  Quantifying uncertainty in weather forecasts is critical, especially for
predicting extreme weather events. This is typically accomplished with ensemble
prediction systems, which consist of many perturbed numerical weather
simulations, or trajectories, run in parallel. These systems are associated
with a high computational cost and often involve statistical post-processing
steps to inexpensively improve their raw prediction qualities. We propose a
mixed model that uses only a subset of the original weather trajectories
combined with a post-processing step using deep neural networks. These enable
the model to account for non-linear relationships that are not captured by
current numerical models or post-processing methods. Applied to global data,
our mixed models achieve a relative improvement in ensemble forecast skill
(CRPS) of over 14%. Furthermore, we demonstrate that the improvement is larger
for extreme weather events on select case studies. We also show that our
post-processing can use fewer trajectories to achieve comparable results to the
full ensemble. By using fewer trajectories, the computational costs of an
ensemble prediction system can be reduced, allowing it to run at higher
resolution and produce more accurate forecasts.
