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# Non-local parameterization of atmospheric subgrid processes with neural networks

Subgrid processes in global climate models are represented byparameterizations that are a major source of uncertainties in simulations ofclimate. In recent years, it has been suggested that new machine-learningparameterizations learned from high-resolution model output data could besuperior to traditional parameterizations. Currently, both traditional andmachine-learning parameterizations of subgrid processes in the atmosphere arebased on a single-column approach. Namely, the information used by theseparameterizations is taken from a single atmospheric column. However, asingle-column approach might not be ideal for the parameterization problemsince certain atmospheric phenomena, such as organized convective systems, cancross multiple grid boxes and involve slantwise circulations that are notpurely vertical. Here we train neural networks using non-local inputs spanningover 3$\times$3 columns of inputs. We find that including the non-local inputssubstantially improves the prediction of subgrid tendencies of a range ofsubgrid processes. The improvement is especially notable for cases associatedwith mid-latitude fronts and convective instability. Using an explainableartificial intelligence technique called layer-wise relevance propagation, wefind that non-local inputs from zonal and meridional winds contain informationthat helps to improve the performance of the neural network parameterization.Our results imply that use of non-local inputs has the potential tosubstantially improve both traditional and machine-learning parameterizations.

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