The Madden–Julian Oscillation (MJO) is the dominant source of
sub-seasonal variability in the tropics. It consists of an Eastward
moving region of enhanced convection coupled to changes in zonal winds.
It is not possible to predict the precise evolution of the MJO, so
sub-seasonal forecasts are generally probabilistic. We present a deep
convolutional neural network (CNN) that produces skilful state-dependent
probabilistic MJO forecasts. Importantly, the CNN’s forecast uncertainty
varies depending on the instantaneous predictability of the MJO. The CNN
accounts for intrinsic chaotic uncertainty by predicting the standard
deviation about the mean, and model uncertainty using Monte-Carlo
dropout. Interpretation of the CNN mean forecasts highlights known MJO
mechanisms, providing confidence in the model. Interpretation of
forecast uncertainty indicates mechanisms governing MJO predictability.
In particular, we find an initially stronger MJO signal is associated
with more uncertainty, and that MJO predictability is affected by the
state of the Walker Circulation.