The variability of the Atlantic meridional circulation since 1980, as hindcast by a data-driven nonlinear systems model

Abstract

The Atlantic meridional overturning circulation (AMOC), an important component of the climate system, has only been directly measured since the RAPID array’s installation across the Atlantic at 26°N in 2004. This has shown that the AMOC strength is highly variable on monthly timescales; however, after an abrupt, short-lived, halving of the strength of the AMOC early in 2010, its mean has remained ~ 15% below its pre-2010 level. To attempt to understand the reasons for this variability, we use a control systems identification approach to model the AMOC, with the RAPID data of 2004–2017 providing a trial and test data set. After testing to find the environmental variables, and systems model, that allow us to best match the RAPID observations, we reconstruct AMOC variation back to 1980. Our reconstruction suggests that there is inter-decadal variability in the strength of the AMOC, with periods of both weaker flow than recently, and flow strengths similar to the late 2000s, since 1980. Recent signs of weakening may therefore not reflect the beginning of a sustained decline. It is also shown that there may be predictive power for AMOC variability of around 6 months, as ocean density contrasts between the source and sink regions for the North Atlantic Drift, with lags up to 6 months, are found to be important components of the systems model.

Appendix: Model averaging

One of the model performance metrics, RMSE (root mean squared error), given in Table 2 is used to implement a model averaging scheme. Note that the RMSE values for the three models are MSE₁ = 2.2382, MSE₂ = 2.0761, and MSE₃ = 2.2852, respectively. Using these values, we define the following parameters:

$$ c_{1} = \frac{1}{{{\text{MSE}}_{1} }},\;c_{2} = \frac{1}{{{\text{MSE}}_{2} }},\;c_{3} = \frac{1}{{{\text{MSE}}_{3} }} $$

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$$ w_{1} = \frac{{c_{1} }}{{c_{1} + c_{2} + c_{3} }} = 0.3276,\;w_{2} = \frac{{c_{2} }}{{c_{1} + c_{2} + c_{3} }} = 0.3563,\;w_{3} = \frac{{c_{3} }}{{c_{1} + c_{2} + c_{3} }} = 0.3201 $$

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Let $\hat{y}_{1}$, $\hat{y}_{2}$, and $\hat{y}_{3}$ be the predicted output values by the three models of the three cases in Table 2, the model averaging prediction is defined as:

$$ \hat{y} = w_{1} \hat{y}_{1} + w_{2} \hat{y}_{2} + w_{3} \hat{y}_{3}$$

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The three model performance metrics, ME, MAE, and RMSE produced by the model averaging prediction are listed in Table 5.

Table 5 A comparison of the prediction performance of the best linear model, the model for Case 2 (in Table 2), and the model averaging of the three models in Table 2

The graphical illustration of the model averaging prediction performance is shown in Fig. 9.

Fig. 9

An illustration of the model averaging prediction performance. Training data: April 2004–March 2014; Test data: April 2014–February 2017