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We address the problem of data augmentation in a rotating turbulence set-up,a paradigmatic challenge in geophysical applications. The goal is toreconstruct information in two-dimensional (2D) cuts of the three-dimensionalflow fields, imagining to have spatial gaps present within each 2D observedslice. We evaluate the effectiveness of different data-driven tools, based ondiffusion models (DMs), a state-of-the-art generative machine learningprotocol, and generative adversarial networks (GANs), previously considered asthe best-performing method both in terms of point-wise reconstruction and thestatistical properties of the inferred velocity fields. We focus on twodifferent DMs recently proposed in the specialized literature: (i) RePaint,based on a heuristic strategy to guide an unconditional DM for flow generationby using partial measurements data and (ii) Palette, a conditional DM trainedfor the reconstruction task with paired measured and missing data. Systematiccomparison shows that (i) DMs outperform the GAN in terms of the mean squarederror and/or the statistical accuracy; (ii) Palette DM emerges as the mostpromising tool in terms of both point-wise and statistical metrics. Animportant property of DMs is their capacity for probabilistic reconstructions,providing a range of predictions based on the same measurements, enabling foruncertainty quantification and risk assessment.

Multi-scale Reconstruction of Turbulent Rotating Flows with Generative Diffusion Models