Deep-learning-based convection schemes have garnered significant attention for their notable improvements in simulating precipitation distribution and tropical convection in Earth system models. However, these schemes struggle to capture the stochastic nature of moist physics, which can degrade the simulation of large-scale circulations, climate means, and variability. To address this issue, a stochastic parameterization scheme called DIFF-MP, based on a probabilistic diffusion model, is developed. Cloud-resolving data are coarse-grained into resolved-scale variables and subgrid contributions, which serve as conditional inputs and outputs for DIFF-MP. The performance of DIFF-MP is compared with that of generative adversarial networks and variational autoencoders. The results demonstrate that DIFF-MP consistently outperforms these models in terms of prediction error, coverage ratio, and spread–skill correlation. Furthermore, the standard deviation, skewness, and kurtosis of the subgrid contributions generated by DIFF-MP more closely match the test data than those produced by the other models. Interpretability experiments confirm that DIFF-MP’s parameterization of moist physics is physically consistent.

Tropical cyclone (TC) is among the most destructive weather phenomena on the earth, whose structure and intensity are strongly modulated by TC boundary layer. Mesoscale model used for TC research and prediction must rely on boundary layer parameterization due to low spacial resolution. These boundary layer schemes are mostly developed on field experiments under moderate wind speed. They often underestimate the influence of shear-driven rolls and turbulences. When applied under extreme condition like TC boundary layer, significant bias will be unavoidable. In this study, a novel machine learning model—one dimensional convolutional neural network (1D-CNN)—is proposed to tackle the TC boundary layer parameterization dilemma. The 1D-CNN saves about half of the learnable parameters and accomplishes a steady improvement compared to fully-connected neural network. TC large eddy simulation outputs are used as training data of 1D-CNN, which shows strong skewness in calculated turbulent fluxes. The data skewness problem is alleviated in order to reduce 1D-CNN model bias. It is shown in an offline TC boundary layer test that our proposed model, the 1D-CNN, performs significantly better than popular schemes now utilized in TC simulations. Model performance across different scales is essential to final application. It is found that the high resolution data contains the information of low resolution data but not vise versa. The model performance on the extreme data is key to final performance on the whole dataset. Training the model on the highest resolution non-extreme data plus extreme data of different resolutions can secure the robust performance across different scales.

Deep-learning-based convection schemes receive wide attention due to its impressive im-provement on precipitation distribution and tropical convections of earth system simulation. But they cannot represent the stochasticity of moist physics, which will degrade the simulation of large-scale circulations, climate mean, and variability. To solve this problem, a stochastic pa-rameterization scheme based on probabilistic diffusion model named DIFF-MP is developed. The cloud-resolving data from GRIST model is coarse-grained into resolved-scale variables and sub-grid contributions due to moist physics to form the training data. DIFF-MP’s performance is compared against generative adversarial network and variational autoencoder. Results show that DIFF-MP is consistently better than the other two models on prediction error, coverage ratio, and spread-skill correlation. The standard deviation, skewness, and kurtosis of subgrid contributions generated by DIFF-MP is also closer to the testing data than the others. Interpretability experiment shows that DIFF-MP’s parameterization of moist physics is physically reasonable.