Geothermal heating : the unsung diva of abyssal dynamics

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Geothermal heating : theunsung diva of abyssal dynamics

Julien Emile-GeayJulien Emile-Geay

Lamont-Doherty Earth Observatory, Lamont-Doherty Earth Observatory, Palisades, NY, USAPalisades, NY, USA

Gurvan MadecGurvan Madec

LODYC, Paris, FranceLODYC, Paris, France

Solid Earth cooling in the abyssSolid Earth cooling in the abyss

The spatial structureThe spatial structure

Qgeo = 86.4 mW .m−2

IntroductionIntroduction

“Qgeo ~ 100 mW.m-2 / Solar is ~100 W.m-2”

Why is geothermal heating generally neglected in dynamical oceanography ? (except by Scott,

Adcroft and Marotzke, JGR, 2001)

OutlineOutline

1. Analytical balance2. Density-binning3. Numerical approach

Geothermal Heating is a Driving force of the MOC

Heat EquationHeat Equation

2 ways of comparing :1. Plot downward heat flux2. “Equivalent Kz”

Bryan, 1987 : MOC is controlled by the heat supplied to the abyss

How big is geothermal heating in the heat budget ?

Diffusion Geothermal Heatflow

Measured Kz : ~0.1 cm2.s-1

Implied Kz : ~1 cm2.s-1 (advection-diffusion balance)

Munk, 1966

Geothermal Heating vs Diapycnal Mixing (2)Geothermal Heating vs Diapycnal Mixing (2)

Keq =Qgeo

ρ oCp

(z=-3500m)

ru • ∇T =

ρ oCp

δ(z + H)

A simple scaling law A simple scaling law

Tr =Qgeo A

ρ oCpΔT∝

Results Results

BasinBasin AtlanticAtlantic IndianIndian PacificPacific GlobalGlobal

Area (10Area (101414 m m22)) 0.340.34

1.901.90

0.50.5

0.450.45

0.960.96

0.80.8

0.990.99

0.420.42

5.25.2

1.781.78

6.56.5T ( C)T ( C)

ScalingScaling

(Sv)(Sv)

Tr ∝QgeoA

Geothermal circulation is commensurable to the Stommel-Arons circulation

Density-binning the abyssal ocean

F(σ ) = A(σ ) +∂D

M(σ ) =∂ 2D

∂σ 2−

∂σ= Ψc (Steady-state)

Transformation equation :

B=-α 4

Qgeo(x, y)

A(σ ) = u • ndSSσ

∫€

F(σ ) = B(x, y) δ ′ σ (x, y) −σ( )∫∫ dxdy

D(σ ) = κ∂σ

∂nSσ∫ dS

Formation equation :

Geothermal Circulation

Results :Results :

F(σ)≈A(σ)Q(σ)

•Transformation of ~6.5 Sv•Centered on = 45.90

•Transformation of ~6 Sv•Shifted towards = 45.85

Uniform Heatflow

Realistic Heatflow

A numerical approachA numerical approachOPA model v8.1 (Madec et al, 1998):•Primitive equation model, non-linear equation of state •Horizontal physics : Isopycnal mixing with Gent & McWilliams•Conservation of haline content (Roullet and Madec 2000)

ORCA2 configuration x*y=2 * [0.5(Tropics) ; 2] - 31 vertical levels ( 15 in upper 200m)

Coupled to LIM (LLN sea-ice model)

Equilibrium runs from Levitus (1998) forced by climatological fluxes•Geothermal Heat flux passed like a surface flux

Control runsControl runs

Kz=0.1cm2.s-1

Cold bottomwater

Kz=0.1

Kz=1Hadley center

Effect of a uniform heatflow(CBW)Effect of a uniform heatflow(CBW)

Effect of a uniform heatflow (STD)Effect of a uniform heatflow (STD)

Transformation (Sv)

Effect of vertical physicsEffect of vertical physics

ConclusionsConclusions

• Qgeo ~ Kz = 1.2 cm2.s-1 (at 3500m)

•Three independent approaches predict a circulation of 5-6 Sv, inversely proportional to deep temperature gradients(modulated by mixing)

•Changes the thermal structure to first order (cf Scott et al.), in particular the meridional temperature gradient

Geothermal Heating is a major AABW consumer

Major forcing of the abyssal circulation

Summary (continued)Summary (continued)

•Details of the spatial structure are secondary :

Circulation is weakened by ~ 20% (STD)

Warming enhanced in the NADW depth range weakened on abyssal plains

(by ~10-20%)

ConclusionConclusion

“Viewed as a heat engine, the ocean circulation is extraordinarily inefficient. Viewed as a mechanically-drivensystem, it is a remarkably effective transporter of the energy”

Walter Munk and Carl Wunsch, 1998

Geothermal Heating is a major actor of abyssal dynamics

• Influences mostly PE, not KE • Provides 1/3 of APE for deep mixing• May help resolve the “diffusivity dilemna”• Does it have a role in climate change ? (Little Ice Age ? Glacial THC ?)

Geothermal Heating vs Diapycnal mixing (1)

Kz∂zTLevitusDownward Heat Flux =

What happens to the What happens to the Sverdrup balance ?Sverdrup balance ?

• If , then : (Sverdrup balance)

• Now , then :

Integrating :

dt= −Β z

βv = f∂w

ρβv = f ρ w + B( )z

ρβvdz− H

∫ = f ρ w(z)10−4

+ ′ ρ w(z)10−8

+ B(z)10−8

− B(−H)10−8

⎛ ⎝ ⎜

⎞ ⎠ ⎟

(Joyce et al. [1986])

Life cycle of AABWLife cycle of AABW

Formation

Transformation

Consumption

Deep convection,cabelling

Entrainment,Downhill mixing,

Diapycnal mixingUpwelling (NADW)Getohermal Heating

Density-binning the abyssal oceanDensity-binning the abyssal ocean

F(σ ) − A(σ ) −∂D

∂σ= 0

M(σ ) =∂ 2D

∂σ 2−

∂σ= Ψc (Steady-state)

Transformation equation :

Effect of a spatially variable heatflowEffect of a spatially variable heatflow

Impact on the circulationImpact on the circulation

Impact on the thermal structureImpact on the thermal structure

Three views of the problemThree views of the problem

1. Geothermal Heating as a source of mixing• Gordon and Gerard (1970)• Huang (1999)

2. Localized hydrothermal venting• Stommel (1983)• Helfrich and Speer (1995)

3. The new wave• Adcroft et al (2001), Scott et al (2001)• This study

Three sets of experimentsThree sets of experiments

SetSet ExperimentsExperiments QQgeogeo (mW.m (mW.m-2-2)) KKzz(cm(cm22.s.s-1-1))

CBWCBWCBWCBW

CBW_Q_uniCBW_Q_uni

0.10.1

STDSTD

STD_Q_uniSTD_Q_uni

STD_Q_varSTD_Q_var

86.486.4

QQgeogeo(x,y)(x,y)

0.10.1

MIXMIXMIXMIX

MIX_Q_varMIX_Q_var

QQgeogeo(x,y)(x,y)

1 (Hadley)1 (Hadley)

Geothermal heating : the unsung diva of abyssal dynamics

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