^{1}

^{1}

^{2}

^{1}

^{2}

^{1}

^{1}

<p>Global Navigation Satellite Systems (GNSS) have been proved to be an excellent technology for retrieving precipitable water vapor (PWV). In GNSS meteorology, PWV at a station is obtained from a conversion of the zenith wet delay (ZWD) of GNSS signals received at the station using a conversion factor which is a function of weighted mean temperature (<i>T</i><sub><i>m</i></sub>) along the vertical direction in the atmosphere over the site. Thus, the accuracy of <i>T</i><sub><i>m</i></sub> directly affects the quality of the GNSS-derived PWV. Currently, the <i>T</i><sub><i>m</i></sub> value at a target height level is commonly modelled using the <i>T</i><sub><i>m</i></sub> value at a specific height and a simple linear decay function, whilst the vertical nonlinear variation in <i>T</i><sub><i>m</i></sub> is neglected. This may result in large errors in the <i>T</i><sub><i>m</i></sub> result for the target height level, as the variation trend in the vertical direction of <i>T</i><sub><i>m</i></sub> may not be linear. In this research, a new global grid-based <i>T</i><sub><i>m</i></sub> empirical model with a horizontal resolution of 1°×1°, named GGNTm, was constructed using ECMWF ERA5 monthly mean reanalysis data over the 10-year period from 2008 to 2017. A three-order polynomial function was utilized to fit the vertical nonlinear variation in <i>T</i><sub><i>m</i></sub> at the grid points, and the temporal variation in each of the four coefficients in the <i>T</i><sub><i>m</i></sub> fitting function was also modelled with the variables of the mean, annual and semi-annual amplitudes of the 10-year time series coefficients. The performance of the new model was evaluated using its predicted <i>T</i><sub><i>m</i></sub> values in 2018 to compare with the following two references in the same year 1) <i>T</i><sub><i>m</i></sub> from ERA5 hourly reanalysis with the horizontal resolution of 5°×5°; 2) <i>T</i><sub><i>m</i></sub> from atmospheric profiles from 428 globally distributed radiosonde stations. Compared to the first reference, the mean RMSEs of the model predicted <i>T</i><sub><i>m</i></sub> values over all global grid points at the 950 hPa and 500 hPa pressure levels were 3.35 K and 3.94 K respectively. Compared to the second reference, the mean bias and mean RMSE of the model predicted <i>T</i><sub><i>m</i></sub> values over the 428 radiosonde stations at the surface level were 0.34 K and 3.89 K respectively; the mean bias and mean RMSE of the model’s <i>T</i><sub><i>m</i></sub> values at all pressure levels in the height range from the surface to 10 km altitude were −0.16 K and 4.20 K respectively. The new model results were also compared with that of the GPT3, GTrop and GWMT_D models in which different height correction methods were also applied. Results indicated that significant improvements made by the new model were at high-altitude pressure levels; in all five height ranges, GGNTm results were generally unbiased, and their accuracy varied little with height. The impact of <i>T</i><sub><i>m</i></sub> on GNSS-PWV was evaluated in terms of relative error, and significant improvement was found compared to the widely used GPT3 model. These results suggest that considering the vertical nonlinear variation in <i>T</i><sub><i>m</i></sub> and the temporal variation in the coefficients of the <i>T</i><sub><i>m</i></sub> model can significantly improve the accuracy of model-predicted <i>T</i><sub><i>m</i></sub> for a GNSS receiver that is located in anywhere below the tropopause (assumed to be 10 km), which has significance for applications needing real-time or near real-time PWV converted from GNSS signals.</p>