# Delineation of the Flooded Areas in Urban Environments Based on a Simplified Approach
## 3 Case Study and Mathematical Model
### Mathematical Model  
To set up the hydrological models for the Tulcea municipality, most of the data processing activities were performed using GIS tools based on a digital terrain model, ortho-photos, the administrative boundary of the Tulcea municipality, delineation of the urban catchments, pictures of the frequently flooded areas, and the sewage network in the.dwg format files. All the above elements used the Stereo 70 projection. Inside the urban limits, the majority of land cover is classified as a discontinuous urban area, followed by industrial units and parks or recreational areas (Figure 15). Outside the urban limits, the land cover is mainly classified as orchards and wet areas. Based on this information, the values for the CN parameter were defined in the range 75-89, depending on the location of the urban catchment. Usually, any hydrological model must be calibrated and validated using a set of recorded events at the urban catchments level. For a correct calibration besides the recorded precipitation, which represents the upstream boundary condition, registered flows at each collector output and/or at the pumping stations are necessary as the modelled downstream boundary condition. Because the multiple outputs from the system were not recorded, the calibration and validation were performed indirectly, using the storage-elevation curves and the extension of the flooded areas according to the various photos taken during the flood events. Of course, the water level in each case was approximated with variable accuracy depending on the available information. Thus, the calibration and validation are likely affected by incorporated uncertainties not yet quantified. As previously mentioned, for the calibration of the parameters, the event between 12 September 2013 10:00 and 13 September 2013 8:20 was analysed. The total duration of the rainfall was approx. 22.3 h and the amount of precipitation was 67.8 mm. When the discharge capacity of the sewage system is exceeded, excess water flows or accumulates at the ground surface. The maximum water level in the depression areas was approximated based on photos and then the corresponding accumulated volume was estimated. The calibration was considered good when the computed volume was close to the estimated volume of the depression areas. The validation was performed for the 14 June 2016 event, which had a 25.6 mm rain depth, but which also flooded the centre of the municipality. It should be mentioned that a hydrological model does not answer the real problem of water movement at the ground surface; it only evaluates the amount of water generated by each basin or sub-basin. For an accurate simulation, a 2D hydrodynamic model coupled with a 1D model for the sewage system should be adopted [33]. At the same time, a digital terrain model with a floodplain topography at 1-m or finer resolution and high horizontal and vertical accuracy is needed. Figure 15: CLC classification of land cover for the Tulcea municipality. The simulations, both for the recorded events and for the design rainfall, were performed in two hypotheses:  
**Hypothesis 1 (H1). **: _The sewage system is 100% non-operational (or the streets do not have a sewage system)._  
**Hypothesis 2 (H2). **: _The sewage system collects the overland flow up to the limit of its designed capacity._  
The simulations considering the design storm were based on the information contained in the Intensity-Duration-Frequency (IDF) curves. The IDF curves are derived through a frequency analysis of the rainfall measurements. Each year, the maximum precipitation of duration \(D\) is selected. Hence, resulting statistical series have a number of values equal to the number of years. The duration \(D\) is valued in the range 5-1440 min, with a time step of 5 min for the first 2 h and greater time steps moving forward. Each statistical series is usually analysed with the Gumbel distribution, joining the points corresponding to the same frequency results in the IDF curves.