Recent developments of the NERSC version of MICOM

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1 Recent developments of the NERSC version of MICOM Mats Bentsen Nansen Environmental and Remote Sensing Center Bjerknes Centre for Climate Research Nansen-Zhu International Research Centre

2 Outline New formulation of the pressure gradient force A suitable equation of state Modified mode splitting Results Two time-level time stepping

3 New formulation of the pressure gradient force (PGF) Classical approach in isopycnic ocean models: A more accurate approach was introduced by Sun et al. (1999): A different approach for layered ocean model was shown in the talk A proposed fix for HYCOM s thermobaricity problem by Rainer Bleck, Balu Nadiga, and Shan Sun:

4 Finite difference representation of

5 A suitable equation of state Functional form inspired by McDougall et al. (2003): Potential density is defined as Quadratic equations to solve Linear equation to solve

6 Analytic expression of specific enthalpy Can be used to accurately integrate geopotential over an isopycnic layer

7 Estimating coefficients by a weighted least square fit to the equation of state proposed by Feistel (2003). A funnel in (θ,s,p) space is used for the fit: In the pressure range [-750,2000] db, the potential temperature and salinity range used are [-5,37] C and [0,42] psu, respectively. For pressures above 2000 db, the potential temperature and salinity range are changing linearly towards [-3,10] C and [30,40] psu, respectively, at 6000 db. Density error [kg/m 3 ] at 2000 db RMS error in fitting range Black: McDougall et al. (2003) Blue: IES80 (UNESCO 1981) Magenta: Brydon et al. (1999), wide range Cyan: Brydon et al. (1999), narrow range Red: the proposed EOS

8 Modified mode splitting First order Taylor expansion of around Assume that on external gravity wave time scales On these time scales we arrive at an approximate sensitivity of vertical geopotential difference on bottom pressure changes:

9 Barotropic equation system solved: The bottom pressures in the barotropic and baroclinic systems are made consistent by correcting the baroclinic mass field with the mass flux difference between the two systems (Higdon, 2005).

10 Experience from initial testing Model layers that are statically stable in terms of potential density may be unstable in terms of in situ density. Currently we fix this by enhancing vertical diffusion in unstable regions. Local vertical density difference [kg/m 3 ]

11 Results Global model configuration with ~2.4 horizontal resolution and 35 isopycnic layers. We compare a model with reference pressure at 0 db and old PGF formulation with a model with reference pressure at 2000 db and the new PGF formulation. Initial conditions from Levitus (1994). NCEP daily forcing from is used. Strong surface relaxation with 30 days e-folding time scale. Results are averaged over the period and are from the second NCEP cycle.

12 Atlantic meridional overturning stream function [Sv] Old New

13 Sea surface height [m] Old New

14 Stream function of the vertically integrated mass transport [Sv] Old New

15 Two-level time-stepping schemes The scheme of Higdon (2002) applied to the linearized shallow water equations assuming wave solutions in space: u,v: non-dimensional velocities η: non-dimensional height γ: f t α k,l : ck k,l t Test various schemes with γ=0.25, α l =0, α k =α.

16 Higdon (2002): Hallberg (1997):

17 Generalized forward-backward method Schemes based on the work of Shchepetkin and McWilliams (2005). Expanded with optimized treatment of the Coriolis term. Explicit 2. order treatment of Coriolis term, possible with different odd/even updating of velocities

18 Non-time staggered version: Time staggered version:

19 Barotropic equation system solved: F k is a finite difference version of fk u k that in MICOM follow the formulation in Bleck and Smith (1990), based on the Sadourny (1975) potential enstrophy conserving scheme.

20 Time-stepping method for barotropic/baroclinic system Predictive barotropic integration Prediction of baroclinic variables Correction of baroclinic variables Corrective barotropic integration Correction of baroclinic bottom pressure

21 Bottom pressure at a grid point in the North Atlantic

22 Sea surface height [m] Old New

A Two-Level Time-Stepping Method for Layered Ocean Circulation Models: Further Development and Testing

A Two-Level Time-Stepping Method for Layered Ocean Circulation Models: Further Development and Testing Robert L. Higdon Department of Mathematics Oregon State University Corvallis, Oregon 97331-4605 This