# Multitemporal SAR Data and 2D Hydrodynamic Model Flood Scenario Dynamics Assessment
## 4 Results and Discussion  
### Model Calibration  
Model calibration is essential for checking model performance before it can reasonably be used for near real-time flood forecasting and monitoring or for flood risk management in general [60]. The FLORA-2D hydrodynamic model was calibrated using the 3-4 November 2010 Bradano River flood event, with flood hazard maps derived from the two SAR images acquired, respectively, at 4:47 a.m. of 3 November 2010 (during the rising phase of the event) and at 4:47 a.m. of 4 November 2010 (during the recession phase of the flood event). As stated before (Section 3.4), model calibration was performed over six different sets of channel and floodplain Manning coefficients, since the roughness parameters determine mainly flooding and receding rate in a flat area with complex topography [15]. Firstly, the performance of each model simulation was analyzed in terms of flood extent, when comparing these simulated flood hazard maps (pixel to pixel) with the temporal series of SAR images at the same time step. As shown in Figure 3, the result of the comparison of each flood extent map simulated with a FLORA-2D model, characterized by a specific set of Manning coefficients, and the SAR-derived flood extent map at the same time step, produced a matrix (or contingency table) of four possible outcomes. Taking the SAR-derived maps as a reference, there are two ways for the hydraulic simulated flooded area to be correct (either by representing flooded or non-flooded pixels correctly) and two ways to be incorrect (either by erroneously under- or over-predicting the observed inundation extent). Figure 3: Example of contingency map obtained by pixel-to-pixel comparison of the hydraulic simulation using variable spatio-temporal Manning coefficients, as in [45], and the Synthetic Aperture Radar (SAR)-derived flood extent map at the same time step, i.e., 4:47 a.m. of 3 November 2010. To provide a quantitative description of the efficacy of each hydraulic simulation, we summarize in Tables 2 and 3 the performance of each defined set of Manning coefficients investigated, respectively, by a comparison with the two SAR images acquired during 3 November and 4 November 2010. The optimal performance values for each time step were identified by utilizing the above-mentioned minimized sum of errors (_MSE_). In particular, Tables 2 and 3 provide the following information: the relative value of the Manning coefficients \(c\), the false positive rate \(r_{fp}\), the true positive rate \(r_{tp}\), false negative rate \(r_{fn}\), the minimized sum of errors (_MSE_), and some additional statistical performance measurements, such as _accuracy_, _sensitivity_, and _specificity_ for each hydraulic simulation. _Sensitivity_ (also referred to as \"recall\") refers to the proportion of correctly classified instants of flood pixels, whereas _Specificity_ evaluates the proportion of correctly classified instants of non-flood pixels. _Accuracy_ refers to the proportion of pixels that are classified correctly. _Sensitivity_, _Specificity_, and _Accuracy_ are calculated using the following formulas [57]:  
\[Sensitivity=\frac{TP}{TP+FN} \tag{6}\]  
\[Specificity=\frac{TN}{FP+TN} \tag{7}\]  
\[Accuracy=\frac{TP+TN}{TP+TN+FB+FN} \tag{8}\]  
where \(TP\) is true positive and defined as the total number of pixels predicted positive that are positive; \(FR\) is false positive and equal to the number of pixels predicted positive that are negative; \(TN\) is true negative and equal to the number of pixels predicted negative that are negative; and, finally, \(FN\) is false negative and equal to the number of pixels predicted negative that are positive. i.e., error type 1, which varies in the range 7-20% and the false negative rate, i.e., error type 2, that varies in the range 12-28%, and can be considered an indication of the reliability of products generated to perform the flood extent assessment.