  Subgrid processes in global climate models are represented by
parameterizations which are a major source of uncertainties in simulations of
climate. In recent years, it has been suggested that machine-learning (ML)
parameterizations based on high-resolution model output data could be superior
to traditional parameterizations. Currently, both traditional and ML
parameterizations of subgrid processes in the atmosphere are based on a
single-column approach, which only use information from single atmospheric
columns. However, single-column parameterizations might not be ideal since
certain atmospheric phenomena, such as organized convective systems, can cross
multiple grid boxes and involve slantwise circulations that are not purely
vertical. Here we train neural networks (NNs) using non-local inputs spanning
over 3$\times$3 columns of inputs. We find that including the non-local inputs
improves the offline prediction of a range of subgrid processes. The
improvement is especially notable for subgrid momentum transport and for
atmospheric conditions associated with mid-latitude fronts and convective
instability. Using an interpretability method, we find that the NN improvements
partly rely on using the horizontal wind divergence, and we further show that
including the divergence or vertical velocity as a separate input substantially
improves offline performance. However, non-local winds continue to be useful
inputs for parameterizating subgrid momentum transport even when the vertical
velocity is included as an input. Overall, our results imply that the use of
non-local variables and the vertical velocity as inputs could improve the
performance of ML parameterizations, and the use of these inputs should be
tested in online simulations in future work.
