## 3 Methodology
### Comparison of Hydrodynamic Model Outputs  
To evaluate the suitability of the different hydrodynamic models that were generated in the calibration process, the flow depth parameter was selected since it was the most commonly used parameter for flood risk analysis through magnitude-damage models as a flood vulnerability approach. The hydraulic outputs (flow depth) generated by the Iber software were exported into geo-referenced ASCII raster files (*.asc files) for each of the \"LiDAR scenario + Manning's \(n\) value\" models, and further outputs were compared to the benchmark model generated using the \"real scenario\" topography in the GIS software ESRI(r) ArcGIS 10.6.1. Spatially distributed flow depth differences between calibrated models and the control model, as well as random sample creation and geo-statistical analysis input parameter calculations, were also generated inside the ESRI(r) ArcGIS environment.  
The analysis of different results started with descriptive statistics of the flow depth value differences between the \"LiDAR scenario\" models (with different Manning's \(n\) values) and the \"real scenario\" in the set of random samples (nearly 7000 random points for the 500-year return period peak flow and around 3600 random points for the 100-year return period). The mean, median, mode, standard deviation, variance and Nash-Sutcliffe efficiency index were calculated and compared for analysis purposes. Box plots were used to explore the spatial distribution behavior of different levels of depth errors. First, error location points were classified depending on the distance to the river bank with classes of 100 m width. Then, a boxplot was graphed for each spatial class. Distance bands to the  
Figure 5: Map showing the spatial distribution of the [PERSON]’s \(n\) value best fit option along the Douro River channel in Zamora city, Spain. The [PERSON]’s \(n\) value best fit was found from the relationship between the channel bathymetry differences (“real scenario”–“LiDAR scenario”) and the flow depth differences.  
river were computed using the Near ArcMap tool [48]. The Matplotlib library [49] from Phyton software was used to perform a descriptive and graphical statistical analysis.  
The Nash-Sutcliffe efficiency (NSE) index was used as given in Equation (3):  
\[\text{NSE}=1-\frac{\sum_{\text{i=1}}^{\text{n}}(\text{D}_{\text{m}}-\text{D}_{ \text{o}})^{2}}{\sum_{\text{i=1}}^{\text{n}}(\text{D}_{\text{o}}-\overline{ \text{D}}_{\text{o}})^{2}} \tag{3}\]  
where \(\text{D}_{\text{m}}\) is the flow depth value of the modelled \"LiDAR scenario\", \(\text{D}_{\text{o}}\) is the flow depth value in the \"real scenario\" and \(\overline{\text{D}}_{\text{o}}\) is the mean flow depth value for the \"real scenario\".  
Furthermore, the flood inundation extent that resulted from each calibrated [PERSON]'s n model was also compared with the \"real scenario\" model using the F-statistic, as given in Equation (4):  
\[F\,statistic=\frac{A_{Lr}}{A_{L}+A_{r}-A_{Lr}}\times 100 \tag{4}\]  
where \(A_{L}\) is the observed inundation area (inundation area of the reference model in this case, \"real scenario\"), \(A_{r}\) is the modelled inundation area (\"LiDAR scenario\") and \(A_{Lr}\) is the area that is common to both the \"real scenario\" and the \"LiDAR scenario\" inundation maps.  
The F-statistic index, which was previously used in [23; 29; 50; 51; 52], allowed us to compare floods throughout the inundation extent resulting from each hydrodynamic model, where the hydrodynamic models differed was in the bathymetry data (as previously used) or in the Manning's \(n\) value at the main river reach (as was used here). A value of 100 meant a perfect match between the observed and predicted areas of inundation, and a lower F indicated a discrepancy between the two.