Upload
others
View
2
Download
0
Embed Size (px)
Citation preview
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)
1 / 21
To What Extent Can the AMOC be InferredFrom Surface Information?
2 / 21
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
3 / 21
No study has shown that a reconstruction methodworks in a suite of coupled atmosphere-ocean models.
4 / 21
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.
5 / 21
Variance of AMOC
●
●
●
●
●
●
●
●
●
●
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
●
●
●
●
●
●
●
●
●
●
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
6 / 21
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.
7 / 21
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.
8 / 21
Approach: impose constraints on the equation.
A priori assumption:AMOC affects the large-scale SST.
9 / 21
Approach: impose constraints on the equation.
A priori assumption:AMOC affects the large-scale SST.
10 / 21
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
11 / 21
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)
12 / 21
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.
13 / 21
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
14 / 21
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
15 / 21
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
16 / 21
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 ●
17 / 21
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
18 / 21
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
19 / 21
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
20 / 21
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.
21 / 21