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There are different strategies for training neural networks (NNs) assubgrid-scale parameterizations. Here, we use a 1D model of the quasi-biennialoscillation (QBO) and gravity wave (GW) parameterizations as testbeds. A12-layer convolutional NN that predicts GW forcings for given wind profiles,when trained offline in a big-data regime (100-years), produces realistic QBOsonce coupled to the 1D model. In contrast, offline training of this NN in asmall-data regime (18-months) yields unrealistic QBOs. However, onlinere-training of just two layers of this NN using ensemble Kalman inversion andonly time-averaged QBO statistics leads to parameterizations that yieldrealistic QBOs. Fourier analysis of these three NNs' kernels suggests why/howre-training works and reveals that these NNs primarily learn low-pass,high-pass, and a combination of band-pass filters, consistent with theimportance of both local and non-local dynamics in GW propagation/dissipation.These findings/strategies apply to data-driven parameterizations of otherclimate processes generally.

Explainable Offline-Online Training of Neural Networks for Parameterizations: A 1D Gravity Wave-QBO Testbed in the Small-data Regime