2.2 Methodology

The GRS typically contains four layers (from top to bottom): vegetation, soil, filter, and drainage (Feitosa and Wilkinson, 2016). The single precipitation events and continuous precipitation for three types of roof systems (i.e., TRS, GRS, and IGRS) were simulated using the Storm Water Management Model (SWMM, V. 5.1) which contains the LID package that accommodates green roofs and other new techniques (Carson, et al., 2015). Parameters used to describe the features of the four layers of a green roof can be specifically inputted in SWMM (Carson et al., 2015). Depending on the thickness of the growing media and the vegetation, green roofs are classified as intensive and extensive types (Gregoire and Clausen, 2011). The intensive type typically has thick growing media and diverse vegetation including grass, shrubs, and trees, whereas the extensive type has thinner (≤15 cm) media and drought enduring vegetation (Berndtsson, 2010; Carter and Fowler, 2008; Getter and Rowe, 2006). Extensive green roofs were chosen in this case to build retrofit since it has lower weight loads; is easier to build; and can be used in new or existing buildings (Hui, 2006).

2.2.1 Comparison between TRS and GRS

2.2.1.1 Modeling of TRS and GRS
Two scenarios are studied in the comparison between TRS and GRS: a traditional impervious design, and a typical GRS design. The SWMM was performed in seven steps: (1) Divide the study catchment XIFS into five sub-catchments Si (i = 1,2 … 5; Fig. 3b) according to the existing roads, because surface runoff is discharged into the drainage pipeline under the road. Each sub-catchmentSi was divided into Bi (i = 1,2 … 5) representing characteristic buildings andDi (i = 1,2 … 5) representing impermeable ground (Fig. 3b). Bi are given impermeable parameters in the TRS scenario and green roof related parameters in the GRS scenario. The area of green land is negligible in this study since it only accounts for a small part of the study area ( ~1%) with the remainder being impermeable houses and hardened ground. From the regulatory detailed planning documents of the XIFS, the building density of the study area is 45%, soBi = 0.45Si ,Di = 0.55 Si, andBi + Di =Si, (i = 1,2 … 5). (2) Define all theBi parts as impervious sub-catchments with properties representative of TRS. (3) For Single Event Simulations, use three synthetic designs that represent the 2-, 10-, and 100-year precipitation events to calculate runoff volume. The precipitation duration was set as 2 hours to facilitate comparison between three different precipitation intensities. These idealized precipitation events were synthetized from the 31-year historical data in Nanchang city. (4) For Continuous Simulations, we used long term continuous precipitation data to calculate the hydrological responses of TRS and GRS. The daily precipitation was used as model input. (5) Use the SWMM to set up a green roof treatment simulation for all the Bi parts, and describe physical properties of the simulated GRS. We used the Green roof type as LID type in SWMM. The relevant model parameters, such as substrate thickness, field capacity, wilting point, saturated hydraulic conductivity, and void fraction were determined from sensitivity analyses. The initial moisture content is clearly critical because there will clearly be a far higher level of retention (runoff reduction) if the roof is assumed to be dry, compared with a roof that is already wetted to field capacity (zero retention). For simplicity, we only consider initial condition of dry soil moisture content. (6) Repeat step (3), i.e., the Single Event Simulation for GRS. (7) Repeat step (4), i.e., the Continuous Simulation for GRS. Single Event Simulation results for TRS and GRS can be obtained from steps (3) and (6) and Continuous Simulations results for TRS and GRS can be obtained from steps (4) and (7), respectively. Because Bioretention cell type is also a commonly used LID type in literature to simulate the behavior of green roof (Versini, et al., 2015; Burszta-Adamiak & Mrowiec, 2013), we repeated steps (5), (6), and (7) using the Bioretention cell type in SWMM.
Considering the current climate condition of Nanchang, the capacity of most of CSS / SWS are insufficient and cannot meet the latest design standards of China. The conduits Ci (i = 1,2 … 5) (Fig. 3b) set up in the study area are all redesigned in accordance with the latest Outdoor Wastewater Engineering Code issued by the Ministry of Housing and Construction of the People’s Republic of China in 2016. In this way, we can objectively study how green roofs alleviate urban flooding problem as an innovative rainwater storage and drainage method. According to the Code, the surface runoff volume is calculated by storm intensity calculation formula derived from Chicago hyetograph method and combined with surface runoff coefficient. For Nanchang city, the rainfall intensity is:
\(q=\frac{1598(1+0.69\operatorname{}{P)}}{\left(t+1.4\right)^{0.64}}\)(1)
where
q : rainfall intensity [ 10-3m3 s-1 ha-1]
t: rainfall duration [min]
P: Recurrence period [year]
The diameter of the conduit is calculated on the basis of Chézy formula:
\(v=\frac{1}{n}\times R^{\frac{2}{3}}\times i^{\frac{1}{2}}\) (2)
\(D=\sqrt{\frac{4\times 10^{-3}\times\varphi\times q\times A}{\pi\times v}}\)(3)
where
D : conduit diameter [m]
v : flow velocity [m s-1]
n : manning coefficient
R : hydraulic radius [m]
i : conduit slope [%]
\(\varphi\): surface runoff coefficient
q : rainfall intensity [ 10-3m3 s-1 ha-1]
A : catchment area [ha]
For single event simulations, the 2-, 10-, and 100-year precipitation events are synthesized based on 31 years of rainfall data in Nanchang. Firstly, the Gamma distribution was assumed and fit to the precipitation data because it (Pearson’s \(\gamma\)) has been widely accepted to fit the probability distribution of short-duration precipitation in central and southeastern China (Huang et al, 2017; Huo et al, 2019; Li et al, 2011; Li et al, 2015; Zhong et al, 2019). Since the data obtained are the daily precipitation, there is no distinction of the specific hours of rain per day. Secondly, the precipitation with recurrence periods of 2-, 10-, and 100- year were selected according to probability p=1 / (365*2), p=1 / (365*10) and p=1 / (365*100) after fitting gamma distribution with 31-year daily precipitation data. Thirdly, the Chicago Design Storm (Rainfall Type II) curve was used to calculate the hourly precipitation for the three different recurrence periods. Finally, the maximum 2 hours of 2-, 10-, and 100-year precipitation were chosen for the simulations because the maximum rainfall occurs at 2 hours of noon in each recurrence period and the design time of rain pattern in many literatures is 2 hours also (Fig. 4) (USEPA, 2009; Sun et al.,2018; Ni et al., 2019; Zhu, 2016; Dai et al.,2017; Cheng et al.,2015). For Continuous Simulations, we firstly used the SWMM model to calculate and analyze the cumulative changes of surface runoff and evaporation by performing GRS simulations on the basis of 31-years precipitation and temperature data. Then the differences of yearly surface runoff and evaporation between GRS and TRS were compared with daily precipitation, evaporation, humidity, temperature and wind speed data of 2015 being applied.
For the flow routing model, we selected the Kinematic wave equation because it is numerically stable, computationally efficient, and appropriate for heavy precipitation simulations (USEPA, 2013). Manning’s roughness coefficients (n ) were set as 0.011 for impervious areas and 0.04 for vegetated areas (USEPA, 2013).
2.2.1.2 Sensitivity Analysis of Soil Parameters
The relevant soil parameters in the GRS model were chosen from our sensitivity analysis. Total 14 parameters are required to input in the SWMM:berm height, vegetation volume fraction, surface roughness, conductivity slope, surface slope, drainage mat thickness, drainage void fraction, drainage roughness parameters, soil thickness, soil porosity, field capacity, wilting point, conductivity, and suction head. Among these parameters, the first 8 ones are defined in the manual of SWMM 5.1 with definite range of values, and changes in these parameters in the range of maximum and minimum values have little effect on the surface runoff in our tests by simply adjusting the values of the parameters (Table 1). However, soil thickness does have an effect on water storage capacity. The soil thickness is usually 50-150 mm, and the interception rate of rainwater would reduce with the decrease of the thickness of the soil layer (Lee et al., 2015; Berndtsson, 2010). In order to achieve good storage effect, the maximum thickness of extensive green roof, 150 mm, was used in this simulation. The parameters like substrate composition, structure, and texture (hence pore distribution) are not optional in the SWMM. So, only five important parameters were chosen for sensitivity analysis: saturated hydraulic conductivity, suction head, porosity, field capacity, and wilting point. Firstly, we analyzed the five parameters in the whole point view of the 11 groups of soil texture types (sand, loamy sand, sandy loam, loam, silt loam, sandy clay loam, clay loam, silty clay loam, sandy clay, silty clay, and clay) provided in the SWMM manual. In the cases of an extensive green roof, although lightweight and coarse-grained engineered mixtures are usually used comprising crushed brick or pumice mineral fraction and small amounts of fines and organic matter, we still measured all the 11 groups of soil texture types in the SWMM manual to achieve the integrity of the sensitivity analysis. Moreover, uncertainty analysis is necessary because a variety of materials may be used and even fixed materials also have great uncertainty in parameter measurement. Therefore, 11 groups of soil texture types are considered in the first step and the Monte Carlo method was used to select the four groups (maximum, minimum, median and average) of reference values for testing (USEPA, 2015; Table 2). Secondly, as the practical application of soil in green roofs, three sets of reference values were selected, one of which is the value used by other scholars in a reference literature (Carson, et al., 2015); the other two groups are the maximum and minimum values of six sets of data from silt clay to silt loam in the SWMM manual because the soil characteristics of green roof is generally between silt clay and silt loam (USEPA, 2015;Table 2). The corresponding objectives of the sensitivity test are: evaporation, runoff, initial LID storage, and final storage. We chose the vegetation volume fraction (i.e., volume occupied by leaves and stems) to be in the range of 0-0.2 and the ratio of void volume to total volume in drainage layer to be 0.5-0.6 (USEPA, 2015).
2.2.1.3 Evapotranspiration
We applied five methods to evaluate ET uncertainty and their effects on the GRS effectiveness: Hargreaves (Hargreaves and Merkley, 1998), Penman–Monteith (Allen, Richard G. et al., 1998), Pan Evaporation (Allen, Richard G. et al., 1998), Advection-Aridity method (Brutsaert and Stricker, 1979) and Granger-Gray method (Granger and Gray, 1989).
The first method (Hargreaves) is the default method in SWMM to compute potential ET (PET) (USEPA: 2013; Ugwu and Ugwuanyi, 2011):
\(e=\frac{0.0023*\text{Ra}}{\lambda}*\sqrt{T_{r}}*(T_{a}+17.8)\) (4)
Where
\(\lambda\): latent heat of vaporization,\(\lambda=2.50-0.002361*T_{a}\) (5)
Ra: extraterrestrial solar radiation that can be calculated according to latitude and day of the year [ MJ m-2day-1]
\(\text{Ra}=37.6*d_{r}(\omega_{s}\sin\phi\sin\delta+\cos\phi\cos\delta\sin{\omega_{s})}\)(6)
\(d_{r}\): relative distance from the earth to the sun
\(d_{r}=1+0.033\cos\left(\frac{2\pi}{365}*J\right)\) (7)
\(\omega_{s}:\) sunset hour angle(rad),\(\omega_{s}=arc\cos\left[-\tan{\left(\varphi\right)\tan\left(\delta\right)}\right]\)
\(\varphi\): latitude(rad)
\(\delta:\ \)declination of the sun(rad),\(\delta=0.409\sin\left(\frac{2\pi}{365}*J-1.39\right)\) (8)
J: calendar day from 1 to 365 or 366
\(T_{r}=T_{\max}-T_{\min}\) (9)
\(T_{a}=\frac{\left(T_{\max}+T_{\min}\right)}{2}\) (10)
Tmax : daily maximum air temperature
Tmin : daily minimum air temperature
However, the Hargreaves method only considers a few of meteorological parameters such as air temperature and extraterrestrial radiation. So, methods use more meteorological data are needed to calculate the values of RET (Reference Evapotranspiration) and AET (Actual Evapotranspiration) (Allen et al., 1998; Hargreaves and Samani, 1985; Jensen et al., 1997). Furthermore, several authors (Peng et al., 2019) have highlighted that the use of Potential ET rather than actual ET (which is influenced by the substrate moisture content) seriously limits the accuracy or retention estimations in SWMM. Therefore, the values of AET, RET and PET are compared on the consideration of the important role of ET in the hydrodynamic process of green roofs. We also applied the Penman–Monteith approach, which has more parameters than the Hargreaves approach and is a widely accepted method for calculating reference ET (RET) (Allen, Richard G. et al., 1998):
\(\text{ET}_{0}=\frac{0.408\left(R_{n}-G\right)+\gamma\frac{900}{T+273}u_{2}\left(e_{s}-e_{a}\right)}{+\gamma\left(1+0.34u_{2}\right)}\)(11)
where
\(\text{ET}_{0}\): reference evapotranspiration [mm day-1]
\(R_{n}\): net radiation at the crop surface [MJ m-2day-1]
\(G\): soil heat flux density [MJ m-2day-1]
\(T:\ \)air temperature at 2 m height [°C]
\(u_{2}:\) wind speed at 2 m above land surface [m s-1]
\(e_{s}:\) saturation vapor pressure [kPa]
\(e_{a}:\) actual vapor pressure [kPa]
\(e_{s}\ -\ e_{a}:\) saturation vapor pressure deficit [kPa]
By assuming a grass reference surface, the ET calculated by the FAO Penman-Monteith equation provides a standard ET over time and space, which can be used to infer ET from other plants (i.e., those used in LID; Allen, Richard G. et al., 1998).
The third method, Pan Evaporation, relates ET to a reference ET value by
an empirically derived pan coefficient (Allen, Richard G. et al., 1998):
ETo = Kp Epan (12)
where
ETo: reference evapotranspiration [mm day-1]
Kp: pan coefficient [-]
Epan: pan evaporation [mm day-1]
Pan coefficients vary based on the type of pan, humidity, wind, surface vegetation, and condition of the upwind buffer zone (Allen, Richard G. et al., 1998). In our simulations, wind speed ranges from 2 to 5 m s-1 and the mean Relative Humidity (RH) is about 75%, so Kp should range from 0.8 to 1.1 (Allen, Richard G. et al., 1998). Continuous daily precipitation, pan evaporation data, humidity, and wind speed data covers year 2015.
The fourth method is Advection-Aridity method that was first proposed to calculate the actual regional ET (Brutsaert and Stricker, 1979; Marasco, et al., 2015):
\(E=1.56\frac{\Delta}{\Delta+\gamma}Rn-0.35\frac{\gamma}{\Delta+\gamma}\left(1+0.54U_{2}\right)\left(e_{\alpha}^{*}-e_{\alpha}\right)\)(13)
where
: slope of the saturation vapor pressure curve at air temperature
\(\gamma\): psychometric constant
\(R_{n}\): net radiation at the crop surface [mm day-1]
\(U_{2}:\) wind speed at 2 m above land surface [m s-1]
\(e_{\alpha}\): vapor pressure of the air [mm Hg]
\(e_{\alpha}^{*}\): saturation vapor pressure at air temperature [mm Hg]
The fifth method is Granger-Gray method that is widely applied to various surface conditions (Granger and Gray, 1989; Xu and Chen, 2005; Kim and Kaluarachchi, 2017):
\(ET=\frac{2.56\times\Delta\times Rn}{\left(2+0.028e^{8.045\times\frac{0.35(1+0.54U)(es-ea)}{0.35(1+0.54U)(es-ea)+Rn}}\right)\times\left(\gamma+\Delta\right)}\)(14)
where the meanings of the parameters are the same as those in the fourth method.
Both the Advection-Aridity method and the Granger-Gray method are widely used methods to calculate the actual ET (AET) (Kim and Kaluarachchi, 2017).

2.2.2 Comparison Between GRS and IGRS

The IGRS is a combination of green roof and rooftop disconnection (See Fig. S1 in Supplementary Information). Instead of discharging rainwater directly into a drainage pipeline under the road, the outlets of the downspouts in IGRS are permeable greenbelts or landscape areas. Therefore, the IGRS can take excess surface runoff from the drainage layer of the green roof and transport it to the grassed lawn nearby.
Although the GRS could manage small precipitation events well, the effect will decrease greatly for large precipitation events (Li and Babcock, 2014). Within a heavy precipitation, most surface runoff is discharged via the drainage layer of GRS into the CSS / SWS. As an important structure of the IGRS, rooftop disconnection can direct runoff from rooftops to grassed lawns to help to keep water away from the drainage ditches besides buildings so as to increase infiltration (Carmen, et al., 2016). Application opportunities for rooftop disconnection include any location where rooftop runoff can be directed onto a vegetated area (Carmen, et al., 2016), such as adjacent greenbelts. This improvement has the potential to better mitigate urban flooding and recharge groundwater.
As shown in Fig. 3c, the difference from part 1 is that the XIFS catchment was divided into five sub-catchments, and each sub-catchment (Si , i = 1, 2, … , 5 ) in part 2 was further divided into three compartments, withBi representing the buildings which accounts for 45% of the total area, Gi standing for the greenbelts next to the buildings, and Hirepresenting the impervious ground. Therefore, Si= Bi + Gi + Hi (i = 1, 2, …, 5 ). Define all the Gi parts as separate pervious sub-catchments with properties representative of the most common green belt on the streets of the city studied. Because the most of greenbelt soil texture in Nanchang is clay loam, the infiltration parameter of the greenbelt refers to the value of clay loam in the manual of SWMM 5.1. The Gi parameters are shown in Table 3.
Two scenarios are studied in the comparison between GRS and IGRS. In the GRS scenario, all excess runoff drained from green roofs was diverted into CSS / SWS. In this case, the greenbelts Gi(i = 1,2 … 5) only collect the precipitation that directly falls on them and do not capture the runoff from other areas. In the IGRS scenario, all excess runoff drained from green roofs was diverted to greenbelts. So, the greenbelts Gi (i = 1,2 … 5) collect direct precipitation and the outflow runoff from green roofsBi (i = 1,2 … 5).
Because the width of green belts next to buildings is generally 1-3 meters in China, we tested the effectiveness of IGRS using 1-, 2-, and 3- meter widths for Gi . In addition, according to China’s architectural design code, the minimum distance between two buildings is 6 meters, so it is feasible to arrange a 1-3 meters wide green belt.