Data fusion aims at integrating multiple data sources that can be redundant or complementary to produce complete, accurate information of the parameter of interest. In this work, data fusion of precipitable water vapor (PWV) estimated from remote sensing observations and data from the Weather Research and Forecasting (WRF) modeling system is applied to provide complete, accurate grids of PWV. Our goal is to infer spatially continuous, precise grids of PWV from heterogeneous data sets. This is done by a geostatistical data fusion approach based on the method of fixed-rank kriging. The first data set contains absolute maps of atmospheric water vapor produced by combining observations from Global Navigation Satellite Systems (GNSS) and Interferometric Synthetic Aperture Radar (InSAR). These PWV maps have a high spatial density and an accuracy of submillimeter; however, data are missing in regions of low coherence (e.g., forests and vegetated areas). The PWV maps simulated by the WRF model represent the second data set. The model maps are available for wide areas, but they have a coarse spatial resolution and a yet limited accuracy. The PWV maps inferred by the data fusion at any spatial resolution are more accurate than those inferred from single data sets. ... mehrIn addition, using the fixed-rank kriging method, the computational burden is significantly lower than that for ordinary kriging.