We introduce a hierarchical Bayesian model (HBM) for precipitation monitoring data that incorporates numerical weather prediction (NWP) model output at high spatial and temporal resolution and a physics-based stochastic partial differential equation (SPDE). The SPDE explicitly models phenomena such as advection and diffusion that occur in many natural processes. We approximate the solution of the SPDE in the spectral space using the method of eigenfunctions to reduce the dimensionality of the problem. The incorporation of NWP predictions in a rainfall model is commonly called postprocessing of precipitation forecasts; it provides calibrated probabilistic precipitation forecasts. We demonstrate this modeling approach using precipitation data and NWP forecasts for northern Switzerland.