“…The rise of machine learning (ML, i.e., data-driven models) capabilities has fostered new approaches to improving parameterizations (Gentine et al, 2018). Examples include replacing computationally intensive physical parameterizations with ML emulation (Keller & Evans, 2019;Krasnopolsky et al, 2005Krasnopolsky et al, , 2010Lagerquist et al, 2021;O'Gorman & Dwyer, 2018;Perkins et al, 2023) and training ML against observations (Chen et al, 2023;McGibbon & Bretherton, 2019;Watt-Meyer et al, 2021) or more accurate and computationally intensive parameterizations (Chantry et al, 2021). ML parameterizations for coarse-grid models have been trained on coarsened (coarse-grained) outputs of fine-grid or super-parameterized reference simulations, for example, to predict the effect of the full physics parameterization (Brenowitz & Bretherton, 2019;Han et al, 2020;Rasp et al, 2018;Watt-Meyer et al, 2024;Yuval et al, 2021), or a column-wise correction to the coarse-grid model physics (Bretherton et al, 2022;Clark et al, 2022;Kwa et al, 2023).…”