## 3 Data and Methods
### Cloud Shadows Removal  
In this study, we investigated, for the first time, the potential of the RST approach to identifying cloud shadows, using the VIIRS I-bands. It is worth pointing out that, to our knowledge, this is the first attempt to exploit these data to detect cloud shadows. The current cloud mask algorithm for VIIRS I-Band indeed does not contain any confidence flag for shadows [57]. It is also important to specify that the approach we are proposing is based on a preliminary version, implemented for identifying (and removing before further analyses) clouds shadows (just for clouds on land). The performances it offers using the developed criterion, shown in this paper, refers exclusively to the flood analysed in this work. Other tests on wider regions are needed to confirm its feasibility and make it working well for all situations. In this first approach, the algorithm does not use geometry-based information (e.g., view angle of the satellite sensor, the solar zenith angle, the solar azimuth angle and the relative height of the cloud) to assess the cloud shadow location. In any case, it is worth mentioning that an assessment of the reliability of the RST-based cloud shadow product is beyond the scope of this paper and will be object of future works.  
Cloud shadows can be considered, from a statistical point of view, as anomalous signals randomly perturbing the investigated signal at pixel level for the considered scene. Therefore, they can be analysed by implementing the RST approach selecting spectral radiances most sensitive to their presence [58], namely the reflectance values measured in the II, I2 and I3 VIIRS bands. [58] showed the difference of reflectance values between clear pixels and cloud shadow contaminated pixels on vegetation, settlement and water bodies are shown, for the Landsat 8 bands (from Blue to SWIR). They found that NIR and SWIR bands have the biggest difference in average between clear pixels and cloud  
Figure 6: Reflectance variability profile along the red segment shown in Figure 1 for: (**a**) RED (I1), NIR (I2), SWIR (I3) VIIRS I-bands of 04/12/2013 at 12.10 GMT and the combinations (**b**) RED \(-\) SWIR, RED/SWIR, NDSI \(=\) (RED \(-\) SWIR)/(RED \(+\) SWIR).  
shadow contaminated pixels. Despite this, the choice of the most suitable metric (e.g. between the single or a bands combination) is not trivial, as shadows show a spectral response in the VIS-SWIR spectral range almost similar to those of flooded area [59]. Investigating the differences in values of the ALICE indices (i.e., ALICE\({}_{\text{RED}}\), ALICE\({}_{\text{NIR}}\) and ALICE\({}_{\text{SWIR}}\)) for shadows and flooded area, it is worth considering that:  
* in the RED (I1), flooded pixels should show higher values of ALICE\({}_{\text{RED}}\) than the shadow-affected ones, due to their relative increase in reflectance at this wavelength;
* in the NIR (I2) and SWIR (I3), both flooded and shadow pixels show low (negative) values of ALICE\({}_{\text{NIR}}\) and ALICE\({}_{\text{SWIR}}\).  
Therefore, a combination of those signals can allow a quite reliable identification of cloud shadows, which were mapped using the following rule:  
\[\text{if [ALICE}_{\text{RED}}<\text{-2 and ALICE}_{\text{NIR}}<\text{-2 and ALICE}_{\text{SWIR}}<\text{-2] then \"shadow\"}\]  
where the value \"-2\" used for all ALICE indices is the minimum level assuring the statistical significance of detected pixels. Besides, a 1.5 km - buffer zone around each potential cloud shadow affected pixel has been applied, to compensate for missed detections.  
For its inherent construction, such a criterion, applied only on cloud-free pixels, looks for those areas concurrently showing a statistically significant decrease in the signal acquired in the first three VIIRS Imagery bands. Therefore, apart from a few spurious and random signals, it should allow at discriminating flooded area from cloud shadows.