Assuming 16 cm standard deviation

The final result – 5 of these records were noisy

Halifax

Grand Banks

Line W

4100 m

2700 m

3250 m

2250 m

1800 m

3650 m

OCCAM: First EOF of bottom pressure over this region

OCCAM: correlation of bottom pressure with subpolar overturning

MICOM: correlation of bottom pressure with subpolar overturning

A good rule of thumb:

Assume a layer thickness of 1000 m, and a midlatitude f = 10-4

Then 1 cm of sea level or 1 mbar of pressure represents 1 Sv of transport

Dynamics: The geostrophic calculation at 42N

Conclusion:

Knowledge of western boundary pressure variations are sufficient to monitor to interannual variability of the MT at 42N

Upper layer transportRMS error: 0.28Sv

93% of variance captured

Lower layer transportRMS error: 0.31Sv

ActualInferred from western boundary pressure

Bingham and Hughes, JGR 2008

OCCAM MOC and Sea Level

In OCCAM, interannual sea level and MOC covary, as expected

2 cm/Sv

GECCO MOC and Sea Level

The same in GECCO

2 cm/Sv

4

3

2

1

0

-1

-2

-3

-4

sverdrups

Standard deviation 1.25 Sv

This is the overturning variation which would be implied by the tide gauge data

The message:

• Pressure differences give integrals of transport• Bottom pressure variability is much smaller

than mid-ocean pressure variability• Only integrals all the way across the basin are

meaningful – other integrals are dominated by eddies/meanders/Rossby waves

• These pressure signals are spatially coherent, so they relate to something meaningful for the large-scale ocean circulation, but this is an Eulerian measure of the MOC.

Meridional transport anomaly between 100m and 1000m depth

OCCAMHadCM3

Bingham et al, GRL 2007

MICOM simulations

Fine resolution Coarse resolution

Annually-repeating forcing

Origin of meridional differences: Key latitudes

1000 years of HadCM3 overturning circulation

Origin of meridional differences: Evolution of boundary density

P1

P2

P3

P1

P2

P3

Anomalous density along the 1000m isobath

Advection

Convection + advection+ waves

50N

42N

Advection+ waves

advection0.9cms-1

wave:1.8ms-1

• Seasonal cooling events associated with NAO are integrated to give low frequency mode clear at 50N

• 50N signal advected to lower latitudes, and degraded along the way

ρfwz = ρu.(f + ζ) + × τz

and the bottom boundary condition:

ρfwb = - J(pb,H) = - ρfub.H

Why should bottom pressure not be dominated by eddies too?

It comes down to the (steady) vorticity balance:

ρfwz = ρu.(f + ζ) + × τz

ρfw = ρh(βv + u2/L2) + × τ

= 2×10-6 + 10-6 + 10-7

ρfwb = - ρfub.H = - J(pb,H)

=0.01 H

Scalings in SI, with u=10 cm/s, h=1000m, L=100 km, β=2×10-11 m-1s-1

So 10-6 would need H = 10-4 or 10m/100km

But actual continental slope H is between 10-1 & 10-2

Standard deviation of

Sea level

(18 years of 5-day means)

Bottom pressure

in OCCAM

Bingham and Hughes, GRL 2008

Admittance (BP/SL)

Shallow

Deep

Deep (spatial smoothing)

Mid-latitudes

High latitudes

Eddying regions

Quiet regions

Time series of bottom pressure from 3 instruments, 300km apart, in a triangle around Tristan da Cunha island (S Atlantic)

Hughes and Smithson, GRL 1996

2.5 mbar RMS

Altimetry: sea level signals 5 degrees east of continental slope

Altimetry: sea level signals on continental slope

5 deg east of continental slope

Continental slope

RAPID WAVE array

26N array, with thanks toTorsten Kanzow et al

Bottom pressure (mbar) at three of the WAVE array positions and at the Western and Eastern end at 26.5ºN

0

0.5

1

1.5

2

2.5

A1 B2 W1 26 W 26 E

Full record

Commonperiod

Standard deviation of bottom pressure records 3 to 100 day periods, mbar

00.10.20.30.40.50.60.70.80.9

1

A1 B2 W1 26 W 26 E

A1

B2

W1

26 W

26 E

Correlations between BPRs: 3 to 100 day periods

Near-five-day bottom pressure (mbar) at three of the WAVE array positions and at the Western and Eastern end at 26º N

5-day waves

Arctic

Southern Ocean

AtlanticPacific

Indian

Spectra of basin-averaged sea level and bottom pressure

5 days5 days

8-100 day bottom pressure (mbar) at three of the WAVE array positions and at the Western and Eastern end at 26º N

EOFs of BPR data

Start with 2 mbar standard deviation

Subtract common signal, explaining (at least) 60% of variance

Leaves 2 x sqrt(0.4) = 1.26 mbar

A factor of 13 smaller than Wunsch’s assumed 16 mbar

Continental slope

5 deg east of continental slope

5 deg east of continental slope

Continental slope

Continental slope

5 deg east of continental slope

5 deg east of continental slope

Continental slope

geostrophy

hydrostatic balance

MOC measurement

Bottom geostrophic

current

Bottom density

1 Sv over 1 km depth range requires accuracy of about 1 mbar

Accuracy needed for current depends on how steep the slope is: more gentle slopes need greater accuracy.

The steeper part of Section B requires about 4cm/s accuracy for averaged bottom current, to give 1 Sv for MOC.

Gentler slopes require about 1 cm/s

BPR measurements still needed initially to test integrity of the system. Longer term, only current and density needed for monitoring.

With much thanks to Bedford Institute of Oceanography

Summary

• MOC changes have both advective and wave-like causes.

• Advection is slow, highly eddy dependent, difficult to monitor.

• Bottom pressure ‘filters out’ eddy effects (in most places).

• The wave propagation speed is much faster than advection, resulting in much more spatial coherence than eddies would suggest, although subtropical and subpolar regions remain independent to decadal periods or longer.

• Despite the importance of eddies, Eulerian measures of the MOC (integrated at constant level) are possible with accuracy of better than 1 Sv.

• This can be done, for interannual variations, with only western boundary bottom pressure.

Leading EOFs of interannual sea-surface height and bottom pressure

SSH BP

SSHBP

Leading EOFs of interannual sea-surface height

Altimetry OCCAM

AltimetryOCCAM

Bottom Pressure

Bottom Pressure