Data-assisted uncertainty quantification and extreme event prediction in climate models using physically-consistent neural networks.*

We present a novel approach for improving the predictions of statistical quantities for turbulent systems, with focus on climate models. The method utilizes neural networks to learn a mapping between high-fidelity reference data and nudged coarse-scale simulations. Then, during testing, free-running coarse- scale data are used as input for the model, with the corrected time-series having statistics that approximate that of the reference data. The ability to transfer the mapping the model has learned during training with nudged input data to free-running data during testing is achieved by (a) a novel appropriate spectral nudging method and (b) incorporation of physical constraints during training. These constraints are vital for capturing the correct statistics of climate models, while the proposed nudging allows for a scheme that generalizes well when used on out-of-sample data. The method is first validated on a 2-layer quasigeostrophic model, a prototypical system mimicking baroclinic instability in mid-latitude and high-latitude atmospheric flows. After that, the model is tested on realistic free-running, coarse-scale climate simulations of Earth's atmosphere. Predictions of extreme events like tropical cyclones, extratropical cyclones and atmospheric rivers are presented. The model agrees well with reference data, outperforming standard climate closure schemes computationally.