## 3 Evaluation and Application of PWV Derived from CPRAP
### Performance of CPRAP-Derived PWV  
#### 3.1.1 Accuracy Analysis of GNSS-Derived PWV  
Fifty-six collocated stations between GNSS and RS were selected in China over the period of 2012 to 2020 to evaluate the performance of GNSS-derived PWV based on CPRAP. The collocated principle is that the horizontal differences between GNSS and RS is less than 0.4\({}^{\circ}\)[13] and the altitude difference is less than 500 m. Furthermore, the empirical PWV correction model at collocated stations was used to reduce the PWV residual caused by the height difference [16]. RS-derived PWV can only be obtained at UTC 00:00 and 12:00; therefore, the corresponding comparison at collocated stations was only performed at those epochs over the selected period. RMS, Bias, MAE and R\({}^{2}\), in Equation (13) were chosen to evaluate the accuracy of GNSS-derived PWV.  
\[\begin{split}\text{RMS}=\sqrt{\frac{1}{\text{A}}\sum\limits_{i=1} ^{\text{n}}\left(X_{i}-\overline{X}\right)^{2}}\\ \text{MAE}=\frac{1}{\text{i}}\sum\limits_{i=1}^{\text{n}}\left| \left(X_{i}-\overline{X}\right)\right|\\ \text{Bias}=\frac{1}{\text{i}}\sum\limits_{i=1}^{\text{n}}\left(X_ {i}-\overline{X}\right)\\ \text{R}^{2}(X,Y)=\frac{\text{cov}(X,Y)}{\text{cov}Y}\end{split} \tag{13}\]  
where \(X_{i}\) is the PWV derived from the GNSS, whereas \(\overline{X}\) is the PWV mean value derived from the RS and used as the reference value. \(Y\) is the PWV derived from the RS. \(\sigma_{X}\) and \(\sigma_{Y}\) are the standard deviation of X and \(Y\), respectively.  
PWV was derived from four collocated stations (URU2, NMEL, LNJZ and GXNN) and those stations are randomly selected and evenly distributed in China with different climate conditions. Figure 3 gives the scatter density diagram of those stations over the period of 2012 to 2020. It can be observed that the RMS values of those stations generally increased from subfigures (a) to (d) and an excess of 3 mm was observed at the GXNN station, which are acceptable because the averaged PWV value is 42.68 mm at the GXNN station. The corresponding values of the other three stations are 9.58, 8.49 and 17.44 mm. Furthermore, an error in the empirical formula of PWV correction at different heights also exists between collocated RS and GNSS stations. Figure 4 presents the RMS and Bias distributions of PWV difference between GNSS and RS over the period of 2012 to 2020. It can be observed that the RMS generally increased as latitude decreased. Furthermore, Bias is positive in the north of China and negative in the south of China. The GNSS-derived PWV inversion has poor accuracy at low latitudes in China, and the PWV values in low latitudes are larger, resulting in larger errors. Statistical result (Table 2) reveals that the averaged RMS, Bias and MAE are 2.15, 0.05 and 1.65 mm, respectively, which shows the good performance of the established CPRAP for retrieving PWV data using the GNSS technique.  
Figure 4: RMS and Bias distributions of PWV differences between GNSS and RS over the period of 2012 to 2020.  
Figure 3: Scatter density diagram of PWV derived from four collocated stations over the period of 2012 to 2020.