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Semi- vs. Fully-Distributed Urban Stormwater Models: Model Set Up and Comparison with Two Real Case Studies Rui Daniel Pina 1,2, *, Susana Ochoa-Rodriguez 1 , Nuno Eduardo Simões 2 , Ana Mijic 1 , ˇ Alfeu Sá Marques 2 and Cedo Maksimovi´c 1 1

2

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Department of Civil and Environmental Engineering, Imperial College London, London SW7 2AZ, UK; [email protected] (S.O.R.); [email protected] (A.M.); [email protected] (C.M.) MARE—Marine and Environmental Sciences Centre, Department of Civil Engineering, University of Coimbra, Coimbra 3030-788, Portugal; [email protected] (N.E.S.); [email protected] (A.S.M.) Correspondence: [email protected]; Tel.: +44-0-20-7594-6018

Academic Editor: Andreas N. Angelakis Received: 27 November 2015; Accepted: 3 February 2016; Published: 16 February 2016

Abstract: Urban stormwater models can be semi-distributed (SD) or fully distributed (FD). SD models are based on subcatchment units with various land use types, where rainfall is applied and runoff volumes are estimated and routed. FD models are based on the two dimensional (2D) discretization of the overland surface, which has a finer resolution with each grid-cell representing one land use type, where runoff volumes are estimated and directly routed by the 2D overland flow module. While SD models have been commonly applied in urban stormwater modeling, FD models are generally more detailed and theoretically more realistic. This paper presents a comparison between SD and FD models using two case studies in Coimbra (Portugal) and London (UK). To enable direct comparison between SD and FD setups, a model-building process is proposed and a novel sewer inlet representation is applied. SD and FD modeling results are compared against observed records in sewers and photographic records of flood events. The results suggest that FD models are more sensitive to surface storage parameters and require higher detail of the sewer network representation. Keywords: urban drainage; urban pluvial flooding; urban stormwater models; fully-distributed models; semi-distributed models; rainfall–runoff modeling

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

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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 [5–9]. In the late 2000s, 1D2D models become more popular with the development of technology and the increase in the computer power [10–13]. 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 [24–26]). 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

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on photographic records of flooding events. Models were calibrated against monitoring data and catchment, flooding extents have been analyzed based on photographic records of flooding events. photographic records of flooding events. Further analyses are presented with design rainfall events to Models were calibrated against monitoring data and photographic records of flooding events. access the importance of surface storage in both models. Further analyses are presented with design rainfall events to access the importance of surface The remainder of the paper is structured as follows: Section 2 presents insights into SD and FD storage in both models. modeling approaches and conceptsasfor modelSection building and to represent theSD interactions The remainder of thedefines paper isthe structured follows: 2 presents insights into and FD between modules of SD and FD models. In Section 3, the case studies are introduced and Section 4 modeling approaches and defines the concepts for model building and to represent the interactions presents the comprehensive and detailed analysis of modeling results. Section 5 presents the discussion between modules of SD and FD models. In Section 3, the case studies are introduced and Section 4 andpresents conclusions of the presentedand work. the comprehensive detailed analysis of modeling results. Section 5 presents the discussion and conclusions of the presented work. 2. Semi- and Fully-Distributed Modeling Approaches 2. The Semiand Fully-Distributed Modeling concepts of SD and FD models areApproaches discussed in this Section, followed by the definition of

the innovative modelofbuilding andare thediscussed new sewer inletSection, representation in this work. The concepts SD and process FD models in this followedproposed by the definition of Thethe model building process and process sewer inlet for the case studies implemented innovative model building and concept the new were sewerdefined inlet representation proposed in this work.in The model building process and sewer inlet concept were forcan the be case studies implemented Infoworks ICM v.5.5 software (Innovyze: Wallingford, UK)defined [27] and replicated for any urban in Infoworks ICM v.5.5 software (Innovyze: Wallingford, UK) [27] and can be replicated for any stormwater modeling package. urban stormwater modeling package. 2.1. Conceptual Basis of Semi-Distributed and Fully Distributed Models 2.1. Conceptual Basis of Semi-Distributed and Fully Distributed Models SD models are based on the definition of subcatchment units, delineated based upon analysis SD models are based on the definition of subcatchment units, delineated based upon analysis of of the areas draining towards a given discharge point (Figure 1a). This discharge point is referred thethe areas draining towards a given discharge point (Figure 1a). This discharge point is referred to as to as subcatchment outlet, it is represented by a computational node and usually corresponds the subcatchment outlet, it is represented by a computational node and usually corresponds to a to a node of the sewer system. Each subcatchment unit is approximated by a regularly shaped node of the sewer system. Each subcatchment unit is approximated by a regularly shaped surface to surface to which uniform morphological and hydrological characteristics are assigned (e.g., area, mean which uniform morphological and hydrological characteristics are assigned (e.g. area, mean slope, slope, imperviousness, and infiltration properties). A spatially uniform rainfall input is assigned to imperviousness, and infiltration properties). A spatially uniform rainfall input is assigned to each each subcatchment. Runoff volumes are estimated for the subcatchment and are then routed to the subcatchment. Runoff volumes are estimated for the subcatchment and are then routed to the subcatchment outlet by means of a conceptual or physically-based model. The result of this process subcatchment outlet by means of a conceptual or physically-based model. The result of this process are runoff hydrographs at the subcatchments’ outlets. SD models can be implemented in 1D, 1D1D are runoff hydrographs at the subcatchments’ outlets. SD models can be implemented in 1D, 1D1D and 1D2D models. and 1D2D models. FD models are defined by a 2D overland mesh discretization (Figure 1b). The rainfall is directly FD models are defined by a 2D overland mesh discretization (Figure 1b). The rainfall is directly applied to to each 2D2D element, and the therouting routingofofsurface surfacerunoff runoff then applied each element,generating generatinggrid-point grid-point runoff, runoff, and is is then simulated directly by the 2D overland flow module. Therefore, FD models are physically-based that simulated directly by the 2D overland flow module. Therefore, FD models are physically-based that cancan replicate runoff processes more realistically. Moreover, because of the type of discretization, replicate runoff processes more realistically. Moreover, because of the type of discretization, FDFD models cancan only bebe applied models). models only appliedwith with2D 2Doverland overlandflow flow modules modules (1D2D (1D2D models).

(a)

(b)

Figure 1. Semi-distributed (a) and fully-distributed (b) models. Figure 1. Semi-distributed (a) and fully-distributed (b) models.

The main differences between SD and FD models are related to rainfall losses calculation (initial The main differences between and FD models related to as rainfall losses calculation (initial and continuing losses) and runoff SD routing. They can beare summarized follows. and continuing losses) and runoff routing. They can be summarized as follows.

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Initial losses: The main difference is related to the representation of the depression storage. Depression storage is the stormwater that is retained in small depressions on the overland surface (puddle forming) and in pores of surface materials, both in impervious and pervious areas (surface wetting) [30]. In SD models, these two phenomena are usually considered with a constant value or a single value that is subtracted directly from the rainfall and is dependent on subcatchments’ slope and surface type [31]. In FD models, due to the finer resolution, the overland flow module can account for more detailed depressions that origin puddle forming [28]. Continuing losses: The main difference is related to the infiltration modeling. Infiltration is the percentage of rainfall draining into the soil. In SD models, infiltration is estimated for each subcatchment based on soil saturation, and subtracted from the rainfall before being applied to the model. In FD models, rainfall is applied directly to the overland mesh and infiltration is estimated for each 2D element, based on soil saturation and water depth. Therefore, infiltration predicted by FD models takes into account the runoff quantity on the overland surface, and can capture infiltration into permeable surfaces of runoff routed from upstream impermeable areas. Runoff routing: In SD models, the generated runoff is transformed by the rainfall–runoff module into an inflow hydrograph that is usually applied to the sewer flow module. In FD models, the generated runoff is directly applied to the overland flow module and routed in the overland surface. SD runoff routing functions are based on both physically based as well as empirical or conceptual methods, with resolutions defined by subcatchments sizes [32,33]. FD runoff routing is simulated by applying physically based approaches with resolutions defined by the surface overland mesh. While FD models enable the representation of the real connection between impervious and pervious areas on the surface, SD models usually merge the runoff discharges to sewers from impervious and pervious area of subcatchments, unless the subcatchments are either pervious or impervious. In addition, runoff volumes captured by surface ponds are captured by FD models, since they consider the runoff on the overland mesh, whereas in SD models can neglect these volumes depending on subcatchment delineation and their discharge definition.

2.2. Model Building Process The proposed model building process was defined to assign exactly the same data to both SD and FD models. While the 1D sewer flow and the 2D overland flow modules are equally set up for both models (both SD and FD models can be based on the same 1D2D model), the rainfall–runoff module needs a different procedure to assign data to subcatchments in SD models, and to the overland surface mesh in FD models. The procedure proposed is based on assigning percentages of land use types for each subcatchment (in the SD model) and a land use category for each element of the overland surface mesh (in the FD model) (Figure 2). In SD models, each subcatchment is defined by the percentage of the land use cover (e.g., has a percentage of area covered by road, parks, etc., each surface having the modeling attributes of the defined land use type). In FD models, each mesh element is characterized by one land use type (e.g., can be considered road or park with corresponding properties). The 2D mesh should be delineated considering boundaries of land use polygons to ensure that each 2D mesh element has only one land use type. Buildings polygons can be considered as voids in the 2D mesh, and their roof runoff is modeled in the FD model as subcatchments that discharge directly to the sewer network to take into account private connections. This procedure guarantees the input of the same data for both SD and FD models, despite their different spatial resolution.

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Figure 2. 2. SD SD (Semi-distributed) (Semi-distributed) and and FD FD (fully (fully distributed) distributed) rainfall–runoff rainfall–runoff land Figure land use use assignment. assignment.

2.3. Connections between Modules and Inlet Capacity sewer system is, in limited by the of sewer inlets; The amount amountof ofwater waterentering enteringthe the sewer system is,reality, in reality, limited bycapacity the capacity of sewer nonetheless, this fact is fact not is always considered in urban drainage models. SD models can take into inlets; nonetheless, this not always considered in urban drainage models. SD models can take account the inlet capacity if the subcatchments are delineated for each sewer inlet. However, SD models into account the inlet capacity if the subcatchments are delineated for each sewer inlet. However, SD usually apply all apply the runoff estimated a given subcatchment directly into the selected computational models usually all the runoff in estimated in a given subcatchment directly into the selected node of the sewer system, without for the inlet capacityfor (Figure 3a). Neglecting the limited computational node of the seweraccounting system, without accounting the inlet capacity (Figure 3a). capacity of inlets meanscapacity that the model fails to represent stormwater that Neglecting the limited of inlets means that thethe model fails to ponding representand theflooding stormwater may occur due to limited even before runoff reaches even the sewer As a result, ponding and flooding thatinlet maycapacity, occur due to limited inlet capacity, beforesystem. runoff reaches the flooding only occurs when the sewer system surcharges. sewer system. As a result, flooding only occurs when the sewer system surcharges. as Infoworks ICMICM v.5.5 v.5.5 software [27], have the inletthe capacity FD modeling modelingpackages, packages,such such as Infoworks software [27],included have included inlet of sewer of inlets in network connected with the 2D overland mesh (Figure 3b).(Figure In general, capacity sewer inlets in nodes network nodes connected with the 2Dsurface overland surface mesh 3b). a weir or orifice equation is defined in the manhole to control the inlet capacity with the water level on In general, a weir or orifice equation is defined in the manhole to control the inlet capacity with the the surface. water level on the surface. To overcome the limited representation representation of sewer inlets in SD models, a concept based on virtual These virtual virtual nodes nodes have have an an infinitesimal infinitesimal volume, volume, nodes was developed, as represented in Figure 3c. These connected with the overland surface and with They are They also connected and are aredirectly directly connected with the overland surface andsubcatchments. with subcatchments. are also with the sewer manholes through orifices with the limited capacity of sewer inlets. Therefore, connected withnetwork the sewer network manholes through orifices with the limited capacity of sewer the inflow to the sewer system to from and overlanddischarges module is and limited by the inlets. Therefore, the inflow thesubcatchments sewer systemdischarges from subcatchments overland inlet capacity of gullies by the discharge of orifices. If the inlet capacity is exceeded, module is limited by thedefined inlet capacity of gullies curve defined by the discharge curve of orifices. If the runoff remains on the overland surface, as it cannot enter the sewer systems. In addition, flap valves inlet capacity is exceeded, runoff remains on the overland surface, as it cannot enter the sewer were adopted in the opposite direction of orifices enable runoff to flowof from the sewers onto the 2D systems. In addition, flap valves were adopted into the opposite direction orifices to enable runoff to surface model once sewer occurs. The discharge curve that defines sewer capacity is flow from the sewers ontosurcharge the 2D surface model once sewer surcharge occurs. The inlets discharge curve based on recommendations presented by Pina al. (2010) [34] andpresented Ally (2011) that defines sewer inlets capacity is based on et recommendations by[35]. Pina et al. (2010) [34] To consider the same inlet capacity in SD and FD models, the representation of sewer inlets in FD and Ally (2011) [35]. models based the on an equivalent concept as models the but representation without subcatchments (Figure Towas consider same inlet capacity in defined SD andfor FDSD models, of sewer inlets3d). in The sewer inlet definedconcept in FD models (Figure 3b)models was notbut adopted tosubcatchments guarantee the FD models was concept based ontypically an equivalent as defined for SD without same connections between both SDdefined and FDin models, making them3b) comparable. (Figure 3d). The sewer inletmodules concept in typically FD models (Figure was not adopted to guarantee the same connections between modules in both SD and FD models, making them comparable.

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Figure 3. Connections of rainfall–runoff with overland and sewer flow modules: (a) traditional Figure 3. Connections of rainfall–runoff with overland and sewer flow modules: (a) traditional connections for SD models; (b) traditional connections for FD models; (c) developed connections for connections for SD models; (b) traditional connections for FD models; (c) developed connections for SD models; and (d) developed connections for FD models. SD models; and (d) developed connections for FD models.

3. Case Studies 3. Case Studies The selected case studies are the Cranbrook catchment, in London, UK, and the Zona Central The selected case studies are the in London, UK, were and the Zona Central catchments, in Coimbra, Portugal. ForCranbrook each case catchment, study, SD and FD models implemented in 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 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 To enable comparison between studies, similar data weredata, collected to build the models. sewer flow model was built both withcase the network and operational provided by 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 respective water companies of the study catchments. The 2D overland flow model was created based on on available LiDAR-based Digital Terrain Models (DTM) with 1 m horizontal resolution. Buildings available LiDAR-based Terrain Models (DTM) with 1the m horizontal resolution. Buildings polygons polygons and land useDigital data were used to characterize model (e.g., roughness and infiltration and land use data were used to characterize the model (e.g., roughness and infiltration parameters) parameters) and to define the surface mesh (e.g. mesh resolution, break lines, voids, and boundaries). and to define surface (e.g., from mesh the resolution, break lines, voids, boundaries). The were land The land use the data weremesh obtained OpenStreetMap [19] and and buildings polygons use data were obtained from the OpenStreetMap [19] and buildings polygons were provided by provided by local authorities. The SD models for these case studies have been developed and local authorities. The SD models for these case studies have been developed and updated since 2010 updated since 2010 and 2009, respectively [34,36]. These SD models were improved and calibrated and 2009, the respectively [34,36]. models were and calibrated following thecase UK following UK standards [37]These usingSD local rainfall andimproved flow records. The FD model for both standards [37] using local rainfall and flow records. The FD model for both case studies was developed studies was developed with the exact same data as the calibrated SD model, following the with the exact presented same data in as Section the calibrated the methodology presented in Section 2, methodology 2, so asSD tomodel, achievefollowing comparable models. so as to achieve comparable models. 3.1. Cranbrook case study 3.1. Cranbrook Case Study The Cranbrook catchment is located in the North-East part of London, UK, and is presented in 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. Figure 4. It is predominantly urban (residential and commercial units), with some open green spaces. It covers an area of 8.5 km22 with an average slope of 5%. The stormwater sewer system is nearly 98 km It covers an area of 8.5 km 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 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. 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 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) (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 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 km22 that is mostly (Barkingside) was installed in December 2014, and covers a limited area of 2 km that is mostly residential. Valentine sewer and Valentine channel sensors are located almost in the middle of the 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 km22, respectively. As the names suggest, one catchment, with upstream drainage areas of 5.0 and 5.5 km , respectively. As the names suggest, one sensor is installed in the sewers entering Valentine Park and the other on an open channel in the sensor is installed in the sewers entering Valentine Park and the other on an open channel in the Park. Park. Cranbrook sewer is a sensor installed in the downstream area and covers most of the Cranbrook sewer is a sensor installed in the downstream area and covers most of the catchment area catchment area (8.0 km2). There is also a level gauge in the main discharge of the catchment to (8.0 km2 ). There is also a level gauge in the main discharge of the catchment to validate the outfall validate the outfall conditions, since they can be influenced by the level of Roding River. conditions, since they can be influenced by the level of Roding River.

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Figure 4. 4. Cranbrook Cranbrook case case study—London, study—London, United United Kingdom: Kingdom: (a) (Digital Terrain Terrain Model) Model) and and Figure (a) DTM DTM (Digital network data. (b) Monitoring stations and upstream network: (b1) Barkingside (flow and depth network data. (b) Monitoring stations and upstream network: (b1) Barkingside (flow and depth sensor); (b2) (b2)Valentine Valentine sewer (depth sensor); (b3) Valentine (depthand sensor); and (b4) sensor); sewer (depth sensor); (b3) Valentine channelchannel (depth sensor); (b4) Cranbrook Cranbrook sewer (flow and depth sensor). sewer (flow and depth sensor).

The SD and FD models for the Cranbrook case study include a 1D network based on a sewer 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 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 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 of open channels with cross sections of up to 6 m width, and five storage ponds, four of which are2 recreational lakes. The SD rainfall–runoff model has 4409 subcatchments with areas ranging from 50 m recreational lakes. The SD rainfall–runoff model has 4409 subcatchments with areas ranging from 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 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 0.05 m/m, and widths are ranging from 4 m to 357 m, with an average of 22 m. It considers initial 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 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, 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 which defines the resolution of the FD model, is based on a 2D mesh with 117,712 elements with areas areas ranging from 25 m2 to 992 m2 and mean of 61 m2. ranging from 25 m2 to 992 m2 and mean of 61 m2 . 3.2. Zona Central case study 3.2. Zona Central Case Study The Zona Central catchment is located in Coimbra, Portugal (Figure 5). It covers highly The Zona Central catchment is located in Coimbra, Portugal (Figure 5). It covers highly urbanized urbanized zones, mainly residential and commercial, including the downtown area of Coimbra, zones, mainly residential and commercial, including the downtown area of Coimbra, where important where important services and historical buildings are located. It has a total drainage area of services and historical buildings are located. It has a total drainage area of approximately 1.5 km2 approximately 1.5 km2 with an average slope of 24%. The sewer system is nearly 35 km long, most of with an average slope of 24%. The sewer system is nearly 35 km long, most of which is combined and which is combined and discharges into the Coselhas brook and into the Coimbra Waste Water discharges into the Coselhas brook and into the Coimbra Waste Water Treatment Plant, from where it is Treatment Plant, from where it is further directed to Mondego River. This catchment has suffered further directed to Mondego River. This catchment has suffered several floods during recent years, the 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

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occurrence Water 2016, of 8, 2which is exacerbated by the steep topography and the limited inlet capacity of the 8 ofsewer 20 system. The area at highest risk of flooding is the Praça 8 de Maio (Figure 5b), a square in the center of City Council and tourist attractions) andlocated where flood waters tend toand pond due toattractions) topographic the(e.g., catchment, where important services are (e.g., City Council tourist and conditions. where flood waters tend to pond due to topographic conditions.

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(b)

Figure Zona Central catchment—Coimbra, Portugal: sewer network, DTM monitoring Figure 5. 5. Zona Central catchment—Coimbra, Portugal: (a)(a) sewer network, DTM andand monitoring point point locations; and (b) extents of Praça 8 de Maio. locations; and (b) extents of Praça 8 de Maio.

A monitoring campaign was conducted in this catchment between 2010 and 2012 by Simões, A [36]. monitoring campaign was conducted in this and catchment between andThe 2012 by Simões, 2012 The campaign included three rain gauges two water depth 2010 sensors. latter were 2012 [36]. The campaign included three rain gauges and two water depth sensors. The latter located along the main sewer, upstream of the Praça 8 de Maio, covering drainage areas of 0.4 km2 were in located along thestation main sewer, the Praça 8 de Maio,gauges covering drainage areas of 0.4 In km2 the “Mercado” and 1.0upstream km2 in theof“Praça da Républica” (Figure 5a), respectively. 2 in addition, the “Mercado” station and 1.0 km in theÁguas “PraçadedaCoimbra Républica” gaugesmaintained (Figure 5a), respectively. the water utility of the area—AC, E.M.—has a single rain In gauge addition, the water utility of the area—AC, Águas de Coimbra E.M.—has maintained a single rain in the catchment for several years (since approximately 2005); from this gauge continuous gauge in the catchment for several years (since 2005); storms. from this rainfall records are available, including recordsapproximately of flood-generating Thegauge data continuous collected rainfall records records the of flood-generating storms. The data collected between between 2010 are andavailable, 2012 wereincluding used to calibrate SD model and the rain gauge records collected by Águas Coimbra are used as inputthe for SD the model flood simulations presented in this paper. 2010 andde 2012 were used to calibrate and the rain gauge records collected by Águas de The SDused and as FDinput models Zona Central casepresented study arein based a 1D sewer network model Coimbra are forfor thethe flood simulations this on paper. comprising 1016FD conduits manhole nodes. conduits haveon anaaverage slope of 5% and The SD and modelsand for 1014 the Zona Central caseThe study are based 1D sewer network model cross-sections dimensions ranging from 200 mm The circular diameter to an closed rectangular section comprising 1016with conduits and 1014 manhole nodes. conduits have average slope of 5% and of dimensions 3.5 dimensions × 1.7 m2. Theranging SD rainfall–runoff model has 911 subcatchments with areas ranging cross-sections with from 200 mm circular diameter to closed rectangular section 2 to 4.8 ha and a 2, slopes ranging from 0.00 m/m to 1.13 m/m and a mean of from 50 m mean of 1722m 2 of dimensions 3.5 ˆ 1.7 m . The SD rainfall–runoff model has 911 subcatchments with areas ranging 0.2450m/m, and 6 m to 493 m and a mean of 0.00 51 m.m/m In the model, 2 , slopes from m2 to 4.8widths ha andranging a meanfrom of 1722m ranging from toSD 1.13 m/minitial and a losses mean of are given as an absolute value and runoff volumes are routed to subcatchments’ outlets using the 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 SWMM routing model. For both SD and FD models, infiltration losses are estimated with the Horton are given as an absolute value and runoff volumes are routed to subcatchments’ outlets using the equation for pervious areas, whereas a fixed runoff coefficients approach was adopted for SWMM routing model. For both SD and FD models, infiltration losses are estimated with the Horton impervious areas. The overland flow module, which defines the resolution of the FD model, is based equation for pervious areas, whereas a fixed runoff coefficients approach was adopted for impervious on a 2D mesh with 10,741 elements, with areas ranging from 25 m2 to 678 m2, with a mean of 89 m2. 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 . 4. Results and Discussion

4. 4.1. Results and Case Discussion Cranbrook Study The analysis of the Cranbrook case study was based on three selected events, for which rainfall 4.1. Cranbrook Case Study and water depth and flow records in sewers were available. The rainfall records are summarized in The analysis of the Cranbrook case study was based on three selected events, for which rainfall Table 1, considering the average rainfall in the entire catchment area. For each event, the entire day and water depth and flow the records sewers were available. rainfall records was simulated, but only time in frame corresponding to theThe main rainfall event are wassummarized analyzed to in Table 1, considering the average rainfall in the entire catchment area. For each event, the entire day minimize errors related to the impact of the initial conditions. was simulated, but only the time frame corresponding to the main rainfall event was analyzed to minimize errors related to the impact of the initial conditions.

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Table 1. Summary of rainfall records used for the Cranbrook case study.

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Maximum Duration Total rainfall Average rainfall StartTable 1. Summary Endof rainfall records used for rainfall the Cranbrook case study. intensity (mm/h) (h) depth (mm) (mm/h) 12 December 2014 12 December 2014 Duration Maximum Total10.9 Rainfall Average Rainfall 141212 6.5 12 2 Event ID * 1:30 a.m. Start End 8:00 a.m. (h) Rainfall (mm/h) Depth (mm) Intensity (mm/h) 3 January 2015 3 January 2015 12 December 12 December 2014 150103 13.2 12 16.6 6.5 12 10.9 21 141212 3:50 a.m. 5:00 A.M. p.m. 2014 1:30 A.M. 8:00 8 January 2015 83 January 2015 3 January 2015 January 2015 150108 7.0 12 11.6 13.2 12 16.6 12 150103 A.M. 5:00 P.M. 7:303:50 a.m. 2:30 p.m. 8 January 2015 8 January 2015 7.0 12 11.6 2 150108 Note: * This code yymmdd and it is used in the next figures to reference these events. 7:30represents A.M. 2:30 P.M. Event ID*

Note: * This code represents yymmdd and it is used in the next figures to reference these events.

The balances presented in Figure 6 show the distribution of volumes among the modules for all the events analyzed. Runoff in volumes generated by the rainfall–runoff module, and theyfor were The balances presented Figure 6were show the distribution of volumes among the modules all calculated with the subcatchments discharges in SD models, and with the runoff volume generated the events analyzed. Runoff volumes were generated by the rainfall–runoff module, and they were on the 2Dwith mesh FD models. Volumes ininthe flow module werevolume calculated with the calculated theinsubcatchments discharges SDoverland models, and with the runoff generated on difference between volumesVolumes at the end of the simulation the ones the beginning of each event. the 2D mesh in FD models. in the overland flowwith module were at calculated with the difference The volumes in the sewer flow were defined by at thethe discharges in the sewer between volumes at the end of thesystem simulation with the ones beginningat of outfalls each event. The1D volumes network. in the sewer flow system were defined by the discharges at outfalls in the 1D sewer network. In all allthree threeevents, events, total runoff volumes are similar to the total combined from In total runoff volumes are similar to the total combined volumes volumes from overland overland and sewer flow modules. The insignificant differences in the total runoff volumes are and sewer flow modules. The insignificant differences in the total runoff volumes are caused by small caused by small differences in subcatchments’ areas in the SD model when compared to the differences in subcatchments’ areas in the SD model when compared to the FD model. However, in FD all model. However, in all simulations FD model retained more water on the surface in contrast to SD simulations FD model retained more water on the surface in contrast to SD model, where most of the model,iswhere mostthrough of the runoff is conveyed through the drainage system. runoff conveyed the drainage system.

Figure Volume balance Figure 6. 6. Volume balance for for the the Cranbrook Cranbrook case case study study model model runs. runs.

To further further explore explore the the source source of of water water accumulation accumulation on on the the overland overland surface, surface, the the differences differences To between FD and SD maximum volumes at the surface were divided by land use groups (Figure 7). The most mostsignificant significant differences are observed for and roads and buildings (residential, and The differences are observed for roads buildings (residential, retail and retail industrial industrial areas) zones, leading to thethat conclusion on inthe FD models is areas) zones, leading to the conclusion runoff onthat the runoff overland FDoverland models isinretained due to retainedponding due to and surface ponding and building singularities. The category “Other areas” includes surface building singularities. The category “Other areas” includes non-classified zones non-classified in the land use data that open coverareas a mixand between areas zones covered by in the land usezones data that cover a mix between zones open covered byand buildings. buildings.

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volumes on the surface generated by SD by andSD FDand models, Figure 7. 7. Differences Differencesbetween betweenrunoff runoff volumes on overland the overland surface generated FD Figure 7. Differences between runoff volumes on the overland surface generated by SD and FD distributed by land use in groups Cranbrook case study. case The bars correspond the three storm models, distributed by groups land use in Cranbrook study. The bars to correspond to theevents three models,7.distributed land userunoff groupsvolumes in Cranbrook study.surface The bars correspond to the Figure Differencesbybetween on thecase overland generated by SD andthree FD under events consideration (see Table 1). (see Table 1). storm under consideration storm events under consideration (see Table 1). models, distributed by land use groups in Cranbrook case study. The bars correspond to the three storm events under consideration (see Table 1).

As As water volumes in the sewer flow module are generally lower in FD than in SD models, FD As water water volumes volumes in in the the sewer sewer flow flow module module are are generally generally lower lower in in FD FD than than in in SD SD models, models, FD FD results tend to underestimate water depth and flows in sewers, as exemplified in Figures 8 and 99 results totounderestimate depth and flows in generally sewers, aslower exemplified in Figures and89and with results tend underestimate water depth and flows in sewers, as exemplified in Astend water volumes in thewater sewer flow module are in FD than in Figures SD8models, FD with two monitoring locations for Event 150103. These figures also show the correct calibration of two locations for Event 150103. These figures also show the correct calibration of8 initial withmonitoring two monitoring locations for Event These also show the correct calibration results tend to underestimate water depth150103. and flows infigures sewers, as exemplified in Figures and of 9 initial losses (intersection and depression storage) in both models, because flow is initialized at the losses (intersection and depression storage) in both because flow is initialized at the at same initialtwo losses (intersection and depression storage) inmodels, both models, flow is initialized the with monitoring locations for Event 150103. These figures alsobecause show the correct calibration of same time as observed In general, SD results tend to temporal pattern and time observed data. data. In general, SD results tend to temporal pattern andispeak values sameas time as(intersection observed data. Indepression general, SDstorage) results tend to predict predict temporal pattern and peak peakvalues values initial losses and inpredict both models, because flow initialized atwith the with more accuracy. more accuracy. with more accuracy. same time as observed data. In general, SD results tend to predict temporal pattern and peak values with more accuracy.

FigureFigure 8. Predicted flow and observed data in data the Barkingside gauge for Eventfor 150103—Cranbrook case study. 8. Predicted flow and observed in the Barkingside gauge Event 150103—Cranbrook Figure 8. Predicted flow and observed data in the Barkingside gauge for Event 150103—Cranbrook case study. case study. Figure 8. Predicted flow and observed data in the Barkingside gauge for Event 150103—Cranbrook case study.

Figure 9. Predicted water depth and observed data in the Cranbrook Sewer gauge for the Event Figure 9. Predicted water depth and observed data in the Cranbrook Sewer gauge for the Event 150103—Cranbrook case study. 150103—Cranbrook Figure 9. Predicted case waterstudy. depth and observed data in the Cranbrook Sewer gauge for the Event Figure 9. Predicted water depth and observed data in the Cranbrook Sewer gauge for the Event 150103—Cranbrook case study. 150103—Cranbrook case study.

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The last considerations are generalized to all the events simulated with the statistical analysis presented in Figure 10, based on the following indicators: ‚

Relative error (RE) in peak (Figure 10, left column): RE “ pVmaxobs ´ Vmaxres q {Vmaxobs

‚

(1)

where RE is the relative error in the peak results (Vmaxres ) compared to the peak in observed data (Vmaxobs ). RE was applied to flow and water depth peaks. Positive RE values indicate underestimation by the peak results and negative values imply overestimation. The RE has the advantage of being a “tangible” statistic that evaluates the performance of a critical parameter such as the peak flow or water depth. It is important to note that very large RE can be obtained when low values are evaluated, even if the absolute difference in peak is small. In general, for all simulated events the RE is higher in FD than in SD models, which means that FD underestimates results against observed data. In the Cranbrook sewer sensor, the SD model predicted accurate water depths but overestimated flows. This can be due to the location of the sensor in a zone where turbulence can occur and affect monitoring data accuracy. In the FD model this variation does not occur, because both water depth and flows results are smoothened and underestimated. In conclusion, while the SD model captured water depth and flow peaks, the FD model underestimated these results. Coefficient of determination (R2 ) (Figure 10, middle column) and Regression coefficient (β) (Figure 10, right column): Resulting from a simple linear regression analysis applied between each simulated results time series and the observed data. These two statistics provide an indication of how well the results replicate observed data, both in terms of pattern (R2 ) and accuracy (β). The R2 measure ranges from 0 to 1 and describes how much of the observed data variability is according with the simulated results. In practical terms, R2 provides a measurement of the similarity between the patterns of the observed data time series and the simulated results time series, i.e., indicates how the hydrodynamics are captured by the model. The regression coefficient, β, is employed to provide supplementary information to the R2 . β « 1 represents good agreement in the magnitude of observed data and results time series; β ą 1 means the results are overestimated against observed data (by a factor of β); and β ă 1 means the results are underestimated against observed data (by a factor of β). For most simulated events, the R2 is close to 1 for both SD and FD models, which implies that the variations of modeling results match the observed data, i.e., the models can capture the hydrodynamics of observed data. The differences between SD and FD models are not so evident, but FD models tend to have higher R2 , which suggest that they have the potential to better represent the dynamic behavior of stormwater flows in urban catchments. The β is in general closer to 1 for SD model results, which indicates that SD results are matching the observed data more accurately than FD ones. The exceptions in the results analysis can be noticed in the data for the Valentines and the Cranbrook Sewer sensors. For the Valentines Sewer sensor, network elements tend to overestimate water depths in the SD model. For the Cranbrook Sewer sensor, the errors in observed flow data due to turbulence also affect this indicator as verified for the RE. These two aspects are not verified in the FD model as it underestimates overall results. Combining the R2 and the β results, it can be concluded that SD and FD models capture the hydrodynamics registered and the SD model tend to capture the magnitude of observed data while FD model underestimates it.

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Coefficient of determination (R2)

Regression coefficient (β)

Cranbrook sewer

Valentine channel

Valentine sewer

Barkingside

Relative error in peak (RE)

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Figure10. 10. Statistical Statistical analysis analysis of of modeling modelingresults resultsagainst againstobserved observeddata dataof ofCranbrook Cranbrookcase casestudy. study. Figure

4.2.Zona ZonaCentral CentralCase CaseStudy Study 4.2. Theanalysis analysisofof Zona Central study was based onflooding four flooding events forrainfall which The thethe Zona Central casecase study was based on four events for which rainfall records and photographic records of the flooding in Praça 8 de Maio were available. The records and photographic records of the flooding in Praça 8 de Maio were available. The rainfall rainfall are records are summarized 2, considering the average rainfall the entire catchment records summarized in Tablein2,Table considering the average rainfall in thein entire catchment area.area. The balances presented in Figure 11 show the distribution of volumes between the modules for The balances presented in Figure 11 show the distribution of volumes between the modules for all the all theanalyzed, events analyzed, in accordance to thepresented analysis presented before for the Cranbrook case events in accordance to the analysis before for the Cranbrook case study. In thisstudy. case In this case study, FD models also tend to have higher water volumes at the 2D overland surface study, FD models also tend to have higher water volumes at the 2D overland surface than in SD models, and than in SD models, and less volume discharged by the outfalls of the 1D sewer network. However, in less volume discharged by the outfalls of the 1D sewer network. However, in this case study the differences this caseSD study SD and FD are not as significant for is the Cranbrook between andthe FDdifferences models arebetween not as significant as models for the Cranbrook catchment.as This because the catchment. This is because the rainfall events selected caused floods in both SD and FD rainfall events selected caused floods in both SD and FD models, which increased the overland models, surface which increased overland in the SD model. There are also insignificant volumes in the SD the model. There surface are also volumes insignificant differences in the runoff volumes caused by differences in theinrunoff volumes by small of differences in buildings’ at the boundary of small differences buildings’ area caused at the boundary the catchment in the FDarea model. the catchment in the FD model.

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Water 2016, 8, 58 Event Start Event name* Start name*

Table 2. Summary of rainfall records in Zona Central case study. Table 2. Summary of rainfall records in Zona Central case study.

Total Average Maximum Total Average Duration rainfall rainfall Maximum End rainfall Duration rainfall rainfall (h) depth intensity End rainfall (mm/h) depth intensity Table 2. Summary of rainfall(h) records in(mm/h) Zona Central(mm) case study. (mm/h) (mm) (mm/h) 9 June 2006 9 June 2006 4:30 060609 1.7 144.0 36.6 22.0 92:50 June 2006 9 June 2006 4:30 p.m. p.m. Average 060609 1.7 144.0 36.6 22.0 Total Maximum 2:50 p.m. p.m. 2006 Rainfall Event 25 October Duration 2006 25 October Rainfall Rainfall Start End 061025 5.0 (h) 102.0 56.6 11.3 Intensity Name * 2512:30 October 25 5:30 October a.m.2006 a.m. 2006 Depth (mm) (mm/h) 061025 5.0 102.0 56.6 11.3 (mm/h) 12:30 a.m. 5:30 a.m. 21 September 9 June2008 2006 9 June 2006 21 September 22.0 060609 21 September 080921 2008 2.2 1.7 60.6144.0 21.436.6 9.9 4:30 P.M. 21 September 2008 3:10 2:50 p.m.P.M. 080921 2008 2.2 60.6 21.4 9.9 5:20 p.m. 25 October 2006 25 October 2006 3:10 p.m. 061025 5.0 102.0 56.6 11.3 5:20 p.m. 24 December 12:30 A.M. 5:30 A.M. 24 December 2013 131224 2013 31.5 48.9 4.3 21 September 2008 2421December September 2008 11.3 2.2 60.6 21.4 9.9 080921 24 December 6:40 a.m. 2013 3:10 P.M. 5:20 P.M. 131224 11.3 31.5 48.9 4.3 6:002013 p.m. 6:40 a.m. 24 December 2013 24 December 2013 6:00 p.m. 11.3 31.5 48.9 4.3 131224 Note: *This code 6:40 represents is used in next figures to reference these events. A.M. yymmdd and 6:00itP.M. Note: *This code represents yymmdd and it is usedand in next figures reference events.these events. Note: * This code represents yymmdd it is used in to next figures these to reference

13 of 20 Return Return period period (yr.) (yr.)

50 50 Return Period 50 (yr.) 50 505 5 50 5

5 5

5

Figure 11. Volumes balance for the Zona Central case study model runs. Figure 11. 11. Volumes Volumes balance Figure balance for for the the Zona Zona Central Central case case study study model model runs. runs.

To investigate where the FD model retains water on the surface, Figure 12a presents the To investigate investigate where FD model retains on the surface, Figure 12athe presents the To thethe FDmaximum model retains water water on the Figure 12a differences differences betweenwhere FD and SD volumes the surface, surface divided bypresents the land use groups. differences between FD and SD maximum volumes on the surface divided by the land use groups. between FD and SD maximum volumes on the surface divided by the land use groups. Larger discrepancies Larger discrepancies are registered in zones covered by buildings (residential areas). This means Larger discrepancies in zones covered buildings (residential areas). means are registered zonesare covered buildings (residential areas). This means that runoff is This retained on that runoff is in retained onregistered the by overland surface in FDby models due to building singularities, as thatoverland runoff with issurface retained onmodels the surface on in FD models to building as the in FD due toponding building singularities, exemplified with singularities, Figure 12b, and exemplified Figure 12b, andoverland surface roads is notasadue significant problem, opposite to exemplified with Figure 12b, and surface ponding on roads is not a significant problem, opposite to surface ponding on roads is not a significant problem, opposite to the Cranbrook case study. the Cranbrook case study. the Cranbrook case study.

(a) (a)

(b) (b)

Figure Figure12. 12.Differences Differencesin inrunoff runoffvolumes volumeson onthe theoverland overlandsurface surfacegenerated generatedby bySD SDand andFD FDmodels modelsin in Figure 12. Differences in runoff volumes on the overland surface generated by SD and FD models in Zona ZonaCentral Centralcase casestudy: study:(a) (a)runoff runoffvolumes volumesdistributed distributedby byland landuse usetypes; types;and and(b) (b)example exampleof ofrunoff runoff Zona Central case study: (a) runoff volumes distributed by land use types; and (b) example of runoff retained retainedon onthe theoverland overlandsurface surfacein inFD FDmodels modelsdue dueto tobuilding buildingsingularities singularities. retained on the overland surface in FD models due to building singularities

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The comparison of floodplains generated in the Praça 8 de Maio is summarized in Table 3 for all The comparison of floodplains generated in the Praça 8 de Maio is summarized in Table 3 for the events analyzed. In general, flooding volumes are higher in SD than in FD model, and water all the events analyzed. In general, flooding volumes are higher in SD than in FD model, and water depth and flooding areas follow the same pattern. This means that as FD model stores more water depth and flooding areas follow the same pattern. This means that as FD model stores more water on the overland surface, runoff volumes are retained in the upstream areas and do not get to lower on the overland surface, runoff volumes are retained in the upstream areas and do not get to lower zones where water accumulates in reality. The predicted floods at Praça 8 de Maio were also zones where water accumulates in reality. The predicted floods at Praça 8 de Maio were also compared compared to photographic records of floodplains, as presented in Figure 13 for the events with the to photographic records of floodplains, as presented in Figure 13 for the events with the two highest two highest return periods. It can be concluded that flooding extent is well predicted with the SD return periods. It can be concluded that flooding extent is well predicted with the SD model, but model, but underestimated with the FD model. underestimated with the FD model. 061025

Photo evidence

060609

(b)

SD model

(a)

(d)

(e)

(f)

FD model

(c)

Figure13. 13.Comparison Comparisonofofphotograph photographrecords recordswith withpredicted predictedfloodplains floodplainson onPraça Praça88de deMaio, Maio,Zona Zona Figure Central case study. (a) Flood registered on Event 060609, photo adapted from [38]; (b) Flood Central case study. (a) Flood registered on Event 060609, photo adapted from [38]; (b) Flood registered registered on Event 061025, photo of local Diário newspaper Diário de(c)Coimbra; (c) generated Floodplain on Event 061025, photo courtesy of courtesy local newspaper de Coimbra; Floodplain generated by the for SD Event model 060609; for Event (d) Floodplain the SD Event by the SD model (d)060609; Floodplain generatedgenerated by the SDbymodel formodel Eventfor 061025; 061025; (e) Floodplain the SD for Event (f) Floodplain generated by the (e) Floodplain generatedgenerated by the SDby model for model Event 060609; (f) 060609; Floodplain generated by the FD model FDEvent model for Event 061025. for 061025.

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Table 3. Summary of modeling results on Praça 8 de Maio, Zona Central case study. Table 3. Summary of modeling results on Praça 8 de Maio, Zona Central case study. Table study.

Max water depth (m) Flooding volume (m3) Event Max water depth (m) Flooding volume (m3) 3 Flooding Volume FDDepth (m) SD FD (m ) Event Event SD Max Water SD FD SD FD SD 0.11 FD 060609 0.44 275 SD 68FD 060609 0.44 0.11 275 68 061025 0606090.51 0.44 0.25 0.11 360 275 13868 061025 0.51 0.25 360 360 138138 080921 0610250.10 0.51 0.08 0.25 63 42 080921 0.10 0.08 63 080921 0.10 0.08 63 4242 131224 1312240.14 0.14 0.06 0.06 79 79 34 34 131224 0.14 0.06 79 34

Flooding area (m2) Flooding area (m 2 ) 2) Flooding SD Area (m FD SD FD SD FD 324 1092 1092 324 1092 324 630 1693 1693 1693 630 630 324 248 324 248 248 324 569 569 248 248 569 248

4.3. Rainfall Magnitude 4.3. Assessing Assessing the the Importance Importance of of Surface Surface Storage Storage as as aaa Function Function of of 4.3. Assessing the Importance of Surface Storage as Function of Rainfall Rainfall Magnitude Magnitude The aforementioned analyses analyses indicatethat, that, general, models retain volumes of The aforementioned in in general, FD FD models retain largerlarger volumes of water The aforementioned analysesindicate indicate that, in general, FD models retain larger volumes of water on the overland surface as compared to the corresponding SD setup. Depending on thestudy, case on the overland surface as compared to the corresponding SD setup. Depending on the case water on the overland surface as compared to the corresponding SD setup. Depending on the case study, the volume retained be stored in surface depressions, as occurred the Cranbrook case the volume retained can becan stored in surface depressions, as occurred in the in Cranbrook case study, study, the volume retained can be stored in surface depressions, as occurred in the Cranbrook case study, or it can be retained in building singularities, as occurred in the Zona Central case study. or it canorbeit retained in building singularities, as occurred the Zona case study. case To analyze study, can be retained in building singularities, as in occurred in Central the Zona Central study. To the of importance the surface storage in relation to the rainfall intensity, anonanalysis the analyze importance the surfaceof in relation to the rainfall intensity, an analysis based design To analyze the importance ofstorage the surface storage in relation to the rainfall intensity, an analysis based on design storms was performed. The models of Cranbrook case study were tested with with five storms was performed. The models of Cranbrook case study were tested with five design storms based on design storms was performed. The models of Cranbrook case study were tested with five design returns 10, 20, 30, 200 of years, the models of Zona returnsstorms period with (RP) 10, 20,period 30, 100(RP) and of 200 years, and100 the and models Zonaand Central case study were design storms with of returns period (RP) of 10, 20, 30, 100 and 200 years, and the models of Zona Central case study were tested with six design storms with RP of 2, 5, 10, 20, 50 and 100 years. tested with six design storms with RP of 2, 5, 10, 20, 50 and 100 years. Central case study were tested with six design storms with RP of 2, 5, 10, 20, 50 and 100 years. Figures Figures 14 14 and and 15 15 present present the the relative relative flooding flooding volumes volumes for for each each land land use use group group type, type, calculated calculated Figures 14 and 15 present the relative flooding volumes for each land use group type, calculated based on the maximum water depth predicted at the 2D mesh of the overland surface. It based on on the It can can be be based the maximum maximum water water depth depth predicted predicted at at the the 2D 2D mesh mesh of of the the overland overland surface. surface. It can be concluded that the percentage of flooding volume on roads is higher in the SD model for the two concluded that the percentage of flooding volume on roads is higher in the SD model for the two case concluded that the percentage of flooding volume on roads is higher in the SD model for the two case studies. In both situations, the increase of the rainfall return period, and thus intensity, led to studies. In both the increase of the rainfall return period, and thus intensity, led to decrease case studies. In situations, both situations, the increase of the rainfall return period, and thus intensity, led to decrease of thevolumes relative in volumes in roads and anofincrease ofinvolumes in areas covered byfor buildings of the relative roads and an increase volumes areas covered by buildings both SD decrease of the relative volumes in roads and an increase of volumes in areas covered by buildings for both SD and FD models. and FD models. for both SD and FD models.

FigureFigure 14. Relative flooding volumes on eachonland use group design case study. 14. Relative flooding volumes each land usefor group for storms design events, storms Cranbrook events, Cranbrook Figure 14. Relative flooding volumes on each land use group for design storms events, Cranbrook case study. case study.

Figure 15. Relative flooding volumes of each land use group for design storms events, Zona Central case study. Figure 15. Relative flooding volumes ofland eachuse land use group for design Zona Central Figure 15. Relative flooding volumes of each group for design stormsstorms events,events, Zona Central case study. case study.

Figure 16 shows the difference between SD and FD models in predicting flooding volumes for Figure 16 shows the difference between SD and FD models in predicting flooding volumes for each land use group type in the Cranbrook case study. In addition to the increase in the relative each land use group type in the Cranbrook case study. In addition to the increase in the relative volume in residential areas, as shown in Figure 14, the differences in flooding volumes between SD volume in residential areas, as shown in Figure 14, the differences in flooding volumes between SD

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Figure 16 shows the difference between SD and FD models in predicting flooding volumes for 16 16 of of 20 20 each land use group type in the Cranbrook case study. In addition to the increase in the relative volume in residential areas, as shown in Figure 14, the differences in flooding volumes between SD and FD and and FD FD models models are are similar similar in in residential residential areas areas for for all all events. events. For For roads, roads, the the flooding flooding volume volume models are similar in residential areas for all events. For roads, the flooding volume decreases as decreases as water tends to accumulate more in these zones leading to higher volumes in decreases as water tends to accumulate more in these zones leading to higher volumes in the the SD SD water tends to accumulate more in these zones leading to higher volumes in the SD model for high model model for for high high rainfall rainfall intensities. intensities. Figure Figure 17 17 presents presents the the same same analysis analysis applied applied to to the the Zona Zona Central Central rainfall intensities. Figure 17 presents the same analysis applied to the Zona Central case study. In this case case study. study. In In this this catchment, catchment, the the increase increase in in the the rainfall rainfall return return period period led led to to the the increase increase in in the the catchment, the increase in the rainfall return period led to the increase in the difference between FD difference difference between between FD FD and and SD SD volumes volumes for for both both roads roads and and residential residential areas. areas. This This means means that that with with and SD volumes for both roads and residential areas. This means that with the increase in the rainfall the the increase increase in in the the rainfall rainfall intensity, intensity, higher higher volumes volumes are are retained retained on on the the overland overland surface surface by by the the FD FD intensity, higher volumes are retained on the overland surface by the FD model, as compared to the model, model, as as compared compared to to the the SD SD simulations. simulations. SD simulations. Water Water 2016, 2016, 8, 8, 22

onon flooding volumes of each group design storms events, Cranbrook Figure 16. Differences flooding volumes of each land use group for design storms events, Figure 16. 16.Differences Differences on flooding volumes of land eachuse land usefor group for design storms events, case study. case Cranbrook Cranbrook case study. study.

Figure Figure 17. 17. Differences flooding volumes volumes of each land land use use group group for for design design storms storms events, events, Zona Zona Differences on on flooding flooding volumes of each Central Central case case study. study.

To assess the importance of the volume that retained the overland surface, Figures To assess assessthe theimportance importanceof ofthe thevolume volumethat thatisis isretained retained on the overland surface, Figures 18 and and To onon the overland surface, Figures 18 18 and 19 19 analyze the differences between flow volumes in the 1D network. It can be verified that 19 analyze the differences between flow volumes in the 1D network. It can be verified that analyze the differences between flow volumes in the 1D network. It can be verified that differences differences SD FD models rise increase in areas decrease for differences between SD and andrise FDwith models rise with withinthe the increase in drainage drainage areas and decrease for between SDbetween and FD models the increase drainage areas and decrease forand higher intensity higher intensity rainfalls. However, the differences have significantly distinct trends for each case higher intensity rainfalls. However, the differences have significantly distinct trends for each case rainfalls. However, the differences have significantly distinct trends for each case study. In the study. Cranbrook case study, storage be high rainfalls, study. In In the the Cranbrook casestorage study, surface surface storage can can be neglected neglected for high intensity intensity rainfalls, Cranbrook case study, surface can be neglected for high intensity for rainfalls, converging to low converging to low percentages for all monitoring point locations. In the Zona Central case study, converging to low percentages for all monitoring point locations. In the Zona Central case study, percentages for all monitoring point locations. In the Zona Central case study, however, surface storage however, surface storage is significant for downstream monitoring point locations for all the rainfall however, surface storage is significant for downstream monitoring point locations for all the rainfall is significant for downstream monitoring point locations for all the rainfall intensities tested. While in intensities While in Cranbrook case study the surface storage is related surface intensities tested. tested. Whilethe in surface Cranbrook caseis study therelated surfacewith storage is mainly mainly related with with surface Cranbrook case study storage mainly surface depressions, in the Zona depressions, in the Zona Central catchment the surface storage verified in the FD model is also related depressions, in the Zona Central catchment the surface storage verified in the FD model is also related Central catchment the surface storage verified in the FD model is also related to buildings singularities, to singularities, and the of about drainage to buildings buildings singularities, and private the absence absence of data data about private private drainage networks networks and and connections. connections. and the absence of data about drainage networks and connections.

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Figure 18. Differences on flowonvolumes in the 1D for designfor storms events, Cranbrook case study. Figure 18. Differences flow volumes innetwork the 1D network design storms events, Cranbrook case study. Figure 18. Differences on flow volumes in the 1D network for design storms events, Cranbrook case study.

Figure 19. Differences on flow volumes in the 1D network for design storms events, Zona Central case study. Figure 19. Differences onvolumes flow volumes 1D network for design Zona Central Figure 19. Differences on flow in the in 1Dthe network for design storms storms events, events, Zona Central case study.

5. Discussion case study.and Conclusions 5. Discussion Conclusions This paperand presented a comparison between SD and FD models using two real case studies with 5. Discussion and Conclusions different anda flooding mechanisms. Innovative concepts were proposed the model Thischaracteristics paper presented comparison between SD and FD models using two real casefor studies with building and to and establish the connections between the modules of SD and models. different characteristics flooding mechanisms. Innovative concepts were proposed for the model This process paper presented a comparison between SD and FD models using two realFD case studies with FD models were generally found to inaccurately retain runoff volumes on the overland building characteristics process and toand establish the mechanisms. connections between theconcepts moduleswere of SDproposed and FD models. different flooding Innovative for thesurface model due FD to surface depressions, buildings singularities, and the lack of representation of private models generally found to inaccurately retain volumes on the surface building process were and to establish the connections between therunoff modules of SD and FDoverland models. connections to the sewer network. This has not been observed in the SD model, since the runoff is due FD to models surface depressions, buildings singularities, and the lack of representation of private were generally found to inaccurately retain runoff volumes on the overland surface due directly discharged from subcatchments to network nodes. While surface depressions and buildings connections to the sewer network. This has not observed in the SD model, since the runoffto is to surface depressions, buildings singularities, andbeen the lack of representation of private connections singularities are dependent on the resolution of surface module, the lack and of discharged connection directly fromhas subcatchments to network nodes. While surface depressions buildings the sewerdischarged network. This not been observed inthe theoverland SD model, since the runoff is directly to thesubcatchments minor system relies onon the resolution onofthe flowsurface module. singularities are dependent the resolution thesewer overland module, the lack of connection from to network nodes. While surface depressions and buildings singularities are In the overland flow module, surface depressions are related with thetosurface overland to the minor relies on on themodule, sewer flow dependent onsystem the resolution of the the resolution overland surface the module. lack of connection the minor system definition and buildings are dependent on the definition of with building In the In overland flow surface depressions are related the boundaries. surface overland relies on the the resolution onsingularities themodule, sewer flow module. Cranbrook case study, surface depressions are the main cause of retaining water on the overland definition buildings are depressions dependent on definition of building boundaries. In the In the and overland flow singularities module, surface arethe related with the surface overland definition surface and case the differences between SD and FD the models neglected forwater high In intensity rainfall Cranbrook study, surface depressions maincan cause of retaining onthe the overland and buildings singularities are dependent on are the definition of be building boundaries. Cranbrook events. thethe Zona Central case studySD buildings accumulate runoff volume, surface In and differences between and FD singularities models can be neglectedsignificant for high intensity rainfall traducing significant differences between SD and FD models, even for high intensity rainfall events. 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.

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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. Acknowledgments: Rui Pina acknowledges the financial support from the Fundação para a Ciência e Tecnologia-Ministério para a Ciência, Tecnologia e Ensino Superior, Portugal (SFRH/BD/88532/2012). Susana Ochoa-Rodriguez acknowledges the support of the Interreg IVB NWE RainGain project. This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No. 641931. Special thanks are due to AC, Águas de Coimbra, E.M., Coimbra, Portugal for providing rainfall and sewer data of the pilot location, to Innovyze, Wallingford, UK for providing research licences of InfoWorks ICM software, and to Diário de Coimbra for providing photographic records of flooding events. Author Contributions: Rui Daniel Pina, Susana Ochoa-Rodriguez, Nuno Eduardo Simões had the original ideas discussed and all the authors defined the studies presented in this manuscript. Rui Daniel Pina built the hydraulic models and together with Susana Ochoa-Rodriguez and Nuno Eduardo Simões, collected the data and analyzed hydraulic results. The manuscript was written by Rui Daniel Pina with contribution from all co-authors. The work ˇ presented is a part of Rui Daniel Pina’s Ph.D. which is supervised by Cedo Maksimovi´c, Alfeu Sá Marques and Ana Mijic. All authors read and approved the final manuscript. Conflicts of Interest: The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.

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