Analysis of Spatiotemporal Properties and Modeling of the Nonisotropy of GNSS Tropospheric Slant Path Delay

The Slant Path Delay (SPD) exhibits “non-isotropy” in the horizontal direction, validated by ray-tracing. This non-isotropy can cause decimeter-level errors in SPD, yet specific models and influencing factors remain under-researched. This study aims to quantify SPD non-isotropy with the non-isotropic value (ΔN), which represents the deviation between SPD and average SPD at corresponding elevations. We analyzed the spatiotemporal characteristics of non-isotropic SPD by estimating ΔN at 77 grid points (2019–2021, 1-day interval) and 804 grid points at different altitudes (2019–2021, 90-day interval). Using the IGG-Ⅲ scheme, we developed a non-isotropic SPD model considering azimuth continuity. We validated this model by incorporating VMF1 with horizontal gradient correction and VMF1 with horizontal gradient correction combined with the non-isotropic model into static PPP, tested at 16 IGS stations. Results indicate ΔN depends on time, latitude, altitude, elevation, and azimuth. The model categorizes SPD into positive anisotropy, undetermined isotropy, or negative anisotropy. For the 16 IGS stations, the non-isotropic model reduced the STD by 7.5%, 5.8%, and 2.8% in the E, N, and U directions, respectively, and decreased convergence time by 12.8%, 25.4%, and 1.4%. This confirms the model's effectiveness, offering a valuable tool for accurate SPD estimation and improved navigation under real atmospheric conditions.