The proposed framework was applied to the Santarém district in central Portugal (
Figure 2), which lies along the Tagus River. The lower valley of the Tagus River is where the more extreme flood events in Portugal have occurred in recent decades, which have resulted in an extensive floodplain (over 800 km
2) being completely submerged [
31]. Therefore, this case study is considered appropriate for the demonstration of the framework, since indirect impacts on the road network because of closed roads throughout one to several days frequently occur. Moreover, given the strategic importance of the Tagus valley to agriculture and groundwater resources within Portugal, flooding events have led to significant economic consequences, as well as harmful social and health conditions [
32]. Thus, the application of the integrated framework will provide insights regarding the behavior of the road network under this type of disruptive event, which will endorse the definition of priority plans for enhancing the resilience of the transportation system in that area.
4.1. Flood Model
The case study area of Santarém 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.
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), Ómnias (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 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. Based on the streamflow measured, i.e., 5470 m
3/s, it can be stated that this event has a high probability of occurrence (the estimated 20-year return period peak flow at Almourol hydrometric station is around 10,000 m
3/s). Damage surveys provided by the Portuguese National Authority of Civil Protection recorded the submersion of several national and municipal roads in the Santarém region, beginning on the 24 and until 29 November 2006. Therefore, this flood event with an approximate duration of five days was selected for demonstrating the proposed framework. Since the flood event has a high occurrence probability, the water-depth hazard map corresponding to a 20-year return period was used for both the flood model for static and dynamic traffic integration (see
Figure 4a). Moreover, the instantaneous water level measurements from the period of analysis at each station were retrieved from the SNIRH database (
Figure 4b). Thereby, through the application of the methodology, both the static and the dynamic characterization of the flood event were achieved. It is worth noting that the impact of a flood depends on several factors, including water depth, flood duration, the spatial extent of inundation, and water velocity [
34]. These factors were considered explicitly in the methodology except for water velocity. However, the flood event under analysis conducts to flow velocities lower than 1 m/s. Therefore, the flood intensity and its impacts are driven mainly by the water depth [
8]. Thus, the assumption of using the water depth to perturbate the road network is reasonable.
More detailed and precise models can be employed to derive the flood propagation information, i.e., the spatial and temporal attributes of the flood event. However, because of the Tagus River basin extent (approximately 25,000 km2 in Portuguese territory) and the demand for detailed data to develop precise hydrologic and hydraulic models for different time steps of the flood event such as digital elevation model (DEM), Manning roughness coefficients, among others, render the use of more sophisticated models a time-consuming task with elevated computational cost, which are beyond the objective of this research. Therefore, the methodology conducted based on data from past events is sufficient for illustrating the proposed dynamic integrated framework for indirect impact quantification of flooding. Nonetheless, the framework supports the updating of the employed models for more advanced and accurate ones, and thus the analysis can be easily updated in the future if such models are made available.
4.2. Traffic Model
All traffic models comprise two main parts, which are the traffic supply and the traffic demand. Traffic supply determines the capacity of the infrastructures, whereas traffic demand describes the behavior of travelers. Traffic modelling simulates how these two components interact with each other. In the current study, the Open Source “Simulation of Urban Mobility” (SUMO) [
35] software is used for developing the traffic model.
The analyzed network consists of 7025 links and 879 nodes. Links have multiple attributes including, but not limited to, the free-flow speed, number of lanes, and capacity. The geometric configuration of the model includes 917 traffic assignment zones. The static origin/destination (OD) matrix included 462,720 vehicles in a day. Based on the initial static OD matrix and using the od2trips tool of SUMO, a time-dependent OD matrix was estimated. The od2trips is a program that generates trip tables from the OD matrix and assumes that the matrix is coded as the number of vehicles that travel from one district or traffic assignment zone (TAZ) to another in a certain time. In traffic demand modelling, a trip is defined with starting point (origin), end point (destination) and beginning time. The traffic demand data of the pilot zone was obtained from Infraestruturas de Portugal (IP), the Portuguese transportation infrastructures management. A constant demand was assumed, i.e., users do not change their travel mode because of the flooding.
Od2trips allows splitting OD matrices, which define a long time period, into smaller parts that contain definite percentages of the whole. It is possible to split the matrix into 24 subparts—this means the number of fields is fixed to 24—allowing to spread an OD matrix over a day describing it by hours. In dependence to the week day and the type of traffic, one could set the appropriate time line. Some common daily time lines from Germany are retrieved and could be found in SUMO documentation [
20]. In the current paper since there is no available information regarding daily time lines from Portugal, data from Germany were used to determine the vehicles distribution over time during the simulation to approximate rush-hour flows.
Figure 5 depicts the number of vehicles introduced to the network over time during the simulation for a 462,720-vehicle scenario.
Because of the interactions of the individual drivers during their travel through the network, the route choice and travel times are strongly coupled. The route choice is based on travel times and the travel times result from the route choice. Therefore, it is necessary to apply a model for link flows that reproduce the dynamic findings of traffic flow. In this paper, a mesoscopic simulation-based dynamic traffic assignment (DTA) model on the road network of Santarém region was performed. Traffic assignment models, especially simulation-based dynamic traffic assignment models, are commonly used in a wide range of applications, including traffic management and transportation planning [
36,
37,
38]. Route choice and network loading, as the main components of DTA models, aim to represent the dynamics of vehicle movements in a network. The Santarém road network was imported to SUMO using shapefiles of this network, which were received from IP. The evolution of the traffic flow over the links of the network once the route choice was determined are represented by network loading. Although the stability and the convergence of the simulation-based assignment algorithms usually cannot be proven, a realistic description of traffic dynamics which is essential with respect to the usability in real-world applications, could be gained.
Generally, Santarém has a robust road transportation system, but there is a factor that may affect mobility in this network. Since drivers may not be permitted to make a U-turn before passing through a flooded part of the roads, the existence of a large number of one-directional roads could limit rerouting options. Following the definition of trips, a route assignment model should be used to compute the most likely routes to connect origins and destinations. This model was represented by an incremental assignment that is an alternative to the iterative user assignment. In this case, each vehicle computed a fastest-path computation at the time of departure that prevented all vehicles from driving blindly into the same traffic jam. As a result, rather than assuming that cars travel in an isolated manner, their travel times were calculated as interacting participants of the travel system. The basic assumption in this paper was that drivers have complete knowledge of the road network, which is reasonable to assume in commuter traffic.
4.3. Validation and Verification of Results
Because of the lack of traffic data during the flood situation, the model could be validated with the average travel time of the typical traffic for a day that was obtained from IP. The calibration of the traffic model was achieved by comparing the estimated average travel time matrices between TAZs for all of the departed vehicles from one TAZ to another. To this end, this matrix was compared to the IP results matrix. Then, one of the most common metrics to measure the forecasting accuracy of a model, which is mean absolute percentage error (
MAPE), was calculated. The formula to calculate the
MAPE is as Equation (1):
where
n is the number of fitted data,
is the travel time reported by IP,
is the predicted travel time. This measure is estimated to be 12%. Overall, this measure indicates reasonable prediction fits. Therefore, it can be said that the potential uncertainties of the model and concerns about its accuracy in the next stages of the model integration with flood spots decreases.
Table 1 shows the estimated average travel times received from IP and predicted values in the current research for the first 10 TAZs in the network. The average travel times in
Table 1 are rounded to the closest minute.
It is worth mentioning that the applied method in the current research for validation of results is similar to that published in Bhat [
39]. In addition, the model results can be verified in case of disruption, but at the moment those are credible predictions but not validated. Although a higher uncertainty is found for the situation where the disruption took place, the framework presented in this paper demonstrates the potential of combining flood maps and traffic models to estimate the probable consequences of changes. It also indicates that impact of flooding includes the time it takes for the network to be recovered in addition to the time when there is standing water on the road surface.