Chapter VI: Conclusion remark
Chapter 3. Assessment of a green roof practice using the coupled SWMM and HYDRUS models
3.2 Materials and methods .1 Study sites
3.2.2. SWMM-H
SWMM is a useful tool to simulate urban hydrology and hydraulics (Barco et al., 2008). With the increased awareness of LID, the Environmental Protection Agency’s (EPA) SWMM (version 5.1.010) has recently been extended to include the simulation of the hydrological performance of LID practices (Khader and Montalto, 2009). In this study, the SWMM-H model was developed to improve the simulation of LID. This model consists of LID and watershed modules that can simulate LID simulation with a minimum time step of 1 min. A schematic diagram of the methodology for the SWMM-H is shown in Fig. 3.2. The watershed module based on the SWMM produces the rainfall and surface runoff from the urban subbasin (Fig. 3.2(a)). This information serves as the input for the LID module based on HYDRUS-1D. The LID module produces the soil moisture percentage and water potential, surface runoff from LID, and the water flow through the soil in the LID. The soil moisture percentage and water potential are updated depending on rainfall and surface runoff from the urban subbasin. The flow of water through the soil in the LID was calculated with variations in the soil moisture percentage and water potential. Surface runoff from LID can be produced when the water level above the surface is larger than the berm height (Fig. 3.2(b)). The surface runoff and water that flow through the soil in the LID then enter the conduit in the watershed module. The SWMM is unable to set the initial soil moisture conditions using observed values and can only set those using the wilting point, which is a model parameter (Rossman, 2016). However, it possible to set the initial conditions in the SWMM-H is using observed data. Both models used measured soil moisture data as the initial soil moisture conditions.
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Figure. 3.2. Model framework and schematic diagram of the process of the SWMM-H.
3.2.2.1. LID module– HYDRUS-1D
The LID module (Fig. 3.2(b)) of the SWMM-H used HYDRUS-1D (version 4.04) to simulate water flow in the variably saturated soil media of the LID. HYDRUS-1D was developed to solve the Richards equation following a finite element method (Šimůnek et al., 2005; Zeng et al, 2014; Tafteh and Sepaskhah, 2012; Šimůnek et al., 2008; Provenzano, 2007; Turco et al., 2017). The model could simulate surface ponding and water flows in variably saturated soils. The Richards equation governs water flow in partially saturated soil (Šimůnek et al., 2005):
∂𝜃
∂𝑡 = ∂
∂z[𝐾(ℎ) (∂ℎ
∂𝑧) + 1] (1)
where θ is the volumetric soil water content (cm3/cm3), t is the time (min), h is the soil water pressure head (cm), z is the vertical coordinate (cm), and K(h) is the unsaturated hydraulic conductivity (cm/min).
Soil water retention, θ(h), and K(h) were obtained from the Van Genuchten (1980) equations using
40
the statistical pore distribution model of Mualem (1976):
𝜃(ℎ) = 𝜃r+ 𝜃s−𝜃r
[1+(𝛼|ℎ|)𝑛]𝑚, ℎ < 0 (2)
𝜃(ℎ) = 𝜃s, ℎ ≥ 0 (3)
𝐾(ℎ) = 𝐾𝑠𝑆𝑒0.5[1 − (1 − 𝑆𝑒1/𝑚)𝑚]2 (4)
where θs is the saturated water content (cm3cm-3), θr is the residual water content (cm3cm-3), Ks is the saturated hydraulic conductivity (cm/min), m is 1-1/n, and Se is the relative saturation calculated as:
𝑆𝑒 = 𝜃−𝜃𝑟
𝜃𝑆−𝜃𝑟 (5)
Parameters α (cm-1) and n control the shape of the water retention function (Šimůnek et al., 2005).
3.2.2.2. Watershed module – stormwater management model (SWMM)
The SWMM-H model adapted the surface runoff and channel routing algorithms to simulate the stormwater runoff and drainage systems of an urban watershed, which is implemented in the SWMM (version 5.1.010) as shown in Fig. 3.2(a) (Rossman, 2005; Ghodsi et al., 2016). This model can be used to simulate the channel/pipe routing and quantity of runoff from urban drainage (Rossman, 2005; Gironás et al., 2010). This model uses the Manning’s equation to simulate flow across the sub-catchment’s surface (Rossman, 2015a).
Q =1.49
𝑛𝑠 𝑊𝑆12(𝑑 − 𝑑𝑠)5/3 (5)
where ns is the surface roughness coefficient, W is the width (m2), S is the average slope (m/m), d is the ponding depth (m), ds is the depression storage depth (m), and Q is the surface runoff (m3/s) of the sub- catchment.
The one-dimensional Saint-Venant equation was used to express the flow routing (Peterson and Wicks, 2006; Rossman, 2015b):
∂𝑦
∂x+v
𝑔
∂v
∂x+1
𝑔
∂v
∂t = 𝑠𝑜− 𝑠𝑓 (6)
∂𝑄𝑟
∂x +∂𝐴
∂t = 0 (7)
where y is the depth (m) and v is the velocity of the water (m/s), x is the longitudinal distance (m), t is time (min), sf is the friction slope (m/m), so is the channel slope (m/m), A is the area of the flow cross- section (m2), and Qr is the flow-through routing (m3/s). The friction slope, sf, was calculated using
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Manning’s equation (Peterson and Wicks, 2006):
𝑠𝑓 = 1 𝑄2
𝑛𝑟2𝐴2𝑅4/3 (8)
where nr is the surface roughness coefficient of the conduit, and R is the hydraulic radius of the channel (m).
3.3. Parameter estimation
The SWMM-H uses α, n, Ks, θs, and θr in equations (3) and (4) as soil hydraulic parameters (Table 3.1). The measurement of these parameters is relatively time-consuming and expensive (Maqsoud et al., 2007). Pedotransfer functions (PTFs) have been developed as empirical relationships to estimate van Genuchten hydraulic parameters from readily available soil data, such as its textural composition and porosity (Wösten et al., 2001). PTFs have been developed for both natural and engineered soils, and they differ depending on the database used for their development and the type of regression equations used in them (Wösten et al., 2001). Table 3.2 contains two PTFs that are commonly used with engineered soils.
Both PTFs are implemented in the SWMM-H. Table 3.2 exhibits results for the pedotransfer functions of set 1 from Table 3.3. The estimates for set 2 in Table 3.2 were similar to those for set 1.
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Table 3.1. Parameters of the Van Genuchten and PTF methods.
Method Parameters Description
Van Genuchten
𝜃r Residual water content (cm/cm) 𝜃s Saturated water content (cm/cm)
𝛼 Empirical value for shape of water retention curve 𝑛 Empirical value for shape of water retention curve 𝐾𝑠 Saturated Hydraulic conductivity (cm/min)
PTF
𝐷10 The soil particle diameter corresponding to 10% passing on the cumulative grain-size distribution (Maqsoud et al., 2012)
𝐷60 The soil particle diameter corresponding to 60% passing on the cumulative grain-size distribution (Maqsoud et al., 2012)
𝑒 Porosity
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Table 3.2. Equations used to estimate the van Genuchten parameters from readily available engineered soil data.
1/α n Reference Ks Reference
Set 1 19.57 [ 0.75 𝑒𝐷101.17 log (𝐷60
𝐷10) + 1 ]
2.8E−03/D60
1.94(D10)
−9.19/( 0.75 𝑒𝐷101.17 log(𝐷60
𝐷10)+1
)Maqsoud et al., 2007
𝑔
ν6 ∙ 10−4[1 + 10[0.255 (1 + 0.83
𝐷60 𝐷10)
− 0.26](𝐷10)2
Hazen, 1892
Set 2 72 [0.11D60/𝐷10 𝑒𝐷10 ]
(−18/ 0.75 𝑒𝐷101.17 log(𝐷60
𝐷10)+1)
7.3 [𝐷10
𝐷600.11𝐷60𝐷60/𝐷10 𝑒𝐷10 ]
−0.27
Maqsoud et al., 2012
𝑔 ν8.3
∙ 10−3
[
(0.255 (1 + 0.83
𝐷60 𝐷10))
3
(1 − 0.255 (1 + 0.83
𝐷60 𝐷10))
2
]
(𝐷10Kozeny, 1927 )2
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Table 3.3. Soil properties classified by soil texture for SWMM-H.
Texture class Residual saturation (θr)
Porosity (θ)
Saturated Hydraulic
Conductivity, Ks (cm/min) n α (1/cm)
Sand 0.045 0.43 0.495 2.68 0.035
Loamy sand 0.057 0.41 0.243 2.28 0.034
Sandy loam 0.065 0.41 0.073 1.89 0.026
Silt loam 0.067 0.45 0.0075 1.41 0.02
Sandy clay 0.1 0.38 0.002 1.23 0.027
Clay 0.068 0.38 0.003 1.09 0.01
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Using parameters D10 and D60 in the PTFs, the SWMM-H allowed the identification of van Genuchten parameter values close to those obtained from HYDRUS for each of textural classes. The D10 and D60 parameters of the pedotransfer functions were estimated using the pattern search algorithm (Lewis and Virginia, 2002) in MATLAB (MathWorks, Inc.). Pattern search is a global optimization method that can determine an optimal point with a systematic direct search method (Sahu et al., 2015).
This method has been demonstrated to be effective for finding an optimal parameter set using the time series data (Cho et al., 2011; Lewis and Virginia, 2002; Baek et al., 2015; Park et al., 2015). The flow- associated parameters that were used to simulate water movement in the urban subbasin were also optimized using the pattern search algorithm.
3.2.4 Performance evaluation
3.2.4.1. Model accuracy and model selection
The root mean square error (RMSE) and the ratio of RMSE to the observed standard deviation ratio (RSR) (Chu and Shirmohammadi, 2004; Singh et al., 2004) were used to compare the accuracies of the two models for predicting soil moisture in the pilot-scale green roof system (Moriasi et al., 2007).
RMSE = [√[∑ (𝑌𝑖
𝑜𝑏𝑠−𝑌𝑖𝑠𝑖𝑚)2
𝑛𝑖=1 ]
𝑛 ] (9)
RSR =
[√∑𝑛𝑖=1(𝑌𝑖𝑜𝑏𝑠−𝑌𝑖𝑠𝑖𝑚)2]
[√∑𝑛𝑖=1(𝑌𝑖𝑜𝑏𝑠−𝑌𝑚𝑒𝑎𝑛)2]
(10)
where 𝑌𝑖𝑜𝑏𝑠 is the ith observation, 𝑌𝑖𝑠𝑖𝑚 is the ith simulated data, 𝑌𝑚𝑒𝑎𝑛 is the average of the observed values, and n is the total number of observed values.
We calculated the Akaike information criteria (AIC), and considered the discrepancies between the simulations and observations and the number of parameters to provide model selection information (Akaike, 1973; Snipes and Taylor, 2014), as our study defined the wilting point as the initial soil moisture of the SWMM. This is a powerful method that can be used to select the “best model” based on the lowest AIC score (Snipes and Taylor, 2014). We applied the five parameters to calculate the AIC scores without the wilting point. AIC was calculated as:
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AIC = n × ln (𝑅𝑆𝑆
𝑛 ) + 2 × 𝐾 (11)
RSS = ∑𝑛𝑖=1(𝑌𝑖𝑜𝑏𝑠− 𝑌𝑖𝑠𝑖𝑚)2 (12) where K is the number of parameters.
3.2.4.2 Sensitivity analysis
The sensitivity of the SWMM-H was analyzed using the Morris method (Morris et al., 1994), which has been demonstrated to be useful for capturing the effect of interactions between several parameters for nonlinear models (Campolongo and Braddock, 1999; Saltelli et al, 2008; Morris et al., 2014). The elementary effects (EEs) can be expressed as follows (Morris et al., 2014):
EEi = [𝑌̅(𝑋1,𝑋2,….,𝑋𝑖−1,𝑋𝑖+Δ,…𝑋𝑘)−𝑌(𝑋1,𝑋2,…,𝑋𝑘)]
Δ (13)
where 𝑌̅ is the new outcome, Y is the original outcome, and Δ is the increase depending on the range of Xi. The mean and standard deviation of the elementary effect values (EEs) indicate the extent to which a parameter influences the model output and level of interaction between parameters (Saltelli et al., 2008).
A detailed explanation of the Morris method can be found in Morris et al. (2014) and Saltelli et al. (2008).
The ranges of the parameters for the auto calibration and sensitivity analysis of SWMM-H and SWMM were obtained from previous literature (Rawls et al., 1982; Schaap et al., 2001; Rossman, 2015; Simunek et al., 2005) (Table 3.3). In this study, we used the SAFE toolbox (sensitivity analysis for everybody) in MATLAB (MathWorks, Inc.), which was developed by Pianosi et al. (2015).
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Table 3.3. Ranges of model parameters for sensitivity analysis and auto-calibration, and optimized parameter values.
* SWMM used Wilting point as initial soil moisture. Thus, Wilting point was defined based on observed soil moisture.
Model Parameters Description Min Max Value
SWMM-H
𝜃r Residual water content (cm/cm) 0.05 0.15 0.12 𝜃s Saturated water content (cm/cm) 0.32 0.48 0.33
𝛼 Empirical value for shape of water retention
curve 0.01 0.138 0.013
𝑛 Empirical value for shape of water retention
curve 1.05 2.5 1.13
𝐾𝑠 Saturated Hydraulic conductivity (cm/min) 0.001 0.35 0.15
SWMM
∅ Porosity 0.32 0.6 0.39
𝜃FC Field capacity 0.3 0.5 0.33
𝜃𝑊𝑃 Wilting point 0.05 0.3 *0.22(Calibration),
0.29(Validation) 𝐾𝑠 Saturated Hydraulic conductivity (cm/min) 0.001 0.35 0.15
K-slope Percolation parameter 30 55 50
ψ Suction head (cm) 5.08 10.16 7.09
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3.2.5. Scenario analysis
3.2.5.1. Changes in design factors for a green roof system
We conducted scenario analysis for an urban subbasin to evaluate the performance of field-scale green roof systems in the SWMM and SWMM-H. The green roof modules of the two models developed using pilot-scale data were tested using two sub-scenarios: (1) expanding application areas by 10%, 30%, 50%, and 70% of the impervious areas, and (2) changing the soil types between sand, loamy sand, sandy loam, silt loam, sandy clay, and clay.
3.2.5.2 Changes in rainfall patterns
The relationship between rainfall intensity, duration, and frequency (IDF) was used to develop rainfall scenarios for analyzing the effect of a green roof on stormwater parameters. This method has been employed to assess the performance of best management practices (BMP) and LID facilities (Guo and Adams, 1998; Park et al., 2013; Pochwat et al., 2017). Here, we used the design storm of a two-year return period to simulate the green roof LID. The return period was applied and recommended as a representative rainfall event (NCHRP, 2006; Zhan and Chui., 2016; Gilroy and McCuen, 2009). As the temporal rainfall distribution was the essential element of rainfall scenarios, we adapted Huff’s method (Huff, 1967) to analyze the temporal changes in rainfall intensity and generate the temporal rainfall distribution (Huff, 1967, Azli and Rao, 2010; Baek et al., 2015).
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3.3 Results and Discussion 3.3.1. Model sensitivity analysis
The sensitivity results of the LID module in the SWMM are presented in Fig. 3.3(a). Overall, the sensitivity of SWMM exhibited a linear relationship between the mean and standard deviation of the EEs, as defined in Eq. (13). The parameters with larger mean EEs presented larger standard deviations. The standard deviations and means of the EE values of field capacity and porosity were larger than those of other parameters. These parameters significantly influenced the model output and interacted with other parameters. Field capacity was used as a threshold value to determine whether the water in a LID system can flow (Rossman, 2016). Porosity was used to calculate infiltration based on the modified Green-Ampt equation (Mein and Larson 1973; Rossman, 2016). In contrast, the influence of the suction head parameter on the model output and its interaction with other parameters was the lowest.
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Fig. 3.3. Sensitivity of LID modules in the (a) SWMM and (b) SWMM-H
Figure 3.3(b) presents the mean and standard deviation of the EEs in the SWMM-H. The sensitivity analysis of the SWMM-H exhibited a linear relationship between the standard deviation and mean of
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EEs. The standard deviation and mean EEs of Ks and n were larger than those of other parameters; the values of these parametersgreatly influenced the model output and interacted with other parameters. The user should consider these parameters when running the SWMM-H. Parameter n is present in the power law term for the calculations of water retention and unsaturated hydraulic conductivity according to Eqs (3) and (4). As this parameter was involved in shaping the water retention and hydraulic conductivity curves, this suggests that the water movement in the soil profile was sensitive to the water retention and hydraulic conductivity curvatures (Inoue et al., 1998; Rocha et al., 2006). Ks was an essential element that affected water movement and influenced the calculation of unsaturated hydraulic conductivity according to Eq. (4). Rocha et al (2006) and Abbasi et al. (2003) also noted that n and Ks were influential parameters in the Richard equation (Eq. 1). Parameters α and θr had little effect on model output.
Figure 3.4 shows the sensitivity of the PTF parameters to the Van Genuchten parameters: 1/α, n, and Ks. In set 1 of the PTFs, the EE mean and standard deviation values of D10 were the highest in the n and Ks plots, while D60 exhibits the highest mean and standard deviation of EEs in the 1/α plot. These results indicate that D10 greatly influences n and Ks and D60 influences 1/α. The sensitivity of set 2 is similar to that of set 1.
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Fig. 3.4. Sensitivity of the PTF parameters for set 1. The plots in the standard deviations vs. mean values of EEs for the following parameters: 1/a, n, and saturated hydraulic conductivity (Ks).
3.3.2. Comparison of module performance in the pilot-scale green roof system
The observed and simulated soil moisture time series are presented in Fig. 3.5. The observed data of the events on 1 July and 3 July, 2016 were used to calibrate and validate both models. The initial soil moisture values for calibration and validation were set at 0.22 and 0.29, respectively, based on the observed soil moisture. The rainfall accumulated during both events was 57.7 and 25.9 mm, respectively. During calibration, both models overestimated the soil moisture, and the SWMM overestimated the value to a greater extent than SWMM-H. During validation, the soil moisture simulated by SWMM-H was close to the observed value, while the SWMM still overestimated the parameter. The optimal parameters of the SWMM-H and SWMM are presented in Table 3.3. From 01:00 AM to 12:00 PM on 1 July, there was no
53
significant variability in the soil moisture presented by the SWMM-H and SWMM. After the rainfall events on 1 July ended, the soil moisture presented by the SWMM-H decreased slowly as the model’s values of n and α were small, which resulted in a gradual change in soil moisture (Hodnett and Tomasella, 2002). The soil moisture presented by the SWMM simulation cannot fall below that of the field capacity (0.33; Table 3.3). This is in accordance with the concept of field capacity related to water movement (Rossman, 2016). From 1:00 AM to 12:00 PM on July 3, the soil moisture presented by the SWMM-H decreased slightly, while that of the SWMM was retained. In the SWMM-H, soil moisture may decrease due to the flow of soil water generated when the soil water potential was below the gravity head (Blum et al., 2001; Radcliffe and Simunek, 2010). The soil moisture presented by the SWMM cannot decrease below the field capacity, as was also the case on July 1, 2016. The RMSE values of the SWMM-H were 0.01 and 0.007 (m3/m3) for the calibration and validation steps, respectively, while those for SWMM were 0.02 and 0.012 (m3/m3). The RMSE values of the SWMM were two times higher than those of the SWMM-H. The RSR values of the SWMM-H in the calibration and validation steps were below 0.6, which is within the “good” performance range (0 to 0.6) proposed by Moriasi et al. (2007). However, the RSR values obtained by SWMM exceeded 0.70, suggesting that the model’s performance was
“unsatisfactory.” According to the RMSE and RSR, the ability of the SWMM-H to simulate soil moisture was superior for both the calibration and validation steps. The results of the AIC analysis are presented in Table 3.4. The model with the lowest AIC score was considered as the best model for the given data (Snipes and Taylor, 2014). In the calibration and validations steps, the AIC scores of SWMM-H were - 1307.07 and -1409.08, while those for SWMM were -1108.84 and -1254.93, respectively. The AIC score of the SWMM-H was lower than that of the SWMM, indicating that it is the better model (Wagenmakers and Farrel, 2004).
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Figure 3.5. Comparison of the observed and predicted soil moisture during the events on July 1 (a) and July 3, 2016 at the pilot-scale green roof; gray areas represent the observed soil moisture with a measurement error of ±3%, and the black and dashed lines indicate the soil moisture predicted by the SWMM-H and SWMM, respectively
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Table 3.4. Results of AIC analysis for determining SWMM-H and SWMM.
Model *K Calibration Validation
RSS AIC RSS AIC
SWMM-H 5 0.0143 -1307.0787 0.0070 -1409.0877
SWMM 5 0.0572 -1108.8386 0.0206 -1254.9347
* K = the number of parameters for model
Figure 3.6 shows the temporal variations in discharge from the pilot-scale green roof system during the events on July 1 and July 3, 2016. The peak flow from SWMM-H was greater than that from SWMM because the SWMM-H presented high flows when the soil was saturated. From 20:00 PM to 23:00 PM on July 3, the discharge predicted by the SWMM was more sensitive to rainfall than that predicted by the SWMM-H because the soil moisture of SWMM reached field capacity. The SWMM can only generate water movement in soil if the soil moisture exceeded the field capacity, while the SWMM-H can generate water movement based on the soil water potential without considering field capacity (Rossman, 2016). This discrepancy is due to the different approaches for simulating water movement in the soil profile. The SWMM-H was based on the numerical simulation of water flow in a variably saturated soil from the HYDRUS model (Šimůnek et al., 2005), while the SWMM used the simplified flow equations for simulating LID (Rossman, 2016). Thus, the SWMM-H model could consider the water pressure and fluxes in soil in addition to its moisture content, which enables the SWMM-H to reasonably simulate the LID system. Figure 3.7 shows the spatiotemporal patterns of soil moisture simulated by the SWMM-H for two events. The soil moisture in each layer varied according to rainfall patterns. For the rainfall event on July 1, the rate of vertical change in soil moisture was relatively slow during the early stages compared to the event on 07/03/2016. This may be attributed to the lower initial soil moisture values on July 1 than those on July 3. After the rainfall ended on July 1, 2016, the soil moisture decreased over time (Fig. 3.5(a)). However, Fig. 3.7(b) shows that the fluctuations in the moisture of each soil layer on July 3 were greater than those on July 1, 2016. This was due to the relatively high variability in rainfall patterns on July 3, 2016.
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Fig. 3.6. Comparison of the predicted discharge from the pilot-scale green roof system between the SWMM-H and SWMM during the events on July 1 (a) and July 3, 2016 (b); the red and dashed lines indicate the discharge predicted by the SWMM-H and SWMM, respectively.