Investigating the role of clouds and precipitation in the Earth system necessitates microphysical schemes capable of accurately describing the evolution of hydrometeor particle size distribution (PSD), while maintaining low computational costs implementable in atmospheric models. Machine learning (ML) offers a promising approach for replacing detailed binned yet computationally expensive schemes with efficient emulations. However, many existing emulations still rely on moments as prognostic variables, inheriting structural limitations from traditional bulk schemes. In contrast, latent variables directly discovered by ML are potential to represent PSDs more accurately, but their inherent nonlinearity breaks the conservation property under advection and diffusion, limiting their applicability in online simulations. To address this dilemma, we propose Weighted Integral Parameters (WIPs), formulated as weighted integrals of PSD with learnable weight functions, providing the most general mathematical form for advectable microphysical prognostic variables. Using autoencoders that are physics-informed by WIP’s formulation to learn the optimal PSD representations, we conducted unsupervised learning over a liquid droplet PSD dataset generated from ensemble large eddy simulations with Spectral Bin Microphysics, to compare WIPs with traditional moment approaches in bulk schemes on their ability to represent “actual” PSDs. Results show that WIPs can automatically capture the critical information of medium-sized droplets unprecedentedly with traditional moment approaches, and outperform partial and full integral moments in terms of PSD reconstruction error, indicating superior PSD information compression efficiency. With these properties, WIPs are potential to replace moments as fully prognostic variables to build more accurate ML-based bin-emulating schemes.

The uncertainty of climate projection is significantly contributed by warm cloud feedback, which involves a complex interplay of various mechanisms. However, it is hard to unentangle temperature’s impact on a single cloud with experiments, since the cloud dynamics always covaries with environmental thermodynamical conditions. In this study, we investigate a simulated single shallow cumulus cloud’s response to temperature using two perturbation methods, namely “uniform” and “buoyancy-fixed”, the latter of which keeps the buoyancy profile unchanged in temperature perturbation. High-resolution large eddy simulation shows that uniform warming significantly increases cloud buoyancy, reducing cloud adiabaticity. If buoyancy is fixed, warming only reduces cloud area, leaving adiabatic fraction almost unchanged. Such response can be explained by Clausius-Clapeyron effect with an idealized 1D diffusion model, showing that warming increases the cloud-environment absolute humidity difference more than the increase in cloud liquid water content, resulting in a faster loss in both cloud coverage and total liquid water solely by lateral mixing. The responses of cloud coverage and total liquid water counteract, making adiabatic fraction insensitive to temperature change. Our works shows that cloud adiabatic fraction’s response to temperature is sensitive to the perturbed structure of the boundary layer, and the cloud coverage reduction by diffusion acts as positive cloud feedback mechanism in addition to the adjustment processes of the boundary layer.

Marine low clouds significantly cool the climate, but predicting these clouds remains challenging: the response of these clouds to various factors is highly non-linear. Previous studies usually overlook the effects of cloud droplet number concentration (Nd) and the non-local information of the target grids. To address these challenges, we introduce a convolutional neural network model (CNNMet-Nd) that uses both local and non-local information and includes Nd as a cloud-controlling factor to enhance the predictive ability of cloud cover, albedo, and cloud radiative effects (CRE) for global marine low clouds. CNNMet-Nd demonstrates superior performance, explaining over 70% of the variance in these three cloud variables for instantaneous scenes of 1°×1°, a notable improvement over past efforts. CNNMet-Nd also accurately replicates geographical patterns of trends in marine low clouds from 2003 to 2022. In contrast, a similar convolutional neural network model without Nd input (CNNMet) fails to predict global mean cloud properties effectively, underscoring the critical role of Nd. Further comparisons with an artificial neural network (ANNMet-Nd) model, which uses the same inputs but without considering spatial dependence, show CNNMet-Nd’s superior performance with R2 values for cloud cover, albedo, and CRE being 0.16, 0.11, and 0.18 higher, respectively. This highlights the importance of incorporating non-local information into low cloud predictions to enhance climate model parameterizations.