# Flow Duration Curves from Surface Reflectance in the Near Infrared Band
## 1 Introduction  
In a flow duration curve (FDC), each recorded discharge is associated with the percent of time (e.g., expressed as percentage or number of days) for which it was exceeded, or equaled, during a reference period (e.g., a year or longer periods) [1, 2]. As an alternative way to estimate the flow characteristics, FDC is largely used in many applications, such as for water-resource engineering and water-quality management, flood and inundation control and mapping, river and reservoir sedimentation, etc. [1, 2, 3]. Generally, the longer the period of observation on which FDCs rely, the better the reliability of the statistical information gathered from them. Nevertheless, in light of the common data scarcity, the hydrological community and practitioners generally agree on the assumption that a reliable and accurate FDC requires river flow records covering a period of at least 10 years. Due to the discontinuity and lack of data for a large number of rivers worldwide, the possibility of building reliable FDCs is problematic, even in developed areas. Being strongly related to the site in which the river flow is measured, numerous studies in the literature are focused on finding solutions for ungauged sites [2, 4] and the use of satellite remote sensing data is emerging as an aid for river monitoring [5]. The increasing number of satellites in orbit and improved technologies allow exploiting satellite data as a valuable and additional source for the observation of the Earth's physical parameters. Characterized by a global coverage and continuous monitoring over time (at least for the mission period),satellite data can be complementary to ground hydro-monitoring data providing possibly additional information for river monitoring [6]. In the literature, to the best of our knowledge, [PERSON] et al. [5] is the only study involving the FDC and the satellite data, so far. Specifically, mimicking the discharge values from the upcoming Surface Water and Ocean Topography satellite (SWOT; in orbit from 2022), the authors tested the ability to observe the hydrological regime of the Po River, through the reconstruction of the FDC during the mission lifetime (three years). By the comparison with the FDC obtained with extended (e.g., 20-70 years) gauge datasets, the study demonstrated that the SWOT mission has sufficient potential to provide a realistic reconstruction of the flow regimes, except for very low or very high flows due to the low probability of occurrence of extreme events (floods or droughs) during the mission lifetime period. Except for the mentioned synthetic study, no other attempts have been made involving other satellite sensors to estimate the FDCs on purpose. However, if we interpret the FDC as an empirical cumulative distribution of river flows at the location where discharges have been recorded, the study of [PERSON] et al. [7] should be mentioned. They proposed a statistical approach based on quantile functions to infer the river discharge from altimetry observations of water levels not observed simultaneously. In fact, the use of the quantile, instead of the variables themselves, offers the possibility to link river discharge and altimetry-derived water levels through the functional law, called rating curve, even if the measurements of the two variables are not synchronically observed. Their results demonstrated that the statistical approach provides the same range of error as the common empirical method (that uses rating curve based on the variables themselves). Based on these first attempts and considering recent developments on remote sensing instruments dedicated to hydrological scopes, the present analysis promotes the use of the surface reflectance in the Near Infrared, NIR, band for the estimation of the FDC. Recent studies [8; 9; 10; 11; 12; 13] demonstrated that the variation of the river discharge provides a likewise variation on the Surface Reflectance in the NIR band in the areas close to the riverbank and not fully vegetated.