Introduction

In urban stormwater management, green roofs help to absorb rainwater and thus reduce peak runoff and delay runoff time (Hakimdavar et al. 2014). Green roofs have been widely explored as an effective low-impact development measure. The rainwater retention capacity (RRC) of green roofs is defined as the percentage of rainwater retention and accumulated rainfall. To improve the RRC of green roofs, many researchers have focused on improving the water holding capacity (WHC) of soil (Bollman et al. 2019; Poë et al. 2015 and Stovin et al. 2015). These soil improvement methods include mixing peat, crushed bricks, perlite, vermiculite, pumice, coconut bran, and biochar in a certain proportion (Peng et al. 2019; Werdin et al. 2021; Xue and Farrell 2020). However, soil improvement may also lead to an increase in cost and delay in green roof construction. Shafique et al. (2018b) pointed out that the cost of the soil and drainage layer accounted for approximately 48% of the total cost of green roofs. Additionally, the available water storage of extensive green roofs increased by soil improvement is limited, which usually increases the RRC by approximately 10% (Dusza et al. 2017).

In addition to improving the WHC of soil, the structural configurations of green roofs are optimized to improve the RRC under a given soil. Increasing the soil depth of green roofs is considered to be a common method. The soil depth of extensive green roofs is usually 50 to 150 mm based on FLL guidelines (FLL 2002). Dusza et al. (2017) pointed out that the water storage capacity obtained by increasing the soil depth is usually less than the theoretical value due to the limitation of evapotranspiration (ET) conditions. Gong et al. (2019) found an increase in RRC by 5% as the depth of green roof soil increases from 100 to 150 mm. In addition, the increase in soil depth is directly related to the increase in the vertical load on the roof, which is not suitable for building green roofs in many old buildings. Cascone et al. (2018) indicated that when the soil depth increases from 100 to 150 mm, all lightweight soil used exceeds the load requirements of the old buildings.

By installing the bottom water storage layer, the water storage capacity of green roofs can be increased. The bottom water storage layer can provide water for the soil by ET during the drought period, thus delaying water stress and the irrigation cycle of vegetation (Loiola et al. 2019). In previous studies, plastic drainage plates with grooves and aggregates (i.e., ceramsite, gravels, pebbles) were usually used as the bottom water storage layers (Qin et al. 2016; Zhang et al. 2019). The drainage through the soil layer is retained by the bottom water storage layer until the water storage layer is saturated. Wang et al. (2021) showed that the rainwater retention of a plastic drainage board with a water storage capacity of 5 mm was approximately 1% higher than that of a green roof without a water storage layer. Zhang et al. (2019) used a green roof plastic tray with a water storage capacity of approximately 6 mm in the drainage layer. However, these plastic drainage plates with grooves have little water storage capacity and are mainly used for drainage. Rainwater retention is still dominated by the soil layer of green roofs. Qin et al. (2016) established a green roof model with a 50-mm-deep water storage layer for analyzing irrigation management. The water storage layer was filled with gravels with a porosity of 0.43. However, the rainwater retention, peak drainage delay, and reduction in the water storage layer with high storage capacity under rainstorms are still unclear.

The infiltration rate and rainwater retention of green roofs are affected by rainstorm characteristics (Huang et al. 2020; Wang et al. 2021). Only the infiltrated rainwater can be retained by the soil layer and water storage layer of the green roof. Surface runoff under rainstorms will be directly discharged from green roofs. Villarreal and Bengtsson (2005) show that surface runoff begins after the rainfall intensity is higher than the saturated hydraulic conductivity of the soil, and a higher rainfall intensity means a lower RRC. Allowing the water storage layer on the soil surface may increase the cumulative infiltration, thus increasing the RRC of green roofs. Huang et al. (2020) pointed out that the maximum height of ponding on the surface of a biochar-amended soil column reached 20 mm. Gan et al. (2021) observed that under simulated rainfall conditions, the maximum water storage on the soil surface of a green roof is between 5 and 15 mm. However, the influence of the maximum surface water storage depth on the rainwater retention characteristics of green roofs has not been fully investigated.

This technical note or short communication aims to analyze the influence of the water storage layer and surface water storage on infiltration, surface runoff, rainwater retention, drainage delay, and peak drainage reduction of green roofs under rainstorm conditions. Numerical simulations were established using the Hydrus-1D model, which was calibrated and verified by the observed results. It is hoped that the optimum water storage layer depth and maximum surface storage depth under different rainstorm conditions can be proposed. The results can provide basic data support and technical guidance for the optimization of green roof structures, the setting of the water storage layer, and maximum water storage on the soil surface.

Materials and methods

Experimental setup

The experimental platform was installed on the roof of a campus in South China. Each experimental model box had dimensions of 300 mm × 300 mm × 250 mm. In this study, the green roof models of three different water storage layer depths (i.e., WSL-0, WSL-19, and WSL-25) were considered (Fig. 1a). Green roof models WSL-0, WSL-19, and WSL-25 include bottom water storage layers with no water storage and 19 mm and 25 mm depth of water storage layers, respectively. The depth of the 25-mm water storage layer was equivalent to the depth of the drainage board commonly used in green roofs. This is similar to the water storage capacity with an additional 100 mm soil depth of green roofs. A smaller water storage layer depth (i.e., 19 mm) was used for comparative analysis. The soil is composed of rural soil, river sand, and peat (volume ratio is 1:1:1), which are commonly used in green roofs in China (Liu et al. 2019a). Before filling the soil column, the inner wall of the model was coated with a thin layer of Vaseline to minimize the influence of vertical infiltration (Li et al. 2016). The soil columns were filled in layers, and the soil column depth of all green roof models was 100 mm. As the container wall was 100 mm above the soil surface, the upper surface of the soil column allows water storage (Huang et al. 2020). Filter geotextile was used to prevent soil loss through the drainage layer and at the same time allows planting of Manila grass. All experiments were conducted 6 months after the natural growth of the plants (Fig. 1b).

Fig. 1
figure 1

a Different water storage layers of green roof models, b field experiment platform

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The moisture sensor (METER Devices, 5TE, USA) was installed in the middle of the soil layer. It was used to observe the change in the water content of the soil column before rainfall and after infiltration of the water content. All data were collected using a data logger (Decagon Devices, EM50, USA) every 5 min. A measuring cylinder was used to observe the drainage rate and cumulative drainage at the bottom of the soil column container (Wang et al. 2022). Recording was performed in real time using a high-definition camera. The experimental platform was installed in an outdoor transparent tent, which was convenient for simulating the rainfall and natural evaporation of green roof models.

Simulated rainfall experiments

The simulated rainfall equipment used a spray nozzle as a raindrop generator, whereas the rainfall intensity was controlled by a flowmeter (Fig. 2). The water supply equipment adopts a 100-l water tank. The water supply head was provided by the water pump. Four measuring cylinders were evenly arranged in the test area to observe the uniformity of simulated rainfall, and the calculated uniformity coefficient was 0.9. The flowmeter was calibrated before every simulated rainfall event, and the flow errors were controlled within 0.4%. The simulated rainfall intensity can be calculated as follows (Wang et al. 2014):

$$I = 6 \times 10^{4} \times \frac{Q}{A}$$
(1)

where I is the rainfall intensity, mm/h; Q is the flow of the flowmeter, ml/min; and A is the area of the experimental area, mm2.

Fig. 2
figure 2

Schematic diagram of the simulated rainfall experiment

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Simulated rainfall experiments with four different characteristics were conducted on three green roof models. Two different types of rainfall intensities, i.e., 30 mm/h and 50 mm/h, which are commonly occurring in South China region, were considered. The four simulated rainfall characteristics include (a) rainfall of 30 mm/h for 60 min; (b) rainfall of 30 mm/h for 100 min; (c) rainfall of 50 mm/h for 60 min; and (d) variable rainfall intensity (i.e., rainfall 30 mm/h for 38 min, 50 mm/h for 15 min, and 30 mm/h for 37 min). Procedures followed by Cai et al. (2020) have been adopted. The 30-mm rainfall is considered a common rainstorm in South China, and the 50-mm rainfall is equivalent to a 1-year return period rainstorm. The interval of each simulated rainfall test was approximately 7 days to obtain a consistent initial water content.

In addition, rainfall types of 1-year, 5-year, 10-year, and 20-year return periods as found in South China were used as the upper boundary condition. The intensity and duration of these storm events were designed according to the local storm formulation, which is described as follows:

$$I=\frac{32.287+18.194\mathrm{lg}{\text{P}}}{{(t+18.880)}^{0.851}}$$
(2)

where I is the rainfall intensity, mm/min; P is the recurrence period of the storm, year; and t is the rainfall duration, minute. The formula for Chicago storms (Keifer and Chu 1957) was used to determine the rainfall intensity curve of design storm events. The time-to-peak ratio r was 0.4, which was commonly used in many studies (Peng and Stovin 2017). Finally, the intensity-duration curves used for numerical simulation calculation are shown in Fig. 3.

Fig. 3
figure 3

The intensity-duration curves of design storm events in different rainstorm return periods

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Data analysis

The hydrological performance of green roofs mainly includes RRC, peak drainage reduction, and initial drainage. These hydrological response indices are calculated using the following equations (Liu et al. 2019b; Wang et al. 2021):

$${\text{RRC}}=\frac{P-D}{P}\times 100\mathrm{\%}$$
(3)
$${\text{R}}_{P}=\frac{{I}_{p}-{D}_{p}}{{I}_{p}}\times 100\%$$
(4)

where RRC is rainwater retention, %; P is cumulative precipitation, mm; D is cumulative drainage or runoff, mm; RP is peak reduction, %; IP is the peak rainfall intensity, mm/min; and DP is peak drainage, mm/min.

In this study, the Nash–Sutcliffe efficiency coefficient (NSE) was used to evaluate the quality of the model (Soulis et al. 2017). The equation is as follows:

$${\text{NSE}}=1-\frac{{\sum }_{t=1}^{T}{\left({Q}_{ot}-{Q}_{st}\right)}^{2}}{{\sum }_{t=1}^{T}{\left({Q}_{ot}-\overline{{Q }_{o}}\right)}^{2}}$$
(5)

Here, Qot refers to the observed result at time t, Qst refers to the simulated result at time t, and \(\overline{{Q_{o} }}\) represents the average of the observed results. The value of NSE was close to 1, which indicates that the model has high reliability. If the NSE was less than 0, the model was not reliable.

Modeling with Hydrus-1D

Hydrus-1 D is a program commonly used to simulate the migration of water and solutes in saturated–unsaturated porous media. This program can set the water time variation of atmospheric boundary conditions and free drainage boundary conditions. It has been widely used in numerical simulations of the hydrological performance of green roofs under rainfall conditions (Hilten et al. 2008; Qin et al. 2016; Zhang et al. 2021). Hydrus-1D simulates 1-D vertical water movement in soil using the Richards equation (Simunek et al. 2005). The basic governing equation is as follows:

$$\frac{\partial \theta }{\partial {\text{t}}}=\frac{\partial }{\partial z}\left[K\left(h\right)\left(\frac{\partial h}{\partial z}-1\right)\right]$$
(6)

where t is time, min; θ is volumetric water content, mm3/mm3; h is the suction head (mm), z is the soil depth, mm; and K(h) is unsaturated hydraulic conductivity (mm/min).

The hydraulic properties for an unsaturated medium can be calculated using the van Genuchten–Mualem (Van genuchten 1980) equations:

$$\theta \left({\text{h}}\right)\text{=}\left\{\begin{array}{l}{\theta }_{r}+\frac{{\theta }_{s}-{\theta }_{r}}{{\left[1+{\left|\alpha h\right|}^{n}\right]}^{m}},h<0\\ {\theta }_{s},h\ge 0\end{array}\right.;\left(m=1-\frac{1}{n},0<m<1\right)$$
(7)
$${S}_{e}=\frac{\theta -{\theta }_{r}}{{\theta }_{s}-{\theta }_{r}}$$
(8)
$$K\left({S}_{e}\right)={K}_{s}{S}_{e}^{1/2}{\left[1-\left(1-{S}_{e}^{1/m}\right)m\right]}^{2}$$
(9)

where Se is the effective saturation; θs is the saturated water content, mm3/mm3; θr is the residual water content, mm3/mm3; Ks is the saturated hydraulic conductivity (mm/min); and α, m, and n are empirical parameters.

The numerical model assumes that the soil is homogeneous. The soil depth was set to 100 mm, which is consistent with the size of the model test. The upper boundary condition was set as the atmospheric boundary (i.e., rainfall) changing with time. The ET was set to nil because this study focuses on the infiltration process under a single rainfall event. The lower boundary condition was set as the free drainage boundary. According to the simulation calculation, the surface runoff and the maximum water storage depth on the soil surface were set. The initial condition was set in the form of the soil water content. The initial values of the hydraulic parameters were set based on laboratory measurement results. The details are mentioned in Wang et al. (2022). The inverse solution module of the Hydrus-1D program was used to calculate the optimum hydraulic parameters. It should be noted that the drainage of the green roof with a water storage layer was obtained by subtracting the storage of the water storage layer from the simulation results of a single soil layer.

Results and discussion

Hydrological response of green roofs

Rainwater retention capacity

Under four simulated rainfall conditions, the cumulative rainfall was observed to be 180 mm, and only 43.83 mm of rainwater was retained on the green roof WSL-0 (Table 1). The rainwater retention of green roof WSL-19 and WSL-25 with water storage layers exceeded 100 mm. Compared with WSL-0, the RRCs of WSL-19 and WSL-25 increased by 34% and 46%, respectively. As expected, the results show that the RRC of green roofs can be significantly improved by increasing the water storage layer. It should be pointed out that the water storage layer depth of green roofs does not represent the corresponding water storage capacity. This is related to the available water storage (i.e., water storage capacity minus current water storage) provided by ET during the dry period. Similarly, Talebi et al. (2019) believe that increasing the depth and porosity of green roof soil on rainwater retention is more efficient in a location with a high ET rate for releasing water storage.

Table 1 Rainwater retention capacity of simulated rainfall experiments
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At the beginning of rainfall, the initial drainage time of green roofs was delayed to varying degrees (Fig. 4). This was mainly caused by the available water storage provided by the green roof soil and water storage layer. After initial drainage, the drainage gradually increased with rainfall. After rainfall stops, it continued to rise and gradually stabilizes. Since the effective water storage of green roofs after initial drainage was almost zero, drainage was directly proportional to rainfall. When the initial water content was 0.1 mm3/mm3 (near the wilting point), the green roof soil with a depth of 100 mm provided approximately 25 mm of available water storage (Wang et al. 2021). The available water storage provided by the 19-mm and 25-mm water storage layers was direct under different rainfall conditions, both of which significantly reduce drainage at the bottom of green roofs. As shown in Fig. 4a and b, the cumulative rainfall was enhanced with an increase in duration, thus increasing the cumulative drainage, while the initial drainage time was consistent with the same rainfall intensity. However, for different rainfall intensities with a cumulative rainfall of 50 mm (Fig. 4b and c), the initial drainage was advanced with an increase in rainfall intensity, while the cumulative drainage is consistent. The cumulative drainage curves of green roofs vary according to the variability in rainfall intensity (Fig. 4d). The initial drainage time corresponds to the initial drainage time between the two constant rainfall tests (30 mm/h and 50 mm/h). It should be pointed out that under different rainfall conditions, the cumulative rainfall corresponding to the initial drainage time was similar. Similarly, the cumulative drainage under the condition of variable rainfall intensity was consistent with Fig. 4b and c due to the similar cumulative rainfall. The errors in cumulative drainage (Fig. 4a, b and c) may be related to the difference in the initial water content before simulated rainfall.

Fig. 4
figure 4

The relationship of bottom drainage and time of green roof models WSL-0, WSL-19 and WSL-25 under different rainfall conditions: a rainfall 30 mm/h for 60 min; b rainfall 30 mm/h for 100 min; c rainfall 50 mm/h for 60 min; and d variable rainfall intensity

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Under the condition of soil surface water storage, the RRC of green roofs depends on cumulative rainfall and available water storage of green roofs. Until the cumulative rainfall is higher than the available water storage of soil, the green roof will not produce drainage (Bettella et al. 2018). Therefore, adding an extra water storage layer can significantly improve the RRC of green roofs. Compared with the grooved plastic water storage layer and aggregate (e.g., pebbles and ceramics) water storage layer, this study added a direct water storage layer with a higher water storage capacity (Qin et al. 2016; Zhang et al. 2019). Li et al. (2019) indicated that the green roof with a 50-mm water storage layer filled with ceramics increased the RRC by 7% compared with WSL-0. Compared with WSL-0, the maximum available water storage of WSL-19 and WSL-25 increased by 76% and 100%, respectively.

Peak drainage and time delay

With the difference in rainfall intensity and duration, the characteristics of initial drainage time, drainage rate, peak drainage, and drainage time delay were significantly different. Compared with the rainfall intensity of 30 mm/h, in the case of 50 mm/h rainfall, there was an advancement in the initial drainage time of WSL-0 by approximately 5 min (Fig. 5). Similarly, with an increase in rainfall intensity from 30 mm/h to 50 mm/h, the initial drainage times of WSL-19 and WSL-25 were advanced by 26 min and 31 min, respectively (Fig. 5a, c). Under a rainfall of 30 mm/h that lasted for 100 min, WSL-19 and WSL-25 delayed the drainage time by 36 min and 50 min, respectively, compared with WSL-0 (Fig. 5b). When the rainfall lasted for 60 min, WSL-19 delayed drainage for a longer time, while WSL-25 did not produce drainage (Fig. 5a). Compared with WSL-0, WSL-19 and WSL-25 delayed drainage for 17 min and 24 min, respectively, under a rainfall intensity of 50 mm/h (Fig. 5c). The results show that the initial drainage time was advanced with an increase in rainfall intensity up to a certain point. The initial drainage time was delayed with an increase in water storage depth.

Fig. 5
figure 5

The drainage rate of green roofs under different rainfall characteristics: a rainfall 30 mm/h for 60 minutes; b rainfall 30 mm/h for 100 minutes; c rainfall 50 mm/h for 60 minutes and d variable rainfall intensity

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At a rainfall intensity of 30 mm/h, the average peak drainage rate of green roofs was 0.45 mm/min, which was close to the rainfall intensity (Fig. 5). However, the average peak drainage rate of green roofs was 0.7 mm/min under a rainfall intensity of 50 mm/h. This indicated that the peak drainage rate was mainly affected by rainfall intensity and soil saturated hydraulic conductivity. Obviously, with an increase in the water storage layer depth, the peak drainage duration of green roofs is significantly shortened. In addition, under the condition of variable rainfall intensity, the drainage time of green roofs was earlier than 30 mm/h and later than 50 mm/h. The peak drainage time was delayed by approximately 15 min. Compared with WSL-0 and WSL-19, the peak drainage rate of WSL-25 on the green roof was reduced by 0.2 mm/min. The results show that the peak drainage rate was related to the rainstorm types (i.e., storm peak time) and the RRCs of green roofs. When the storm peak period is earlier than the drainage time of green roofs, the peak drainage rate will decrease.

During rainfall, the infiltration rate of soil decreases exponentially with time and eventually tends to stabilize (Wang et al. 2014). In the unsaturated infiltration stage, the greater the rainfall intensity is, the shorter the time for the soil to reach saturation. In contrast, the longer it takes for the soil to reach saturation, the longer it takes for the initial drainage to be generated. Morbidelli et al. (2017) pointed out that the steady deep flow rates under the condition of ponding infiltration are considered the saturated hydraulic conductivity of soil. When the rainfall intensity was less than the saturated hydraulic conductivity, the infiltration rate of soil was approximately equal to the rainfall intensity (Dong et al. 2017). This means that the green roof soil can effectively reduce the peak drainage under rainstorms. Liu et al. (2021) pointed out that earlier peak rainfall intensity resulted in better peak drainage reduction, which is due to the great potential of green roof available water storage during the early rainfall stage. This shows that an additional water storage layer provides a higher available water storage for green roofs, thus delaying the drainage time and reducing the cumulative drainage and peak drainage.

The response of soil water content

Before each simulated rainfall experiment, the water storage layer was drained manually, and the subsequent experiments are all separated by 1 week. Therefore, the initial soil water content before each simulated rainfall experiment was between 0.2 and 0.25 mm3/mm3, with an average value of 0.22 mm3/mm3 (Fig. 6). With the progress of rainfall, the water content of green roof soil rapidly increased to the maximum value (i.e., θmax). For constant rainfall intensity (30 mm/h, 50 mm/h), the green roof maintains a stable θmax during rainfall. When the rainfall intensity changes, the water content will fluctuate obviously with the rainfall interval. After the rainfall stops, the water content that gradually decreases and tends to be stable was considered the WHC of the soil (approximately 0.31 mm3/mm3). This shows that the green roof soil loses its water storage capacity after reaching θmax, and the drainage was equal to the precipitation. Finally, the RRC of green roof soil depends on the WHC after rainfall stops, not the θmax. The WHC of sandy soil used by Verheijen et al. (2019) in the experiment was 0.37 mm3/mm3. The WHC of sandy soil can be increased by 60% with 20% small particle biochar. Peng et al. (2019) shows that the increase in porosity and the decrease in pore size of porous media lead to a higher WHC. Obviously, in the stage of rainfall infiltration, increasing the water storage layer has no influence on the change in the soil water content. However, the influence of evaporation of the water storage layer on the soil water supply in the upper layer of the green roof needs to be further studied.

Fig. 6
figure 6

Response of green roof water content under different rainfall conditions: a WSL-0; b WSL-19; c WSL-25

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Model calibration and validation results

The best soil hydraulic parameters were calculated by using the inverse solution module of the Hydrus-1D program. The fitting results of the hydraulic parameters obtained by the inverse solution module are shown in Table 2. The bottom drainage simulation values based on inversion parameters are in good agreement with the observed values, and NSE is 0.98 (Fig. 7a). Overall, the simulated results were consistent with the measured results in the initial drainage time and overall drainage trend. The initial drainage time of the simulated and observed results was 24 min. The observed and simulated cumulative drainage was 19.72 mm and 20.98 mm, respectively, with a relative error of 6%. Similarly, the simulated results of the water content in the middle of the soil are in good agreement with the observed results (Fig. 7b). The initial response of the water content, peak value, and water content decreased to a stable level, which maintained good consistency.

Table 2 Hydraulic parameters of soil estimated by the HYDRUS-1D inverse solution module
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Fig. 7
figure 7

Simulated results predicted by inverse solution vs. observed results under the simulated rainfall of 30 mm/h for 60 min: a Cumulative drainage; b water content

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To verify the reliability of the numerical model, another set of simulated rainfall experimental data (i.e., 30 mm/h, 100 min) for green roof models WSL-0, WSL-19, and WSL-25 was used for further verification. The results show that the simulated results of the three green roof models have a good fitting degree with the observed results, and NSE is 0.96, 0.99, and 0.98, respectively (Fig. 8a, b and c). The relative errors between the simulation results and the observation results of cumulative drainage of WSL-0, WSL-19, and WSL-25 were 3%, 0.2%, and 0.4%, respectively. The fitted curve of the soil water content was roughly consistent with the observed curve, which can reflect the increase, decrease, and stability of the soil water content (Fig. 8d, e and f). Therefore, the infiltration model of green roofs based on hydraulic parameters calculated by the inverse solution module can well reflect the changes in bottom drainage and water content of green roofs.

Fig. 8
figure 8

Verification of numerical model by different green roof models under the condition of rainfall 30 mm/h for 100 min: a, b, c are the cumulative drainage of WSL-0, WSL-19 and WSL-25, respectively; d, e, f are the water content curves of WSL-0, WSL-19 and WSL-25, respectively

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Sensitivity analysis of parameters

Sensitivity analysis of the main green roof parameters was conducted by assuming that one parameter increased by 50% while the other parameters remained unchanged (Liu et al. 2021). The most sensitive parameter of green roofs was saturated water content, and the variation in rainwater retention exceeds 40%, so there was no drainage (Fig. 9). Second, affected by the depth of the water storage layer, the rainwater retention changed by 35%, and the initial drainage time changed by 39%. In addition, the initial water content and soil depth changed the rainwater retention by 28% and 17%, respectively (Fig. 9a). However, rainfall intensity and saturated hydraulic conductivity have a slight influence on rainwater retention. It should be pointed out that the change in saturated hydraulic conductivity advances the initial drainage time by 27%. The initial water content and soil depth advance the initial drainage time by 26% and 14%, respectively (Fig. 9b). Liu et al. (2021) concluded that the initial soil water content, saturated hydraulic conductivity, and soil depth are the key parameters that affect the runoff simulation of green roofs. When the rainfall intensity was higher than the saturated hydraulic conductivity of the soil, the initial drainage time of the green roof depends on the saturated hydraulic conductivity (Peng and Stovin 2017). Therefore, the change in saturated water content was the most sensitive parameter for rainwater retention and initial drainage time. In addition to soil improvement, increasing the depth of the water storage layer was far more effective than increasing the soil depth in retaining rainwater and delaying the initial drainage time.

Fig. 9
figure 9

Sensitivity analysis of parameters: a rainwater retention and b initial drainage time

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Simulation of bottom and surface water storage depth

The impact of the bottom water storage layer

To investigate the impact of the green roof water storage layer on rainwater retention performance under rainstorm conditions. Based on the verified hydraulic model, the rainstorm corresponding to different return periods in South China was designed using Chicago storms for input into the numerical model (Fig. 3). The rainfall lasted for 1 h. The cumulative rainfall distributions in the design return period of 1-year, 5-year, 10-year, and 20-year were 47 mm, 66 mm, 74 mm, and 82 mm, respectively. Generally, after the initial drainage of the green roof, the cumulative bottom drainage increases linearly (Fig. 10). After rainfall stops, it continued to increase until the maximum drainage finally stabilizes. This was mainly caused by the green roof model, which allows soil surface water storage and soil gravity drainage. For green roofs without a water storage layer, the drainage at the bottom increases with an increase in cumulative rainfall (i.e., with an increase in return period, as shown in Fig. 10a). The RRCs of green roofs corresponding to rainfall with return periods of 1-year, 5-year, 10-year, and 20-year are 19%, 17%, 15%, and 14%, respectively. As the designed rainfall intensity was higher than the saturated hydraulic conductivity of the soil, ponding infiltration was applied in this simulation experiment (i.e., the maximum water storage on the soil surface was 50 mm). Therefore, the drainage rate at the bottom of green roofs depends on the saturated hydraulic conductivity of soil under rainstorms of different return periods (Fig. 10b). This was also the reason why the initial drainage time (i.e., 25 min) of green roofs was consistent in different return periods. It should be pointed out that after rainfall stops, the peak drainage time at the bottom of green roofs was extended by 39 min, 70 min, 87 min, and 101 min, respectively. This means that the green roof allows surface water storage, which can effectively reduce peak drainage and extend peak drainage time.

Fig. 10
figure 10

Hydrological response of green roofs with different depths of the bottom water storage layer under the condition of no surface runoff: a b no storage layer; c d 25mm depth of storage layer; e f  50mm depth of storage layer

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The RRCs of the green roof with WSL-25 in different return periods were 72%, 55%, 49%, and 45%, respectively (Fig. 10c). The initial drainage time was delayed to 75 min, which was 50 min later than that of the green roof without a water storage layer (Fig. 10d). The RRCs of the green roof with WSL-50 in different return periods were 100%, 93%, 83%, and 76%, respectively (Fig. 10e). Compared with WSL-25 and WSL-0, the average RRC of WSL-50 in different return periods increased by 33% and 71%, respectively. Similarly, compared with the green roof with WSL-0, WSL-50 delayed the drainage time by 100 min (Fig. 10f).

Under the condition of rainstorms, rainfall intensity was usually higher than soil-saturated hydraulic conductivity, which leads to surface runoff and stable infiltration. Villarreal and Bengtsson (2005) pointed out that the RRCs of green roofs may be reduced with an increase in rainfall intensity. This happens due to an increase in surface runoff. However, ponding infiltration of green roofs is produced under the boundary of enough water storage on the soil surface (e.g., 50 mm). When surface water is stored, the drainage rate at the bottom of the green roof decreases with an increase in rainfall intensity. At this time, due to the same infiltration rate, the initial drainage time of green roofs under different rainstorm conditions (rainfall intensity is greater than saturated hydraulic conductivity) almost occurs at the same time. By increasing the additional water storage capacity provided by the water storage layer, drainage is significantly reduced, and drainage time is delayed. This is consistent with previous research (Qin et al. 2016; Li et al. 2019; Zaremba et al. 2016). Li et al. (2019) pointed out that the depth of the water storage layer increased from 0 to 40 mm, and the runoff decreased from 50 to 10 mm during storm events. Qin et al. (2016) indicated that with an increasing water storage layer depth, the days of water stress and the total irrigation amount decreased. Zaremba et al. (2016) pointed out that the undrained green roof system had less runoff than the drainage system. In South China region, the RRC goal of low-impact development is defined as no less than 70%. In this case, the 100-mm soil layer and an additional 50-mm water storage layer are considered to be the optimal structural configurations to improve the RRC of green roofs.

The impact of surface water storage depth

Generally, after the initial drainage, the cumulative drainage and surface runoff of green roofs gradually increased and tended to stabilize (Fig. 11). However, the curve of the bottom drainage rising stage is slower than that of surface runoff. This was mainly because the surface runoff rate was much higher than the bottom drainage rate. In addition, the surface runoff increased with an increase in rainfall intensity (different return periods). The difference in bottom drainage was kept within 5 mm. As shown in Fig. 11a, the surface runoff in different return periods was 10 mm, 22 mm, 29 mm, and 35 mm higher than the bottom drainage, respectively. At this time, only an extra-average 15-mm water storage was retained by adding a 25-mm bottom water storage layer. With an increase in the surface water storage depth to 10 mm and 20 mm, the average bottom drainage of green roofs was increased by 28 mm and 38 mm, respectively (Fig. 11c, e). The surface runoff decreases gradually and was even lower than the bottom drainage. This means that increasing the effectiveness of the bottom water storage layer for rainwater retention is influenced by the maximum water storage depth on the soil surface. The surface runoff may be much higher than the drainage at the bottom under the rainstorm condition.

Fig. 11
figure 11

Influence of surface water storage depth on surface runoff and bottom drainage performance of green roofs: a, b under surface runoff; c, d 10 mm maximum water storage on the soil surface; e, f 20 mm maximum water storage on the soil surface

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Under the condition that there is no water storage on the soil surface, the initial surface runoff time under different rainstorm conditions is earlier than the initial drainage time, with an average of 5 min and 30 min, respectively (Fig. 11b). The surface runoff was almost direct, and the peak runoff reduction in different return periods was 19%, 13%, 12%, and 6%, respectively. The peak drainage at the bottom was at a constant low level, with a peak drainage decreasing by 81%, 86%, 88%, and 89%, respectively. When the maximum water storage capacity at the soil surface was 10 mm, the peak runoff decreases by 22%, 15%, 14%, and 12%, respectively (Fig. 11d). The initial runoff time was delayed, and the average initial runoff time was 22 min. The peak drainage at the bottom was extended by approximately 16 min on average. With an increase in the maximum water storage at the soil surface to 20 mm, the surface peak runoff decreases more significantly (Fig. 11f). The initial surface runoff time was delayed (27 min on average), and the duration of bottom peak drainage was extended. When the maximum water storage of the soil surface was 50 mm, the peak runoff in the 20-year return period was reduced by 89% (Fig. 10).

The surface runoff rate was much higher than the soil infiltration rate under rainstorm conditions. Adding a water storage layer at the bottom of the green roof may lose its effectiveness of water storage. Shafique et al. (2018a) found that if the soil becomes saturated enough, the rainwater on the green roof will overflow from the surface. It depends on the intensity and duration of rainfall. Zhao et al. (2018) indicate that under a rainfall intensity of 120 mm/h, the runoff of the rough surface is up to 79% of the total rainfall. With an increase in the maximum water storage depth on the soil surface, the reduction in runoff increases, which is more beneficial to the effectiveness of the bottom water storage layer. In this study, a maximum soil surface water storage depth of 50 mm was considered to be the optimal setting for no surface runoff under given rainstorm conditions.

Conclusion

Based on the results of the rainfall experiments and Hydrus-1D program simulations, the hydrological performance of extensive green roofs under the condition of rainstorms in different return periods was analyzed. In particular, the influence of the bottom water storage layer and surface maximum water storage depth on the rainwater retention, peak runoff, and drainage time of green roofs was analyzed. The main conclusions are as follows:

  1. 1.

    Under the condition of ponding infiltration, the RRC of green roofs mainly depends on cumulative rainfall and available water storage rather than the rainfall intensity. When the rainfall intensity was less than the permeability coefficient, the permeability is enhanced with an increasing rainfall intensity, whereas it was dependent on the permeability coefficient.

  2. 2.

    For green roofs with a certain soil material, adding a bottom water storage layer was the most sensitive parameter for rainwater retention and initial drainage time. The sensitivity of this parameter was much greater than increasing the soil depth. The water storage layer has less load and is more practical than increasing the soil depth.

  3. 3.

    Adding a bottom water storage layer can be an effective measure to improve the RRC of extensive green roofs. Under the rainstorm conditions of 1-year, 5-year, 10-year, and 20-year return periods in South China, an additional water storage layer of 50 mm deep can increase the RRC of green roofs by 100%, 93%, 83%, and 76%, respectively. In addition, the bottom water storage layer has obvious advantages in reducing peak runoff and delaying peak runoff time. In this case, the 100-mm soil layer and 50-mm water storage layer were considered the best settings.

  4. 4.

    Allowing water storage on the soil surface can effectively reduce peak runoff and delay the initial runoff time and duration. In this study, the maximum water storage of 50 mm deep on the soil surface of green roofs was considered to be the optimal setting for no surface runoff under rainstorm conditions.

However, due to the limitation of ET, the actual available water storage provided by the green roof water storage layer is usually less than the theoretical depth. Further studies are needed to analyze RRC performance under long term drying-wetting cycles considering influence of climate change.