Representing buildings and urban features in hydrodynamic flood models

Flood risk in cities and built‐up areas is a major threat which is likely to grow due to increased urbanisation and climate change. It is a priority for urban planning, civil defence and insurance to accurately represent buildings and urban features in hydrodynamic models to assess flood risk to people, properties, assets and infrastructure in an uncertain future. The correct representation of urban features in models is currently blocked by the lack of detailed and accurate techniques and has become a priority for the improvement of urban flood modelling now that better data and computational resources are available. This study has reviewed the available approaches for the representation of buildings and urban features and implemented the widely used ‘stubby building’ approximation as well as a more realistic and innovative ‘building hole’ approach using the hydrodynamic model CityCAT. The city centre of Newcastle upon Tyne, UK, was used as a case study, allowing independent validation of the methods and direct, systematic comparison of performance. Shortcomings of the approximate method are described, and guidance given on limits to its reliable application and scope for improvement.

Flood inundation models have become an essential tool in understanding flood events, assessing flood risk and predicting future risk to urban fabric (Willis et al., 2019).The latest generation of hydrodynamic models is capable of simulating flooding in the urban environment where the topography with buildings, drainage networks, and critical infrastructure are complex (Guo et al., 2021).
High-resolution Digital Elevation Models (DEMs), Digital Surface Models (DSMs) and Digital Terrain Models (DTMs) play a key role in hydraulic models in defining the pathways of flood into cities (McClean et al., 2020).Hydrodynamic models have undergone rapid development exploiting new numerical schemes, more powerful computational implementation, as well as higher resolution data and a major leap in predictive capabilities is possible.The increasing demand of accurate and reliable estimates of surface water flood risk and flood risk protection of the assets, infrastructure and man-made constructions for flood insurance purposes and for urban planning by local authorities, drives this development of hydraulic models with more realistic results (Kilsby et al., 2020).Such studies are important due to global change and the possible 'unknowns' to be faced.Several studies have been conducted applying 2D hydrodynamic models to complex urban problems, including numerical solutions of the 2D shallow water equations (Choley et al., 2021;Leandro et al., 2009;Mignot et al., 2006;Paquier et al., 2015), the surface water movement around buildings and the underground drainage system.A few of these studies have focused on the demanding issue of how to represent buildings within 2D hydraulic models as obstacles to water flow (Bellos & Tsakiris, 2015;Beretta et al., 2018;Bisht et al., 2016;Glenis et al., 2013;Maksimovi c et al., 2009;Néelz & Pender, 2013;Rak et al., 2018;Schubert & Sanders, 2012;Schubert et al., 2008;Syme, 2008;Zhou et al., 2016) for pluvial flooding applied in urban areas.
A large proportion of urban areas is covered by buildings and during flood events they exert significant influence on flow paths as water will only flow through them in cases when the main entrance or windows are open or the flood water exceeds the threshold of the entrance (Fewtrell et al., 2008;Wang et al., 2010).Alcrudo (2004) presented different approaches for the representation of buildings including (a) vertical walls to exclude buildings from the computational grid; (b) the bottom elevation approach, that is, raising the elevation of the building to reach the rooftop; and (c) the local friction based representation of buildings, increase the friction coefficient (values between 0.50 and 1.00) where buildings exist; he concluded that removing buildings from the computational grid is the most accurate representation.Hunter et al. (2008) presented a test study to compare the performance of six 2D hydraulic models to simulate surface flooding of an urban catchment in the city of Glasgow, UK which showed an effective approach is to represent a building in hydrodynamic models by raising its elevation up to 12 m (high buildings) or 6 m (small houses) to allow water flow around it, the so-called 'island method'.Chen et al. (2012) proposed another approximation by abstracting the buildings from a coarse grid and using the building coverage ratio and a conveyance reduction factor.Glenis et al. (2018) showed how the buildings' footprint can be excluded from the computational grid and replaced by no-flow boundaries to improve the ability of the model to capture realistic flow paths in the built environment.In their method, the buildings are retained as objects which can support other process representation (e.g., storage and/or flow of rainfall from roof surfaces, and ingress of flood water).
In this study the two most widely used approaches for representation of urban features in hydrodynamic are assessed by validation against a real flood event: (a) the exclusion of buildings from the computational grid ('Building Hole'), and (b) the raising of the buildings' footprint by 30 cm ('Stubby Building').Moreover, a detailed analysis of multiple 'stubby' models is presented and an improved version of the 'Stubby Building' technique is proposed.

| Modelling system
Among the many hydraulic models developed for surface flows, one of the most advanced and fully featured is CityCAT-City Catchment Analysis Tool, a fully coupled 1D/2D urban flood modelling tool, developed at Newcastle University for surface flow, representation of buildings, sewer network and blue-green infrastructure with interventions (Glenis et al., 2013(Glenis et al., , 2018)).It also enables the assessment of benefits of different flood alleviation measures.CityCAT can produce maps and time series for given rainfall inputs of flood depth, flow velocity and volume in and out of manholes, gully drains, buildings etc (Kilsby et al., 2020).The software architecture in City-CAT is based on the object-oriented method which offers flexibility in development and rapid function extension (Glenis et al., 2018;Kutija & Murray, 2007).The DTMs for the topography and the UK Ordnance Survey Master-map© (Lidar, 2016;MasterMap, 2020;Ordnance Survey, 2020) data for urban features such as roads, permeable surfaces, and buildings, are standard datasets used by CityCAT.
The building footprint is excluded from the computational grid with no-flow conditions implemented along the building walls, which improves the ability to capture the flowpaths where they are constrained by buildings.
In general, exclusion of buildings also delivers a reduced simulation time due to the reduction in the number of computational cells of 29% in this application, which will be greater in other more densely built areas.The concentration of flow between buildings and consequent increased flow velocity may require a reduction in time step to ensure stability resulting in longer computational time, but this is limited to a small proportion of the simulation at the flood peak when high flows occur.This is also counteracted by a further reduction in computational time, as the more concentrated flows resulting from no-flow building walls transfer the flood wave more rapidly than the more dispersed wave in the stubby building case, so requiring shortened timesteps for a reduced duration.Timings of equivalent simulations using Building Hole and Stubby Building methods show a reduction of 28% in computational times, therefore confirming that the dominant effect is the reduction of the number of computational cells.
To simulate the free surface flow, the 2D shallow water equations are used in their conservative form and the solution is obtained by using a high-resolution finite volume method with shock-capturing schemes (Glenis et al., 2018).The infiltration for green areas is calculated with the Green-Ampt method (Warrick, 2003) allowing 1-D, vertical, transfer of water.

| State of the art
Hydraulic models generally approach the representation of features like bridges, embankments, leaky barriers and buildings as an obstacle inside the model, so the simulations are much quicker and easier to run but often deliver incorrect and unrealistic results.The most common techniques to represent buildings in 2D hydraulic models are: (a) the 'Building Block' (BB) method where the buildings are modelled by raising the local topography to the roof level, so the flood cannot flow into cells unless the water levels reaches the roof.This method is not often used as the large water surface elevation difference between roof and ground level causes instabilities in most numerical schemes; (b) 'Building Hole' (BH) where the cells with buildings will be clipped from the DEM/DTM and they are not involve in the simulation; (c) 'Stubby Building' (SB) where the buildings are represented by raising the DEM/DTM within the buildings' footprint by (typically) 30 cm, thus avoiding large elevation differences between neighbouring cells (CH2M, 2019; Kilsby et al., 2020;SEPA, 2018;Shen et al., 2018;Syme, 2008;TUFLOW, 2018).
Furthermore some studies (Bach et al., 2014;Beretta et al., 2018;Hunter et al., 2008;Schubert et al., 2008;SEPA, 2018;Syme, 2008;Teng et al., 2017) replaced buildings by a flat area with high roughness, for example, Manning coefficient between 0.50 and 10, which is intended to slow and store water on the building footprint to reduce downstream transfer.With sufficient calibration, such models can deliver plausible large-scale results for some situations, but at a local street or building scale methods such as SB or enhanced roughness introduce un-realistic flow paths and systematic underestimation of 'blocking' of flow which may in some situations cause significant ponding.

| Aims of this study
In this study, we will assess the performance and identify the differences between the 'Building Hole' and the 'Stubby Building' approaches.These two techniques are widely used in industry to estimate flood risk in cities, where the hazard is higher, due to human lives, assets etc, and depth damage calculations are applied to buildings (SEPA, 2018).The other technique identified earlier, using increased roughness is less widely used and presents major issues with non-realistic flow pathways, so is not assessed here.
The BH approach represents buildings as void space where the cells within the building are removed from the computational grid.The surface water cannot flow into the building voids, so the water flows around the building boundary (Bertsch, 2019).In addition, reduction of the simulation time from a smaller number of computational cells is an advantage, especially for dense built-up areas.In this study the BH numerical grid has 29% fewer cells than the SB numerical grid.With the SB approach, the threshold (h) of the building entrance height is used for the representation of buildings into the model.However, due to the variable entrance height of the buildings and to avoid instabilities in the model with large elevation differences, the most common values are 30 to 40 cm.Typically, buildings are assumed to be constant 30 cm above the local ground level elevation of the DEM/DTM which prevents water from flowing into buildings until the water depth exceeds 30 cm and can then flow over the building (Pettit, 2014;SEPA, 2018).

| Study area
Having outlined the principles behind the techniques to represent urban features in hydrodynamic models, a case is conducted in the city centre of Newcastle upon Tyne, UK.The domain has complex topography due to some substantial slopes and a range of roads of different widths, as well as green areas, and a variety of buildings of different plan areas and heights.This diversity provides a substantial opportunity to explore the behaviour of the urban features in the model with some 5422 buildings present.An additional advantage is that the area was subject to a major pluvial flood on 28 June 2012, and documentation of the flow paths and damage to exposed buildings is available for validation (see Section 3.4).Figure 1 shows the area of the case study with the general downslope flow direction is to the bottom, right (south-east) corner into the river Tyne.

| Model set up
CityCAT (Glenis et al., 2018) was used to simulate flooding and urban features in this study for all models.The flow domain was constructed using Light Detection And Ranging (LiDAR) terrain data at resolution of 1 m (area of each cell is 1 m 2 ), while the building footprints and the green spaces were extracted from Edina Digimap (Lidar, 2016;Ordnance Survey, 2020).The catchment comprises 4,000,000 cells resulting in a total area of 4.0 km 2 (2,842,209 cells for the BH as the buildings footprint is excluded from the computational grid and 4,000,000 cells for the SB).The infiltration of water in pervious areas is estimated using the Green-Ampt method (Warrick, 2003) and the outer boundaries of the domain are transmissive.MasterMap data are used to delineate urban features such as roads, permeable areas, and impermeable areas.The centroid of each computational cell and the polygons for the urban features are used to classify each cell and assign friction coefficients and soil properties.
For the SB approach, an algorithm was developed to prepare the DEM for CityCAT starting from the DTM (i.e., the lidar coverage with the buildings removed) and adding 30 cm to cells identified within the building footprint shapefiles.This process replicates the standard procedure in the flood modelling industry (CH2M, 2019).Furthermore, we identified some 'errors' (see Section 4) affecting DTMs inside the building footprints in specific locations in the Area of Interest (AOI), where a new algorithm was developed to identify anomalous depressions within a building footprint and restore the elevation of these areas to ground level, adding 30 cm for the 'stubby platform' approach.
For the BH approach, a custom mesh generation procedure is used which removes any cell of which more than half falls within the building shapefile (see Glenis et al. (2018) for full description, Figure 2).A spatially F I G U R E 1 Urban features in the study area of Newcastle city centre, UK.Grey represents the buildings, green the permeable spaces, yellow the impermeable surfaces and blue the main river.
uniform rainfall series is used to drive all the simulations, based on the depth of the historical storm of 28 June 2012 (45 mm in 2 h, see Figure 3).The rainfall falling onto roofs is redistributed to the neighbouring cells of the computational grid.A range of simulations with storm events of 1 h duration and return periods of 50 and 100 years (2% and 1% Annual Exceedance Probability, respectively) are used to compare the two approaches and identify the differences in flow paths.The primary aim is to validate and better understand the techniques for the representation of buildings, so we excluded the sub-surface drainage network system from the simulations reported here.While model results with and without the sub-surface network show differences in some locations, the main features of flooding are similar for this very large event, and acceptably close to the observed impacts (Glenis et al., 2018).

| Flood exposure analysis
Building outlines from OS (MasterMap, 2020; Ordnance Survey, 2020) were used to estimate the flood risk to buildings by analysing each model's maximum flood depth output in a one-cell wide buffer around the building outline.Buildings were classified as flooded if the flood water is above a typical property threshold of 30 cm (Bertsch, 2019;Bertsch et al., 2022;Environment Agency, 2021; Table 1).

| RESULTS AND DISCUSSION
The performance of each simulation was compared in terms of the flood depth, the number of buildings inundated and the water flowpaths.The complex topography and the high slopes around the city centre allow examining detailed water flowpaths and the direct influence on buildings.Figure 4a presents the study area with the 'Building Hole' technique for the storm of 28 June 2012, and it can be seen that the flowpaths change direction or stop when there are buildings in the way, which is physically realistic.Thus, Figure 4b shows, for the same storm event, that with the 'Stubby' approach, while the broad distribution of flood water is similar, the flood flowpaths frequently traverse the buildings where the water depth outside them exceeds the 30 cm threshold, which is not physically realistic.Proponents of the SB approach suggest that this process represents ingress to the building and subsequent egress, but this is very speculative, and the number of instances in this simulation show that there is a major mis-representation of flow pathways due to the approximation of 30 cm roof elevation of the buildings.
Table 2 presents the water mean depths between the two techniques in different storm events, and it is clear that the mean depths are higher with the BH approach than with SB, which is plausible due to the exclusion of buildings from the computational grid and increased number of cases of flow blocking.

| Velocity comparison
Furthermore, a useful extension of flood modelling in dense cities is to capture the correct direction of water flow paths and velocity considering the roads, pavements, all types of buildings, topography etc.A detailed comparison of velocity of flows is presented in this section between the 'Building Hole' and the 'Stubby Building' approach.
Figure 5a presents the mean velocity of flow averaged over all grid squares in the domain for the two approaches.It can be seen that the velocity of flow with the BH approach is somewhat higher than with the SB which is consistent with the higher friction in the SB domain due to lower water depths overall, relative to the BH case where flows are channelled between buildings.Figure 5b shows that the differences in percentiles of the velocity of flow for the 70 min of the storm event are minor until the 70th, where the BH values are larger.The differences are largest for the 90th and the 99th percentiles, that is, the deepest flood waters.
A detailed comparison of modelled flows is presented in Figure 6, near the Merz Court building on Newcastle University campus which was severely flooded.It is clear that in graphs (a) and (c) with the BH approach, the flood water changes direction on reaching the building and flows around it, as observed during the storm event.In contrast, with the SB approach the flood water flows over the building, generating unrealistic flowpaths.T A B L E 1 Classification scheme for calculating flood exposure likelihood for buildings (Bertsch, 2019;Bertsch et al., 2022).

Exposure class
Mean

| Comparison of modelled flow depths
To examine the differences between generated flow paths from the two approaches, two small areas of the domain were extracted.First, Figure 7  map.Figure 8 shows photographs taken during the storm event which provide detailed validation of the modelled depths upstream of Merz Court.
Figure 9 shows results from CityCAT simulations with BH and the SB approaches and it is apparent that with the SB the flood water flows over/through the Merz Court building, and a deep pond was created in the roof on that building.While the building is documented as having suffered major flood ingress in the 2012 event, the observed flooding closely corresponds to that generated by the BH method, including the deep upstream ponding (see Figure 8).
Results from a second area on the city centre which was subject to severe flooding are shown in Figures 10  and 11 where it can be seen that the SB model again generates flood flows which overtop and flow 'through' buildings.This creates small 'ponds' on buildings due to 'errors' in the DTMs, as discussed in Section 4, which are then characterised as high flood risk, which is not physically realistic.These 'errors' in the DEM are likely to be associated with buildings located on sloping ground (around 1 in 5, 20% gradient in this instance) due to poor identification of a mean 'ground level' for the area to allow interpolation within the building outline.

| Flood hazard to urban features
In order to identify the critical differences to water flowpaths between the two approaches, flood depth maps buildings in the high-risk class are around one third less of the totals due to the flood water which spreads more frequently onto buildings.Thus, SB30 models underestimate the flood risk to buildings due to the widespread ingress of water.
An artefact of the SB approach is that systematic differences in ground level across the domain are introduced, so generating increased gradients (at building outlines).Figure 13 shows the distribution of local slope calculated as the maximum elevation differences between grid square and its four neighbours.It can be seen that the initial DEM is smoother in contrast with the generated DEM for the 'Stubby Building' approach, where a variation in elevation has been introduced between 0.20 and 0.40 m.This is further evidence that water flow will be modified in the simulations, with consequent change in flow paths and velocities.

| Validation of the 'Building Hole' and the 'Stubby Building' against a real storm event
The approach taken here to validation of the models is to estimate the flood exposure of each building and compare it with flooding in areal observed event.In a recent study by Bertsch et al. (2022), a new tool was developed to assess exposure of buildings to flooding and validate against a real flood event in Newcastle upon Tyne, UK.The 'Building Hole' approach was used for the representation of buildings and the model successfully predicted between 68% and 75% of the surveyed buildings that suffered from flooding.
In this section, a validation between the BH and the SB approaches will be presented for the buildings of the Newcastle University campus that suffered from different causes of flooding (from the surface and from the drainage system) during the storm event on the June 28 2012, also called the 'Toon Monsoon'.Of 100 buildings on the campus 20 were flooded and are presented in Table 4 with a description of the flooding mechanism.The location of the buildings and the dominant flooding mechanism are shown in Figure 14.
Additionally, Figure 15 shows the water depth modelled with the BH approach in four different locations where observed data existed.The CityCAT model correctly identified 80% (16 of the 20 buildings) of the affected buildings.Exposure calculated with water depths modelled with the 'stubby' approach is presented in Figure 16 showing an underestimation of flood impact as the model was able to identify only 15% (3 of the 20 buildings) of the exposed buildings.

| IMPROVED APPLICATION OF THE 'STUBBY BUILDING' APPROACH
An important question in modelling practice is why a value of 30 cm is used to represent building heights in F I G U R E 1 2 Differences in water depth between the 'Building Hole' (BH) and the 'Stubby Building' (SB) models at Newcastle City Centre.Red is where SB predicts larger water depths than the BH and blue is vice versa.flood models, and how this could be improved in order to obtain more realistic results.The 'Stubby Building' (as described in Section 2.2) approach increases the building threshold, usually by 30 cm, and in some cases, an increased hydraulic roughness to the building footprint (Environment Agency, 2021;SEPA, 2018;TUFLOW, 2018).The schematic framework in Figure 17 highlights the issues of the modeller and the actions that could be taken before using the 'Stubby Building' approach.DEMs are mostly used in pluvial flood modelling but according to McClean et al. (2020) there are instabilities in the accuracy of the elevation ('errors'), where a modeller should first think of an effective way to identify them and correct them inside the model to avoid the overprediction of flooding in places with minor hazards.
Furthermore, there is a range of actions that could improve the model using the 'stubby' approach.An obvious action is to increase the elevation of the building from 30 cm, if the model numerical stability allows this.Otherwise, the modeller could avoid using this approach, or to flag the results as low confidence, in areas with steep slopes, as these are more likely to create conditions for overtopping the 'stubby' platforms due to interpolation 'errors' within the building footprint.A further option is to generate a uniformly flat roof in every building in the study area, thus avoiding relative low points for water to overtop.Section 4.2 will describe methods to 'clean' the DEM and thus improve the 'Stubby Building' approach.

| 'Stubby' models
To assess the magnitude of the DEM errors in using the SB approach, and to attempt to identify a good choice of platform height as a trade-off with DEM error, a range of scenarios was generated with different platform heights.While this height is essentially selected in industry models to maintain numerical stability, it can also be considered as representing an ingress threshold.The variant models have been set up as in Section 2.4 but as well as 30 cm, the ground elevation of the DEMs was raised in the buildings' footprints by 20, 40, 60, 80 and 100 cm. Figure 18 presents the generated variants of SB, and it can be seen in Figures (a-SB20), (b-SB40) and (c-SB60) that the water more frequently spreads over the buildings, while in Figures (d-SB80) and (e-SB100) there is as expected a reduction of spread to flood water in buildings which is more realistic.Newgate Street in  F I G U R E 1 4 The flooded buildings from the 'Toon Monsoon' storm event and dominant mechanism of flooding.
Newcastle city centre was selected to validate the behaviour of the different thresholds for the 'stubby' models due to the complexity of the topography and the high slopes of the ground.

| A 'cleaned Stubby' approach
In this section, a new corrected version of 'Stubby Building' is discussed.After the first simulation with the 'stubby' approach, the results have shown that there are anomalous depressions on some building footprints, with resultant flood depths above 1 m.These anomalies are assumed to arise from lack of robustness in the interpolation algorithm used to assign a 'ground elevation' to building footprints when converting from DTM to DEM in areas with high gradient.In order to develop a corrected DEM accounting for this systematic error source, the buildings with 1 m (or more) of inundated depth within the footprint were first identified.A total of 191 urban features in the AOI were found (highlighted in red in Figure 19).Next the elevation of the DEMs was raised to the 95 percentile values of the elevations around the building perimeter to create flat roofs to these buildings.Then, a step of 30 cm was added to all buildings in the AOI, including the 'cleaned' buildings with the flat roofs, and the CityCAT model was run again with these new variants.This correction or cleaning of the DEM can be an important step in the modelling, as it removes spurious occurrences of potentially large flood depths and avoid overestimating flood risk in a complex urban area with elevation instabilities.
To illustrate the effect of the various modified 'stubby' treatments, the case of the Merz Court building is examined again in detail (Table 5).Figure 20 shows flood depths in the area around the flooded Merz Court building at Newcastle University with the three different approaches: BH, SB and 'cleaned' SB with flat roofs.It can be seen the 'cleaned' variant model SB30 FR-100y rp (Figure 20c), shows a more realistic condition, closer to the BH-100y rp (BH) model-'Building Hole', (Figure 20a) due to the generation of a flat roof and the correction of the elevation.
While looking at individual buildings is helpful to understand the effects of different model treatments, most exposure analysis will be for larger areas with many buildings, so the total number of flooded buildings for all the 'stubby' variant models has been calculated and is shown in Table 6.The models SB20-100y rp (20 cm threshold) and SB30-100y rp (30 cm threshold) generate the highest number of buildings at high flood risk due to the low threshold, while the total appears to reach a steady limit value above 60 cm threshold.While these total numbers are not closer to the BH benchmark value, the number of 'high risk' is still a factor of two larger.
A comparison of the SB results with the more physically realistic BH approach shows that for the widely used 30 cm platform, an underestimation of some 34% in the identification of high flood risk buildings is evident, as shown in Figure 21 which highlights the buildings according to flood risk with BH and SB approaches.This F I G U R E 1 9 The identified buildings with depressions in the AOI.
T A B L E 5 List of codes for the modified 'stubby' models.

SB20
The 'Stubby Building' method with 20 cm threshold SB30 The 'Stubby Building' method with 30 cm threshold SB40 The 'Stubby Building' method with 40 cm threshold SB60 The 'Stubby Building' method with 60 cm threshold SB80 The 'Stubby Building' method with 80 cm threshold SB100 The 'Stubby Building' method with 100 cm threshold BH The 'Building Hole' method SB30 FR The 'cleaned Stubby' method with flat roofs and 30 cm threshold difference is reduced by raising the platform height, but of course at the expense of introducing numerical instabilities into codes less robust than CityCAT.

| CONCLUSIONS
This study presents an analysis of the performance of two widely used approaches for the representation of buildings in hydrodynamic flood models and presents an improved method for the 'Stubby Building' approach which corrects for common errors in DEM generation.
For the first time, a direct comparison of the SB approach with the more realistic BH approach has been carried out and shows that the BH approach generates larger flood depths, as is to be expected since the SB approach allows re-distribution of deep water over building footprints and presents fewer flow blocking situations.The flood paths with the SB approach are more dispersed, resulting in more buildings being affected.
The velocity of flood water is also somewhat higher with the BH approach due primarily to larger flow depths (see Figure 6a,c with 'Building Hole').The SB allows the water to flow more frequently over the buildings, and the direction of the water can be seen very clearly over and on top of them (see Figure 6b,d with 'Stubby Building').
Furthermore, on some buildings, a 'pond' is generated on roofs with the SB approach due to 'errors' in the DEM which the modeller should check and correct before the simulations.An advantage of the 'Building Hole' approach is that this task of checking and correcting the DEM is not required, as the area within the building footprint is simply removed from the model domain and does not require an interpolated elevation to be assigned.
Aside from 'errors' caused by artefacts in the DEM, in general, the SB approximation underestimates water depths, and the highest category of flood risk in the urban fabric, due to unrealistic flow paths over-riding the building forms.The validation of the affected buildings on the Newcastle University campus showed that the difference between the two approaches for the classification of building flood risk is very large (80% for the BH and 15% for the SB).This large difference suggests that a modified version of the exposure tool is needed to correctly identify high risk buildings.
In conclusion, the 'Building Hole' approach offers more realistic results which validate well against observed flooding where flow paths and flood depths are well captured by the model.The computational time and cost, especially in big urban areas with high resolution, to run a simulation is an important factor that favours the BH, due to fewer computational cells in the model (29% fewer cells in this study).Additionally, it is simple and easy to identify buildings at high flood risk according T A B L E 6 A total number of flooded buildings per scenario for each 'stubby' model, and for the 'Building Hole' approach for reference.to the water depth around their perimeter.An important advantage of this approach is that is suitable in any area, and especially for dense built-up areas, regardless of with the presence of steep slopes, in contrast to the 'Stubby Building' approach which is suggested in this study to be more suitable for use in flatter areas.

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I G U R E 2 The Digital Elevation Model and the extracted results from CityCAT of the study area (a and b) with the 'Building Hole'; (c and d) with the 'Stubby Building'.

F
I G U R E 3 Storm profile corresponding to the historical storm on 28 June 2012, at Newcastle Upon Tyne.
illustrates the flood depth maps with the two techniques around Newcastle University main campus for a storm event of 60 min with 100 years return period.On the left-hand map, a major surface flow path from the (mostly culverted) Pandon Burn can be seen which is blocked by the Merz Court building (distinctive trapezoidal shape with central open space) and subsequent buildings, whereas the flow overtops every building in the SB model in the right-hand F I G U R E 4 (a) Water depths from CityCAT for the storm on 28 June 2012 with the 'Building Hole' approach for Newcastle city centre.(b) Water depths from CityCAT for the storm on 28 June 2012 with the 'Stubby Building' approach for Newcastle city centre.
Summary of mean water flood depth for each model in different storm scenarios.BH denotes the 'Building Hole' method; SB30 denotes the 'Stubby Building' method with a 30 cm threshold; Final code denotes either observed event rainfall used, or depth corresponding to an estimated return period.F I G U R E 5 (a) The domain average flow velocity for the 'Building Hole' and the 'Stubby Building' approaches during the 2012 storm; (b) the distribution of flow velocity (left axis) and water depth (right axis) for the 70 min for the storm event plotted against its quantile.simulated with the 'Building Hole' were subtracted from those with 'Stubby Building' and are shown in Figure 12.It can be seen that, systematically, blue grid squares (positive depth difference) are where BH approach depths are greater than corresponding SB depths (e.g., on roads), (BH depths > SB) and red grids are generally on buildings where SB flowpaths exist and BH are absent (SB depths > BH).With the 'Building Hole' the flood water is forced to flow around the buildings, whereas with 'Stubby Building' the flow paths are different, as the flood water overtops almost 35% of the buildings in this area.The total number of flooded buildings for each model is shown in Table3.The BH models present the largest number of inundated buildings (high flood risk) in the AOI in contrast with the SB30 models where the F I G U R E 6 (a and c) Water depths and flow velocity (black arrows) for the 'Building Hole' approach and (b and d) for the 'Stubby Building' approach for two frontages of the Merz Court building-north (a and b) and west (c and d).

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I G U R E 7 Flood depth from CityCAT simulations around Newcastle University main campus.Left graph (a) is with 'Building Hole' and the right graph (b) with 'Stubby Building' approach.F I G U R E 8 Observation points upstream of Merz Court building for the validation of flood paths with 'Building Hole' and 'Stubby Building' approaches.

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I G U R E 9 Flooding in Merz Court building at Newcastle University for a storm event of 60 min duration and 100 years return period with (a) 'Building Hole' and (b) 'Stubby Building' approaches.F I G U R E 1 0 Flooding in a steep location of the city, Dean Street, with (a) 'Building Hole' and (b) 'Stubby Building' approaches.F I G U R E 1 1 Flooding at a second location with steep slopes, Westgate Street, with (a) 'Building Hole' and (b) 'Stubby Building' approaches.
U R E 1 3 Distribution in grid-by-grid elevation differences for (a) 'Building Hole' approach (original Digital Elevation Model [DEM]); (b) the generated DEM for 'Stubby Building' approach.

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I G U R E 1 7 A framework with suggested steps to improve the 'Stubby Building' approach.F I G U R E 1 8 Water depths at Newgate Street, Newcastle city centre, for a storm event of 60 min and 100 years return period with the generated 'stubby' scenarios.(a) model refers to 'stubby' approach with a raised platform of 20 cm; (b) 40 cm; (c) 60 cm; (d) 80 cm; (e) 100 cm.

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I G U R E 2 0 Flooding in Merz Court Building for a storm event of 60 min and 100 years return period with (a) 'Building Hole' approach; (b) 'Stubby Building' approach; (c) the 'fixed' version of 'Stubby Building'.
T A B L E 4 Flooded buildings at Newcastle University campus during the 2012 flood event.