1. Introduction
Sufficient atmospheric water vapor is one of the necessary conditions for precipitation formation, and water vapor detection plays an important role in weather forecasting, disaster monitoring and global climate change monitoring [
1]. GNSS precipitable water vapor (GNSS-PWV) can be used to reflect the atmospheric water vapor variations in GNSS meteorology. It has the potential to forecast severe weather phenomena [
2,
3,
4] and examine the effects of climate change [
5,
6]. Previous studies [
3,
7,
8,
9,
10] have shown that there will be severe rainstorms in the downward trend process after GNSS-PWV reaches its peak value. Benevides et al. [
11] proposed that the accuracy of weather forecasting could be improved after analyzing 3D distribution variations of PWV [
12,
13,
14,
15,
16].
The inversion process of GNSS-PWV requires the zenith wet delay (ZWD) and the water vapor conversion coefficient (
). ZWD can be obtained by subtracting the zenith hydrostatic delay (ZHD) from the zenith total delay (ZTD) [
17]. ZHD is the main delay for the GNSS signals transmitted in the neutral atmosphere, accounting for more than 90% of ZTD. It means that the precision of ZHD will indirectly affect the precision of ZWD. The weighted mean temperature (
) is one of the important parameters to calculate
for the conversion of ZWD to PWV [
18]. The ZHD and
play a crucial role in obtaining high-precision real-time GNSS-PWV [
19,
20].
Currently, the commonly used ZHD models can be divided into two categories. One is the empirical models based on the measured meteorological parameters, including the Saastamonien [
21], Hopfield [
22], and Black [
23] models. For example, the Saastamonien model uses meteorological sensors to measure surface pressure and can calculate the ZHD at a millimeter level. However, it is difficult to obtain the measured meteorological parameters in real time at any place in the world, which limits the application of tropospheric delay models that need measured meteorological parameters with respect to GNSS meteorology. In this case, the use of atmospheric data to establish regional or global real-time tropospheric delay models has been widely concerned, such as UNB3m [
24], EGNOS [
1] and GPT [
25,
26,
27,
28]. ERA-Interim [
29] and ERA5 [
30] are also used to interpolate surface meteorological parameters at the GNSS stations. At the same time, a series of studies have achieved fruitful results in this research area. Ghaffari Razin and Voosoghi [
31] use Bernese GNSS software and Saastamoinen model to calculate the ZTD and ZHD, then the ZWD obtained by subtracting the ZHD from the ZTD is modeled by two different machine learning methods, which can obtain PWV with high accuracy. A site-specific ZHD model was established by collecting an atmospheric vertical profile from radiosondes stations. It provides an error about 0.19 mm, which can be used to accurately estimate PWV [
32]. Yang, et al. [
33] analyzed the global performance of the three most commonly used ZHD models, the best temperature and pressure models were established by evaluating the influence of different modeling factors and the meteorological parameters estimated by the above-mentioned models. Based on the ERA5 reanalysis data of the European Centre for Medium-Range Weather Forecasts (ECMWF), Mateus, et al. [
34] developed a one-hour global air pressure and temperature model (HGPT) to provide pressure, temperature, ZHD, and
. Climate studies, GNSS meteorology and other atmospheric research can significantly benefit from it.
The
is a necessary parameter to calculate the K value and plays a key role in atmospheric water vapor conversion. Among various
calculation methods, the accuracy of radiosonde-derived
is the highest, but it is difficult to popularize due to the spatiotemporal limitation of radiosondes [
35,
36,
37]. Therefore, Bevis used the ground surface temperature (
) from the profiles of vapor partial pressure and dewpoint temperature of North American radiosondes over a two-year period to establish a global mean temperature model in 1992 (
= 0.72
0.2) [
38]. However, due to the influence of location, time, and other factors, the regional accuracy of Bevis model is inconsistent. In general, the systematic deviation is greater than 4.0 K, and even greater than 8.0 K in some areas [
39,
40]. When encountering bad weather, it may even lead to a significant deviation of GNSS-PWV [
41,
42]. Considering the linear relationship between
and
, many scholars have established different regional
models (RTM) based on local radiosondes [
40,
42,
43,
44]. The RTM established in Hong Kong can control the deviation within 4.0 K, which is superior to the Bevis model [
45]. Singh, et al. [
46] have found that the site specific
model is better than the developed regional
model and global model at New Delhi and Patiala. Elhaty, et al. [
47] use radiosonde profiles from four stations situated in Egypt during 2015–2016 and Bevis linear regression method to develop a new
model. Several RTMs using one factor (
) have been established in China [
45,
48,
49,
50]. Li and Mao [
48] deeply studied the monthly coefficient of RTM in eastern China. Guo, et al. [
51] established a good annual single factor RTM model based on sounding data in the Yangtze River Delta region. Based on the above research, the researchers established many multi-factor RTM models [
52,
53,
54]. Considering the influence of pressure (
) and water vapor pressure (
) on
, Gong [
52] analyzed the relationship between meteorological elements using the data of 123 radiosonde stations in China, and established multi-factor models in different climatic regions, effectively improving the accuracy of single factor models. However, the models established by Wang, Song, Dai, and Cao [
53] show that there is little difference in accuracy between the single factor model and the multi-factor model in Hong Kong. According to the above linear regression models, the precision of non-linear RTM between
and
proposed and established by Yao, et al. [
55], which is slightly better than that of linear RTM. Zhu, et al. [
56] established a non-linear
model for China with elevation corrections, which provides a significant correction effect for
in the vertical direction. Lan, Zhang, and Geng [
39] adopt the sliding average method to calculate the correlation coefficient between
of the ECMWF and
from the “GGOS Atmosphere”. Compared to the
-
relation of Bevis model, the
Grid model shows higher precision. Most researchers will analyze its precision comparing the PWV calculated by different ZHD and
models [
57,
58].
As mentioned above, when GNSS stations lack meteorological instruments, GPT series models are usually used to obtain real-time meteorological parameters. Boehm, Heinkelmann and Schuh [
25] first proposed GPT in 2007, which can provide the pressure and temperature at any geographical location on the earth surface. Lagler, Schindelegger, Böhm, Krásná, and Nilsson [
28] developed the GPT2 by combining the GPT with global mapping function (GMF), which can provide more meteorological parameters. Böhm, Möller, Schindelegger, Pain and Weber [
26] introduced the vertical gradient of water vapor pressure and
to establish GPT2w on the basis of GPT2 in 2015. The GPT3 model is the latest version of the GPT series models, it can provide not only parameters from GPT2w, but also empirical gradient grids and is one of the most accurate and widely used tropospheric delay models [
27]. Many studies have shown that the GPT3 model can provide high-precision ZTD and horizontal gradient information on a global scale, however, due to the limitation of terrain and other conditions, the GPT3 model based on European Centre for Medium-Range Weather Forecasts (ECMWF) data cannot be perfectly applied to any area [
59,
60,
61]. Therefore, in a specific time and area, the precision of GPT3 model may not meet the requirements of some high-precision GNSS-PWV applications
Based on the GNSS products and radiosondes data in the Yangtze River Delta region during the 2016–2020 period, this paper analyzed the seasonal variations of the
and ZHD of GPT3 model in the
Section 2, and then the Fourier function was used to establish the improved ZHD and
models in the
Section 3. Meanwhile, the precisions of these improved ZHD and
models were verified by comparing them with the GNSS and radiosondes products in the
Section 3. The
Section 4 is the conclusion.
4. Conclusions
The precision of the GPT3 model (ZHD, and PWV) in the Yangtze River Delta region was first analyzed with reference to GNSS and radiosondes products. Aiming at the problem that the ZHD and from GPT3 model have obvious seasonal periodic deviations, the third-order Fourier function was used to establish improved ZHD and models, and their precision were analyzed and verified. The main research conclusions are as follows.
The mean biases of the GPT3-ZHD, and PWV are −0.5 mm, −0.8 K, and 2.7 mm, respectively, and the mean RMS of those are 2.1 mm, 3.2 K, and 11.1 mm, respectively. Compared to the reference values of the GNSS products and radiosondes, the ZHD and PWV deviations have obvious seasonal variations. Specifically, the deviation of ZHD is negative in spring and winter, but positive in summer and autumn, and the deviation of PWV is smaller in spring and winter, but larger in summer and autumn.
Compare with the GPT3 model, the mean Bias and RMS of the improved-ZHD based on Fourier function from 2019 to 2020 are −0.1 mm and 0.5 mm, respectively, improved by 0.7 mm and 1.6 mm, while the mean Bias and RMS of the improved- in 2019 are −0.6 K and 2.7 K, respectively, which are 0.8 K and 0.5 K better than GPT3-. The precision of two models is improved slightly.
The mean Bias and RMS of the improved-PWV based on GNSS-ZTD and the improved ZHD and models are 0.5 mm and 0.6 mm, respectively, which are 2.2 mm and 10.5 mm better than that of GPT3-PWV, and the overall precision is improved greatly. Compared to the radiosonde-derived PWV, the mean Bias and RMS are −1.1 mm and 3.7 mm, respectively, which are 0.5 mm and 0.3 mm higher than that of the GNSS-PWV, and the precision of the two methods performs similarly. Therefore, the improved ZHD and models based on GPT3 and Fourier function established in the Yangtze River Delta region can be used for real-time high-precision PWV inversion.