## 4 Results and Discussion
### Flow Depth Models Analysis and Optimal Model Selection  
The hydrodynamic output parameter of flow depth, which was derived from each [PERSON]'s \(n\) value calibration model that was constructed upon the topography of the \"LiDAR scenario\" model, was compared to the control model, i.e., the so-called \"real scenario\". First, the global results were analyzed both as flow depth differences and as flood area extensions by using descriptive statistics parameters, such as mean, median, variance or standard deviation, and with the use of the Nash-Sutcliffe efficiency index and the F-statistic index. All these statistical indexes are shown in Table 1.  
From the analysis of the simulation points as a function of the flow depth values, it was found that the differences between the \"real scenario\" and the \"LiDAR scenario ([PERSON]'s \(n\) value = 0.011)\" had the lowest mean deviation, with a perfect average fit (0.000); the lowest median deviation results were found for the \"LiDAR scenario (spatially distributed Manning's \(n\) value)\", which slightly underestimated the flow depth (0.005); the lowest mode value was related to the scenario with [PERSON]'s \(n\) value equal to 0.012; the variance of the deviation had a random behavior. The Nash-Sutcliffe efficiency index was calculated as one minus the ratio of the error variance of the modelled hydrodynamic output divided by the variance of the observed hydrodynamic output. In our assessment, the output was the flow depth parameter. The NSE index showed very similar values for almost all of the hydrodynamic models. The best value was associated with the hydrodynamic model with a [PERSON]'s \(n\) value of 0.010, but the differences relative to other models (like models with \(n\) = 0.015, 0.016 or a spatially distributed \(n\) value) were not significant. All models showed high values of the NSE; therefore, the error variance of the modelled hydrodynamic outputs was much lower than the actual variance of the \"real scenario\" hydrodynamic model flow depth parameter. From the results of the NSE index, it was difficult to make the selection of the best [PERSON]'s calibrated hydrodynamic model. Just as the results of the flow depth parameter given by the NSE index were not fully significant to select the best calibrated hydrodynamic model option, the results from the  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Mean** & **Median** & **Mode** & \begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular}  & **Variance** & **F-Statistic** & **NSE Index** \\ \hline LiDAR Scenario + \(n\) = 0.001 & 0.231 & 0.417 & 0.100 & \(-\)0.110 & 0.174 & 81.76 & 0.9976 \\ \hline LiDAR Scenario + \(n\) = 0.010 & 0.024 & 0.326 & 0.026 & 0.050 & 0.106 &  
F-statistic index (Table 1) produced the same result. The F-statistic index showed many close values for the hydrodynamic models, with [PERSON]'s \(n\) value ranging from 0.010 to 0.018 (always above a value of 90), with the best value of the F-statistic index linked to the [PERSON]'s \(n\) value of 0.015. The F-statistic improvement from [PERSON]'s \(n\) value of 0.010 to 0.015 was only about 1.5%. As a conclusion, we could say that the analysis of the flow depth results from all calibrated models not giving us a strong criterion for the better option selection means that all models using [PERSON]'s \(n\) values ranging from 0.010 to 0.016 may be suitable to reproduce the conditions shown by the control model, i.e., the \"real scenario\" hydrodynamic model. The results shown by these models were similar in quality to those obtained by the use of the variable and spatially distributed Manning \(n\) value model, and they were better than the result shown by the HDCM approach. Based on the results obtained up to this point, a second phase of flow depth values analysis was necessary and a geo-statistical approach was carried out, where the distance to the main river channel was taken into account for the flow depth analysis.