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Over the last couple of years, machine learning parameterizations haveemerged as a potential way to improve the representation of sub-grid processesin Earth System Models (ESMs). So far, all studies were based on the samethree-step approach: first a training dataset was created from ahigh-resolution simulation, then a machine learning algorithm was fitted tothis dataset, before the trained algorithm was implemented in the ESM. Theresulting online simulations were frequently plagued by instabilities andbiases. Here, coupled online learning is proposed as a way to combat theseissues. Coupled learning can be seen as a second training stage in which thepretrained machine learning parameterization, specifically a neural network, isrun in parallel with a high-resolution simulation. The high-resolutionsimulation is kept in sync with the neural network-driven ESM through constantnudging. This enables the neural network to learn from the tendencies that thehigh-resolution simulation would produce if it experienced the states theneural network creates. The concept is illustrated using the Lorenz 96 model,where coupled learning is able to recover the "true" parameterizations.Further, detailed algorithms for the implementation of coupled learning in 3Dcloud-resolving models and the super parameterization framework are presented.Finally, outstanding challenges and issues not resolved by this approach arediscussed.

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