# Flow Duration Curves from Surface Reflectance in the Near Infrared Band
## 2 Materials and Methods
### Methods
#### 2.2.1 Estimation of the Reflectance Ratio  
Reflectance is a measure of directly incident light, conventionally expressed as a percentage, which is reflected off a surface. The reflectance depends on the wavelength and assumes different values for different surfaces [19]. In the Near Infrared (NIR), the surface reflectance of wet soil is lower than that of dry soil and for a watercourse it assumes even lower values. For this reason, often NIR is used with Short-wave infrared (SWIR) or visible (through the Normalized Different Water Index, NDWI) to discriminate between water and no water during flood events and inundations [20; 21; 22; 23]. The variation of the moisture content in an area affected by inundations causes a variation of the surface reflectance. Specifically, during a flood event, when the river discharge of a natural channel increases, the water extent increases too, and the riparian zone changes its status from dry to wet. Consequently, the surface reflectance over these areas decreases. If the area is not subject to occasional flood inundation or, more generally, to water content variation, the surface reflectance does not show significant variations. The consideration of the ratio between the dry pixel (C for calibration) and the wet pixel (M for measurement) reduces the effects of vegetation and/or atmosphere existent in both (i.e., wet and dry) pixels signals and provides a clearer signal of water variation, which is expected to be detected with the increasing of river discharge.  
The variation of the surface reflectance with the river discharge, or other flow-related variables (i.e., flow velocity, water level, flow area, and water surface) has been already tested in several studies through the analysis with different satellite sensors: Landsat, MODIS, MERIS, OLCI, and Sentinel-2 [11; 12; 13; 14; 24; 25]. Recently, [PERSON] et al. [25] demonstrated that the surface reflectance ratio calculated between a dry and a wet pixel is a good estimator of the flow related variables. Here, we propose the same procedure to extract the C/M ratio at each site by carrying out the following steps:  
1. Cut the MODIS images over a square of size proportional to the width of the river (the side ranges from 0.05 to 0.11 km) and centered on the selected site.
2. Calculate the temporal coefficient of variation for every pixel of the box considering the set of available MODIS images.
3. Calculate, for each image, the spatial average of the reflectance considering the pixels with the coefficient of variation lower than the 5 th percentile; this represents the time series of dry pixel (C) at a given location.
4. Select a buffer of 1 km around the river and calculate all possible C/M ratios by considering M values of the pixels within the buffer and the average C obtained at step (3).
5. Compare every C/M time series against the discharge recorder by the ground monitoring network and calculate the coefficient of correlation.
6. Identify the C/M combination and, hence, M pixel that maximizes the coefficient of correlation.  
Finally, once the M and the C pixels are found, the surface reflectance ratio C/M is calculated for all the temporal span of the analysis and filtered with a pass filter (movingwindow average) in order to obtain the temporal series of satellite data (see Supplementary Material). For a detailed description of the procedure, the reader is invited to read [PERSON] et al. [25].  
Assuming the reflectance ratio as a proxy of the flow variables, and in particular of the river discharge (see e.g., [11; 13; 25]), in this study, we investigated how and to what extent the C/M ratio can be suitable for the estimation of reliable FDCs and, thus, for the evaluation the hydrological regime of a river.