On mixing and advection in the BBL and

On mixing and advection in the BBL and how they are affected by the model grid: Sensitivity studies with a generalized coordinate ocean model Tal Ezer and George Mellor Princeton University • The generalized coordinate model (Mellor et al. , 2002; Ezer & Mellor, Ocean Modeling, In Press, 2003) • Sensitivity experiments: 1. effect of grid (Z vs Sigma) 2. effect of horizontal diffusion & vertical mixing 3. effect of model resolution

The generalized coordinate system Z(x, y, t)= (x, y, t)+s(x, y, k, t) ; 1<k<kb, 0< <-1 Special cases Z-level: s= (k)[Hmax+ (x, y, t)] Sigma coord. : s= (k)[H(x, y)+ (x, y, t)] S-coordinates (Song & Haidvogel, 1994): s=(1 -b) func[sinh(a, )]+b func[tanh(a, )] a, b= stretching parameters Other adaptable grids Semi-isopycnal? : s=func[ (x, y, z, t)]

Potential Grids

Effect of model vertical grid on large-scale, climate simulations Experiments: • Start with T=T(z) • Apply heating in low latitudes and cooling in high latitudes • Integrate model for 100 years using different grids (all use M-Y mixing)

The problem of BBLs & deep water formation in z-level models is well known (Gerdes, 1993; Winton et al. , 1998; Gnanadesikan, 1999) I-1 I I+1 Some Solutions: K-1 T K W T K+1 U T • Embedded BBL (Beckman & Doscher, 1997; Killworth & Edwards, 1999; Song & Chao, 2000) • “Shaved” or partial cells (Pacanowski & Gnanadesikan, 1998; Adcroft et al. , 1997)

Dynamics of Overflow Mixing & Entrainment (DOME) project Bottom Topography (top view) embayment slope deep Initial Temperature (side view)

Simulation of bottom plume with a sigma coordinate ocean model (10 km grid)

Experiment Horizontal Resolution Vertical Resolution Number of Layers Diffusion Coeff. S 1 10 km 12 -72 m 50 10 S 2 10 km 12 -72 m 50 100 S 3 10 km 12 -72 m 50 1000 Z 1 10 km 50 -100 m 50 10 Z 2 10 km 50 -100 m 50 100 Z 3 10 km 50 -100 m 50 1000 S 4 10 km 60 -360 m 10 100 Z 4 2. 5 km 25 m 90 10

The effect of horizontal diffusivity on the Sigma coordinate model (tracer concentration in bottom layer)

DIF=10 10 days 20 days DIF=1000

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

ZLV-10 days SIG-10 days ZLV-20 days SIG-20 days

SIG DIF=1000 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 resolution or Is there a convergence of the z-lev. model to the sigma model solution when grid is refined? The Problem: to resolve the slope the z-lev. grid requires higher resolution for both, horizontal and vertical grid. New high-res. z-grid experiment: quadruple hor. res. , double 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 observations? Density section along the plume Thickness across the plume From: Girton & Sanford, Descent and modification of the overflow plume in the Denmark Strait, JPO, 2003

Experiment Resolution Diffusion Coeff. Plume Thickness 10 Plume Area 100 km 2 13. 3 S 2 10 km/50 L S 3 10 km/50 L 1000 14. 6 276 m Z 2 10 km/50 L 10 7. 5 414 m Z 3 10 km/50 L 1000 6. 0 498 m S 4 10 km/10 L 100 10. 3 276 m Z 4 2. 5 km/90 L 10 9. 0 272 m Denmark Strait Obs. (Girton & Sanford, 2003) 244 m ~200 m

Comments: • Terrain-following grids are ideal for BBL and dense overflow problems. (Isopicnal models are also useful for overflow problems, but may have difficulties in coastal, well mixed regions) • Hybrid or generalized coordinate models may be useful for intercomparison studies, or for optimizing large range of scales or processes in a single code. • However, how to best construct such models and how to optimizing such grids for various applications are open questions that need further research.