*2.5. Calibration and Validation Process*

The calibration process consists of adapting model parameters to achieve correspondence among simulated flood behavior and recorded or observed flooding. The calibration parameters are listed in Table 2. This process trains the model concerning selected hydraulic conditions that are compared with the observed data. Specifically, the computed water levels in both the surroundings of the Metro stations' access and the tunnels were validated in this study.

TMB selects the pluvial flooding event dated 2018-09-06 as a flood event suitable for calibration purposes in two stations of Line 3 (Paral·lel and Drassanes). Throughout this precipitation, the water depth in the Metro tunnels of these two stations induced a service disruption, the presence of water already generates the false occupation phenomenon. Metro operators can remark on how risky it is to have a station open to possible water flows. However, it is the false occupation that disrupts the service. With a variable water depth in the tunnel service, although the train can pass through the station it cannot stop to pick up or drop off passengers, as it is technically incapable of stopping.


**Table 2.** Selected calibration parameters of the hydrodynamic model, including calibrated values.

A calibration method employing a large data sample is not feasible in this model, due to the water level measurements shortage inside tunnels, hence this study tests to check its performance in real-world applications after calibration and before practice utilization, as the validation phase. Validation process applies another recorded surface flood event to ensure that the model acceptably reproduces recorded results, in this case, the pluvial flooding event dated 2018-08-17. This surface flooding event affected potential water entry points to the Metro system, but regular Metro service continued. The water level was not enough for the TMB operators to set the service interruption, nor was the water accumulated in the tunnels ample for the Metro system's self-protection system to produce a disruption in service.

#### *2.6. Flood Risk Assessment under the Impact of Climate Change*

One of the most used approaches in assessing the vulnerability of underground mass transport systems is the identification of the effects of service disruptions [9], giving a primary role to the ridership flow at Metro stations. Some authors have mainly been interested in questions concerning risk assessment for Metro stations [51,52] in a holistic manner. Metro system flooding events can lead to risk conditions involving both ridership and infrastructure, for instance, its impact on passengers' stability and safety [12,53]. Other authors focus their research on the optimization of evacuation processes during flood events in underground infrastructure [54–58]. However, this study defines risk according to the interruption of the Metro service, as a result of rainwater flooding on the urban transport system.

The concept of risk used in this research encompasses the combination of hazard and vulnerability. Hazard is characterized by flooding water depths (as the intensity of the hazard) along the Metro tunnel related to design storms of different return periods (probability of flooding events). Vulnerability criterion focuses on the ridership number affected by service interruptions. Therefore, the flood risk assessment process for Metro stations involves a hazard assessment, following the vulnerability assessment, and the procedure to obtain the risk data and maps for Barcelona Metro Line 3, as Figure 7 illustrates. For the hazard assessment, one, five, 10, and 20 years return period design storms are employed as inputs for Barcelona hydrodynamic 1D/2D coupled model for this study.

These design storms were selected following the recommendations of the municipal operator of the city drainage system (Barcelona Cicle de l'Aigua, SA—BCASA). The principal criteria for establishing this hazard estimation is to ensure continuity of Metro services, as the primary concern of the Metro administrator. One of the operational thresholds which defines Metro service operation is the water depth within the Metro tunnels. Considering a flood event, after the water depth reaches 0.15 m inside Metro station tunnels, Depending on the state of the railway road track in front of the train, if there is false occupation due to water, the train would not reach that circuit because it would stop before arriving, impacting the entire line service. Through operational experience and based on technical assumptions with support from TMB, the hazard ranges are defined as follows: water depths between 0 and 0.15 m are defined as low, between 0.15 and 0.30 m as medium, and depths greater than 0.30 m are high. These values are variable in a real operation scheme and depend on the track circuit, so they are only taken as a reference.

**Figure 7.** Risk concept definition and datasets required in each stage.

For the vulnerability assessment, registered Line 3 station user entrance data, for every hour in the months November and December 2019, reflect the ridership flow, defining peak hours (18:00–19:00) and off-peak hours (12:00–13:00). Vulnerability assessment development uses ridership flows as inputs. It applies the Jenks natural breaks algorithm as a standard method for dividing a dataset into three homogenous classes; low, medium, or high. The hazard and vulnerability limits proposal and matrices are summarized in Table 3. Methods for risk assessment can be qualitative or quantitative, both having limitations [59]. To defining risk as to the probability or threat to a hazard occurring in a vulnerable area, flood risk was assessed through a risk map related to a determined scenario and return period by combining hazard and vulnerability maps. Metro stations and ridership are affected by floods in Barcelona, and their assessment defines hazard, vulnerability, and risk levels by significance levels such as "high," "medium," and "low," evaluating the resultant risk level against qualitative criteria.


Hazard range assignment relates to Metro trains' capacity to operate under tunnel flooding conditions, considering the maximum water levels for the inundation events and the consequent service disruption. For the low hazard level defined by floodwater levels between 0 m and 0.15 m, service continuity disruption starts, and the Metro operation is subject to substantial supervision until the water level reaches 0.1 m when the service might be disrupted. At the medium hazard level, service disruption is likely because trains can no longer stop, affecting service availability on affected stations. High hazard level corresponds to floodwater level exceeding 0.3 m, under this water depth condition, the rail is likely covered by water, thus services are disrupted and trains cannot ride.

The creation of risk and vulnerability maps implies multiplying the vulnerability index (1, 2, or 3, corresponding to the low, medium, and high vulnerability) by the risk index (1, 2, or 3, corresponding

to the low, medium and high). The total risk ranges from 1 to 9, where higher levels indicate a higher risk. This approach is compiled in the risk matrix shown in Table 4.


**Table 4.** The risk matrix for Metro stations and ridership.

The entry of water into the subway system due to surface flooding is since the flood levels are higher than the elevation of the Metro infrastructure, which allows access to water, e.g., ground ventilation grates and user entrances to the system. This study identifies these water entry accesses according to different rainfall conditions. It suggests some non-structural and structural measures [5], combining both as a successful strategy facing the increased risk of flooding, according to Barcelona Metro system-specific factors.
