Abstract

Green roofs are a sustainable, low-impact development technique. They can reduce peak stormwater runoff and runoff volume and improve the quality of runoff from individual buildings and developments, which can lower the risk of frequent urban flooding and improve the quality of receiving waters. Few studies have compared different types of green roof models under the same rainfall intensities; thus, in this study, the predictions of a non-linear storage reservoirs model, Storm Water Management Model (SWMM), and a physical process model (HYDRUS-1D) were discussed. Both models were compared against measured data obtained from a series of laboratory experiments, designed to represent different storm categories and rainfall events. It was concluded that the total runoff of the SWMM model is always less than that of HYDRUS-1D. The maximum flowrate of the SWMM model is more than that of HYDRUS-1D during all events.

INTRODUCTION

Green roofs are a sustainable, low-impact development (LID) technique. They are an alternative to roofs constructed from other materials (concrete, clay or slate tiles, sheet metal, thatch, etc), so they do not require additional space on a lot. They can reduce peak stormwater runoff and runoff volume and improve the quality of runoff, which can lower the risk of frequent urban floods and improve the quality of receiving waters (Versini et al. 2015).

Green roofs are typically divided into two main engineering categories, namely intensive and extensive. Intensive green roofs have deep soil layers, while extensive vegetated roofs have thin soil layers (Saadatian et al. 2013). Each green roof includes the following common elements: vegetation layer, growing media, filter fabric, drainage layer, protection layer, waterproof barrier and roof structure.

To explore the benefits of green roofs in urban runoff management, the quantitative impacts of the hydrological characteristics of green roofs have already been studied in several works based on experimental observation or modeling. Typically, quite small surfaces of experimental green roofs were instrumented to set continuous runoff and precipitation data in short periods of time (not exceeding 3 years). These data are then analyzed to study and explain the fluctuation of green roof response in terms of peak discharge and runoff volumes (Getter et al. 2007).

On the other side, some studies have attempted to simulate the hydrological response of green roofs by using adapted models. They were usually devoted to reproducing observed runoff at the experimented roof scale or to extrapolate green roof impact at the urban catchment scale (Locatelli et al. 2014; Versini et al. 2015; Castiglia Feitosa & Wilkinson 2016).

Villarreal & Bengtsson (2005) found that water retention within a green roof was dependent to a great extent on rainfall intensity; the lower the intensity the greater the retention. For a rain intensity of 0.4 mm/min and slopes with gradients of 1 in 2 and 1 in 14, the retention was 62% and 39% of the simulated precipitation, respectively, whereas for a rain intensity of 1.3 mm/min and slopes with gradients of 1 in 2 and 1 in 14, the retention was 21% and 10% of the applied precipitation, respectively. In addition, more research has focused on the observation and simulation of the hydrologic process of green roofs in the case of low rainfall (Kasmin et al. 2010; Carbone et al. 2014; Castiglia Feitosa & Wilkinson 2016). As a result, This study aims to compare the ability of a linear/non-linear storage reservoirs model (SWMM) and a physical process model (HYDRUS-1D) to predict the hydrologic behaviors of a green roof system during the same extreme heavy rain cases.

Hydrological processes of a green roof

The hydrological processes of a green roof do not include recharge of subsurface systems, as the bottom of the system consists of the roof construction and a waterproof barrier, which are impermeable (Soulis et al. 2017).

Between storms, moisture levels reduce through evaporation from the soil surface and through evapotranspiration by vegetation. During storms, rain falls on the surface of the system, starts to infiltrate from the soil surface, and becomes interflow. With gravity, the water infiltrates to the drainage layer where it is conveyed to an outlet. A similar process can occur under snowmelt conditions. Under conditions where the rain intensity does not exceed the hydraulic conductivity of the filter media, the outflow can be considered the only runoff source. If the stored water in the substrate is less than the field capacity, then there is no free runoff toward the substrate layer. Evapotranspiration (ET) dries the substrate when the stored water remains above the wilting point (Li & Babcock 2014).

Model categorization

At the spatial scale of urban areas, there are two types of models, namely building-scale and urban-scale models. Generally, there are four methods available for modeling a green roof, namely, curve methods, linear/non-linear storage reservoirs, single reservoir models and physical models. Curve methods rely on the statistical analysis of runoff collected at experimental stations. Linear/non-linear storage reservoirs treat green roofs as a combination of storage reservoirs, which generally includes a vegetation storage reservoir, subsurface storage reservoir, and transient storage reservoir. Single reservoir models depend on the water balance equation in a single reservoir (or single system) and focus on the vegetation layer and transient storage; they only consider the substrate layer. Physical models focus on representing real-world conditions and processes (Liu et al. 2017).

Examples of these various alternative modeling approaches and where they have been described in the literature are summarized in Table 1.

Table 1

Green roof stormwater retention models

Scale Modeling approach Name Related papers 
Building scale Curve methods NA Roehr & Kong (2010)  
NA Carter & Rasmussen (2006)  
Linear/non-linear storage reservoirs NA Locatelli et al. (2014)  
NA Berthier et al. (2011)  
NA Kasmin et al. (2010)  
SWMM Versini et al. (2015)  
Mathematical model Zimmer & Geiger (1997)  
One reservoir models NA Yang et al. (2015)  
NA Stovin et al. (2013)  
NA Sherrard & Jacobs (2012)  
NA Vanuytrecht et al. (2014)  
Analytical probabilistic model Zhang & Guo (2013)  
SWAM Hakimdavar et al. (2016)  
Physical models PROM Sun et al. (2013)  
HYDRUS-1D Hakimdavar et al. (2014)  
SWAP Metselaar (2012)  
SWMS_2D Palla et al. (2009)  
NA She & Pang (2010)  
Urban scale Curve methods NA Carter & Jackson (2007)  
Linear/non-linear storage reservoirs SWMM Versini et al. (2015)  
One reservoir model NA Yang et al. (2015)  
Liu et al. (2017)  
Scale Modeling approach Name Related papers 
Building scale Curve methods NA Roehr & Kong (2010)  
NA Carter & Rasmussen (2006)  
Linear/non-linear storage reservoirs NA Locatelli et al. (2014)  
NA Berthier et al. (2011)  
NA Kasmin et al. (2010)  
SWMM Versini et al. (2015)  
Mathematical model Zimmer & Geiger (1997)  
One reservoir models NA Yang et al. (2015)  
NA Stovin et al. (2013)  
NA Sherrard & Jacobs (2012)  
NA Vanuytrecht et al. (2014)  
Analytical probabilistic model Zhang & Guo (2013)  
SWAM Hakimdavar et al. (2016)  
Physical models PROM Sun et al. (2013)  
HYDRUS-1D Hakimdavar et al. (2014)  
SWAP Metselaar (2012)  
SWMS_2D Palla et al. (2009)  
NA She & Pang (2010)  
Urban scale Curve methods NA Carter & Jackson (2007)  
Linear/non-linear storage reservoirs SWMM Versini et al. (2015)  
One reservoir model NA Yang et al. (2015)  
Liu et al. (2017)  

Note: NA – not available

METHODS

The approach to compare the performance of green roofs predicted by the SWMM model and HYDRUS-1D is divided into two steps. In the first step, the rainfall–runoff model of the green roof field study site is constructed based on SWMM and HYDRUS-1D, and its specified parameters are calibrated based on observed rainfall and runoff data. In the second step, the models which have been completed in calibration and verification are used to simulate higher rainfall intensities to facilitate analysis under more rainy conditions.

Field study sites and measurements

In this study, three open-top water tanks with outflow pipes were converted into green roof test beds and subjected to various simulated rainfall conditions to provide runoff results against which to benchmark the predictions of the two numerical models. The base area of each tank was 50 cm by 50 cm and each was filled with a representative green roof media profile with a total depth of 135 mm (see Figure 1).

Figure 1

Experimental green roof tanks: (a) experimental media profile; (b) typical view of green roof tanks.

Figure 1

Experimental green roof tanks: (a) experimental media profile; (b) typical view of green roof tanks.

The outlet pipe was arranged at the bottom midline position on one side of the tank. The profile comprised a drainage layer, perlite, vermiculite and other lightweight aggregates and plants in the surface soil layer; the layers were separated by geotextiles.

In this study, rain intensities of 1 mm/min, 1.5 mm/min and 2 mm/min for a period of 30 minutes were tested to obtain the experimental data to assess the predictions from SWMM and HYDRUS-1D. Ten experiments were carried out for each rainfall intensity. In order to eliminate the uncertainty of the experimental process and improve the reliability of the paper as much as possible, we took the average value of multiple experimental results under the same rainfall intensity, and compared them with the simulated value for analysis.

The same artificial rainfall intensity was applied to each of the three tanks, the outflow hydrograph was recorded, and then different parameter combinations were explored.

The runoff volume was collected at an adjacent site, where identical modular green roof blocks were mounted atop bins fitted with pressure transducers. These transducers sampled the water depth every 2 minutes, starting at the onset of a storm event, using an automated data logger.

Evapotranspiration was ignored because the duration of rainfall in each experiment was too short for it to be an influence.

Modeling with SWMM

The Storm Water Management Model (SWMM) is a dynamic rainfall–runoff model developed by the US Environmental Protection Agency for urban/suburban areas (Versini et al. 2015). The SWMM module for modeling green roofs is a three-reservoir model which represents the vegetation storage reservoir, subsurface storage reservoir, and a routing reservoir for the drainage layer.

The vegetation storage reservoir represents the vegetation layer, which intercepts precipitation. Smax indicates its maximum capacity. The capacity of the surface storage is continuously re-established through evaporation. When Smax is exceeded, the effective precipitation Peff infiltrates into the subsurface storage.

The subsurface storage reservoir represents the substrate layer. Precipitation can be stored both in the green roof substrate and in the drainage layer. The volume is referred to as subsurface storage R. Rmax represents the maximum capacity of the substrate and drainage layer together. This can be estimated as the difference between the water content at field capacity θfc (after drainage with macropores emptied) and the permanently retained water content θwp (comparable to the permanent wilting point with the mesopores emptied). The water content in the subsurface storage is continuously reduced by evapotranspiration.

In the subsurface storage reservoir, SWMM divides the Qss into the surface runoff Qsat(t) and output discharge Qsub(t). Qsat(t) is produced when it is not infiltrating water as follows: 
formula
(1)
where fsub is the substrate porosity, representing the soil fraction where water can be stored, θ(t) is the volumetric water content at time t, and Hsub is the substrate depth.

Nsub(t) =θ(t) × Hsub represents the substrate reservoir water level at time t.

The output discharge (Qsub(t)) is produced when the water content in the substrate is greater than the field capacity as follows: 
formula
(2)
Before the output discharge (Qsub(t)) flows into the routing reservoir for the drainage layer, there is a transitional state that evaluates a small fraction Qfrac(t) of the output discharge representing the water temporarily stored in the drainage layer as follows: 
formula
(3)
where fdra is the void fraction of the drainage layer, Ndra(t) is the routing reservoir water level, and Hdra is the routing reservoir depth.
Runoff Qdra1(t) and Qdra2(t) are directly available while the capacity of the temporary water stored in the drainage layer is satisfied as follows: 
formula
(4)
 
formula
(5)

Every contribution to the total discharge (Qsat(t), Qdra1(t), and Qdra2(t)) is first routed to the outlet using a transfer function based on the Manning–Strickler equation before being summed for runoff.

Modeling with HYDRUS

The HYDRUS-1D model (Hakimdavar et al. 2014) adopts a Galerkin-type linear finite element scheme to numerically solve the one-dimensional form of the Richards equation: 
formula
(6)
where θ is the volumetric water content [L3 L−3], k(θ) is the hydraulic conductivity, z is the vertical coordinate (L, positive upward), and ψ is the tensiometer pressure potential [L].

In order to obtain an analytical expression for the unsaturated hydraulic conductivity, the van Genuchten (1980) and Mualem (1976) relationships are adopted. This model assumes that the effective saturation of the unit is equivalent to the effective saturation of the green roof substrate prior to each storm event.

This study uses HYDRUS-1D version 4.04, the combined heat and moisture transport program. The study system was simulated based on measured or estimated parameters by automated dataloggers and time domain reflectometry. The experimental soil column was divided into three mats, namely, sand, clay loam and sand.

Calibration and validation procedures

The volume of discharged storm water from the roof was assumed to be a crucial factor; therefore, the total runoff ratio (RV), Nash–Sutcliffe efficiency (NSE), and the ratio of maximum flowrate (RQM) were used through the calibration procedure. This NSE has a range of −∞ to 1.0. Values less than 0.0 indicate that the observed mean is a better predictor than the model, while a value of 1.0 shows that the model is a perfect fit. 
formula
(7)
 
formula
(8)
 
formula
(9)
where Qsim(t) = simulated flowrate, Qmea(t) = measured flowrate, Δt= time step, QAmea = average measured flowrate, QAsim = average simulated flowrate, QMsim = maximum simulated flowrate, and QMmea = maximum measured flowrate.

The runoff and rainfall of 1 mm/min and 1.5 mm/min, 2 mm/min recorded events, respectively, are used as calibration and validation data for the rainfall–runoff model of those models. The initial values for the model parameters were taken from pertinent literature (Simunek et al. 1999; Hilten et al. 2008; Burszta-Adamiak & Mrowiec 2013). The model parameters were tuned by the trial-and-error method to obtain a reasonable estimation of the measured data. The corresponding results are shown in the following Tables 2 and 3.

Table 2

Summary of calculated parameters, NSE, RV, and RQM

  Rainfall intensity Model NSE RV RQM 
Calibration 1 mm/min SWMM 0.747 0.921 0.845 
HYDRUS-1D 0.875 0.798 0.618 
Validation 1.5 mm/min SWMM 0.879 0.866 0.926 
HYDRUS-1D 0.795 0.802 0.824 
2 mm/min SWMM 0.812 0.913 1.089 
HYDRUS-1D 0.764 1.278 0.893 
  Rainfall intensity Model NSE RV RQM 
Calibration 1 mm/min SWMM 0.747 0.921 0.845 
HYDRUS-1D 0.875 0.798 0.618 
Validation 1.5 mm/min SWMM 0.879 0.866 0.926 
HYDRUS-1D 0.795 0.802 0.824 
2 mm/min SWMM 0.812 0.913 1.089 
HYDRUS-1D 0.764 1.278 0.893 
Table 3

Calibrated values of some model parameters

Model Parameters Value Unit 
SWMM Vegetation volume Fraction 0.2 – 
Top Width of Overland Flow Surface 800 
Roughness of Drainage Mat 0.1 Manning's n 
HYDRUS-1D Saturated hydraulic conductivity, Ks 4.95 mm/hour 
Shape parameter of the soil moisture retention curve, n 2.86 – 
Fitting parameter of the soil moisture retention curve, α 0.5 1/mm 
Model Parameters Value Unit 
SWMM Vegetation volume Fraction 0.2 – 
Top Width of Overland Flow Surface 800 
Roughness of Drainage Mat 0.1 Manning's n 
HYDRUS-1D Saturated hydraulic conductivity, Ks 4.95 mm/hour 
Shape parameter of the soil moisture retention curve, n 2.86 – 
Fitting parameter of the soil moisture retention curve, α 0.5 1/mm 

The results show that the calculations obtained using the rainfall–runoff model meet the general requirements of urban drainage system hydraulic modeling (Caiqiong & Jun 2016; Zahiri & Najafzadeh 2017).

RESULTS AND DISCUSSION

After calibration and validation procedures, more rainfall events were input into SWMM and HYDRUS-1D to further analyze the differences between the two models. The volume of outflow was assumed to be a crucial factor; root mean square error (RMSE), BIAS and scatter index (SI) in terms of error indicators were used for quantitative evaluation of the models (Najafzadeh 2015): 
formula
(10)
 
formula
(11)
 
formula
(12)
The complexity of hydrological phenomena and the incomplete information of hydrological prototypes often lead to the diversity or non-uniqueness of hydrological models (Xia et al. 1997).

We use a sequence , where J is a finite set or an infinite set, . and X is called the difference information sequence if and only if X has the following connotations:

  • (1)

    the greater the difference of X component values, the greater the information contained in the sequence;

  • (2)

    there is no difference in X component values, and the information contained in the sequence is zero.

Let be the set composed of finite difference information sequences with length S, where and is the index set of the sequence. If is a non-normalized sequence, an appropriate information structure operator can be found, making a normalized sequence, then is the information entropy of the differential sequence. When and only when the sequence elements are equal, the information entropy measure is the largest.

The measured runoff flowrate sequence of a green roof is selected as ., which is the standard sequence (or reference sequence). For a hydrological model , the calculated runoff flowrate sequence is .

The residuals of model and the measured sequence are, and then: 
formula
(13)
In order to evaluate the model information by using the information measure of the differential information sequence, the normalized residual order is defined as: 
formula
(14)
The information entropy information measure of the model is calculated: 
formula
(15)
In this part, the simulated flowrate by SWMM represents measured flowrate. The calculated NSE, RV, RQM, RMSE, BIAS, SI, and I(Q) are presented in Table 4. Total runoff and maximum flowrate for each event is presented in Figures 2 and 3.
Table 4

Summary of calculated parameters, NSE, RV, RQM, RMSE, BIAS, SI and I(Q)

Event Rain intensity [mm/min] NSE RV RQM RMSE BIAS SI I(Q
0.4 −0.215 0.000 0.000 0.028 0.0083 0.0009 2.357 
0.5 −1.023 0.320 0.995 0.096 0.0206 0.0009 2.354 
0.6 −1.120 1.002 0.945 0.162 −0.0001 0.0007 2.351 
0.7 −0.707 1.049 0.913 0.199 −0.005 0.0006 2.348 
0.8 0.634 1.298 0.903 0.116 −0.039 0.0002 2.353 
0.9 0.693 1.254 0.898 0.126 −0.041 0.0002 2.353 
0.649 1.259 0.885 0.156 −0.0539 0.0002 2.351 
1.1 0.826 1.026 0.800 0.124 −0.0064 0.0001 2.354 
1.2 0.821 0.802 0.859 0.139 0.0572 0.0001 2.353 
10 1.3 0.291 1.360 0.944 0.302 −0.1185 0.0003 2.341 
11 1.4 0.486 1.204 0.854 0.279 −0.0757 0.0002 2.344 
12 1.5 0.459 1.263 0.923 0.307 −0.1082 0.0002 2.341 
13 1.6 0.351 1.294 0.930 0.358 −0.1334 0.0002 2.337 
14 1.7 0.540 1.219 0.929 0.320 −0.1086 0.0002 2.341 
15 1.8 0.472 1.230 0.936 0.362 −0.1240 0.0002 2.337 
16 1.9 0.528 1.201 0.934 0.361 −0.1170 0.0002 2.338 
17 0.555 1.192 0.944 0.367 −0.1200 0.0002 2.337 
Event Rain intensity [mm/min] NSE RV RQM RMSE BIAS SI I(Q
0.4 −0.215 0.000 0.000 0.028 0.0083 0.0009 2.357 
0.5 −1.023 0.320 0.995 0.096 0.0206 0.0009 2.354 
0.6 −1.120 1.002 0.945 0.162 −0.0001 0.0007 2.351 
0.7 −0.707 1.049 0.913 0.199 −0.005 0.0006 2.348 
0.8 0.634 1.298 0.903 0.116 −0.039 0.0002 2.353 
0.9 0.693 1.254 0.898 0.126 −0.041 0.0002 2.353 
0.649 1.259 0.885 0.156 −0.0539 0.0002 2.351 
1.1 0.826 1.026 0.800 0.124 −0.0064 0.0001 2.354 
1.2 0.821 0.802 0.859 0.139 0.0572 0.0001 2.353 
10 1.3 0.291 1.360 0.944 0.302 −0.1185 0.0003 2.341 
11 1.4 0.486 1.204 0.854 0.279 −0.0757 0.0002 2.344 
12 1.5 0.459 1.263 0.923 0.307 −0.1082 0.0002 2.341 
13 1.6 0.351 1.294 0.930 0.358 −0.1334 0.0002 2.337 
14 1.7 0.540 1.219 0.929 0.320 −0.1086 0.0002 2.341 
15 1.8 0.472 1.230 0.936 0.362 −0.1240 0.0002 2.337 
16 1.9 0.528 1.201 0.934 0.361 −0.1170 0.0002 2.338 
17 0.555 1.192 0.944 0.367 −0.1200 0.0002 2.337 
Figure 2

Comparison of total runoff of the simulations (SWMM, HYDRUS-1D).

Figure 2

Comparison of total runoff of the simulations (SWMM, HYDRUS-1D).

Figure 3

Comparison of maximum flowrate of the simulations (SWMM, HYDRUS-1D).

Figure 3

Comparison of maximum flowrate of the simulations (SWMM, HYDRUS-1D).

The results displayed in Figures 2 and 3 show that no runoff appears in HYDRUS-1D when the rain intensity is less than 0.5 mm/min, and no runoff appears in SWMM when the rain intensity is less than 0.4 mm/min. In addition, the SWMM model fits well with HYDRUS-1D in relation to the overall runoff volume during 0.6–1.3 mm/min rain intensity. Between 1.3 and 2.0 mm/min rain intensity the total runoff of the SWMM model is less that of the HYDRUS-1D. In Figure 3, the maximum flowrate of the SWMM model is more than that of HYDRUS-1D during all events. These features are also reflected in the RV, RQM values listed in Table 4.

The results displayed in Table 4 show that the fitting degree of the SWMM model and HYDRUS-1D varies with the change of rainfall intensity. The SWMM model fits well with HYDRUS-1D in relation to the runoff process during 0.8–1.2 mm/min rain intensity, and the fitting is basically complete during 1.3–2.0 mm/min rain intensity. When the rain intensity is less than 0.7 mm/min, the value of NSE is negative; the SWMM model fits badly with HYDRUS-1D. These features are also reflected in the NSE, RMSE, BIAS, SI values listed in Table 4.

The information entropy information measure I(Q) is listed in Table 4. The larger values of I(Q) indicate that the model contains more information. The I(Q) of HYDRUS-1D decreases with the increase of rainfall intensity. Although they are very close, this means that HYDRUS-1D contains less information with the increase of rainfall intensity.

SENSITIVITY ANALYSIS

This study aims to analyze the sensitivity of three parameters for each model except those with clear physical meaning and definite value (see Table 5) (Rossman 2005; Wang et al. 2013).

Table 5

Rankings of sensitivities of parameters

Model Parameters Value range SN in Event 7 Sensitivity sequencing SN in Event 17 Sensitivity sequencing 
SWMM Vegetation Volume Fraction 0–0.2 15.76 23.45 
Roughness of Drainage Mat 0.1–0.4 42.01 68.99 
Top Width of Overland Flow Surface – 30.23 52.56 
HYDRUS-1D Ks – 22.15 34.33 
n – 53.27 64.33 
α – 24.62 32.45 
Model Parameters Value range SN in Event 7 Sensitivity sequencing SN in Event 17 Sensitivity sequencing 
SWMM Vegetation Volume Fraction 0–0.2 15.76 23.45 
Roughness of Drainage Mat 0.1–0.4 42.01 68.99 
Top Width of Overland Flow Surface – 30.23 52.56 
HYDRUS-1D Ks – 22.15 34.33 
n – 53.27 64.33 
α – 24.62 32.45 

It is worth noting that the Top Width of Overland Flow Surface is the width of the outflow face of each identical LID unit (in ft or m). This parameter only applies to LID processes such as Porous Pavement and Vegetative Swales that use overland flow to convey surface runoff off the unit. (The other LID processes, such as Bio-Retention Cells and Infiltration Trenches, simply spill any excess captured runoff over their berms.) In addition, whenever an LID occupies the entire subcatchment, the values assigned to the subcatchment's standard surface properties (such as imperviousness, slope, roughness, etc.) are overridden by those that pertain to the LID unit (Rossman 2005). Hence, in this study the Top Width of Overland Flow Surface replaces the subcatchment width. An initial estimate of the characteristic width is given by the subcatchment area divided by the average maximum overland flow length. The maximum overland flow length is the length of the flow path from the outlet to the furthest drainage point of the subcatchment. Maximum lengths from several different possible flow paths should be averaged. These paths should reflect slow flow, such as over pervious surfaces, more than rapid flow over pavements, for example. Adjustments should be made to the width parameter to produce good fits to measured runoff hydrographs.

Sensitivity analysis of model parameters adopted the modified Morse test method, that is, the percentage change of fixed step size was adopted, and the average value of multiple Morse coefficients was taken as the final sensitivity discrimination factor, and the calculation formula was as follows: 
formula
(16)
where SN is the sensitivity discriminating factor, Yi is the output value of the model running for the ith time, Yi+1 is the output value of the model's i + 1 run, Y0 is the initial test value of calculated results after parameter adjustment, Pi refers to the change percentage of the parameter value of the ith model operation relative to the parameter value after calibration, Pi+1 is the change percentage of the operation parameter value of the ith +1 model relative to the initial parameter value after calibration, and N is the number of model runs.

A fixed step of 10% was adopted to conduct disturbance analysis on each parameter of the model, and the values were −30%, −20%, −10%, 10%, 20% and 30% respectively. When the selected parameters of variables are changed in the calculation, other model parameters remain unchanged.

The results of the analysis indicated that Roughness of Drainage Mat is the most effective parameter for the SWMM model, and the Shape parameter of the soil moisture retention curve n is the most effective parameter for HYDRUS-1D (see Table 5).

CONCLUSIONS

Green roofs are a sustainable, LID technique. They can reduce peak stormwater runoff and runoff volume and improve the quality of runoff from individual buildings and developments, which can lower the risk of frequent urban flooding and improve the quality of receiving waters. Few studies have compared different types of green roof models under the same conditions; thus, in this study, the predictions of a non-linear storage reservoirs model, Storm Water Management Model (SWMM), and a physical process model (HYDRUS-1D) were compared against measured data obtained from a series of laboratory experiments, designed to represent different storm categories and rainfall events. After calibration and validation procedures, more rainfall events were input into SWMM and HYDRUS-1D to further analyze the differences between the two models.

While it was found that, after parameter calibration, both models can well reflect the measured data, the fitting degree of the SWMM model and HYDRUS-1D varies with the change of rainfall intensity. It is best during 0.8–1.2 mm/min rain intensity, second best during 1.3–2.0 mm/min rain intensity, and worst when the rain intensity is less than 0.7 mm/min.

The results displayed in Figures 2 and 3 show that no runoff appears in HYDRUS-1D when the rain intensity is less than 0.5 mm/min, and no runoff appears in SWMM when the rain intensity is less than 0.4 mm/min. In addition, the total runoff of the SWMM model is always less than that of HYDRUS-1D. The maximum flowrate of the SWMM model is more than that of HYDRUS-1D during all events. This requires special attention when modeling.

The information entropy information measure I(Q) of HYDRUS-1D decreases with the increase of rainfall intensity. Although they are very close, this means that HYDRUS-1D can reflect that the information in SWMM is relatively fixed and decreases with the increase of rainfall intensity. Also, the results of the sensitivity analysis indicate that Roughness of Drainage Mat is the most important parameter in the SWMM model. The Shape parameter of the soil moisture retention curve n is the most effective parameter for HYDRUS-1D.

There are two directions for further research. One is the development of a more refined physical model for better understanding hydraulic processes, and the other is the development of a simple but accurate reservoir model at an urban scale.

ACKNOWLEDGEMENTS

The authors thank Dr Kefeng Zhang for his thoughtful comments and edits. The authors also thank Kaili Shi for her guidance in photoshop.

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