Machine learning (ML) is actively being explored as a potential way of representing unresolved sub-grid processes with more realism than traditional parameterizations. A typical approach has been to generate training data with cloud-resolving simulations, and concatenate the vertical profiles of several atmospheric variables into input and output vectors of a feed-forward neural network. However, these networks lack the connections to directly propagate information through the vertical column. 

Here we examine if predictions can be improved by instead traversing the vertical column using a recurrent neural network (RNN), which also respects the fact that physical laws do not change by height. By using datasets published in other studies, we test ”vertical RNNs” on three different problems (non-orographic gravity waves, moist physics and non-local unified parameterization). In each case, we find that bidirectional RNNs have similar or higher offline accuracy as feed-forward models while using fewer trainable parameters. While prognostic climate simulations were not performed in this exploratory work, the RNNs are more stable in offline autoregressive tests than ResNets, the previous state-of-the-art.