E ﬀ ect of Independent Variables on Urban Flood Models

: The simulation accuracy of urban ﬂood models is a ﬀ ected by independent variables describing terrain resolution and artiﬁcial land cover. An evaluation of these e ﬀ ects could provide suggestions for the improvement of simulation accuracy when the available terrain resolutions and representation methods of land cover are di ﬀ erent. This paper focused on exploring and evaluating these e ﬀ ects on simulation accuracy using two indicators, relative depth accuracy (RDA) and relative area accuracy (RAA). The study area was the Nanjing Jianye district in China, which has experienced extensive urbanization. Designed rainfall (2 and 10 year return periods) and three terrain resolutions (17, 35, and 70 m) were used in this paper. Building blocks (BB), road drainage (RD), and a combination of both (BB + RD) were compared to present the e ﬀ ect of artiﬁcial land cover. Real ﬂood events were initially simulated as a model veriﬁcation case, and hypothetic modeling scenarios were simulated to evaluate the e ﬀ ects of di ﬀ erent resolutions and representation methods. The results indicate that the e ﬀ ect of terrain resolutions on simulation accuracy was more obvious than that of artiﬁcial land cover in the study area. In this paper, 20–30% higher accuracy could be achieved in the 35 m resolution model with respect to the 70 m resolution model. A relative accuracy of 94% was achieved in the 17 m resolution model when using the BB method, which was 5% higher than that using the RD method. This paper shows that evaluating the e ﬀ ects of terrain resolution and artiﬁcial land cover is e ﬀ ective and helpful for improving the simulation accuracy of urban ﬂood models in extensively urbanized districts.


Introduction
Urban flooding has become a significant issue due to the frequent occurrence of urban storms. More than 60% of the cities in China encountered flooding events in recent years [1]. Many studies were undertaken by researchers in the field of flood disasters [2][3][4][5]. Recently, new modeling methods were proposed in attempts at urban flood simulation [6][7][8]. Urban flood models are widely used as a reliable tool in flood management. High-accuracy flood simulations can effectively help managers to prevent and mitigate urban flood disasters. However, the simulation accuracy of urban flood models is easily affected by independent variables in the process of flood simulation [9], particularly terrain resolution, artificial land cover, and rainfall intensity. Hu et al. [10] previously analyzed 48 peer-reviewed journal articles published between 2015 and 2019 on the Web of Science™ database, studying the impact of rainfall input. Their findings were of great significance for the future development of urban flood models. Studies on the effect of terrain resolution and artificial land cover are also important for an improvement in simulation accuracy.

Accuracy Evaluation
In order to evaluate the effect of buildings and roads, three representation methods were used: building block (BB), road drainage (RD), and a combination of both (BB + RD). In the first method, buildings appear as blocks, and ground elevation data are raised to heights that cannot be inundated [22]. In the second method, the spatially distributed elevation data of roads are reduced by taking the height of the kerb as the standard. Hence, roads appear as shallow channels that can affect surface flow in the urban flood model. The BB + RD method simultaneously represents buildings as solid blocks and roads as shallow channels. A total of ten modeling scenarios were developed using various resolutions, representation methods, and rainfall intensities, as shown in Table 1.

Accuracy Evaluation
In order to evaluate the effect of buildings and roads, three representation methods were used: building block (BB), road drainage (RD), and a combination of both (BB + RD). In the first method, buildings appear as blocks, and ground elevation data are raised to heights that cannot be inundated [22]. In the second method, the spatially distributed elevation data of roads are reduced by taking the height of the kerb as the standard. Hence, roads appear as shallow channels that can affect surface flow in the urban flood model. The BB + RD method simultaneously represents buildings as solid blocks and roads as shallow channels. A total of ten modeling scenarios were developed using various resolutions, representation methods, and rainfall intensities, as shown in Table 1. Jianye district is relatively complete and independent, including roads, buildings, green spaces, water systems, and other land cover. It features a flat terrain with a ground elevation of 5.5-7.5 m, as shown in Figure 1. In this paper, three terrain resolutions (17,35, and 70 m) were resampled on the basis of the ASTER GDEM data collected on the Geospatial Data Cloud platform.

Accuracy Evaluation
In order to evaluate the effect of buildings and roads, three representation methods were used: building block (BB), road drainage (RD), and a combination of both (BB + RD). In the first method, buildings appear as blocks, and ground elevation data are raised to heights that cannot be inundated [22]. In the second method, the spatially distributed elevation data of roads are reduced by taking the height Water 2020, 12, 3442 4 of 16 of the kerb as the standard. Hence, roads appear as shallow channels that can affect surface flow in the urban flood model. The BB + RD method simultaneously represents buildings as solid blocks and roads as shallow channels. A total of ten modeling scenarios were developed using various resolutions, representation methods, and rainfall intensities, as shown in Table 1. This paper focused on quantitatively evaluating the effect of terrain resolution and artificial land cover. Table 2 shows the four categories of simulated results encompassing the reference case (RC) and contrast case (CC), where h t,RC is the simulated inundation depth at moment t in the reference case, h t,CC is the simulated inundation depth at moment t in the contrasting cases, S i,RC is the simulated inundation area at inundation depth grade i in the reference case, and S i,CC is the simulated inundation area at inundation depth grade i in the contrasting case. The relative depth accuracy (RDA) and relative area accuracy (RAA) were used to evaluate the accuracy of modeling results, as defined in Equations (1) and (2), respectively.
where t is the time (min), T is the duration of rainfall (min), and k is the number of random observation points.
where m is the number of inundation depth grades, and i indicates the inundation depth grade.

Hydraulic Model
In this paper, the urban flood model was established by coupling a one-dimensional pipe network model and a two-dimensional surface flow model with the mature MIKE 21 model [25]. The sewer flow in the pipe network was considered as one-dimensional flow, solved by using the Saint-Venant equations. In a one-dimensional flow regime, it is assumed that the water body is incompressible and homogeneous. The bottom slope of the open channel is small, and the water surface is parallel to the bottom slope (the length was much longer than the inundation depth in this paper: L/H > 100). Saint-Venant equations were discretized using the six-point Abbott-Ionescu scheme and solved using the catch-up method. The ADI central difference scheme was used to solve the depth-averaged two-dimensional shallow water equations.
The vertical connection between the one-dimensional pipe network model and the two-dimensional surface flow model was established using a manhole and gutter inlet, whereas the weir flow equation and orifice equation were used to calculate the flow exchange.

Model Verification
ASTER GDEM elevation data were resampled to 17 m resolution through data reclassifying and depression filling in ARCGIS software. Road and building elevation data extracted from a satellite image map were merged with the resampled data using the MIKE solver. The terrain distribution map is shown in Figure 3.
Water 2020, 12, x FOR PEER REVIEW 5 of 16 paper: L/H > 100). Saint-Venant equations were discretized using the six-point Abbott-Ionescu scheme and solved using the catch-up method. The ADI central difference scheme was used to solve the depth-averaged two-dimensional shallow water equations. The vertical connection between the one-dimensional pipe network model and the twodimensional surface flow model was established using a manhole and gutter inlet, whereas the weir flow equation and orifice equation were used to calculate the flow exchange.

Model Verification
ASTER GDEM elevation data were resampled to 17 m resolution through data reclassifying and depression filling in ARCGIS software. Road and building elevation data extracted from a satellite image map were merged with the resampled data using the MIKE solver. The terrain distribution map is shown in Figure 3. The pipe network model was established on the basis of the measured data and relevant specifications. The sub-catchment area was divided according to node location using the Tyson polygon method. As shown in Figure 4, the impermeability of sub-catchment areas was obtained according to the runoff coefficients of different surfaces and the area-weighted average. The surface flow model and the pipe network model were coupled through vertical connections at manholes. The water resistance coefficients for different land cover according to the surface condition of the study area and software recommendations were as follows: road, 62.5 m 1/3 /s; green space, 25 m 1/3 /s; vacant land, 36 m 1/3 /s; building, 12.5 m 1/3 /s. The remaining parameters were as follows: dry boundary value, 0.002 m; wet boundary value, 0.003 m; eddy viscosity coefficient (E) = 0.1 × ∆x 2 /∆t, where ∆x is the space interval and ∆t is the time step. The model parameters for different spatial resolutions were the same, regardless of the Coriolis force and other source terms.
The pipe network model was established on the basis of the measured data and relevant specifications. The sub-catchment area was divided according to node location using the Tyson polygon method. As shown in Figure 4, the impermeability of sub-catchment areas was obtained according to the runoff coefficients of different surfaces and the area-weighted average. The surface flow model and the pipe network model were coupled through vertical connections at manholes. Water 2020, 12, x FOR PEER REVIEW 6 of 16 In this paper, a real flood event on 7 August 2017 was simulated using historical rainfall data ( Figure 5). The model was tested via an investigation of inundation positions and simulation results. The validation result is shown in Figure 6. Fifteen inundation positions (Table 3) according to previous investigations were verified in the simulation results, thus indicating the good applicability of the established model.  In this paper, a real flood event on 7 August 2017 was simulated using historical rainfall data ( Figure 5). The model was tested via an investigation of inundation positions and simulation results. The validation result is shown in Figure 6. Fifteen inundation positions (Table 3)   In this paper, a real flood event on 7 August 2017 was simulated using historical rainfall data ( Figure 5). The model was tested via an investigation of inundation positions and simulation results. The validation result is shown in Figure 6. Fifteen inundation positions (Table 3) according to previous investigations were verified in the simulation results, thus indicating the good applicability of the established model.

Terrain Resolution Simulation Analysis
The urban flood models of cases C1 to C6 were established. Using the simulation results of cases C1 and C2 as standard data, the inundation areas for cases C3 to C6 were analyzed, as visualized in Figure 7.  Fuchunjiang west street Nanxijiang street 4 Bailongjiang street 5 Jinshajiang street 6 Taishan Road 7 Xinglong street 8 Jiqingmen street to Changhong road from west to east 9 Yikang street to Lushan road 10 Hengshan road 11 Songshan road 12 Fuchunjiang street 13 Xin'anjiang street 14 Mudanjiang street 15 Shazhou police station

Terrain Resolution Simulation Analysis
The urban flood models of cases C1 to C6 were established. Using the simulation results of cases C1 and C2 as standard data, the inundation areas for cases C3 to C6 were analyzed, as visualized in Figure 7. The contrast results under the same rainfall conditions showed that the inundation area at 35 m resolution was highly consistent with the reference data. The contrast results at 70 m resolution presented a relatively large inundation location, and the overlap area with the standard data was small. The inundation area decreased with the improvement in terrain resolution. The distribution of inundation locations along the roads was obvious. As shown in Figure 8, four observation points were observed to analyze the process of inundation depth with time. The depth-time curves of cases C1 to C6 are shown in Figure 9, showing a relatively similar trend for the three terrain resolutions. The trend for the 35 m resolution case was more consistent with the reference case than that for the 70 m resolution case. The contrast results under the same rainfall conditions showed that the inundation area at 35 m resolution was highly consistent with the reference data. The contrast results at 70 m resolution presented a relatively large inundation location, and the overlap area with the standard data was small. The inundation area decreased with the improvement in terrain resolution. The distribution of inundation locations along the roads was obvious. As shown in Figure 8, four observation points were observed to analyze the process of inundation depth with time. The depth-time curves of cases C1 to C6 are shown in Figure 9, showing a relatively similar trend for the three terrain resolutions. The trend for the 35 m resolution case was more consistent with the reference case than that for the 70 m resolution case.    Figure 10. The total inundation areas for cases C1, C3, and C4 were 13.13 km 2 , 15.02 km 2 , and 19.63 km 2 , respectively. The inundation area for the 70 m resolution case was 30.7% larger than that for the 35 m resolution case and 49.5% larger than that for the 17 m resolution case. The inundation area for the 35 m resolution case was 14.4% larger than that for the 17 m resolution case. The total inundation areas for cases C2, C5, and C6 were 10.35 km 2 , 11.52 km 2 , and 14.35 km 2 , respectively. The inundation area for the 70 m resolution case was 24.5% larger than that for the 35 m resolution case and 38.7% larger than that for the 17 m resolution case. The inundation area of the 35 m resolution case was 11.42% larger than that for the 17 m resolution case. Furthermore, the error for the 35 m resolution case was reduced by approximately 30% with respect to the 70 m resolution case. According to a comprehensive evaluation of the data, the inundation area error was obviously less for the of 35 m resolution case than the 70 m resolution case.  Figure 10. The total inundation areas for cases C1, C3, and C4 were 13.13 km 2 , 15.02 km 2 , and 19.63 km 2 , respectively. The inundation area for the 70 m resolution case was 30.7% larger than that for the 35 m resolution case and 49.5% larger than that for the 17 m resolution case. The inundation area for the 35 m resolution case was 14.4% larger than that for the 17 m resolution case. The total inundation areas for cases C2, C5, and C6 were 10.35 km 2 , 11.52 km 2 , and 14.35 km 2 , respectively. The inundation area for the 70 m resolution case was 24.5% larger than that for the 35 m resolution case and 38.7% larger than that for the 17 m resolution case. The inundation area of the 35 m resolution case was 11.42% larger than that for the 17 m resolution case. Furthermore, the error for the 35 m resolution case was reduced by approximately 30% with respect to the 70 m resolution case. According to a comprehensive evaluation of the data, the inundation area error was obviously less for the of 35 m resolution case than the 70 m resolution case.

Artifical Land Cover Simulation Analysis
Using the simulation results for cases C1 and C2 as standard data, the effects of artificial land cover for cases C7 to C10 are presented in Figure 11. It can be found that most inundation areas overlapped well, whereas the nonoverlapping areas were located in the middle of the study area and distributed along the road (Figure 11a,b). This was predominantly due to the drainage effects of roads on local shallow surface flow. The nonoverlapping areas were distributed in the north of the study area, where urban buildings were concentrated (Figure 11c,d), as the water resistance of building blocks was not considered. Figure 12 presents the inundation depth-time curves for the four observation points, showing that the trends were coincident at points A-C. However, there was an obvious anomaly at point D, whereby the turning point of inundation depth was significantly ahead of time when using the RD method. Under a 2-year return period, buildings had a greater effect on surface flow than roads, even affecting the drainage process at local inundation areas. The effect of buildings on the evolution trend in local areas can be helpful in the exploration of local flood and drainage.
Hundreds of locations in the study area were randomly observed to conduct fitting analysis on the maximum inundation depth. As shown in Figure 13, the simulation results using the BB and RD methods matched well with the results using the BB + RD method at points with small inundation depth, but varied at points with large inundation depth. The correlation coefficient (R 2 ) was used to estimate the similarity of two groups of data in this paper. Under the two rainfall conditions, cases C1 and C8 (R 2 = 0.97) and cases C2 and C10 (R 2 = 0.922) were highly similar, as opposed to cases C1 and C7 (R 2 = 0.70) and cases C2 and C9 (R 2 = 0.613). This indicates that the effect of buildings on

Artifical Land Cover Simulation Analysis
Using the simulation results for cases C1 and C2 as standard data, the effects of artificial land cover for cases C7 to C10 are presented in Figure 11. It can be found that most inundation areas overlapped well, whereas the nonoverlapping areas were located in the middle of the study area and distributed along the road (Figure 11a,b). This was predominantly due to the drainage effects of roads on local shallow surface flow. The nonoverlapping areas were distributed in the north of the study area, where urban buildings were concentrated (Figure 11c,d), as the water resistance of building blocks was not considered. Figure 12 presents the inundation depth-time curves for the four observation points, showing that the trends were coincident at points A-C. However, there was an obvious anomaly at point D, whereby the turning point of inundation depth was significantly ahead of time when using the RD method. Under a 2-year return period, buildings had a greater effect on surface flow than roads, even affecting the drainage process at local inundation areas. The effect of buildings on the evolution trend in local areas can be helpful in the exploration of local flood and drainage.
Hundreds of locations in the study area were randomly observed to conduct fitting analysis on the maximum inundation depth. As shown in Figure 13, the simulation results using the BB and RD methods matched well with the results using the BB + RD method at points with small inundation depth, but varied at points with large inundation depth. The correlation coefficient (R 2 ) was used to estimate the similarity of two groups of data in this paper. Under the two rainfall conditions, cases C1 and C8 (R 2 = 0.97) and cases C2 and C10 (R 2 = 0.922) were highly similar, as opposed to cases C1 and C7 (R 2 = 0.70) and cases C2 and C9 (R 2 = 0.613). This indicates that the effect of buildings on shallow water flow was significantly greater than that of roads in the urban flood model. The data distributed along the horizontal axis in Figure 13d indicate that the inundation points were mainly positioned alongside buildings when using the RD method.
shallow water flow was significantly greater than that of roads in the urban flood model. The data distributed along the horizontal axis in Figure 13d indicate that the inundation points were mainly positioned alongside buildings when using the RD method.
The statistical results of inundation area are shown in Figure 14. The total inundation areas for cases C1, C7, and C8 were 13.22 km 2 , 13.81 km 2 , and 13.01 km 2 , respectively. The total inundation areas for cases C2, C9, and C10 were 10.34 km 2 , 10.68 km 2 , and 10.14 km 2 , respectively. The inundation area for case C7 was increased by 4.48% with respect to case C1, due to the effect of buildings being ignored. The same phenomenon was observed for case C2 with respect to C9. The observed growth rate was 3.27%. However, the inundation area decreased if the effect of roads was ignored for cases C8 and C10. The growth rates for cases C8 and C10 were −1.57% and −1.94%, respectively, thus indicating that buildings had a greater effect on surface flow than roads.  The statistical results of inundation area are shown in Figure 14. The total inundation areas for cases C1, C7, and C8 were 13.22 km 2 , 13.81 km 2 , and 13.01 km 2 , respectively. The total inundation areas for cases C2, C9, and C10 were 10.34 km 2 , 10.68 km 2 , and 10.14 km 2 , respectively. The inundation area for case C7 was increased by 4.48% with respect to case C1, due to the effect of buildings being ignored. The same phenomenon was observed for case C2 with respect to C9. The observed growth rate was 3.27%. However, the inundation area decreased if the effect of roads was ignored for cases C8 and C10. The growth rates for cases C8 and C10 were −1.57% and −1.94%, respectively, thus indicating that buildings had a greater effect on surface flow than roads.

Comparative Analysis of All Simulation Schemes
As can be seen from Table 4 and Figure 15, a reduction in terrain resolution had little effect on the inundation depth, but seriously affected the inundation area under a 2-year rainfall return period.

Comparative Analysis of All Simulation Schemes
As can be seen from Table 4 and Figure 15, a reduction in terrain resolution had little effect on the inundation depth, but seriously affected the inundation area under a 2-year rainfall return period. Both inundation depth and inundation area were obviously affected by a decrease in terrain

Comparative Analysis of All Simulation Schemes
As can be seen from Table 4 and Figure 15, a reduction in terrain resolution had little effect on the inundation depth, but seriously affected the inundation area under a 2-year rainfall return period. Both inundation depth and inundation area were obviously affected by a decrease in terrain resolution under a 10 year rainfall return period. A lower resolution led to a greater effect on the simulation results. For both rainfall events at 17 m resolution, greater errors were obtained when using the RD method with respect to the BB method.

Conclusions
This paper took the Jianye district, which has experienced extensive urbanization, as the study area and focused on exploring and evaluating the effect of terrain resolution and artificial land cover on the simulation accuracy of urban flood models. The validated model was used to simulate hypothetic scenarios, which were developed using various resolutions (17,35, and 70 m), representation methods (BB, RD, and BB + RD), and rainfall intensities (2 and 10 year return periods). RDA and RAA were calculated to evaluate the accuracy difference. Due to the extensive urbanization of the study area, the effect tendencies reflected in the results of this study could be helpful for flood models of similar urban districts. The most important study results based on Jianye district were as follows: (1) The 35 m terrain resolution presented good accuracy in terms of the distribution of inundation area and flood evolution. Compared with the 70 m resolution, the error obtained for total inundation area was reduced by about 30% when using the 35 m resolution. (2) In terms of representation methods of artificial land cover, the urban flood model using the BB method could better reflect the actual flood evolution than that using the RD method. Compared with the RD method, the correlation (R 2 ) of the maximum inundation depth increased by about 30% when using the BB method. (3) The effect of terrain resolution on simulation accuracy was more obvious than that of artificial land cover. In the models using the BB + RD method, values of RAA and RDA could reach above 80% for the 35 m resolution models (20-30% higher than the 70 m terrain resolution models). In the models using the 17 m terrain resolution, values of RAA and RDA could reach above 94% when considering only the effect of buildings (5% higher than models only considering the effect of roads). In addition, the effect of independent variables was evaluated using RDA and RAA indicators ( Table 4). The requirements of terrain resolution were substantial compared with artificial land cover in terms of higher simulation accuracy. For inundation depth and inundation area, the relative accuracy could reach above 80% in the 35 m terrain resolution models (20-30% than with the 70 m terrain resolution models). For the 17 m terrain resolution model, the relative accuracy could reach above 94% when considering only the effect of buildings (5% higher than models only considering the effect of roads).

Conclusions
This paper took the Jianye district, which has experienced extensive urbanization, as the study area and focused on exploring and evaluating the effect of terrain resolution and artificial land cover on the simulation accuracy of urban flood models. The validated model was used to simulate hypothetic scenarios, which were developed using various resolutions (17,35, and 70 m), representation methods (BB, RD, and BB + RD), and rainfall intensities (2 and 10 year return periods). RDA and RAA were calculated to evaluate the accuracy difference. Due to the extensive urbanization of the study area, the effect tendencies reflected in the results of this study could be helpful for flood models of similar urban districts. The most important study results based on Jianye district were as follows: (1) The 35 m terrain resolution presented good accuracy in terms of the distribution of inundation area and flood evolution. Compared with the 70 m resolution, the error obtained for total inundation area was reduced by about 30% when using the 35 m resolution.
(2) In terms of representation methods of artificial land cover, the urban flood model using the BB method could better reflect the actual flood evolution than that using the RD method. Compared with the RD method, the correlation (R 2 ) of the maximum inundation depth increased by about 30% when using the BB method. (3) The effect of terrain resolution on simulation accuracy was more obvious than that of artificial land cover. In the models using the BB + RD method, values of RAA and RDA could reach above 80% for the 35 m resolution models (20-30% higher than the 70 m terrain resolution models).
In the models using the 17 m terrain resolution, values of RAA and RDA could reach above 94% when considering only the effect of buildings (5% higher than models only considering the effect of roads).

Conflicts of Interest:
The authors declare no conflict of interest.