High-Precision GNSS PWV and Its Variation Characteristics in China Based on Individual Station Meteorological Data

The Global Navigation Satellite System (GNSS) plays an important role in retrieving high temporal–spatial resolution precipitable water vapor (PWV) and its applications. The weighted mean temperature (Tm) is a key parameter for the GNSS PWV estimation, which acts as the conversion factor from the zenith wet delay (ZWD) to the PWV. The Tm is determined by the air pressure and water vapor pressure, while it is not available nearby most GNSS stations. The empirical formular is often applied for the GNSS station surface temperature (Ts) but has a lower accuracy. In this paper, the temporal and spatial distribution characteristics of the coefficients of the linear Tm-Ts model are analyzed, and then a piecewise-linear Tm-Ts relationship is established for each GPS station using radiosonde data collected from 2011 to 2019. The Tm accuracy was increased by more than 10% and 20% for 86 and 52 radiosonde stations, respectively. The PWV time series at 377 GNSS stations from the infrastructure construction of national geodetic datum modernization and Crustal Movement Observation Network of China (CMONC) were further obtained from the GPS observations and meteorological data from 2011 to 2019. The PWV accuracy was improved when compared with the Bevis model. Furthermore, the daily and monthly average values, long-term trend, and its change characteristics of the PWV were analyzed using the high-precision inversion model. The results showed that the averaged PWV was higher in Central-Eastern China and Southern China and lower in Northwest China, Northeast China, and North China. The PWV is increasing in most parts of China, while the some PWVs in North China show a downward trend.


Introduction
Water vapor is an important part of the Earth's hydrosphere and plays a key role in the energy exchange and water cycle in nature. The atmospheric water vapor content is limited by local temperature and pressure and is closely related to the formation of various precipitation, such as clouds, rain, and snow [1]. Accurate measurements of water vapor and its distribution changes have become one of the basic problems in synoptics, weather forecasting, and climate research [2][3][4][5]. One of the indicators to measure the amount of atmospheric water vapor is the precipitable water vapor (PWV), which represents a certain height of the water column produced by the condensation of all tropospheric atmospheric water vapor in the column per unit bottom area at any time into liquid water. Since the demand for real-time and accurate weather services is becoming more and more urgent, the traditional detection technologies such as radiosondes, water vapor radiometers, and

Observation Data
The infrastructure construction of national geodetic datum modernization in China was launched in 2012 and completed in 2017, which contained 210 GPS stations. A highprecision, dynamic, and unified modern surveying and mapping datum system was established to provide coordinate frame services, including data products, real-time positioning, processing and analysis, and other services [28]. Crustal Movement Observation Network of China (CMONC) was established in 2006 and completed in 2012, which contained 360 GPS stations [29,30]. The National Geomatics Center of China (NGCC) provided the hourly ZTD data and 1-h measured temperature and atmospheric pressure data at these GPS stations from 2011 to 2019. We used BERNESE 5.2 software [31] to process the raw data, including the implementation of daily solutions and adjustments [32]. The Integrated Global Radiosonde Archive (IGRA) has released radiosonde and pilot balloon observations with more than 2700 stations around the world since 1905, including air pressure, temperature, geopotential height, and relative humidity (ftp://ftp.ncdc.noaa. gov/pub/data/igra, accessed on 24 January 2021), whose temporal resolution is 12 h. We used IGRA-released radiosonde profiles in China from 2011 to 2019 to calculate the T m at each radiosonde station. Figure 1 shows all the used GPS stations and radiosonde stations.
Remote Sens. 2021, 13, x FOR PEER REVIEW 3 of 15 at these GPS stations from 2011 to 2019. We used BERNESE 5.2 software [31] to process the raw data, including the implementation of daily solutions and adjustments [32]. The Integrated Global Radiosonde Archive (IGRA) has released radiosonde and pilot balloon observations with more than 2700 stations around the world since 1905, including air pressure, temperature, geopotential height, and relative humidity (ftp://ftp.ncdc.noaa.gov/pub/data/igra, accessed on 24 January 2021), whose temporal resolution is 12 h. We used IGRA-released radiosonde profiles in China from 2011 to 2019 to calculate the Tm at each radiosonde station. Figure 1 shows all the used GPS stations and radiosonde stations.

Establishment of Site-Specific Piecewise-Linear Tm-Ts Relationship
Tm is related to the temperature and vapor pressure at different altitudes in the atmosphere, which can be obtained from the IGRA. The method to calculating the 12-h Tm can be expressed as [13]: where e (hPa) refers to the water vapor pressure, T (K) is the corresponding temperature, and Z (m) denotes the starting height of integration. ∆ (m) denotes the altitude of the ith atmospheric layer, denotes the number of the atmospheric layer, (hPa) denotes the water vapor pressure of ith atmospheric layer, and (K) denotes the temperature of ith atmospheric layer. We converted the geopotential height into the geoid height in the calculation process.
The empirical formula based on the long-term radiosonde data in the study area and the linear relationship between surface temperature Ts and Tm can be established by a regression analysis as: where and are the linear regression equation parameters.
The Tm variation has a significant annual variation. In some studies, the half-year variations and the daily variations are also considered when building the model. In order The green circle is the radiosonde station, and the red triangle is the GPS station.

Establishment of Site-Specific Piecewise-Linear T m -T s Relationship
T m is related to the temperature and vapor pressure at different altitudes in the atmosphere, which can be obtained from the IGRA. The method to calculating the 12-h T m can be expressed as [13]: where e (hPa) refers to the water vapor pressure, T (K) is the corresponding temperature, and Z (m) denotes the starting height of integration. ∆z i (m) denotes the altitude of the ith atmospheric layer, N denotes the number of the atmospheric layer, e i (hPa) denotes the water vapor pressure of ith atmospheric layer, and T i (K) denotes the temperature of ith atmospheric layer. We converted the geopotential height into the geoid height in the calculation process. The empirical formula based on the long-term radiosonde data in the study area and the linear relationship between surface temperature T s and T m can be established by a regression analysis as: where a and b are the linear regression equation parameters. The T m variation has a significant annual variation. In some studies, the half-year variations and the daily variations are also considered when building the model. In order to get the time-varying characteristics of the T m -T s coefficient, a piecewise-linear least squares fitting is performed for each radiosonde station for one month.

PWV from Site-Specific Piecewise-Linear T m -T s Relationship
Three hundred and seventy-seven GPS stations were selected for estimating the PWV time series. Since the cubic spline method has a higher accuracy than the nearest-neighbor interpolation method and linear interpolation method, we used the cubic spline method to obtain the T m -T s model coefficients a and b at the GPS stations in the corresponding time period.
ZTD is the sum of Zenith Hydrostatic Delay (ZHD) and Zenith Wet Delay (ZWD), as The Saastamoinent model has been widely used for ZHD computation [33], as where P (hPa) denotes the ground pressure of the GPS station, φ denotes the latitude of the GPS station, and h 0 (m) denotes the elevation of the GPS station. The ZWD is caused by water vapor in the atmosphere under nonstatic equilibrium. Generally, empirical models and meteorological parameters at GPS station are used to obtain the ZHD, and then, the ZHD is deducted from the ZTD to obtain the ZWD.
The linear relationship between the ZWD and PWV can be expressed as [13] PWV = Π·ZWD (6) where Π is the conversion factors between the ZWD and PWV; Π is a function of T m ; ρ w represents the density of the liquid water; R is the universal gas constant and R = 8314 Pa·m 3 ·K −1 ·kmol −1 ; m w represents the molar mass of water vapor and m w = 18.02 kg·kmol −1 ; m d represents the molar mass of the dry atmosphere and m d = 28.96 kg·kmol −1 ; and k 1 , k 2 , and k 3 are constants (k 1 = 77.604 ± 0.014 K/hPa, k 2 = 70. 4 K/hPa, and k 3 = (3.776 ± 0.014) × 10 5 K 2 /hPa) [13]. In general, approximately 6.7 mm of ZTD error will cause a PWV error of 1 mm. Hence, the ZTD with a Root Mean Square Error (RMSE) of greater than 6.7 mm are eliminated. In addition, ZTD data and meteorological parameters are missing at some stations in a few time periods. For sites with missing data for more than one year, they will not be used when analyzing the long-term changes. Then, Equations (3)-(6) were used for high-precision PWV estimations based on the site-specific piecewise-linear T m -T s relationship in China. Finally, the PWV time series derived from 377 GPS stations in China from 2011 to 2019 were obtained.

PWV from Radiosonde
The PWV at the radiosonde station is calculated as follows: where p (hPa) denotes the atmospheric pressure, p 0 (hPa) is the ground pressure at the GPS station, q (g·kg −1 ) denotes the specific humidity, g (m·s −2 ) is the acceleration of gravity, and ρ w (g·cm −3 ) refers to the density of the liquid water. By discretizing Equation (8), the integral equation of PWV from the ground to the top of the atmosphere is obtained as follows:

Fitting Function of the PWV Time Series
Jin and Luo [34] analyzed the PWV series derived from 155 globally distributed GPS sites observations and found that most of the periods of the PWV series were 1 year, 0.5 years, 1 day, and 0.5 days. To fit the PWV time series of 377 GPS stations in China, we established the following equation: where k 0 is a constant term; k 1 , k 2 , k 3 , k 4 , c 1 , c 2 , c 3 , and c 4 are the amplitude and phase at the period (1 year, 0.5 years, 1 day, and 0.5 days); DOY is the day of year; HOD is the hour of day; and ε is the residual. The least square method was used to determine the unknown parameters in Equation (10) with the PWV time series. the integral equation of PWV from the ground to the top of the atmosphere is obtained as follows:

Fitting Function of the PWV Time Series
Jin and Luo [34] analyzed the PWV series derived from 155 globally distributed GPS sites observations and found that most of the periods of the PWV series were 1 year, 0.5 years, 1 day, and 0.5 days. To fit the PWV time series of 377 GPS stations in China, we established the following equation: where is a constant term; , , , , , , , and are the amplitude and phase at the period (1 year, 0.5 years, 1 day, and 0.5 days); DOY is the day of year; HOD is the hour of day; and is the residual. The least square method was used to determine the unknown parameters in Equation (10) with the PWV time series.   Figure 3 shows the distribution diagram of the slope coefficient with the elevation, latitude, and longitude. No evident correlation is found with the elevation and longitude, whereas there is strong positive correlation with the latitude, especially in low-latitude areas. Some studies have shown that when the same Tm-Ts coefficient is used at a global scale, it will cause different errors in the Tm of different latitudes [35,36]. Wang et al. found that the Tm derived from the Bevis Tm-Ts relationship has a cold bias in the tropics and subtropics and a warm bias in middle and high latitudes, and furthermore, the RMS was  Figure 3 shows the distribution diagram of the slope coefficient with the elevation, latitude, and longitude. No evident correlation is found with the elevation and longitude, whereas there is strong positive correlation with the latitude, especially in low-latitude areas. Some studies have shown that when the same T m -T s coefficient is used at a global scale, it will cause different errors in the T m of different latitudes [35,36]. Wang et al. found that the T m derived from the Bevis T m -T s relationship has a cold bias in the tropics and subtropics and a warm bias in middle and high latitudes, and furthermore, the RMS was dominated by the mean bias rather than the random error. Therefore, the distribution of the T m -T s coefficients is mostly related to the latitude. The slope coefficient a is generally less than 0.6 in low-latitude areas, which is consistent with the previous results of some global T m -T s models.

Spatial Distribution and Time-Varying Characteristics of the Tm-Ts Coefficient
Remote Sens. 2021, 13, x FOR PEER REVIEW 6 of 15 dominated by the mean bias rather than the random error. Therefore, the distribution of the Tm-Ts coefficients is mostly related to the latitude. The slope coefficient is generally less than 0.6 in low-latitude areas, which is consistent with the previous results of some global Tm-Ts models. The monthly coefficients of the Tm-Ts model are obtained. The slope coefficients have obvious annual cycle at most stations. The time series of slope coefficients at four radiosonde stations are randomly selected and shown in Figure 4. The information of the four stations is shown in Table 1. The slope coefficients of the Tm-Ts model vary greatly with the time, from about 0.5-1. The regression slope and its changing tendency are smaller at the SIMAO station, which is due to the lower latitude.   The monthly coefficients of the T m -T s model are obtained. The slope coefficients have obvious annual cycle at most stations. The time series of slope coefficients at four radiosonde stations are randomly selected and shown in Figure 4. The information of the four stations is shown in Table 1. The slope coefficients of the T m -T s model vary greatly with the time, from about 0.5-1. The regression slope and its changing tendency are smaller at the SIMAO station, which is due to the lower latitude.
global Tm-Ts models. The monthly coefficients of the Tm-Ts model are obtained. The slope coefficients have obvious annual cycle at most stations. The time series of slope coefficients at four radiosonde stations are randomly selected and shown in Figure 4. The information of the four stations is shown in Table 1. The slope coefficients of the Tm-Ts model vary greatly with the time, from about 0.5-1. The regression slope and its changing tendency are smaller at the SIMAO station, which is due to the lower latitude.

Comparison with Bevis T m -T s Relationship
We calculated the root mean square error (RMSE) (in unit of K) and accuracy improvement (%) of T m for 94 radiosonde station, which are shown in Figure 5. Compared with the Bevis model, the site-specific piecewise-linear model has a significant improvement in the regression accuracy at most stations due to the consideration of the temporal and spatial distributions of the T m -T s conversion coefficient. According to the statistics, the T m accuracy with 86 radiosonde stations is increased by more than 10% and by more than 20% with 52 radiosonde stations, and the lowest is increased by 6% (station 58457, 30

Comparison with Bevis Tm-Ts Relationship
We calculated the root mean square error (RMSE) (in unit of K) and accuracy improvement (%) of Tm for 94 radiosonde station, which are shown in Figure 5. Compared with the Bevis model, the site-specific piecewise-linear model has a significant improvement in the regression accuracy at most stations due to the consideration of the temporal and spatial distributions of the Tm-Ts conversion coefficient. According to the statistics, the Tm accuracy with 86 radiosonde stations is increased by more than 10% and by more than 20% with 52 radiosonde stations, and the lowest is increased by 6% (station 58457, 30.23° N, 120.17° E), and the highest is increased by 69% (station 56691, 26.87° N, 104.28° E).    Figure 6 shows the RMSE distribution of the Bevis model and the site-specific piecewiselinear model. As we can see, compared with the Bevis model, the single-station piecewiselinear model has a greater accuracy improvement in the southern, southwest, and northeastern regions by more than 30%. The increase in the central and northwestern regions is relatively small and approximately 15%.

Comparison with GPS-Derived PWV and Radiosonde PWV
The selected GPS stations are closer to the radiosonde, in which the horizontal distance is less than 10 km and the elevation difference is less than 100 m. The water vapor obtained by the integral of the radiosonde profile data was used to evaluate the ground-

Comparison with GPS-Derived PWV and Radiosonde PWV
The selected GPS stations are closer to the radiosonde, in which the horizontal distance is less than 10 km and the elevation difference is less than 100 m. The water vapor obtained by the integral of the radiosonde profile data was used to evaluate the ground-based GPS PWV based on the Bevis model and the site-specific piecewise-linear T m -T s model. We calculated the deviation bias (in unit of mm) and relative errors. For example, Figure 7 shows the results at GXHC station in 2018. The accuracy of the PWV is better based on the site-specific piecewise-linear T m -T s relationship when compared to the Bevis's model.

Comparison with GPS-Derived PWV and Radiosonde PWV
The selected GPS stations are closer to the radiosonde, in which the horizontal distance is less than 10 km and the elevation difference is less than 100 m. The water vapor obtained by the integral of the radiosonde profile data was used to evaluate the groundbased GPS PWV based on the Bevis model and the site-specific piecewise-linear Tm-Ts model. We calculated the deviation bias (in unit of mm) and relative errors. For example, Figure 7 shows the results at GXHC station in 2018. The accuracy of the PWV is better based on the site-specific piecewise-linear Tm-Ts relationship when compared to the Bevis's model. The distribution of water vapor in the atmosphere is not uniform. Thus, the groundbased GPS water vapor can get the average distribution of water vapor in each satellite signal direction. In addition, the layered meteorological parameter data of the radiosonde is not strictly vertical. These factors will bring errors into the PWV results. However, it still can be seen that the accuracy of the PWV is significantly improved based on site- The distribution of water vapor in the atmosphere is not uniform. Thus, the groundbased GPS water vapor can get the average distribution of water vapor in each satellite signal direction. In addition, the layered meteorological parameter data of the radiosonde is not strictly vertical. These factors will bring errors into the PWV results. However, it still can be seen that the accuracy of the PWV is significantly improved based on site-specific piecewise-linear T m -T s relationship, especially when there are more atmospheric water vapors in the summer.

Spatial Distribution of PWV in China
The annual averaged PWV at all GPS stations from 2011 to 2019 in China range from 0 to 48 mm. As shown in Figure 8, the annual averaged PWV in Central-Eastern China and Southern China are relatively high, reaching above 25 mm, while the annual averaged PWV in Northwest, Northeast, and Northern China regions are lower, below 15 mm. Southeast China has a low latitude and is close to the East China Sea and the South China Sea, which are subject to subtropical monsoons. Monsoons transport water vapor from the sea to these areas, resulting in the higher annual averaged PWV [37]. Northwest China has a relatively high latitude and is an inland region with a temperate continental climate, so the annual averaged PWV is lower.
The  Figure 9 shows the nine-year daily averaged PWV of these four regions. The variation characteristics of the PWV in each region are consistent throughout the year, with the peaks in June and July and the droughts in January and December. Among them, the peak in Southern China appeared the earliest, which was affected by the south-to-north monsoon. Atmospheric circulation transported the water vapor to the Yangtze River Basin and then continued to transport it to other regions [38].

Spatial Distribution of PWV in China
The annual averaged PWV at all GPS stations from 2011 to 2019 in China range from 0 to 48 mm. As shown in Figure 8, the annual averaged PWV in Central-Eastern China and Southern China are relatively high, reaching above 25 mm, while the annual averaged PWV in Northwest, Northeast, and Northern China regions are lower, below 15 mm. Southeast China has a low latitude and is close to the East China Sea and the South China Sea, which are subject to subtropical monsoons. Monsoons transport water vapor from the sea to these areas, resulting in the higher annual averaged PWV [37]. Northwest China has a relatively high latitude and is an inland region with a temperate continental climate, so the annual averaged PWV is lower.  Figure 9 shows the nine-year daily averaged PWV of these four regions. The variation characteristics of the PWV in each region are consistent throughout the year, with the peaks in June and July and the droughts in January and December. Among them, the peak in Southern China appeared the earliest, which was affected by the south-to-north monsoon. Atmospheric circulation transported the water vapor to the Yangtze River Basin and then continued to transport it to other regions [38].     China   Figures 10 and 11 show the annual and semiannual PWV variation amplitudes at 377 GPS sites. The spatial distribution of the annual PWV variations is similar to the annual average distribution of the PWV. Central China, Southern China, and the southeast coastal areas have higher annual PWV variation amplitudes, reaching about 15 mm, while the annual cycle amplitude in Northwest China is lower, below 10 mm. The semiannual PWV variation amplitudes are relatively small, about 3-9 mm. Among them, the semiannual PWV variation amplitudes are the highest in Central China and Southwest China, reaching above 6 mm, while the semiannual PWV variation amplitudes in Southern China and Northwestern China are lower, below 5 mm.   Figure 12 shows the long-term variation trends of the PWV (mm/year) of all GPS stations from 2011 to 2019. It can be seen that the PWV has been increasing in most parts of China, while the PWV in Northeast China shows a downward trend. To understand the variations of the PWV in more detail, a monthly anomaly of the PWV is obtained by subtracting the monthly averaged PWV of every month from the mean value of the monthly averaged nine-year PWV in each region, which can be seen in Figure 13. The monthly anomaly of the PWV was mainly negative before 2015 and then turned negative. The PWV in Northwest China, Northeast China, and Northern China were relatively stable, and the monthly mean value changed little, which was related to the dry inland climate.

Discussion
Most of the published Tm models that considered the temporal and spatial distributions of the relationship between the Tm and meteorological measurements have been empirical models on a global scale. Their accuracy remains to be verified in a specific area and a period of time. Here, we estimated the monthly coefficients at each station, and  Figure 12 shows the long-term variation trends of the PWV (mm/year) of all GPS stations from 2011 to 2019. It can be seen that the PWV has been increasing in most parts of China, while the PWV in Northeast China shows a downward trend. To understand the variations of the PWV in more detail, a monthly anomaly of the PWV is obtained by subtracting the monthly averaged PWV of every month from the mean value of the monthly averaged nine-year PWV in each region, which can be seen in Figure 13. The monthly anomaly of the PWV was mainly negative before 2015 and then turned negative. The PWV in Northwest China, Northeast China, and Northern China were relatively stable, and the monthly mean value changed little, which was related to the dry inland climate. and some PWV in North China is downward from 2011 to 2019. The monthly averaged PWV increased significantly in 2015, which was affected by the El Niño.

Conclusions
In this study, we analyzed the temporal and spatial distribution characteristics of the coefficients of the linear Tm-Ts model and showed that the distribution of Tm-Ts coefficients is mainly related to the latitude. The Tm-Ts conversion coefficient changes with the time Figure 13. Monthly anomaly (mm) of the PWV in four regions of China.

Discussion
Most of the published T m models that considered the temporal and spatial distributions of the relationship between the T m and meteorological measurements have been empirical models on a global scale. Their accuracy remains to be verified in a specific area and a period of time. Here, we estimated the monthly coefficients at each station, and Table 2 shows the comparison between the piecewise-linear model and two recently published representative models: the time-varying global-gridded T s -T m model (TVGG) and neural network-based T m model (NN). We tested our model with radiosonde data from 2011 to 2019, and the results showed that our model has the best accuracy. The spatial distribution characteristics of the PWV are consistent with other studies in different years [39,40]. There are bimodal characteristics of the PWV in Southern China, and the formation mechanism of the bimodal characteristics remains to be further studied. The past results of some studies in China indicated that the PWV showed a downward trend from 1995 to 2012 [41][42][43], while the trends of this article are upward from 2011 to 2019. Most PWV in Central and Eastern China and Southern China show an upward trend and some PWV in North China is downward from 2011 to 2019. The monthly averaged PWV increased significantly in 2015, which was affected by the El Niño.

Conclusions
In this study, we analyzed the temporal and spatial distribution characteristics of the coefficients of the linear T m -T s model and showed that the distribution of T m -T s coefficients is mainly related to the latitude. The T m -T s conversion coefficient changes with the time and has an obvious annual cycle. Based on the spatial distribution and time-varying characteristics of the T m -T s coefficients, a site-specific piecewise-linear model was established. Compared with the Bevis model, this model reduced the T m RMS by more than 20% for the most of the tested radiosondes. The accuracy of GPS PWV is better based on the site-specific piecewise-linear T m -T s relationship when compared to the Bevis model. Furthermore, the PWV time series at 377 GNSS stations were further obtained and analyzed from the GPS observations and meteorological data from 2011 to 2019. The results showed that the average PWV in Central and Eastern China and Southern China is higher, reaching more than 25 mm, while the average value is lower and below 15 mm in Northwest China, Northeast China, and North China. The PWV is increasing in most parts of China, while some PWV in North China show a downward trend.