# Urban flood prediction using a coupled 2-dimensional surface-runoff and 1-dimensional channel flow model

Floods are an increasing problem in urban areas. One potential effect of climate change are more extreme rain events, which can lead to floods. As a result peoples lives and properties are put at risk. Consequently, it is important to take measures to prevent danger and loss in affected areas. What to do with the excess water? A holistic approach is the most effective approach for precaution. In a combined sewer system, rainwater cannot be drained completely over the sewer systems or be stored in reservoirs due to technical limitations and for economic reasons. However, there is the possibility of utilizing already existing infrastructures such as parking lots or parks as temporary reservoirs. Nevertheless, safe methods for capturing the water in these areas and thus utilizing them needs to be developed. How to achieve the goal? One important tool is to predict floods through computer models. Models can help to answer the three key questions: Where does the flood occur? How can damages be prevented? How feasible and efficient are the measures to prevent damage? The quality of the results depends on the input data and the model approach used for the simulation. In this blog, we compare two model approaches that differ in the way how they calculate the rainfall runoff. The newer of both models was under development at the time of this research. Model approaches and software used Conventional punctual input models ( PI) calculate runoff on the 2-dimensional surface model basically only using punctual input from the sewer system models. Thus water occurs only on the surface near the interfaces to the sewer system. In the real-world, however, rainfall runoff is produced from streets, courtyards, and buildings. This runoff then flows to the sewer system, a body of water, or is trapped in small sinks. If there is too much water, then the sewer system cannot capture all the water. This leads to overflow from the sewers or to surface flooding as the water is no longer able to enter the sewer system. In most cases, it is a combination of both processes and the distinction between the processes is hardly possible. Comprehensive input models ( CI ) take these effects into account and thus may reflect the real world better than PI models. Clearly, a better reflection of the real world leads to better solutions for preventive measures. The CI model used for comparison is implemented in the software Hystem-Extran 2D from the Institute for Technical and Scientific Hydrology (itwh GmbH). Hystem-Extran 2D is used throughout Germany and allows calculating the flow through the sewer system as well as water levels on the surface. It contains a 1-dimensional channel network model (1D sewer model) and a 2-dimensional surface model (2D surface model) to represent the sewer systems and the surface, respectively. The two models are coupled through manholes and inlets. For rooftops, the rainfall runoff is computed over the 1D sewer model. For all other areas the rainfall runoff is computed over the 2D surface model. This means the input data is distributed comprehensive. The 1D sewer model and the 2D surface model as well as the results are visualized using ArcGIS. The PI model used for the comparison is also implemented in Hystem-Extran 2D. PI models compute the rainfall runoff completely over a 1D sewer model. The input data for calculation of the flow on the 2D surface model comes as point-sources from manholes. Figure 1 depicts how Hystem-Extran 2D visualizes a model using ArcGIS. Note that the layer for the sewer and the surface are combined for this image and are usually separately visible. Figure1 In the following, we compare the two model approaches through a case study. Case Study Both models were tested for a part of the old town of Dresden (Germany). This area was chosen as there are lots of new buildings with below ground garages as well as open spaces. Consequently, this test area is ideal as it has a huge potential for damages caused by flooding but also provides open spaces to test preventive measures. The input data is based on a rain event with a recurrence interval of 50 years which ensures that the amount of rain is large enough to cause water levels on the 2D surface model. This rain event was chosen to identify flow paths on the 2D surface model. Simulating flow in the 1D sewer model When running the 1D sewer model for the case study, the volume of water is simulated correctly. However, the hydrographs may vary between the PI and the CI model approach depending on the amount of connected areas. The smaller the overall area connected to the sewer, the larger the differences between the two approaches. Whether CI models are more suitable than PI models is subject to future work and goes beyond the scope of this study. Computing the water levels using the 2D surface model Water levels and flow velocities are computed for every time step of the simulation and every cell of the 2D surface model. Figure 2 shows the maximum water levels during the rain event in blue and marks the area of the buildings in gray. Compared to the PI model approach, the CI model approach gives a more detailed picture of the water levels. After running the simulation for the case study we find that there are two major improvements: (1) Water appears in every cell of the 2D surface model and (2) a difference in the height of the water levels can be seen. Figure 2 (1)Water appears in all areas of the 2D surface model, which is a significant improvement compared to the PI model. In the PI model approach, the water entered the 2D surface model through manholes. Therefore, sinks separated from streets through higher elevations were not reached by the water. In the CI model, the rain occurs on every cell of the 2D surface model and therefore waterreaches all sinks in the study area. Thus, it is possible to calculate how much water does not reach the sewer system and predict flow patterns including all areas. (2) In the CI model, the maximum water levels near manholes and inlets on streetsare significantly lower. This can be explained with the source of the water on the 2D surface model. Instead of point-sources on streets, the water is extensivelydistributed over the 2D surface model, but the volume remains the same. When the same volume is distributed over a greater area it leads to lower water levels, which seems plausible. Advantages and limitations of the proposed model From the time when the rain occurs on the CI's 2D surface model to the incorporation of the water in the 1D sewer model, the path of the water can be calculated in a manner that closely represents the real-world process. This has a significant influence on the simulation of the water levels in the 2D surface model. In the case study three main advantages of the CI model approach were identified: Water levels are calculated in every cell of the 2D surface model. The maximum water levels on streets are lower, which is likely but needs further evaluation. The flow in the sewer system is calculated correctly. However, there are limitations to consider. The detailed simulation of urban flooding calls for high requirements on the data. Due to a lot of effort in preparing the data we recommend to use the model approach just for small areas. Potentially hazardous areas should be identified with less detailed models, for example the 1D sewer model could be used to calculate overflow volumes separately. The objective of the CI model approach is to achieve high accuracy for the simulation of the 1D sewer model and to improve the quality of the simulation for the 2D surface model. The case study shows that this goal is reached.