## 4 Result and Validation
### Internal/External Accuracy Testing  
The slant wet delays of six stations (XIUW, BAIY, YONG, QINZ, QINY and KAIY) for the data of Doy 303 to 317, 2015 were used to validate the internal/external accuracy of the proposed method based on the tomographic modeling established in Section 2.1. For the internal accuracy testing, six stations are both used to reconstruct the atmosphere wet refractivity, two elevation angle masks of 10\({}^{\circ}\) and 15\({}^{\circ}\) were both selected for the two schemes. The residuals of tropospheric delay in the two schemes are shown in Figure 4, where the top and bottom represent the case of 10\({}^{\circ}\) and 15\({}^{\circ}\) of elevation masks, separately. It is clearly seen that the residual of the proposed method (Scheme 2) is smaller than that of conventional method (Scheme 1) for two cases. The Root Mean Square (RMS) error and the mean bias (Bias) for schemes 1 and 2 are 3.0 / \(-\)0.3 mm and 2.3/0.1 mm, respectively, under the condition of 10\({}^{\circ}\) elevation angle mask while those values are 2.9 / \(-\)0.2 mm and 2.1/0.1 mm, respectively, under the condition of 15\({}^{\circ}\) elevation angle mask. In addition, Figure 5 also gives the change of slant wet delay residuals with elevation angle for two schemes under different elevation angle masks. It is clear that the residuals decreased with ascending elevation angles. The residuals of Scheme 2 (red dots) are obviously smaller than those in Scheme 1 (blue dots) for two cases of 10\({}^{\circ}\) and 15\({}^{\circ}\) of elevation angle masks. Figure 4: Residuals of the slant wet delay using two schemes with 10\({}^{\circ}\) (top) and 15\({}^{\circ}\) (bottom) elevation angle mask over the experimental period of Doy 303 to 317, 2015. Figure 3: The statistics of Bartlett test and iterations under two conditions with elevation angle masks of 10\({}^{\circ}\) and 15\({}^{\circ}\), respectively, over the experimental period of Doy 303 to 317, 2015. To further assess the proposed method of troposphere tomography using the multi-GNSS observation, another experiment was carried out to validate the external accuracy of the tomography modeling. In this experiment, only five stations (XIUW, YONG, QINZ, QINY and KAIY) were used to reconstruct the wet refractivity for the data of Doy 303 to 317, 2015 with two elevation angle masks of 10\({}^{\circ}\) and 15\({}^{\circ}\), respectively. The slant wet delay of BAIY derived from GNSS PPP-estimated is regarded as a reference. Figure 6 shows the residuals of the slant wet delay of the BAIY station for the whole day, where the blue and red lines represent the slant wet delay residuals obtained by Schemes 1 and 2, respectively. It can be clearly seen that the trend of residuals acquired by Scheme 2 fluctuates less wildly than that acquired by Scheme 1. The RMS/Bias for schemes 1 and 2 are 13/\(-\)0.9 mm and 9.4/0.9 mm, respectively, under the condition of 10\({}^{\circ}\) elevation angle mask while those values are 12.4/0.7 mm and 8.4/0.9 mm, respectively, under the condition of 15\({}^{\circ}\) elevation angle mask. Figure 5: Scatter diagram of the slant wet delay residual using two schemes with 10\({}^{\circ}\) (top) and 15\({}^{\circ}\) (**bottom**) elevation angle mask over the experimental period of Doy 303 to 317, 2015. Figure 6: Residuals of the slant wet delay for the station of BAIY using two schemes with 10\({}^{\circ}\) (top) and 15\({}^{\circ}\) (bottom) elevation angle mask over the experimental period of Doy 303 to 317, 2015. In addition, the trend of slant wet delay residuals of station BAIY with elevation angle were also analyzed and shown in Figure 7. It is clear that the slant wet delay residuals for two schemes decreased with ascending elevation angles. The residuals distribution calculated from Scheme 2 (red dots) obviously shows a smaller change trend than those obtained from Scheme 1 (blue dots) for all ranges of elevation angles.