# An Algorithm to Retrieve Precipitable Water Vapor from Sentinel-2 Data
## 4 Discussion
### Error Analysis of the Algorithm  
Section 3 analyzed the overall accuracy of the PWV retrieved by S2-L2A. However, before applying remote sensing data, it is necessary to analyze the error distribution and its causes in different regions to determine whether the data can be used for quantitative analysis. Five factors (AOT, sensor zenith angle, solar zenith angle, elevation, and normalized difference vegetation index (NDVI)) were selected and divided into eight grades  
Figure 6: Spectral response functions of Sentinel-2 and MODIS PWV retrieval channels. (**a**) atmospheric window channel, (**b**) water vapor absorption channel. Figure 7: GPS site deployed on 1 August 2021, and parts of PWV retrieved from (**a**) S2-L2A, (**b**) ESA-L2A, and (**c**) MOD05. according to the natural breaks classification. RMSE between S2-L2A PWV and MOD05 at different grades was compared; the grading table is presented in Table 4. As shown in Figure 8a,b, there was no significant difference in RMSE among different grades of sensor zenith angle and solar zenith angle. Although the study area reaches 185,000 km\({}^{2}\), the range of sensor zenith angle and solar zenith angle is small. Therefore, these two factors have little influence on the PWV results. As shown in Figure 8a, the RMSE between S2-L2A and MOD05 PWV increased with AOT. This is because as the AOT value increased, the deviation of simulated path radiance increased, resulting in a higher PWV estimation error. It can be seen from Figure 8d that the RMSE between S2-L2A and MOD05 PWV decreased with elevation. This was because as elevation increased, the atmospheric column shortened and PWV reduced, so the corresponding error decreased. As shown in Figure 8e, the RMSE between S2-L2A and MOD05 PWV decreased with elevation. This was because as elevation increased, the atmospheric column shortened and PWV reduced,  
MOD05 PWV decreased as the NDVI value increased. In this study, standard plant and soil spectra were selected and mixed in different proportions to represent the spectra of varying vegetation coverage. The reflectance ratio of B9 and B8A is shown in Figure 9, where the horizontal axis represents the ratio of bare soil to plants, and vegetation coverage increases gradually from left to right. As shown in Figure 9, as vegetation coverage increased, the reflectance ratio changed from higher than one to lower than one, and the absolute values of ratios higher than one were generally larger than those of ratios lower than one. The proposed method was based on the equal reflectance of the atmospheric window channel and the water vapor absorption channel. Namely, when the reflectance ratio was higher than one, atmospheric transmittance was overestimated, resulting in an underestimation of the PWV value; but when the reflectance ratio was lower than one, transmittance was underestimated, resulting in an overestimated PWV value. Based on the results in Figure 9, when NDVI was low over sparsely vegetated regions, PWV was underestimated, but as the vegetation coverage increased, PWV changed from being underestimated to overestimated, and the degree of underestimation was generally larger than the degree of overestimation. MOD05 showed consistent overestimation. Therefore, the PWV inversion error decreased as the NDVI value increased. According to the above analysis, S2-L2A-retrieved PWV data is suited to PWV monitoring in a dense-vegetation region with high NDVI, but its accuracy in a barren-vegetation region with low NDVI needs further improvement.