## 3 Method  
### Water Vapor Retrieval  
As mentioned before, the NIR water vapor retrieval algorithm is only applicable to sensors with both the water vapor absorption band and band not affected by water vapor absorption in the spectral range of 850-1250 nm [11]. Therefore, bands 5 and 6 (865 and 910 nm) of PSAC are bands selected for water vapor retrieval. Among them, band 5 is located in the spectral range of the atmospheric window and is basically not affected by gas absorption, while band 6 is strongly absorbed by the atmosphere, almost all of which is caused by water vapor. For NIR bands, the apparent reflectance observed by the satellite (\(R_{TOA}\)) at the top of the atmosphere can be expressed as [29; 30]:  
\[R_{TOA}=T_{g}\Big{(}\rho_{0}+T_{\uparrow}T_{\downarrow}R_{surf}\Big{)}\,, \tag{1}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No.** & **Center Wavelength** & **Spectral Range** & **Spectral Width** & **Spatial Resolution** \\ \hline Band 1 & 0.410 μm & 0.400–0.420 μm & 20 nm & 6 km \\ Band 2 & 0.443 μm & 0.433–0.453 μm & 20 nm & 6 km \\ Band 3 & 0.555 μm & 0.545–0.565 μm & 20 nm & 6 km \\ Band 4 & 0.670 μm & 0.660–0.680 μm & 20 nm & 6 km \\ Band 5 & 0.865 μm & 0.845–0.885 μm & 40 nm & 6 km \\ Band 6 & 0.910 μm & 0.900–0.920 μm & 20 nm & 6 km \\ Band 7 & 1.380 μm & 1.360–1.400 μm & 40 nm & 6 km \\ Band 8 & 1.610 μm & 1.580–1.640 μm & 60 nm & 6 km \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The specific band settings of the polarized scanning atmospheric corrector (PSAC). Figure 2: Spatial distribution of AERONET sites used in this study. Each point represents a site. where \(T_{g}\) is the total gaseous absorption transmittance, \(\rho_{0}\) denotes the atmospheric path reflectance caused by the atmosphere, \(R_{surf}\) is surface reflectance, \(T_{\uparrow}\) and \(T_{\downarrow}\) represent the total transmittance (direct + diffuse) upward and downward, respectively. Due to their relatively long and close wavelengths, the difference between path radiation and atmospheric transmittance of bands 5 and 6 can be ignored. In addition, the difference in surface reflectance between the two bands is very small. For the above reasons, it can be considered that the apparent reflectance of band 5 is equal to that of band 6 without considering water vapor absorption [21]. Since the effect of gases other than water vapor on the absorption of radiation observed by PSAC in bands 5 and 6 is negligible, the water vapor absorption transmittance of band 6 can be calculated by dividing the apparent reflectance of band 6 by that of band 5. \[T_{g}^{910\text{ nm}}=R_{TOA}^{910\text{ nm}}/R_{TOA}^{865\text{ nm}}, \tag{2}\]  
where \(T_{g}^{910\text{ nm}}\) is the water vapor absorption transmittance of band 6, \(R_{TOA}^{865\text{ nm}}\) and \(R_{TOA}^{910\text{ nm}}\) are the TOA reflectance of bands 5 and 6, respectively. Previous studies have shown that the water vapor absorption transmittance of the NIR channel is strongly correlated with CWV. This relationship can be written as [31; 32]:  
\[V_{\text{C}WW}=\frac{A*\left(ln\big{(}T_{g}\big{)}\right)^{2}+B*ln\big{(}T_{g }\big{)}+C}{L}, \tag{3}\]  
\[L=\frac{1}{cos(\theta_{s})}+\frac{1}{cos(\theta_{v})}, \tag{4}\]  
where \(V_{C}\)/\(V_{C}\) denotes CWV, \(T_{g}\) represents the water vapor absorption transmittance of NIR band, \(\theta_{s}\) is the solar zenith angle, \(\theta_{v}\) is the satellite zenith angle, and \(A\), \(B\), and \(C\) are three constants related to the characteristics of the NIR band, respectively. In this paper, the selected PSAC data was divided into two parts. Among them, PSAC data in East Asia (18-53\({}^{\circ}\)N, 73-130\({}^{\circ}\)E) was used to determine above three parameters (\(A\), \(B\), and \(C\)), and the remaining PSAC data was used to test the effectiveness of the water vapor retrieval algorithm. For the convenience of description, the region used to determine parameters of algorithm model is referred to as region 1, and the region used to test the algorithm is referred to as region 2.