Machine-learning prediction of tipping with applications to the Atlantic Meridional Overturning Circulation

TL;DR

This work addresses the problem of predicting the potential collapse of the Atlantic Meridional Overturning Circulation (AMOC), possibly driven by climate-induced changes in the freshwater input to the North Atlantic.

Abstract

Anticipating a tipping point, a transition from one stable steady state to another, is a problem of broad relevance due to the ubiquity of the phenomenon in diverse fields. The steady-state nature of the dynamics about a tipping point makes its prediction significantly more challenging than predicting other types of critical transitions from oscillatory or chaotic dynamics. Exploiting the benefits of noise, we develop a general data-driven and machine-learning approach to predicting potential future tipping in nonautonomous dynamical systems and validate the framework using examples from different fields. As an application, we address the problem of predicting the potential collapse of the Atlantic Meridional Overturning Circulation (AMOC), possibly driven by climate-induced changes in the freshwater input to the North Atlantic. Our predictions based on synthetic and currently available empirical data place a potential collapse window spanning from 2040 to 2065, in consistency with the results in the current literature.

Figures (7)

• Figure 1: Schematic illustration of the machine-learning framework for anticipating tipping in nonautonomous dynamical systems. The system begins in a stable steady state with no deterministic oscillations in the dynamical variables. Dynamic noise is leveraged to perturb the system, enabling the machine-learning model to detect changes and predict the tipping point even when the system is in a parameter regime prior to tipping.
• Figure 2: Random realizations of a tipping point transition in the 1D stochastic AMOC fingerprint model \ref{['Eq: 1D AMOC']}. The bifurcation parameter $\lambda(t)$ increases exponentially with time, while other parameters are the best-estimated values extracted from the empirical fingerprint data ditlevsen2023warning: $A=0.95$, $m=-1.3$, $\lambda_0 = -2.7$, $\sigma = 0.3$, $t_0 = 1924$, and $\lambda_c =0$. Ten random realizations are shown, with the dashed green and red curves indicating the stable and unstable equilibria. In the underlying deterministic system, a backward saddle-node bifurcation and hence a tipping point occurs at $\lambda_c = 0$. In the presence of stochastic driving, the value of $\lambda$ at which the system collapses, characterized by the dynamical variable $X$'s approaching a large negative value, varies among the realizations, but they are near $\lambda=0$ on the positive side.
• Figure 3: Reservoir-computing prediction of the time window of AMOC collapse from the 1D time-dependent fingerprint model. (a) The exponential growth with time of the bifurcation parameter $\lambda (t)$, which starts from the value $\lambda_0 = -2.7$ in the year 1870. The horizontal dashed line indicates the tipping point $\lambda_c=0$. (b) A realization of the time series $X(t)$, where the purple (blue) segment represents the training and testing (validation and prediction) data, respectively. (c) The testing data (blue) and reservoir-computing prediction (red) in the time window from year 2022 to year 2065. For this particular realization, the AMOC variable $X(t)$ collapses between the years 2062 and 2063 (blue, real data). The reservoir computer predicts an abnormal behavior in $X(t)$ at about the same critical time $T_c$, signifying a tipping point. (d) Histogram of the predicted AMOC collapse time $T_c$ obtained from 1000 machine realizations. Tipping is likely to occur between year 2055 and year 2066.
• Figure 4: Reservoir-computing prediction of the time window of AMOC collapse from the 2D time-dependent conceptual AMOC model. (a) One realization of 2D conceptual AMOC model for $\gamma = 3$ and $\sigma = 0.1$. (b) Time-varying freshwater forcing parameter $\beta$. (c) An example of testing data (solid blue trace) and reservoir-computing prediction (dash-dotted red trace). (d) Histogram of the predicted critical point from $1000$ random reservoir realizations.
• Figure 5: Reservoir-computing prediction of the time window of potential AMOC collapse from the CESM synthetic data. (a) Linear time-varying freshwater flux. (b) AMOC strength, where the purple and blue segments represent the training and testing (validation and prediction) data, respectively. The horizontal dashed line indicates the tipping point $T_c = 1758$. (c) Testing data (blue) and reservoir-computing prediction (red). AMOC strength ($x(t)$) collapses at model year $1758$ (blue, real data). The reservoir computer predicts an abnormal behavior in $x(t)$ at about the same critical time $T_c$, signifying a tipping point. (d) Histogram of the predicted AMOC collapse time $T_c$ obtained from 1000 reservoir network realizations. Tipping is likely to occur between model years 1740 and 1775.