Abstract. 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 40 km×200 km 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. 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.

Wind profile observations near the surface are rarely assimilated into numerical weather prediction models. More and more ground-based remote sensing devices for wind profile observations are used to get profiles up to the hub height of wind turbines. However, an observation impact of LiDAR-like wind profile measurements on data assimilation in the atmospheric boundary layer is unknown. We show here the observation impact of boundary layer wind profile measurements on a sub-kilometre-scale data assimilation system for the metropolitan area of Hamburg. This data assimilation system is based on the Kilometre-scale ENsemble Data Assimilation system and the COnsortium for Small-scale MOdelling model. In three stably stratified test cases, we show a positive observation impact of wind profile observations on wind speed in analyses and for forecasts. The analysis improvements in wind speed are propagated to improvements in temperature at forecast time in two of three cases. Additional assimilation of temperature and relative humidity increases the mean absolute increments only by a small amount compared to increments due to wind profile observations. Wind profile observations in the atmospheric boundary layer have therefore valuable information for data assimilation on small scales.

Ensemble data from Earth system models has to be calibrated and post-processed. I propose a novel member-by-member post-processing approach with neural networks. I bridge ideas from ensemble data assimilation with self-attention, resulting into the self-attentive ensemble transformer. Here, interactions between ensemble members are represented as additive and dynamic self-attentive part. As proof-of-concept, global ECMWF ensemble forecasts are regressed to 2metre-temperature fields from the ERA5 reanalysis. I demonstrate that the ensemble transformer can calibrate the ensemble spread and extract additional information from the ensemble. Furthermore, the ensemble transformer directly outputs multivariate and spatially-coherent ensemble members. Therefore, self-attention and the transformer technique can be a missing piece for a member-by-member post-processing of ensemble data with neural networks.