One of the most important parameters for calculating the atmospheric precipitable water vapor (PWV) is the atmospheric weighted mean temperature (Tm). Meteorological parameters that are measured typically constrain the accuracy and regional applicability of commonly used empirical models. When precipitable water is inverted using the Global Navigation Satellite System (GNSS), it results in erroneous Tm being obtained. Thus, in this paper, a small-scale Tm model for Xi’an is proposed by least squares method based on data provided by the European Centre for Mesoscale Weather Forecasts (ECMWF) from 2019 to 2022, while improving the functional model’s capacity to fit nonlinear residuals through the Random Forest method and enabling it to predict peaks more accurately. It is based on a random forest to confirm the weighted average temperature model’s correctness (RF Tm). When comparing the RF Tm model’s projected Tm accuracy to the GPT3, UNB3, and regional Bevis models, using the 2023 ERA5 data as the experimental data, the improvements are 23.6 %, 18.6 %, and 11.4 %, respectively. With the sounding station data as the reference value, the BIAS of RF Tm is only 1.51 K. In determining the atmospheric weighted average temperatures, the two models’ accuracy was comparable to that of the Long Short-Term Memory neural network model (LSTM). However, the LSTM model requires short-term forward data for practical usage, the RF Tm model compensated for the shortfall. The RF Tm model is used to invert the atmospheric precipitable water vapor at the appropriate monitoring stations using data from GNSS monitoring stations in Xi’an. It was demonstrated that the RF Tm model’s PWV inversion accuracy outperformed the PWV inverted by the GPT3 model by at least 30 %. Moreover, Xi’an rainfall data integration shows that the PWV inverted by the RF Tm model reacts to brief rainfall episodes efficiently. To sum up, this study’s RF Tm model provides a dependable and effective approach to meteorological observation and climate research.
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