Investigation of the Application of Measured Meteorological Observations in Real-Time Precise Point Positioning

Abstract

Tropospheric delay is the main error source that affects the further improvement of the accuracy of space geodesy. High-precision zenith tropospheric delay (ZTD) can be used as a prior value for precise point positioning (PPP) in global navigation satellite systems (GNSSs) to enhance the speed and accuracy of real-time PPP solutions. Using the Saastamoinen ZTD model, we computed ZTDs using different meteorological elements. One ZTD was termed MZTD and was obtained from 80 reference sites in the China Mainland Crustal Movement Observation Network (CMONOC), the other was termed HZTD and was obtained from elements acquired from the improved version of the hourly global pressure and temperature atmospheric model (HGPT2). The results indicate that the accuracy of the MZTD was 12.94% higher than that of the HZTD, with the ZTDs estimated by post-processing GNSS values as the reference values. Additionally, the MZTD and HZTD were both applied as constraints to the PPP solution. The application of the MZTD constraints to the PPP floating-point solution resulted in a 28.9% improvement in accuracy and a 36.4% decrease in convergence time in the U-direction as a maximum, compared with the application of the HZTD constraints.

1. Introduction

ZTD (zenith tropospheric delay) is a key factor affecting the accuracy and speed of real-time PPP, while the accuracy of meteorological parameters such as temperature, humidity, and pressure directly affects the accuracy of ZTD. Real-time PPP users usually do not measure meteorological parameters and often calculate them from atmospheric models. We analyzed the accuracy of ZTD calculated from meteorological elements that we measured and obtained from a model and their contributions to real-time PPP accuracy and positioning speed. Our results provide a guide on how to improve real-time PPP positioning.

Tropospheric delay is a significant source of error in global navigation satellite systems (GNSSs). It is caused by variation in the vertical refractive index of the neutral atmosphere and affects electromagnetic wave signal propagation. However, recent research has increasingly recognized that ZTD serves as a disruptive factor and an additional information source that can enhance the speed and accuracy of real-time precise point positioning (PPP) in GNSSs. Therefore, the real-time acquisition of high-precision tropospheric delay is crucial in real-time GNSS navigation and positioning.

ZTD is one of the key parameters describing tropospheric delay and has recently become a focal point of research aimed at improving the accuracy of real-time GNSS positioning. There are primarily three methods for obtaining ZTD: the first relies on high-precision atmospheric observational data, such as radio sondes and GNSS radio occultation products, and involves numerical integration; the second involves constructing global/regional high-precision empirical ZTD models; and the third involves ground-based GNSS observations processed through double-differencing or undifferenced methods. Owing to limitations in the spatiotemporal resolution of observational data, empirical ZTD models have become the primary means for real-time ZTD acquisition. These models are mainly categorized into those dependent on surface meteorological observations (such as the Saastamoinen, Hopfield, and Black models) and those independent of such observations.

Constrained by the availability of actual meteorological parameters, numerous scholars have conducted in-depth studies on troposphere models that do not rely on actual meteorological parameters [1,2,3,4]. Currently, non-meteorological parameter correction models are mainly of two types: the first type includes spatiotemporal atmospheric parameter models that compensate for missing meteorological parameters; and the second type fits long-term ZTD series to functions of time, geographic location, and elevation.

The first type of non-meteorological parameter models primarily includes the UNB (University of New Brunswick)- and EGNOS (European Geostationary Navigation Overlay Service)-series models. Based on global meteorological data, the UNB series (including UNB1-4 and UNB3m) provides meteorological parameters required for estimating tropospheric delay in the form of 15°-latitude-interval grid tables. The UNB3m model simply replaces the water vapor pressure in the UNB1-4 meteorological tables with relative humidity. Global statistics indicate that the accuracy of the UNB3m model is approximately 4.9 cm [5]. The EGNOS model is an advancement over the UNB3 model and incorporates coefficients that depend on the latitude and longitude of the measuring station and time. The accuracy of the EGNOS model is comparable to that of the Saastamoinen model, which relies on actual meteorological parameters [6]. Given that the global meteorological observation points are dispersed, only low-resolution meteorological parameter tables can be acquired. However, this challenge can be mitigated using numerical weather model data. Böhm et al. developed the global pressure and temperature (GPT) model based on numerical weather model products [2,7]. To address the limitations of the GPT model, researchers have successively developed a series of improved GPT models, such as GPT3, an hourly global pressure and temperature model (HGPT), and HGPT2. Global-scale statistical results have revealed that the incorporation of the tropospheric delay correction effect of the GPT series into classical models dependent on actual meteorological parameters results in a delay reduction of approximately 4 cm [3,8,9]. However, both meteorological models and classical troposphere models contain systematic errors. While the combination of the models can compensate for the lack of meteorological observations, it can also introduce errors into the tropospheric delay.

Considering the shortcomings of the first type of non-meteorological parameter models, researchers have developed a second type. These models, based on single or multiple sources of troposphere products such as global IGS (International GNSS Service) troposphere products, ECMWF (European Centre for Medium-Range Weather Forecasts) products, NCEP(National Centers for Environmental Prediction) atmospheric data, and GGOS (Global Geodetic Observing System) atmosphere troposphere data, have shown significant improvements in accuracy compared with EGNOS- and UNB-series models [3,10,11,12]. Owing to the non-uniform distribution of the IGS stations worldwide, the relatively low temporal resolution of multisource atmospheric products (6 h intervals), and substantial climatic differences across various global regions, the ZTD model constructed using average meteorological observation data can exhibit significant deviations in local areas. Numerous researchers have developed accurate tropospheric delay correction models for specific regions using atmospheric products from different areas. Regional models can enhance the accuracy by 1–2 cm compared with global models [11]. However, both global and regional forms of the second type of meteorological parameter-free models are complex, which makes them unsuitable for practical application.

In summary, our objective was to utilize ground-based GNSS station-configured actual meteorological observations in conjunction with ZTD models dependent on surface meteorological observations to evaluate the accuracy and convergence speed of real-time PPP solutions. First, we assessed the accuracy of the Saastamoinen model with actual meteorological observations and compared the model with the HGPT2 + Saastamoinen model. Subsequently, we used the ZTD estimated by the actual meteorological observation + Saastamoinen model as a constraint for real-time PPP solutions and analyzed and discuss the impact of ZTD on improving the accuracy and reducing the convergence time of real-time PPP solutions.

In Section 2, we introduce the data and methods, describe the process of obtaining the ZTD through the PPP method, and present the ZTD model’s role in enhancing real-time PPP. Section 3 presents the results and discussion, and Section 4 presents the conclusions.

2. Data and Methods

2.1. Data Collection

The China Mainland Crustal Movement Observation Network (CMONOC) is one of the major national scientific infrastructure projects initiated during China’s 11th Five-Year Plan. The network primarily relies on GNSS observations, supplemented by several space technologies, including very-long-baseline interferometry and satellite laser ranging and precision gravimetry and leveling techniques. The CMONOC monitors crustal movements, gravitational field morphology and variations, troposphere water vapor content, and ionospheric ion concentrations over mainland China. It provides foundational data and products for scientific inquiries into spatiotemporal variations in crustal movements, three-dimensional tectonic deformations, short-term seismic precursors, the establishment and maintenance of modern geodetic reference systems, large-scale water vapor transport models during flood seasons, ionospheric dynamics, and space weather. The network comprises 260 stations equipped with Trimble NETR8 receivers, which are capable of dual-frequency GPS observations at a sampling rate of 30 s.

This study collected GNSS observation data for 2022 from 80 stations distributed across mainland China (Figure 1), with an average inter-station distance of 350 km. The meteorological data were sourced from VAISALA tri-element meteorological instruments configured at the base stations with a height difference of less than 3 m with respect to the antenna. These instruments capture temperature, humidity, and pressure at 30 s intervals. The GNSS receivers were connected with the VAISALA tri-element meteorological instruments, obtained data from them in real-time, including temperature, humidity, and pressure, and recorded them as raw data together with the GNSS signals.

The 80 stations are relatively uniformly distributed across the country, with a higher concentration in central and southwestern regions (Figure 1). Owing to geographical and communication constraints, stations on the Tibetan Plateau are relatively sparse.

2.2. Traditional ZTD Model

Numerous classical models for ZTD rely on empirical meteorological observations. Among these, the Saastamoinen model exhibits a slight advantage over other ZTD models in terms of accuracy and complexity. The Saastamoinen model is based on variables such as station latitude ∅, elevation h, satellite elevation angle E, atmospheric pressure at the surface $P_s$, atmospheric temperature at the surface $T_s$, and water vapor pressure at the surface $e_s$. The model is mathematically represented as follows:

$$\delta \rho ={\displaystyle \frac{0.002277}{\sin \mathrm{E}}}\left[P_s+({\displaystyle \frac{1255}{T_s}}+0.05)e_s-B·\cot ·E\right]\mathrm{W}\left(\varnothing ,h\right)+\mathsf{\delta }R$$

(1)

where $\mathrm{W}\left(\varnothing ,h\right)={\displaystyle \frac{1}{1-0.0026\cos 2\varnothing -0.0028h_s}}$, and B and $\mathsf{\delta }R$ are functions of h and E, respectively. For a real-time and efficient computation while maintaining accuracy, the above equation can be approximated and simplified as follows:

$$\delta \rho ={\displaystyle \frac{0.002277}{\sin E^{\prime }}}\left[P_s+({\displaystyle \frac{1255}{T_s}}+0.05)e_s-{\displaystyle \frac{a}{{\tan }^{2}E}}\right]$$

(2)

where $E^{\prime }=E+\Delta E$, $\Delta E={\displaystyle \frac{{16}^{″}}{T_s}}\left(P_s+{\displaystyle \frac{4810}{T_s}}{e}_s\right)\cot E$, and

$$a=1.16-0.15\times {10}^{-3}h+0.716\times {10}^{-8}{h}^2$$

(3)

2.3. GNSS–PPP Method to Extract the ZTD

The ZTD for a GNSS station was derived through PPP. The fundamental observationsare expressed by Equations (4) and (5) [13,14]:

$$P=\rho +cd{t}_r-cd{t}_s+ZTD+I+d_r-d_s+{\epsilon }_p$$

(4)

$$L=\rho +cd{t}_r-cd{t}_s+ZTD-I+\lambda N+b_r-b_s+{\epsilon }_L$$

(5)

where P and L are the pseudo-range and carrier-phase observations, $\rho$ is the distance between the satellite and the Earth, c represents the wave speed, $d{t}_r$ represents the receiver clock difference, $d{t}_s$ represents the satellite clock difference, $ZTD$ is the tropospheric delay, $I$ is the ionospheric delay, $d_r \mathrm{and} d_s$ are the pseudo-range hardware delays of the receiver and the satellite, respectively, $\lambda$ is the carrier wavelength, $N$ is carrier-phase ambiguity, $b_{r }$ and $b_s$ are the carrier-phase hardware delays of the receiver and the satellite, respectively, and ${\epsilon }_p and {\epsilon }_L$ are pseudo-range and carrier-phase observation noises, respectively.

The ionospheric delay can be mitigated through ionospheric-free combinations. The dry component of the troposphere delay is corrected using a specified model, while the wet component is estimated using parameters that incorporate additional horizontal gradient estimates. The tropospheric delay ZTD can be modeled as follows:

$$ZTD=ZHD·m_h\left(\epsilon \right)+ZWD·m_w\left(\epsilon \right)+\left[G_N·cos\alpha +G_E·sin\alpha \right]·m_G\left(\epsilon \right)$$

(6)

where $\epsilon \mathrm{and} \alpha$ represent the satellite cutoff height angle and the azimuth angle, respectively, ZHD is the troposphere hydrostatic delay, $m_h$ is the dry delay projection function, ZWD is the troposphere wet delay, $m_w$ is the wet delay projection function, $G_N$ is the north–south gradient, $G_E$ is the east–west gradient, and $m_G$ is the gradient projection function.

The BeiDou navigation satellite system/GPS real-time orbit and clock difference correction values from the CNES (Centre National d’Etudes Spatiales) analysis center are used to fix the coordinates of reference stations according to the known information on the reference stations. During the real-time processing of the GNSS observation data, ZTD, an unknown parameter, is calculated, and other parameters are estimated. The parameters to be estimated are indicated as follows [15]:

$$\overline{\mathit{X}}{=(\mathit{dt}}_r{, \mathit{ISB}}^{\mathrm{GC}}{, \mathit{ZTD}, \mathit{G}}_{\mathit{N}}{, \mathit{G}}_{\mathit{E}}{, \mathit{N}}_{\mathit{IF}}^{\mathit{S}})$$

(7)

where ${\mathit{dt}}_{\mathit{r}}$ is the receiver clock difference, $\mathit{ISB}$ is inter-system deviation, ${\mathit{G}}_{\mathit{N}}{ \mathrm{and} \mathit{G}}_{\mathit{E}}$ is indicate the troposphere horizontal gradient, and ${\mathit{N}}_{\mathit{IF}}^{\mathit{S}}$ is ionospheric-free combination ambiguity.

Table 1. Processing strategy for extracting ZTD using GNSS observation values.

Items	Processing Options
Product for satellite orbit and clock difference	Use of real-time orbit and clock difference products archived by CNES
Relativistic effect correction	Model correction
Cutoff angle	10°
Pseudo-range and phase observation noise tolerance	Pseudo-range: 0.3 m Phase observation: 0.003 m
Ionospheric delay correction	Use of the IF combination to eliminate the first-order ionospheric effects
Tropospheric delay correction	Use of the HGPT2 model to correct the zenith dry delay and estimate the zenith wet delay and gradient
Carrier-phase ambiguity fixing method	Use of a floating solution without fixed ambiguity
Antenna-phase correction	Use of igs14.atx for correction
Phase wrapping	Model correction
Earth tide effect correction	Model correction
Receiver clock difference correction	White noise estimation
Code deviation correction	Use of CODE DCB product for correction

presents the PPP-based processing strategy for the high-precision real-time acquisition of ZTD using GNSS observation values.

2.4. ZTD Model in Enhancing Real-Time PPP

Ionospheric-free combined observations are used to mitigate first-order ionospheric effects. ZTD products obtained using the Saastamoinen model with actual meteorological observations serve as external virtual observations, offering a validation mechanism for the effectiveness of atmosphere in PPP. The governing equations for these observations are Equations (8)–(11) [16,17].

$$P_{IF}=\rho +cd{t}_r-cd{t}_s+ZTD+{\epsilon }_{P_{IF}}$$

(8)

$$L_{IF}=\rho +cd{t}_r-cd{t}_s+ZTD+{\lambda }_{IF}{N}_{IF}+{\epsilon }_{L_{IF }}$$

(9)

$$ZT{D}_{\mathrm{saas}}=ZTD+{\epsilon }_{ZTD}$$

(10)

$$R=\left[\begin{array}{ccc}{\sigma }_{P_{IF}}& 0& 0\\ 0& {\sigma }_{L_{IF}}& 0\\ 0& 0& {\mathsf{\sigma }}_{ZT{D}_{\mathrm{saas}}}\end{array}\right]$$

(11)

In the above equations,$P_{IF}$ represents the pseudo-range observation of the ionospheric-free combination, $L_{IF}$ is the ionospheric-free carrier-phase observation, $\rho$ is the distance from the satellite to the receiver, $cd{t}_r$ is the receiver clock error, $cd{t}_s$ is the satellite clock error, $N_{IF}$ is the ambiguity of ionospheric-free combinations, and ${\lambda }_{IF}$ is the wavelength of ionospheric-free combinations. ${\epsilon }_{P_{IF}} \mathrm{and} {\epsilon }_{L_{IF}}$ are the pseudo-range and carrier noises of ionospheric-free combinations, respectively. $ZT{D}_{\mathrm{saas}}$ is the ZTD obtained using the Saastamoinen model. ${\sigma }_{P_{IF}},{\sigma }_{L_{IF}},\mathrm{and} {\sigma }_T$ are the variances of the pseudo-range, carrier, and ZTD, respectively. R represents the covariance matrix of the accuracy of $P_{IF}$,$L_{IF}ZT{D}_{saas}$.

3. Results and Discussion

3.1. ZTD Accuracy Assessment

To evaluate the effectiveness of the proposed ZTD estimation method, which involves the utilization of actual meteorological elements, we selected observational data from two stations—WUHN and GZGY—of an entire year. The ZTD values obtained through post-processed PPP served as the reference true values for a comparative analysis of the accuracy of two types of ZTD results. The ZTD estimation accuracies DZTD (with respect to reference true values) of two methods—termed DMZTD, which provides estimations based on the actual measured meteorological elements combined with the results of the Saastamoinen model, and DHZTD, which is based on the HGPT2 model combined with the Saastamoinen model—were compared (Figure 2). In Figure 2, the red line represents the difference between the ZTD calculated using actual meteorological elements and the Saastamoinen model and the reference true values, while the blue line represents the difference between the ZTD calculated using the HGPT2 model and the Saastamoinen model and the reference true values.

In Figure 2, the amplitude of the red line is generally smaller than that of the blue line across both stations. This indicates that the accuracy of the ZTD values estimated using the Saastamoinen model with actual meteorological elements was significantly higher than that of the ZTD values obtained using the HGPT2 model combined with the Saastamoinen model.

To further analyze the applicability of the method based on actual meteorological elements and the Saastamoinen model for calculating ZTD in the Chinese region, we selected 80 stations uniformly distributed across China for an experimental analysis. Using the two aforementioned methods, we processed the observational data from these stations for an entire year. The data were segmented into four seasons—spring, summer, autumn, and winter—to calculate the root-mean-square error (RMS) for each station in each season. The results are shown in Figure 3 and Figure 4. Figure 3 presents the RMS of the difference between the ZTD calculated using actual meteorological elements and the Saastamoinen model and the reference values, while Figure 4 shows the RMS of the of the difference between the ZTD calculated using the HGPT2 model and the Saastamoinen model and the reference values.

In Mainland China, there is a significant difference in humidity, especially atmospheric water content, between the north and the south. The air in the north is dry, while that in the south is humid. The examination of Figure 3 and Figure 4 reveals that the accuracy of the ZTD estimation was strongly correlated with both the latitude of the observation stations and seasonal variations. In high-latitude regions, the discrepancies between the estimated ZTD values and the reference values were generally within 3 cm. In low-latitude regions, these discrepancies were notably larger. During the winter season, the RMS values across various stations were approximately 3 cm, indicating smaller differences between the estimated and the reference values. In contrast, during the summer season, these discrepancies could reach 6 cm in low-latitude areas.

According to the data presented in Figure 3 and Figure 4, the observation stations were segmented into four sub-regions within China, each spanning a 10° latitude interval.

Table 2. Accuracy statistics of ZTD models in different seasons (unit: cm).

Latitude (°N)	Number of Stations	Model		Spring	Summer	Autumn	Winter
15–25	11	DMZTD	Mean	−1.08	−1.69	−0.85	−0.72
			RMS	3.82	4.95	4.27	3.25
		DHZTD	Mean	−1.27	−1.74	−0.93	−0.90
			RMS	4.38	6.03	5.29	4.27
25–35	26	DMZTD	Mean	−0.97	−1.06	−0.78	−0.74
			RMS	3.35	4.58	4.21	2.98
		DHZTD	Mean	−1.23	−1.46	−1.09	−0.75
			RMS	3.59	5.28	4.87	3.45
35–45	34	DMZTD	Mean	0.71	1.08	−0.42	0.34
			RMS	3.19	4.48	3.93	2.90
		DHZTD	Mean	−1.02	1.14	−0.81	−0.43
			RMS	3.37	5.01	4.14	3.21
45–55	8	DMZTD	Mean	−1.01	0.91	−0.54	−0.55
			RMS	2.73	3.31	2.94	2.67
		DHZTD	Mean	−0.72	0.86	0.63	−0.43
			RMS	3.08	4.28	3.52	2.81

presents the mean and RMS values of the ZTD discrepancies calculated using both methods under different seasonal conditions within these latitude intervals. The method involving actual meteorological elements yielded significantly higher accuracy than the HGPT2 model-based method. Specifically, the largest improvement in accuracy (23.89%) occurred in low-latitude regions (15°N–25°N) during the winter season. In high-latitude regions (45°N–55°N), the accuracy improvement was the smallest during winter, yet it still reached 4.99%. When inputted with country-wide data for the entire year, the model based on actual meteorological elements yielded a 12.94% improvement in accuracy.

In summary, the method based on actual meteorological elements for ZTD estimation outperformed the HGPT2 model-based method. The meteorological element-based method enables the calculation of more accurate ZTD values, which facilitates convergence in PPP.

3.2. Application in PPP

To enhance the testing of various ZTD constraints in PPP models, the ZTDs obtained from the measured meteorological elements and the HGPT2 model were used as additional constraints. We randomly selected observation data from the WUHN and GZGY stations on DOY (day of year) 200 of 2022 to compare the convergence effects of PPP under different constraint conditions.

We use the ZTD calculated by the Saastamoinen model based on measured meteorological elements and data from the HGPT2 model, including temperature, pressure, and water vapor partial pressure, as two constraints for the PPP model. Figure 5 and Figure 6 present the accuracy and convergence time of the PPP float solution in the E, N, and U directions under two ZTD constraints.

The red line represents the convergence time after the application of the ZTDs obtained through the introduction of the measured meteorological elements into the Saastamoinen model as constraints. The blue line represents the convergence time for static PPP float solutions in various E, N, and U directions using the ZTD obtained by imposing each atmospheric parameter from the HGPT2 model as a constraint in the Saastamoinen model. The term “MZTD” denotes the ZTDs obtained by integrating measured meteorological elements into the Saastamoinen model, and the term “HZTD” denotes the ZTDs obtained by integrating the temperature, pressure, and water vapor partial pressure obtained from the HGPT2 model into the Saastamoinen model.

The deviations of the static PPP float solutions for the two sites under two types of ZTD constraints are depicted in Figure 5 and Figure 6. No significant difference was found between the two static PPP float solutions based on different ZTD constraints, particularly after several hours of PPP convergence. As shown in Figure 5 and Figure 6, the PPP float solution achieved smaller errors by using the ZTD calculated from the measured meteorological elements as prior values for the constraints in both the eastward (E) and the upward (U) directions. This is in contrast to the results obtained with the ZTD calculated with atmospheric parameters from the HGPT2 model. The limited impact of the ZTD constraints on the PPP float solution in the N direction can be attributed to the fact that the ZTD primarily affects the vertical propagation path of electromagnetic waves, with a relatively smaller effect on horizontal propagation. This led to insignificant differences in the N-directional curves under the two ZTD constraint conditions. In addition, compared to the E and U directions, the N direction had fewer sources of error, such as multipath effects and satellite clock biases, which had a smaller impact on the N direction. Therefore, even if there were differences in the accuracy in relation to the ZTD constraints, their impact on the N direction was limited. Furthermore, PPP solutions are also affected by other factors, such as the quantity and quality of the observation data, the accuracy of satellite orbit and clock difference products, and ionospheric delays, which may mask the impact of the ZTD constraints on the N direction, resulting in insignificant differences in the N-directional curves under the two constraint conditions. In addition, Figure 5 and Figure 6 only show data from two stations for one day, and the statistical sample size was limited. A larger sample size may reveal differences between the two constraint conditions in the N direction.

The convergence times of the two ZTD constraint-based static PPP float solutions at the 95% and 68% confidence levels in both horizontal and vertical directions were examined. To achieve a convergence time at a 95% confidence level, horizontal and vertical deviations <0.2 m werenecessary, while a convergence time at a 68% confidence level required deviations <0.1 m. Figure 6 and Figure 7 present the PPP statistical results for the convergence times under the two ZTD constraints on DOY 200 of the year 2022.

The application of the ZTD constraints calculated from the measured meteorological elements to the PPP float solution resulted in shorter convergence times with respect to those obtained when using the constraints calculated with the HGPT2 model in both horizontal and vertical directions (Figure 7 and Figure 8).

Table 3. Statistics of the convergence times of PPP with the MZTD constraints and with the HZTD constraints at different confidence levels (unit: min).

Date	Confidence Level	Horizontal		Vertical
		With MZTD	With HZTD	With MZTD	With HZTD
DOY (087–100)	95%	20.5	22.0	22.5	24.5
	68%	18.5	19.5	19.5	22.0
DOY (200–213)	95%	18.5	20.0	21.0	23.0
	68%	17.0	18.5	19.5	21.5

presents the statistical results of the convergence times of PPP solutions with the MZTD constraints of and PPP solutions with the HZTD constraints at different confidence levels.

The application of the MZTD constraints resulted in shorter convergence times than those obtained using the HZTD constraints in both horizontal and vertical directions. Between DOY 087 and 100 of the year 2022, at a 95% confidence level, the application of the MZTD constraints to the PPP float solution resulted in 6.82% and 8.16% decreases in the convergence times in the horizontal and vertical directions, compared with the application of the HZTD constraints; the corresponding reduction rates at a 68% confidence level were 5.13% and 11.36%, respectively. Similarly, between DOY 200 and 213 of the year 2022, the application of the MZTD constraints resulted in 7.50% and 8.70% shorter convergence times in the horizontal and vertical directions, respectively, compared with the application of the HZTD constraints at a 95% confidence level, with reduction percentages of 8.11% and 9.30% at a 68% confidence level.

4. Conclusions

Using the Saastamoinen model, we computed the ZTD for individual stations according to meteorological elements obtained from 80 reference stations in the Crustal Movement Observation Network of China and data derived from the HGPT2 atmospheric model. The GNSS-estimated ZTD for each station served as the reference true value. Comparative analyses were conducted across different latitudinal zones and seasons. The results indicated that the ZTDs calculated using measured meteorological elements were significantly more accurate than those calculated using elements obtained from atmospheric models. The RMS of ZTD products calculated using measured meteorological elements ranged from 2.67 to 4.95 cm, while that of ZTD products calculated using the HGPT2 model ranged from 2.81 to 6.03 cm. Moreover, the largest accuracy improvement (approximately 23.89%) occurred under winter conditions in low-latitude regions (15°N–25°N), whereas the smallest accuracy improvement (4.99%) occurred under winter conditions in high-latitude regions (45°N–55°N). On a national scale, the annual improvement was 12.94%.

For evaluation, we selected the data of DOY 087–100 and 200–213 of the year 2022 from the WUHN and GZGY stations. The ZTD results obtained through both methods were used as tropospheric delay constraints in PPP solutions. The assessment was conducted from the perspectives of both PPP positioning accuracy and convergence time. The statistical results revealed that the use of ZTD products based on measured meteorological elements as constraints resulted in a significant improvement in the accuracy of the PPP float solution, particularly in the vertical direction. The application of the MZTD constraints to the PPP floating-point solution resulted in a 28.9% improvement in accuracy as a maximum and a 36.4% decrease in convergence time in the U-direction as a maximum, compared with the application of the HZTD constraints. Moreover, the application of the MZTD constraints to the PPP float solution resulted in shorter convergence times with respect to those obtained using the HZTD constraints. Specifically, at the 95% and 68% confidence levels, during DOY 087–100 of 2022, the application of the MZTD constraints resulted in 8.16% and 11.36% shorter vertical convergence times and 6.82% and 5.13% shorter horizontal convergence times, respectively. Similarly, during DOY 200–213, the vertical convergence time was shortened by 8.70% and 9.30%, and the horizontal convergence time was shortened by 7.5% and 8.11%. Therefore, constructing a high-resolution, high-accuracy ZTD grid based on high-density measured meteorological elements holds significant promise for applications in high-precision positioning and water vapor inversion.