| 30 Dec 2025
New insights into decadal climate variability in the North Atlantic revealed by data-driven dynamical models
Abstract. The Atlantic Multidecadal Variability (AMV) and the North Atlantic Oscillation (NAO) are the dominant modes of oceanic and atmospheric variability in the North Atlantic, respectively, and are key sources of predictability from seasonal to decadal timescales. However, the physical processes and feedback mechanisms linking the AMV and NAO, and the role of diabatic processes in these feedbacks, remain debated. We present a data-driven dynamical modelling framework which captures coupled decadal variability in AMV, NAO, and North Atlantic precipitation. Applying equation discovery methods to observational data, we identify low-order models consisting of three coupled ordinary differential equations. These models reproduce observed decadal variability and show robust out-of-sample predictive skill on multi-annual to decadal lead times. The resulting model dynamics include a distinct quasi-periodic 20-year oscillation consistent with a damped oceanic mode of variability. Notably, precipitation-related terms feature prominently in the low-order models, suggesting an important role for latent heat release and freshwater fluxes in mediating ocean–atmosphere interactions. We propose new feedback mechanisms between North Atlantic sea surface temperature and the NAO, with precipitation acting as a dynamical bridge. Overall, these results illustrate how equation discovery can provide mechanistic hypotheses and new insight beyond conventional analyses of observations and climate model simulations.
I thoroughly enjoyed reading this paper. The authors use quadratic regression in the spirit of Kravtsov et al. (2005) and a slew of model selection criteria to construct a three-variable representation of decadal coupled dynamics over the North Atlantic. They end up with the model that produces realistic continuous spectra and is able to forecast out-of-sample data at multi-year lead times. The algebraic structure of the model provides essential clues as to the dynamics of the observed climate variability over the North Atlantic region and guides the targeted data analysis to support the emerging hypotheses.
A couple of personal first-reading  impressions on presentation and content:
(1) section 3.1.2 and Fig. 3 are a bit in the way of paper's presentation flow, IMO (with the only message in ll. 308-310 about the key role of precipitation). I'd remove this section or put it in the appendix.
(2) Â section 3.2 and Fig. 5 suggest skill, but would benefit from including a few concrete numbers in text - and, maybe, comparison with a benchmark forecast (say, persistence, or three-variable LIM model).
(3) Section 3.3.1 Algebraic structure of the model and the hypothesis of "damped oscillatory mode forced by the atmosphere", connections with linear inverse models, importance of the nonlinear feedbacks involving precipitation, etc. These are the issues the papers prompts (me) to think about. The key difference between the present approach and the previous data-driven approaches, I think, is the focus on a deterministic nonlinear model, rather than stochastic linear model. In my experience, the residual tendencies unexplained by the dynamical operators, say, on the right-hand side of (8–10) are typically large (maybe boxcar running-mean annual smoothing reduces them by a lot, maybe not). The apparent success of the deterministic model indicates that these residual dynamics are unimportant for the phenomenon of interest; at the same time,  the "stochastic driving" is internally generated within the model. It is surprising to me that such low-order dynamics generate realistic spectra.
In any case, having the actual model (8-10) provides one with a tool to study the sources of the decadal variability and predictability in this model (by looking, for example, at the importance of various terms in the "dynamical" experiments with, say, suppressed, or one-way coupling between equations, just like it is done with more complex dynamical climate models, or by parameterizing further the model dynamics with linear operators and stochastic driving etc. etc.)
Once again, a very interesting paper!
Refs:
Kravtsov, S., D. Kondrashov, and M. Ghil, 2005: Multi-level regression modeling of nonlinear processes: Derivation and applications to climatic variability. J. Climate, 18, 4404-4424. DOI: 10.1175/JCLI3544.1.