# An Algorithm to Retrieve Precipitable Water Vapor from Sentinel-2 Data
## 1 Introduction  
Water vapor is an important greenhouse gas that affects weather changes [1; 2; 3; 4]. Water vapor is also a critical factor in studying various parameters, such as the Earth's radiation budget, global climate changes, cloud formation, and the hydrological cycle [5; 6; 7]. Precipitable water vapor (PWV) refers to the total amount of water vapor per unit column from the ground to the top of the atmosphere, which represents the amount of precipitation formed by converting all water vapor contained into rain and snow [8]. Accurate estimation of the PWV value is of great significance for both achieving efficient use of water resources and climate-related research. Radiosonde has been the most basic means to measure upper-air meteorological parameters [9; 10; 11]. It provides information on the air pressure, temperature, and relative humidity needed to calculate the PWV value from the Earth's surface to the top of the atmosphere [12]. Radiosonde data have high accuracy and vertical resolution but are expensive to obtain and have few stations. These data are usually used to evaluate the accuracy of other water vapor products [13; 14]. The Global Positioning System (GPS) isanother way to retrieve PWV based on the delayed signal between GPS satellites and receivers [15; 16]. PWV retrieval using GPS is widely used due to its all-weather coverage, high temporal resolution, and easy operation [17; 18]. In addition, a sun photometer can retrieve PWV with high temporal resolution from solar radiation transmittance [19; 20; 21]. It measures the extinction effect of the atmosphere on direct solar radiation through a water vapor absorption channel and uses the radiative transfer model to realize PWV inversion [22]. The above-mentioned methods all monitor PWV values at a single point, which cannot meet application requirements on a large scale. In recent years, the development of satellite remote sensing has provided a new means of studying water vapor in continuous space [23; 24; 25]. Inversion methods include the near-infrared ratio and split window algorithms [7; 26; 27]. Remote sensing data have been obtained by satellites that include moderate resolution imaging spectroradiometer (MODIS) [28; 29; 30], visible and infrared radiometer (VIRR) [31; 32], and medium resolution spectrum imager (MERSI) [33; 34]. [PERSON] et al. [35] used the near-infrared and thermal infrared bands of MODIS to retrieve PWV values and compared accuracy at different bands. [PERSON] et al. [36] used GPS and MODIS to estimate PWV in Iran, and used PWV retrieved from GPS to correct the MODIS PWV. [PERSON] et al. [37] improved the PWV estimation algorithm based on radiance ratio technology, and used the FengYun 3D Medium Resolution Spectral Imager 2 (FY-3D MERSI-2) as an example to verify the proposed algorithm's accuracy. Although these satellite data have been successfully applied to PWV monitoring, their spatial resolution is low (1 km), which makes it challenging to provide high-resolution water vapor products. The Sentinel-2 is a cluster of satellites launched by the European Space Agency (ESA), and consists of two satellites in the same group: 2A launched in 2015, and 2B launched in 2017 [38]. The multispectral instrument (MSI) has a near-infrared water vapor absorption channel (B9, with a spatial resolution of 60 m) and an adjacent atmospheric window channel (B8A, with a spatial resolution of 20 m), which allows PWV detection with an extensive range and high spatial resolution. ESA provides Level-2A products (ESA-L2A) based on an implementation of the Sen2 Cor algorithm, and also provides an offline version of the Sen2 Cor L2A processor (S2C-L2A) to produce Level-2A products. Both ESA-L2A and S2C-L2A products include bottom of the atmosphere (BOA) reflectance images, maps of the aerosol optical thickness (AOT), and PWV, among others [39].