Hydrological forecasts strongly rely on predictions of precipitation amounts as meteorological inputs to hydrological models. Ensemble weather predictions provide a number of different scenarios that reflect the uncertainty about these meteorological inputs, but are often biased and underdispersive, and therefore require statistical postprocessing. In hydrological applications it is crucial that spatial and temporal (i.e. between different forecast lead times) correlations are adequately represented by the postprocessed forecasts. We discuss the two main approaches proposed in the weather forecasting literature to model the space-time variability of precipitation forecasts, and propose variants of both techniques that make them applicable in the situation where high-resolution precipitation fields need to be constructed based on the output of the (lower resolution) Global Ensemble Forecast System (GEFS). A case study is presented that demonstrates that the precipitation forecast fields generated by the two new techniques are physically more realistic, and systematic verification shows that they also have better multivariate statistical properties.