An Improved Spatiotemporal Weighted Mean Temperature Model over Europe Based on the Nonlinear Least Squares Estimation Method

Weighted average temperature (Tm) plays a crucial role in global navigation satellite system (GNSS) precipitable water vapor (PWV) retrieval. Aiming at the poor applicability of the existing Tm models in Europe, in the article, we used observations from 48 radiosonde stations over Europe from 2014 to 2020 to establish a weighted average temperature model in Europe (ETm) by the nonlinear least squares estimation method. The ETm model takes into account factors such as ground temperature, water vapor pressure, latitude, and their annual variation, semiannual variation and diurnal variation. Taking the Tm obtained from the radiosonde data by the integration method in 2021 as the reference value, the accuracy of the ETm model was evaluated and compared with the commonly used Bevis model, ETmPoly model, and GPT2w model. The results of the 48 modeled stations showed that the mean bias and root mean square (RMS) values of the ETm model were 0.06 and 2.85 K, respectively, which were 21.7%, 11.5%, and 31.8% higher than the Bevis, ETmPoly, and GPT2w-1 (1° × 1° resolution) models, respectively. In addition, the radiosonde data of 12 non-modeling stations over Europe in 2021 were selected to participate in the model accuracy validation. The mean bias and RMS values of the ETm model were –0.07 and 2.87 K, respectively. Compared with the Bevis, ETmPoly, and GPT2w-1 models, the accuracy (in terms of RMS values) increased by 20.5%, 10.6%, and 35.2%, respectively. Finally, to further verify the superiority of the ETm model, the ETm model, and other Tm models were applied to the GNSS PWV calculation. The ETm model had mean RMSPWV and RMSPWV/PWV values of 0.17 mm and 1.03%, respectively, which were less than other Tm models. Therefore, the ETm model has essential applications in GNSS PWV over Europe.