Generative Modelling of Stochastic Rotating Shallow Water Noise

The paper empirically shows that the learned transport noise is non-Gaussian (KS rejections at 64 grid points) and that it improves CRPS/RMSE at low initial uncertainty, with details on the transport-noise operator, divergence-free construction, and forecast set-up (figures and text) . However, it offers no rigorous proof of optimality; some descriptions (rank-histogram text vs. figure labels) are internally inconsistent . The model’s solution adds plausible theory (strict propriety of CRPS, RMSE bias decomposition) but requires unverified assumptions (that the learned predictive law equals the true conditional law under small initial uncertainty), so it is also incomplete.