OCEAN MODELING II. Parameterizations

Transcription

1 OCEAN MODELING II Parameterizations Gokhan Danabasoglu Oceanography Section Climate and Global Dynamics Division National Center for Atmospheric Research NCAR is sponsored by the National Science Foundation

2 SPACE - TIME SCALES and OCEAN MODELS FAST WORKHORSE (CLIMATE) O( years/day) FAST O( years/ day) HI- RES O(<<10 years/day)

3 PARAMETERIZATIONS: - ACCOMPLISH PHYSICAL EFFECTS OF UNRESOLVED SUB-GRID-SCALE PROCESSES (ALL INVOLVING TURBULENCE), - PHYSICALLY-BASED / JUSTIFIED, - AS SIMPLE AS POSSIBLE, - AS FEW PARAMETERS AS POSSIBLE. Development, Implementation, Verification, Impacts

4 PARAMETERIZATIONS IN CESM1 POP2 Vertical mixing (momentum and tracers) - surface boundary layer, - interior Horizontal viscosity (momentum) Lateral mixing / mesoscale eddies (tracers) Overflows Submesoscale eddies (tracers) Diurnal cycle for short-wave heat flux Solar absorption Langmuir circulation Near-inertial wave mixing

5 VERTICAL MIXING SCHEME: K-PROFILE PARAMETERIZATION (KPP) Large, McWilliams, and Doney (1994, Rev. Geophys.) A first-order turbulent closure scheme KPP involves three high-level steps: 1. Determination of boundary layer depth, 2. Calculation of interior diffusivities, 3. Evaluation of boundary layer diffusivities.

6 KPP BOUNDARY LAYER DEPTH The boundary layer depth, h, is determined based on a bulk Richardson number, h is equated to the smallest value of d at which the bulk Ri equals Ri cr =0.3.

7 INTERIOR MIXING s Shear instability: K X w Internal wave breaking: K X d Double diffusion: K X c Local static instability (convection): K X t Tidal mixing: K X K X (interior) = K X s + K X w + K X d + K X c + K X t

8 with l = d / h, KPP BOUNDARY LAYER MIXING K X (l) = h w X (l) G(l) w X (l): turbulent velocity scale, G(l): cubic shape function. K X is non-local, Interior mixing at the base of the boundary layer influences the turbulence throughout the boundary layer, There is also a non-local counter-gradient term.

9 HORIZONTAL VISCOSITY Spatially uniform, isotropic, Cartesian, Δ=250km grid for illustration D(U) = A U xx + A U YY D(V) = A V xx + A V YY Grid Re (Diffuse Noise) A > 0.5 V Δ = 100,000 m 2 /s Resolve WBC (Munk Layers) A > β Δ 3 = 80,000 m 2 /s Diffusive CFL A < 0.5 Δ 2 / Δt = 8000,000 m 2 /s Realism (EUC, WBC) A ~ physical = 1,000 m 2 /s Smagorinsky A = C Δ 2 ( x U) 2 +( y V) 2 +( x V+ y U) 2

10 ANISOTROPIC HORIZONTAL VISCOSITY t u +... = x ( A x u) + y ( B y u) t v +... = x ( B x v) + y ( A y v) Grid Re (Diffuse Noise) Live with the noise Resolve WBC (Munk Layers) A = B = β Δ 3, only near WBC elsewhere: Realism (EUC, WBC) A = 300 m 2 /s B = 300 m 2 /s in the tropics = 600 m 2 /s polewards of 30 o Subject to diffusive CFL, but NO Smagorinsky

11 ANISOTROPIC HORIZONTAL VISCOSITY at 100-m DEPTH CCSM4 Ocean : -Minimally Numerically Viscous -Maximally Physically Viscous x 1000 m 2 /s Large et al. (2001, JPO), Jochum et al. (2008, JGR) x10 3 m 2 /s

12 IMPACTS ON LABRADOR SEA CIRCULATION AND SEA-ICE w/ SMAGORINSKY NO SMAGORINSKY Jochum et al. (2008, JGR) T (46.6m)

13 MESOSCALE EDDY PARAMETERIZATION FOR TRACERS Lateral Mixing (Interior, Tracer Diffusion) DENSITY DEPTH Ocean Observations suggest mixing along isopycnals is ~10 7 times larger than across isopycnals. Horizontal mixing causes spurious diapycnal mixing. An example: The Veronis (1975) effect For steady WBC w ρ z = κρ xx

14 GENT & McWILLIAMS (1990) MESOSCALE EDDY PARAMETERIZATION Mimics effects of unresolved mesoscale eddies as a sum of - diffusive mixing of tracers along isopycnals (Redi), - an additional advection of tracers by an eddy-induced velocity (u*, divergence-free), Quasi-adiabatic and valid for the ocean interior, Flattens isopycnals, thereby reducing potential energy, Eliminates any need for horizontal diffusion, no Veronis effect. Gent & McWilliams (1990, JPO)

15 GENT & McWILLIAMS (1990) MESOSCALE EDDY PARAMETERIZATION T t + ρ * ( u + u *) T = K T + F 3D 3D 3D z ( u*, v*) = ( A ITD s) w* = ( A ITD s) Here, T is a generic tracer, s is the 2D isopycnal slope vector, and K is the isopycnal diffusion tensor. There are two diffusivities: A I : isopycnal in K, A ITD : thickness

16 IMPACTS ON DEEP WATER FORMATION / CONVECTION HORIZONTAL MIXING GM90 PARAMETERIZATION 4 o x3 o x20l ocean model Danabasoglu et al. (1994, Science)

17 NEAR-SURFACE EDDY FLUX (NSEF) SCHEME GM90 is valid only in the quasi-adiabatic ocean interior, therefore the usual practice has been to taper both A I and A ITD to zero as the surface is approached. Diffusivities Eddy-induced velocity profile Diabatic Layer Transition Layer Interior (quasiadiabatic) (GM 90) -z Horizontal Horizontal/Isopycnal Isopycnal NSEF replaces the usual approach of applying near-surface taper functions for the diffusivities. Ferrari et al. (2008, J. Climate), Danabasoglu et al. (2008, J. Climate)

18 EDDY-INDUCED MERIDIONAL OVERTURNING CIRCULATION CONTROL NSEF units: Sv = 10 6 m 3 s -1 Vertical profiles of zonallyintegrated total advective heat transport at 49 o S Danabasoglu et al. (2008, J. Climate)

19 SPATIAL VARIATIONS OF THE EDDY DIFFUSIVITIES Following Ferreira et al. (2005), the diffusivities are specified as N 2 : Local buoyancy frequency, A = A REF ( N 2 / N 2 REF ) N 2 REF : Reference buoyancy frequency just below the transition layer, A REF : Constant reference value of A within the surface diabatic region. Surface -z Diabatic Layer Transition Layer Interior (N 2 /N 2 REF ) = 1 ; A REF N min <= (N 2 /N 2 REF ) <= 1 N min is a lower limit, N min = 0.1. Ferreira et al. (2005, JPO)

20 THICKNESS DIFFUSIVITY UPPER-OCEAN [0-945 m] MEAN ZONAL-MEAN m 2 s -1 Danabasoglu & Marshall (2007, Ocean Modelling)

21 Model Eddy-Induced Transport Comparisons with Roemmich and Gilson (2001) Observational Estimate (Repeat hydrographic line in the North Pacific at an average latitude of 22 o N) NSEF Roemmich and Gilson (2001) Danabasoglu & Marshall (2007, Ocean Modeling)

22 The eddy-induced meridional velocity is given by v* = ( A ITD z S y ) A = z where S y is the meridional slope of the isopycnal surfaces and z is the vertical coordinate (positive upwards). I ITD S y + A ITD S y z Horizontal-mean v* profiles computed between 20 o N and 40 o N in the North Pacific I ITN2 NSEF Danabasoglu & Marshall (2007, Ocean Modelling)

23 GRAVITY CURRENT OVERFLOWS GREENLAND Denmark Strait ICELAND Faroe-Bank Channel SCOTLAND Latitude from J.Price

24 GRAVITY CURRENT OVERFLOW PARAMETERIZATION surface Inflow : M i Interior : ρ i T i S i d s Sill Depth h e Ou0low: M S W s Width Entrainment ρ E T E S E M E Shelf Break Slope, α Source : ρ S T S S S X ssb M P = M S + M E Product ρ p T p S p TRACER CONSERVATION Reduced GraviUes : g s ' =(g/ρ o ) (ρ s - ρ i ) g e ' =(g/ρ o ) (ρ s - ρ e ) Based on Price & Yang (1998); described in Briegleb et al. (2010, NCAR Tech. Note) and Danabasoglu et al. (2010, JGR)

25 OVERFLOW PARAMERERIZATION MODEL SCHEMATIC

26 BOTTOM TOPOGRAPHY OF THE x1 RESOLUTION OCEAN MODEL

27 VERIFICATION AND IMPACTS OF THE OVERFLOW PARAMETERIZATION UNCOUPLED COUPLED Control (no overflows) OCN CCSM With overflows OCN* CCSM* Each experiment is run for 170 years.

28 NORDIC SEA OVERFLOW TRANSPORTS All in Sv Observed VerificaUon Steps Diagnostic model (offline) OCN* CCSM* M I M S M E M P

29 ATLANTIC MERIDIONAL OVERTURNING CIRCULATION (AMOC) OCN OCN* CCSM CCSM* in Sv

30 AMOC TRANSPORT AT 26.5 o N RAPID is observational data

31 TEMPERATURE AND SALINITY DIFFERENCES FROM OBSERVATIONS AT 2649-m DEPTH OCN OCN* mean= 0.45 o C rms= 0.50 o C mean= o C rms= 0.13 o C o C OCN OCN* mean= 0.02 psu rms= 0.03 psu mean= psu rms= 0.03 psu Obs: Levitus et al. (1998), Steele et al. (2001) psu

32 ZONAL VELOCITY ACROSS 69 o W IN THE NORTH ATLANTIC OCN OCN* velocity: cm/s, density:kg/m 3

33 EQUATORWARD VOLUME TRANSPORTS σ o 44⁰W ⁰W ⁰W ⁰W OCN OCN* OBS 13.3 Dickson and Brown(1994) 14.7 Fischer et al. (2004) 26 ± 5 Fischer et al. (2004) 12.5 Joyce et al. (2005) All in Sv

34 IMPACTS ON SEA-ICE CONCENTRATION CCSM* CCSM CCSM* - CCSM % of grid area

35 THANK YOU