## 3 Data and Methods
### Rst-Flood  
The RST-FLOOD approach has already been implemented on AVHRR and MODIS data exploiting the above cited particular spectral behaviour of water in the VNIR (VIS and NIR) region of the electromagnetic spectrum [12; 14]. This has led to the development of the two following Absolutely Local Index of Change of the Environment (ALICE--[13]) indices:  
\[\mathrm{ALICE_{NIR-VIS}(x,y,t)} = \frac{\mathrm{R_{NIR-VIS}(x,y,t)-\mu_{NIR-VIS}(x,y)}}{\mathrm{ \sigma_{NIR-VIS}(x,y)}}, \tag{1}\] \[\mathrm{ALICE_{NIR/VIS}(x,y,t)} = \frac{\mathrm{R_{NIR/VIS}(x,y,t)-\mu_{NIR/VIS}(x,y)}}{\mathrm{ \sigma_{NIR/VIS}(x,y)}}, \tag{2}\]  
where \(\mathrm{R_{NIR-VIS}(x,y,t)}\) (or \(\mathrm{R_{NIR/VIS}(x,y,t)}\)) is the reflectance difference (ratio) signal measured at time \(t\) for each pixel (\(x\),\(y\)) of the analyzed satellite scene, \(\mathrm{\mu_{NIR-VIS}(x,y)}\) (or \(\mathrm{\mu_{NIR/VIS}(x,y)}\)) and \(\mathrm{\sigma_{NIR-VIS}(x,y)}\) (or \(\mathrm{\sigma_{NIR/VIS}(x,y)}\)), the named reference fields, are, respectively, the \"normal\" value expected for the signal and its natural variability. They are both computed by processing a multi-year dataset of co-located cloud-free imagery, collected under homogeneous observational conditions (e.g., around the same time of day and during the same month of the year). For its inherent formulation, each ALICE provides, at the pixel level, a measure of the deviation of the recorded signal from its expected (in unperturbed or normal conditions) value and automatically compares this deviation with its normal variability, which includes all the possible noise sources not related to the event being monitored. For example, the normal signal variability (i.e., the standard deviation reference field) is high for those pixels characterized both by the presence of water and land, because they are likely to be affected by a high signal fluctuation due to both residual geo-location errors and the natural cross-section changes. Therefore, for those areas, anomalous ALICE values will only be detected when high signal deviation from the expected one will be measured. In any case, in correspondence to flooded areas, negative ALICE\({}_{\mathrm{NIR-VIS}(x,y,t)}\) (and ALICE\({}_{\mathrm{NIR/VIS}(x,y,t)}\)) values should be observed. Moreover, for their construction, both ALICE indices are standardized variables that, as the number (N) of the records increases, tend toward a Gaussian like distribution. Under this hypothesis, values of ALICE\({}_{\mathrm{NIR/VIS}}\) (or ALICE\({}_{\mathrm{NIR-VIS}}\)) \(<\)\(-2\) can be associated to rare events (probability of occurrence less than 2.5%) and values \(<\)\(-3\) to very rare events (probability of occurrence less than 0.13%). Hence, statistically significant signal anomalies are expected for ALICE\({}_{\mathrm{NIR/VIS}}\) (or ALICE\({}_{\mathrm{NIR/VIS}}\)) \(<\)\(-2\) at least, with an increasing level of confidence when moving to the lowest ones (i.e., \(-3\), \(-4\)) [12; 14; 24]. In order to investigate the selected flood event, the above-cited MODIS and VIIRS historical temporal series were separately processed, firstly generating their corresponding reference fields (i.e., temporal mean and standard deviation) for both difference and ratio signals, and then looking for signal anomalies in the event images. During the generation of the reference fields and during the change detection step, cloudy pixels were identified and discarded from the detection step by implementing the One Channel Algorithm (OCA) method [30; 31]. Such an approach, still based on the RST prescriptions, analyzes the historical series of MODIS channel 2 to identify clouds as statistically high reflectivity objects, or VIIRS I5 data to identify them as statistically cold bodies.