# Multitemporal SAR Data and 2D Hydrodynamic Model Flood Scenario Dynamics Assessment
## 3 Method
### Hydraulic Model Calibration Framework Using SAR- and DEM-Derived Flood Maps
The first step of the calibration procedure is based on flood extent maps derived from a temporal series of SAR images (resampled, avoiding unsustainable computational times, at the same resolution as the hydraulic model, i.e., 10 m) for the 3-4 November 2010 Bradano event. The FLORA-2D hydraulic model does not have a routine that is able to simulate soil water infiltration and does not therefore account for soil permeability. Hence, water-depth values of less than 0.1 m could be not considered to be significant in the model results because cannot influence assessment of flood losses [9]. To guarantee the consistency of calibration and validation processes, the pixels in the SAR- and DEM-derived and in the hydraulic model flood maps were labeled as flooded where water depth exceeded 0.1 m.  
When comparing each SAR-derived map pixel to pixel with the flood map obtained with the hydraulic model at the same time step, there were four possible conditions in each map point/cell: (i) if the hydraulic model detected a flooded area when this condition was present in the SAR-derived flood map, the point was counted as a true positive; otherwise; (ii) if it identified a point as non-flooded (negative), it was counted as a false negative; (iii) if the site was defined non-flooded by the SAR map and classified as negative, it was counted as a true negative; otherwise, (iv) if it was classified as positive, it was counted as a false positive. From this, the true positive rate (also called hit rate) was estimated as:  
\[r_{fp}\approx\frac{Positive\ correctly\ classified}{Total\ positives} \tag{1}\]  
The false positive rate (also called false alarm rate) was:  
\[r_{fp}\approx\frac{Negatives\ incorrectly\ classified}{Total\ negatives} \tag{2}\]  
The proposed contingent matrix is similar to a confusion matrix and is successfully and widely used in the field of flood susceptibility assessment, e.g., in [57; 58; 18; 59; 47]. Moreover, the performance measurement, used to give a deterministic indication on how well each FLORA-2D-simulated flood map represented the SAR-derived flood extent map was obtained by minimizing the sum \(r_{fp}+(1-r_{tp})\) in the different time instants that were considered, of the false positive rate, i.e., error type 1, and the false negative rate, i.e., error type 2, assigning equal weights to the two rates. The sum of the two errors represents an objective function that can be used for calibration purposes ([47; 58]), hereafter called minimized sum of errors (_MSE_). The outcomes of the performance measurement evaluated through the comparison between a SAR-derived flood map and the flood map obtained by the hydraulic model at the same time step, were used in the following equation to identify the hydraulic model run concordance and discordance with respect to SAR-derived flood maps:  
\[\sum_{i}^{n}(MSE_{t_{i}}^{c_{j}})/\sum_{i}^{n}(MSE\mathit{min}_{t_{i}}) \tag{3}\]  
where \(MSE_{t_{i}}^{c_{j}}\) is the _MSE_ value obtained by pixel-to-pixel comparison of each FLORA-2D-simulated flood extent map computed with a roughness coefficient of \(c_{j}\) and the SAR-derived map for a CSK revisit time of \(t_{i}\); \(MSE\mathit{min}_{t_{i}}\) is the minimum value of all the _MSE_ values, at the same \(t_{i}\) temporal instant, associated to all FLORA-2D-simulation runs characterized by different values of the \(c_{j}\) Manning coefficient. The equation outcome (Equation (3)) was used to judge the performance of the hydraulic model runs. In the second step, the remotely sensed water levels were integrated to enhance the hydraulic model calibration. We compared the water depth maps of the concordance model run sets selected in the first step with floodwater depth extracted, as described in Section 3.2, by combining SAR images and the Digital Elevation Model.