Niklas Boers

A wide body of work has applied the concept of critical slowing down to estimate the stability of different Earth system components. Most of them – such as global vegetation – are inherently non-stationary, for example due to strong seasonal forcing that complicates the estimation of their resilience to external perturbations. Here, we introduce a method to account for non-stationarity in estimating the resilience of diverse synthetic and real-world systems via a regression-based formulation of the Langevin equation. Our method does not require extensive data pre-processing, is robust to gaps in the data record, and does not require regular time sampling. We further show that our method can incorporate time-varying data uncertainties, derive uncertainty bounds for stability estimates, and can be natively extended to examine spatial systems. Our method is a drop-in replacement for widely-used autocorrelation-based resilience estimates, and can be applied across diverse Earth system components.

Low-dimensional chaotic systems such as the Lorenz-63 model are commonly used to benchmark system-agnostic methods for learning dynamics from data. This study shows that learning from noise-free observations in such systems can be achieved up to machine precision: using ordinary least squares regression on high-degree polynomial features with 512-bit arithmetic, a system-agnostic method is introduced that matches the accuracy of standard 64-bit numerical ODE solvers using the systems’ governing equations. For the Lorenz-63 system, the method achieves valid prediction times of 36 Lyapunov times, and even up to 105 Lyapunov times with favorable precision configurations, dramatically outperforming prior work, which reaches 13 Lyapunov times at most. The results are further validated on Thomas’ Cyclically Symmetric Attractor, a non-polynomial chaotic system that is considerably more complex than the Lorenz-63 model, and similar results extend to higher dimensions using the spatiotemporally chaotic Lorenz-96 model. These findings suggest that forecasting low-dimensional chaotic systems from noise-free data is effectively a solved problem.

Forest ecosystems are vital to the global carbon cycle, yet their long-term aboveground carbon (AGC) dynamics remain uncertain. Here, we integrate multi-source satellite observations with probabilistic deep learning models to reconstruct a harmonized, uncertainty-aware global forest AGC record from 1988 to 2021 at 0.25 ^∘ . We find that, although global forests sequestered 6.2 PgC, moist tropical and boreal forests have progressively transitioned toward carbon sources since the early 2000s. Tropical AGC variability became increasingly negatively correlated with atmospheric CO ₂ growth rates (r = – 0.63 in 2011–2021), suggesting tropical forests increasingly modulate the global carbon cycle. In the Brazilian Amazon, the contribution of intact forests to the year-to-year variations in AGC losses increased from 33% in the 1990s to 76% in the 2010s. Our findings highlight the vulnerability of carbon stocks in key biomes and provide a benchmark to track emerging sink-source shifts under anthropogenic climate change.

While the artificial intelligence (AI) revolution is advancing rapidly, the open-source paradigm offers key pathways and potential risks for accelerating progress towards the Sustainable Development Goals and beyond. This comment introduces four governance actions that consider how sustainability, evaluation, safety, and cooperation can be integrated into the transformation of open-source AI, thereby reducing uncertainties and challenges posed by open-source AI for sustainable global prosperity. This comment introduces four governance actions that consider how sustainability, evaluation, safety, and cooperation can be integrated into the transformation of open-source AI, thereby reducing uncertainties and challenges posed by open-source AI for sustainable global prosperity.

Predicting chaotic dynamical systems is critical in many scientific fields, such as weather forecasting, but challenging due to the characteristic sensitive dependence on initial conditions. Traditional modeling approaches require extensive domain knowledge, often leading to a shift toward data-driven methods using machine learning. However, existing research provides inconclusive results on which machine learning methods are best suited for predicting chaotic systems. In this paper, we compare different lightweight and heavyweight machine learning architectures using extensive existing benchmark databases of low-dimensional systems, as well as a newly introduced database that allows for uncertainty quantification in the benchmark results. In addition to the state-of-the-art methods from the literature, we also present new advantageous variants of established methods. Hyperparameter tuning is adjusted based on computational cost, with more tuning allocated to less costly methods. Furthermore, we introduce the cumulative maximum error, a novel metric that combines desirable properties of traditional metrics and is tailored for chaotic systems. Our results show that well-tuned simple methods, as well as untuned baseline methods, often outperform the state-of-the-art deep learning models, but their performance can vary significantly with different experimental setups. These findings highlight the importance of aligning prediction methods with data characteristics and caution against the indiscriminate use of overly complex models.

Models of complex dynamical systems like the Earth’s climate often involve large numbers of uncertain parameters. Comprehensive exploration of the parameter space is typically prohibitive due to excessive computational costs, and systematic gradient-based parameter optimization is not feasible because such models are typically not differentiable. This is especially problematic in cases where the models intend to describe highly nonlinear and possibly abrupt dynamics, where sensitivity to parameter changes is high. Components of Earth’s climate system, such as the North Atlantic Overturning Circulation, the polar ice sheets, or the Amazon rainforest, are at risk of undergoing critical transitions in response to anthropogenic climate change. However, estimates of the critical forcing thresholds are highly uncertain because the parameter spaces of complex climate models cannot be fully explored. Concerns have been raised that the above Earth system components are too stable in state-of-the-art models. Here, we introduce a method for efficient, systematic, and objective calibration of dynamical complex system models, targeted at adjusting system stability. Given a number of physical or observational constraints, our method moves the system in a direction where the system loses or gains stability, guided by indicators of “critical slowing down”. In contrast to a brute force approach, where the computational cost would exponentially increase with the number of parameters, our method scales polynomially and thus evades the curse of dimensionality. We successfully apply our method to a conceptual double-fold bifurcation model and a physically plausible reduced-order model of the global ocean circulation. Our method can efficiently adjust stability biases across a range of complex system models, helping to reveal hidden instabilities and resulting state transitions they induce. In particular, it can help us to explore and improve the representation of key multistable components of the Earth system in climate models.

The Atlantic Meridional Overturning Circulation (AMOC) plays a key role in the climate system, especially in the global meridional heat transport. Historical reconstructions indicate that the AMOC has weakened by about 15% since the mid‐20th century. Paleoclimate records, ocean theory, as well as a hierarchy of climate models suggest that the AMOC is a tipping element, sensitive to changes in buoyancy fluxes at the air‐sea interface, and could transition into a substantially weaker or fully collapsed state. Such a transition would have significant climate impacts on decadal to centennial timescales, potentially exceeding societal adaptability. Assessing the probability of such a transition, particularly before 2100, requires evaluating whether a collapsed AMOC state is possible under current forcing conditions. While conceptual and intermediate‐complexity models have long identified collapsed states, comprehensive global climate models have only recently done so. Based on integrating model diagnostics with observations and current AMOC theory this review article critically evaluates the current arguments for and against the evidence of a multi‐stable AMOC regime. We conclude that the evidence base in favor of such a regime has broadened over the last years and that the present‐day AMOC is in such a regime. This article is categorized under: Paleoclimates and Current Trends > Modern Climate Change Paleoclimates and Current Trends > Earth System Behavior Climate Models and Modeling > Knowledge Generation with Models