1. Introduction
Urban stormwater models are simulation tools that include algorithms and methods to describe the main physical processes related to the flow of stormwater across urban catchments. They are usually based on coupling three main modules: rainfall–runoff, overland flow and sewer flow. Rainfall is the main data input for the rainfall–runoff module that transforms it into the runoff. Runoff is then input to the overland module, which routes the flow over the urban surface area, and to the sewer flow module, which accounts for the flow in the sewer system.
Urban stormwater models can be considered semi-distributed (SD) or fully distributed (FD), depending on the spatial discretization of the rainfall–runoff module. SD models are based on subcatchment units with various land use types, where rainfall is applied and runoff volumes are estimated and routed. In FD models, runoff volumes are estimated and applied directly on the elements of a two-dimensional (2D) model of the overland surface. In SD models, conceptual empirical or physically based methods transform runoff routing into inflows hydrographs, which are applied to the selected computational nodes of the sewer system. Not every inlet is modeled but they are clustered to computational ones. FD models are based on a more realistic approach, since the generated grid-cell runoff is directly routed in the 2D overland flow module.
Traditional urban stormwater models have mostly been SD. One of the first widely implemented urban storm water models is the Storm Water Management Model (SWMM) [
1] with an initial release in 1971. It is based on the integration of a rainfall–runoff and one-dimensional (1D) sewer flow modules, and was initially developed to analyze combined sewers overflows [
2]. Later on, Ellis
et al. (1982) [
3] introduced the application of the overland flow module with the dual-drainage concept, by coupling a 1D sewer flow module with a 1D overland flow module that is known as 1D1D model. This concept was extended by Abbott (1993) [
4] with a 2D model of the overland flow, which is known as 1D2D model.
However, the use of the overland flow module only had major developments with the introduction of the Geographical Information Systems (GIS) in the end of 1990s and first decade of 2000. At first, 1D1D models were significantly improved and opened the discussion about overland flow modeling [
5,
6,
7,
8,
9]. In the late 2000s, 1D2D models become more popular with the development of technology and the increase in the computer power [
10,
11,
12,
13]. Nonetheless, rainfall–runoff modules that have been usually applied in urban stormwater modeling are commonly simplified with SD models. FD models have been typically applied in the large-scale hydrology modeling, with models like Mike SHE [
14,
15] and MOHID Land [
16,
17], amongst others. In these large-scale applications, modeled catchments usually have a larger area than the urban ones, coarser spatial resolution, and models do not take into account urban features, such as buildings and curbs.
Recent developments, however, bring new opportunities for detailed and physically based modeling of urban stormwater systems. Examples of important advancements are: increase of available data (e.g., digital map [
18], advanced collaborative sources of information [
19], weather radar data [
20]); advances in technology (e.g., remote sensing [
21], computing techniques [
22]); and improvements of numerical methods (e.g., reduction in simulation times in 2D overland modeling [
23], new mathematical approaches [
24,
25,
26]). These improvements are opening the discussion for the application of FD urban stormwater models. Infoworks ICM [
27] already implemented FD models, but its application has not yet become a standard practice in the water industry. Bailey and Margetts, 2008 [
28] discussed the potential of FD models to replace the limitations of rainfall–runoff theories adopted in SD models. By analyzing a small case study, the authors achieved similar results with SD and FD models to demonstrate the viability of FD models, but they noted that FD models may still be computationally limited for large scale catchments and should require a significant amount of detailed information to represent all roof and gully connections. Chang
et al., 2015 [
29] compared different approach setups of 1D2D models applied to a mid-size real case study. They compared flood extents with performance indicators for different models, and concluded that a combination of SD and FD models is the suitable approach for the analyzed case study; however, they noted that FD models require information which is seldom readily available and pre-processing is therefore needed to generate/estimate such information (e.g., to define building connections).
This paper presents a full-scale comparison between SD and FD urban stormwater models and suggests innovative concepts for the model building process, and to establish the connection between modules of SD and FD models. The model building process proposed assigns the same data to both SD and FD models to enable a direct comparison of the two models. The connection between modules accounts for the limited sewer inlet capacity, and enable representation of the same interactions in both SD and FD models. The comparison of SD and FD models were based on two real case studies: Cranbrook catchment, London, UK; and Zona Central catchment, Coimbra, Portugal. The Cranbrook catchment has an area of 8.5 km2 and a flat topography, hence surface water ponding is the main cause of flooding. The Zona Central is a very steep catchment with an area of 1.5 km2 and the main cause of flooding is related with the insufficiency of inlet capacity, i.e., overland and gutter flow that cannot enter the sewer system. Comprehensive and detailed analyses of modeling results were applied for both case studies. In the Cranbrook catchment, modeling results were compared with flows and water depths records in sewers. In the Zona Central catchment, flooding extents have been analyzed based on photographic records of flooding events. Models were calibrated against monitoring data and photographic records of flooding events. Further analyses are presented with design rainfall events to access the importance of surface storage in both models.
The remainder of the paper is structured as follows:
Section 2 presents insights into SD and FD modeling approaches and defines the concepts for model building and to represent the interactions between modules of SD and FD models. In
Section 3, the case studies are introduced and
Section 4 presents the comprehensive and detailed analysis of modeling results.
Section 5 presents the discussion and conclusions of the presented work.
3. Case Studies
The selected case studies are the Cranbrook catchment, in London, UK, and the Zona Central catchments, in Coimbra, Portugal. For each case study, SD and FD models were implemented in Infoworks ICM v. 5.5 [
27] based on the same 1D sewer network and 2D overland flow models (1D2D models). To enable comparison between both case studies, similar data were collected to build the models. The sewer flow model was built with the network and operational data, provided by the respective water companies of the study catchments. The 2D overland flow model was created based on available LiDAR-based Digital Terrain Models (DTM) with 1 m horizontal resolution. Buildings polygons and land use data were used to characterize the model (e.g., roughness and infiltration parameters) and to define the surface mesh (e.g., mesh resolution, break lines, voids, and boundaries). The land use data were obtained from the OpenStreetMap [
19] and buildings polygons were provided by local authorities. The SD models for these case studies have been developed and updated since 2010 and 2009, respectively [
34,
36]. These SD models were improved and calibrated following the UK standards [
37] using local rainfall and flow records. The FD model for both case studies was developed with the exact same data as the calibrated SD model, following the methodology presented in
Section 2, so as to achieve comparable models.
3.1. Cranbrook Case Study
The Cranbrook catchment is located in the North-East part of London, UK, and is presented in
Figure 4. It is predominantly urban (residential and commercial units), with some open green spaces. It covers an area of 8.5 km
2 with an average slope of 5%. The stormwater sewer system is nearly 98 km long; it is mainly separate and discharges into the Roding River. This catchment has suffered several floods during recent years (e.g., in 2000 and 2009), which have affected hundreds of properties.
A real time monitoring system has been operated in the Cranbrook catchment since April 2010 (
Figure 4b). It includes four rain gauges, three water level sensors (one in sewers and two in channels) and two flow gauges in sewers that record water depth and velocity. The most upstream sensor (Barkingside) was installed in December 2014, and covers a limited area of 2 km
2 that is mostly residential. Valentine sewer and Valentine channel sensors are located almost in the middle of the catchment, with upstream drainage areas of 5.0 and 5.5 km
2, respectively. As the names suggest, one sensor is installed in the sewers entering Valentine Park and the other on an open channel in the Park. Cranbrook sewer is a sensor installed in the downstream area and covers most of the catchment area (8.0 km
2). There is also a level gauge in the main discharge of the catchment to validate the outfall conditions, since they can be influenced by the level of Roding River.
Figure 4.
Cranbrook case study—London, United Kingdom: (a) DTM (Digital Terrain Model) and network data. (b) Monitoring stations and upstream network: (b1) Barkingside (flow and depth sensor); (b2) Valentine sewer (depth sensor); (b3) Valentine channel (depth sensor); and (b4) Cranbrook sewer (flow and depth sensor).
Figure 4.
Cranbrook case study—London, United Kingdom: (a) DTM (Digital Terrain Model) and network data. (b) Monitoring stations and upstream network: (b1) Barkingside (flow and depth sensor); (b2) Valentine sewer (depth sensor); (b3) Valentine channel (depth sensor); and (b4) Cranbrook sewer (flow and depth sensor).
The SD and FD models for the Cranbrook case study include a 1D network based on a sewer system with 2596 conduits and 2546 manhole nodes. The conduits have an average slope of 1% and cross sections with diameters ranging from 100 mm to 1950 mm. The 1D network also includes 565 m of open channels with cross sections of up to 6 m width, and five storage ponds, four of which are recreational lakes. The SD rainfall–runoff model has 4409 subcatchments with areas ranging from 50 m2 to 40 ha, and average of 0.2 ha; slopes are varying from 0.015 m/m to 0.408 m/m with an average of 0.05 m/m, and widths are ranging from 4 m to 357 m, with an average of 22 m. It considers initial losses dependent on subcatchments’ slopes and the Wallingford routing model. Infiltration losses are estimated for both SD and FD models with fixed runoff coefficients. The overland flow module, which defines the resolution of the FD model, is based on a 2D mesh with 117,712 elements with areas ranging from 25 m2 to 992 m2 and mean of 61 m2.
3.2. Zona Central Case Study
The Zona Central catchment is located in Coimbra, Portugal (
Figure 5). It covers highly urbanized zones, mainly residential and commercial, including the downtown area of Coimbra, where important services and historical buildings are located. It has a total drainage area of approximately 1.5 km
2 with an average slope of 24%. The sewer system is nearly 35 km long, most of which is combined and discharges into the Coselhas brook and into the Coimbra Waste Water Treatment Plant, from where it is further directed to Mondego River. This catchment has suffered several floods during recent years, the occurrence of which is exacerbated by the steep topography and the limited inlet capacity of the sewer system. The area at highest risk of flooding is the Praça 8 de Maio (
Figure 5b), a square in the center of the catchment, where important services are located (e.g., City Council and tourist attractions) and where flood waters tend to pond due to topographic conditions.
Figure 5.
Zona Central catchment—Coimbra, Portugal: (a) sewer network, DTM and monitoring point locations; and (b) extents of Praça 8 de Maio.
Figure 5.
Zona Central catchment—Coimbra, Portugal: (a) sewer network, DTM and monitoring point locations; and (b) extents of Praça 8 de Maio.
A monitoring campaign was conducted in this catchment between 2010 and 2012 by Simões, 2012 [
36]. The campaign included three rain gauges and two water depth sensors. The latter were located along the main sewer, upstream of the Praça 8 de Maio, covering drainage areas of 0.4 km
2 in the “Mercado” station and 1.0 km
2 in the “Praça da Républica” gauges (
Figure 5a), respectively. In addition, the water utility of the area—AC, Águas de Coimbra E.M.—has maintained a single rain gauge in the catchment for several years (since approximately 2005); from this gauge continuous rainfall records are available, including records of flood-generating storms. The data collected between 2010 and 2012 were used to calibrate the SD model and the rain gauge records collected by Águas de Coimbra are used as input for the flood simulations presented in this paper.
The SD and FD models for the Zona Central case study are based on a 1D sewer network model comprising 1016 conduits and 1014 manhole nodes. The conduits have an average slope of 5% and cross-sections with dimensions ranging from 200 mm circular diameter to closed rectangular section of dimensions 3.5 × 1.7 m2. The SD rainfall–runoff model has 911 subcatchments with areas ranging from 50 m2 to 4.8 ha and a mean of 1722m2, slopes ranging from 0.00 m/m to 1.13 m/m and a mean of 0.24 m/m, and widths ranging from 6 m to 493 m and a mean of 51 m. In the SD model, initial losses are given as an absolute value and runoff volumes are routed to subcatchments’ outlets using the SWMM routing model. For both SD and FD models, infiltration losses are estimated with the Horton equation for pervious areas, whereas a fixed runoff coefficients approach was adopted for impervious areas. The overland flow module, which defines the resolution of the FD model, is based on a 2D mesh with 10,741 elements, with areas ranging from 25 m2 to 678 m2, with a mean of 89 m2.
5. Discussion and Conclusions
This paper presented a comparison between SD and FD models using two real case studies with different characteristics and flooding mechanisms. Innovative concepts were proposed for the model building process and to establish the connections between the modules of SD and FD models.
FD models were generally found to inaccurately retain runoff volumes on the overland surface due to surface depressions, buildings singularities, and the lack of representation of private connections to the sewer network. This has not been observed in the SD model, since the runoff is directly discharged from subcatchments to network nodes. While surface depressions and buildings singularities are dependent on the resolution of the overland surface module, the lack of connection to the minor system relies on the resolution on the sewer flow module.
In the overland flow module, surface depressions are related with the surface overland definition and buildings singularities are dependent on the definition of building boundaries. In the Cranbrook case study, surface depressions are the main cause of retaining water on the overland surface and the differences between SD and FD models can be neglected for high intensity rainfall events. In the Zona Central case study buildings singularities accumulate significant runoff volume, traducing significant differences between SD and FD models, even for high intensity rainfall events. This implies that FD models are likely to be inaccurate in highly urbanized areas with dense buildings zones characterized by several singularities and delimited private areas, which could retain runoff volumes.
The resolution of sewer network data defines the connections between the overland flow and sewer flow modules. In addition to the typically available data of the public sewer network, as used in the analyzed case studies, FD models should also include information on private networks and connections that drain areas delimited by buildings. However, these data are difficult to obtain for most studies and can make the sewer flow module very complex. An alternative is to define the FD model only for open areas (without buildings, e.g., roads and green areas), combined with SD approach for the other areas in the catchment. In any case, setting up a combined SD and FD model depends on the case study and could require pre-processing to decide which areas should be SD or FD.
It should be mentioned that the overland module usually considers a minimum water depth threshold that can also traduce differences in runoff generation on FD models. Usually, a minimum water depth threshold defines the wetting and drying mechanism for numerical stability, and in the presented models this threshold was considered 1 mm. If the water depth at a given 2D surface element is below this limit, any water falling over the given element is stored in it until the threshold is reached, and only mass conservation is considered. This threshold can increase the depression storage of both SD and FD models and can reduce the runoff generated by FD models for events with low rainfall depths. However, the rainfall events tested in this paper makes this volume insignificant. The defined threshold is much lower than the rainfall depth of the storm events under consideration and is smaller than the depression storage considered in the SD subcatchments.
In conclusion, physically based FD models are more realistic, avoiding the simplifications and spatial data aggregation of hydrological models applied on a subcatchment level in SD models. Nevertheless, the necessary resolution and accuracy of the available data requirements, either to define modules connections, hydrological characterization, or even to do a proper calibration, are significantly higher for FD models. In cases where detailed network data are not available and overland surface data are not accurate or do not have the necessary resolution, SD models are a recommended modeling approach. In the near future, FD models will benefit from the increase in data availability and their resolution, as well as data sources.