  Deep learning has proven to be a valuable tool to represent subgrid processes
in climate models, but most application cases have so far used idealized
settings and deterministic approaches. Here, we develop ensemble and 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: 1) a single Deep Neural
Network (DNN) with Monte Carlo Dropout; 2) a multi-network ensemble; and 3) a
Variational Encoder Decoder with latent space perturbation. We show that the
multi-network ensembles improve the representation of convective processes in
the planetary boundary layer compared to individual DNNs. The respective
uncertainty quantification illustrates that the two latter methods are
advantageous compared to a dropout-based DNN ensemble regarding the spread of
convective processes. We develop a novel partial coupling strategy to sidestep
issues in condensate emulation to evaluate the multi-network parameterizations
in online runs coupled to the ESM. We can conduct Earth-like stable runs over
more than 5 months with the ensemble approach, while such simulations using
individual DNNs fail within days. Moreover, we show that our novel ensemble
parameterizations improve the representation of extreme precipitation and the
underlying diurnal cycle compared to a traditional parameterization, although
faithfully representing the mean precipitation pattern remains challenging. Our
results pave the way towards a new generation of parameterizations using
machine learning with realistic uncertainty quantification that significantly
improve the representation of subgrid effects.
