# Multitemporal SAR Data and 2D Hydrodynamic Model Flood Scenario Dynamics Assessment
## 4 Results and Discussion
### Model Calibration
The value of the sum of each minimized sum of errors (_MSE_) for the various time steps (i.e., 3 and 4 November 2010) was lowest for the hydraulic simulation using variable Manning time-and-space coefficients \(c\) as compared to all of the other simulations. It was seen that variable Manning time-and-space coefficients \(c\) estimated observed data better than all the others, while all of the simulations put in place showed good performance in terms of flood extent maps during the 3-4 November 2010 flood event. Moreover, the results obtained highlighted the highest information content that could be found in those SAR flood maps that were acquired near the peak of the flood hydrograph and improved when more images were combined. In the second calibration step, SAR- and DEM-derived water levels were integrated to enhance the hydraulic model calibration. The remotely sensed images were converted into floodwater depth maps, as described in Section 3.2. Taking the SAR-derived maps as reference and considering only the overlap between the SAR-derived and model flooded area, the overall accuracy, the root square mean errors (_RSME_) and the Nash and Sutcliffe efficiency (_NSE_) coefficients were used to compute for both the 3 and 4 November 2010 timeframes. As seen in Tables 4 and 5, the performance values of the hydraulic model vary widely depending on the basis of the set of the different Manning coefficient values utilized. It was seen that a successful depth calibration could only be obtained when channel roughness values were confined to a plausible range. Indeed, the performance of the simulation characterized by a Manning value of 0.1 in terms of both extent and water-depth maps, was the lowest, confirming literature theories that this value remains unexpectedly high [15]. It is also confirmed that is not realistic to find that Manning coefficient values for the channel are higher than those for the floodplain [26]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{1}{c}{**Statistical Performance Measurements of Water-Depth Estimation 3 November 2010**} & \multicolumn{1}{c}{\multirow{2}{*}{\(\boldsymbol{\mathrm{R}}\)\(\boldsymbol{\mathrm{S}}\)\(\boldsymbol{\mathrm{\Delta}}\)**}} & \multicolumn{1}{c}{\multirow{2}{*}{\(\boldsymbol{\mathrm{R}}\)\(\boldsymbol{\mathrm{\Delta}}\)**}} & \multicolumn{1}{c}{\multirow{2}{*}{\(\boldsymbol{\mathrm{R}}\)\(\boldsymbol{\mathrm{\Delta}}\)**}} & \multicolumn{1}{c}{\multirow{2}{*}{\(\boldsymbol{\mathrm{\Delta}}\)**}} \\ \hline  & & & & & & \\ _0.04 for channel and floodplains_ & **0.39** & **0.53** & 0.64 & 0.46 & 0.21 & 0.84 \\ _0.08 for channel and floodplains_ & **0.50** & **0.22** & 0.51 & 0.45 & \(-\)0.26 & 0.78 \\ _0.1 for channel and floodplains_ & **0.68** & \(\boldsymbol{-0.41}\) & 0.24 & 0.47 & \(-\)0.34 & 0.66 \\ _0.033 for channel and 0.06 for floodplains_ & **0.36** & **0.61** & 0.63 & 0.45 & \(-\)0.76 & 0.88 \\ _0.025 for channel and 0.01 for floodplains_ & **0.40** & **0.50** & 0.64 & 0.45 & 0.23 & 0.82 \\ _variable in time and space_ & **0.32** & **0.69** & 0.7 & 0.45 & 0.06 & 0.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of the calibration performance of the hydraulic simulation model for 3 November 2010 in terms of water depth: the relative value of Manning coefficients \(c\), Root Mean Square Error _RMSE_, Nash- Sutcliffe Efficiency Coefficient (_NSE_), coefficient of determination \(R^{2}\), Unsystematic _RSME_ FB, prediction within a factor of two of observation _FA2_.