A simplified approach for flood modeling in urban environments

Flooding in urban areas is characterized by strong intensity and a short response time that would cause enormous human and economic losses (Apel et al. 2009). With changes in global climate and urbanization, urban flood is increasing and resultant damage has been reported worldwide (Lin et al. 2014). As a consequence, it still remains a challenging issue for hydrologists and needs further investigation (Kjeldsen et al. 2013; Paz et al. 2016).

Flood dynamics across urbanized areas are difficult to understand because of the complex urban infrastructures, underlying surface conditions and drainage systems, which play important roles in flood propagation and accumulation (Leandro et al. 2016). Scientists have sought to study urban flood by means of different methodologies, including investigation of historical floods (Swan 2010), indicator-based flood assessment (Leitão et al. 2013), and numerical modeling (Liang & Smith 2015). Among these, numerical modeling is an effective and prevailing method to deal with urban flood problems at present (Leandro et al. 2009; Bach et al. 2014). Considerable progress has been made in the development and application of hydrologic/hydraulic models for urban flood simulation over the past decades. The typical models that are broadly recognized include the MIKE 21, XP-SWMM (XP Software 2013), InfoWorks RS (Salarpour et al. 2011), and so on. These models respectively use one-dimensional (1D) sewer models and two-dimensional (2D) overland models for flow routings along the pipelines and the ground surfaces covered with buildings, streets and sidewalls, and are capable of reproducing the interaction between sewer systems and overland surfaces (Seyoum et al. 2012; Willems et al. 2012). While these models are proved able to make reasonable predictions of the likely flood damage, their abilities can vary with the objective of the study, the characteristics of the study region, and data availability (Bach et al. 2014; Chang et al. 2015). It is therefore impossible to identify a universal model which is best suitable for modeling urban flood. On the other hand, the foregoing models are mostly commercial and non-open for users, which, to some extent, has hampered their widespread use. Indeed this would become a major problem for researchers or engineers who do not have access to commercial modules, due to lack of model techniques for the study of urban flood processes.

Limited attempts have been made to propose other approaches for urban flooding estimation without access to commercial modules so far. Some researchers have coupled pre-existing open-source 1D sewer models with 2D overland models (e.g. Leandro et al. 2009; Paz et al. 2016), while others have developed their own 1D (2D) models and integrated them with existing 2D (1D) models (e.g. Seyoum et al. 2012). The former approach is much more simplified and commonly used than the latter one, largely because it does not rely heavily on specialized programing knowledge. Generally, for coupling existing 1D and 2D models, researchers usually employ the open-source Storm Water Management Model (SWMM), known as a simple but robust 1D sewer model, to calculate hydraulics in pipelines (Leandro & Martins 2016). However, there is little agreement on the choice of 2D overland models. More recently, with the increasing availability of high resolution Digital Elevation Models (DEMs) and extensive use of Geographic Information System (GIS), raster-based 2D hydrodynamic models are preferable because they can be readily integrated with DEMs, simplifying model setup and post-processing (Paz et al. 2016). LISFLOOD-FP, first developed by Bates & De Roo (2000), is a raster-based 2D model that has been well demonstrated to be able to predict flood inundation (Bates et al. 2010). With relatively simple formulation, LISFLOOD-FP is easy to set up and run, computationally efficient, and suitable for non-expert users. Inspired by this, the authors firstly coupled SWMM and LISFLOOD-FP in the present research, with the aim to provide another alternative for urban flood modeling.

In the coupling 1D/2D model framework, estimation of the interacting discharge between sewer and overland models is fairly important because it has a significant impact on model performance. Previous studies have adopted weir and orifice formulas to calculate the interacting discharge (Seyoum et al. 2012; Chen et al. 2015). These formulas make an assumption of the completely open state of manholes (i.e. without covers). In the real-world, however, manholes are usually covered and their discharge capacities may be much lower than expected. In this regard, the interacting discharge may be overestimated if manholes are regarded as completely open, which could result in a large deviation in model results. Even if a model is tested to perform well in an application without consideration to the manhole cover effect, the parameter specification might be ‘unreal’ and suspicious resulting from the equifinality effect (Her & Chaubey 2015). To reveal the role of the manhole cover in modeling, in this paper the authors preliminarily discuss its effect on parameter specification and model performance in some example applications.

The paper is organized as follows: the next section describes SWMM and LISFLOOD-FP model structures and the method to couple them. Then example applications of the coupled model and the testing results are presented. Next, a brief discussion is given and finally, the conclusion is presented.

Introduced in 1971, SWMM is considered a landmark of urban hydrologic models and is broadly regarded as an efficient 1D sewer model (Delleur 2003). It is capable of simulating runoff quantity and quality according to the 1D Saint-Venant equations from primarily urban areas. In the SWMM framework, the whole study area is divided into a collection of sub-catchments that receive precipitation and generate runoff. The surface runoff in a sub-catchment flows entirely into a single outlet (manhole or any other sub-catchment) and thus there is no surface routing in SWMM. Storm water is then transported in pipes, channels, storage/treatment devices, pumps, and regulators, and finally flows toward the area outlets. In SWMM, when all pipes connected to a manhole are full of storm water, or when the water surface at the manhole is between the crown of the connected highest pipe and the ground surface, surcharging will occur. Flooding takes place when the hydraulic grade line is above the ground surface. A detailed description of SWMM can be found in earlier studies (Delleur 2003; Leandro & Martins 2016). There have been several versions of SWMM since its first release and this study employed the latest version (SWMM5) which was downloaded from https://www.epa.gov/water-research/storm-water-management-model-swmm#downloads.

LISFLOOD-FP is a raster-based hydraulic model originally developed by Bates & De Roo (2000). It can reflect the flood process and yield good prediction of maximum flood extent (Bates et al. 2010). An intelligent volume-filling process based on hydraulic principles and the key physical notions of mass conservation and hydraulic connectivity, are both used in the model, to treat flooding (Bates et al. 2010). Like SWMM, this model has been improved since its first release, and in the study the freeware of LISFLOOD-FP (V5.9.6) which was recently released was used. It is available under http://www.bristol.ac.uk/geography/research/hydrology/models/lisflood/downloads/. The basic formulations of LISFLOOD-FP (V5.9.6) are described in detail in some existing publications (Bates et al. 2010; de Almeida et al. 2012).

SWMM and LISFLOOD-FP are combined for simulating the flow dynamics in sewers and on overland surfaces. The hydrological rainfall-runoff process and flow routing in pipelines are performed through SWMM, while surcharged flows that spill onto the ground surface from manholes are routed on the 2D domain by using LISFLOOD-FP. For floodplains with river networks, LISFLOOD-FP is applied to solve 2D floodplain flows and 1D river flows.

The models are linked by exchanging information at the connecting nodes (manholes) and the 2D grids containing the manholes are regarded as the locations where the interactions occur. Given that the coupled model employs LISFLOOD-FP freeware without access to the source code (currently unavailable), the two models are executed separately and repeatedly during a complete simulation. In other words, for each execution, both models run within a small, equivalent time interval (see the timing synchronization section) and at the end of the execution the initial conditions (see the interacting discharge section) of SWMM and LISFLOOD-FP are updated for the next execution. A program is compiled on a C# platform to invoke SWMM and LISFLOOD-FP engines and force both models to exchange information during each execution process.

The time step of SWMM is fixed and can be reset before execution, however that of LISFLOOD-FP is variable and determined by the model itself and thus cannot be changed manually (Bates et al. 2010). Therefore, for each execution either the SWMM time step or the execution time of LISFLOOD-FP should be adjusted to ensure that the two models run within the same time interval and exchange information properly.

In Equation (1), is also considered as the ith execution time of SWMM.

In Equation (2), is also considered as the ith execution time of LISFLOOD-FP. Equations (1) and (2) indicate that for the ith execution, the simulation times of the two models are equivalent, enabling the two models to exchange information at the same time (Figure 1).

The coupled model was first tested on a real-world case study. The study concerns a watershed, i.e. the Shiqiao Creek District (SCD) in the downtown of Dongguan City, South China (Figure 2(a)–2(c)). This place is a nearly closed watershed and is one of the most severe flood-prone areas in Dongguan City (Wu et al. 2016), which is located along the Dongyin Canal and the Shiqiao Creek, with an approximate area of 2 km². Terrain elevations vary from 1.78 to 31.21 m and the climate regime belongs to the subtropical monsoon (Wu et al. 2017a, 2017b). The annual average rainfall and temperature are 1,770 mm and 22 °C, respectively. SCD is a highly urbanized area where urban land use accounts for over 80% of the total. The drainage system in SCD consists of the open Dongyin Canal, the closed Shiqiao Creek (covered by roads at present), as shown in Figure 2(c), and sewers. The sewers have been reinforced several times recently, yet some of the pipelines are still inadequate to drain surface storm water away, resulting in severe flooding problems.

The DEM of SCD, with a high resolution of 1 × 1 m, was processed and quality controlled by the Urban Planning Bureau of Dongguan City (UPBDC). To reflect the blockage effect of buildings on surface flows, a Google satellite image of SCD was used to delineate the building profiles from the original DEM. For building height, note that there is no need to consider the actual height in the modeling, the elevation of the building zones in SCD was set to a fixed value of 10 m (Figure 2(d)).

Hourly rainfall data used in this case study were collected from a local rain gauge operated by the Meteorological Bureau of Dongguan City. The data set contains four extreme storm events, as listed in Table 1. There are no aerial images or instrument measurements of flood extent for these four events. However, point-based field surveys of flood locations and depths are available. The surveys mainly cover zones A, B, C and D (Figure 2), where instrument measurements of flooding depths were carried out by a crew from the Water Authority of Dongguan City. The crew are specialized in flood information collection and have visited the four zones mentioned above during the storm events (Wu et al. 2017a, 2017b). Therefore, the surveys, on the whole, can estimate a reasonable set of flooding depths over these zones. With the flooding depth data, the above-ground water levels across these zones were determined, based on elevations and flooding depths. In other words, water levels in zones A, B, C and D are approximately equal to local elevations plus flooding depths (this process was done by means of GIS). Regions with water levels greater than zero were regarded as flooding and then the flooding extents over these regions were obtained (Table 2).

The drainage network data were obtained from UPBDC. Some of the pipelines and manholes were constructed around the 1940s, and are now blocked and should be neglected when modeling. Finally, the simplified sewer network contains seven outlets, 989 manholes and 990 pipelines (Figure 2(d)). In addition, this case study took the water level of Dongyin Canal as one of the boundary conditions (Figure 3), and the corresponding data were provided by the Disaster Prevention Headquarters of Dongguan City.

The SWMM time step in this study was set to a fixed value of 2s. In regard to the LISFLOOD-FP time step, an adaptive time step was used in order to avoid model instability (Bates et al. 2010). The total simulation time was 24 h covering the whole day. With respect to the boundary conditions, the Shiqiao Creek is closed and covered by roads at present and should be regarded as a sub-drain that belongs to the sewer network. Therefore, all boundaries except the fixed river level boundary (the Dongyin Canal) in the west side of the modeled area were free. Because base flow data of the sewers were unavailable in the application, the base flows in the pipelines were assumed to be zero before simulation. Given the fact that in rainy days evapotranspiration in a region is always weak due to the high humidity condition, the evapotranspiration in SCD during a storm event is negligible and was not considered in the modeling.

The major parameters that play key roles in the coupled 1D/2D model and need to be calibrated consist of Manning's coefficients of the 2D overland surface, the 1D river channel and pipelines, and the soil infiltration rate (Bates et al. 2010; Leandro & Martins 2016). These parameters were calibrated based on two historical storm events that respectively occurred on August 19th, 2005 and on March 30th, 2014 in the study area. The three metrics, i.e. RE, F statistic, and RMSE, were used for goodness-of-fit measurements between the observed and simulated flooding. The reduction coefficient proposed in the current study is also a key parameter, however it is mainly determined by Equation (3) and should be kept constant during the calibration process. The other parameters, including the depression storage depth and the Horton infiltration parameters, because they usually show little influence on simulation results (Zhu et al. 2016), were not calibrated and the default values based on the SWMM operators were used. The calibrated ranges of the aforementioned key parameters and the other parameters with default values are presented in Table 3.

Figure 4 shows the simulated flooding for the two observed storm events. Note that the simulated severely flooding sites coincide with the flood-prone areas outlined in Figure 2. Table 4 further summarizes the predicted and observed maximum flooding depths and extents for two events at the severe flooding sites. As the results show, the coupled model is capable of capturing the maximum flooding depths and extents in these regions, on the whole. The RE values of predicted extents for two calibrated events fall between −12.5% and 0, while those of the predicted extents range from −2.5 to −0.77%, with F values all greater than 0.8. In terms of RMSE, the values are between 0.7 and 0.26, which again indicates a reasonable model performance. For SCD as a whole, the RE, F and RMSE metrics are within the acceptable ranges. Figure 5 depicts the water balance (mass balance) components over the model domain for two calibration events. It is shown that the input water volume, i.e. rainfall, is approximately equal to the sum of outflow and flooding volumes. Overall, the coupled 1D/2D model is considered to perform well for two calibration flooding events, which further suggests that the calibrated values of model parameters in Table 3 are reasonable and suitable for the subsequent model validation.

After the calibration process, the coupled model was validated against another two historical flood events that respectively struck SCD on June 13th, 2008 and on May 20th, 2015. Results indicate that Zones A, B, C and D are the most severe flooding areas across SCD (Figure 6). For the two flood events, the simulated maximum flooding depths and extents at these sites are in accord with the records on the whole (Table 5). When looking more closely at the results, the relative errors of the depths vary from −16.67 to −5%, and those of the extents are between −6.67 and −0.75%. At the same time, the F statistics for these regions are generally greater than 0.8, with RMSE values within the range of 0.23–0.31. In regard to water balance, as Figure 7 indicates, no significant differences are seen in the water balance errors. These results altogether can provide confidence in model capability in predicting urban flooding.

Although simplified 2D models or coupled 1D/2D models have advantages of simulating 2D floodplain flows, computational cost, which is due to the need to adopt very small time steps to avoid numerical instabilities in relation to small water depths and surface irregularities (Paz et al. 2016), has become a main drawback of these models. Such a drawback would become more apparent when high-quality data are used (Dottori et al. 2013; Bach et al. 2014). This specific case study used detailed data sets, including rainfall data of four historical 24-h storm events, a high spatial resolution (1 × 1 m) DEM, and a complex sewer network (even has been simplified before simulation) consisting of approximately 1,000 manholes and pipelines. The application also employed a 2-s time step of SWMM along with an adaptive time step of LISFLOOD-FP, for the purpose of relatively accurate simulation. Accordingly, the model managed to run each simulation within 6 h in a 3.3 GHz Intel processor with 8 GB RAM. The 6-h runtime seems long in terms of flood prediction, but is within the acceptable range considering that detailed data sets were utilized and it is computationally demanding (Hunter et al. 2005; Dottori et al. 2013; Paz et al. 2016; Ming et al. 2017a 2017b).

The interacting discharge between sewer and surface is influenced by multiple factors, such as the size and shape of the manhole, and debris-induced blocking. It is therefore impossible to precisely measure the real discharge capacity for a manhole. In the current research the effect of manhole shape on interacting discharge is preliminarily considered and reflected by the reduction coefficient involved in the pre-existing weir and orifice formulas. The model capability of capturing the surface flow routing dynamics in the application on one hand indicates the reasonability of coupling SWMM and LISFLOOD-FP, and to some extent supports the use of such a reduction coefficient on the other.

To further assess how the reduction coefficient affects model parameter specifications and simulated results, the coupled 1D/2D model was additionally operated without considering the reduction coefficient to simulate the four historical flood events. Correspondingly, the model parameters listed in Table 3 were recalibrated against the August 19th, 2005 and March 30th, 2014 floods. The recalibrated parameter values and the simulation results were then compared to those presented earlier. It is found that the 2D surface roughness is sensitive to the reduction coefficient while other parameters are less so. As Table 6 illustrates, the upper ranges of roughness will generally increase if the reduction coefficient is not involved in simulation. The means of roughness values are larger than those with the reduction coefficient considered in the modeling. In particular, the mean roughness of building areas would increase approximately 50%. Table 7 compares the modeled results of four flood-prone areas before and after the reduction coefficient was applied to the coupled model. It is also clear that the model accuracy will decrease if the reduction coefficient is not considered. All these findings indicate that the 1D/2D model with reduction coefficient applied somewhat outperforms that without the reduction coefficient. Therefore, the effect of manhole-cover on manhole discharge capacity is indeed an important factor which may cause divergence of model parameter specifications and affect model accuracy. However, given that it is the first attempt to discuss the manhole-cover effect, the reduction coefficient and its estimation formula acquires stepwise demonstration or improvement in future work.

The coupled 1D/2D model proposed here can be readily integrated with GIS because its output file format is raster-based (Bates & De Roo 2000), and such a feature is considered convenient for model post-processing and is something that many existing coupled 1D/2D models do not have. Another potential advantage is that it does not employ commercial modules which means that it can possibly be used by all users. Also, the simple structures of SWMM and LISFLOOD-FP allow the coupled model to be set up easily, and therefore suitable for non-expert users.

It is worth mentioning that although the coupled 1D/2D model is verified to make a reasonable fit to the observed flood events, the model accuracy is almost invariably affected by various uncertainty sources derived from assumptions of modeling conditions, parameter specification and data quality (Wang et al. 2014), which have not been quantitatively investigated in this research. Therefore, substantially more validation should be carried out to further verify the model and caution should be taken when applying it to other scenarios (Ming et al. 2017a, 2017b).

This paper has sought to introduce a simplified approach for predicting urban flooding by means of coupling SWMM and LISFLOOD-FP. In the coupled model framework, SWMM is used to simulate dynamic flows in 1D sewers, while LISFLOOD-FP deals with 1D river channel flows and 2D overland flow propagation. Meanwhile, the model is able to reproduce the interaction between the sewer flow and the surcharge-induced flooding.

The real-life application results demonstrate the ability of the coupled 1D/2D model in dealing with urban flooding problems. While the successful coupling of SWMM and LISFLOOD-FP provides another approach for predicting urban flood, further studies should be done in the future, working around the model uncertainty, improvement of computational efficiency, and integration with GIS.

This work is supported by the National Natural Science Foundation of China (Grant Nos. 51579105, 51210013, 51209095); the Water Resource Science and Technology Innovation Program of Guangdong Province (2016-25); and the Science and Technology Program of Guangzhou City (201707010072).