Atmospheric Weighted Average Temperature Enhancement Model for the European Region Considering Daily Variations and Residual Changes in Surface Temperature

The retrieval of precipitable water vapor (PWV) through Global Navigation Satellite System (GNSS) meteorology critically depends on the precise determination of atmospheric weighted mean temperature (Tm). Existing empirical models for Tm retrieval over Europe offer speed but suffer accuracy limitations due to complex local environmental and climatic factors. Aiming to improve Tm model accuracy in Europe, this study constructed the European Tm Enhanced Model (EurTm). The model was constructed based on 2014–2023 radiosonde data from 40 stations across Europe, with its parameters optimized through least squares estimation. The EurTm model integrates multiple factors, including Tm from Hourly Global Pressure and Temperature 2 (HGPT2), the difference between Ts obtained by HGPT2 and Ts measured by radiosonde stations, and diurnal variation. The EurTm model’s accuracy was validated by comparing its outputs with reference values derived from 2024 radiosonde data. The EurTm model underwent comparative analysis against the widely used Bevis, ETmPoly, and HGPT2 models. The EurTm model’s accuracy was 13.2%, 4.1%, and 32.7% higher than the Bevis, ETmPoly, and HGPT2 models at 40 modeling stations. At 13 non-modeling stations, the EurTm model outperformed the Bevis, ETmPoly, and HGPT2 models with accuracy enhancements of 16.1%, 4.7%, and 30.0%, respectively. Theoretical evaluation showed that the EurTm model achieved an RMSE of 0.20 mm and a relative error of 1.11% for GNSS-derived PWV, outperforming all comparative models. In conclusion, the EurTm model not only holds significant application value for GNSS PWV retrieval in Europe but also provides a novel approach for region-specific enhancements of global empirical Tm models by addressing characteristic regional features such as diurnal variations.