Development of a refined nonlinear Tm estimation model using power function for improved atmospheric water vapor inversion

To address the low calculation accuracy of the current one-dimensional linear model between Weighted Average Temperature (<i>T</i>_m) and Surface Temperature (<i>T</i>_s) in certain regions, this study proposes an improved <i>T</i>_m modeling method tailored to the Qinghai region. The aim is to enhance the calculation accuracy of both Tm and the retrieved Precipitable Water Vapor (PWV).Using five years of data (2019–2023) from four radiosonde stations in the Qinghai region, four types of nonlinear functions — power function, exponential function, quadratic polynomial, and first-order Fourier series — are employed to construct region-specific <i>T</i>_m–<i>T</i>_s nonlinear models. The models are then validated for out-of-sample temporal accuracy using 2024 data from the same four radiosonde stations. To further evaluate the reliability of different Tm models in practical GNSS-based water vapor retrieval, the PWV values calculated at GNSS stations using the models are interpolated to the locations of radiosonde stations using the inverse distance weighting (IDW) method, taking into account the spatial differences between GNSS and radiosonde stations. Accuracy validation of model-inverted PWVs by comparing interpolated and observed values from radiohsonde stations. Experimental results show that the power function model yields lower Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) for <i>T</i>_m estimation compared to the other three nonlinear models. Compared with the traditional Bevis model, the national model by Gong Shaoqi, and the localized linear model, the MAE of the power function model is reduced by 5%, 13%, and 2%, respectively; the RMSE is reduced by 2%, 12%, and 2%, respectively. In terms of PWV retrieval, the power function model also achieves lower MAE and RMSE values than the other models across the four regions of Golmud, Dulan, Xining, and Yushu. Specifically, compared with the linear model, the power function model reduces the MAE of PWV by 4%, 4%, 6%, and 3% in the respective regions, and reduces the RMSE by 5%, 4%, 6%, and 4% in the same areas. Therefore, the power function model established in this study effectively improves the inversion accuracies of Tm and PWV, and provides a valuable reference for GNSS-based water vapor inversion studies in Qinghai.