# Multitemporal SAR Data and 2D Hydrodynamic Model Flood Scenario Dynamics Assessment
## 4 Results and Discussion
### Model Calibration
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{1}{c}{**Statistical Performance Measurements of Water-Depth Estimation 4 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}{*}{\(\boldsymbol{\mathrm{R}}\)\(\boldsymbol{\mathrm{\Delta}}\)**}} \\ \hline  & & & & & & \\ _0.04 for channel and floodplains_ & **0.30** & **0.28** & 0.70 & 0.25 & 0.37 & 0.81 \\ _0.08 for channel and floodplains_ & **0.27** & **0.50** & 0.68 & 0.44 & \(-\)0.16 & 0.93 \\ _0.1 for channel and floodplains_ & **0.37** & **0.07** & 0.64 & 0.46 & \(-\)0.32 & 0.84 \\ _0.033 for channel and 0.06 for floodplains_ & **0.26** & **0.53** & 0.57 & 0.34 & 0.08 & 0.91 \\ _0.025 for channel and 0.01 for floodplains_ & **0.31** & **0.22** & 0.69 & 0.24 & 0.4 & 0.8 \\ _variable in time and space_ & **0.19** & **0.76** & 0.76 & 0.33 & 0.01 & 0.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of the calibration performance of the hydraulic simulation model for 3 November 2010: the relative value of Manning coefficients \(c\), Root Mean Square Error _RMSE_, Nash- Sutcliffe Efficiency Coefficient (_NSE_), coefficient of determination \(R^{2}\), Unsystematic _RSME_ _RSMEu_, fraction _bias_ FB, prediction within a factor of two of observation _FA2_. The comparable values (greater than 0.7) of the estimated coefficient of determination (\(R^{2}\)) for the simulation with variable Manning time-and-space coefficients in all of the considered time steps indicated that this simulated scenario was in substantial agreement with the SAR observations performed on the subsequent days and that water recession as observed by SAR was consistent from the physical point of view. The coefficient of determination (\(R^{2}\)) was calculated using the following formulas:  
\[R^{2}=\left[\frac{\sum_{i=1}^{n}\bigl{(}O_{i}-\overline{\mathcal{O}}\bigr{)} \bigl{(}P_{i}-\overline{\mathcal{P}}\bigr{)}}{\sqrt{\sum_{i=1}^{n}\bigl{(}O_{i }-\overline{\mathcal{O}}\bigr{)}^{2}}\sqrt{\sum_{i=1}^{n}\bigl{(}P_{i}- \overline{\mathcal{P}}\bigr{)}^{2}}}\right]^{2} \tag{9}\]  
where \(0_{i}\) and \(P_{i}\) are the observed SAR and DEM derived water levels and predicted by the hydraulic model of the \(i\)th cell, respectively; \(\overline{\mathcal{O}}\) and \(\overline{\mathcal{P}}\) are the means of the observed and simulated value. \(R^{2}\) ranges from 0 to 1, where higher values represent good model performance, and \(R^{2}\) > 0.5 is generally considered satisfactory [60]. Tables 4 and 5 provide the following information: the relative value of the Manning coefficients \(c\), Root Mean Square Error _RMSE_, Nash Efficiency Coefficient (\(NSE\)), coefficient of determination \(R^{2}\), Unsystematic _RSME RSMEu_, fraction bias _FB_, prediction within a factor of two of observation _FA2_, i.e., fraction of data contained in the interval \(0.5\,O_{i}<P_{i}<2.0\,\,O_{i}\). Unsystematic _RSME_ and fraction bias are calculated using the following formulas:  
\[RSME_{u}=\sqrt{N^{-1}\sum_{i}^{n}\bigl{(}P_{i}-\overline{\mathcal{P}}\bigr{)} ^{2}} \tag{10}\]  
\[FB=2\bigl{(}\overline{\mathcal{O}}-\overline{\mathcal{P}}\bigr{)}/\bigl{(} \overline{\mathcal{O}}+\overline{\mathcal{P}}\bigr{)} \tag{11}\]  
In Figures 4 and 5, water depth shows large variations, but also a clear spatial pattern. The areas where floodwater was still present during the SAR time series basically correspond to the more sunken areas, those where the largest water elevations were predicted by the hydrodynamic model.