We propose a computationally efficient statistical method to obtain distributional properties of annual maximum 24 hour precipitation on a 1 km by 1 km regular grid over Iceland. A latent Gaussian model is built which takes into account observations, spatial variations and outputs from a local meteorological model. A covariate based on the meteorological model is constructed at each observational site and each grid point in order to assimilate available scientific knowledge about precipitation into the statistical model. The model is applied to two data sets on extreme precipitation, one uncorrected data set and one data set that is corrected for phase and wind. The observations are assumed to follow the generalized extreme value distribution. At the latent level, we implement SPDE spatial models for both the location and scale parameters of the likelihood. An efficient MCMC sampler which exploits the model structure is constructed, which yields fast continuous spatial predictions for spatially varying model parameters and quantiles.