Progress and perspective of convection and cloud parameterization in numerical models

This article reviews advances of convection and cloud parameterizations in numerical models. This article begins by outlining the development of convection parameterization, including the Kuo scheme, the moist convective adjustment scheme, the widely used mass flux schemes, and the machine learning-based schemes. It introducues in detail the schemes developed and revised by Chinese scientists, as well as the resulting improvements in the numerical models by these schemes. This article then explores advances in cloud parameterization schemes and highlights the achievements of Chinese scientists in both cloud macrophysics and microphysics schemes. Finally, this review discusses possible future directions in the development of convection and cloud parameterization, emphasizing the crucial role expected for deep learning, and proposes pathways for the advancement of hybrid models and multi-scale climate modeling methods.