# An Algorithm to Retrieve Precipitable Water Vapor from Sentinel-2 Data
## Materials and Methods
### Retrieval Algorithm Validation  
In this study, the PWV data retrieved from the GPS, MOD05, and ESA-L2A were used to validate the precision of the S2-L2A _PWV_. The principle of GPS inversion of _PWV_ data is that electromagnetic waves are affected by atmospheric delay when passing through the Earth's atmosphere [16; 45]. The zenith total delay (ZTD) consisted of zenith hydrostatic delay (ZHD) and _ZWD_. The ZHD was calculated by the Saastamoinen model using data on station latitude, geodetic height, and atmospheric pressure, and the _ZWD_ was obtained by subtracting the ZHD from the ZTD. The relationship between the _ZWD_ and _PWV_ is expressed by:  
\[PWV=\frac{10^{6}}{\rho_{w}R_{\mathrm{\tiny E}}(k_{2}^{\prime}+k_{3}/T_{m})} \cdot ZWD=\prod\cdot ZWD \tag{6}\]  
where \(\prod\) is a dimensionless scale factor, which is used to convert the proportional relationship between _ZWD_ and water vapor; \(\rho_{w}\) is the density of water, where the value is \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Value** & **Instruction** \\ \hline MODEL & 2, 3 & Mid-Latitude Summer (MLS), Mid-Latitude Winter (MLW) \\ ITYPE & 2 & Vertical path between two altitudes \\ IEMGST & 2 & Radiance/scattering model \\ TPTEMP & 298.15 & Temperature (Kelvins) \\ IMULT & 1 & Multiple scattering \\ VISIBILITY & 10–200, step 20 & Visibility (km), corresponding to an aerosol optical thickness of 0.70–0.05 at 550 nm \\ CSALB & 1, 2, 3, 4, 7 & spectral albedo curve (snow cover, forest, farm, desert, old grass) \\ H\({}_{2}\)OSTR & 0.2–5.0, step 0.2 & Defined column water vapor value (g/cm\({}^{2}\)) \\ LFLTLNM & Sentinel2.flt & Spectral response function of Sentinel-2 \\ IHAZE & 1 & RURAL extinction, default VIS = 23 km \\ H1 & 786 & Sensor Altitude (km) \\ H2 & 0–3.0, step 0.5 & Ground Elevation (km) \\ ANGLE & 164–180, step 4 & Sensor zenith angle (\({}^{\circ}\)) \\ PARM1 & 0–180, step 30 & Relative azimuth angle (\({}^{\circ}\)) \\ PARM2 & 20–60, step 10 & Solar zenith angle (\({}^{\circ}\)) \\ \hline \end{tabular}
\end{table} 
Table 1: Important input parameters of MODTRAN 5. Figure 2: An example of the relationship between transmittance and PWV. (**a**) Mid-latitude summer, (**b**) Mid-latitude winter. \(1\times 10^{3}\) kg/m\({}^{3}\); \(R_{v}\) is the gas constant of the water-vapor ratio, with a value of 461 J kg\({}^{-1}\).K\({}^{-1}\); \(k_{2}\)\({}^{\prime}\) and \(k_{3}\) are physical constants obtained from the experiment, with values of 16.48 K\(\cdot\)hPa\({}^{-1}\) and (3.776 \(\pm\) 0.014) \(\times\) 10\({}^{5}\) K\({}^{2}\)-hPa\({}^{-1}\) respectively; and \(T_{m}\) is the weighted average temperature related to local meteorological elements, in a unit of K.  
MOD05 is a PWV product calculated based on the MODIS data. This product assumes that the underlying surface is single and uses the radiative transfer equation to calculate and establish LUTs for various data, such as water vapor content and transmittance. PWV was retrieved using the 940-nm water vapor absorption channel [42]. Data similar to the Sentinel-2 transit times were downloaded from LAADS DAAC ([[https://ladsweb.modaps.eosdis.nasa.gov/search/](https://ladsweb.modaps.eosdis.nasa.gov/search/)]([https://ladsweb.modaps.eosdis.nasa.gov/search/](https://ladsweb.modaps.eosdis.nasa.gov/search/))). For a fair comparison, the spatial resolution of S2-L2A PWV was resampled to 1000 m, the same as the MOD05. ESA-L2A products downloaded from ESA SciHub ([[https://sciHub.copernicus.eu/dhus/#/home](https://sciHub.copernicus.eu/dhus/#/home)]([https://sciHub.copernicus.eu/dhus/#/home](https://sciHub.copernicus.eu/dhus/#/home))) included BOA reflectance, PWV, AOT, and so on. The PWV's spatial resolution was resampled to 60 m using SNAP.