Accurately representing vertical turbulent fluxes in the planetary boundary layer is vital for moisture and energy transport. Nonetheless, the parameterization of the boundary layer remains a major source of inaccuracy in climate models. Recently, machine learning techniques have gained popularity for representing oceanic and atmospheric processes, yet their high dimensionality limits interpretability. This study introduces a new neural network architecture employing non-linear dimensionality reduction to predict vertical turbulent fluxes in a dry convective boundary layer. Our method utilizes turbulent kinetic energy and scalar profiles as input to extract a physically constrained two-dimensional latent space, providing the necessary yet minimal information for accurate flux prediction. We obtained data by coarse-graining Large Eddy Simulations covering a broad spectrum of boundary layer conditions, from weakly to strongly unstable. These regimes are employed to constrain the latent space disentanglement, enhancing interpretability. By applying this constraint, we decompose the vertical turbulent flux of various scalars into two main modes of variability: wind shear and convective transport. Our data-driven parameterization accurately predicts vertical turbulent fluxes (heat and passive scalars) across turbulent regimes, surpassing state-of-the-art schemes like the eddy-diffusivity mass flux scheme. By projecting each variability mode onto its associated scalar gradient, we estimate the diffusive flux and learn the eddy diffusivity. The diffusive flux is found to be significant only in the surface layer for both modes and becomes negligible in the mixed layer. The retrieved eddy diffusivity is considerably smaller than previous estimates used in conventional parameterizations, highlighting the predominant non-diffusive nature of transport.

Accurate prediction of precipitation intensity is of crucial importance for both human and natural systems, especially in a warming climate more prone to extreme precipitation. Yet climate models fail to accurately predict precipitation intensity, particularly extremes. One missing piece of information in traditional climate model parameterizations is sub-grid scale cloud structure and organization, which affects precipitation intensity and stochasticity at the grid scale. Here we show, using storm-resolving climate simulations and machine learning, that by implicitly learning sub-grid organization, we can accurately predict precipitation variability and stochasticity with a low dimensional set of variables. Using a neural network to parameterize coarse-grained precipitation, we find mean precipitation is predictable from large scale quantities only; however, the neural network cannot predict the variability of precipitation (R 2 ∼ 0.4) and underestimates precipitation extremes. Performance is significantly improved when the network is informed by our novel organization metric, correctly predicting precipitation extremes and spatial variability (R 2 ∼ 0.95). The organization metric is implicitly learned by training the algorithm on high-resolution precipitable water, encoding organization degree and humidity amount at the subgrid-scale. The organization metric shows large hysteresis, emphasizing the role of memory created by sub-grid scale structures. We demonstrate this organization metric can be predicted as a simple memory process from information available at the previous time steps. These findings stress the role of organization and memory in accurate prediction of precipitation intensity and extremes and the necessity of parameterizing sub-grid scale convective organization in climate models to better project future changes in the water cycle and extremes.