## 4 Materials and Method
### Flood Model  
The case study area of Santarem is particularly prone to progressive floods, i.e., those caused by prolonged heavy rainfall in large basins such as that of the Tagus River [32]. Hazard maps for flood scenarios with return periods of 20, 100 and 1000 years, related to events with a high, medium, and low probability of occurrence, respectively, were elaborated for Portugal within the scope of the EU directive 2007/60/CE on the assessment and management of flood risks. The maps are accessible to the general public on a Web GIS portal and include the delineation of the flood extent, the water depth, and the flow velocity for each scenario. Historical time series of precipitation and annual maximum instantaneous stream flows were used to build hydrological and hydraulic models for flood calculation [3]. The methodology implemented for obtaining flood models for static and dynamic integration is shown in Figure 3. For the case of static integration between the flood and the traffic model, the water-depth hazard maps were used to identify the closed links through geographical coincidence with the road network, since the goal was to simulate the disruption effect in the days following the flood event and it is assumed that the flooded links remain closed to traffic because of cleaning up and/or repairing works. Conversely, for the dynamic integration, flood maps at different time steps during the event are needed to analyze the spatial-temporal evolution of the flood. The latter is required to estimate the impacts on road traffic during the event. To this end, the proposed methodology builds on water-level measurements from past flood events to characterize the progression of the flood. Figure 2: Location of the case study area in Portugal. After identifying the affected links using the water-depth hazard maps, the next step consisted of selecting a hydrometric station for each link following a geographical proximity criterion. The main assumption here was that the temporal evolution of the water depth in the link follows the same shape of the instantaneous water levels measured at the closest hydrometric station. Subsequently, the base water level was removed from the recorded measurements to determine the portion corresponding to the flood event itself and, afterwards, the obtained values were normalized by the peak water level at the hydrometric station. At the same time, the maximum water depth at each flooded link was extracted from the overlapping of the water-depth hazard map with the road network. Lastly, the normalized curve was multiplied by the maximum depth found for each link. In this manner, the temporal series of water depth were defined at each time step for every flooded link and were later interpreted as speed reductions or road closures in the traffic model. For the application of the methodology to the case study, instantaneous water levels and annual maximum stream flows measured at six hydrometric stations over the Tagus River (see Figure 4a), namely Ponte de Abrantes (17H/03H), Tramagal (17H/02H), Almourol (17G/02H), Ponte Chamusca (17G/07H), Omnias (18E/04H) and Morgado (19E/02H), were retrieved from the National Water Resources Information System database (SNIRH, Lisbon, Portugal) [33]. The oldest available records at some of the stations (e.g., Tramagal and Almourol) date from 1990 while the oldest records available at others (e.g., Chamusca) date from 2002. However, there are large periods of unavailability of data in several stations, and some of them are allegedly out of service since the latest records  
Figure 3: Methodology for producing flood models for static and dynamic integration. date from 2010. Consequently, only records from the period between 2002 and 2010 were considered for further analysis. During this period, the highest instantaneous streamflow was recorded in Almourol hydrometric station, on 25 November 2006.