How to calibrate a neural network parameterization?

<em>Submitted to Geophysical Research Letters.</em> <strong>Abstract.</strong> In current climate models, parameterization for each modeled process is tuned offline, individually. Thus, interactions between subgrid scale processes can be missed. To address this issue, a neural network (NN)-based emulator of the resulting parameterization is trained to predict subgrid-scale tendencies as a function of atmospheric state variables and some of the tuned model parameters, \(\boldsymbol{\theta}\). Then, the fitted NN is implemented to replace the parameterization tuned offline. The optimal value of \(\boldsymbol{\theta}\) is determined by tuning its value online, with respect to a metric computing longterm prediction errors. Our approach has been demonstrated using the Lorenz’63 toy model (L63). The online optimization led to parameter values used to generate a reference dataset. In a second experiment, one of the model parameters was willingly biased. The resulting longterm prediction error was significantly reduced by optimizing online the value of one of \(\boldsymbol{\theta}\) parameters.