Gent-McWilliams Gent-McWilliams parameterization:parameterization: 20/20 Hindsight 20/20 Hindsight

Peter R. Gent Peter R. Gent

National Center for Atmospheric National Center for Atmospheric ResearchResearch

Isopycnal DiffusionIsopycnal Diffusion

).(. TTutT

Following Montgomery (1930) and Solomon (1971), Redi (1982) implemented diffusion along isopycnal surfaces in MOM (with small slope approximation) it’s

However, in long climate runs the model would fail, often near the ACC, and horizontal diffusion with a small coefficient was used to make the model stable.

Gent/Cane tropical upper ocean Gent/Cane tropical upper ocean modelmodel• Constant salt => Constant salt => ρρ = = ρρ (T) (T). . • Someone I can’t remember suggested that I Someone I can’t remember suggested that I

try isopycnal, not horizontal, mixing. try isopycnal, not horizontal, mixing. • BEFORE IMPLEMENTATION I realized that, if BEFORE IMPLEMENTATION I realized that, if

done correctly, it would have zero effect. done correctly, it would have zero effect. • In a simple situation, the eddies do nothing? In a simple situation, the eddies do nothing? • Surely must do something and adiabatically. Surely must do something and adiabatically. • HINDSIGHT: Perhaps we should have HINDSIGHT: Perhaps we should have

deduced that this had to be an advection.deduced that this had to be an advection.

The GM ParameterizationThe GM Parameterization

).(*).( TTuutT

.0*.),/.(* uw z

Was shown to be an eddy advection in Gent et al. (1995), which took nearly 2 years to get published. The form was chosen because it ensures a global sink of potential energy.

Isopycnal CoordinatesIsopycnal Coordinates

hThTuutT

hhuth

zhThickness

/).(*).(

).().(

/:

GM is very often called thickness diffusion, but this is incorrect. It is an extra advection whether it’s in z-coords or in ρ-coords.

The Veronis (1975) EffectThe Veronis (1975) Effect

xxzw Steady Western Boundary Current

Horizontal diffusion produces a false upwelling that would not occur if diffusion was along isopycnal surfaces. This reduces the North Atlantic MOC and the associated northward heat transport.

(NCOM)

Non-Acceleration Non-Acceleration TheoremTheorem

• Consider the stratospheric circulation, and Consider the stratospheric circulation, and define eddies as deviation from zonal define eddies as deviation from zonal mean.mean.

• Under certain conditions, Andrews and Under certain conditions, Andrews and McIntyre (1978) showed there is a steady McIntyre (1978) showed there is a steady solution where the eddy advection exactly solution where the eddy advection exactly balances advection by the mean flow. balances advection by the mean flow.

• This is relevant to the ACC below the This is relevant to the ACC below the surface mixed layer, but above the highest surface mixed layer, but above the highest topography where zonal integral of ptopography where zonal integral of pxx = 0. = 0.

• HINDSIGHT: Perhaps we should have HINDSIGHT: Perhaps we should have anticipated the effect of GM in the ACC.anticipated the effect of GM in the ACC.

Deep Water Formation 3˚ 3˚

Horizontal Mixing GM 1990Danabasoglu et al. (1993)

Conclusions IConclusions I• With GM, ocean models were stable for With GM, ocean models were stable for

very long integration times. very long integration times. • Eliminated the Veronis effect, and eddy Eliminated the Veronis effect, and eddy

advection opposed mean flow in the ACC. advection opposed mean flow in the ACC. • Big improvements in solutions, especially Big improvements in solutions, especially

the MOC, ACC, and deep water formation. the MOC, ACC, and deep water formation. • Z-coord and Z-coord and ρρ-coord models were now -coord models were now

solving the same tracer equations, and solving the same tracer equations, and their solutions were now quite similar. their solutions were now quite similar.

CSM 1 was the first climate model to produce a non-drifting control run without “flux corrections”

<Temperature> at 290m and 520m depths from runs of the ocean component of the PCM starting from Levitus ICs :=

A) Horizontal tracer diffusion and P/P (1981) vertical mixing.

B) Horizontal tracer diffusion and KPP vertical mixing.

C) GM and KPP vertical mixing. From Gent et al (2002)

D) Visbeck et al (1997) form of GM and KPP vertical mixing.

Conclusions IIConclusions II

• The CSM 1 with GM was the first climate The CSM 1 with GM was the first climate model to run without flux correction, and model to run without flux correction, and maintain a reasonable present day climate. maintain a reasonable present day climate.

• Other climate models with GM ran without, Other climate models with GM ran without, or with much smaller, flux corrections. or with much smaller, flux corrections.

• A paper documenting the no flux A paper documenting the no flux correction result of CSM 1 was rejected by correction result of CSM 1 was rejected by ScienceScience. .

More Recent More Recent DevelopmentsDevelopments

• Known that somehow had to turn off GM Known that somehow had to turn off GM in the mixed layer where it does not in the mixed layer where it does not apply. apply.

• Done by various methods, such as slope Done by various methods, such as slope limiting or taper functions. Well known limiting or taper functions. Well known that the ocean solutions depend quite that the ocean solutions depend quite strongly on how this is done. strongly on how this is done.

• Suggested early that Suggested early that кк could be could be кк(x,y,z,t)(x,y,z,t). . • Number of suggestions, such as Visbeck Number of suggestions, such as Visbeck

et al. (1997), and several climate models et al. (1997), and several climate models now have a varying now have a varying кк. .

Diabatic LayerTransition Layer

Interior (quasi-

adiabatic) -z

Eddy-induced velocity profile

(GM 1990)

Diffusivities

Horizontal

Isopycnal

Horizontal/Isopycnal

This replaces the standard approach in the past of applying near-surface taper functions for the isopycnal and thickness diffusivities.

NEAR-SURFACE EDDY FLUX SCHEME (Ferrari et al. 2008, Danabasoglu et al. 2008)

EDDY-INDUCED MERIDIONAL OVERTURNING (GLOBAL)Control

Transition Layer

Vertical profile of zonally-integrated total advective heat flux at 49oS

Danabasoglu et al. (2008)

Model Eddy-Induced Transport Comparisons with Roemmich and Gilson (2001) Observational

Estimate(Repeat hydrographic line in the North Pacific at an average latitude of 22oN)

Roemmich and Gilson (2001)

Danabasoglu and Marshall (2007), where к is assumed to vary as N2.

Residual Mean Ocean Residual Mean Ocean Model ?Model ?

• Solutions in global (Ferreira and Marshall 2006) Solutions in global (Ferreira and Marshall 2006) and midlatitude (Zhao and Vallis 2008) domains. and midlatitude (Zhao and Vallis 2008) domains.

• Does require the geostrophic approximation to Does require the geostrophic approximation to get the get the ккff22/N/N22 vertical viscosity term => vertical viscosity term => solutions will be different at the equator, and solutions will be different at the equator, and hence globally. hence globally.

• Still requires near surface tapering of coefficient, Still requires near surface tapering of coefficient, and solutions are sensitive to how this is done. and solutions are sensitive to how this is done.

• Can argue that still need Eulerian velocity in KPP Can argue that still need Eulerian velocity in KPP scheme and surface fluxes => doesn’t eliminate scheme and surface fluxes => doesn’t eliminate the need to carry two different velocities. the need to carry two different velocities.

Ferreira and Marshall (2006)

Potential Vorticity Potential Vorticity Diffusion ?Diffusion ?

• Justification is that PV is homogenized in QG Justification is that PV is homogenized in QG models at midlatitudes, and PV is materially models at midlatitudes, and PV is materially conserved, obeying same eqn as a passive tracer. conserved, obeying same eqn as a passive tracer.

• Wardle and Marshall (2000) use a midlatitude Wardle and Marshall (2000) use a midlatitude channel model, and equations use QG PV, and channel model, and equations use QG PV, and then “PV when the relative vorticity is neglected”. then “PV when the relative vorticity is neglected”.

• Zhao and Vallis use a midlatitude domain, and find Zhao and Vallis use a midlatitude domain, and find small changes when small changes when ккββ/f term added to GM v*/f term added to GM v*. .

• We use the primitive eqns, where the PV isn’t the We use the primitive eqns, where the PV isn’t the QG form, or just fQG form, or just fρρzz !! If going to diffuse PV, then !! If going to diffuse PV, then should use the full Ertel form, not approximations.should use the full Ertel form, not approximations.

Cerovecki et al (2009). Mean isopycnals are in blue, dT/dz or the inverse of mean thickness is in black.

Cerovecki et al (2009). Mean isopycnals are in blue, the mean Ertel potential vorticity is in black.

Cerovecki et al (2009) Mean isopycnals are in blue, the mean Ertel potential vorticity is in black.

Conclusions IIIConclusions III• Can use ‘Residual Mean’ form of equations, Can use ‘Residual Mean’ form of equations,

but it will give different global solutions. but it will give different global solutions. • I don’t see a compelling reason to do so. I don’t see a compelling reason to do so. • I see several compelling reasons not to use I see several compelling reasons not to use

a PV mixing parameterization: it’s not true a PV mixing parameterization: it’s not true in most of ocean, real problem at equator, in most of ocean, real problem at equator, and PV is an active, not a passive, tracer. and PV is an active, not a passive, tracer.

• HINDSIGHT: Excellent choice not to base HINDSIGHT: Excellent choice not to base GM eddy parameterization on PV mixing. GM eddy parameterization on PV mixing.

Limerick 2000

There

There once was an ocean model called MOM,Which occasionally used to bomb,

But eddy advection, and much less convection,Turned it into a stable NCOM.