  Over the last couple of years, machine learning parameterizations have
emerged as a potential way to improve the representation of sub-grid processes
in Earth System Models (ESMs). So far, all studies were based on the same
three-step approach: first a training dataset was created from a
high-resolution simulation, then a machine learning algorithm was fitted to
this dataset, before the trained algorithm was implemented in the ESM. The
resulting online simulations were frequently plagued by instabilities and
biases. Here, coupled online learning is proposed as a way to combat these
issues. Coupled 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 ESM through constant
nudging. This enables the neural network to learn from the tendencies that the
high-resolution simulation would produce if it experienced the states the
neural 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 3D
cloud-resolving models and the super parameterization framework are presented.
Finally, outstanding challenges and issues not resolved by this approach are
discussed.
