Advancing Artificial Neural Network Parameterization for Atmospheric Turbulence Using a Variational Multiscale Model

Data-driven parameterizations offer considerable potential for improving the fidelity of General Circulation Models. However, ensuring that these remain consistent with the governing equations while still producing stable simulations remains a challenge. In this paper, we propose a combined Variational-Multiscale (VMS) Artificial Neural Network (ANN) discretization which makes no a priori assumptions on the model form, and is only restricted in its accuracy by the precision of the ANN. Using a simplified problem, we demonstrate that good predictions of the required closure terms can be obtained with relatively compact ANN architectures. We then turn our attention to the stability of the VMS-ANN discretization in the context of a single implicit time step. It is demonstrated that the ANN parameterization introduces nonphysical solutions to the governing equations that can significantly affect or prevent convergence. We show that enriching the training data with nonphysical states from intra-time step iterations is an effective remedy. This indicates that the lack of representative ANN-induced errors in our original, exact training inputs underpin the observed instabilities. In turn, this suggests that data set enrichment might aid in resolving instabilities that develop over several time steps.