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A novel generation of sea-ice models with elasto-brittle rheologies, such as neXtSIM, can represent sea-ice processes with an unprecedented accuracy at the mesoscale for resolutions of around 10 km. As these models are computationally expensive, we introduce supervised deep learning techniques for surrogate modeling of the sea-ice thickness from neXtSIM simulations. We adapt a convolutional U-Net architecture to an Arctic-wide setup by taking the land–sea mask with partial convolutions into account. Trained to emulate the sea-ice thickness at a lead time of 12 h, the neural network can be iteratively applied to predictions for up to 1 year. The improvements of the surrogate model over a persistence forecast persist from 12 h to roughly 1 year, with improvements of up to 50 % in the forecast error. Moreover, the predictability gain for the sea-ice thickness measured against the daily climatology extends to over 6 months. By using atmospheric forcings as additional input, the surrogate model can represent advective and thermodynamical processes which influence the sea-ice thickness and the growth and melting therein. While iterating, the surrogate model experiences diffusive processes which result in a loss of fine-scale structures. However, this smoothing increases the coherence of large-scale features and thereby the stability of the model. Therefore, based on these results, we see huge potential for surrogate modeling of state-of-the-art sea-ice models with neural networks. [ABSTRACT FROM AUTHOR]

We propose denoising diffusion models for data-driven representation learning of dynamical systems. In this type of generative deep learning, a neural network is trained to denoise and reverse a diffusion process, where Gaussian noise is added to states from the attractor of a dynamical system. Iteratively applied, the neural network can then map samples from isotropic Gaussian noise to the state distribution. We showcase the potential of such neural networks in experiments with the Lorenz 63 system. Trained for state generation, the neural network can produce samples, almost indistinguishable from those on the attractor. The model has thereby learned an internal representation of the system, applicable on different tasks than state generation. As a first task, we fine-tune the pre-trained neural network for surrogate modelling by retraining its last layer and keeping the remaining network as a fixed feature extractor. In these low-dimensional settings, such fine-tuned models perform similarly to deep neural networks trained from scratch. As a second task, we apply the pre-trained model to generate an ensemble out of a deterministic run. Diffusing the run, and then iteratively applying the neural network, conditions the state generation, which allows us to sample from the attractor in the run's neighboring region. To control the resulting ensemble spread and Gaussianity, we tune the diffusion time and, thus, the sampled portion of the attractor. While easier to tune, this proposed ensemble sampler can outperform tuned static covariances in ensemble optimal interpolation. Therefore, these two applications show that denoising diffusion models are a promising way towards representation learning for dynamical systems. [ABSTRACT FROM AUTHOR]

A novel generation of sea-ice models with Elasto-Brittle rheologies, such as neXtSIM, can represent sea-ice processes with an unprecedented accuracy at the mesoscale, for resolutions of around 10 km. As these models are computationally expensive, we introduce supervised deep learning techniques for surrogate modeling of the sea-ice thickness from neXtSIM simulations. We adapt a convolutional UNet architecture to an Arctic-wide setup by taking the land-sea mask with partial convolutions into account. Trained to emulate the sea-ice thickness on a lead time of 12 hours, the neural network can be iteratively applied to predictions up to a year. The improvements of the surrogate model over a persistence forecast prevail from 12 hours to roughly a year, with improvements of up to 50 % in the forecast error. The predictability of the sea-ice thickness measured against a daily climatology additionally lays by around 8 months. By using atmospheric forcings as additional input, the surrogate model can represent advective and thermodynamical processes, which influence the sea-ice thickness and the growth and melting therein. While iterating, the surrogate model experiences diffusive processes, which result into a loss of fine-scale structures. However, this smoothing increases the coherence of large-scale features and hereby the stability of the model. Therefore, based on these results, we see a huge potential for surrogate modelling of state-of-art sea-ice models with neural networks. [ABSTRACT FROM AUTHOR]

We introduce a proof of concept to parametrise the unresolved subgrid scale of sea-ice dynamics with deep learning techniques. Instead of parametrising single processes, a single neural network is trained to correct all model variables at the same time. This data-driven approach is applied to a regional sea-ice model that accounts exclusively for dynamical processes with a Maxwell elasto-brittle rheology. Driven by an external wind forcing in a 40km×200km domain, the model generates examples of sharp transitions between unfractured and fully fractured sea ice. To correct such examples, we propose a convolutional U-Net architecture which extracts features at multiple scales. We test this approach in twin experiments: the neural network learns to correct forecasts from low-resolution simulations towards high-resolution simulations for a lead time of about 10 min. At this lead time, our approach reduces the forecast errors by more than 75% , averaged over all model variables. As the most important predictors, we identify the dynamics of the model variables. Furthermore, the neural network extracts localised and directional-dependent features, which point towards the shortcomings of the low-resolution simulations. Applied to correct the forecasts every 10 min, the neural network is run together with the sea-ice model. This improves the short-term forecasts up to an hour. These results consequently show that neural networks can correct model errors from the subgrid scale for sea-ice dynamics. We therefore see this study as an important first step towards hybrid modelling to forecast sea-ice dynamics on an hourly to daily timescale. [ABSTRACT FROM AUTHOR]

We introduce a scalable approach to parametrise the unresolved subgrid-scale of sea-ice dynamics with deep learning techniques. We apply this data-driven approach to a regional sea-ice model that accounts exclusively for dynamical processes with a Maxwell-Elasto-Brittle rheology. Our channel-like model setup is driven by a wave-like wind forcing, which generates examples of sharp transitions between unfractured and fully-fractured sea ice. Using a convolutional U-Net architecture, the parametrising neural network extracts multiscale and anisotropic features and, thus, includes important inductive biases needed for sea-ice dynamics. The neural network is trained to correct all nine model variables at the same time. With the initial and forecast state as input into the neural network, we cast the subgrid-scale parametrisation as model error correction, needed to correct unresolved model dynamics. We test the here-proposed approach in twin experiments, where forecasts of a low-resolution forecast model are corrected towards high-resolution truth states for a forecast lead time of about 10 min. At this lead time, our approach reduces the forecast errors by more than 75 %, averaged over all model variables. The neural network learns hereby a physically-explainable input-to-output relation. Furthermore, cycling the subgrid-scale parametrisation together with the geophysical model improves the short-term forecast up to one hour. We consequently show that neural networks can parametrise the subgrid-scale for sea-ice dynamics. We therefore see this study as an important first step towards hybrid modelling to forecast sea-ice dynamics on an hourly to daily timescale. [ABSTRACT FROM AUTHOR]