A new global grid-based weighted mean temperature model considering vertical nonlinear variation
Authors: Sun Peng , Wu Suqin , Zhang Kefei , Wan Moufeng , Wang Ren 
Published: March 2021

Abstract. 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 (Tm)
along the vertical direction in the atmosphere over the site. Thus, the
accuracy of Tm directly affects the quality of the GNSS-derived PWV.
Currently, the Tm value at a target height level is commonly modeled
using the Tm value at a specific height and a simple linear decay
function, whilst the vertical nonlinear variation in Tm is neglected.
This may result in large errors in the Tm result for the target height
level, as the variation trend in the vertical direction of Tm may not
be linear. In this research, a new global grid-based Tm 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 Tm at the grid
points, and the temporal variation in each of the four coefficients in the
Tm fitting function was also modeled 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 Tm
values in 2018 to compare with the following two references in the same year: (1) Tm from ERA5 hourly reanalysis with the horizontal resolution of
5∘ × 5∘; (2) Tm from atmospheric profiles
from 428 globally distributed radiosonde stations. Compared to the first
reference, the mean RMSEs of the model-predicted Tm values over all
global grid points at the 950 and 500 hPa pressure levels were 3.35 and
3.94 K, respectively. Compared to the second reference, the mean bias and mean
RMSE of the model-predicted Tm values over the 428 radiosonde stations
at the surface level were 0.34 and 3.89 K, respectively; the mean bias and
mean RMSE of the model's Tm values over all pressure levels in the
height range from the surface to 10 km altitude were −0.16 and 4.20 K, respectively. The new model results were also compared with that of the
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 improvement in PWV brought by GGNTm was also
evaluated. These results suggest that considering the vertical nonlinear
variation in Tm and the temporal variation in the coefficients of the
Tm model can significantly improve the accuracy of model-predicted Tm
for a GNSS receiver that is located anywhere below the tropopause
(assumed to be 10 km), which has significance for applications requiring
real-time or near real-time PWV converted from GNSS signals.