Abstract. Large-eddy simulations (LES) are essential tools for studies on atmospheric turbulence and clouds and play critical roles in the development of turbulence and convection parameterizations. Current numerical weather models have approached kilometer-scale resolution as supercomputing facilities advance. However, this resolution range is in the so-called gray zone, where subgrid-scale (SGS) turbulence actively interacts with resolved motion and significantly influences the large-scale characteristics of simulated weather systems. Thus, a novel LES framework is required to enable the development of new SGS approaches for the gray zone. Here we used the Python library JAX to develop a new LES model. It is based on the generalized pseudo-incompressible equations formulated by Durran (2008). For a classic warm bubble case, the traditional Smagorinsky model fails to reproduce the correct structure evolution of the warm bubble, though it can modestly correct the rising speed in gray-zone resolution simulations. Utilizing the capability of JAX for automatic differentiation, we trained a deep learning-based SGS turbulence model for the same case. The trained deep learning SGS model, based on a simple autoencoder (AE), enables this physics-deep learning hybrid model to accurately simulate the expansion of the thermal bubble and the development of rotors surrounding the center of the bubble at a gray-zone resolution. The gray-zone simulation results are comparable to those of the benchmark LES resolution.
Zhu et al. (2026) studied this question.