1994) 6 Vertical convective mixing
Bryan-Lewis Profile Want diffusivity to increase towards bottom of ocean. At right: diffusivity profile of two columns representing columns in different latitudes. Diffusivity and Viscosity Depend on Depth κ = c 0 + c 1 π tan 1 ν = Prκ ( ) c 2 ( z c 3 ) M. Levy (mlevy@ucar.edu) Vertical Mixing June 18, 2013 8 / 15
Shear Mixing Want diffusivity to decrease as Richardson number (Ri) increases; κ = 0 if Ri Ri 0 = 0.7. At right: The stand-alone driver produces the shear mixing diffusivity profile plot from Fig. 3 of Large, et al. (1994). Diffusivity and Viscosity Depend on Richardson Number κ = ν = Prκ κ 0 Ri 0 κ 0 [1 (Ri/Ri 0 ) p 1 ] p 2 0 < Ri < Ri 0 0 Ri Ri 0 M. Levy (mlevy@ucar.edu) Vertical Mixing June 18, 2013 9 / 15
Double Diffusion Mixing Two regimes Determine which regime we are in via stratification parameter R ρ = α ( ) Θ/ z, β S/ z where α is the thermal expansion coefficient and β is the haline contraction coefficient 1 Salt Fingering ( S/ z > 0 and 1 < R ρ < R 0 ρ ): salt water above fresher water salt water will sink 2 Diffusive Convective Instability ( Θ/ z < 0 and 0 < R ρ < 1): cold water above warm water cold water will sink M. Levy (mlevy@ucar.edu) Vertical Mixing June 18, 2013 10 / 15
Double Diffusion Mixing The stand-alone driver produces the double diffusivity profile plots from Fig. 4 of Large, et al. (1994). Salt-Fingering Regime Diffusive Convective Regime ( ) p1 ] p2 ( [ ]) R ρ 1 1 R ρ κ = κ 0 [1 κ = ν mol c 1 exp c 2 exp c 3 R 0 ρ 1 R ρ M. Levy (mlevy@ucar.edu) Vertical Mixing June 18, 2013 11 / 15
Tidal Mixing Tidal Energy Flux Map Diffusivity North of Madagascar Diffusivity Depends on Tidal Energy Flux, Depth, Density, and Buoyancy F(x,y,z) = κ = qγe(x,y)f(x,y,z) ρn 2 e z/ζ ζ(e H(x,y)/ζ e η(x,y)/ζ ) M. Levy (mlevy@ucar.edu) Vertical Mixing June 18, 2013 12 / 15
What s Been Done and What s Coming Progress Finished / tested modules from previous slide Built much of the needed infrastructure for stand-alone drivers (building, IO, etc) Working on a POP branch that can use CVMix modules Timeline Still need to add KPP module as well as a few other modules MOM & MPAS-O need to test CVMix interfaces Need to release code for public use Not release-quality yet (pressing issue: need to document APIs) If you re interested in helping pre-release testing, come talk to me! Goal: have KPP (including standalone driver) ready ASAP M. Levy (mlevy@ucar.edu) Vertical Mixing June 18, 2013 13 / 15
Summary Multi-lab collaboration to build vertical mixing library No change in POP interface, but changes under the hood Ability to run stand-alone / single-column mixing Should be available by end of summer M. Levy (mlevy@ucar.edu) Vertical Mixing June 18, 2013 14 / 15
References 1 Bryan, K. and L. J. Lewis, 1979: A water mass model of the world ocean. Journal of Geophysical Research, 84, 2503-2517. 2 Danabasoglu, G., W. G. Large, J. J. Tribbia, P. R. Gent, B. P. Briegleb, and J. C. McWilliams, 2006: Diurnal coupling in the tropical oceans of CCSM3. Journal of Climate, 19, 2347-2365. 3 Henyey, F., J. Wright, and S. M. Flatte, 1986: Energy and action flow through the internal wave field: an eikonal approach. Journal of Geophysical Research, 91, 8487-8496. 4 Jackson, L., R. Hallberg, and S. Legg, 2008: A parameterization of shear-driven turbulence for ocean climate models. Journal of Physical Oceanography, 38, 1033-1053. 5 Large, W., J. McWilliams, and S. Doney, 1994: Oceanic vertical mixing: a review and a model with a nonlocal boundary layer parameterization. Reviews of Geophysics, 32, 363-403. 6 Melet, A., R. Hallberg, S. Legg, and K. Polzin, 2013: Sensitivity of the ocean state to the vertical distribution of internal-tide-driven mixing. Journal of Physical Oceanography, 43, 602-615. 7 Pacanowksi, R. C. and G. Philander, 1981: Parameterization of vertical mixing in munerical models of the tropical ocean. Journal of Physical Oceanography, 11, 1442-1451. 8 Polzin, K. L., 2009: An abyssal recipe. Ocean Modelling, 30, 298-309. 9 Schmitt, R. W., 1994: Double diffusion in oceanography. Annual Review of Fluid Mechanics, 26, 255-285. 10 Simmons, H. L., S. R. Jayne, L. C. St. Laurent, and A. J. Weaver, 2004: Tidally driven mixing in a numerical model of the ocean general circulation. Ocean Modelling, 6, 245-263. M. Levy (mlevy@ucar.edu) Vertical Mixing June 18, 2013 15 / 15