Fusion-Based Regional ZTD Modeling Using ERA5 and GNSS via Residual Correction Kriging

Zenith Tropospheric Delay (ZTD) and its associated atmospheric water vapor information constitute essential environmental variables for Earth observation (EO)-based atmospheric monitoring and environmental variable retrieval. High-quality ZTD products are therefore of great importance for the post-processing, refinement, and reconstruction of atmospheric environmental variables at regional scales. Among existing observation techniques, Global Navigation Satellite System (GNSS) measurements provide high-precision ZTD estimates and have become an important means for retrieving tropospheric delay and water vapor. However, the sparse and uneven spatial distribution of GNSS stations limits their direct applicability for continuous environmental monitoring. Reanalysis-based products, such as ERA5 provided by the European Centre for Medium-Range Weather Forecasts (ECMWF), offer EO big data with excellent spatiotemporal continuity but suffer from pronounced systematic biases compared to precision GNSS retrievals, restricting their direct use in high-accuracy regional applications. To address these limitations, this study proposes a Residual Correction Kriging method for ZTD (RK ZTD) that integrates GNSS ZTD and ERA5 ZTD grids through a multi-source data fusion framework. High-precision GNSS ZTD is treated as reference data, and the differences between GNSS ZTD and ERA5 ZTD at modeling stations are defined as residuals to characterize the systematic bias in ERA5 ZTD grids. A Kriging interpolation algorithm is then employed to model the spatial distribution of these residuals and generate residual correction grids. By superimposing the interpolated residual grids onto the ERA5 ZTD grids, a refined and high-precision regional ZTD product is reconstructed. Experiments were conducted using observations collected in 2023 from 36 GNSS stations in the Netherlands, including 10 modeling stations and 26 independent validation stations, together with concurrent ERA5-derived ZTD grids. The results demonstrate that the proposed RK ZTD model provides spatially robust and high-precision ZTD products across the study region. The RK ZTD achieves a Root Mean Square Error (RMSE) of 5.70 mm, representing improvements of 58.4% and 35.4% compared with the original ERA5 ZTD (13.69 mm) and the GNSS-Kriging ZTD (8.82 mm), respectively. Moreover, the absolute bias is reduced to 0.41 mm, in contrast to 5.15 mm for the ERA5 ZTD, indicating that systematic biases are effectively mitigated. Spatial and seasonal analyses further confirm that the proposed method maintains stable performance across all seasons and significantly alleviates interpolation inaccuracies caused by sparse GNSS stations, even under extreme weather conditions such as Storm Ciarán, proving its value for advanced Earth environmental science applications.