Performance Analysis for Road-Bioretention with Three Types of Curb Inlet Using Numerical Model

: The FullSWOF-ZG (Full Shallow Water Overland Flow with inﬁltration determined by Zones and Grate-inlet submodules) program was used to simulate the road-bioretention (RB) stripe and evaluate the performance of the RB stripe with three types of curb inlet. The program was revised from the open-source FullSWOF-2D program and the validation results indicated FullSWOF-ZG pre-dicts the RB stripe performance accurately. The model cases of 27 RB with different longitude slopes ( S 0 ), cross slopes ( S x ), and curb inlet lengths ( L ci ) for the undepressed, composite depressed, and local depressed curb inlets were established in this study. Therefore, 81 cases in total were simulated to explore the curb inlet type and design parameter’s inﬂuence on the RB stripe performance. Overall, it was found that the bioretention control efﬁciency will increase with the S 0 decrease, S x increase, and L ci increase. The composite depressed curb inlet was the most efﬁcient to intercept the road runoff into the bioretention strip, the next best is the local depressed curb inlet, and the undepressed curb inlet was the least efﬁcient. The curb inlet and grate inlet combination in composite depressed curb inlet cases were able to deal with all the road surface runoff for the small longitudinal slope ( S 0 = 0.1% and 0.3%) to relieve the road local ﬂood inundation.


Introduction
To endorse sustainable urbanization plans, the Sponge City (SPC) paradigm based on green/gray stormwater management infrastructure integration was announced in 2013 as a relief countermeasure to urban syndromes such as water shortage, water pollution, flood inundation, and ecologic deterioration in China [1,2]. As an important component of SPC, road-bioretention (RB) [3,4] is a water quantity and quality control practice that benefits decreasing surface runoff, increasing groundwater recharge, and treating various pollutants through a variety of processes [5,6]. The bioretention facilities near a road could be individual isolated cells and long stripes or plots along a road (Figure 1), which receive the runoff from the road surface and/or other adjacent surfaces. Figure 1a shows the plan view for a road-bioretention stripe that includes the road surface with longitudinal (S 0 ) and cross (S x ) slopes, a curb inlet, a grate inlet along the roadside, the bioretention stripe, an overflow great inlet and a berm near the end of the bioretention stripe, and the curb separating the road and bioretention. Typically, the RB stripe has the same or a similar longitudinal slope of the road. It may have several RB stripes separated by berms, especially when the longitudinal slope is large. The curb inlet length is L ci (see the description for all symbols listed in Abbreviation part). The RB stripe that combine green/gray infrastructures to facilitate road runoff control through infiltration and ponding length is Lci (see the description for all symbols listed in Abbreviation part). The RB stripe that combine green/gray infrastructures to facilitate road runoff control through infiltration and ponding as well as relieve road local flood inundation risk is widely used in pilot SPC construction in China [7].  Traditional curb inlets are to intercept the surface runoff into the underground stormwater pipeline network, but the curb inlets for the RB stripes are to intercept the surface runoff into the bioretention facilities to store, retain, infiltrate the runoff to remove the pollutants and improve the water quality. Two types of curb inlets are commonly used over the world: the undepressed and composite depressed curb inlets. Figures 1b and 2a show the undepressed curb inlet with a single cross slope Sx at any cross-sections, e.g., along the road and passing the curb inlet, which is section A-A in Figure 1. The composite depressed curb inlet is shown in Figures 1c and 2b placed along gutters of the street, and has a composite section with two cross slopes (Sx for the road and Sw for the gutter over a width of wcom) at all sections along the road. The third type of length is Lci (see the description for all symbols listed in Abbreviation part). The RB stripe that combine green/gray infrastructures to facilitate road runoff control through infiltration and ponding as well as relieve road local flood inundation risk is widely used in pilot SPC construction in China [7].  Traditional curb inlets are to intercept the surface runoff into the underground stormwater pipeline network, but the curb inlets for the RB stripes are to intercept the surface runoff into the bioretention facilities to store, retain, infiltrate the runoff to remove the pollutants and improve the water quality. Two types of curb inlets are commonly used over the world: the undepressed and composite depressed curb inlets. Figures 1b and 2a show the undepressed curb inlet with a single cross slope Sx at any cross-sections, e.g., along the road and passing the curb inlet, which is section A-A in Figure 1. The composite depressed curb inlet is shown in Figures 1c and 2b placed along gutters of the street, and has a composite section with two cross slopes (Sx for the road and Sw for the gutter over a width of wcom) at all sections along the road. The third type of Traditional curb inlets are to intercept the surface runoff into the underground stormwater pipeline network, but the curb inlets for the RB stripes are to intercept the surface runoff into the bioretention facilities to store, retain, infiltrate the runoff to remove the pollutants and improve the water quality. Two types of curb inlets are commonly used over the world: the undepressed and composite depressed curb inlets. Figures 1b and 2a show the undepressed curb inlet with a single cross slope S x at any cross-sections, e.g., along the road and passing the curb inlet, which is section A-A in Figure 1. The composite depressed curb inlet is shown in Figures 1c and 2b placed along gutters of the street, and has a composite section with two cross slopes (S x for the road and S w for the gutter over a width of w com ) at all sections along the road. The third type of curb inlet is the local depressed curb inlet shown in Figures 1d and 2c which has a local depression over the opening length of the inlet but a single cross slope S x for all other parts of the road. The local depressed inlet is widely used in some SPC pilot projects in China [7] for improving the inlet interception efficiency. In various construction projects, the local depressed inlet could be constructed using a composite slope S w over the gutter width w com (Figure 1d) or just simply cuts the road to form a small depression (Figure 2c) over the curb inlet length. The local depressed curb inlet is also different from Texas type C and D curb inlets [8,9] that have 1.52 m (5 ft) transition before and after the local depression over the inlet opening. The transition before the inlet is to change the cross slope gradually from S x to S w (S w > S x ) in the gutter width or from S w to S x after the inlet. Type C and D inlet could be more efficient for intercepting the surface runoff but it is more complex to construct in the field or should be precast.
Most of the previous studies point out that bioretention has good hydrologic performance and pollutant removal efficiency dealing with urban road runoff based on experimental and monitored data [10]. There was barely any detailed guidance and study on the influence of longitudinal slope and cross slope of the road as well as the opening length and the type (Figures 1 and 2) of curb inlet on RB stripe performance that could be found in China [11,12]. Li et al. [13] emphasized the importance of inlet hydraulics and the spatial distribution of inflow for a road-bioretention stripe, and they proposed and integrated a hydraulic and hydrologic modeling approach to simulate the overall runoff control performance of the RB stripe. Li et al. [14] conducted a full-scale laboratory RB stripe numerical experiments and simulation to explore the influence of S 0 and S x on RB stripe performance while the experiment scenarios were limited to explore the detailed influence of different parameters.
It is a complex problem to design the RB stripe that needs to consider the curb inlet interception efficiency, grate inlet capacity, as well as the bioretention ponding and infiltration capacity systematically to make the RB stripe perform well on road runoff control. The influence of design parameters on the RB stripe with undepressed curb inlet (Figure 1b) was studied in a previous study [15] while the RB stripe performance with different types of curb inlet ( Figure 1) still needs to be explored. Understanding and clarifying the influence of design parameters (S 0 , S x , and L ci ) and curb inlet type on RB stripe performance is particularly important and useful to SPC construction in China [16]. In this study, the FullSWOF-ZG (Full Shallow Water Overland Flow with infiltration determined by Zones and Grate-inlet submodules) program [17], that has a submodule determining the different rainfall, infiltration, and friction in zones, as well as the two-dimensional-one-dimensional (2D-1D) surface-to-grate-inlet flow exchange submodule, was used to explore the RB stripe performance and design concerns. The program was revised from the open-source hydraulic program FullSWOF-2D (version 1.07, Lab. J. A. Dieudonné and EPU Nice Sophia, Nice, France) [17] that solves the full shallow-water equations (SWEs) for overland flow (OF) in 2D simulation domain. With the help of the validated FullSWOF-ZG program, the objective of this study is to explore the mechanism and influence of those design parameters on RB stripe performance through building numerical models for different scenarios.

Road-Bioretention (RB) Stripe Design
Curb inlet interception efficiency, road grate inlet capacity, as well as the bioretention ponding and infiltration capacity, should be taken into consideration to design the RB stripe for better RB performance. Three types of curb inlet are commonly used in the USA and China (Figures 1 and 2). The undepressed curb inlet with a single cross slope is widely used in China. The composite depressed curb inlet is commonly used in the USA [18]. The local depressed curb inlet used in some SPC pilot projects in China [19] is also studied here. Current curb inlet design practices in the USA are based on documents produced by the Federal Highway Administration entitled Hydraulic Engineering Circular No. 22   [20] and Urban Street Stormwater Guide produced by the National Association of City Transportation Officials [11]. The design of commonly used inlet types is presented in HEC-22 and specific design guidance for other inlets is also provided in two previous studies [9,21].
The ponding depth of the RB stripe is controlled by the height of the overflow grate inlet and the berm height ( Figure 1). The overflow height provides for the temporary storage of the stormwater before it filters downward through the bioretention facility. The temporary ponding depth for bioretention facilities range from 5 cm (for mitigating sidewalk runoff alone, or in fast-draining soils) to up to 30 cm (for mitigating roadway runoff, or in slower-draining soils) [11]. The Delaware Green Technologies Design Manual and Model provide design guidance for bioretention systems and allow a maximum ponding depth of 45 cm [22]. Davis et al. [6] declared the overall principles of bioretention ponding volume and infiltration capacity design in their study. The ponding volume is designed by the corresponding catchment area (e.g., contributing road surface are) and design rainfall depth. It also should be calculated based on the RB geometry such as bioretention length L b , width w b , and slope.
The bioretention design specifications envisioned the use of natural soils with high permeability [23]. Three soil textural classifications were specified which include: loamy sand, sandy loam, and loam. Sites with subsoils of an infiltration rate less than 13 mm/h are required to use an underdrain system that provides positive drainage to a defined outfall point [6]. The Green-Ampt model [17] was adapted to simulate the bioretention infiltration process in this study. The infiltration parameters include saturated hydraulic conductivity (K), moisture deficit (∆θ), and dry suction head (ϕ). In this study, RB stripe with loamy sand soil was modeled. The infiltration parameter values: K = 51 mm/h, ∆θ = 0.410, ϕ = 0.09 m, were adapted based on the soil type [24]. The thickness of the soil layer is 0.45 m according to the bioretention design guidelines [25].

FullSWOF-ZG Program
As a Saint-Venant system [26], the simplified SWEs model is widely used to simulate the incompressible Navier-Stokes flow occurring in rivers, channels, ocean, and land surfaces [27]. The conservative form of the 2D SWEs for FullSWOF-2D program, including the continuity equation and two momentum equations for xand ydirections, is stated as the following equations for each computational cell (center coordinates x and y):

∂(hv) ∂t
where R (x, y) (m/s) is the cell's rainfall intensity; I (x, y) (m/s) is the cell's infiltration rate; h (m) is the cell's water depth; z (m) is the cell topography elevation as a function of the cell location or x and y coordinates; u (m/s) and v (m/s) is the cell's depth-averaged velocities in x and y directions, respectively; S fx and S fy are the cell's friction slopes in x and y directions, respectively; g (m/s 2 ) is gravity acceleration; t (s) is time.
The FullSWOF-2D program fully solves SWEs on a structured mesh (square cells) in two dimensions using the finite volume method (FVM) that ensures mass conservation [28]. A well-balanced numerical scheme was adapted to guarantee the positivity of water depth and the preservation of steady states for specific hydrological features such as during wet-dry transitions and tiny water depths [17,29]. Different boundary conditions, friction laws, and numerical schemes were developed that make the program a very powerful overland flow simulation software. A modified bi-layer (crust-and soil-layer) Green-Ampt (GA) infiltration model [30] to calculate I (x, y) for Equation (1) was coded in the FullSWOF-2D [28] that enables the program to simulate overland flow on impervious and pervious surfaces simultaneously.
The FullSWOF-2D program was revised and improved in this study: the updated FullSWOF-ZG program included the spatialized rainfall, infiltration, and friction determination as well as a new 2D-1D drainage inlet submodule. Therefore, the program can simulate impervious and pervious surfaces in the same domain simultaneously. The simulation domain can have several grate inlets, therefore, the 2D overland flow can drain into these 2D drainage inlets (rectangles) to become 1D flow in underground drainage pipes. Currently, the FullSWOF-ZG program does not further simulate 1D flow in the drainage pipes assuming the pipe capability is large enough to accept all inflow from inlets. The simulation domain has curb inlets connecting the road and bioretention where normally the runoff on the road flows through the curb inlet into the bioretention. The grate-inlet discharge capacity from the 2D overland flow to the 1D drainage pipe flow is calculated using the weir equation [31] applied to the cells surrounding the grate inlet.
The FullSWOF-ZG program was tested against the data from undepressed curb inlet cases in Spaliviero's [32] study, local depressed curb inlet cases conducted by Hammonds and Holley [9], and overland flow on pervious surface cases measured and simulated by Esteves et al. [30], but this comprehensive model validation was presented elsewhere by Li et al. [14,15]. The differences of simulated and observed curb inlet interception efficiencies (∆E) ranged from −3.7% to 4.4% with an average ± standard deviation of 0.8 ± 2.6% for undepressed curb inlet cases [33]. The ∆E ranged from −3.2% to 13.2%, with an average ± standard deviation of 3.5 ± 3.5% for local depressed curb inlet cases [34]. In a previous study by Fang et al. [8], the ∆E ranged from −7.0% to 17.6%, with an average ± standard deviation of 1.0 ± 4.87% in their FLOW-3D simulations for local depressed curb inlet. The goodness of fit for the simulated hydrograph is evaluated using the Nash-Sutcliffe efficiency (NSE) coefficient [35]. The NSE coefficient of FullSWOF-ZG and Esteves's study ranged from 0.64 to 0.95 (average ± standard deviation as 0.75 ± 0.11) and from 0.46 to 0.93 (0.79 ± 0.15) for overland flow on pervious surfaces simulation, respectively [36]. The simulated results for undepressed curb inlet, local depressed curb inlet, and overland flow on pervious surface cases were matched well with the observed data, which proves that the FullSWOD-ZG program can not only simulate overland flow on pervious and impervious surfaces accurately but can also predict the curb inlet efficiency very precisely. Figure 3a shows the plan view for the road-bioretention modeling case which includes different parts of the RB stripe: the road with longitude and cross slopes, the bioretention, curb inlet, grate inlet on the road, a berm at the end of bioretention, and the curb separating the road and bioretention. The RB performance is affected by longitude slope S 0 , cross slope S x , curb inlet interception efficiency E ci , bioretention depth D b , overflow height h b , and the RB's soil infiltration parameters in Table 1. Different modeling cases were established to explore the influence of design parameters on RB performance. Even bioretention is flat in the y-direction with lower elevation (i.e., D b ) than the road surface, bioretention has the same length and longitude slope in the x-direction as the road does ( Figure 3). Figure 3c,d show the full and zoomed-in view digital elevation models (DEMs) for the modeling cases with composite depressed Case 01 in Table 2.  (Table 2). Qci is the curb inlet intercepted flow, Qrg for road grate inlet captured flow, Qbp for road end bypass flow, and Qog for the bioretention grate inlet overflow. L and wr are the road surface length and width upstream the curb inlet. Lb and wb are the road-bioretention (RB) stripe length and width. wcom is the width for the composite slope ( Figure 1c).     (Table 2). Q ci is the curb inlet intercepted flow, Q rg for road grate inlet captured flow, Q bp for road end bypass flow, and Q og for the bioretention grate inlet overflow. L and w r are the road surface length and width upstream the curb inlet. L b and w b are the road-bioretention (RB) stripe length and width. w com is the width for the composite slope ( Figure 1c).  There is a berm at the end of bioretention to pond the runoff inside bioretention that is allowed for infiltration downward and possible overflow into a grate inlet. The berm height used in this study is large enough to prevent the longitudinal outflow from bioretention. There is a grate inlet at the end of bioretention where the grate inlet opening is above the bioretention ground surface. The elevation difference between the grate inlet opening and the bioretention ground surface is called the overflow height, h b which is 0.30 m in this study. Only when the water depth near the grate inlet is greater than h b , the runoff in bioretention will flow (Q og in Figure 3a) into the grate inlet then to the underground drainage pipe system. Part of the runoff generated on the road surface after rainfall begins was intercepted by curb inlet (Q ci in Figure 3a), then the extra runoff was captured by the road grate inlet (Q rg in Figure 3a), and finally, the rest part of the runoff was discharged to road end (Q bp in Figure 3a). The free outfall boundary condition was used for the downstream (right boundary) of the simulation domain to avoid runoff flow back to the upstream.  Figure 3d, S 0 , S x , and L ci are the same for each undepressed, composite depressed, and local depressed curb inlet case.

Performance Evaluation Cases
The bioretention ponding volume (V pc ) calculated for each modeling case in this study did not consider the vegetation volume fraction of the bioretention facility. For all cases, the ponding length is larger than the upstream bioretention length time longitudinal slope (L b × S 0 < h b ), therefore, the V pc was calculated using the following Equation (4): where V pc (m 3 ) is the calculated ponding volume based on bioretention geometry, w b (m) is the bioretention width (1 m), L b (m) is upstream bioretention length, S 0 is bioretention longitudinal slope, and h b (m) bioretention overflow height, A gr (m 2 ) is overflow grate inlet area. For all cases, the whole simulation domain length and width are 13 m (x-direction, Figure 3) and 7.7 m (y-direction, Figure 3), respectively. The road length L (Figure 3a) and width w r (Figure 3c) before the dividing line in Figure 3 are 10 m and 6.7 m, respectively. The runoff generated before the curb inlet was calculated by L, w r , and rainfall intensity. When y = 0, it is the centerline of the road, when y = 6.7 m, it is the curb [37]. The curb inlet is located after the curb lasts 10 m to allow the runoff generated on the road surface to get into the bioretention. The width of the bioretention cell is 1.0 m (w b in Figure 3b Twenty-seven cases for every type of curb inlet were simulated in this study by having three longitudinal slopes, three cross slopes, and three curb inlet lengths ( Table 2). The RB stripe has eight key design parameters which include upstream catchment length L, longitudinal slope S 0 , cross slope S x , curb inlet length L ci , overflow height h b , saturated hydraulic conductivity K, dry suction head ϕ, and soil moisture deficit ∆θ. To fully understand the RB stripe performance and the influence from each parameter will require setting a large number of modeling cases, which is not studied here. Only the influence of RB stripe geometry, as well as the curb inlet type and length, were explored in this study which parameters for every case were shown in Table 2. Therefore, the loamy sand which was commonly used in the road-bioretention stripe was adopted in all simulation cases with the parameters K = 51 mm/h, ∆θ = 0.41, and ϕ = 0.09 m.
The  Figure 3c. The road surface and bioretention ground elevations, therefore, vary with longitudinal and cross slopes set for each modeling case ( Table 2). All cells for the 0.1 m curb were set 0.2 m higher than the road surface cells. The cell's elevations inside the curb inlet cells were calculated using the same cross slope of the road surface, which helps and allows the runoff to flow into the bioretention. The uniform rainfall intensity is 6.94 × 10 −5 m/s (250 mm/h) and last 1200 s (20 min) to generate enough runoff to reach the ponding volume, but the total simulation period is 2400 s.

Simulated Hydrograph of RB Modeling Cases
As an example of modeling results for the RB stripe, the performances of the case Und27, Com27, and Loc27 were first evaluated and compared in Figure 4. Figure 4 shows the simulated hydrograph and bioretention water depth of three cases Und27, Com27, and Loc27. The upstream catchment length L = 10 m, longitudinal slope S 0 = 0.007, cross slope S x = 0.04, curb inlet opening length L ci = 0.90 m, overflow grate inlet height h b = 0.30 m for cases Und27, Com27, and Loc27.
The hydrograph of curb inlet intercepted flow (Q ci ), road grate inlet captured flow (Q rg ), road end bypass flow (Q bp ), and the bioretention grate inlet overflow (Q og ) are shown in Figure 4. The rainfall intensity was 250 mm/h and maintained to 1200 s (20 min) for all simulation cases. Therefore, all hydrograph grow slowly at the beginning of the rainfall then reach the peak discharge and start to decrease after the rainfall stopped. The peak discharge of Q ci was 3.544 L/s for Und27, 4.557 L/s for Com27, and 4.575 L/s for Loc27 which shows the composite and local depressed curb inlet have similar and larger interception capacity than the undepressed curb inlet. The peak discharge of Q gr was 1.721 L/s for Und27, 0.996 L/s for Com27, and 0.782 L/s for Loc27 which shows that the composite gutter improved the grate inlet capture efficiency compared to the local depressed case. The peak discharge of Q bp was 0.516 L/s for Und27, 0.416 L/s for Com27, and 0.516 L/s for Loc27 which shows the road-bioretention with composite curb inlet discharge the smallest runoff flow to the downstream road. The peak discharge (Q pog ) was 3.982 L/s for Und27, 4.918 L/s for Com27, and 4.930 L/s for Loc27, respectively. The Q pog for Und27 was the smallest which due to the undepressed curb inlet intercepted the smallest runoff volume into the bioretention in this case. The overflow beginning time for Und27, Com27, and Loc27 was also 820 s, 673 s, and 673 s when the water depth in the bioretention becomes higher than the overflow grate inlet height. The detailed comparison results for all cases with three types of curb inlet is shown in Table 3. The hydrograph of curb inlet intercepted flow (Qci), road grate inlet captured flow (Qrg), road end bypass flow (Qbp), and the bioretention grate inlet overflow (Qog) are shown in Figure 4. The rainfall intensity was 250 mm/h and maintained to 1200 s (20 min) for all simulation cases. Therefore, all hydrograph grow slowly at the beginning of the rainfall then reach the peak discharge and start to decrease after the rainfall stopped. The peak discharge of Qci was 3.544 L/s for Und27, 4.557 L/s for Com27, and 4.575 L/s for Loc27 which shows the composite and local depressed curb inlet have similar and larger interception capacity than the undepressed curb inlet. The peak discharge of Qgr was 1.721 L/s for Und27, 0.996 L/s for Com27, and 0.782 L/s for Loc27 which shows that the composite gutter improved the grate inlet capture efficiency compared to the local  Note: Q pci (L/s) is road curb inlet peak discharge for RB cases, Q prg (L/s) is road grate inlet peak discharge, h max (m) is the maximum bioretention water depth, T bog (s) is the time of bioretention overflow start, Q pog (L/s) is bioretention overflow peak discharge, "-" means there is no overflow occurred in the bioretention.
As shown in Table 3, the average ± standard deviation of Q pci is 2.32 ± 0.85 L/s for undepressed curb inlet cases, 4.25 ± 0.50 L/s for composite depressed curb inlet cases, and 3.94 ± 0.71 L/s for local depressed curb inlet cases, respectively. The simulation results show that the composite gutter will improve the curb inlet interception efficiency to a large extent. The peak curb inlet interception efficiency varies a lot for the undepressed curb inlet cases. The average ± standard deviation of Q prg is 3.16 ± 0.69 L/s for undepressed curb inlet cases, 1.97 ± 0.72 L/s for composite depressed curb inlet cases, and 1.71 ± 0.55 L/s for local depressed curb inlet cases, respectively. The Q prg for undepressed curb inlet cases was the largest which means the largest portion of runoff was discharged into the drainage pipe. The simulation results show the composite depressed gutter improves the grate inlet capture capacity when the Q prg is compared to local depressed cases.
As shown in Table 3, bioretention overflow did not occur in 14 cases where the maximum water depth (h max ) did not reach the overflow height (h b ) during the whole simulation period. The bioretention overflow beginning time (T bog ) and overflow peak discharge (Q pog ) is mainly related to the curb inlet flow volume (V ci ) and bioretention overflow height (h b ). The average ± standard deviation of Q pog is 2.81 ± 1.39 L/s for undepressed curb inlet cases, 4.59 ± 0.50 L/s for composite depressed curb inlet cases, and 4.24 ± 0.80 L/s for local depressed curb inlet cases. Case09 has the largest peak overflow discharge among these 27 cases. The overflow first occurs at 812 s then reached the highest overflow peak discharge as 4.63 L/s for undepressed case Und09. The overflow first occurs at 700 s and 708 s for Com09 and Loc09 then reached the highest overflow peak discharge as 5.39 L/s and 5.41 L/s, respectively. The bioretention overflow time (T bog ) was delayed when the curb inlet inflow volume (V ci ) decreases and overflow water height (h b ) increase. Figure 5 shows different part runoff volumes and percentages for road-bioretention cases with three types of curb inlets. In Figure 5, group I are results for cases with S 0 = 0.001, group II are results for cases with S 0 = 0.003, and group III are results for cases with S 0 = 0.007. Figure 5a and Table 4 show the runoff volume (V rg ) and percentage (P rg ) captured by road grate inlet as well as the road end bypass volume (V bp ) and percentage (P bp ). The average ± standard deviation of the difference between simulated runoff volume (V rg + V bp + V inf + V bog + V bio ) and calculated rainfall volume fell on the road-bioretention surface (V rb ) are −1.83 ± 0.55%, −1.83 ± 0.57%, and −1.82 ± 0.55% for undepressed, composite depressed, and local depressed cases. It proved the simulation results are accurate enough for analysis of the overall road-bioretention stripe performance.
where V rb is the calculated rainfall volume that fell on the road-bioretention surface equal to 8.34 m 3 .
In Table 4, the negative values of V bp for cases Und01-Und09, Com01-Com18, and Loc01-Loc09 means the runoff moved from left to right and captured by the grate inlet rather than flow to the right downstream of the simulation domain. The simulation results show that the runoff on the road surface was 100% intercepted by the curb inlet and grate inlet combination of cases Und01-Und09 (S 0 = 0.1%), Com01-Com18 (S 0 = 0.1% and 0.3%), and Loc01-Loc09 (S 0 = 0.1%). Therefore, the curb inlet and grate inlet combination were able to deal with the whole road surface runoff for the small longitudinal slope cases when the grate inlet was 0.05 m depressed than the surrounding road cells.
The curb inlet intercepted runoff percentage, P ci = V ci /(V ci + V rg + V bp ), range from 14.64% (Und19) to 70.41% (Und09) with average ± standard deviation as 38.90 ± 14.04% for undepressed cases, from 52.47% (Com19) to 83.37% (Com09) with 70.31 ± 8.11% for composite slope cases, from 40.42% (Loc19) to 83.78% (Loc09) with 65.49 ± 11.60% for local depressed cases. It is easy to find that the composite slope depressed curb inlet was the most efficient to intercept the road runoff into the bioretention strip, then is the local depressed curb inlet, and the undepressed curb inlet was the least efficient. As shown in Figure 5, the curb inlet interception efficiency will increase as the curb inlet length and cross slope increase as well as the longitudinal slope decrease.
The grate inlet captured runoff percentage ranges from 28.09% (Und27) to 73.35% (Und01) with average ± standard deviation of 51.48 ± 11.22% for undepressed cases, from 15.90% (Com21) to 55.66% (Com04) with 32.26 ± 11.66% for composite slope cases, from 12.90% (Loc27) to 48.56% (Loc01) with 27.72 ± 8.74% for local depressed cases. The road end bypass runoff percentage ranges from −12.32% (Und07) to 30.32% (Und19) with average ± standard deviation as 5.44 ± 11.53% for undepressed cases, from −25.42% (Com07) to 17.45% (Com19) with −4.97 ± 13.32% for composite slope cases, from −12.32% (Loc07) to 25.51% (Loc19) with 4.51 ± 10.42% for local depressed cases. It is indicated that the grate inlet capacity was large enough to capture the upstream and downstream inflow for that the road end bypass flow of some cases is negative. Therefore, the grate inlet captured runoff percentage was limited by the upstream and downstream inflow rather than by the grate inlet capacity when combined with the curb inlet. In this case, the grate inlet in undepressed road-bioretention captured the most runoff percentage, then the grate in composite slope cases, and the grate inlet in local depressed road-bioretention cases captured the least runoff percentage. The V rg of local depressed curb inlet cases was smaller than the corresponding composite depressed curb inlet cases with similar V ci which proves the composite gutter improves the grate inlet capture capacity in all cases.
The sensitivity analysis results for P ci of undepressed, composite depressed, and local depressed curb inlet RB stripe cases are presented in Figure 6. Three design parameters (S 0 , S x , and L ci ) were considered in the P ci sensitivity analysis. In general, the curb inlet intercepted runoff volume percentage will increase as the S 0 decrease, S x increase, and L ci increase for all three types of curb inlet. For undepressed cases, the longitudinal slope S 0 is less sensitive than the cross slope S x as shown in Figure 6a. The S 0 varies from 0.001 to 0.007 while S x only change from 0.015 to about 0.027 when P ci = 0.40. The inlet opening length L ci seems similar sensitive as S x when checking different P ci in Figure 6b for the P ci change evenly when L ci and S x change. Therefore, the parameter sensitivity sequence of undepressed curb inlet cases is S 0 < S x ≈ L ci .  For composite depressed cases, S 0 is more sensitive than S x as shown in Figure 6c. S x varies from 0.01 to 0.04 while S 0 only changes from about 0.0022 to about 0.0051 when P ci = 0.72. L ci seems more sensitive than S x as shown in Figure 6d. S x varies from 0.01 to 0.04 while L ci only changes from about 0.55 m to about 0.72 m when P ci = 0.72. Therefore, the parameter sensitivity sequence of composite depressed curb inlet cases is S x < S 0 and S x < L ci .
For local depressed cases, S x is more sensitive than S 0 as shown in Figure 6e. S 0 varies from 0.001 to 0.007 while S x only change from about 0.015 to about 0.028 when P ci = 0.68. L ci seems less sensitive than S x as shown in Figure 6f. L ci varies from 0.45 m to 0.90 m while S x only change from about 0.016 to about 0.03 when P ci = 0.68. Therefore, the parameter sensitivity sequence of local depressed curb inlet cases is S 0 < S x and L ci < S x . Overall, the undepressed curb inlet cases are the least sensitive to S 0 while evenly sensitive to S x and L ci ; the composite depressed curb inlet cases are the least sensitive to S x while the local depressed curb inlet cases are the most sensitive to S x .
The infiltration volume of bioretention (V inf ) which was mainly influenced by the bioretention inflow and overflow process were shown in Table 4. The bioretention inflow includes curb inlet intercepted runoff volume (V ci ) and rainfall fell on the bioretention. The infiltration volume shows a similar trend to V ci in Figure 5 because the rainfall that fell on the bioretention was the same for all cases. The infiltrated runoff volume ranges from 1.09 m 3 (Und19) to 1.38 m 3 (Und09) for undepressed cases, from 1.30 m 3 (Com19) to 1.40 m 3 (Com09) for composite slope cases, and 1.27 m 3 (Loc19) to 1.40 m 3 (Com09) for local depressed cases. The bioretention outflow is overflow grate inlet discharge volume (V bog ). The overflow grate inlet discharge volume ranges from 0.03 m 3 (Und19) to 1.95 m 3 (Und09) for undepressed cases, from 1.12 m 3 (Com19) to 2.81 m 3 (Com09) for composite slope cases, and 0.27 m 3 (Loc19) to 2.82 m 3 (Com09) for local depressed cases.
The total runoff volume that stays in the bioretention cell (V bio ) at the end of the simulation for RB cases is shown in Table 4. The runoff that stays in the bioretention cell will be infiltrated and evaporated after the rainfall stops, therefore, the sum of V bio and V inf could be regarded as the runoff controlled by the bioretention. The ratio of V bio + V inf and V rb is shown in Table 4. The ratio ranges from 26.78% (Und19) to 52.20% (Und09) with average ± standard deviation as 43.8 ± 6.95% for undepressed cases, from 45.31% (Com19) to 52.26% (Com09) with 48.9 ± 2.21% for composite slope cases, from 44.90% (Loc19) to 52.42% (Loc09) with 48.91 ± 2.31% for local depressed cases. The simulation results show that the bioretention stripe with composite depressed curb inlet cases controlled the most runoff volume, then the local depressed curb inlet cases, and the undepressed curb inlet controlled the least runoff volume. The difference for each undepressed curb inlet cases was the biggest, which proves that the performance of undepressed curb inlet cases varies to a large extent with S 0 , S x , and L ci . The runoff ponded by bioretention at the end of the simulation (V bio ) is smaller than the calculated ponding volume (V pc ) based on bioretention geometry. Therefore, it is necessary to consider S 0 when determining the ponding capacity of bioretention, especially in the continuous road-bioretention stripe.

Conclusions
The updated and tested open-source FullSWOF-ZG program was used to evaluate the road-bioretention stripes' performance. Eighty-one road-bioretention models of undepressed curb inlets, composite depressed curb inlets, and local depressed curb inlets with different S 0 , S x , and L ci were established and simulated with FullSWOF-ZG. The simulation results were analyzed and found that the RB performance was influenced by different types of curb inlet complexly. Three main conclusions were drawn based on the simulation results: (1) the composite depressed curb inlet was the most efficient to intercept the road runoff into the bioretention stripe, then the local depressed curb inlet, and the undepressed curb inlet was the least efficient; (2) the curb inlet and grate inlet combination can intercept/drain almost all of the road surface runoff for small longitudinal slopes (0.1-0.3%) with a composite depressed curb inlet to relieve the road local flood inundation; (3) the undepressed curb inlet cases are the least sensitive to S 0 ; the composite depressed curb inlet cases are the least sensitive to S x while the local depressed curb inlet cases are the most sensitive to S x . Overall, the composite depressed curb inlet should be considered as a good choice in road-bioretention stripe design.
Author Contributions: The work was conducted by X.L., X.F., C.W., G.C., S.Z. and Y.Y.; X.L. promoted the idea, conducted the study, and prepared the manuscript draft. X.F. supervised model development, data analysis, and manuscript writing. C.W., G.C., S.Z. and Y.Y. supervised the writing and data analysis. All authors made contributions to the study. All authors have read and agreed to the published version of the manuscript. Data Availability Statement: Some or all data, models, or code generated or used during the study are proprietary or confidential and may only be provided with restrictions. The model input and output data are specifically designed for a research numerical model. They are available upon request but are not useful for the general public.

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

Abbreviation
A summary of the definitions or descriptions of acronyms and symbols used in the paper is given below. bioretention water depth at time t K saturated hydraulic conductivity ϕ suction head ∆E differences of simulated and observed interception efficiencies ∆θ moisture deficit ∆V runoff volume percent difference of whole simulation domain L upstream catchment length L ci curb inlet length NSE Nash-Sutcliffe efficiency P bp percent of bypass runoff volume P ci percent of runoff volume intercepted by curb inlet P inf percent of bioretention cumulative infiltration volume P rg percent of road grate inlet captured runoff volume Q bp remainder of runoff discharged downstream along the road Q ci road runoff intercepted by the curb inlet Q og overflows runoff through the bioretention grate inlet Q pog overflow grate inlet peak discharge Q prg peak discharges of the grate inlet Q rg road runoff captured by the road grate inlet S 0 longitudinal slopes of the road/street SPC Sponge City SWEs shallow-water equations S x cross slope of the road/street T bog bioretention overflow-start-time V bio bioretention ponding runoff volume V bog bioretention overflow grate inlet discharge volume V bp bypass runoff volume V ci runoff volume intercepted by curb inlet V inf bioretention cumulative infiltration volume V pc calculated bioretention ponding volume V rb runoff generated on the bioretention surface from rainfall V rg runoff volume captured by the road grate inlet