On mixing and advection in the BBL On mixing and advection in the BBL and how they are affected by the and how they are affected by the

model grid: Sensitivity studies with a model grid: Sensitivity studies with a generalized coordinate ocean modelgeneralized coordinate ocean model

Tal Ezer and George MellorTal Ezer and George Mellor

Princeton UniversityPrinceton University

• The generalized coordinate modelThe generalized coordinate model((Mellor et al., 2002; Ezer & Mellor, Ocean Modeling, In Press, Mellor et al., 2002; Ezer & Mellor, Ocean Modeling, In Press, 20032003) )

• Sensitivity experiments: Sensitivity experiments:

1. effect of grid (Z vs Sigma) 1. effect of grid (Z vs Sigma)

2. effect of horizontal diffusion & vertical 2. effect of horizontal diffusion & vertical mixingmixing

3. effect of model resolution3. effect of model resolution

The generalized coordinate The generalized coordinate systemsystem

Z(x,y,t)=Z(x,y,t)=(x,y,t)+s(x,y,k,t)(x,y,t)+s(x,y,k,t) ; 1<k<kb, ; 1<k<kb, 0<0<<-1<-1

Special casesSpecial cases

Z-level:Z-level: s=s=(k)[H(k)[Hmaxmax+ + (x,y,t)](x,y,t)]

Sigma coord.: Sigma coord.: s=s=(k)[H(x,y)+ (k)[H(x,y)+ (x,y,t)](x,y,t)]

S-coordinates (Song & Haidvogel, 1994):S-coordinates (Song & Haidvogel, 1994):

s=(1-b) func[sinh(a,s=(1-b) func[sinh(a,)]+b func[tanh(a,)]+b func[tanh(a,)])]a, b= stretching parametersa, b= stretching parameters

Other adaptable gridsOther adaptable grids

Semi-isopycnal?: Semi-isopycnal?: s=func[s=func[(x,y,z,t)](x,y,z,t)]

Potential Grids

Effect of model vertical grid on large-scale, Effect of model vertical grid on large-scale, climate simulationsclimate simulations

Experiments:Experiments:

• Start with T=T(z)Start with T=T(z)• Apply heating in low Apply heating in low

latitudes and cooling latitudes and cooling in high latitudesin high latitudes

• Integrate model for Integrate model for 100 years using 100 years using different gridsdifferent grids

(all use M-Y mixing) (all use M-Y mixing)

T T

T

U

W

I-1 I I+1

K-1

K

K+1

Some Solutions:

• Embedded BBL(Beckman & Doscher, 1997;Killworth & Edwards, 1999;

Song & Chao, 2000)

• “Shaved” or partial cells(Pacanowski & Gnanadesikan,

1998;Adcroft et al., 1997)

The problem of BBLs & deep water formation in z-level models

is well known(Gerdes, 1993; Winton et al.,

1998;Gnanadesikan, 1999)

Dynamics of Overflow Mixing & Entrainment (DOME) Dynamics of Overflow Mixing & Entrainment (DOME) projectproject

Bottom Topography Initial Temperature Bottom Topography Initial Temperature(top view) (side view) (top view) (side view)

embayment

slope

deep

Simulation Simulation of bottom of bottom

plume plume with a with a sigma sigma

coordinate coordinate ocean ocean model model (10km (10km grid)grid)

ExperimeExperimentnt

Horizontal Horizontal ResolutioResolutio

nn

Vertical Vertical ResolutioResolutio

nn

Number Number of Layersof Layers

Diffusion Diffusion Coeff.Coeff.

S1S1 10 km10 km 12-72 m12-72 m 5050 10 10

S2S2 10 km10 km 12-72 m12-72 m 5050 100100

S3S3 10 km10 km 12-72 m12-72 m 5050 10001000

Z1Z1 10 km10 km 50-100 m50-100 m 5050 10 10

Z2Z2 10 km10 km 50-100 m50-100 m 5050 100100

Z3Z3 10 km10 km 50-100 m50-100 m 5050 10001000

S4S4 10 km10 km 60-360 m60-360 m 1010 100100

Z4Z4 2.5 km2.5 km 25 m25 m 9090 1010

The effect of horizontal diffusivity The effect of horizontal diffusivity on the Sigma coordinate modelon the Sigma coordinate model

(tracer concentration in bottom layer)(tracer concentration in bottom layer)

10 days

20 days

DIF=10 DIF=100 DIF=1000

The effect of grid type- The effect of grid type- Sigma vs. Z-level coordinatesSigma vs. Z-level coordinates

SIG-10 days

SIG-20 days

ZLV-10 days

ZLV-20 days

SIG

DIF=10

SIG

DIF=1000

ZLV

DIF=10

ZLV

DIF=1000

Increasing hor. diffusion

causes thinner BBL in sigma

grid but thicker BBL

in z-level grid!

The BBL:

More stably stratified & thinner in

SIG

Larger downslope vel. in SIG, but much

larger (M-Y) mixing coeff.

in ZLV

The difference in mixing mechanism: SIG is dominated by downslope advection, the ZLV by vertical mixing

The effect of grid resolutionThe effect of grid resolution

oror

Is there a convergence of the z-lev. model Is there a convergence of the z-lev. model to the sigma model solution when grid is to the sigma model solution when grid is

refined?refined?

The Problem: to resolve the slope the z-lev. The Problem: to resolve the slope the z-lev. grid requires higher resolution for both, grid requires higher resolution for both,

horizontal and vertical grid.horizontal and vertical grid.

New high-res. z-grid experiment: New high-res. z-grid experiment:

quadruplequadruple hor. res., hor. res., doubledouble ver. res. ver. res.

10 km grid

2.5 km grid

Increasing resolution in the z-lev. grid resulted in thinner BBL and larger downslope extension of

the plume.

ZLV: 10 km, 50 levels ZLV: 2.5 km, 90 levels

The thickness of the BBL and the extension of the plume are comparable to much coarse res. sigma

grid.

SIG: 10 km, 10 levels ZLV: 2.5 km, 90 levels

How do model results compare with How do model results compare with observations?observations?

From: Girton & Sanford, Descent and modification of the overflow plume in the Denmark Strait, JPO, 2003

Density section along the plume Thickness across the plume

ExperimeExperimentnt

ResolutioResolutio

nn

Diffusion Diffusion Coeff.Coeff.

Plume Plume AreaArea

100km100km22

Plume Plume ThicknessThickness

S2S2 10 10 km/50L km/50L

10 10 13.313.3 244 m244 m

S3S3 10 10 km/50Lkm/50L

10001000 14.614.6 276 m276 m

Z2Z2 10 10 km/50Lkm/50L

10 10 7.57.5 414 m414 m

Z3Z3 10 10 km/50Lkm/50L

10001000 6.06.0 498 m498 m

S4S4 10 10 km/10Lkm/10L

100100 10.310.3 276 m276 m

Z4Z4 2.5 2.5 km/90Lkm/90L

1010 9.09.0 272 m272 m

Denmark Denmark Strait Strait Obs.Obs.

(Girton &(Girton & Sanford,Sanford, 2003)2003) ~200 m~200 m

Comments:Comments:

• Terrain-following grids are ideal for BBL and Terrain-following grids are ideal for BBL and dense overflow problems.dense overflow problems.(Isopicnal models are also useful for overflow problems, but may (Isopicnal models are also useful for overflow problems, but may have difficulties in coastal, well mixed regions)have difficulties in coastal, well mixed regions)

• Hybrid or generalized coordinate models may be Hybrid or generalized coordinate models may be useful for intercomparison studies, or for useful for intercomparison studies, or for optimizing large range of scales or processes in a optimizing large range of scales or processes in a single code.single code.

• However, how to best construct such models and However, how to best construct such models and how to optimizing such grids for various how to optimizing such grids for various applications are open questions that need further applications are open questions that need further research. research.