Abstract

Urban development has led to increased impervious surfaces, disrupting the natural hydrological cycle, and necessitating effective stormwater management solutions. Green stormwater infrastructure, such as green roofs, offers a sustainable approach to mitigate runoff volume and peak flow rates. However, their hydrological performance can be limited during significant storm events. Blue-green roofs, which incorporate an additional water storage layer beneath the growth medium, have emerged as a promising solution. This study aims to develop a discharge strategy for blue-green roofs tailored to the marine pacific west coast climate, maximizing water retention during wet seasons, and ensuring irrigation during dry periods. Using a continuous SWMM hydrological model calibrated with data from a pilot-scale blue-green roof in Vancouver, various discharge designs in the blue storage layer were assessed for their hydrological performance. The calibrated SWMM blue-green model demonstrated a good fit for wet seasons. Different discharge designs significantly impacted the detention and retention performance of blue-green roofs during wet seasons. Active water level control designs, in particular, showed improved hydrological performance compared to passive drainage designs in the storage layer. The study suggests that future blue-green roof designs should consider alternative drainage methods to achieve improvements in annual retention and detention performance.

1 Introduction

Urban development leads to significant changes in land use patterns, notably increasing impervious surfaces within urban areas. This shift impacts the natural hydrological cycle by reducing the rate of rainwater infiltration into the soil and lowering evapotranspiration rates from existing vegetation (Shuster et al. 2005; Walsh et al. 2005). Consequently, there is an increase in both the volume and peak flow rates of surface runoff. These hydrological alterations result in several negative outcomes, including higher volumes of combined sewer overflows (CSO) and detrimental downstream environmental effects. These effects include damage to aquatic ecosystems, bank erosion, channel incision, and degradation of water quality (Klein 1979; Arnold and Gibbons 1996; Goonetilleke et al. 2005; Young et al. 2018). In response, many municipalities in Canada have adopted stormwater management objectives. These objectives focus on capturing and either reusing or infiltrating runoff from smaller storms, and detaining runoff from larger storms for controlled release (DFO 1993).

Green stormwater infrastructure (GSI) addresses key stormwater management goals by emulating the natural water cycle. It captures rainwater through infiltration and vegetation evapotranspiration, thereby reducing runoff volume, lowering peak flow rates, and improving water quality. One viable GSI approach, particularly in areas with limited space or unsuitable subsurface conditions for infiltration-based systems, is the implementation of green roofs. These roofs are composed of multiple layers, each serving a specific function in rainwater retention or detention. The topmost vegetation layer, comprising a variety of plants, not only absorbs water but can also store it within its structure. Below this, the growing medium layer retains water, providing detention and supporting water absorption by plants or evaporation. Finally, the drainage layer, situated beneath the growing medium, facilitates the removal of excess water. It also contributes to water detention by slowing the flow of runoff.

Extensive research demonstrates that green roofs contribute positively to stormwater management by improving water quality, reducing runoff volume, and providing detention during smaller rainfall events (Simmons et al. 2008; Carter and Rasmussen 2006; Mentens et al. 2006; Rowe et al. 2011; Stovin et al. 2012; Johannessen et al. 2018). However, their effectiveness is limited during significant rainfall events due to reduced storage capacity, particularly when soil moisture approaches saturation after prolonged wet periods (Villarreal and Bengtsson 2005; Bengtsson et al. 2005; Carter and Rasmussen 2006). Long-term monitoring in Portland, a city with a climate similar to Vancouver, BC, underscores this limitation, showing diminished retention during wet seasons compared to drier ones (Schultz et al. 2018; Chang et al. 2021). This reduced efficiency is attributed to persistent soil saturation in wet seasons, limiting the green roof's retention capacity.

Blue-green roofs, an innovative variation of green stormwater infrastructure (GSI), are gaining attention for addressing the limitations of traditional green roofs. These systems include an additional water storage layer, known as the 'blue layer,' situated beneath the growth medium. This layer captures and temporarily holds water that percolates from the green layer above, which would otherwise contribute to runoff, and enter the municipal storm drainage system.

Furthermore, the blue layer is connected to the green layer via absorbent capillary cones made of mineral wool fabric. These cones enable passive capillary water transport to the growing medium, ensuring consistent hydration for the vegetation, even during prolonged dry spells, and preventing plant wilting. As a result, blue-green roofs exhibit higher evapotranspiration rates, offering enhanced cooling benefits compared to traditional green roofs (Shafique and Kim 2017; Cirkel et al. 2018; Almaaitah et al. 2022).

Recent studies on the hydrological performance of blue-green roofs, particularly focusing on their water retention and detention capabilities, have shown promising results. Research by Martin III and Kaye (2020) and Pelorosso et al. (2021) indicate a direct correlation between the storage depth of the blue layer and a reduction in peak discharge. Additionally, Pelorosso et al. (2021) demonstrate a relationship between storage depth and the runoff coefficient of the blue-green roof. Pilot-scale studies have also demonstrated effective retention and peak flow attenuation under specific rainfall conditions (Shafique et al. 2016; Pelorosso et al. 2021; Almaaitah et al. 2022; Busker et al. 2022; Takhar 2022).

Takhar (2022) observed that a pilot blue-green roof module in Vancouver maintained high monthly retention rates (81% to 100%) during late spring and summer. Additionally, in the first fall storm after a dry summer, the blue-green roof achieved 82% retention in both 2020 and 2021, significantly outperforming a reference green roof, which only managed 43% and 29% retention, respectively. Notably, the blue-green roof depleted its soil water content later in the season (late August) compared to the green roof (July), resulting in the blue-green roof remaining hydrated and healthy over the summer, while the green roof exhibited signs of wilting. However, during the rainy winter season, the blue-green roof's retention was markedly lower (3% to 12%) over two years, underperforming compared to the reference green roof.

Presently, there is a gap in design guidelines for the discharge mechanisms of blue-green roofs. Research involving these roofs, such as studies by Shafique et al. (2016) and Almaaitah et al. (2022), lacks a controlled strategy for water discharge from the storage layer. Typically, these designs employ a standpipe with an overflow weir or orifice set at a specific height in the blue layer, allowing water to discharge once it reaches this level.

Busker et al. (2022) introduced a more advanced approach, utilizing precipitation forecast-based control mechanisms with smart valves for discharge. This system operates based on weather predictions, emptying the storage layer before an extreme storm to accommodate new rainfall, and retaining water during dry forecasts to maximize passive irrigation. Busker et al. (2022) found that this smart valve system, integrated with weather forecasts, provided superior precipitation attenuation compared to basic designs with uncontrolled discharge.

However, the implementation of this sophisticated system, as outlined by Busker et al. (2022), requires technical expertise that may not be readily available to all developers. Additionally, its effectiveness hinges on the availability of reliable, local-scale weather projections, which may not always be accessible. Despite these challenges, the findings of Busker et al. (2022) suggest that there are more effective alternatives to uncontrolled discharge designs. This indicates a potential for further research into optimized discharge strategies to enhance the hydrological performance of blue-green roof systems.

This study builds on the work of Takhar (2022), who constructed a pilot-scale blue-green roof module in Vancouver to examine its thermal and water balances. Takhar's research identified a limitation: the absence of a discharge control strategy significantly undermined the blue-green roof's benefits during the rainy winter season. Consequently, the primary aim of this study is to develop an effective discharge strategy for blue-green roofs. This strategy aims to optimize water retention and detention during the wet season typical of the marine pacific northwest coast climate, while ensuring water availability for irrigation in the prolonged dry and hot summer months. The study will explore simpler, passive discharge strategies and water level control mechanisms within the blue storage layer, evaluating their hydrological performance.

2 Methodology

In this study, a continuous SWMM hydrological model of a blue-green roof was developed, calibrated and verified using 12 months of observed data collected from an experimental pilot-scale blue-green, located in the City of Vancouver, Canada. Various discharge designs in the blue storage layer were then simulated using the validated model to assess their impact on the hydrological performance of the blue-green roof. 

2.1 Experimental pilot-scale blue-green roof

A pilot-scale blue-green pilot roof, shown in Figures 1 and 2, was constructed and installed in Vancouver, BC, Canada (Takhar 2022). Each roof is 2 m wide by 2 m long and at a 2% slope. Vegetation on the blue-green roofs includes Fragaria chiloensis, Allium schoenoprasum plugs, and a sedum mat. The growing medium is a 100 mm thick layer of Veratec TierraLITE, which is an engineered soil containing 70% pumice and 30% organics. These roofs are considered extensive, meaning they use a thin growing medium (typically less than 150 mm) and are planted with hardy, drought-tolerant vegetation that requires minimal maintenance. In contrast, intensive green roofs feature deeper growing media and a wider variety of vegetation, often resembling traditional gardens, but they require more structural support and maintenance. The blue storage layer uses an 85 mm deep Permavoid system, which is a modular interlocking stormwater control structure with a void ratio of 0.95. A wicking geotextile membrane layer is placed between the growing medium and the blue storage layer (Permavoid). A standpipe with an internal diameter of 50 mm is positioned within the Permavoid layer. Water discharge from the Permavoid occurs through a weir at the top of the standpipe when the water level reaches 77 mm. This weir serves as the sole outlet for Permavoid discharge. Capillary/wicking cones have been added to this system to allow for water to be passively transported from the storage layer to the soil layer via capillary action.

To attempt to emulate an actual roof’s thermal and water balances, the blue-green roof was built on top of (4-inch) 100 mm-thick extruded polystyrene insulation. Figure 1 shows a section of the blue-green pilot roof. Data such as runoff volume, water level in the storage layer, moisture content at mid-height of the growing media, and temperature at 4 different elevations were collected over 12 months in year 2020, at intervals of 5 minutes. Rainfall intensity, recorded at 5-minute intervals, was measured by a rain gauge located on the roof of a five-story building, approximately 100 meters northwest of the pilot roof, which was installed on a one-story building. The gauge was selected to ensure exposure to rain and wind conditions, similar to those at the pilot roof, despite the roof being situated downhill from the gauge.

Figure 1 Pilot blue-green roof at the Helena Gutteridge Plaza, Vancouver in August 2020.

2.2 Computer hydrological model

In this project, SWMM (PCSWMM version 5.1.015) was used to develop a computer hydrological model of the pilot blue-green roof system presented in Figure 2, herein referred to as the Base Case Model. The SWMM model's Low Impact Development (LID) control modules, which offer capabilities for modeling green infrastructure including green roofs, have been effectively used in previous green roof modeling studies (Burszta-Adamiak et al. 2013; Cipolla et al. 2016; Hamouz and Muthanna 2018; Russwurm et al. 2018; Jeffers et al. 2022). In our approach, we integrated SWMM’s built-in green roof LID module with an additional storage module to represent the blue-green roof system. A continuous simulation model was developed using one year of rainfall data (January to December 2020), obtained from a rain gauge located at the study site in Vancouver, Canada.

Figure 2 Cross-section of the pilot blue-green roof.

Green roof model

In the SWMM framework, the green roof LID module consists of three layers: the surface (vegetation) layer, the soil layer, and a drain mat layer, as illustrated in the green roof layer of Figure 3. The model incorporates several key assumptions, including one-dimensional (1-D) vertical flow, uniform distribution of inflow across the roof surface, and consistent moisture content throughout the soil layer. The water balance within the green roof system is governed by equations detailed in Rossman and Huber (2016):

Figure 3 SWMM blue-green roof representation.

The subscripts of the parameters in Equations 1–3 denote surface layer (subscript 1), soil layer (subscript 2), and drain mat layer (subscript 3). Infiltration and percolation rate f through the soil layer are modeled using the Green Ampt and Darcy’s Law equations, respectively. Details of the model development can be found in the SWMM Manual (Rossman and Huber 2016).

(1)

(2)

(3)

Where:

d	=	depth of water stored in each layer,
θ	=	soil layer volumetric moisture content,
i	=	rainfall rate,
t	=	time,
q	=	runoff or overflow rate,
e	=	evapotranspiration rate,
D	=	thickness of the soil layer,
f	=	infiltration or percolation rate, and
Φ	=	void fraction.

Blue-green roof model

The current version of SWMM (PCSWMM version 5.1) does not include a dedicated module for blue-green roofs. A blue-green roof is characterized by a water storage layer positioned beneath the green roof's soil layer, with wicking cones connecting this storage layer to the soil layer. These cones facilitate passive water transfer to the growing medium through capillary action. To simulate this system in SWMM, we integrated a storage module with the existing green roof module. This integration allows for the drainage from the green roof to be directed to the storage layer. The drain mat layer shown in Figure 3 was not included in the model, as the water storage and evapotranspiration capacity of the thin geotextile membrane between the soil layer and the blue Permavoid layer is negligible. Additionally, the passive flow from the storage Permavoid layer to the growing medium, via the wicking cones, is rerouted back to the growing medium, as depicted in the blue layer storage section of Figure 3.

To simulate the capillary rise of water back to the growing medium through wicking cones, we used SWMM’s pump module. The flow rate for this water transport is approximated by the actual evapotranspiration rate of the system. In SWMM, potential evapotranspiration is modeled using the Hargreaves method, which considers factors such as latitude, daily temperature, and a reference plant type (e.g., grass or alfalfa) as detailed in Rossman and Huber (2016). However, the actual evapotranspiration rate of the blue-green roof system is influenced by specific plant types and the water availability in the growing media, resulting in a deviation from the potential evapotranspiration calculated using the Hargreaves equation (Cirkel et al. 2018). In this study, we estimated the monthly average actual evapotranspiration rate using a water balance equation, based on data observed from the pilot green roof module.

(4)

Where:

R	=	rainfall intensity,
Q	=	runoff,
ET	=	evapotranspiration rate, and
ΔS/Δt	=	water stored in roof.

In the model, the pump flow, representing the transport of water from the Permavoid storage layer to the soil via the wicking cones, was configured to match the calculated monthly evapotranspiration rate. Additionally, the total evapotranspiration rate encompassing the surface, soil, and drain mat layers was set to equal this calculated rate. Surface runoff q₁ was directed to the Permavoid storage layer in the simulation.  

2.3 Model parameters and model calibration

The initial model input parameters were based on measured roof properties and a previous study which modeled a green roof with a sandy loam soil layer, as shown in Table 1.

Table 1 SWMM model input parameters.

Parameter	Initial Value	Source of Initial Value
Surface roughness (Manning’s n)	0.1	(Liu and Chui 2019) calibrated green roof model
Surface slope (%)	2.0	Measured roof property
Soil thickness (mm)	100	Measured roof property
Porosity (volumetric fraction)	0.21	Provided by manufacturer of soil media
Field capacity (volumetric fraction)	0.20	Interpreted from moisture content data
Wilting point (volumetric fraction)2	0.05	Interpreted from moisture content data
Saturated hydraulic conductivity (mm/hr)	1310	Provided by manufacturer of soil media
Conductivity slope (dimensionless)	10	(Liu and Chui 2019) calibrated green roof model
Suction head (mm)	88	(Liu and Chui 2019) calibrated green roof model

The base case model was calibrated using the available continuous data from the pilot blue-green roof, which spanned from January 2020 to December 2020.

Nash Sutcliffe Efficiency (NSE) is a criterion frequently used in hydrologic modeling studies for model calibration (Krause et al. 2005) and is given by the following equation (Nash and Sutcliffe 1970):

(5)

Where:

	=	modeled discharge rate at time t,
	=	observed discharge rate at time t, and
	=	average of all observed discharge values within time T.

The performance ratings for NSE for a 1-month time interval recommended by Moriasi et al. (2007) are: Very good (0.75 < NSE < 1.00), Good (0.65 < NSE < 0.75), Satisfactory (0.50 < NSE < 0.65), and Unsatisfactory (NSE < 0.50).

Base case model calibration using observed data from January to April 2020 was performed by adjusting model input parameters to maximize NSE. Once calibrated, model verification was achieved by comparing observed data with modeled data for October to December 2020. 

A model sensitivity analysis was performed using PCSWMM’s Sensitivity-based Radio Tuning Calibration (SRTC) tool. This tool facilitates the selection of parameters and the assignment of uncertainty ranges for analysis. The sensitivity analysis evaluates the impact of these parameters on model output by adjusting them individually based on their uncertainty, calculating the ratio of normalized output change to parameter variation, and ranking the resulting sensitivity gradients from highest to lowest (James 2003). In this simulation, the soil parameters selected for sensitivity analysis, along with their uncertainty ranges, include field capacity (uncertainty range 25%), conductivity and conductivity slope (50%), wilting point (25%), and suction head (25%).

2.4 Permavoid discharge operation designs

Various Permavoid storage discharge strategies were evaluated using the validated base case model to determine their hydrological efficacy in the blue-green roof system, as outlined in Table 2. These strategies fall into two primary categories: passive and active water level control drainage designs. The passive drainage designs, namely the 10 Passive, 40 Passive, and 60 Passive designs, facilitate passive water discharge from the Permavoid storage layer through a discharge orifice. The position of this orifice varies in height or offset from the base of the Permavoid. In contrast, the active water level control design uses real-time control mechanisms responsive to the water level within the Permavoid. The system is programmed to open the drain valve when the water level reaches 77 mm and to close it once the level decreases to 10 mm.

Table 2 Blue storage discharge design modeled using PCSWMM model.

Base case	Discharge weir at top of Permavoid standpipe (50 mm ID). Weir is the only outlet for Permavoid discharge. Weir is 77 mm from the bottom of Permavoid. There is no orifice for passive drainage in the Permavoid.
10 Passive	Orifice added to base case Permavoid standpipe. Orifice is 10 mm from the bottom of Permavoid. Water depth above 10 mm in Permavoid drains passively through the orifice.
40 Passive	Orifice added to base case Permavoid standpipe. Orifice is 40 mm from the bottom of Permavoid. Water depth above 40 mm in Permavoid drains passively through the orifice.
60 Passive	Orifice added to base case Permavoid standpipe. Orifice is 60 mm from the bottom of Permavoid. Water depth above 60 mm in Permavoid drains passively through the orifice.
Active Water Level Control (WL Control)	Orifice added to base case Permavoid standpipe. Orifice offset is 10 mm from the bottom of Permavoid. Water level in Permavoid = 77 mm triggers opening of the drain valve. When the water level drops to 10 mm the drain valve closes.

The vertical placement of the discharge orifice in the Permavoid system serves two purposes: it separates the water volumes allocated for retention (below the orifice) from those for detention (above the orifice). In this study, the minimum orifice offset was set at 10 mm (i.e., 10 Passive design case), as opposed to an offset of 0 mm. This design choice ensures a consistent water reserve within the Permavoid unit, essential for uninterrupted passive irrigation to the vegetation layer above. Maintaining a water reserve is crucial for optimizing evapotranspiration rates, which are subject to seasonal variations. Previous research indicates that evapotranspiration rates in vegetative systems depend on water availability, with reduced rates observed under conditions of water scarcity (Berghage et al. 2007; Stovin et al. 2013).

The orifice diameter in both passive and active designs is selected to ensure that if the water depth exceeds the orifice height, water will be discharged and the drawdown of the Permavoid to the orifice height occurs within 24 hours. This design criterion ensures that the Permavoid has adequate storage capacity for the next rainfall event.

2.5 Data analysis

The interpretation of rainfall data significantly varies based on the definition of a 'rain event', which in turn affects the calculated hydrological performance (Stovin et al. 2013). The characterization of an event hinges on the duration between rain events and the consideration of the period before and after the rain event, including runoff, as defined by Carson et al. (2013) and Cipolla et al. (2016). In this study, a rain event is defined as a minimum cumulative rainfall of 2 mm with at least 6 hours of no recorded rain or discharge before and after the event. This definition aligns with those used in other hydrological studies on green and blue-green roofs (Carson et al. 2013; Cipolla et al. 2016; Almaaitah et al. 2022). The hydrological performance indicators of the blue-green roof, such as retention performance (RET%), peak attenuation performance (PA%), and peak delays (T_delay), were assessed for each defined event. Equations 6, 7, and 8 detail the calculations for these event-based indicators (Almaaitah et al. 2022).

(6)

(7)

(8)

Where:

RD	=	total rain depth (mm) for the rain event,
DD	=	total discharge depth (mm) discharged for the rain event,
Prain	=	peak 5-minute rainfall intensity,
Pdischarge	=	highest discharge,
TPdischarge	=	time of the drainage peak for the event, and
TPrain	=	time of rainfall peak for the event.

The percent occurrence of peak discharge events from the blue green roof is calculated using Equation 9.

(9)

3 Results and discussion

3.1 Rainfall and evapotranspiration rates

Vancouver has distinct seasonal wet and dry seasons; most of the precipitation in the form of rain occurs in winter, and low amounts occur in summer. The city typically receives an annual average precipitation of approximately 1,200 mm, though this can vary depending on location, with lower amounts near the coastline and higher amounts in areas closer to the mountains (Environment and Climate Change Canada n.d.). In the study area where the pilot roof is located, a total of 1,810 mm of rainfall was recorded in 2020, followed by 1,640 mm in 2021. Monthly total rainfall depth, temperature, and calculated actual evapotranspiration rate of the blue-green roof are presented in Figure 4. Based on our definition of a rain event (a minimum cumulative rainfall of 2 mm with at least 6 hours of no recorded rain or discharge before and after the event), a total of 65 rain events were identified. The rain events are further categorized based on winter and fall wet seasons: Wet Season 1 (January to April), Wet Season 2 (September to December), and Dry Season (May to August). Table 3 summarizes the events in the wet and dry seasons in 2020.

Figure 4 Monthly rainfall, temperature, and calculated actual evapotranspiration rate for year 2020.

Table 3 Precipitation events summary in 2020. 

	Number of events		Events duration (hr) (min and max)	Event rain intensity (mm/hr) (min and max)	Total rainfall of events (mm)
Wet Season 1 (Jan 20 to April 1)	23	12 – 95		1.25 – 6.8	467
Wet Season 2 (Sept 1 to Dec 31)	33	1 – 58		1.25 – 7.8	773
Dry Season (May 1 to Aug 30)	9	15 – 28		1 – 5.5	159

3.2 Model sensitivity analysis

The model's calibration parameters include soil porosity, field capacity, hydraulic conductivity, and conductivity slope. Figure 5 shows the sensitivity of each parameter to the model's performance. A negative normalized sensitivity value indicates that an increase in the parameter value typically results in decreased runoff, whereas a positive sensitivity value suggests the opposite effect. Among these parameters, variations in soil porosity, field capacity, and conductivity slope have the most influence on both runoff volume and peak flow. The parameters identified in the sensitivity analysis are related to the soil characteristics, underscoring the significance of soil type and its properties on the water retention capacity of the green layer in the blue-green roof system. These observations are consistent with the experimental findings reported by Almaaitah et al. (2022).

Figure 5 Parameter sensitivity of flow (total, mean, max) for Permavoid discharge.

3.3 Model calibration and verification calibration (base case)

Wet seasons

The SWMM blue-green base case model was calibrated using observed data from the pilot roof during Wet Season 1, from January to April. Model calibration was accomplished by adjusting porosity, conductivity slope, field capacity, vegetative cover, and wilting point so that the errors between model and observed data are minimized for the rain events in Wet Season 1. A summary of both the initial input parameters and the calibrated base case model parameters are presented in Table 4.

Table 4 SWMM model input parameters.

Parameter	Initial Value	Calibrated Value
Surface roughness (Manning’s n)	0.1	0.3
Surface slope (%)	2.0	2.0
Soil thickness (mm)	100	100
Porosity (volumetric fraction)	0.21	0.25
Field capacity (volumetric fraction)	0.20	0.232
Wilting point (volumetric fraction)2	0.05	0.116
Saturated hydraulic conductivity (mm/hr)	1310	888
Conductivity slope (dimensionless)	10	55
Suction head (mm)	88	88.9

After calibration, the base case model was verified using observed data from the same pilot roof during Wet Season 2, from September to December, also focusing on rain events. The fit between model data and observed data was evaluated using the Nash-Sutcliffe Efficiency (NSE). For the calibrated model corresponding to Wet Season 1, the NSE values for maximum discharge and total discharge volume were 0.766 and 0.872, respectively. In the case of the verified model for Wet Season 2, the NSE values for maximum discharge and total discharge flow rate were 0.783 and 0.861, respectively. Based on these values, both the calibrated and validated models demonstrated a good fit between observed data and model data, with NSE values > 0.75. Table 5 summarizes the comparison between observed data, calibrated and verified model results (Wet Seasons 1 and 2). The small flow magnitudes observed reflect not only the precipitation levels during the monitoring period but also the small scale of the pilot test area (2 m x  2 m). These low flows are consistent with the system’s hydrological behavior under these specific conditions. While the model was calibrated for a range of flows based on observed data, the pilot roof's limited area naturally constrains flow magnitude. Figure 6 provides a comparison between the observed and the verified model discharge flow rates from the blue-green roof for the month of December. 

Table 5 Comparison between observed and calibrated model results (Wet Seasons 1 and 2). 

	Wet Season 1 (Jan to April)		Wet Season 2 (Sept to Dec)
	Calibrated	Observed	Verified	Observed
Maximum discharge (m³/s)	7.42E-06	6.97E-06	8.60E-06	7.41E-06
Mean discharge (m³/s)	2.53E-07	2.73E-07	2.92E-07	2.91E-07
Total discharge out (m³)	1.646	1.781	3.03	2.911
Maximum depth (m)	0.0768	0.0759	0.0769	0.0767
Minimum depth (m)	0.0666	0.0639	0	0
Mean depth (m)	0.0751	0.0737	0.0606	0.0612

Figure 6 Blue-green roof discharge flow rate – comparison between observed data and calibrated model data for the month of December.

Dry season

The NSE values indicated good performance for Permavoid water depth, but poor performance for total discharge volume. Specifically, the NSE for depth was 0.743, but for total discharge volume, it was 0.0602. In general, the base case model overestimated the discharge compared to the observed data in the dry season (May to August), as shown in Table 6.

Table 6 Comparison between observed data and model data for Dry Season.

	Calibrated	Observed
Maximum discharge (m³/s):	5.73E-06	1.44E-06
Mean discharge (m³/s):	1.96E-08	5.04E-09
Total discharge out (m³):	0.204	0.053
Maximum depth (m):	0.0767	0.0759
Minimum depth (m):	0	0
Mean depth (m):	0.0457	0.0460

One contributing factor to the discrepancy between the model and observed data is the evapotranspiration rate used in the model. This rate was calculated as a single monthly average based on observed data based on Equation 4. However, evapotranspiration from the green roof is influenced by various factors, including climate (temperature, solar irradiation, wind) and soil moisture content (Cirkel et al. 2018). The dry season coincides with the summer months, characterized by higher daily climate variations, leading to variable daily evapotranspiration rates that deviate from the monthly averaged value.

During drought periods with no rain, evapotranspiration is the sole water output from the Permavoid. The model generally overestimated Permavoid water depth compared to observed data indicating an underestimation of evapotranspiration rates. In the model, Permavoid water depth is just below the overflow weir (0.077 m), leading to overflow and discharge through the weir even with minor rainfall. However, observed data show lower Permavoid depths, resulting in less discharge than predicted. This discrepancy is evident in the poor NSE value for total discharge volume in the dry season. While the model aligns less with observed data in dry seasons, its performance is better in wet seasons when evapotranspiration is less critical. The study henceforth concentrates on drainage designs to enhance hydrologic performance during wet seasons.

3.4 Impact of Permavoid operation strategy on hydrologic performance during wet seasons

The impact of the different Permavoid discharge designs (Base Case, 10 Passive, 40 Passive, 60 Passive, WL Control) on the overall hydrologic response of the system was evaluated for the wet seasons. The performance metrics—retention, peak attenuation, and peak delay of these designs were compared against the base case model.

Wet seasons’ event-scale retention performance

Event-based RET%

Figure 7 presents the event-based retention performance (RET%) for various rain events, categorized by duration, rainfall depth, and wet season. The RET% varies significantly across storm events for all design cases. Generally, higher RET% is observed for shorter, smaller storms compared to larger ones. In Wet Season 1, the base case and passive designs show lower RET% (mean = 20 to 25%), while the Water Level (WL) Control design achieves the highest RET% (mean = 67%), especially for smaller storms. RET% tends to decrease with increasing rain duration and depth across all designs. In Wet Season 2, RET% is lower than in Wet Season 1, with base case and passive designs averaging 3 to 11%, and WL Control averaging 53%.

Figure 7 Events based retention performance (RET%) for Wet Season 1 and Wet Season 2.
NOTE: Bar graphs on the right show the spread of the RET% for the season. Scatter plot on the right shows the event-based RET% based on event duration and event’s total rainfall.

Season and annual RET%

Event-based retention often overestimates green roof retention performance compared to annual-based retention (Stovin et al. 2012). Figures 8(a) and 8(b) compare annual-scale and season-scale RET%. These figures reveal that for the WL Control design, both annual-scale RET% (mean = 32%) and season-scale RET% (mean = 21% for Wet Season 1, and 10% for Wet Season 2) are lower than the event-based RET% shown in Figure 7 (mean RET% = 67 for Wet Season 1, and 53% for Wet Season 2).

Figure 8 (a) Annual cumulative rainfall and discharge, and annual RET%, and (b) RET% for wet and dry seasons.

The observed discrepancy arises from the overlap of detention and event-scale retention performance. Fundamentally, the retention capacity of a green or blue-green roof is finite, influenced by vegetation type, growing media, soil moisture, and climatic conditions (Stovin et al. 2012). Adding a storage layer, like the Permavoid, marginally impacts annual retention, as retention primarily occurs through water stored in the growing medium and used by vegetation for evapotranspiration. The elevated event-scale RET% seen, especially in the WL Control case, is partly attributed to water detention in the Permavoid post-rain event, rather than complete retention. Thus, event-scale retention metrics partially reflect detention (Stovin et al. 2012). Once the Permavoid is full and its detention capacity is reached, water is still discharged, albeit with a delay. The WL Control design's superiority over the base case lies in its enhanced detention capacity, particularly beneficial for frequent, smaller storms typical of the marine Pacific Northwest coast climate.

The annual and season-scale RET% for the 10 Passive design is lower compared to other designs due to its reduced retention volume in the Permavoid. In this design, discharge occurs when Permavoid water depth exceeds the 10 mm orifice height. In contrast, designs with higher orifice settings (40 mm or 60 mm) or a 76 mm overflow weir, don't always reach the required depth for discharge during some rain events, resulting in no discharge. Figure 9 illustrates this difference in Permavoid depth and discharge between the 10 Passive and 40 Passive designs. Throughout the year, especially in dry periods with long Antecedent Dry Weather Periods (ADWP), the 10 Passive design discharges more frequently, leading to a lower annual-based RET%. The 10 Passive design produced more discharge due to water depth exceeding orifice height of 10 mm during rain events. No discharge was produced for the 40 Passive as the water depth did not exceed the orifice height of 40 mm. 

Figure 9 Permavoid water depth and discharge during rain events from April 20 to April 30, 2020.

Wet Season detention performance

In examining detention performance (i.e., peak attenuation and peak delays) of the design cases, not all rainfall events result in runoff. Figure 10 presents the percent occurrence of peak discharge events from the Permavoid. Among all designs, the WL Control design had the fewest peak discharge occurrences compared to other configurations. In the passive designs, the minimum depth is set by the orifice discharge offset (10, 40, or 60 mm from the bottom of the Permavoid), leading to varied retention and detention capacities. The WL Control design allows water to reach a depth of 77 mm before activating the opening of the orifice, providing better detention, and allowing fewer discharges compared to both the base case and passive designs. This highlights the efficiency of both control strategies in the Permavoid system for managing peak discharges.

Figure 10 Percent of occurrence of discharge peaks after a peak from rain event.

Figures 11 and 12 show the peak attenuation and peak delay for events where peak discharges were observed in both Wet Seasons 1 and 2. Like the observation in RET%, better PA% and T_delay are observed for small storms with short duration and low intensity. Peak attenuation PA% for the Passive and WL Control designs (mean PA% > 50%) are better than that of the base case design (mean PA% < 18%) for both wet seasons. Peak delay T_delay for the passive and WL Control designs (mean T_delay > 100 minutes) are also better than that of the Base Case design (mean T_delay = 30 minutes) for both wet seasons. This is not unexpected, since the Base Case design has no discharge orifice, and therefore has no ability to recover the detention capacity of the Permavoid once the Permavoid is full. Any rain entering the blue-green roof will result in water discharging into the overflow without any delay.

Figure 11 Event-based peak attenuation performance (PA%) for Wet Season 1 and Wet season 2. 
NOTE: Bar graphs on the left show the spread of the PA% for all events in the season. Scatter plot on the right shows the event-based PA% based on the event duration and event’s total rainfall for the season. The passive design PA% are plotted on a different 3D graph than WL Control and base case design for improved readability.

Figure 12 Events based peak delay performance (T_delay ) for Wet Season 1 and Wet Season 2.
NOTE: Bar graphs on the left show the spread of the T_delay  for all events in the season. Scatter plot on the right shows the event based T_delay  based on the event duration and event’s total rainfall for the season. The passive design T_delay% are plotted on a different 3D graph than WL Control and Base Case design for improved readability.

3.5 Dry season

Except for the 10 Passive design, all configurations achieved full water retention and peak attenuation during the dry season. This observation is expected, as the extended intervals between rain events allow the Permavoid system to fully drain. This drainage, facilitated by both drain flow and evapotranspiration, effectively restores the system's retention and detention.

4 Discussion

The model data show that depending on the discharge design case, annual retention of water ranges from 17% to over 30%. Retention in the wet seasons is lower than in the dry season and is like observations of pilot scale blue-green roofs reported by Almaaitah et al. (2022) and by Takhar (2022). Across all designs, event-based retention and detention performance was consistently better in Wet Season 1 compared to Wet Season 2. This difference is attributed to the lower total rainfall in Wet Season 1 (431 mm) as opposed to Wet Season 2 (773 mm). With less rainfall, the Permavoid system had greater capacity to detain water between events, leading to reduced discharge. In contrast, Wet Season 2 had higher rainfall and consequently less available Permavoid storage, resulting in increased discharge and lower retention and peak attenuation performance. These findings underscore the impact of rainfall characteristics on the blue-green roof hydrologic performance, also observed experimentally by Almaaitah et al. (2022) This is also consistent with the findings of Richter and Dickhaut (2023) from experimental studies in Germany, and Cristiano et al. (2023) from studies in Italy, which demonstrate that rainfall patterns significantly influence hydrological performance, with less frequent but more intense rainfall events leading to improved retention.

Our models indicate that various Permavoid discharge strategies can influence the detention (peak attenuation and delay) and, to a lesser extent, the retention performance of blue-green roofs during wet season rainfall typical of the Pacific Northwest coast. Active Water Level (WL) control designs demonstrated better retention and detention compared to both the Base Case and passive orifice discharge designs. This enhanced detention capability can potentially reduce local flood risks and lessen the burden on municipal storm/sewer systems due to combined sewer overflows. Cristiano et al. (2023) also emphasize that active management strategies significantly improve the effectiveness of blue-green roofs, especially in mitigating the impacts of extreme rainfall events. This supports our findings that active control designs outperform passive ones under similar conditions.

When opting for a passive design, it's crucial to carefully select the orifice height, as it affects retention volume and water availability for passive irrigation in dry periods. Our study found that setting the orifice at 10 mm (10 Passive design) led to a lower annual RET% and complete water depletion in the Permavoid during dry spells.

For all design cases, excluding the Base Case, the orifice is sized to ensure the Permavoid storage layer empties to the retention level (i.e., height of discharge orifice) within 24 hours. This design consideration addresses concerns often raised by developers and designers about prolonged water storage on roofs and potential building envelope damage in the event of system failure. If suitable geotechnical conditions (e.g., soil infiltration rate) are present on the site, the reduced flow rate of discharge from the Permavoid or the downstream detention tank can be directly discharged to infiltration-based green storm infrastructure, such as bioretention cells adjacent to the building. However, given the small volume of the blue-green roof storage layer, the orifice diameter required for the desired slow drawdown in the Permavoid is small, measured in millimeters. This small size poses a risk of orifice clogging. Since a functional drain is vital for the success of a blue-green roof (Skjeldrum and Kvande 2017), alternative drainage methods, such as a discharge weir presented by Busker et al. (2022) might be more practical.

Operational strategies during dry seasons differ from those in wet seasons. Instead of focusing on runoff volume reduction and peak attenuation, the primary objective is to ensure adequate water supply for vegetation irrigation on the green layer. During this period, water can be retained in the Permavoid to facilitate passive vegetation irrigation through wicking cones. If the Permavoid's water is exhausted, additional water can be sourced from the installation of a downstream detention tank which acts as a rain cistern and is pumped back into the Permavoid storage layer.

5 Limitations and future work

A limitation of the SWMM blue-green roof model presented in this paper is the use of a monthly averaged evapotranspiration rate calculated from observed data. This resulted in an underestimation of the actual evapotranspiration rate, particularly during summer, with high variation in daily climatic conditions and soil moisture. Future work would include incorporating evapotranspiration models (such as those proposed by Cirkel et al. 2018) into the SWMM model to allow for assessing the hydrologic performance of the blue-green roof under different climatic conditions. An additional limitation is the small flow magnitudes observed in both the measured and modeled data, which are influenced by the precipitation levels during the monitoring period and the limited surface area of the pilot test. These low flows are expected given the small scale of the experimental setup. Furthermore, the model's potential limitations at extreme high-flow events should be noted, as such events were less represented in the dataset. Future work will involve expanding the experimental roof and the model to assess performance over larger roof areas, providing further insights into the system’s reliability under higher flow conditions.

In addition to modifying the discharge design of the blue-green roof, opportunities exist to optimize the whole blue-green roof design, which also include the type of vegetation, porosity, composition of growing media, etc., all of which have been shown by Talebi et al. (2019) and Almaaitah et al. (2022) to influence the water retention capability of the system. 

Environmental stormwater criteria in BC includes volume reduction and discharge rate control criteria to manage stormwater runoff from developments (DFO 1993). Volume reduction is aimed at retaining the small storms frequently occurring in the marine Pacific northwest coast climate. The rate control criteria are for detaining the less frequent large storms and requires a rate control system such as a detention tank to dampen post-development peak flow to match that of pre-development for significant storms (such as the 2-year and 5-year 24-hour storms). Therefore, there is an opportunity to assess the overall detention performance of the blue-green roof coupled with a downstream detention tank, thus representing an integrated system capable of dealing with a spectrum of rain events (small and large storms). The detention tank can also function as a rainwater cistern to return water to the blue green roof and provide water for irrigation of the blue green roof during dry summer seasons, when water in the Permavoid storage is depleted. 

6 Conclusion

Vancouver's distinct wet and dry seasons present unique challenges for stormwater management. The study's data from 2020 highlighted the seasonal variations in rain and their implications for blue-green roof performance.

The SWMM blue-green model, calibrated and verified using observed data, demonstrated a good fit for wet seasons but showed discrepancies during dry seasons, primarily due to evapotranspiration rate variations.

Different Permavoid discharge designs significantly impact the detention and, to a lesser extent, the retention performance of blue-green roofs during wet seasons. In particular, active water level control designs showed improved hydrological performance compared to base case and passive designs.

Future blue-green roof designs should consider alternative drainage methods, such as weir systems, to mitigate potential clogging risks associated with small orifice diameters.

While modifying the discharge design alone offers limited improvements in annual retention performance, optimizing the entire blue-green roof system—including vegetation type, growing media composition, and porosity—can enhance water retention capabilities. Addition of a detention tank downstream of the blue-green roof can further enhance detention capability during the wet seasons, while providing a water source for irrigation during dry seasons.

Acknowledgments

The authors wish to express their gratitude for the support received from Computational Hydraulics International (CHI), which provided a PCSWMM Educational Grant to access the PCSWMM software for the modeling studies conducted in this research. 

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