  Sub-seasonal weather forecasts are becoming increasingly important for a
range of socio-economic activities. However, the predictive ability of physical
weather models is very limited on these time scales. We propose several
post-processing methods based on convolutional neural networks to improve
sub-seasonal forecasts by correcting systematic errors of numerical weather
prediction models. Our post-processing models operate directly on spatial input
fields and are therefore able to retain spatial relationships and to generate
spatially homogeneous predictions. They produce global probabilistic tercile
forecasts for biweekly aggregates of temperature and precipitation for weeks
3-4 and 5-6. In a case study based on a public forecasting challenge organized
by the World Meteorological Organization, our post-processing models outperform
recalibrated forecasts from the European Centre for Medium-Range Weather
Forecasts (ECMWF), and achieve improvements over climatological forecasts for
all considered variables and lead times. We compare several model architectures
and training modes and demonstrate that all approaches lead to skillful and
well-calibrated probabilistic forecasts. The good calibration of the
post-processed forecasts emphasizes that our post-processing models reliably
quantify the forecast uncertainty based on deterministic input information in
form of the ECMWF ensemble mean forecast fields only.
