  Since model bias and associated initialization shock are serious shortcomings
that reduce prediction skills in state-of-the-art decadal climate prediction
efforts, we pursue a complementary machine-learning-based approach to climate
prediction. The example problem setting we consider consists of predicting
natural variability of the North Atlantic sea surface temperature on the
interannual timescale in the pre-industrial control simulation of the Community
Earth System Model (CESM2). While previous works have considered the use of
recurrent networks such as convolutional LSTMs and reservoir computing networks
in this and other similar problem settings, we currently focus on the use of
feedforward convolutional networks. In particular, we find that a feedforward
convolutional network with a Densenet architecture is able to outperform a
convolutional LSTM in terms of predictive skill. Next, we go on to consider a
probabilistic formulation of the same network based on Stein variational
gradient descent and find that in addition to providing useful measures of
predictive uncertainty, the probabilistic (Bayesian) version improves on its
deterministic counterpart in terms of predictive skill. Finally, we
characterize the reliability of the ensemble of ML models obtained in the
probabilistic setting by using analysis tools developed in the context of
ensemble numerical weather prediction.
