## 1 Introduction  
The occurrence of natural hazard events, such as floods, has led in the past to severe impacts to transportation networks and consequently to its users and the society that relies on their proper performance [1]. For instance, in December 2019 two major storms struck the Iberian Peninsula in less than a week, causing severe winds and floods. In central Portugal, the heavy rain disrupted train services after flooding of the rail tracks, brought down power lines, cutting electricity to thousands of citizens, and caused disruption and damages to road infrastructures, namely embankments, slopes, and culverts. The impacts were estimated at EUR7.7 million by the Medio Teleo Intermunicipal Community, an organization that supports local municipalities in regional planning [2]. This region has been identified by the Portuguese Environment Agency (APA) as the river basin district with the largest proportion of affected population due to floods, and thus where the greater investments are needed to implement measures to reduce the impacts of these events [2]. In fact, within the plan of measures to elaborate for the period between 2016 and 2021, a total of 81 measures, estimated at EUR70 million, were needed [3]. The proposed measures, ordered from the highest to the lowest investments, varied among structural measures, green measures, exposure reduction, vulnerability reduction, and learning and recovery. Thus, a deeper understanding of compound interactions between the system's inherent vulnerabilities and the hazard features could lead to cope better with floods.  
Risk reduction of a road transport network can be achieved either by decreasing direct impacts (i.e., caused directly by the flood event physical damage to the infrastructure) or indirect impacts (i.e., resulting from the unavailability of the damaged transport infrastructure, e.g., additional travel time and travel distance, and the loss of access to certain areas) [4]. In particular, the indirect impacts due to rerouting traffic, as a consequence of floods, have been found to be potentially larger than direct impacts [5]. Consequently, it is fundamental to carefully examine these impacts in order to define efficient management strategies to decrease road transport risk. The main aim of this paper is to analyze options for making the flood consequences estimation more valid.  
Previous research mostly analyzed the indirect impacts of floods by considering a static integration of the flood and traffic models [6]. This integration cannot adequately explain the events that occur when a transport system is facing a progressive flood, ignoring the domino effects of the links with reduction speed on other sectors and the whole network [7]. The static integration of the flood and traffic models produced just a binary representation of flooding, which can be a reasonable solution for assessing the effects of the flood on the transport system in the following days of the flood. Progressive flood is indeed a dynamic natural hazard that makes a complex interaction between floodwater and the transport system [7]. Therefore, in flooding duration, dynamic integration of flood and traffic may deem to provide more appropriate conclusions regarding the flood effects on the road network. In order to apply the temporal and spatial variation of traffic during the flood, the mesoscopic simulation can be used to compute vehicle movements with queues that may run up to 100 times faster than a microscopic model [8].  
The remainder of the present paper is developed as follows. Section 2 provides a brief review of the existing literature on the impacts of floods on a road network. Section 3 describes the framework for the integration model, followed by a discussion of the data source and sample used in the empirical analysis, in Section 4. In Section 5, the description of the results is presented. In the final section, conclusions and some directions for future research are put forward.