  Accurate precipitation forecasts have a high socio-economic value due to
their role in decision-making in various fields such as transport networks and
farming. We propose a global statistical postprocessing method for grid-based
precipitation ensemble forecasts. This U-Net-based distributional regression
method predicts marginal distributions in the form of parametric distributions
inferred by scoring rule minimization. Distributional regression U-Nets are
compared to state-of-the-art postprocessing methods for daily 21-h forecasts of
3-h accumulated precipitation over the South of France. Training data comes
from the M\'et\'eo-France weather model AROME-EPS and spans 3 years. A
practical challenge appears when consistent data or reforecasts are not
available.
  Distributional regression U-Nets compete favorably with the raw ensemble. In
terms of continuous ranked probability score, they reach a performance
comparable to quantile regression forests (QRF). However, they are unable to
provide calibrated forecasts in areas associated with high climatological
precipitation. In terms of predictive power for heavy precipitation events,
they outperform both QRF and semi-parametric QRF with tail extensions.
