Because of the impact of extreme heat waves and heat domes on society and biodiversity, their study is a key challenge. We specifically study long-lasting extreme heat waves, which are among the most important for climate impacts. Physics driven weather forecast systems or climate models can be used to forecast their occurrence or predict their probability. The present work explores the use of deep learning architectures, trained using outputs of a climate model, as an alternative strategy to forecast the occurrence of extreme long-lasting heatwave. This new approach will be useful for several key scientific goals which include the study of climate model statistics, building a quantitative proxy for resampling rare events in climate models, study the impact of climate change, and should eventually be useful for forecasting. Fulfilling these important goals implies addressing issues such as class-size imbalance that is intrinsically associated with rare event prediction, assessing the potential benefits of transfer learning to address the nested nature of extreme events (naturally included in less extreme ones). We train a Convolutional Neural Network, using 1,000 years of climate model outputs, with large-class undersampling and transfer learning. From the observed snapshots of the surface temperature and the 500 hPa geopotential height fields, the trained network achieves significant performance in forecasting the occurrence of long-lasting extreme heatwaves. We are able to predict them at three different levels of intensity, and as early as 15 days ahead of the start of the event (30 days ahead of the end of the event).

Abstract. In recent years, several climate subsystems have been identified that may undergo a relatively rapid transition compared to the changes in their forcing. Such transitions are rare events in general, and simulating long-enough trajectories in order to gather sufficient data to determine transition statistics would be too expensive. Conversely, rare events algorithms like TAMS (trajectory-adaptive multilevel sampling) encourage the transition while keeping track of the model statistics. However, this algorithm relies on a score function whose choice is crucial to ensure its efficiency. The optimal score function, called the committor function, is in practice very difficult to compute. In this paper, we compare different data-based methods (analog Markov chains, neural networks, reservoir computing, dynamical Galerkin approximation) to estimate the committor from trajectory data. We apply these methods on two models of the Atlantic Ocean circulation featuring very different dynamical behavior. We compare these methods in terms of two measures, evaluating how close the estimate is from the true committor and in terms of the computational time. We find that all methods are able to extract information from the data in order to provide a good estimate of the committor. Analog Markov Chains provide a very reliable estimate of the true committor in simple models but prove not so robust when applied to systems with a more complex phase space. Neural network methods clearly stand out by their relatively low testing time, and their training time scales more favorably with the complexity of the model than the other methods. In particular, feedforward neural networks consistently achieve the best performance when trained with enough data, making this method promising for committor estimation in sophisticated climate models.

Abstract. In recent years, several climate subsystems have been identified that may undergo a relatively rapid transition compared to the changes in their forcing. Such transitions are rare events in general and simulating long-enough trajectories in order to gather sufficient data to determine transition statistics would be too expensive. Conversely, rare-events algorithms like TAMS (Trajectory-Adaptive Multilevel Sampling) encourage the transition while keeping track of the model statistics. However, this algorithm relies on a score function whose choice is crucial to ensure its efficiency. The optimal score function, called committor function, is in practice very difficult to compute. In this paper, we compare different data-based methods (Analogue Markov Chains, Neural Networks, Reservoir Computing, Dynamical Galerkin Approximation) to estimate the committor from trajectory data. We apply these methods on two models of the Atlantic Ocean circulation featuring very different dynamical behavior. We compare these methods in terms of two measures, evaluating how close the estimate is from the true committor, and in terms of the computational time. We find that all methods are able to extract information from the data in order to provide a good estimate of the committor. Analogue Markov Chains provide a very reliable estimate of the true committor in simple models but prove not so robust when applied to systems with a more complex phase space. Neural network methods clearly stand out by their relatively low testing time, and their training time scales more favorably with the complexity of the model than the other methods. In particular, feedforward neural networks consistently achieve the best performance when trained with enough data, making this method promising for committor estimation in sophisticated climate models.

<p>The Atlantic Meridional Overturning Circulation (AMOC) transports warm, saline water towards the northern North Atlantic, contributing substantially to the meridional heat transport in the climate system. Measurements of the Atlantic freshwater divergence show that it may be in a bistable state and hence subject to collapsing under anthropogenic forcing. We aim at computing the probability of such a transition. We focus on timescales of the century and on temporary collapses of the AMOC. Using simulated data from an idealized stochastic AMOC model, where forcing and white noise are applied via a surface freshwater flux, we compute the transition probabilities versus noise and forcing amplitudes.</p><p>Such transitions are very rare and simulating long-enough trajectories in order to gather sufficient statistics is too expensive. Conversely, rare-events algorithms like TAMS (Trajectory-Adaptive Multilevel Sampling) encourage the transition without changing the statistics. In TAMS, N trajectories are simulated and evaluated with a score function; the poorest-performing trajectories are discarded, and the best ones are re-simulated.</p><p>The optimal score function is the committor function, defined as the probability that a trajectory reaches a zone A of the phase space before another zone B. Its exact computation is in general difficult and time-consuming. In this presentation, we compare data-driven methods to estimate the committor. Firstly, the Analogues Markov Chain method computes it from the transition matrix of a long re-simulated trajectory. The K-Nearest Neighbours method relies on an existing pool of states where the committor function is already known to estimate it everywhere. Finally, the Dynamical Modes Decomposition method is based on a Galerkin approximation of the Koopman operator. The latter is the most efficient one for the AMOC model when using adaptive dimensionality reduction of the phase space.</p>

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