Real-time tropospheric delay modeling over large areas by integrating GFS forecasts and GNSS-derived ZWD for enhanced PPP-AR positioning

The limited spatial distribution of global navigation satellite systems (GNSS) stations constrains the accuracy and spatial resolution of tropospheric delay modeling over large areas, particularly in regions with complex terrain, coastal environments, or sparse observational infrastructure. To address this limitation, we propose a novel tropospheric delay modeling approach that integrates zenith wet delays (ZWDs) estimated from GNSS stations using precise point positioning with ambiguity resolution (PPP-AR) and those derived from global forecast system (GFS) meteorological forecasts. By leveraging the global coverage of GFS, the proposed method enables the construction of virtual reference stations in regions lacking GNSS infrastructure, including coastal and near-ocean areas. These stations effectively bridge observational gaps in ZWD and significantly enhance the spatial continuity and resolution of ZWD fields in complex or under-instrumented regions. For experimental validation, GNSS observations and GFS forecasts over the European region are analyzed. The accuracy of GFS-integrated ZWDs is evaluated against those obtained via PPP-AR, yielding a daily root mean square (RMS) of 11.0 mm. Incorporating GFS-based virtual stations further improves the performance of ZWD modeling, reducing the RMS from 14.6 to 14.1 mm. In regions with altitude differences exceeding 2000 m, the model achieves an RMS of 24.9 mm, representing a 30.1% improvement compared to the traditional GNSS-only approach (RMS of 32.7 mm). In GNSS-sparse regions, such as high-altitude mountainous and coastal areas, the proposed model enhances positioning accuracy by about 20.4% and reduces convergence time by approximately 13.3%, demonstrating its effectiveness in improving service quality under challenging conditions. These results confirm that incorporating GFS-based virtual reference stations substantially improves the spatial coverage and robustness of tropospheric delay modeling in areas with limited GNSS observations or complex geography, without imposing additional communication or computational burdens.