We model the ionospheric delay of Global Positioning System (GPS) signals with high precision and use it to correct single frequency (L1) GPS baseline estimations. We find that baselines up to 30 km in length are more precisely determined using corrected L1 data than using dual frequency data. The high resolution ionospheric modeling technique (called HiRIM in this paper) is demonstrated with 195 days of data from a 25-site GPS network at ~1 km spacing in central Japan. The network was designed for high vertical precision tectonic studies. We compute ionospheric corrections using data from a surrounding grid of nine GPS sites spaced ~50 km. Based on the observations from the surrounding grid, epoch and satellite specific ionospheric delays are interpolated to correct L1 observations from the internal sites. HiRIM has potential post-processing and real-time applications in navigation, surveying, and GPS meteorology. ¿ 2000 American Geophysical Union