Green roof systems have been suggested to ease the growing urban environmental problems resulting from rapid urbanization. However, the irrigation of green roofs heavily depends on using precious potable water and consequently generates negative environmental effects. Rainwater has been recommended to address this dilemma, but the design method has not been well developed. In this study, the major design factors of a rainwater harvesting system for green roof irrigation systems are examined, and a simulation-based mathematical model is established to elucidate the correlation between tank volume and system performance. The optimal system design and probability distribution of the potable water replacement rate are also discussed on the basis of a case study of a university building in Keelung, Northern Taiwan. The results show that the optimal tank volume, potable water replacement rate, and probability of exceedance are 9.41 m3, 92.72%, and 88.76% (±1SD), respectively. In addition, the economic performance is identified to be feasible. Hence, the design method has been verified to be a useful tool to ease the urban environmental issues.

## INTRODUCTION

Rapid urbanization has worsened environments worldwide with problems such as the heat-island effect, energy waste, air pollution, and urban flooding. Recent research has identified green roof systems as an effective approach to address several issues: detaining and retaining stormwater, adjusting microclimates, purifying water and air, mitigating the urban heat-island effect, and establishing ecological cities (Villarreal et al. 2004; Getter et al. 2007; Kasmin et al. 2009). In addition to providing energy-saving benefits for buildings, green roof systems constitute an effective insulator that can prolong the lifespan of buildings (Ouldboukhitine et al. 2014). The local governments of numerous major cities, such as Tokyo, Taipei, Beijing, and Shanghai, have promoted the concept of green roofs to ease the worsening of urban environmental problems. However, the major limitation of green roofs, especially in tropical and subtropical cities, is that the involved irrigation depends primarily on potable water, which not only increases the burdens of scarce water resources but also consumes electricity for municipal pumping. The energy consumed for the potable water supply can amount to 3.25 kWh/m3, implying emissions of 1.73 kg CO2 in Taiwan alone (Chiu et al. 2009; Bureau of Energy 2012). Therefore, the inherent dilemma of the effects of green roofs on urban potable water demand is one of the key urban environmental issues. Rainwater is the onsite available water resource that should not be neglected. Some researchers suggest that future research may focus on how to use rainwater as an innovative irrigation water source (Alsup et al. 2010).

The recognized importance of water conservation has resulted in researchers recommending development of rainwater harvesting systems (RHSs) that alleviate water shortage problems worldwide. Some researchers have adopted hydraulic simulations by incorporating rainfall history and system behavior models to evaluate the system performance or design tank volume (Su et al. 2009; Chiu 2012). However, for RHSs that incorporate green roof irrigation systems, the specific design factors (e.g. water demand and runoff coefficient) differ considerably from traditional RHS designs. Moreover, the majority of previous studies have focused on employing RHSs as an alternative water source for toilets only, which is typically a constant value for calculating system performance. For green roof irrigation systems that support plant life, the water demand is subject to variations based on climate, the types of soil, and vegetation. Thus, these RHS design parameters require further clarification to be integrated into green roof irrigation systems. Furthermore, there has been no report of an efficient method for evaluating rainwater harvesting (RWH) for green roof irrigation systems. Because of this, all of the major design factors must be assessed to develop a suitable method for determining the optimal tank volume. Only with sufficient understanding of RWH for green roofs can architects and urban planners make sound decisions based on good design to deal with urban environmental issues.

This study focuses on tank volume design and proposes a simulation-based RHS design method for green roof irrigation to achieve the optimal tank volume. A case study in Keelung, Northern Taiwan is conducted to verify the proposed method. The purpose of this study is therefore threefold: first, to identify the major RHS design factors for green roofs, which differ from the traditional RHSs; second, to develop the simulation model to analyze the correlation between the tank volume and its performance in order to obtain the optimal tank volume; third, to verify the performance of RHSs using probability distribution analysis and economic feasibility analysis based on the case study.

## METHODOLOGY

Figure 1 shows the research diagram. The green roof system was established to harvest rainfall runoff, which was channeled to the storage tank via the rainwater drainage pipe. Subsequently, the water was pumped to the roof based on the demand of the green roof irrigation system. When the water level became insufficient, the potable water was supplemented.

Figure 1

RHS with green roof irrigation.

Figure 1

RHS with green roof irrigation.

### Simulation model

According to Liaw & Tsai (2004), the yield before spill model (YBS) is suitable for comparatively smaller tank volume in rainwater harvesting. Several previous researchers have also applied a probability approach to analyze the RHS's performance of water supply (Su et al. 2009; Kim et al. 2012; Youn et al. 2012).

Figure 2 shows the simulated calculation flowchart, where Q(t) (m3) is the rainfall runoff volume at time t. Determining whether irrigation is required at the beginning of the simulation is based on the rainfall data; if Q(t) is greater than zero, the irrigation is not needed. Prior to irrigation, if the storage volume exceeds the irrigation water demand, it indicates a sufficient supply. This study calculates the daily usage as the base period. The calculation can be expressed as follows:
1

2
where D(t) (m3) is the water supply of the RHS, DET(t) (m3) is irrigation demand, S(t) (m3) is the storage volume, and PW(t) (m3) is the potable water supplement volume. Prior to irrigation, if S(t) > DET(t), then the water supply is sufficient; otherwise, PW(t) can be calculated as Equation (2).
Figure 2

Simulation model.

Figure 2

Simulation model.

In the YBS model, the spillover amount should be calculated following irrigation, which is expressed as
3

4
where S(t) (m3) is the storage volume prior to inspecting the spillover after the water has been supplied, S(t+1) (m3) is the storage volume after spillover, and VS (m3) is the tank volume.
The performance of RHSs is evaluated using potable water replacement rate (PRR), which can be written as
5

6
where n is the number of simulation days.

### RHS design parameters for the green roof

The rainfall runoff volume into tank depends on the rainfall, catchment area, and the runoff coefficient of the green roof, which is expressed as
7
where C is the runoff coefficient, I(t) (m3) is the rainfall depth, and A (m2) is the rooftop area. For the green roof, the C value differs in conjunction with variations in soil thickness, plant type, and roof slope. These parameters need to be based on the current situation and experimental results (Mentens et al. 2006). Taiwan's Architecture and Building Research Institute (ABRI) conducted onsite tests to explore retaining and detaining of rainfall on green roofs and plotted charts based on the abovementioned parameters (ABRI, Architecture and Building Research Institute 2010). This study applies the result charts from ABRI to derive the C value for the simulation.
The irrigation demand DET(t) (m3) can be considered as the evapotranspiration (ET) of the green roof. Shih suggested that the ET estimation equation developed by Penman–Monteith which adopts micrometeorological principles is suitable for conditions in Taiwan (Shih et al. 1983). The equation for the irrigation demand can therefore be expressed as
8
where K is the ET correction coefficient, ET0(t) (mm) is estimated ET at time t based on the Penman–Monteith formula. This study also used the result charts of K value based on ABRI experiments (ABRI, Architecture and Building Research Institute 2010).

### Tank volume selection

To achieve the optimal tank volume design, this study adopts marginal benefit theory to enhance the efficiency of the tank volume's PRR for each unit, and to determine the optimal design. Marginal benefit theory refers to maximum output with the minimum input, which is known as the marginal physical product (MPP) (Pindyck & Rubinfeld 2009). In this study, MPP refers to the corresponding PRR produced by the input of a specific tank volume for each unit. In mathematical terms, MPP is the PRR curve slope produced by a given tank volume; MPP is the partial differentiation of PRR on the tank volume.
9
The PRR function indicates that the extent of increase is greater in the initial segment, and the slope is m > 1. When m = 1, the optimal tank volume occurs.

### Probabilistic analysis of PRR

In this study, the relation between PRR and RHS tank volume is examined using the probabilistic distribution curve to reduce the risk of design deviation. The PRR is obtained from continuous and random meteorological record variables, which are applied as random variables. Assuming that the PRR is normally distributed, the probability density function (PDF) describes the probability of PRR occurrence; cumulative distribution function (CDF) describes the probability of less-than-expected PRR; and exceedance probability (EP) describes the probability of achieving the expected PRR (Su et al. 2009; Kim et al. 2012; Youn et al. 2012).

## BACKGROUND OF THE CASE STUDY

National Taiwan Ocean University (NTOU) intends to increase the number of green roofs installed on campus and to be included in the Taiwan Sustainable Campus Program. However, increase of green roofs implies increase of potable water consumption in irrigation. To install green roofs without potable water consumption, a section of the Harbor and River Engineering Department Building was selected and examined as a potential option to install RHS for green roof irrigation. The building is a single five-story building with a flat reinforced concrete roof. The catchment area and green roof was 100 m2, the medium was 10-cm-thick, the slope was 1%, and the type of plant was Eremochloa ophiuroides (centipede grass).

Table 1 shows the major meteorological data (from 1990 to 2009) employed. The mean annual rainfall in the Keelung area was 3,659 mm. During the past 20 years, the rainy season occurs in the winter, and the irrigation requirements increased substantially from July to September because of the high ET rates of the soils and plants.

Table 1

Hydrological and meteorological data

Average annual meteorology of Keelung weather station (1990–2009)
Rainfall 3,659 mm
Sunshine days 141.8 days
Temperature 22.6 °C
Atmospheric pressure 1,010.8 hPa
Wind speed 3.0 m/s
Humidity 77.9%
Average annual meteorology of Keelung weather station (1990–2009)
Rainfall 3,659 mm
Sunshine days 141.8 days
Temperature 22.6 °C
Atmospheric pressure 1,010.8 hPa
Wind speed 3.0 m/s
Humidity 77.9%

## RESULTS AND DISCUSSION

By applying the proposed green roof RHS tank volume design method, the optimal tank volume was obtained based on the MPP. Furthermore, the PRR distribution and economic analysis were examined.

### Potable water replacement rate

Using the physical data from the study case and ABRI's research, the major parameters for simulation – i.e. runoff coefficient C and ET correction coefficient K – are derived as 0.85 and 0.70, respectively.

Using the simulation model illustrated in Figure 2, the simulation results of case study presented in Figure 3(a) show that increasing the storage tank also increased the rainwater usage, whereas the potable water usage decreased. Table 2 also lists the standard deviation of PRR and spillover corresponding to the tank volumes. Figure 3(b) demonstrates that the PRR increased with the tank volume which coincides with the actual situation because more rainwater was collected as tank volume increased. The increased replacement rate at the frontend of the curve was obvious, whereas the increase in the backend was steady.

Table 2

Characterization of green roof integration of RHS

RHS tank volume (V) (m3)PRR (%)Rainwater usage (m3)Potable water usage (m3)Spillover (m3)
Mean (μ)Standard deviation (σ)
69.25 6.40 41.1 19.1 269.9
78.15 5.69 46.4 13.7 264.6
85.24 4.45 50.8 9.3 260.2
92.09 4.30 55.0 5.2 256.1
10 93.91 4.25 56.1 4.0 254.9
20 98.30 2.91 59.1 1.0 251.9
30 99.70 1.33 60.0 0.2 251.0
RHS tank volume (V) (m3)PRR (%)Rainwater usage (m3)Potable water usage (m3)Spillover (m3)
Mean (μ)Standard deviation (σ)
69.25 6.40 41.1 19.1 269.9
78.15 5.69 46.4 13.7 264.6
85.24 4.45 50.8 9.3 260.2
92.09 4.30 55.0 5.2 256.1
10 93.91 4.25 56.1 4.0 254.9
20 98.30 2.91 59.1 1.0 251.9
30 99.70 1.33 60.0 0.2 251.0
Figure 3

Relationship of RHS tank volume, use amount, and replacement rate. (a) Rainwater and potable water use; (b) PRR.

Figure 3

Relationship of RHS tank volume, use amount, and replacement rate. (a) Rainwater and potable water use; (b) PRR.

### Optimal tank volume determination

In this study, the optimal tank volume design was examined based on the calculated simulation results, ascending curve of the PRR system, and the designed tank volume. By employing the MPP method, Microsoft Excel was used to identify the PRR and subsequently conduct the logarithmic trend analysis to derive the following equation:
10
This equation underwent differentiation to obtain the MPP. The optimal tank volume was achieved as 9.41 m3 when the slope m = 1. Based on the optimal tank volume, the mean PRR was 92.72%, whereas the rainwater usage, potable water usage, and rainwater overflow were 55.6–4.4 and 255.4 m3/yr, respectively.

### PRR probabilistic analysis

By assuming that the PRR is a normal distribution, this study examined the RHS design probability distribution. Based on the mean PRR and standard deviation of the design capacity, we examined probability distribution, the PDF, CDF, and EP, as shown in Figures 4(a), 4(b), and 4(c), respectively.

Figure 4

Probability distributions of potable water replacement rate. (a) PDFs; (b) CDFs; (c) EPs.

Figure 4

Probability distributions of potable water replacement rate. (a) PDFs; (b) CDFs; (c) EPs.

Figure 4(a) shows that an increase in the tank volume facilitated an increase in PRR, whereas a smaller tank volume resulted in a partial water supply shortage and wider variations. This finding indicates that a comparatively smaller tank volume results in inadequate water supplies and a higher probability of a failure to achieve the anticipated PRR in the actual operation because of the higher standard deviation of the tank volume. Figure 4(b) shows the CDFs by cumulative probabilities of PDFs. When the tank is smaller, there is a higher probability of less-than-expected PRR. Figure 4(c) shows the EPs by decumulative probabilities of PDF. When the tank is bigger, there is a higher probability of achieving the expected PRR, and the potable water supplements and probabilities are lower; consequently, the potable water expense also decreases. Therefore, the risk of design deviation in this case study has been reducing by applying the probability distribution analysis.

For the optimal design of 9.41 m3, the standard deviation was 4.27%. In one standard deviation of optimal design, the EP is 88.76%. This means, under the MPP method and probabilities analysis, there is 82.77% probability to reach the expected design and 17.23% risk in the actual operation.

### Economic feasibility analysis

This study adopts the benefit–cost ratio (B/C) to measure economic feasibility, where a B/C ratio greater than 1 is considered cost-effective. The costs of this RHS mainly involve the costs for tanks and pipeline connection; the costs of pumps, irrigation systems, and related energy consumption are included in the green roof installation, and thus are excluded from the RHS cost calculation. The initial cost of RHS provided by the contractors is TWD$27,500 (about US$932, using five PE tanks of 2 m3, and PVC pipe lines of ψ65 mm).

According to public construction standards in Taiwan, the lifetime, interest rate, and reasonable potable water fee (reservoir development costs) are assigned as 30 years, 1.36%, and US\$0.81/m3, respectively (Lee & Lin 2001; Public Construct Commission, Taiwan 2013). The B/C ratio is therefore derived as 1.19, which indicates that using rainwater as a water source for the green roof irrigation system is economically beneficial in this case study.

## CONCLUSION AND RECOMMENDATIONS

Green roof systems have been promoted to ease the negative effects of rapid urbanization. However, the overconsumption of potable water should be addressed. In this study, an RHS for a green roof irrigation system is proposed to alleviate the burden of urban potable water consumption. The simulation-based design method was established, and the optimal tank volume design was achieved using the MPP method. To verify the system reliability, the probability function concept was adopted to explain the relationship between the tank volume and PRR. A case study of a university building at NTOU was also conducted. The results showed that the optimal tank volume is 9.41 m3, where the PRR reached 92.72%, and the EP within one standard deviation was 88.76%; furthermore, the proposed approach is economically feasible.

Consequently, the methods presented in this study can constitute a useful tool that enables designers and urban planners to use RHS for green roof irrigation systems and reduce the risk of design failure, thereby ensuring RHS reliability in green roof irrigation systems. However, this method is at the experimental stage and further research is necessary. For example, future studies should focus on quality control of stored water, spatial and temporal meteorological complexity analyses, and plant growth conditions. Further refinement of this method is necessary for the wider application of RHS in green roof irrigation systems to alleviate specific urban environmental issues.

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