  Ensemble weather predictions require statistical post-processing of
systematic errors to obtain reliable and accurate probabilistic forecasts.
Traditionally, this is accomplished with distributional regression models in
which the parameters of a predictive distribution are estimated from a training
period. We propose a flexible alternative based on neural networks that can
incorporate nonlinear relationships between arbitrary predictor variables and
forecast distribution parameters that are automatically learned in a
data-driven way rather than requiring pre-specified link functions. In a case
study of 2-meter temperature forecasts at surface stations in Germany, the
neural network approach significantly outperforms benchmark post-processing
methods while being computationally more affordable. Key components to this
improvement are the use of auxiliary predictor variables and station-specific
information with the help of embeddings. Furthermore, the trained neural
network can be used to gain insight into the importance of meteorological
variables thereby challenging the notion of neural networks as uninterpretable
black boxes. Our approach can easily be extended to other statistical
post-processing and forecasting problems. We anticipate that recent advances in
deep learning combined with the ever-increasing amounts of model and
observation data will transform the post-processing of numerical weather
forecasts in the coming decade.
