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
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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)
AABW
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)
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Keq =Qgeo
ρ oCp
∂T
∂z
−1
(z=-3500m)
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ru • ∇T =
Qgeo
ρ oCp
δ(z + H)
A simple scaling law A simple scaling law
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Tr =Qgeo A
ρ oCpΔT∝
Qgeo
ΔT
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)
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Tr ∝QgeoA
ΔT
Geothermal circulation is commensurable to the Stommel-Arons circulation
Density-binning the abyssal ocean
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F(σ ) = A(σ ) +∂D
∂σ
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M(σ ) =∂ 2D
∂σ 2−
∂F
∂σ= Ψc (Steady-state)
Transformation equation :
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B=-α 4
Cp
Qgeo(x, y)
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A(σ ) = u • ndSSσ
∫€
F(σ ) = B(x, y) δ ′ σ (x, y) −σ( )∫∫ dxdy
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D(σ ) = κ∂σ
∂nSσ∫ dS
Formation equation :
Geothermal Circulation
Results :Results :
A
Q
F
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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)
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Kz∂zTLevitusDownward Heat Flux =
What happens to the What happens to the Sverdrup balance ?Sverdrup balance ?
• If , then : (Sverdrup balance)
• Now , then :
Integrating :
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dρ
dt= 0
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dρ
dt= −Β z
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βv = f∂w
∂z
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ρβv = f ρ w + B( )z
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ρβvdz− H
z
∫ = 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
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F(σ ) − A(σ ) −∂D
∂σ= 0
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M(σ ) =∂ 2D
∂σ 2−
∂F
∂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
00
86.4
0.10.1
0.10.1
STDSTD
STDSTD
STD_Q_uniSTD_Q_uni
STD_Q_varSTD_Q_var
00
86.486.4
QQgeogeo(x,y)(x,y)
0.10.1
0.10.1
0.10.1
MIXMIXMIXMIX
MIX_Q_varMIX_Q_var
00
QQgeogeo(x,y)(x,y)
1 (Hadley)1 (Hadley)
1 (Hadley)1 (Hadley)
