Inferring the AMOC from Surface Observations

Timothy DelSole

George Mason University, Fairfax, Va andCenter for Ocean-Land-Atmosphere Studies

July 21, 2018

Collaborators: Michael Tippett (Columbia), Barry Klinger (GMU), ArindamBannerjee (U. Minnesota)

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To What Extent Can the AMOC be InferredFrom Surface Information?

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Past Work

Latif et al., 2004; J. Climate: Reconstructing, Monitoring, and PredictingMultidecadal-Scale Changes in the NA Thermohaline Circulation with SST

Hirschi and Marotzke 2007; JPO: Reconstructing the Meridional OverturningCirculation from Boundary Densities and the Zonal Wind Stress

Zhang, 2008; GRL: Coherent surface-subsurface fingerprint of the AMOC

Zhang, Rosati, Delworth, 2010; J. Climate: The Adequacy of Observing Systems inMonitoring the AMOC and North Atlantic Climate

Mahajan et al. 2011; Deep-Sea Res. II: Predicting AMOC variations using subsurfaceand surface fingerprints

Lopez et al., 2017; GRL: A reconstructed South Atlantic Meridional OverturningCirculation time series since 1870

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No study has shown that a reconstruction methodworks in a suite of coupled atmosphere-ocean models.

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New Analysis with CMIP5

I Analyze CMIP5 simulations

I Only piControl simulations at least 500 years long

I 5-year running mean SST North Atlantic basin (0-60N).

I AMOC index: maximum streamfunction at 40N

I AMOC index is 5-year running mean

I Only 11 models have 500-year control, AMOC index, and SST.

I MIROC5 has SST discontinuity, leaving 10 models.

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Variance of AMOC

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●

●

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0.6 0.8 1.0 1.2

standard deviation (Sv)

CanESM2

CNRM−CM5

inmcm4

MPI−ESM−LR

MPI−ESM−MR

MPI−ESM−P

MRI−CGCM3

CCSM4

NorESM1−M

CESM1−BGC

AMOC index

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●

●

●

●

●

●

●

●

●

0.06 0.08 0.10 0.12

standard deviation (K)

CanESM2

CNRM−CM5

inmcm4

MPI−ESM−LR

MPI−ESM−MR

MPI−ESM−P

MRI−CGCM3

CCSM4

NorESM1−M

CESM1−BGC

Mean North Atlantic SST

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Linear Regression

Assume reconstruction model of the form

reconstructed AMOC(t) = w1X1(t) + w2X2(t) + · · ·+ wMXM(t)

Least squares: select the weights w to minimize∥∥∥∥ y − X wAMOC SST weights

∥∥∥∥2

Problem: Not enough data.There are more SST grid points than data.

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Linear Regression

Assume reconstruction model of the form

reconstructed AMOC(t) = w1X1(t) + w2X2(t) + · · ·+ wMXM(t)

Least squares: select the weights w to minimize∥∥∥∥ y − X wAMOC SST weights

∥∥∥∥2

Problem: Not enough data.There are more SST grid points than data.

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Approach: impose constraints on the equation.

A priori assumption:AMOC affects the large-scale SST.

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Approach: impose constraints on the equation.

A priori assumption:AMOC affects the large-scale SST.

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Laplacians

Laplacian 1

−0.8

−0.6

−0.4 −0.2

0.2 0.4

0.6

0.6

0.8

Laplacian 2

−0.6

−0.4

−0.

2

0.2

0.4 0.6 0.8

Laplacian 3

0 100 200 300 400 500

Time Series for Laplacian 1

CanESM2CNRM−CM5inmcm4MPI−ESM−LR

MPI−ESM−MRMPI−ESM−PMRI−CGCM3CCSM4

NorESM1−MCESM1−BGC

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Normalized Variance Spectrum for N. Atlantic SST

1 2 5 10 20 50 100

Laplacian

0.1

1

10

tos

varia

nce

(% o

f tot

al)

−5/3 power law

Normalized Variance Spectrum for North Atlantic SST

Empirical Spectrum = 200/(K^5/3 + 20)

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Constrained Least Squares

Constrained least squares is equivalent to minimizing the function∥∥∥∥ y − L wAMOC SST weights

∥∥∥∥2

+ λR(w),

where R(w) is a non-negative “penalty” function of the weights.

LASSO corresponds to R(w) =∑

i |wi |. It tends to sign zeroweight to high-wavenumbers because they have small variance.

λ controls the strength of the penalty:

I large λ means most w’s are zero: field is smooth

I small λ means more w’s are non-zero: field can be noisy.

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AMOC Prediction

lambda

CV

−M

SE

of A

MO

C P

redi

ctio

n

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

LASSO Prediction Based on North Atlantic SST

MPI−ESM−P; 5−yr running mean

lambda

Lapl

acia

n

0

20

40

60

80

100

0.01 0.1 1 10

59 50 38 33 27 21 17 13 11 8 7 6 5 3 2 1 0000

lambda

CV

−M

SE

of A

MO

C P

redi

ctio

n

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

LASSO Prediction Based on North Atlantic SST

MPI−ESM−P; 5−yr running mean

lambda

Lapl

acia

n

0

20

40

60

80

100

0.01 0.1 1 10

59 50 38 33 27 21 17 13 11 8 7 6 5 3 2 1 0000

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AMOC Prediction

lambda

CV

−M

SE

of A

MO

C P

redi

ctio

n

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

LASSO Prediction Based on North Atlantic SST

MPI−ESM−P; 5−yr running mean

lambda

Lapl

acia

n

0

20

40

60

80

100

0.01 0.1 1 10

59 50 38 33 27 21 17 13 11 8 7 6 5 3 2 1 0000

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AMOC Prediction

lambda

CV

−M

SE

of A

MO

C P

redi

ctio

n

0.4

0.6

0.8

1.0

1.2

LASSO Prediction Based on North Atlantic SST

MPI−ESM−MR; 5−yr running mean

lambda

Lapl

acia

n

0

20

40

60

80

100

0.01 0.1 1 10

50 47 39 32 28 24 19 17 13 10 7 5 5 3 2 1 0000

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AMOC Prediction

0.0

0.2

0.4

0.6

0.8

1.0

lambda

CV

−M

SE

of A

MO

C

0.001 0.01 0.1 1 10

CanESM2●

CNRM−CM5 ●

inmcm4●

MPI−ESM−LR ●

MPI−ESM−MR●

MPI−ESM−P

●

MRI−CGCM3 ●

CCSM4 ●

NorESM1−M ●CESM1−BGC ●

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Cross-Model Predictions

Train on one model, test in another model.

0.0

0.5

1.0

1.5

2.0

lambda

CanESM2

0.0

0.5

1.0

1.5

2.0

lambda

devi

ance

CNRM−CM5

0.0

0.5

1.0

1.5

2.0

lambda

inmcm4

0.0

0.5

1.0

1.5

2.0

lambda

devi

ance

MPI−ESM−LR

0.0

0.5

1.0

1.5

2.0

lambda

MPI−ESM−MR

0.0

0.5

1.0

1.5

2.0

lambda

devi

ance

MPI−ESM−P

0.0

0.5

1.0

1.5

2.0

lambda

MRI−CGCM3

0.0

0.5

1.0

1.5

2.0

lambda

devi

ance

CCSM4

0.0

0.5

1.0

1.5

2.0

NorESM1−M

0.001 0.01 0.1 1 10

0.0

0.5

1.0

1.5

2.0

devi

ance

CESM1−BGC

0.001 0.01 0.1 1 10

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AMOC Prediction

0.0

0.5

1.0

1.5

2.0

lambda

CanESM2

0.0

0.5

1.0

1.5

2.0

lambda

devi

ance

CNRM−CM5

0.0

0.5

1.0

1.5

2.0

lambda

inmcm4

0.0

0.5

1.0

1.5

2.0

lambda

devi

ance

MPI−ESM−LR0.

00.

51.

01.

52.

0

lambda

MPI−ESM−MR

0.0

0.5

1.0

1.5

2.0

lambda

devi

ance

MPI−ESM−P

0.0

0.5

1.0

1.5

2.0

lambda

MRI−CGCM3

0.0

0.5

1.0

1.5

2.0

lambda

devi

ance

CCSM4

0.0

0.5

1.0

1.5

2.0

NorESM1−M

0.001 0.01 0.1 1 10

0.0

0.5

1.0

1.5

2.0

devi

ance

CESM1−BGC

0.001 0.01 0.1 1 10

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SST that Co-Varies with AMOC (λ = optimal)

−5

5

5

10

15

20

CanESM2

41

5

5

10

10

15

20

CNRM−CM5

37

2

2

2

2

2

4

4

6 8

10

10

inmcm4

1

1

1

1

1

2

2 3

3

4

5

MPI−ESM−LR

3

5

5 10

15

MPI−ESM−MR

39

2 2

2

2 4 6

MPI−ESM−P

5

5

5

10

MRI−CGCM3

33

−5

5

5

5

5

5

10

10

15

20

25

CCSM4

24

−8

−6

−4

−2

−2

−2

−2

2

2

2

2

2

2 2

2

2

4

4

4

4

6

NorESM1−M

36

−10

−5

5

5

5

5

5

5

10

15

20

CESM1−BGC

20

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Conclusions

1. We reconstruct the AMOC based on surface observations using acombination of regularized regression and Laplacian basis functions.

2. Fraction of AMOC that is predictable from Atlantic SST: 10-70%.

3. A reconstruction equation that works well in one climate model canperform poorly in other climate models.

4. Reconstructions at λ = 1 tend to have skill in all models.

5. Reconstructions at λ = 0.1 suggest model clusters:

I CCSM4, CESM1-BGC, NorESM1-MI MPI modelsI CanESM2, CNRM-CM5I INMCM4I MRI-CGCM3

Next step: include time lags and other variables (e.g,. SSS).Optimal Fingerprinting.

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