Flood4castRTF: A Real-Time Urban Flood Forecasting Model

: Worldwide, climate change increases the frequency and intensity of heavy rainstorms. The increasing severity of consequent ﬂoods has major socio-economic impacts, especially in urban environments. Urban ﬂood modelling supports the assessment of these impacts, both in current climate conditions and for forecasted climate change scenarios. Over the past decade, model frameworks that allow ﬂood modelling in real-time have been gaining widespread popularity. Flood4castRTF is a novel urban ﬂood model that applies a grid-based approach at a modelling scale coarser than most recent detailed physically based models. Automatic model set-up based on commonly available GIS data facilitates quick model building in contrast with detailed physically based models. The coarser grid scale applied in Flood4castRTF pursues a better agreement with the resolution of the forcing rainfall data and allows speeding up of the calculations. The modelling approach conceptualises cell-to-cell interactions while at the same time maintaining relevant and interpretable physical descriptions of ﬂow drivers and resistances. A case study comparison of Flood4castRTF results with ﬂood results from two detailed models shows that detailed models do not necessarily outperform the accuracy of Flood4castRTF with ﬂooded areas in-between the two detailed models. A successful model application for a high climate change scenario is demonstrated. The reduced data need, consisting mainly of widely available data, makes the presented modelling approach applicable in data scarce regions with no terrain inventories. Moreover, the method is cost effective for applications which do not require detailed physically based modelling.


Introduction 1.Urban Flood Modelling
Due to the devastating effect of floods, understanding the drivers of floods has been an important research topic for decades.Since the 1970s the development and application of flood inundation models has been an important part of research on floods [1].Especially in urban environments, floods can have a very high economic and social cost.These impacts will certainly further increase in future due to climate change and further urbanisation.Due to the specific characteristics of urban environments and the high socio-economic impact of floods in urban areas, urban flood models have been developed.These urban flood models take into account the urban drainage system which has an important influence on the occurrence of floods in urban environments.
Urban flood models are currently extensively used for flood risk mapping, urban drainage planning and engineering, water resource management, and real-time flood forecasting [1].To cover the requirements of the different uses of urban flood models, a range of different model systems were developed [2,3].Worldwide, there is a tendency towards the application of (semi-)distributed physically based models for urban run-off modelling.This tendency is understandable given the complex physical interactions in urban catchments [4].Additionally, the increase in computational power facilitates a higher differentiation and complexity of such models, further explaining the tendency for 1D-2D detailed physically based models [5].These full 1D-2D models represent the urban drainage network in one dimension (1D) and couple a 2D free surface model for overland flow.The Saint-Venant equations are used to simulate the flow dynamics for both the urban drainage and flow at the surface.
Costabile et al. [6] demonstrated the necessity to apply such fully dynamic modelling when the goal of the urban flood inundation mapping activity includes the local estimation of flood hazard and vulnerability based on a combination of computed water depths and velocities.Flow velocities are particularly relevant to assess safety issues concerning people, for example, pedestrians and drivers' vulnerability in a certain flood scenario because walking and driving in floodwaters are identified as the main danger for people during floods [7].
Despite the advantage with respect to accuracy and a superior local estimation of flood hazard and vulnerability, the detailed physically based modelling approach also has disadvantages.Distributed physically based models are known to exhibit over-parameterisation and over-complexity [8].Especially the high computation demand and extensive data requirements complicate setting up detailed physically based models for larger areas or in regions where less data are available [9].On top of that, the resolution of their discretisation often largely exceeds the resolution of the forcing rainfall data [10].Especially, the high computation demand complicates the use of detailed physically based models for real-time flood forecasting [1].
In the past, methods have been introduced to partly overcome the high computational demand of fine mesh discretisations.For example, flexible meshing avoids the need to apply a fine resolution throughout the complete model domain [11][12][13].Ferraro et al. [12] present a method to derive the mesh size limits applied to the unstructured flexible mesh from a spectral analysis to the terrain.Alternatively, subgrid techniques can be applied to speed up the calculations [14].Section 2.1.3presents a more complete literature study on subgrid applications.
Teng et al. [1] reviewed state-of-the-art methods for flood inundation modelling and conclude that there is no such thing as a "perfect model" and the aim of developing and using models that are 'as realistic as possible' should be balanced against computational demand, investment in data collection and model set-up, and the requirements of the end user.

Real-Time Flood Forecasting
Real-time flood forecasting tools, however, can provide lifesaving information to local inhabitants or emergency services and are therefore value tools to mitigate the impact of flash floods.Spatial understanding of high-risk areas which enables emergency responders to prioritise evacuations and other actions are ideally implemented at the onset of a predicted extreme event [7].Driven by the advances in high-resolution numerical weather predictors and the increasing frequency of high intensity rainfall events, due to climate change, there is a growing demand for flood models that are suited to real-time applications.
To allow using detailed physically based flood models for real-time flood forecasting, various approaches have been proposed to decrease the computational speed [15].Graphical processing units (GPU) have been successfully applied to decrease simulation time for both 1D [16] and 2D models [17].Additionally, parallel computing (e.g., on cloud servers) and code parallelisation have been applied to reduce simulation time of detailed physically based models [15].Using a lower spatial resolution is another option to reduce the computational demand.However, using lower spatial resolutions compromises model accuracy.Despite the developments in computer capability and advances in computation efficiency of hydrodynamic models, the use of these kind of models for real-time flood forecasting is still difficult [1].To overcome the difficulties of the detailed physically based models for real-time flood forecasting, alternative modelling approaches have been proposed.Different approaches can be used to reduce the computational demand of the flood models: simplifying the 2D shallow water equations by for example omitting the inertia terms (e.g., [18]), using cellular automata approaches [19], using simplified, non-physicalbased methods [1], or by applying empirical/data driven surrogate models [20] or a hybrid approach using a series of lumped models in combination with logistic regression [21].Despite these recent advantages in simplifying and reducing the computational demand of urban flood models, several difficulties remain.The high data requirements and associated model set-up costs for 1D-2D detailed physically based models constitute another difficulty in setting up urban flood models.Required data such as properties of the sewer system are often not readily available.In these cases, a measuring campaign is required before the model can be prepared.This high cost prevents many cities from setting up detailed physically based models.

Improved Flood Modelling Approach
To overcome the disadvantages of the high calculation power and extensive data needs of detailed physically based models, the Flood4castRTF model is developed.The Flood4castRTF model is meant for real time flood forecasting and scenario analysis.RTF is short for Real Time Forecasting.The model is not meant for detailed urban drainage infrastructure designing or detailed vulnerability assessments.Flood4castRTF's principle is to maximise the availability of flood risk assessments and flood predictions to a wide range of users minimising the total cost for model set-up and maintenance.Flood4castRTF makes maximal use of readily available (GIS) data and typical design criteria for the modelled region to facilitate the model set-up process.The model integrates hydrological modelling with 2D overland flow and urban drainage flow, while keeping the model equations simple to minimise the computational demand.
This paper presents the Flood4castRTF model based on an application to a typical urban area in Flanders to assess the impact of climate change on the urban flood probability.
To validate the Flood4castRTF model, flood maps of the study area are compared to the Flemish reference flood maps and flood maps generated by an existing detailed physically based model.The case study illustrates the potential of the Flood4castRTF model to set up early flood warning for cities at a relatively low cost compared to systems applying detailed physically based flood models.Flood4castRTF can also be used to scan the effectivity of measures mitigating urban flood under climate change conditions.

Novelty
The main novelty of the presented modelling method is that it preserves a distributed approach, while at the same time addressing the run-off modelling with a conceptualisation and model complexity reduction to represent the processes at a spatial and temporal scale in the order of the rainfall data's scale (i.e., a resolution in-between the typical resolutions of an X-band radar and a C-band or S-band radar, or the resolution of a dense urban network of pluviographs).
This approach yields the following merits: • Integrated modelling remains possible at this scale, incorporating all relevant flow interactions in urban and rural catchments.

•
An optimal balance is offered between model accuracy, model input accuracy, output accuracy and invested time for model build-up and simulations.

•
Minimal data needs and automatic model build-up, as the approach does not require detailed data, for example on sewer elements, manholes, or surface run-off structures.

•
The fast engine offers the opportunity to perform real-time simulations for large areas, and in the future even for real-time scenario simulations.

Model Concept
The integrated modelling approach comprises a modular system of a surface flow layer and one or two (underground) urban drainage layers (Figure 1).These layers interact at the locations of sewer inlets and outlets, overflows and pumps.Additionally, drainage of water flooding from the streets into the sewer is included and vice versa.During run-time, the explicit modelling scheme requires limitation of the variable time stepping of the surface layer as was imposed by the Courant Friedrichs Lewy (CFL) condition [22].An additional constraint of a maximum of 1 min is set for moments of low flow velocities, where the CFL-based time step could exceed 1 min as a consequence of the large spatial discretisation.Such time steps would be undesirable for the interoperability of the model layers.
When approaching the end of the constant time step of the urban drainage layer, the model engine subdivides the remaining sub time steps of the surface layer over the remainder of the urban drainage layer's time step.At the end of each urban drainage layer time step, the summed exchange fluxes between each layer combination from the previous time step are exchanged with their target layers.In the case that the surface layer is targeted, the exchange flux is distributed over the sub time steps within the next time step.
Sections 2.1.1 and 2.1.4present the general concept of the surface and urban drainage modules, respectively.Sections 2.1.2and 2.1.3bring context to specific conceptual approaches applied within the surface module.

Surface Module: General Workflow
Pre-processing of the surface module commences with a stream burning of the digital terrain model (DTM) of the model area (Figure 2).This stream burning (Section 2.1.2) is in most cases necessary as DTM grids generally represent the surface levels of open water bodies rather than the stream bed.Burning the DTM levels to an approximate stream depth generally leads to more accurate storage and conveyance capacities in these streams.
The subsequent steps include the calculation of the surface flow path which serves as an input to the urban drainage module pre-processing to assess the urban drainage capacities downstream of inflows from the surface (Section 2.1.4).The surface flow path algorithm first calculates the local drain direction (LDD) map and subsequently the actual flow paths.The local drain direction (LDD) map is determined by an algorithm that calculates for each cell the steepest downslope gradient.
The pre-processing of the so-called surface subgrids constitutes the major part of the surface layer pre-processing.These subgrids facilitate fast surface run-off calculations and are further detailed in Section 2.1.3.
where Q is the discharge across a cell interface, A is the cross-sectional area at the cell interface, R is the hydraulic radius, S is the slope of the water surface between the two cell centres, and n is the Manning friction.After the flow calculation, cell volumes are updated at the end of each time step.After updating the cell volume, the according water level, cross-sectional areas, hydraulic radii, and connectivity coefficients are derived from the pre-processed subgrid tables (Section 2.1.3).
The choice for the Manning equation is motivated by the scale at which the calculations take place: at these larger scales, any formulation that balances flow driving forces with a representative flow resistance will yield a rough approximation to the occurring run-off.The accuracy is then mainly determined by the representativeness of the parameter values that describe the flow conveyance and resistance.
The calculated Manning fluxes are limited by available volumes in the upstream cell and the connectivity within the cell.Here, connectivity refers to the amount of water that can flow between two cell interfaces of a model cell at a certain water level relative to the amount of water that could flow to the other cell interfaces.For example, a levee subdividing a cell would yield a connectivity of zero between cell interfaces on both sides as long as the water level does not exceed the level of the levee.The flow limitation is effectuated by keeping track of the parts of the storage volume that are available to flow out in each direction based on the connectivity with their respective inflow cell interfaces.

Surface Module: Stream Burning
Before pre-processing the surface layer, notion should be given to the fact that the input DTM data do not always represent the lowest point in the terrain.Rivers and culverts are typical terrain elements that are prone to this issue.At river locations, the represented terrain surface is typically the water level surface.When leaving the surface uncorrected, river runoff can only occur when upstream water levels exceed the river surface level, and the river's conveyance capacity can be highly underestimated.At culvert locations, the land surface can be numerous meters higher than the bottom level of the culvert underneath.Leaving the DTM unchanged on such locations would inhibit simulated run-off until the upstream water levels exceed the terrain surface, potentially flooding significant upstream areas.
River or stream burning is therefore often applied to correct surface runoff paths.Although effective in many cases, developed methods often still exhibit limitations on specific locations like nearby unconnected streams, wide rivers and lakes [23].Another common issue in stream burning algorithms supported by a vectorial hydrography layer is the burning of parallel streams next to the actual stream location when the vectorial data are misaligned or defined too roughly.Lindsay [23] managed to slightly limit the occurrence of parallel streams by assigning a flooding priority to river cells.
A detailed new stream burning algorithm is set up to overcome the issue of parallel streams.Misaligned streams in the input shapefile are relocated to more likely nearby stream locations that are derived from linear depressions in the DTM.In addition, the method is developed so that it is applicable in relatively flat areas as well, and for streams that connect multiple catchment outlets (e.g., canals).The algorithm is integrated into the initial phase of the pre-processing module before further land surface information is derived from the DTM.
The input of the algorithm consists of vectorial GIS data of the predefined hydrography, river outlets, optional culvert locations and the uncorrected DTM.Here, outlets are locations where the rivers leave the catchment or actual inflows into conduits in the urban stormwater layer.If necessary, additional manual corrections to correct the original DTM can be prescribed as well in the input.The actual river locations are sought after within a stream order-dependent buffer distance from the predefined river lines.
Although required input in the process, GIS data of river locations and culverts are not amongst the mandatory data.Many GIS packages allow the derivation of stream networks that can be used as a proxy for the river input when derived at a coarser DTM scale.Additionally, DTM filling and breaching methods exist that allow detection of probable culvert locations through obstacles in the terrain [23].
The main purpose of the algorithm is to find the correct river locations and burn them according to their river class.Per river class, expected mean river widths and depths are assigned.These are obviously only a proxy to the actual widths and depths but serve the purpose of giving the rivers approximate conveyance capacities.
Before burning the rivers, culverts are burned into the terrain: terrain levels along the culvert paths are interpolated between the upstream and downstream surface water level in the original DTM.Afterwards, terrain levels are filled and breached along the previously located river and then smoothened.The resulting burning levels are then obtained by applying: where h burned is the resulting terrain level, and h DTM and h smooth refer to the intermediate results described in the above paragraph: h DTM is the terrain level in the DTM after the initial culvert burning, and h smooth is the terrain level after applying the filling/breaching and smoothing.∆h burn is the burning depth and is dependent on the river class or river order.The method purposely does not ensure a monotonically decreasing downward path but ensures that downward level increments remain limited.

Surface Module: Subgrid Approach
The selected modelling approach simulates run-off on a coarser model grid than commonly applied by state-of-the-art distributed physically based models (Section 1.4).The surface flow is described by the Manning equation and is limited by the available volumes in the upstream cells and the connectivity between the cell's interfaces (Section 2.1.1).Obviously, this coarser-scale model approach with a Manning run-off approximation yields an inability to represent local (subcell) backwater effects in narrow flow paths which are common in urban environments.However, larger-scale run-off patterns can still be represented with sufficient accuracy when incorporating subgrid information in the variables of the Manning equation and the connectivity calculations.
Subgrid techniques have been applied in hydraulic modelling in various applications and on various scales.One of the applications that formed a main driver for the development of subgrid techniques is the development of wetting and drying algorithms which build upon detailed bathymetric data (e.g., [14,24]).Urban applications of subgrid techniques are mainly motivated by the need to represent sub-grid terrain obstacles in coarser-scale grids.Yu and Lane [25] explicitly parameterised the subgrid topographic variability to correctly represent the stored volumes within the cell and the effect of this variability upon the occurrence of horizontal flows in each direction.The study recognised that previous methods that solely parameterised a representative roughness based on the subgrid terrain levels only considered these obstacles as momentum sinks and not as actual blockages for flows and available surface storage.Other studies translate the bathymetry into a representative porosity (e.g., [26]) whereby obstacles in the terrain are translated into a reduced porosity, reducing the available storage capacity and cross-sectional area and increasing the head loss caused by higher friction and turbulence.More recent applications (e.g., [27,28]) exploit the subgrid data more intensively in their hydrodynamic calculations in the coarser grid, recognising that the water level variations are generally more gradual than the topographic variability determining the underlying flow parameters.As an example for shallow overland flows, friction is a dominant term in the momentum equations deserving a determination based on the spatial variation of the underlying parameters (local depths and friction coefficients) within the cell itself.Stelling [27] also points out the added value that pre-processed tables can have for reducing memory and computational requirements during simulations.
Applications of subgrid techniques in further simplified or more conceptualised approaches compared to the detailed physically based modelling studies above are not known by the authors.However, the detailed terrain data that are nowadays widely available can still be a merit for such approaches: • A detailed water level-storage relationship per model cell also benefits these simplified approaches, especially for coarser grid cells that typically contain large topographic variations and therefore often are only partly flooded.

•
The calculation of representative cross-sectional areas and hydraulic radii are facilitated by the detailed terrain data, as these can be processed to representative terrain profiles in-between two cell centres.

•
A connectivity analysis at a variety of depths teaches how model cell sides are connected in different states of flooding.This way, cell internal throughflow can be blocked or limited when physical blockages occur in the terrain.
The current approach puts emphasis on maximising the calculation efforts in the model pre-processing.Detailed terrain data are pre-processed to subgrids (tables) that link the following variables: Hydraulic radius and cross-sectional area (in 4 directions)

•
Connectivity coefficients between each model cell side (12 combinations) The subgrid table size is dependent on the ratio of the model cell size to the DTM cell size.At low ratios, a relatively high number of terrain levels from the DTM are preserved in the model cell's subgrid.Moving to relatively large model cells reduces the relative number of table entries.As an example, 169 table entries are used for a 1 m × 1 m DTM and a 100 m × 100 m model cell.Compared to the 10,000 DTM cells within the model cell, this is a data reduction of a factor 60.

Urban Drainage Module: Sewer and Stormwater Network Conceptualisation
Urban stormwater run-off is typically characterised by short and intense run-off peaks and low concentration times.The underground stormwater drainage occurs either via combined sewer systems or separated stormwater systems.In many places, both systems occur alongside with interactions between both systems via overflows and pumps.The presented model set-up acknowledges this practice by allowing the definition of two separate urban drainage layers with distinct properties and interactions via overflows and pumps.Figure 3 gives an overview of the input used to set-up the urban drainage model including geographical information on the location of sewers and urban structures (WWTP plants, pumps, overflows), interactions with the surface layer, the surface flow path (necessary for the correct interaction with the surface layer), land use and the output of the urban pre-processing.For each layer, the pre-processing comprises spatially distributed urban fractions and urban flow capacities and storages.This subsection further details the concept employing these parameters.The combined and stormwater systems are commonly dimensioned according to design return periods.Basically, these return periods define the severity of the storm that can still be handled by the drainage system.Design rules vary from place to place, as well as over time: in many places, heavy storms are more likely to occur in the future due to climate change.Overall, these systems share the property that they are dimensioned according to some design return period and, on each location, the upstream draining area and the representative time of concentration from the upstream catchment.
The current model set-up makes use of these properties by following a conceptualised cell-to-cell approach based on storage discharge relationships.During the urban preprocessing, the underlying storage and flow capacities are calculated for each location in the sewer network as a function of the upstream paved surface, the upstream path length in the drainage network, and local design properties (Figure 3).The upstream paved surface and path length are intermediate output of the urban pre-processing and are based on the network data (streets or sewers) and the land use map which defines the impervious areas.The applied time step is determined from the sewer's design velocity and the model cell size.
Multiple sewers can run through a single model cell, while not necessarily entering and leaving the model cell through the same cell interfaces.Flow fractioning was introduced to appropriately divide a cell's incoming flux per inflow side over the cell's outflow sides based on the estimated capacities of the various conduits entering through the inflow side (Figure 3).Flow throttles, which are commonly implemented near overflows, can be represented in the model as well.These throttles cause sudden drops in the preprocessed flow and storage capacities of the sewers.During run-time, the flow fractions are updated each time step to account for backwater effects from each of the downstream cells.Additionally, the vertically entering fluxes are divided over the outflow sides: the fractions for dividing these fluxes are determined during pre-processing as well and are based on the (draining) impervious area connected to each outflow side of the cell.
In many places worldwide, the set-up and maintenance of a detailed digitalised sewer inventory still is too costly.As the conceptualised method of the urban drainage layers follows design rules, it does not require such a databank with sewer dimensions.On top of this, design logic even obviates the need to geolocate sewer locations as a model input.Instead, more commonly available street and terrain data can be used to set up a conceptualised sewer network.It is assumed that combined and sanitary sewers are laid to efficiently transport sewage and rainwater from houses and commercial buildings towards wastewater plants and rivers.Based on this assumption, the street network, subject to a least cost function for digging the presumed sewers into the terrain, is used to set up a proxy sewer network.On a local detailed scale, these proxy sewer networks will obviously show deviations compared to the actual sewer locations.However, part of these deviations will already be cancelled out by the coarser modelling scale of the conceptualised approach.On locations where larger-scale deviations occur in the proxy sewer network, the user has the possibility to improve the pre-processing result in a next iteration by applying expert knowledge: known (approximate) locations of sewers that the least cost function originally missed out on and other important transport mains known by the expert can then be specified in the input data.
The model concept for the urban drainage layer allows the inclusion of overflows and pumps for exchange flows between the urban drainage layers and from the urban drainage layers to the surface layer (Figure 1).Overflows commonly come along with a throttling of the ongoing sewer.With no information available on the extent to which the flow is throttled, the model concept allows the assumption of flow reduction percentages from local design rules, which can individually be altered to match observations.These flow throttles alter the local flow fractions and the downstream storage and flow capacities.At pump locations, care is taken that the storage and flow capacities are reduced downstream of the intake node and raised downstream of the outflow node.This way, the downstream system is dimensioned to convey the additional flow brought in by the pump.
In general, the presented method allows automatic setting up of the urban drainage model purely based on terrain data, street information and locations of the sewer outlets or wastewater treatment plants (Figure 3).Optionally, the input data can be amended with data on sewer locations, pumps, overflows and throttling locations.The first automatic set-up of the urban drainage model is extremely quick, and also further pre-processing iterations to finetune the model with locally adapted input data are very time efficient compared to the current practice to set up detailed physically based models.Despite the conceptual approach, the parameters that can be altered for calibration are intuitive from a sewer design perspective: the typical local storage in the sewer (storage volume available per effectively draining area within the cell), the design return period (both uniform over the urban drainage layers), throughflow percentages at flow throttles, and pump capacities and switch-on levels.
During run-time, the urban drainage run-off is calculated as grid-based, making use of the flow fractions described above.For each cell combination, the actual drainage fluxes are calculated from the pre-processed flow capacities and upstream entering volumes in the previous time step.These fluxes are limited by backwater that is calculated from the upstream and downstream degree of filling (cell volume relative to the storage capacity) and, when going downhill, the average slope derived from the DTM.Moreover, water is allowed to flow in upstream direction when the upstream degree of filling is lower, again taking into account terrain slopes.These return flows become relevant when upstream pumps empty the upstream system and the local degree of filling becomes lower than the degree of filling downstream.
Cell volumes are updated at the end of each time step.When the degree of filling becomes more than 100%, excess volumes are diverted to the surface layer or, in the case of cells with overflows, to the target layer of the overflow.Apart from the excess volume calculation, the filling degree of each cell is also used to determine whether pumps switch on and off.Switched-on pumps transport additional volumes from the cell to a target cell in any specified layer.In the current version of the software, pump discharges are set constant based on the user-specified pump discharge.

Case Study and Model Build-Up 2.2.1. Overview of Needed Data
One of the central points of attention during the development of Flood4castRTF was to minimise the data requirements.Global available data suffice to set up Flood4castRTF.However, adding local data will significantly improve the model completeness and accuracy.
The minimal data required to set up a model in Flood4castRTF are: Surface data DTM data (the resolution of the terrain model determines the resolution of the flood maps); Information on the approximate location of the main stream network.

Urban drainage data
Sewer network or street network; Land use map or impervious surface map; Location of urban structures like pumps, wastewater treatment plants, overflows, throttling locations and interactions with the surface layer.

Description Pilot Case
The first pilot case for Flood4castRTF, the catchment of Ekeren, is a Northern district of the municipality of Antwerp in the Flemish part of Belgium (Figure 4).Part of the catchment is densely urbanised, but it also includes natural areas (e.g., the Oude Landen).Due to this combination of urban and rural areas in the pilot case, Flood4castRTF is optimised for both surface and urban runoff and allows a strong interaction between both.The major streams are shown in blue on the map: the Donkse beek, the Oudelandse beek, and the Laarse beek.The catchment area is bounded on the South by the Albert Channel, in the North the catchment is bounded by the river Schoon Schijn.The larger Schijn river, which collects the surface water coming from upstream rivers to the West and South, was vaulted in a large stormwater conduit (Schijnkoker, shown as a red line in Figure 4) due to urbanisation.At the Western border, the Schijnkoker returns to the surface, where the streams Schijn and Schoon Schijn are pumped to the Scheldt river.In the South, the water from the Schijnkoker is also pumped to the Albert Channel.The pumping stations of the River Scheldt and the Albert Channel are the two major downstream boundary locations of the model catchment.Two additional downstream boundaries are located where streams are connected to the Albert Channel.This pilot case therefore comprises a variety of natural water and complex urban drainage systems.

Surface Data
The DTM is the main input to the surface module.Before the actual surface preprocessing, vectorial GIS data of the local stream network (blue lines in Figure 5) and river outlets (blue dots in Figure 5) are burned into the original DTM.As described in Section 2.1.2at river locations, the terrain surface from the DTM represents the level of the water surface and not the stream bed level.As a consequence, the river's capacity can be significantly underestimated.Furthermore, culverts are burned into the terrain to allow water to flow through these structures.Not burning these culverts would largely impede the river run-off at these locations causing unrealistic flooding upstream of these structures.River outlets occur at downstream boundary locations, where the streams leave the model area or where the streams flow into the urban stormwater layer.As GIS information on culverts is available for this pilot case, the culverts (black lines in Figure 5) are also burnt into the surface terrain which will improve the stream burning process and model accuracy.If necessary, the user can provide additional manual corrections for the DTM during the stream burning step, for example at boundary locations or specific structures.The urban stormwater layer (red line in Figure 5, "the Schijnkoker"), which transports inflowing surface water, is not used in the surface pre-processing but is needed to locate the river outlets.

Urban Drainage Data
Flood4castRTF models the urban network conceptually based on limited input data and general design properties (Section 2.1.4). Figure 6 gives an overview of the input data necessary to start the urban drainage pre-processing.The coloured polygons indicate the different wastewater treatment plant (WWTP) zones, connected to the WWTP's.In the pilot case Ekeren, two urban drainage layers are used to model the urban drainage system.The first urban drainage layer (black lines) transports combined wastewater to the WWTP's, the second urban drainage layer (red line) transports surface water of several upstream rivers and urban overflows in a large stormwater conduit back to the surface system at the Western border of the catchment area.In the pilot case, streets (orange lines in Figure 6) are used to set up the basic urban drainage network.However, additional information on the location of the main transport conduits (thick black lines in Figure 6), which do not always follow topography, is used in the urban drainage pre-processing to improve the set-up of the urban drainage network.These transport conduits receive a higher priority in the determination of the urban drainage network.The location of the main transport conduits was determined from GIS information which is publicly available in Flanders [29].The locations of throttling pipes are shown in green squares in Figure 6.Overflows are characterised by two geographic locations, the location where the urban water flows out towards the surface layer (not shown on map) and the location where the urban flow to the WWTP is limited by throttling pipes or flow-limiting structures.The pilot case also has several important pumps which transport water out of the model area or to downstream locations (yellow lines in Figure 6).A detailed land use map (1 × 1 m 2 resolution) is converted during the pre-processing into a map with impervious and pervious surfaces, which is further used to calculate the rainfall towards the urban drainage and surface layer.

Rainfall Data and Climate Scenarios
The pilot case is simulated with a design rainfall storm with a return period of 100 years (Figure 7).The standard Flemish design storms are composite storms based on IDF relationships and durations up to 2 days are included also antecedent rainfall conditions [30].The peaks are representative for extreme convective summer storms that create flash floods in this region.To evaluate the effect of future climate change for this catchment, two scenarios are simulated: a present day scenario and a scenario with a strong climate change effect.
The climate change scenario is based on the high variant summer climate scenario for Flanders [31].The high variant climate change scenario represents the upper-limit of possible changes in temperature, rainfall, wind and sea level as expected for Flanders in 2100.Climate change affects temperature, precipitation and evaporation patterns.Belgium is situated in Europe's transition zone with expected wetting in the winter and desiccation in the summer and a slight increase in annual precipitation.The climate scenarios for Belgium show relative precipitation changes between a status quo and +38% in winter precipitation volume over 100 years, and between +18% and −52% in summer precipitation volume.During summer months, the number of wet days tend to decrease, although peak precipitation intensities are likely to increase in the high climate scenario.For a return period of 2 years, the change in rainfall intensity amounts to +43% by 2100.The more exceptional the precipitation, the greater the change: up to 62% for a return period of 5 years and up to +109% for 20 years (both for 2100) [31].For this reason, the high summer climate change scenario is simulated for this pilot case because the strong increase in extreme short rainfall events will place additional burdens on sewerage and other urban drainage systems in future.Here, the climate change scenario only accounts for the effect of increased summer precipitation and ignores the effect of an increased evapotranspiration.The rainfall profiles for the current climate and the high climate change scenario are shown in Figure 7.The rainfall is divided over the urban drainage and surface layers.In case a model cell lies in an urbanised area connected to a WWTP, the rainfall on paved areas will flow to the urban drainage layer, whereas the rainfall on pervious areas will generate surface runoff.However, in case a model cell is located outside the WWTP catchments the rainfall will drain to the surface layer.The rainfall is multiplied with a runoff-factor which is based on land use and soil type [32].For the pilot case, a high-resolution runoff coefficient map was available to determine an average runoff-coefficient for each model cell.

Post-Processing
In a final step, the simulated water levels (model grid resolution) are converted to water depths in DTM resolution by a post-processing module in order to generate high-resolution flood maps.The post-processing to detailed flood maps at DTM resolution can be either executed at each desired output time step or only once for the maximum flood depths during the simulation.
The simulated water levels on model grid resolution are first interpolated to a custom higher resolution.After interpolation, the water levels are resampled to the DTM resolution.Flood depths are calculated by subtracting the DTM from the water levels.In the current case study, the presented results are based on an interpolation to 10 × 10 m 2 , before subtracting the DTM.
The postprocessing module calculates flood maps for selected timesteps of the model run and calculates the maximum flooded area of the simulation.An optimisation of the post-processing module including additional volume balance corrections is currently in progress.

General
The Flood4castRTF model results are validated by comparing the resulting flood maps with detailed flood maps generated by well-known, state of the art models JFLOW [33] and Infoworks ICM [13].Infoworks ICM integrates full 1D hydrodynamic urban drainage and river flow and 2D surface runoff modelling.The Infoworks ICM 2D component solves the shallow water equations across a flexible irregular mesh [13].JFLOW offers 2D surface modelling by solving the 2D diffusion wave equation, both for surface runoff and river flow [33].
In order to include urban drainage flow in the JFLOW simulations, the rainfall, which falls on paved areas and is drained by sewers, is subtracted from the local runoff.After smoothening, the subtracted volumes are refed into the surface runoff at the corresponding outflow locations, overflows and waste water treatment plants.Detailed pluvial flood maps are calculated for the whole of Flanders and are currently considered as the Flemish policy pluvial flood maps.These pluvial flood maps are publicly available on the Flemish climate portal [34] and used for policy decisions, resilience measures and urban management.However, to calculate these pluvial flood maps for the whole of Flanders within reasonable time, specialised computer infrastructure was needed.The flood maps produced by JFLOW are extensively validated with historical flood data by all water authorities in Flanders [32].
As a comparison, Flood4CastRTF calculates surface flow by applying the Manning equation on a rough-scale regular mesh where the Manning parameters are determined from subgrids containing finer-scale information.The urban drainage is calculated in a conceptualised cell-to-cell approach on the same regular mesh with all possible interactions between both systems being possible for each model cell.

Flood Maps
Figure 8 shows the maximum depth of flooding simulated by Flood4castRTF, Infoworks ICM and JFLOW in the downstream part of the pilot catchment (a) and in the southernmost part of the catchment (b).The large flooded area in the centre of Figure 8a is the 'Oude Landen' region.This open area is surrounded by urbanised areas with urban flooding.Upstream of the 'Oude landen', major fluvial floods occur as well.It can be concluded that the results of Flood4castRTF lie in-between the flood maps generated by JFLOW and Infoworks ICM, especially for the 'Oude Landen' area.
For the urban flooded areas, no clear trend of over-or underprediction can be noticed.At some locations the flooded area is more extensive in Flood4castRTF compared with JFLOW and Infoworks ICM; at other locations the reverse can be noticed.Similar differences however in local flooding can be noticed between JFLOW and Infoworks ICM.The purpose of Flood4castRTF is to integrate urban and surface run-off into one flood prediction model.Based on the generated flood maps for this pilot case, it can be concluded that the result of Flood4castRTF lies between the results calculated using Infoworks ICM, which is set-up based on a detailed inventory of the urban drainage system and the flood maps obtained by using JFLOW, which only models surface run-off in detail, and is currently used as reference maps for pluvial flooding in Flanders.The confusion matrix (Table 1) is calculated to evaluate the correspondence and deviation of the three different flood prediction models with each other.This confusion matrix gives four possible agreements between simulation results and observations [35,36].For this pilot case, the observations are replaced with the flood map, generated by JFLOW and is therefore considered as the reference flood map.
The true positive (TP) value represents the area which is flooded in the reference model simulation and Flood4castRTF simulation, the true negative (TN) value gives the area which is not flooded in the reference model simulation and Flood4castRTF simulation, the false positive (FP) gives the area which is flooded in the Flood4castRTF simulation but not in the reference model simulation, and the false negative gives the area which is not flooded in the Flood4castRTF simulation but flooded in the reference model simulation.These statistics are calculated for the results obtained by Flood4castRTF vs. Infoworks ICM and JFLOW.This allows a broader comparison of the different flood prediction models.
Based on these statistics, the true positive rate (TPR) can be calculated as TP/(TP + FN) and the positive predictive value (PPV) as TP/(TP + FP).Higher TPR and PPV values indicate that the model better approximates the reference flooding.
Before the calculation of the statistics, small water depths (<5 cm) are removed from all the flood maps of the three flood models (Infoworks ICM, JFLOW and Flood4CastRTF) using GIS techniques.As the flood models are very different in model set-up and structure, it is difficult to compare small water depths.Additionally, these small water depths do not generally represent flood risks.Therefore, it is acceptable to remove these small water depths from the flood maps in order to focus on actual flooded areas.For the JFLOW flood maps, a combined criterium, based on water depth and flow velocity, is used to remove minor floods wherefore also a significant amount of water depths in the range 5 to 10 cm are removed from these flood maps.Figure 9 illustrates the differences in flooded areas between the three flood prediction models.The dark blue areas in the flood maps correspond with the true positives.In the comparison of Flood4castRTF with JFLOW, the green areas show the false positives and the light blue areas the false negatives.For the comparison between results of Flood4castRTF and Infoworks ICM, the green areas show the false positives and the red areas the false negatives.Finally, in the comparison of Infoworks ICM and JFLOW, the dark blue areas are the true positives, the red areas the false positives and the light blue areas the false negatives.
From these difference maps, it can be easily noticed that there are both differences and similarities between the maps calculated by the three models.There are more urban floods (streets) in Infoworks ICM compared with Flood4castRTF and JFLOW, however the additional floods in Infoworks ICM on streets have (at most locations) a small water depth (<10 cm).In the southern part of Ekeren, more floods are simulated by JFLOW which are not simulated by Infoworks ICM and Flood4castRTF.This difference in flood maps is caused by the presence of a culvert allowing the southern part to drain in the Infoworks ICM and Flood4CastRTF models.This culvert is present in the JFLOW model as well but the throughflow capacity is not representative.This stresses the importance of the validation steps during the set-up of a flood model surfacing the need of local information on for example constructions.In other words, the quality of the input data and validation is equally important to the model structure.
For urban floods in general, the result of Flood4castRTF is more comparable with the result of JFLOW.Infoworks ICM models the urban drainage system in a very detailed manner based on a sewer inventorying, which is different compared with the simplified approach in JFLOW and the conceptual urban drainage model in Flood4castRTF.For this pilot case (using Flood4castRTF), only street information, the location of the main transport conduits and overflows were considered to set-up the urban drainage system, combined with general design criteria for the total catchment.The result of Flood4castRTF could however be further improved by adding additional information on the actual location of the sewer pipes or modify design properties at specific locations to reduce the flow capacity or storage in the pipes.This detailed model set-up is however not the purpose of Flood4castRTF.It can be concluded that the result of Flood4castRTF, based on basic input data and global urban design criteria, lies between the model results of a detailed physically based model (Infoworks ICM) and the reference pluvial flood model for Flanders (JFLOW).Table 2 gives the validation statistics for Flood4castRTF compared with the two reference models Infoworks ICM and JFLOW for the two selected urbanised zones within the pilot catchment (downstream part of the pilot catchment, Figure 9a, and southernmost part of the pilot catchment, Figure 9b).The validation statistics between the two reference models are also included in the table.Based on these statistics, it can be concluded that Flood4castRTF performs similarly to the two detailed flood models.When the two detailed validation models are compared with each other, it is clear that these models have a similar deviation from each other compared with the deviation with Flood4castRTF.To summarise, it can be concluded that the flood models show different flooded areas, whereby Flood4castRTF lies in between Infoworks ICM and JFLOW.Figures 10 and 11 show for the three flood models the flooded area for different water depth classes (5-10 cm, 10-25 cm, 25-50 cm, 50-75 cm, 75-100 cm and >100 cm) in the downstream part of the pilot catchment and in the southernmost part of the catchment, which are the two main urbanised regions of the pilot catchment.However, during the post-processing of the flood maps of JFLOW, a combined criterium for removing minor floods from the flood maps, based on water depth and flow velocity, is used.This causes a significant amount of water depths in the range 5-10 cm to be removed from the flood maps of JFLOW.This explains the difference between JFLOW and Flood4CastRTF/Infoworks ICM for water depth class 5-10 cm in Figures 10 and 11.However, Flood4CastRTF and Infoworks ICM show comparable flooded areas for low water depths (classes 5-10 cm and 10-25 cm).In general, JFLOW predicts larger areas for each water depth class (expect class 5-10 cm) which can partly be explained by the very simplified modelling of the urban drainage system in JFLOW.In JFLOW the urban drainage system is modelled by subtracting the rainfall which falls on paved areas from the local runoff and refed the subtracted volumes into surface runoff at the corresponding outflow locations, overflows and wastewater treatment plants.This approach to model urban drainage is much more simplified compared with Infoworks ICM and Flood4CastRTF.Infoworks ICM allows full 1D hydrodynamic modelling of urban drainage which is again more detailed than the conceptualised set-up of the sewer network model in Flood4CastRTF.However, based on the results of our first pilot case, it can be concluded that the simulated floods and water depths of Flood4CastRTF approaches these simulated by Infoworks ICM, except for the higher water depths, where the predicted water depths by Infoworks ICM are lower.
In the downstream part of the pilot catchment, there are clearly many more flooded areas in JFLOW compared with Flood4CastRTF and Infoworks ICM (classes 10-25 cm and 25-50 cm), which can also be noticed from the flood maps (Figure 10).This is due to the flooding in the central part of this region in JFLOW.In Infoworks ICM and Flood4CastRTF a culvert is present in the model, draining this area, resulting in less predicted flooded areas.In JFLOW this culvert is also present in the model, however, as explained before, with a lower throughflow capacity.Minor differences in how local urban hydraulic structures are implemented in the model can result in major differences between predicted flood maps.Flood4CastRTF allows inclusion of local urban hydraulic structures as culverts, overflows and pumps in the flood model, wherefore it is possible to optimise the model set-up and improve model results, based on validation data.

Climate Change Scenario
Figure 12 shows the expected effect of a strong climate change scenario (2100) on the flood maps in the downstream urbanised part of the catchment for a storm with a return period of 100 years.The high summer climate change scenario is developed to investigate the effect of high intensity summer storms, related to urban flooding.Flood4castRTF allows the user to investigate very fast the effect of climate change scenarios on future flood extent and water levels.
Flood mapping is a crucial component of flood risk management.The flood hazard maps for 2100 allow governments, water managers or spatial planners to identify areas which are vulnerable to potential flooding due to climate change and prioritise actions in their flood risk management to make areas sensitive to additional flooding in the future and more climate-robust.
The total flooded area for this pilot catchment is expected to increase in 2100 from 996 ha to 1634 ha due to climate change which means an increase of 64%.

Performance
The presented method focuses on reducing the simulations' run-times by transferring computationally intensive tasks as much as possible to the pre-processing.Since this pre-processing is highly automated and can be done initially for a complete catchment within a few iterations of fine-tuning, a relatively high computation time for pre-processing is considered less costly than for run-time simulations.Moreover, short run times facilitate real-time applications in large urban areas in the future.
In this section, pre-processing and run times are analysed for a design storm with a return period of 100 years in the presented pilot case Ekeren (Section 2.2.2), applying 100 × 100 m 2 model cells to the 87.5 km 2 area.Simulations were performed on a notebook PC with an Intel ® Core™ i7-8750H CPU @ 2.20 GHz processor (six cores) and 16 GB of installed RAM memory.

Model Build-Up
Table 3 presents the times needed to build up the model.Except for the parameter optimisation, the model build up is a completely automated process from the moment that the input data are uploaded.In other words: after data collection, the algorithm needs less than a day to automatically generate a first working model.The calibration and finetuning of the model are straightforward with changes to intuitive model parameters (Section 2.1.4)and, where necessary, the input data.Normally, the urban drainage layer pre-processing requires multiple iterations, whereas the surface pre-processing tends to suffice with the initial input data (i.e., the necessary input data typically results from Earth surface sensing products that are relatively accurate).For the urban drainage pre-processing, each iteration results in an additional time of maximum a few hours to implement the model updates and a pre-processing time of 32 min each iteration for the considered pilot case.Changes to the input data for the stream burning lead to more significant additional pre-processing times as the surface LDD and subgrids are pre-processed from the stream burned DTM.However, these are automated pre-processing algorithms that can be run overnight.Moreover, the subgrids are only recalculated for the model cells with effective changes to the DTM, resulting in additional subgrid pre-processing times that can be down to a few minutes.
(1) : Only local re-runs needed when the DTM is changed locally during pre-processing or model updates; (2) : repetitive runs during model finetuning in the pre-processing phase.
In contrast, physically based models thrive on the existence of sewer databanks that require regular updating and data completeness.Typically, such databanks contain sewer links that are not well connected and missing data, for example on sewer dimensions or overflow crest levels.Therefore, the building of a fine functioning model requires a lot of manual work and local finetuning.Typical build-up times for an integral physically based model in the current pilot area are between 6 and 12 months.Conceptual urban run-off models can be built up quicker, but demand more extensive calibration, often with less intuitive parameters.

Run-Time
The simulation of a 36-h design storm with a return period of 100 years in the pilot study area takes 191 s when exporting minimal output to produce flood maps each simulated 5 min (Table 4).The peak of this 36-h design storm occurs at 12 h, so that a post-event duration of 24 h is simulated.The short calculation times make output writing a relatively heavy process, with the export of each additional variable adding about 10 s (~5%) to the simulation time for the current model size and duration.
The different nature of the existing models complicates a 1-to-1 comparison.As a rough comparison, fine-mesh 1D-2D physically based models would typically require between 1 and 3 h on a similar machine (i.e., with possibility for GPU computing) for the same area and storm.Completely conceptual approaches would typically require run times in the order of 1 to a few minutes.In this respect, the presented model concept approaches the simulation times of conceptual models whilst maintaining a spatially distributed approach.Further optimisation of the current code can possibly reduce the run time.

Post-Processing
The post-processing module takes ~3 min on a commercial notebook to produce flood maps.Flood maps are generated by interpolating simulated water levels on model grid resolution to a 10 × 10 m 2 resolution, followed by a resampling of the interpolated water levels to the original DTM resolution of 1 × 1 m 2 .Flood depths are calculated by subtracting the DTM from the water levels (Section 2.2.6).As a reference, subtracting the DTM at 100 × 100 m 2 resolution before resampling only takes ~0.5 min.However, this post-processing approach without initial interpolation to a higher resolution was found to produce inaccurate results.
The current unoptimised post-processing algorithm is still too slow for real-time application at a high output time step resolution (typically 5 min for real-time applications) and at high resolution.Therefore, it is currently under further development to largely reduce the calculation times in post-processing.

On the Use of the MANNING Equation
Due to the aim to develop a model with reduced complexity, a choice was made to apply the Manning equation for flow calculations.This choice does compromise the model accuracy, most notably when it comes down to smaller-scale velocity variations.Flood4CastRTF calculates cell-to-cell velocities that are purely representative as average velocities over the cell interfaces.By using subgrids, the calculations do preserve locality of the terrain when determining the Manning equation variables.The inclusion of these detailed data is needed to accurately predict the average cell-to-cell velocities, and consequently the cell-to-cell flows.
The Manning equation inevitably becomes less accurate when extrapolated to cases for which it was not developed.In particular, the Manning equation is known to behave less accurately for steep and shallow slopes.These effects are not counteracted in the current version of the model, because they are not of first order impact on the accuracy.However, pragmatic solutions could be considered like adaptive Manning friction values for shallow water depths, which could be made part of the subgrids that represent the complete range of possible water levels.Such modifications to the flow calculation with the Manning equation are considered for a later version of the model.

Applicability in Data-Scarce Areas
The presented case study concerns a Belgian urban catchment that is largely described by publicly available detailed GIS data.This subsection discusses the application in datascarce regions.
Although the availability of detailed terrain data facilitates the model accuracy, the model is expected to perform with less detailed digital elevation models (DEM) as well.More precisely, the resolution of the DEM will determine the degree of local topography taken into account in the model set-up and the resolution of the flood maps.High-resolution DEM data include detailed information on urban structures like roads, bridges and dikes which determine the surface runoff.Especially in urban environments small scale topogra-phy, better represented in high resolution DEM, can significantly affect modelled water depth and flood extent [37,38].
On the other hand, a lower-resolution DEM (e.g., the worldwide available ~30 m grid [39]) can be sufficient to apply an accurate stream burning when interpolated to higher resolutions.This way, the important conveyance capacities of streams can be burned in higher detail compared to the detail of the original terrain.
To summarise, the use of less accurate digital elevation models will undoubtedly compromise the model accuracy.However, depending on the situation, the accuracy of the modelled stream run-off can be largely maintained by applying the stream burning method presented in Section 2.1.2.In urban areas, one would always need additional data on building locations to improve rough-scale digital elevation models, as the presence of these buildings largely determine the surface run-off in such areas.
Another required input to Flood4CastRTF is land use information.For accurate modelling, the land use data are at least required to roughly represent the locations of impervious or less pervious areas.These areas determine the fraction of the rainfall that runs off over land or, in areas where an urban drainage system is foreseen, through the sewer network.Lower-resolution data of land use are available from global datasets.For example, a global land use map with a resolution of 30 m was derived from Landsat TM and ETM+ data as described in [40].
The presented case study demonstrates that a valid urban drainage model can be set up based on street data.The model set-up was further improved by adding knowledge on the locations of important transport mains in the sewer system.This information may generally not be available as readily available GIS data in data-scarce region.However, local expert knowledge on the locations is generally available, which allows easy sketching of these mains in a GIS software to prepare this model input.Moreover, the modelling approach of Flood4CastRTF is not sensitive to slight deviations from the actual sewer locations and does not require further dimensional data on the sewers.

Conclusions
To overcome the disadvantages of requiring high calculation power and extensive data needs of detailed physically based models, the Flood4castRTF model was developed.The model is meant for real time flood forecasting and for scenario analysis including climate change scenarios.The principles for the design of Flood4castRTF is to maximise the availability of flood predictions to a wide range of users minimising the total cost and data needs for model set-up and maintenance.
Flood4castRTF makes maximal use of readily available (GIS) data and typical design criteria for the modelled region to facilitate the model set-up process.The model integrates hydrological modelling with 2D overland flow and urban drainage flow, while keeping the model equations sufficiently simple to minimise the computational demand and guaranteeing an optimal balance in accuracy of the different model components.Flood4castRTF can therefore also be applied in data scarce areas and produce reliable results.
The presented approach to predict the flood extent and flood depth is successfully demonstrated for a catchment in Antwerp (Belgium).This catchment includes both urbanised and rural areas and contains several complex hydrological and hydraulic interactions, which allowed evaluation of the Flood4CastRTF model in different environments.Although the model results of Flood4CastRTF could not be validated against actual measured water levels or discharges, the model results have been compared with results obtained from two other state-of-the-art models.However, each state-of-the-art modelling approach is different, because these models have been built with a certain purpose and with certain approximations.The Flood4castRTF model balances these approximations, which often leads to results that are in between these state-of-the-art models.
Although comparison with real floods is difficult, the accuracy of the Flood4castRTF model is expected to be slightly lower than more detailed physically based models, but the drastic decrease in data needs to build and maintain the model as well as the limited time to set up the model are obvious advantages that create a large potential for it.
Due to fast urbanisation in many places in the world combined with climate change, flooding risks will become more and more problematic.Our modelling approach allows to build models for data scarce (urban) areas and obtain reliable model results in a relatively short period.

Figure 1 .
Figure 1.Modular approach and layer interaction in Flood4castRTF.

Figure 2 .
Figure 2. Surface pre-processing (dark blue: minimal input data, light blue: optional input data, green: calculated data/maps during pre-processing).Calculations are shown in italics; input and output data are shown in data containers.The surface layer is spatially discretised by a 2-D uniform Cartesian grid.During run-time, grid cell boundary fluxes are calculated using the Manning formula:

Figure 3 .
Figure 3. Urban drainage pre-processing (dark blue: minimal input data, light blue: optional input data, green: calculated data/maps during pre-processing; input in gray is non-geospatial).Calculations are shown in italics, input and output data are shown in data containers.

Figure 4 .
Figure 4. Pilot catchment Ekeren, north of Antwerp.The major streams are shown in blue.In red the major stormwater conduit ("the Schijnkoker") is shown.The downstream boundaries are indicated.

Figure 5 .
Figure 5. Input data pilot case for the surface pre-processing.

Figure 6 .
Figure 6.Input data pilot case for the urban drainage pre-processing.

Figure 7 .
Figure 7. Design storm with a return period of 100 years for the current climate (estimated for 2016) and high summer climate change scenario in 2100 (high climate change summer, hCC summer, gray line) (based on data published in[30,32]).

Figure 8 .
Figure 8. Maximum flood depths (return period 100 years) in the downstream part of the pilot catchment (a) and southernmost part of the pilot catchment (b) simulated by Flood4castRTF, Infoworks ICM and JFLOW.

Figure 9 .
Figure 9. Differences in maximum flooded area between the three flood prediction models in the downstream part of the pilot catchment (a) and southernmost part of the pilot catchment (b) Flood4castRTF vs. JFLOW (up), Flood4castRTF vs. Infoworks ICM (centre) and Infoworks ICM vs. JFLOW (below).

Figure 12 .
Figure 12.Maximal flooded areas under the current climate (light blue) and in case of climate change (high climate change scenario, dark blue) using Flood4castRTF in the downstream part of the catchment (left) and in the Southern part (right).

Table 2 .
Flooded area (ha) JFLOW vs. Flood4castRTF, Infoworks ICM vs. Flood4castRTF and validation statistics Total positive rate (TPR) and Positive predictive value (PPV) for JFLOW vs. Flood4castRTF and Infoworks ICM vs. Flood4castRTF.Validation statistics between the reference models JFLOW and Infoworks ICM are shown in italics.

Table 3 .
Pre-processing times on a notebook with a 6-core i7 processor without code optimisation for a simulated duration of 36 h in a heterogeneous catchment of 87.5 km 2 .

Table 4 .
Run times on a notebook with a 6-core i7 processor for a simulated duration of 36 h in a heterogeneous catchment of 87.5 km 2 .