Rainfall prediction at the kilometre-scale up to a few hours in the future is key for planning and safety. But it is challenging given the complex influence of climate change on cloud processes and the limited skill of weather models at this scale. Following the set-up proposed by the \emph{weather4cast} challenge of NeurIPS, we build a two-step deep-learning solution for predicting rainfall occurrence at ground radar high spatial resolution starting from coarser resolution weather satellite images. Our approach is designed to predict future satellite images with a physics-aware ConvLSTM network, which is then converted into precipitation maps through a U-Net. We find that our two-step pipeline outperforms the baseline model and we quantify the benefits of including physical information. We find that local-scale rainfall predictions with good accuracy starting from satellite radiances can be obtained for up to 4 hours in the future.