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 The generalized coordinate model (Mellor et al., 2002; Ezer & Mellor, Ocean Modeling, In Press, 2003) Sensitivity experiments: 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)[H max +  (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: Experiments: Start with T=T(z) Start with T=T(z) Apply heating in low latitudes and cooling in high latitudes Apply heating in low latitudes and cooling in high latitudes Integrate model for 100 years using different grids Integrate model for 100 years using different grids (all use M-Y mixing)

TT 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) project Bottom Topography Initial Temperature (top view) (side view) embayment slope deep

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

Experiment Horizontal Resolution Vertical Resolution Number of Layers Diffusion Coeff. S1 10 km m 5010 S2 10 km m S3 10 km m Z1 10 km m 5010 Z2 10 km m Z3 10 km m S4 10 km m Z4 2.5 km 25 m 9010

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

10 days 20 days DIF=10 DIF=100 DIF=1000

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

Experiment Resolution Resolution Diffusion Coeff. Plume Area 100km 2 Plume Thickness S2 10 km/50L m S3 10 km/50L m Z2 10 km/50L m Z3 10 km/50L m S4 10 km/10L m Z4 2.5 km/90L m Denmark Strait Obs. (Girton & Sanford,2003) ~200 m

Comments: Terrain-following grids are ideal for BBL and dense overflow problems. 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. 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. However, how to best construct such models and how to optimizing such grids for various applications are open questions that need further research.