Online learning as a way to tackle instabilities and biases in neural network parameterizations

Over the last couple of years, machine learning parameterizations have emerged as a potential way to improve the representation of sub-grid processes in atmospheric models. All studies so far created a training dataset from a high-resolution simulation, fitted a machine learning algorithms to that dataset, and then implemented the trained algorithm in an atmospheric model. The resulting online simulations were frequently plagued by instabilities and biases. Here, I propose online learning as a way to combat these issues. Online learning can be seen as a second training stage in which the pretrained machine learning parameterization, specifically a neural network, is run in parallel with a high-resolution simulation. The high-resolution simulation is kept in sync with the neural network-driven atmospheric model through constant forcing. This enables the neural network to learn from the tendencies that the high-resolution simulation would produce if it experienced the atmospheric states the neural network creates. The concept is illustrated using the Lorenz 96 model, where online learning is able to recover the "true" parameterizations. Then I present detailed algorithms for implementing online learning in the 3D cloud-resolving model and super-parameterization frameworks. Finally, I discuss outstanding challenges and issues not solved by this approach.