Deep learning is a powerful tool to represent subgrid processes in climate models, but many application cases have so far used idealized settings and deterministic approaches. Here, we develop stochastic parameterizations with calibrated uncertainty quantification to learn subgrid convective and turbulent processes and surface radiative fluxes of a superparameterization embedded in an Earth System Model (ESM). We explore three methods to construct stochastic parameterizations: (a) a single Deep Neural Network (DNN) with Monte Carlo Dropout; (b) a multi-member parameterization; and (c) a Variational Encoder Decoder with latent space perturbation. We show that the multi-member parameterization improves the representation of convective processes, especially in the planetary boundary layer, compared to individual DNNs. The respective uncertainty quantification illustrates that methods (b) and (c) are advantageous compared to a dropout-based DNN parameterization regarding the spread of convective processes. Hybrid simulations with our best-performing multi-member parameterizations remained challenging and crash within the first days. Therefore, we develop a pragmatic partial coupling strategy relying on the superparameterization for condensate emulation. Partial coupling reduces the computational efficiency of hybrid Earth-like simulations but enables model stability over 5 months with our multi-member parameterizations. However, our hybrid simulations exhibit biases in thermodynamic fields and differences in precipitation patterns. Despite this, the multi-member parameterizations enable improvements in reproducing tropical extreme precipitation compared to a traditional convection parameterization. Despite these challenges, our results indicate the potential of a new generation of multi-member machine learning parameterizations leveraging uncertainty quantification to improve the representation of stochasticity of subgrid effects.
