Abstract

Use of sustainable stormwater technologies such as bioretention cells (BRCs) is gaining in popularity across the world as episodes of severe flooding are becoming more frequent due to increased urbanization, and associated costs are rising due to decaying infrastructure and insufficient flood management. The aim of this study is to use numerical modeling to expand the understanding of BRC systems across the Toronto region. There is no one universally accepted approach to designing BRC systems. Local sensitivity analysis (LSA) with the one-factor-at-a-time method and global sensitivity analysis (GSA) with factorial design were conducted to identify the most influential components of BRC design for overflow reduction. Eight different model scenarios were used in a long term simulation to determine the efficacy of Ontario’s BRC design standards for meeting Toronto’s runoff volume control target (RVC_T) of 27 mm. LSA shows that the highest reduction in overflow can be achieved by increasing BRC surface area, the saturated hydraulic conductivity (BSM K_sat) of bioretention soil media, or BRC ponding depth. On the other hand, GSA suggests that the most effective BRC performance can be achieved by simultaneously increasing the area of BRC, BSM K_sat, and BRC storage depth. Continuous simulation results show that Ontario’s minimum BRC design guideline does not meet Toronto’s RVC_T. However, small adjustments to the baseline design, such as a 0.4% increase in BRC surface area, a 5 cm increase in ponding depth, or a 3 cm/h increase in BSM K_sat, can reduce the number of storm events causing overflow by up to 50% and meet RVC_T.

1 Introduction

1.1 Background

As population and urban development increase, so does the risk of urban flooding, mainly due to the increase in impervious areas that prevent the natural hydrological response of a site by reducing evapotranspiration and infiltration of precipitation while increasing surface runoff (Kaykhosravi et al. 2018). To counter these negative impacts, a number of novel stormwater control measures (SCMs) have been suggested across the world, such as low impact development (LID), green infrastructure (GI), water sensitive urban design (WSUD), and sustainable drainage systems (SuDS) (Fletcher et al. 2015). While stormwater infrastructure has been designed to remove stormwater runoff as quickly as possible from the urban setting, these novel SCMs are instead trying to mimic the natural hydrology of a site by reducing runoff and by storing the stormwater at the source of runoff. LID SCMs such as bioretention cells (BRCs) have undergone extensive hydrological performance analyses both in laboratory and field studies (Khan et al. 2012) to determine their effectiveness. However, the results of these studies vary greatly, with inflow volume reductions ranging from 20% to100% (Li et al. 2009; Paus et al. 2016), peak flow reductions between 24% and 99% (DeBusk and Wynn 2011; Winston, Dorsey et al. 2016), and peak delays of between 6 min and 738 min (Géhéniau et al. 2014). Some of the factors that affect the performance of BRCs are associated with their type, shape and size, underlying soils, intensity and duration of the precipitation, weather conditions, and antecedent moisture conditions, among others (Kaykhosravi et al. 2018). These observations show that the performance of BRCs is affected significantly by their design, the temporal rainfall distribution, and the spatial conditions of the area where they are implemented.

With episodes of severe flooding becoming more frequent due to increased urbanization, and associated costs rising due to decaying infrastructure and insufficient flood management (Berggren et al. 2011; Nirupama and Simonovic 2007; Nirupama et al. 2014), the popularity of BRCs as the cost-effective LID SCMs is increasing. As the investment in these practices rises, more research is needed to determine the effectiveness of this technology for different configurations and varying temporal and spatial conditions. This study aims to expand our understanding of BRCs by identifying the most important design aspects for hydrological performance of BRCs and evaluating whether Ontario’s current BRC design guidelines are capable of meeting Toronto’s runoff volume control target (RVC_T) of the 90th percentile storm depth. The following sections define the study area used, the sources of data, and BRC design within the PCSWMM (PC Storm Water Management Model) environment, which is the numerical model used for this research. The SWMM5 model is used as the engine for PCSWMM.

2 Materials and Methods

2.1 Site Description and BRC Design

The site chosen for this research is a small housing complex (Passy Gardens) close to York University’s Keele campus, located in North York, Toronto (Figure 1).

Figure 1 Location of Passy Gardens apartment complex (Google Maps).

A closeup of the study area is also shown in Figure 1 where the area outlined in red indicates the Passy Gardens apartment complex, which is divided into three separate subcatchments. Because of the similarities between the three subcatchments, only S1, the rightmost subcatchment, is analyzed in this study. S1 occupies 4050 m², and the area outlined in green (a vegetated area used for landscaping) within the subcatchment amounts to 560 m². The slope for S1 is set at 2.7% (estimated using data from Google Earth), and the native soil texture in the area is considered to be loam (MOECP 2018). It is also assumed that only 10% of the impervious area in S1 contains depression storage, which is set to 1.5 mm according to standard (ASCE 1992).

The model of the design of the BRC that is to be installed in the vegetated area is based on the Ontario guideline recommendations (MOECC 2017). The MOECC suggestions of both the lower and upper limits are used for the BRC surface area (BSM A), ponding depth (Ponding D), bioretention soil media depth (BSM D) and hydraulic conductivity (BSM K_sat), storage depth (Storage D), internal water storage depth (IWS D) and native soil hydraulic conductivity (Native K_sat). In the case of storage depth only a lower limit is given (≥30 cm), so an upper limit of 90 cm was selected. Guidelines from Victoria, BC (CoV 2015) recommend an upper limit of 2 m, whereas guidelines from Wisconsin (WDNR 2014) recommend an upper limit of 120 cm, meaning that the selected 90 cm upper limit for Ontario fits within the limits of other guidelines (i.e. 30 cm–120 cm and 30 cm–200 cm). Ontario’s BRC guidelines further recommend installing underdrains 100 mm above the bottom of the cell, which creates a 100 mm internal water storage (IWS) area. Since an upper limit for IWS is not given, we set it to 70 cm to keep it 20 cm below the top of the storage layer. It was assumed that the installed BRC will receive 100% of the runoff from the subcatchment impervious area.

Parameters for certain LID inputs (soil porosity, moisture content at field capacity and at wilting point, initial deficit, hydraulic conductivity and suction head) as well as the catchment depth of depression storage and Manning’s roughness coefficient are taken from Rossman and Huber (2016).

2.2 Design Storm Events and Historical Data

Several different precipitation events are considered for local sensitivity analysis (LSA) and global sensitivity analysis (GSA). Event based analyses are conducted using both the 5 min and 1 h hyetographs for the study area, whereas long-term simulations are performed using hourly historical data for the site. Atmospheric Environmental Service (AES) 1 h events are based on North York’s intensity–duration–frequency (IDF) curves obtained from the Environment Canada website (MOECC–MSC 2018), while the Hurricane Hazel 12 h rainfall distribution is based on the inbuilt database records of PCSWMM. The rainfall hyetographs of the synthetic precipitation events for several return periods for the 1 h duration event and for Hurricane Hazel are shown in Figure 2 and Figure 3.

Figure 2 Atmospheric Environmental Service Southern Ontario 1 h rainfall hyetographs (MOECC–MSC 2018).

Figure 3 Hurricane Hazel (Southern Ontario: 0–25 km²) rainfall hyetograph (from PCSWMM).

The continuous model simulations were performed using almost 12 y of precipitation and temperature data. Precipitation data is used from the Dufferin Reservoir HY021 station (43°49’53.9”N 79°28’42.8”W) with hourly precipitation data obtained from the Meteorological Service of Canada (Duncan, J., personal communication, 2017-10-26–2017-11-16). Daily temperature minimums and maximums were obtained from the Environment Canada website (MOECC–MSC 2018) for a nearby area in North York (43°46’45.6”N 79°28’09.2”W) for the same period as the precipitation data, 2005-04-27–2017-01-01. These data are shown in Figure 4.

Figure 4 Precipitation and temperature data, 2005-04-27 12:00–2017-01-01 12:00 (MOECC–MSC 2018).

2.3 Parametric Sensitivity Analysis

To analyze the importance of different BRC design parameters two sensitivity analyses are considered. The performance metric chosen for this study is based on the runoff volume reduction (Equation 1). It represents the incoming stormwater runoff in a BRC in terms of how much water is lost via evapotranspiration, exfiltration (percolation into the native soil), and underdrain flow (after the water was filtered by the media), as opposed to the BRC overflow of this incoming runoff when the BRC capacity is exceeded.

(1)

where:

VR	=	runoff volume reduction (%),
Qin	=	total BRC inflow (mm), and
SO	=	BRC surface overflow (mm).

The runoff volume reduction VR ranges from 0 to 100%: a VR value of 0 implies that no infiltration occurred through the BRC and all the inflow was diverted as surface runoff; and a VR value of 100% implies that all the inflow infiltrated into the BRC media. However, note that due to the presence of an underdrain in all of the BRC design configurations, runoff entering the BRC can exit the BRC through the underdrain into receiving waterbodies (rather than exclusively percolating into the native subsoils). Thus, a VR value of 100% means that there was no surface overflow, and that the BRC may discharge the runoff through the underdrain pipe.

Local Sensitivity Analysis (LSA)

This analysis is based on a one-factor-at-a-time (OFAT), sometimes referred to as one-at-a-time, technique (Czitrom 1999; Saltelli et al. 2004) in which a change in runoff volume reduction is observed for a change of a single design parameter. Thus the greater the output change, the more influential that parameter is. This technique was chosen because it is one of the most commonly used techniques in engineering applications to determine the significance of a parameter.

For this analysis, the Ontario BRC design guidelines are used. Factors are varied between minimum and maximum values to observe the changes in overall water balance. Table 1 gives an overview of the main variables in LSA model set-up and the level (i.e. the ranges) of parameter variations.

Table 1 LSA set-up of the models; regular numbers indicate minimum Ontario recommendations, whereas bold numbers indicate the maximum recommendations.

	BRC Area (%)	Ponding Depth (cm)	BSM Depth (cm)	BSM Ksat (cm/h)	Storage Depth (cm)	IWS Depth (cm)	Native Ksat (cm/h)
M1–Min	6.6	15	100	12	30	10	0.33
M2–BRC Area	20	15	100	12	30	10	0.33
M3–Ponding D.	6.6	25	100	12	30	10	0.33
M4–BSM Depth	6.6	15	125	12	30	10	0.33
M5–BSM Ksat	6.6	15	100	30	30	10	0.33
M6–Storage D.	6.6	15	100	12	90	10	0.33
M7–IWS Depth	6.6	15	100	12	30	70	0.33
M8–Native Ksat	6.6	15	100	12	30	10	1.5
M9–Max	20	25	125	30	90	70	1.5

Note that model M9 in Table 1 should be considered as an extreme design configuration: each of the factors has the maximum recommended value. Other models (M2 to M8) only have a single factor that is different from the baseline model (M1, with minimum values for each factor), whereas in M9 all factors have been adjusted in comparison to model M1.

Global Sensitivity Analysis (GSA)

The LSA OFAT method only investigates the change in the output due to a change in the input value, but it does not evaluate the possible synergistic, combined, or interactive effects of several parameters interacting with one another, which could result in perturbed model output. GSA is an adequate way to see if better model performance could be achieved with different combinations of the perturbed input variables as compared to perturbing a single parameter as in the LSA.

Full factorial design (which was previously explored in an experimental green roof lab set-up, Hill et al. 2017) was chosen for GSA. This means that every single possible combination of a selected number of parameters should be modeled. To perform this GSA, a design of experiments (DOE) set-up is needed. DOE presents a layout of the model input variables (hereafter referred to as factors) and their value ranges (hereafter levels) in terms of model runs needed for full factorial design (Ankenman 1999; Saltelli et al. 2008).

For this research, a 7 factor and 3 level (representing the minimum, maximum and mean of Ontario’s BRC design recommendations) set-up was used. The 7 factors that were used in LSA are divided into two groups, of 3 and 4 factors (to reduce the computation requirements, as a full factorial design for 7 parameters would result in 3⁷ models), shown in Table 2 (group A with 3 factors and group B with 4 factors). To increase variation between factors (to be modeled to measure the impacts of combined inputs) 3 input variable combinations are assessed (each containing two groups of 3 and 4 factors in different orders). The complete DOE for GSA’s factorial design is given in Table 2, Table 3 and Table 4 for groups A-B, C-D and E-F, representing the 3 chosen input variable combinations with the inputs and value levels assigned to each group. According to the Ontario BRC guidelines, the minimum suggested IWS depth is 10 cm, which is included in every single model. However, IWS depth is further increased only by increasing storage depth, but is never greater than the storage depth (e.g. when storage depth is 60 cm IWS is increased to 40 cm, whereas for storage of 90 cm IWS is tested at both 40 cm and 70 cm depths). This DOE results in 243 [(A + B) × 3 combinations = (33 + 33 × 21) × 3] model runs for all three input variable combinations.

Table 2 DOE combination 1 for GSA factorial design.

Combination 1
Group A: Factors	Level 1	Level 2	Level 3
BRC Area (%)	6.6	13.3	20
BSM Ksat (cm/h)	12	21	30
BSM Depth (cm)	100	112.5	125
Group B: Factors	Level 1	Level 2	Level 3
Ponding Depth (cm)	15	20	25
Native Ksat (cm/h)	0.33	0.92	1.5
Storage Depth (cm)	30	60	90
IWS Depth (cm)	-	40	70

Table 3 DOE combination 2 for GSA factorial design.

Combination 2
Group C: Factors	Level 1	Level 2	Level 3
BRC Area (%)	6.6	13.3	20
BSM Ksat (cm/h)	12	21	30
Ponding Depth (cm)	15	20	25
Group D: Factors	Level 1	Level 2	Level 3
Native Ksat (cm/h)	0.33	0.92	1.5
BSM Depth (cm)	100	112.5	125
Storage Depth (cm)	30	60	90
IWS Depth (cm)	–	40	70

Table 4 DOE combination 3 for GSA factorial design.

Combination 3
Group E: Factors	Level 1	Level 2	Level 3
Native Ksat (cm/h)	0.33	0.92	1.5
BSM Depth (cm)	100	112.5	125
BSM Depth (cm)	100	112.5	125
Group F: Factors	Level 1	Level 2	Level 3
BRC Area (%)	6.6	13.3	20
BSM Ksat (cm/h)	12	21	30
Storage Depth (cm)	30	60	90
IWS Depth (cm)	-	40	70

2.4 Continuous Simulation

Event-based modeling is important when exploring extreme case scenarios to determine BRC performance during these infrequent events. However, while these events are important to study, most of the annual rainfall is typically not composed of extreme events, but rather less intense events distributed over long periods of time. Therefore long term continuous simulations were used to assess the designed system performance under regular (not necessarily extreme) precipitation events. Several different BRC designs were selected for long term simulations of ~12 y duration. It was expected that these simulations would help to determine whether Ontario BRC designs are capable of achieving the runoff volume control target (RVC_T). In case RVC_T is not met, this analysis will determine how much perturbation to the BRC design is needed to manage runoff produced within the study area. RVC_T is based on capture and treatment of the 90th percentile of average annual rainfall events (MOECC 2017), sometimes referred to as the one-inch rule. Ontario’s 90th percentile of average annual rainfall in Toronto translates into capture and treatment of all events ≤26 mm–28 mm (MOECC 2017), which is hereafter referred to as the 27 mm event.

Eight different BRC designs were considered for continuous model simulations to see how they performed when exposed to observed long term rainfall patterns. The selection of these eight models was based on the findings of LSA and GSA. These designs are composed of a baseline model (M1) to set a performance criterion for other models, as well as to determine if this model can meet RVC_T. Other models include minimal adjustments to BRC’s surface area (M2, M3 and M4), an increase in BRC’s ponding depth (M5 and M7), BSM’s K_sat (M6, M7 and M8), and storage depth (M8). A full list of BRC designs used for a continuous simulation is given in Table 5.

Table 5 Model setups for continuous simulations.

	BRC Area (%)	Ponding Depth (cm)	BSM Ksat (cm/h)	Storage Depth (cm)
M1 – Base	6.6	15	12	30
M2 – BRC Area	7	15	12	30
M3 – BRC Area	8.5	15	12	30
M4 – BRC Area	10	15	12	30
M5 – Ponding Depth	6.6	20	12	30
M6 – BSM Ksat	6.6	15	15	30
M7 – Ponding Depth & BSM Ksat	6.6	20	15	30
M8 – Storage Depth & BSM Ksat	6.6	15	21	60

3 Results and Discussion

3.1 Parametric Sensitivity Analysis

Local Sensitivity Analysis

Figure 5 and Figure 6 show the hydrological model performance for BRCs designed according to Ontario recommendations. The results are expressed in percentage of runoff volume reduction (calculated using Equation 1) and divided into AES-SO and Hurricane Hazel events. The higher the runoff volume reduction the less untreated stormwater bypasses the BRC system; that is, more water is lost via evaporation, exfiltration into surrounding soil, or discharge to municipal sewers or a nearby surface water body. Figure 5 shows BRC’s efficiency in minimising stormwater runoff for four selected return periods (2.25 y, 5 y, 10 y and 100 y), where the 2.25 y event results in a 27 mm 1 h storm, amounting to Toronto’s RVC_T.

Figure 5 LSA results from AES models.

Figure 6 LSA results from Hurricane Hazel models.

AES-SO rainfall distributions are uniform in nature and peak in the late first and early second quarters (Figure 2) of the 1 h event, indicating that most of the storm volume is generated early on. Since the events are fairly intense, the infiltration capacity of the BRC is exceeded, resulting in surface ponding becoming the controlling variable. The effects of media depth, storage depth, IWS, and hydraulic conductivity do not come into play. The area is more important since it controls the amount that is ponded (along with surface infiltration rate). The parameters that minimize BRC overflow the most, for these distributions, are BRC area, BSM K_sat and BRC ponding depth (Figure 5). The influence of these parameters is more pronounced with increasing return periods. Models M3 and M5 are capable of managing 99% of the runoff of a 2.25 y 1 h event, whereas M2 can capture 100% of the runoff of a 5 y event and 95% of the runoff of a 10 y event. This shows that the most important aspect of BRC design is the ratio between its surface area and the impervious surface area draining into it (the impervious:pervious ratio, Khan et al. 2013)

While the most influential parameters identified in Figure 5 are the same as in Figure 6, Hurricane Hazel better represents the influence of other parameters due to its varied and late-peaking intensity. For instance, for this event, BRC K_sat and ponding depth do not have as large an effect as they have for the AES-SO distribution, since their performance is similar to that of other parameters, very close to a 45% runoff volume reduction (45% is the approximate average for all models except M2 & M9, for which the BRC is area is maximum). Conversely, for this storm event, an increase in almost any parameter from the base level results in an improved performance (no matter how minimal), with the exception of IWS depth. A 60 cm increase in IWS depth resulted in a 10% decrease in BRC volumetric runoff. Since this storm is relatively long and late-peaking the incoming runoff infiltrates the BRC and occupies the storage space; due to the elevated outflow pipe the water keeps pooling from the bottom of the cell upwards, until it reaches the level of the underdrain. Thus this pooling consumed the available BSM pore space and reduced its capacity and thereby its performance during this long and intense storm.

When comparing the AES-SO 100 y storm (Figure 5) to the Hurricane Hazel distribution (Figure 6) it can be seen that BRC performance improves with increasing event duration even though this means that the cumulative precipitation is nearly 2.5 times higher. However, based on rainfall hyetographs (Figure 2 and Figure 3), increased event duration reduces overall intensity, which allows for more water evaporation and infiltration into the BRC over time (since it takes longer to exceed its capacity), thereby improving its performance. As the generated hyetograph of hurricane Hazel extends over a 12 h period, this results in smaller hourly intensities allowing the first half of the storm to be managed quite efficiently (with only minimal overflow when rainfall intensifies to 10 mm/h–20 mm/h). During late peaking events, like hurricane Hazel, BRC capacity is exhausted before the rain intensifies, (Figure 7) and BRC surface ponding capacity reaches its limit (150 mm) ~4.5 h after the start of the event, long before its peak. The efficacy of the cells during these events diminishes at the end of such storms, when most of the intense rainfall bypasses the system without treatment.

Figure 7 Inflow, surface level and surface overflow for Hurricane Hazel M1 scenario.

The M9–Max model (Figure 5 and Figure 6) represents the model performance when meeting the maximum Ontario BRC guidelines (the detailed design criteria are shown in Table 1). As can be seen from the models with various storms, increasing the BRC design to the maximum recommendations allows it to fully capture and treat not only the 100 y event with AES-SO storm distribution but also hurricane Hazel for a given catchment area. It should be noted that a VR value of 100% for these two large events should be considered with caution: for both events, the permanent storage in the BRC (both the ponding depth, and in the storage layer below) is extremely large. This allows the BRC to hold the inflow runoff within the storage volume as it infiltrates through the BRC media (which has the maximum BSM K_sat). In both cases, the losses from the underdrain pipe are large and constitute about 50% of the inflow volume. Also, the relatively large ratio between the BRC area and the upstream area contributes to extremely high permanent storage volume available on the surface of the BRC.

Considering the OFAT perturbations, an increase in a single parameter gives a rather linear response for a given storm, this is not so when considering several parameters at a time, as the combined effects create a nonlinear response. The following section is concerned with the GSA factorial design, where results from combinations of 3 bioretention cell parameters (in 2 groups with 3 or 4 parameters in each group) are given. One of the groups includes the combination of best performing parameters from this section, which is then compared to other parameters groups.

Global Sensitivity Analysis

Graphs in Figure 8 show the GSA results, in terms of runoff volume reduction (on the vertical axis), from all 243 model runs (27 models for plots A, C and E and 54 models for plots B, D and F on the horizontal axis). The titles in each diagram show the input variables that have been perturbed (at 3 levels, min, max and mean values of Ontario BRC guidelines, shown in Tables 2, 3 and 4).

Note that the first 27 models in groups B, D and F do not have any fluctuations in IWS depth, which is set to a minimal 10 cm depth, whereas models 28–54 have increasing IWS depth. The comparison of models 1–27 and 28–54 shows that the runoff volume reductions in models 28–54 are almost exact replicas of the first 27 model runs, with only a minimal reduction in performance (shown in Table 6 when comparing models 1–27 with 28–54 for B, D and F model groups) due to pooled water within the storage layer IWS zone.

Table 6 Average runoff volume reduction (%).

Runs	Combination 1		Combination 2		Combination 3
	Group A	Group B	Group C	Group D	Group E	Group F
1–27	76.34%	47.35%	76.84%	46.11%	47.44%	77.59%
28–54	–	47.37%	–	46.07%	–	76.16%
1–54	–	47.36%	–	46.09	–	76.87%

Figure 8 shows that the combinations of parameters in groups B, D and E do not provide any overall improvements to the system. In fact, even though 3 or 4 parameters are consequently increased, the performance remains almost the same no matter what the degree of increase for a specific parameter (as can be seen in Figure 8 when looking at the maximum increase in models 27 and 54). An average performance in groups B and E (shown in Table 6) is only minimally worse (1.44% lower for group B runs 1–54, and 1.36% lower for group E) than the performance of ponding depth increases in the LSA Hurricane Hazel model, shown in Figure 8. This means that the marginal difference in performance is driven only by BRC ponding depth. Similarly, an average performance in group D models is only slightly worse (0.11%) than the performance of the LSA Hurricane Hazel model, with an increasing BSM depth. This similarity in the results means that the combined effects play little or no part in the model input variable combinations shown in groups B, D and E.

Model groups A, C and F show a much better overall performance (as can be seen in Figure 8 and Table 6). An average runoff volume reduction for these models is ≥76%, which is only matched by LSA model runs with the maximum BRC surface area scenario (as compared to Hurricane Hazel runs). While the BRC surface area contributes most to the increased capacity, the combined effect of a concurrent increase in several design parameters amplifies the overall performance of the cell. Thus while increasing the BRC area, BSM K_sat and ponding depth proved to be the most effective in LSA. GSA suggests that (on average) the most effective BRC performance can be achieved when concurrently increasing BRC area, BSM K_sat and storage depth. This is because increased K_sat of the BRC soil media allows more ponded water to reach the storage space in a shorter time. As storage space is typically filled with coarse gravel, the majority of the space is composed of pores available for the percolating water to occupy. Thus the overall performance of the cell is improved as both surface and subsurface storage are used by the incoming stormwater runoff.

In general, both parametric sensitivity analyses (PSA) provided slightly different results than those obtained by Sun et al. (2011) and Wang et al. (2013). Two of the most influential parameters, BRC surface area and BSM K_sat, were identified in previous studies. Ponding depth (as found using LSA) and storage depth (as found using GSA) are parameters that have not been identified as influential in previous PSA studies. However, since BRCs can be considered for different performance aspects (e.g. groundwater recharge, ET promotion, water quality improvement), the choice of the performance metric used is crucial for PSA. For instance, Winston, Smolek et al. (2016) found that BRC surface area, IWS depth, and native soil type were the most important parameters for promoting exfiltration. As the goal in this research is to minimize BRC overflow (which leads to improved water quality as more potential runoff undergoes filtration), the chosen performance metric is based on volumetric runoff reduction, as given in Equation 1, with the aim of reducing the overflow of untreated stormwater. Thus, in the present research, a different set of parameters was found to give the best overall performance.

3.2 Continuous Simulation

The precipitation time series that was used for the continuous model simulations spans an almost 12 y period and is composed of 1484 individual rain events (considering a minimum interevent time, MIT, of 6 h from the end of one event to the beginning of the next). The durations of these events ranged from 1 h–63 h (including both wet and dry periods) and the total precipitation was between 0.1 mm and 115.4 mm. Out of these 1484 events, only 57 storm events are ≥27 mm (i.e. Toronto’s RVC_T), with duration ranging from 4 h to 63 h. Thus the continuous simulations are primarily measuring how effective Ontario’s BRC recommended design guidelines are at dealing with storms producing ≤27 mm of rainfall.

The continuous simulation results are given in Table 7 and Table 8. Table 7 shows, for each of the 8 modeled scenarios, the simulated evaporation rates, total runoff volume reduction, the number of overflows and the number of storm events that caused them, as well as the number of overflows that were caused by storms smaller than or equal to Toronto’s RVC_T of 27 mm for the simulation period. Table 8 provides a complete list of the overflow-causing storms for the base scenario (M1).

Table 7 Continuous simulation results overview.

Model	Simulated evap. rates (mm/d)	Runoff reduction (%)	No. of overflows	No. of overflow events (≤27 mm)	Overflow storms (see Table 8)
M1	Min: 0 Mean: 1.98 Max: 6.64	98.55	11	10 (2)	1–10
M2		98.68	7	6 (0)	1–2; 4; 6–7; 9
M3		99	4	4 (0)	1; 4; 6; 9
M4		99.17	2	2 (0)	1; 4
M5		98.84	5	5 (0)	1; 4; 6–7; 9
M6		98.8	6	6 (0)	1–2; 4; 6–7; 9
M7		99.01	4	4 (0)	1; 4; 6; 9
M8		99.14	3	3 (0)	1; 4; 6

Table 8 PCSWMM estimates of overflow causing storms for M1 model (MIT = 6 h). Bold represents events ≤27 mm, italics represent an event that caused two separate overflows.

No.	Total duration	Total rainfall	Max 1 h intensity	Storm with >10 mm/h rainfall before max intensity?
1	13 h	115.4 mm	84.8 mm	Yes, for 1 h
2	36 h	41.4 mm	24.8 mm	No
3	4 h	21.9 mm	18.5 mm	No
4	6 h	36.1 mm	27.4 mm	No
5	21 h	54.7 mm	15.9 mm	Yes, for 1 h
6	4 h	47.4 mm	24.5 mm	Yes, for 1 h
7	22 h	68.7 mm	21.7 mm	No
8	8 h	40.7 mm	20.8 mm	No
9	5 h	32.2 mm	24 mm	No
10	8 h	23.2 mm	22 mm	No

The model results shown in Table 7 indicate that even the minimal Ontario BRC design (M1) is capable of capturing and treating well above 90% of the total precipitation for the entire simulation period of almost 12 y. However, comparing this model’s runoff volume reduction to that of other scenarios shows hardly any discernible difference. For example, when increasing BRC surface area from the base scenario (231 m² or 6.6% of impervious catchment draining to it) to 245 m² (7%) in M2, 297.5 m² (8.5%) in M3, or 350 m² (10%) in M4, the runoff volume reduction increased from M1 by 0.13%, 0.45% and 0.62%. Similar increases can be observed from other models. For example, a 5 cm increase in ponding depth (M5) or a 3 cm/h increase in BSM K_sat (M6) increased the runoff reduction to 98.84% and 98.8%, whereas concurrent increase in both of these parameters (M7) resulted in a 99.01% capture rate, which is matched by M3 with a 1.9% increase in BRC area from the base level. On the other hand, while BSM K_sat and increased storage depth proved to be efficient in GSA, a concurrent increase in these parameters (M8) did not result in much greater runoff volume reduction (almost identical to that of M4). Overall, none of the tested models show much improvement in BRC performance as the runoff volume capture is already close to 100% with only extreme events causing overflows.

Runoff volume reduction alone does not provide enough information on the stormwater management improvement. Thus the storms that caused overflow events are also considered. For example, Table 7 shows that for scenario M1 the BRC overflowed 11 times, caused by 10 different storms, whereas any other improvement to the BRC design over the base level reduced the number of overflows by nearly 50% or more. While M8 did not much improve runoff reduction, it overflowed only 3 times (storms 1, 4 and 6 in Table 8). Out of the 10 overflow-causing storms these 3 storms are some of the shortest and most intense, with storm 6 also producing a substantial amount of rainfall (>10 mm) in the 1 h before its peak intensity (i.e. a skewed hyetograph). According to MOECC (2017), focusing on events above the 90th percentile rain event (i.e. RVC_T) is simply uneconomical as the perturbations to a BRC are too great compared to the benefits gained; this is the law of diminishing returns. This analysis explains why the improvements in BRC efficiency are quite minimal when reaching a certain capture rate threshold. While effective at dealing with mild, dispersed storms, BRCs are not designed to capture short, intense storms, which can only be dealt with by increasing BRC surface area, ponding depth or saturated hydraulic conductivity.

RVC_T analysis of the continuous simulation scenarios shows that the design using Ontario’s minimal guidelines (M1) does not actually meet the required 27 mm capture and treatment rate in North York (MOECC 2017). This is because out of the 10 storms that caused 11 overflows for this design, 2 produced <27 mm total precipitation. This means that, based on the RVC_T requirements, the minimal design is inadequate to deal with some storms of this volume of precipitation (27 mm); precipitation intensity plays a large part in determining if the total precipitation is contained within the BRC. A minimal adjustment to the design (especially in BRC area, ponding depth or BSM K_sat) greatly improves BRC efficiency by reducing the number of overflows caused by storms. However, as M1 is already capturing storms that are close in intensity to the 90th percentile storm event, the law of diminishing returns renders most of the levels (ranges) suggested for BRC design (ranges were shown in Table 1) by MOECC (2017) as unnecessary because the cells become overdesigned with little improvement in their efficiency. Hence, the current (especially mean and maximum) Ontario BRC design guidelines seem to be too conservative for regions with similar precipitation patterns to North York.

Finally, as noted by several previous studies, field BRC performance is normally much better than modeled estimates because a BRC can capture more water than it was designed to due to the lateral exfiltration of water to the surrounding native soils. It is important to note, therefore, that the numerical models typically used for BRC simulations do not account for lateral exfiltration to the surrounding soil (as is the case in the SWMM5 model used as the engine for PCSWMM), which can increase BRC performance (as suggested by Traver and Ebrahimian 2017). Thus it is possible that the volumetric runoff reductions predicted in this study would be greater if the BRCs were to be instantiated. Future research should focus on verifying these modeling results at the field scale and modeling the system with heterogeneous subsurface properties in two dimensions.

4 Conclusions and Recommendations

This research investigated the performance of BRCs by computing scenarios based on Ontario’s BRC design guidelines via numerical PCSWMM modeling. First, the most important parameters that contribute to the hydrological performance of the BRCs were identified using LSA with OFAT and GSA in a factorial design experiment. Second, the long term performance of Ontario’s BRC design guidelines was analyzed to determine if they meet the RVC_T; that is, do they capture all storm events up to and including 27 mm. Based on the results of the analysis the following conclusions can be drawn:

1. To reduce BRC overflow, the performance can be improved by increasing BRC surface area, BRC ponding depth or BSM K_sat.
2. Considering synergistic effects, BSM K_sat should be increased together with storage depth; this promotes more rapid water movement through the media, thus allowing the storage space to be better utilized during longer or more intense storms.
3. The minimal recommendations of Ontario’s BRC design guidelines can capture and treat close to 100% of the annual North York runoff, even when the BRC is installed in loamy soils.
4. BRCs sized to the minimal Ontario design guidelines are not capable of managing 27 mm RVC_T in Toronto. However, this requirement can be met by minimal design perturbations of, for example, 0.4% increase in BRC surface area, 5 cm addition to ponding depth, or 3 cm/h increase in BSM K_sat.

This research used the built-in bioretention module in PCSWMM but the model was not specifically calibrated to any field- or lab-scale data. The model was simplified to reduce parameter-associated uncertainty and to minimize numerical errors by using built-in or default values for the bioretention module. Conditions such as snowmelt and media clogging were not considered in this study for the long term continuous simulations. These omissions could reduce the performance of the BRC if proper and regular maintenance is not practiced. Finally, as this study was carried out at one site in Toronto, similar studies should be conducted in other locations within Toronto to determine the impact of site specific characteristics on performance, or other regions in Ontario to determine if they would require more perturbations to BRC designs in order to conform to their RVC_Ts.

Acknowledgments

The authors gratefully acknowledge the assistance received from Karen Finney in PCSWMM Support, regarding some uncertainties associated with SWMM5 bioretention cell model setup. The authors would also like to thank CHI Inc. for granting the license for the student version of the PCSWMM model for this research.

References

1. Ankenman, B. E. 1999. “Design of Experiments with Two- and Four-Level Factors.” Journal of Quality Technology 31 (4): 363-75. https://doi.org/10.1080/00224065.1999.11979943
2. ASCE (American Society of Civil Engineers). 1992. Design and Construction of Urban Stormwater Management Systems. New York, NY: American Society of Civil Engineers (ASCE) and Water Environment Federation (WEF). https://doi.org/10.1061/9780872628557
3. Berggren, K., M. Olofsson, M. Viklander, G. Svensson and A.-M. Gustafsson. 2011. “Hydraulic Impacts on Urban Drainage Systems Due to Changes in Rainfall Caused by Climatic Change.” Journal of Hydrologic Engineering 17 (1): 92-8. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000406
4. CoV (City of Viictoria). 2015. Rainwater Management Standards: Professional Edition. Victoria, BC: City of Victoria, Public Works and Engineering Department. https://www.victoria.ca/assets/Departments/Engineering~Public~Works/Documents/SWVictoria_Professional_Rainwater_Mgmt_Stds_June2015.pdf
5. Czitrom, V. 1999. “One-Factor-at-a-Time Versus Designed Experiments.” The American Statistician 53 (2): 126-31. https://doi.org/10.1080/00031305.1999.10474445
6. DeBusk, K. M. and T. M. Wynn. 2011. “Storm-Water Bioretention for Runoff Quality and Quantity Mitigation.” Journal of Environmental Engineering 137 (9): 800-8. https://doi.org/10.1061/(ASCE)EE.1943-7870.0000388
7. Fletcher, T. D., W. Shuster, W. F. Hunt, R. Ashley, D. Butler, S. Arthur, S. Trowsdale, S. Barraud, A. Semadeni-Davies, J.-L. Bertrand-Krajewski, P. S. Mikkelsen, G. Rivard, M. Uhl, D. Dagenais and M. Viklander. 2015. “SUDS, LID, BMPs, WSUD and More—The Evolution and Application of Terminology Surrounding Urban Drainage.” Urban Water Journal 12 (7): 525-42. https://doi.org/10.1080/1573062X.2014.916314
8. Géhéniau, N., M. Fuamba, V. Mahaut, M. R. Gendron and M. Dugué. 2014. “Monitoring of a Rain Garden in Cold Climate: Case Study of a Parking Lot Near Montreal.” Journal of Irrigation and Drainage Engineering 141 (6): 04014073. https://doi.org/10.1061/(ASCE)IR.1943-4774.0000836
9. Hill, J., J. Drake, B. Sleep and L. Margolis. 2017. “Influences of Four Extensive Green Roof Design Variables on Stormwater Hydrology.” Journal of Hydrologic Engineering 22 (8): 04017019. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001534
10. Kaykhosravi, S., U. Khan and A. Jadidi. 2018. “A Comprehensive Review of Low Impact Development Models for Research, Conceptual, Preliminary and Detailed Design Applications.” Water 10 (11): 1541. https://doi.org/10.3390/w10111541
11. Khan, U. T., C. Valeo, A. V. Chu and J. He. 2013. “A Data Driven Approach to Bioretention Cell Performance: Prediction and Design.” Water 5: 13-28. https://doi.org/10.3390/w5010013
12. Khan, U. T., C. Valeo, A. V. Chu and B. van Duin. 2012. “Bioretention Cell Efficacy in Cold Climates: Part 1—Hydrologic Performance.” Canadian Journal of Civil Engineering 39 (11): 1210-21. https://doi.org/10.1139/l2012-110
13. Li, H., L. J. Sharkey, W. F. Hunt and A. P. Davis. 2009. “Mitigation of Impervious Surface Hydrology Using Bioretention in North Carolina and Maryland.” Journal of Hydrologic Engineering 14 (4): 407-15. https://doi.org/10.1061/(ASCE)1084-0699(2009)14:4(407)
14. MOECC (Ontario Ministry of the Environment and Climate Change). 2017. DRAFT Low Impact Development (LID) Stormwater Management Guidance Manual. Toronto: Ministry of the Environment and Climate Change. http://www.municipalclassea.ca/files/7_DRAFT_MOECC_LID SWM Manual.pdf
15. MOECC–MSC (Ontario Ministry of the Environment and Climate Change–Meteorological Service of Canada). 2018. Historical Climate Data. Toronto: Ministry of the Environment and Climate Change–Meteorological Service of Canada. http://climate.weather.gc.ca/
16. MOECP (Ontario Ministry of the Environment, Conservation and Parks). 2018. Well Records. Toronto: Ministry of the Environment, Conservation and Parks. https://www.ontario.ca/environment-and-energy/map-well-records
17. Nirupama, N., C. Armenakis and M. Montpetit. 2014. “Is Flooding in Toronto a Concern?” Natural Hazards 72 (2): 1259–64. https://doi.org/10.1007/s11069-014-1054-2
18. Nirupama, N. and S. P. Simonovic. 2007. “Increase of Flood Risk Due to Urbanisation: A Canadian Example.” Natural Hazards 40 (1): 25–41. https://doi.org/10.1007/s11069-006-0003-0
19. Paus, K. H., T. M. Muthanna and B. C. Braskerud. 2016. “The Hydrological Performance of Bioretention Cells in Regions with Cold Climates: Seasonal Variation and Implications for Design.” Hydrology Research 47 (2): 291-304. https://doi.org/10.2166/nh.2015.084
20. Rossman, L. and W. Huber. 2016. Storm Water Management Model Reference Manual Volume I, Hydrology. Cincinnati, OH: U.S. EPA Office of Research and Development. EPA/600/R-15/162A. http://nepis.epa.gov/Exe/ZyPDF.cgi?Dockey=P100NYRA.txt
21. Saltelli, A., M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli, M. Saisana and S. Tarantola. 2008. Global Sensitivity Analysis: The Primer. Chichester: John Wiley & Sons Ltd. https://doi.org/10.1002/9780470725184
22. Saltelli, A., S. Tarantola, F. Campolongo and M. Ratto. 2004. Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models. Chichester: John Wiley & Sons, Ltd. https://doi.org/10.1002/0470870958
23. Sun, Y.-W., X.-M. Wei and C. A. Pomeroy. 2011. “Global Analysis of Sensitivity of Bioretention Cell Design Elements to Hydrologic Performance.” Water Science and Engineering 4 (3): 246–57. https://doi.org/10.3882/j.issn.1674-2370.2011.03.002
24. Traver, R. G. and A. Ebrahimian. 2017. “Dynamic Design of Green Stormwater Infrastructure.” Frontiers of Environmental Science and Engineering 11 (4): 15. https://doi.org/10.1007/s11783-017-0973-z
25. Wang, H. W., Y. F. Mao, Y. Gao, J. H. Fan, S. F. Zhang and L. M. Ma. 2013. “Analysis of Bioretention Cell Design Elements Based on Fourier Amplitude Sensitivity Test (FAST).” Advanced Materials Research 779: 1369–75. https://doi.org/10.4028/www.scientific.net/AMR.779-780.1369
26. WDNR (Wisconsin Department of Natural Resources). 2014. Technical Standard 1004: Bioretention for Infiltration. Madison, WI: Wisconsin Department of Natural Resources. https://dnr.wi.gov/news/input/documents/guidance/BioretentionGuidanceFinal.pdf
27. Winston, R. J., J. D. Dorsey and W. F. Hunt. 2016. “Quantifying Volume Reduction and Peak Flow Mitigation for Three Bioretention Cells in Clay Soils in Northeast Ohio.” Science of the Total Environment 553: 83-95. https://doi.org/10.1016/j.scitotenv.2016.02.081
28. Winston, R. J., A. P. Smolek, J. D. Dorsey and W. F. Hunt. 2016. “Modeling Bioretention Hydrologic Performance using DRAINMOD under Current and Future Climate Scenarios.” In Proceedings of Novatech 2016, 9th International Conference on planning and technologies for sustainable management of Water in the City. http://hdl.handle.net/2042/60475