Tropoformer-S: iTransformer-based spatiotemporal reconstruction of three-dimensional tropospheric delay fields integrating ERA5 reanalysis and GNSS observations

Spatially continuous three-dimensional tropospheric delay fields are essential for Earth observation and atmospheric sensing. The ERA5 reanalysis offers continuous coverage but is delayed by several days, whereas Global Navigation Satellite System (GNSS) observations are accurate and near-real-time but pointwise. This study develops Tropoformer-S, an iTransformer-based framework that reconstructs the regional delay field by integrating the two sources. The framework forecasts the ERA5-derived level-wise Zenith Tropospheric Delay (ZTD) at 15 pressure levels from 1000 to 550 hPa for 1 to 120 h, where the variate-token attention explicitly models the spatial correlation among grid points. The forecast field is converted into station ZTD through a physically guided retrieval chain and refined by GNSS-informed corrections along two complementary paths, harmonic self-correction for stations with local GNSS records and spatial reconstruction of the bias field for stations without. Over mainland China, the forecasts attain a level-mean RMSE of 2.84 cm against the ERA5-derived ZTD and outperform five alternative deep-learning architectures. The overall RMSE is 3.20 cm in 2022 and 3.23 cm in 2023 against GNSS, on average 18.64 % and 33.10 % below GPT3 and HGPT2, and the radiosonde evaluation shows a near-zero bias. The harmonic correction path lowers the RMSE to 2.79 and 2.98 cm and reduces the network bias to near zero, while the spatial correction path reaches 2.10 to 2.66 cm at withheld stations under nine network densities and largely removes the lead dependence. The framework thus fills the ERA5 latency gap with continuous tropospheric delay information for geodetic and atmospheric applications.