Ocean energetics in GCMs: how much energy is transferred from the winds to

the thermocline on ENSO timescales?

Alexey Fedorov (Yale)Jaci Brown (CSIRO) and Eric Guilyardi (IPSL)

Funded by DOE, NSF, CNRS

Brown J., Fedorov, A.V., and Guilyardi, E., 2010: How well do coupled models replicate ocean energetics relevant to ENSO? Climate Dynamics, in press

 Brown J. and Fedorov, A.V., 2010: How much energy is transferred from the

winds to the thermocline on ENSO timescales. J. Climate 23, 1563–1580. Brown J. and Fedorov, A.V., 2008: The mean energy balance in the tropical

ocean, J. Marine Research 66, 1-23. Fedorov, A.V., 2007: Net energy dissipation rates in the tropical ocean and

ENSO dynamics. J.Climate 20, 1099–1108

Fedorov, A.V., Philander, S.G., Harper, S.L., B. Winter, B. and A. Wittenberg, 2003: How predictable is El Niño? Bull. Amer. Meteorol. Soc. 84, 911-919.

Buoyancy Poweracts to displace isopycnals

Wind Power generated by wind stress acting on surface currents

Available Potential Energygenerated when isopycnals are distorted

Kinetic Energy of ocean currents

Atmosphere

Ocean

isopycnals

OCEAN ENERGETICS

Goddard and Philander 2000; Fedorov et al 2003

Questions:

What fraction of power generated by the winds reaches the equatorial thermocline on ENSO timescales?

How much damping occurs for thermocline anomalies?

Can we use the energetics of the tropical ocean to compare different coupled models?

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A shallow-water model

5

€

E =1

2(g * h2 + Hu2 )∫∫∫ dxdydz; W = uτ dxdy∫∫

€

∂E

∂t= γW −α sE

What are and in GCMs?Fundamental question: How (well) do GCMs describe the

transfer of energy from the winds to the thermocline?

Wind stress

Surface Currents, U (m/s)

€

W = Uτ∫∫ dxdy

U=U(x,y,t) – zonal velocity(x,y,t) – zonal wind stress

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U and - same

direction

positive wind power

negative wind power

U and - differentdirection

Wind power W is generated when winds work on ocean

currents

MOM4

Buoyancy power B controls vertical

displacements of the thermocline. It is

generated from the conversion of wind power.

€

B = g ρ − ρ *( )wdz dxdy∫∫∫

w – vertical velocityg – gravity(x,y,z,t) – densityz) – reference stratification

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High APE, La Niña:

Low APE, El Niño:

APE (denoted as E) is generated when isopycnals

are distorted, and is proportional to the

thermocline slope along the equator!

€

E =g

2

ρ − ρ *( )2

δρ *

δz

∫∫∫ dxdydz

(x,y,z,t) – density z) –reference stratification

APE variations are highly anti-correlated with the Nino3

SST, correlation up to -0.9

El Nino of 1997

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Integration: tropical Pacific (15oN - 15oS,130oE - 80oW, 0-400m)

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€

dK

dt= W − B − D1

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E – the APE

K – kinetic energy (negligible, less than 1% of E)

B – buoyancy power (describes the conversion of kinetic into potential energy

W – wind power

D1, D2 – viscous and diffusive dissipations

€

dE

dt= B − D2

Wind Power

Buoyancy Power

APE (~thermocline slope)

SST

Wind Stress

D1

D2

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Ocean-only, data assimilating, and coupled GCMs

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Data assimilating

models

Ocean models

Coupled models

€

∂K

∂t= W − B − D10

We introduce efficiency =B/W

€

B = γW

That is, only a fraction of wind power W is converted to buoyancy power B

(our assumption)

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Calculating efficiency

€

B = γW

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Efficiency versus correlation between Buoyancy and Wind powers

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Characteristic ENSO period versus efficiency

€

dE

dt= B − D2

€

D2 = αE

€

dE

dt= B − αE

(-1 is the APE damping timescale

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(our assumption)

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Calculating damping timescale

€

D2 = αE

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Damping timescale versus correlation between E and D2

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Summary

Ocean energetics of ENSO is characterized by two physical parameters

- the efficiency of the energy transfer from the winds to the thermocline. Most of coupled GCMs are less efficient (=15-50%) than ocean-only and data assimilating models (=50-60%).

- the APE damping rate. Most of coupled GCMs produce shorter damping timescales (-1=0.4-1 year) than ocean-only and data assimilating models (-1=1-1.2 year).

The two parameters can be used as metrics for evaluating dissipative properties of the models and other model properties

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Implications

How models describe quantitatively the transfer of energy (and momentum) from the winds down the water column is important

Efficiency 30% vs. 60% mattersEnergy e-folding damping 4 months vs. 1 year matters

Error compensation in GCMs

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Decadal Variability

Wind Power Available Potential Energy

• Shift in late 1970s in Wind power and resulting APE

• Interannual variability consistent.

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Wind Power

Buoyancy Power

APE (~thermocline slope)

SST

Wind Stress

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Coupled models generate lower efficiency and stronger damping than ocean-only or data-assimilating models!

27Annual-mean zonal averages between160oE to 90oW

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K – kinetic energy (small)

B – buoyancy power;

P – the rate of work of ageostrophic pressure;

AM – advection of K away from the tropics

DM – turbulent viscous dissipation; kMV, kMH – viscosities

B – buoyancy powerQ – damping by surface heat fluxesA – advection of APE away from the tropicsD – turbulent diffusive dissipation; kMV, kMH – diffusivities 31

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Wind Power

Buoyancy Power

APE (~thermocline slope)

SST

Wind Stress

Dissipation1

Dissipation2

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Win

d P

owe

r (T

W)

Buoyancy Power (TW)

Efficiency of Wind Power to Buoyancy Power Transfer

W

B 37

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APE damping timescales -1:

ocean models and data assimilations: -1 = 1 year

coupled models: -1 = 0.5 -1 years

Correlation (between D2 and E)

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€

dρ *

dz

Wind Power

Buoyancy Power

APE (Thermocline slope)

Sea Surface Temperatures

Wind Stress

The energetics of the tropical ocean:

D1

D2

40 E is highly anti-correlated with the SST

in the eastern equatorial Pacific (r=-0.9)!

E is highly anti-correlated with the SST in the eastern equatorial Pacific (r=-0.9)! High APE means La Niña; Low APE means El Niño

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El Nino 1997

K – kinetic energy (small)

B – buoyancy power;

P – the rate of work of ageostrophic pressure;

AM – advection of K away from the tropics

DM – turbulent viscous dissipation; kMV, kMH – viscosities

K – kinetic energy (small)

B – buoyancy power;

P – the rate of work of ageostrophic pressure;

AM – advection of K away from the tropics

DM – turbulent viscous dissipation; kMV, kMH – viscosities

€

˜ ρ = ρ − ρ *

B – buoyancy powerQ – damping by surface heat fluxesA – advection of APE away from the tropicsD – turbulent diffusive dissipation; kMV, kMH – diffusivities 44

B – buoyancy powerQ – damping by surface heat fluxesA – advection of APE away from the tropicsD – turbulent diffusive dissipation; kMV, kMH – diffusivities 45

€

˜ ρ = ρ − ρ *

€

dρ *

dz

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Calculating damping rates

Available Potential Energy

Dis

sipa

tion

An

om

aly

E 47

D2

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Correlation (between D2 and E)