## 3 Materials and Methods  
Daily peak flow records and surface topography are the two main data sources (Figure 2) used in the flood hazard and risk analysis in the city of Zamora, Spain. Figure 1: Map of the study area (Zamora city) describing its location (**a**), the main shape of the Douro River valley and floodplain (**b**), and the distribution of the urban area of the city (**c**). Source of data for (**c**) is the Iberpix geographic viewer from the Instituto Geografico Nacional of Spain. The Douro River flow data are recorded in two flow gauge stations near the study area, one located just upstream of Zamora city (gs2121) and another one about 37 km upstream in the city of Toro (gs2062). Between the two gauging stations, there is no large river mouth. The daily peak flow record of gs2121 is only 14 years long, while the gs2062 has a 44-year-long record. So, with the aim of improving the gs2121 peak flow record, annual maximum peak flow values of gs2121 and gs2062 were plotted, as was a linear regression fit with a R\({}^{2}\) value of 0.9807 (Figure 3a). Linear regression Equation (1) was used to improve and extend the gs2121 maximum annual peak flow record. \[\text{gs2121}=0.9231\times\text{gs2062}, \tag{1}\]  
The linear regression equation shows the existence of a flood wave lamination effect between both stations, with a net loss of hydrograph peak flow between them. On the other hand, the study area surface topography is publicly available as point cloud Light Detection and Ranging (LiDAR) data [31], which are filtered and classified following the American Society for Photogrammetry and Remote Sensing (ASPRS) standard classification. The vertical accuracy of the LiDAR data used is reported to be 20 cm [31]. Figure 2: Flow chart of methodological approach for probabilistic flood hazard maps of Zamora city (Spain). The Terrain and Building LiDAR class types were used to derive the Digital Elevation Model (DEM). Due to the absence of LiDAR data in the river channel (since water has a low reflectance), it was modelled from bathymetry data obtained in the form of cross-section measurements from boat-mounted echo sounders with D-GPS (Differential Global Positioning System) data acquisition. Both LiDAR and bathymetry topographic data were combined into a 1 m spatial resolution DEM. The use of Flood Frequency Analysis (FFA) is common to estimate flood design values by fitting a probability distribution to the historical (recorded) flood data series [32]. Commonly used probability distributions for FFA include the Gumbel, lognormal, log-Pearson type III, and the generalized extreme value (GEV) distributions; precisely the latter is the one proposed as the best option for the study area [33]. Distribution fitting is probably usually highly dependent on hydrologic data availability. So, longer data series can improve the hydrologic frequency calculation. However, in practice, the lengths of measured hydrologic data are generally not long enough, and probably not fully representative of the inherent variability of peak flows over time. In fact, the presence of wet and dry periods can affect the maximum annual peak flow records, and this leads to uncertainty in the design and management of water resources. This uncertainty is usually illustrated by a confidence  
Figure 3: Results of annual maximum peak flow value statistical analysis: **(a)** linear regression fit between Zamora city and Toro city gauge stations; **(b)** flow frequency analysis for the extended gs2121 maximum annual peak flow record; **(c)** quantile and confidence intervals from Monte Carlo analysis. The solid black line defines the Monte Carlo quantiles, the dashed red line shows the 50% confidence interval, the dotted green line shows the 67% confidence interval, the dash-dot light blue line shows the 80% confidence interval, the dashed dark blue line shows the 90% confidence interval, the dotted yellow line shows the 95% confidence interval, and the dash-dot pink line shows the 99% confidence interval for the 500-year return period peak flow.