Development and Assessment of the Physically-Based 2D/1D Model "TRENOE" for Urban Stormwater Quantity and Quality Modelling
The widespread use of separate stormwater systems requires better understanding of the interactions between urban landscapes and drainage systems. This paper describes a novel attempt of developing urban 2D-surface and 1D-drainage model "TRENOE" for urban stormwater quantity and quality modelling. The physically-based TREX model and the conceptual CANOE model are integrated into the TRENOE platform, highlighting that the roofs of buildings are represented separately from the surface model, but
... surface model, but simulated as virtual "sub-basins" in the CANOE model. The modelling approach is applied to a small urban catchment near Paris (Le Perreux sur Marne, 0.12 km 2 ). Simulation scenarios are developed for assessing the influences of different "internal" (model structure, numerical issues) and "external" (parameters, input data) factors on model performance. The adequate numerical precision and the detailed information of land use data are identified as crucial elements of water quantity modelling. Contrarily, the high-resolution topographic data and the common variations of the water flow parameters are not equally significant at the scale of a small urban catchment. Concerning water quality modelling, particle size distribution is revealed to be an important factor, while the empirical USLE equations need to be completed by a raindrop detachment process. examining sub-catchments and land-use parcels to simulate overland flows in urban catchments. These approaches are based on a conceptual representation of routing processes governing pollutants' transport from their generation points to the sub catchment outlet  . Most of them are based on Sartor and Boyd formulations of build-up and wash-off on urban surfaces  . These conceptual equations have been criticized by several authors [7,    for their poor performance in reproducing pollutant concentration dynamics. However, current urban stormwater quality models (e.g., SWMM, MUSIC, etc.) still rely on these empirical catchment-scale functions that have not substantially evolved over the last 40 years. An alternative way to improve their performance might be to even out their spatial dimension applications. In this respect, the 2D erosion model (TREX), which was initially developed for rural/agricultural catchments and largely tested by the scientific community to simulate particle transport in natural catchments, represents an interesting tool to apply to urban catchments. This novel modelling approach could lend itself to new ways of thinking in the field of urban stormwater quality modelling, and could potentially advance our modelling techniques. Over the last few years, the modeling approach of combining 2D overland flow and 1D drainage sewer flow has received great attention [15, 16] . Several research models     and commercial tools [21, 22] have already been developed and applied to various case studies. These models are able to accurately represent the spatial and temporal variations of surface runoffs and sewer flows on urban areas. The concept of these 2D/1D models is hence well adapted to introducing more reliable pollutant transport processes. However, present applications of these models are mostly focused on urban flood modelling, while being rarely investigated for urban pollutant transport simulations. On the other hand, existing publications on integrated 2D/1D models rarely compare the influences of different factors on model outputs [16, 23, 24] . In that case, the main drivers of the model outputs are still not sufficiently investigated, which decreases the reliability of the integration of new processes into the existing model, and restricts the transferability of the model to other case studies. In this context, we coupled the physically-based 2D model TREX [25, 26] , which has been initially developed for watershed rainfall-runoff, sediment and contaminant transport modelling, with the 1D pipe routing and subbasin components of the CANOE model  , resulting in the "TRENOE" platform. It is the first time that such a 2D physically-based erosion model, based on USLE equations, has been coupled with an urban model for the simulation of urban stormwater quality. Moreover, TREX is an open source code, well-documented, with a robust numerical scheme, which makes it suitable for modification in an urban context. The coupling between TREX and CANOE models is designed to be able to simulate the 2D overland flows and the 1D sewer network routing. Roofs are simulated separately from the 2D surface model in TRENOE. Since the roof gutters are connected directly to the sewer networks in the studied catchment, roofs are represented as the "subbasins" in the 1D CANOE model. Within the framework of the ANR (French National Agency for Research) Trafipollu project, a detailed Geographic Information System (GIS) database is available for the study of urban catchments (Le Perreux sur Marne, 0.12 km 2 ), such as by using the high-resolution topographic data of LiDAR survey and the detailed land use data derived from ortho photos. Benefitting from this large dataset of detailed source data and continuous measurement at the sewage outlet, the influences of various inherent (model structure, numerical issues) and external (input-data, parameter values) factors on model performance are evaluated. In general, this paper focus on two objectives: firstly, to apply the physically-based 2D/1D TRENOE platform to urban stormwater quantity and quality modelling; secondly, to rank the impacts of different factors on model outputs and to highlight the prerequisites for high performance simulations. The results of this study may be very useful for reducing the cost of urban stormwater management by avoiding some unnecessary data acquisition and modelling efforts (high-resolution topograhic data, calibration, etc.). Perspectives and propositions for improving urban stormwater quality modelling are presented as well. Water 2016, 8, 606 3 of 18 Materials and Methods Model Description The physically-based 2D model TREX and the 1D pipe routing and subbasin components of the CANOE model are integrated into the TRENOE platform. Within TREX, the catchment surface is divided into several rectangular meshes based on GIS topographic data. These grids are then categorized into several classes according to land use information. Different parameters are attributed to each grid point in accordance with the land use type. Interception, infiltration, water runoff and pollutant transfer processes are then calculated. Diffusive wave approximation of Shallow-Water equations (SW) is applied for simulating the surface runoff at the grid scale, which is able to represent the spatial and temporal variations of the water flow and the associated pollutants. With the 1D sewer system CANOE model, stormwater and pollutant routing processes are computed for each portion of pipes between pre-defined junction nodes using the kinematic approximation of SW equations and advection equations, respectively. The modelling processes in TRENOE are described in Table 1 . The "junction nodes" in 1D sewer network model are the connecting points between different parts of the TRENOE platform. From the grids of "sewer inlets" and "roofs", water and pollutants flow directly into the sewer networks via these "junction nodes". "Sewer inlets" are considered as "holes" in the 2D surface model, where surface runoff and the related pollutants disappear at these grid points. In contrast, "roofs" are represented as obstacles, where water flows cannot enter these grids from other types of land uses. As the buildings are not described in the Digital Elevation Model (DEM) data, the grids of "roofs" are increased by 5 m at the step of input data pre-treatment. Since most roofs are directly connected to the sewer networks in the studied urban catchment, we gather the grids of roofs which are linked to the same junction nodes (the nearest), to set the conceptual "sub-catchments" in CANOE model. The size of each "sub-catchment" is equal to the total area of the linking "roofs" grids. The non-linear reservoir method and the exponential washoff equations  are then applied to simulate the rainfall-runoff and the pollutant transport, respectively, for each conceptual "sub-catchment". The model scheme is illustrated in Figure 1 .