A Simple Modelling of Green Roof Hydrological Performance Using Response Surface Methodology
Salinah Dullah1*, Jane Ann Jumi1, Hidayati Asrah1, Siti Jahara Matlan1
1 Faculty of Engineering, University Malaysia Sabah, Kota Kinabalu, Malaysia
*Corresponding Author: [email protected]
Accepted: 15 October 2022 | Published: 1 November 2022
DOI:https://doi.org/10.55057/ajfas.2022.3.3.4
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Abstract: Response Surface Methodology is an optimization tool used for modelling works and has been widely used for modelling, optimizing, and identifying the interrelationship between input parameters and output variables. However, it has yet to be discovered as a tool for modelling green roof performance. This paper aims to explore the feasibility of Response Surface Methodology in Minitab to investigate the green roof hydrological performance in terms of peak runoff, peak attenuation, and water retention. In this study, Response Surface Methodology is used to identify model equations to predict hydrological performance of green roof, as well as to investigate the relationship between green roof slope, water absorption of waste material and water absorption of natural fibre on the hydrological performance of green roof system. The findings showed that the generated mathematical model equations can forecast the peak runoff, peak attenuation, and water retention of a green roof system. The results of the relationship between the input parameters and the output variables are shown using 2D contour plot and surface plot. The generated 2D contour plot and surface plot revealed that the input parameters have significant impact on the peak runoff, peak attenuation, and water retention of a green roof system.
Keywords: green roof, response surface methodology, hydrological performance
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1. Introduction
Topics of interest in many countries nowadays are climate change, scarcity of natural energy resources and urbanization (Shafique, et al., 2013; Cascone, 2019). Thus, the need to adopt sustainability as a centre in urban development has been widely implemented (Siew et al., 2019).
In Malaysia, green technology has been introduced to meet with the needs for environmental sustainability (Fauzi et al., 2013). Efforts have been carried out to rehabilitate greenery in developing cities, however it is not sufficient due to the limited spaces in the cities. This ultimately leads to the construction of a green rooftop on a building (Siew, et al., 2019). Green roof is a roof implanted with vegetation on it, partially or completely. Green roof, in general, consists of several layers where its top is a vegetation layer followed by substrate layer, filter layer, drainage layer, insulation layer (anti- root and waterproof membrane) and the bottom is structural layer (Kirdoc
& Tokuc, 2019). Green roof hydrological efficiency is affected by both physical properties and weather conditions (Li & Babcock, 2013; Asman, 2018) stated that one of the factors influencing
the probability of a typical roof transforming into a green roof is the slope. If the roof slope rises, so does the amount of runoff and the peak flow reduction (Li & Babcock, 2013). However, the impact of runoff retention can be seen with the influence of roof slopes combined with other factors such as the nature of green roof layers and the presence or absence of various types of drainage materials (Asman, 2018).
The testing for optimizing the hydrological performance of green roof have been done through laboratory testing and modelling works over the years. However, there are certain limitations when conducting laboratory testing which are costly, tedious and time consuming. The probability of gathering materials could also be hard because it is not certain whether the materials needed for the green roof experiment will always be available. In a paper by Ewadh (2020), it stated that the best prediction on the parameter optimization could be provided through RSM. Its statistical modelling prediction could also reduce massive laboratorial work. However, the application of RSM in modelling green roof performance have yet been found. Therefore, in this paper, RSM in Minitab software was used to identify the model equations to be used in predicting green roof hydrological performance. The relationship between green roof slope, water absorption of waste material and water absorption of natural fibre on the hydrological performance of green roof was also investigated.
2. Methodology
In this study, data from Asman (2018) were selected as the experimental result to develop the RSM models. Twenty-seven (27) experimental data were used in this study. The input parameters considered in this study were green roof slope, water absorption of waste materials (WA(WM)), and water absorption of natural fibre (WA(NF)) while the investigated outputs are the hydrological performance of green roof which are peak runoff (PR), peak attenuation (PA) and water retention (WR). Table 1 shows a series of data sets used for RSM modelling of green roof in this research.
The Central Composite Design (CCD) method was chosen to develop the RSM model. CCD requires three types of points: centre points, axial points and cube points that come from the factorial design. The alpha number, α, used in CCD is α = 0.05 and a full quadratic model was applied for each response. The abbreviations used in Table 1 are as follows:
i. OPSSF (oil palm shell – sugarcane fibre) ii. OPSOPF (oil palm shell – oil palm fibre) iii. OPSCF (oil palm shell – coconut fibre) iv. PFSF (polyfoam – sugarcane fibre)
v. PFOPF (polyfoam – oil palm fibre) vi. PFCF (polyfoam – coconut fibre) vii. RCSF (rubber crumb – sugarcane fibre) viii. RCOPF (rubber crumb – oil palm fibre)
ix. RCCF (rubber crumb – coconut fibre)
Table 1: Details of data used in modelling
Materials Slope (%) WA(WM) (%) WA(NF) (%) PR (mm) PA (mm) WR (mm)
OPSSF 0 8.87 215 4.04 13.56 26.07
OPSOPF 0 8.87 185.5 2.95 14.65 36.32
OPSCF 0 8.87 176 2.72 14.88 38.34
PFSF 0 0.38 215 3.89 11.38 28.06
PFOPF 0 0.38 185.5 2.56 15.04 40.01
PFCF 0 0.38 176 2.41 15.19 41.39
RCSF 0 3.37 215 3.11 13.71 36.22
RCOPF 0 3.37 185.5 1.09 16.51 43.2
RCCF 0 3.37 176 0.91 16.69 43.54
OPSSF 2 8.87 215 6.29 11.31 22.97
OPSOPF 2 8.87 185.5 5.75 11.85 26.3
OPSCF 2 8.87 176 5.05 12.55 28.14
PFSF 2 0.38 215 5.44 12.16 23.68
PFOPF 2 0.38 185.5 4.04 13.56 29.05
PFCF 2 0.38 176 3.65 13.95 31.66
RCSF 2 3.37 215 5.28 12.32 26.15
RCOPF 2 3.37 185.5 3.89 13.71 31.56
RCCF 2 3.37 176 2.18 15.42 38.64
OPSSF 6 8.87 215 7.77 9.83 15.96
OPSOPF 6 8.87 185.5 6.76 10.84 19.57
OPSCF 6 8.87 176 6.32 11.28 28.38
PFSF 6 0.38 215 6.6 9.44 18.99
PFOPF 6 0.38 185.5 6.22 11.38 25.95
PFCF 6 0.38 176 6.17 11.43 28.38
RCSF 6 3.37 215 5.59 12.01 26.09
RCOPF 6 3.37 185.5 5.75 11.85 27.13
RCCF 6 3.37 176 4.74 12.86 33.5
Table 2: Factor and factors level adopted for RSM Factors Code Factors Level
Low High
Slope A 0 6
WA(WM) B 0.38 8.87
WA(NF) C 176 215
Analysis of Variance (ANOVA) was used to assess the efficacy of the experimental parameters.
The test parameters on the test outcomes are indicated by the P-values from the analysis. If the P- value found is less than 0.05 (P<0.05), the parameter is known as statically significant. If the P- value is more than 0.05 (P>0.05), the parameter is considered statically insignificant. The projected peak runoff, peak attenuation and water retention are calculated using these mathematical formulae. In terms of coded factors, Eqn. 1 depicts the entire quadratic model.
𝑌 = 𝐵0 + 𝐵1A + 𝐵2B + 𝐵3 C + 𝐵11𝐴2 + 𝐵22𝐵2 + 𝐵33𝐶2 + 𝐵12AB + 𝐵13AC + 𝐵23BC (1)
where,
𝑌 = Predicted response, 𝐵0 = Intercept,
𝐵1, 𝐵2, 𝐵3 = Interaction effect coefficient, 𝐵12, 𝐵13, 𝐵23 = Quadratic effect coefficient, A, B, C = Factors or independent variables.
Regression analysis was then performed using plotted fitted line of projected value versus experimental value obtained by the programme. The graph is used to calculate the R-squared value.
The stronger the model, the closer the R- squared number is to 1. The relationship between input parameters for each of the output variables will be shown using 2D contour and surface plots, developed by Minitab. In the 2D contour plots, the darker the colour, the higher the output value, while the lighter the colour, the lower the output value. The relationship for the input parameters is as follows:
(i) Relationship between slope and water absorption of waste materials
(ii) Relationship between slope and water absorption of natural fibre
(iii) Relationship between water absorption of waste materials and water absorption of natural fibre
The graph created by Minitab shows the maximum and minimum slope, water absorption of waste materials, and water absorption of natural fibre that led to minimum and maximum peak runoff, peak attenuation, and water retention of green roof.
3. Results and Discussions
3.1 Model Verification Analysis of Variance (ANOVA)
The importance of variables is determined using ANOVA findings. The F-ratio is used to calculate the importance of the components. It includes a percent P-value, which is defined as the significant rate of the input parameters on each of the output variables which are peak runoff, peak attenuation, and water retention.
a. Peak runoff
ANOVA results provided by the Minitab software for peak runoff are shown in Table 3. The results demonstrate that the linear influence for all input parameters (slope, water absorption of waste materials and waste absorption of natural fibre) is statically significant to peak runoff variables (P<0.05). In the quadratic form, both input parameters of slope and water absorption of waste materials are statically significant to the peak runoff, except for the parameter of waste absorption of natural fibre, P=0.403. In the 2-way interaction, the significance for all the input parameters is opposite to the significance shown in the model form (P>0.05). Generally, the overall ANOVA findings suggest that the primary factors that led to peak runoff is the linear effect of slope, water absorption of waste materials, and waste absorption of natural fibre showing the lowest P-value at 0.000.
Table 3: ANOVA for peak runoff using RSM Model
Source P-Value
Model 0.000
Linear 0.000
Slope 0.000
WA(WM) 0.004
WA(NF) 0.000
Square 0.000
Slope*Slope 0.001
WA(WM)*WA(WM) 0.000
WA(NF)*WA(NF) 0.403
2-Way Interaction 0.262
Slope* WA(WM) 0.819
Slope* WA(NF) 0.054
WA(WM)* WA(NF) 0.856
b. Peak attenuation
ANOVA results provided by the Minitab software for peak attenuation are shown in Table 4.
The results demonstrate that the linear influence for input parameters of slope and waste absorption of natural fibre is statically significant to peak attenuation variables (P<0.05), whereas the parameter of water absorption of waste material (P=0.500) is statically insignificant to peak attenuation (P>0.05). In the quadratic form, it can be P-value for WA(WM)*WA(NF) is statically significant to peak attenuation, while the input parameters of slope (P=0.065) and water absorption of natural fibre (P=0.885) are statically insignificant to the peak attenuation (P>0.05). In the 2-way interaction, the P-value for all interaction are statically insignificant to the peak attenuation (P>0.05). Therefore, the ANOVA result determine that the primary factors that led to peak attenuation is the linear effect of slope, and waste absorption of natural fibre showing the lowest P-value at 0.000.
Table 4: ANOVA for peak attenuation using RSM model
Source P-Value
Model 0.000
Linear 0.000
Slope 0.000
WA(WM) 0.500
WA(NF) 0.000
Square 0.000
Slope*Slope 0.065
WA(WM)*WA(WM) 0.000
WA(NF)*WA(NF) 0.885
2-Way Interaction 0.071
Slope* WA(WM) 0.716
Slope* WA(NF) 0.057
WA(WM)* WA(NF) 0.058
c. Water Retention
ANOVA results provided by the Minitab software for water retention are shown in Table 5. The results show that the linear influence all input parameters (slope, water absorption of waste materials, and waste absorption of natural fibre) is statically significant to water retention variables (P<0.05). In the quadratic form, it can be seen in the table that only the p-value for WA(WM)* WA(NF) (P=0.169) is statically insignificant to water retention, while the input parameters of slope and water absorption of natural fibre are statically insignificant to the water retention (p<0.05). In the 2-way interaction, the P-value for all interaction are statically insignificant to the water retention (P>0.05). Consequently, based on the ANOVA result, it shows that the main factor that led to water retention is the linear effect of slope, water absorption of waste materials, and waste absorption of natural fibre showing the lowest P-value
at 0.000.
Table 5: ANOVA for water retention using RSM model
Source P-Value
Model 0.000
Linear 0.000
Slope 0.000
WA(WM) 0.014
WA(NF) 0.000
Square 0.000
Slope*Slope 0.000
WA(WM)*WA(WM) 0.000
WA(NF)*WA(NF) 0.169
2-Way Interaction 0.781
Slope* WA(WM) 0.865
Slope* WA(NF) 0.337
WA(WM)* WA(NF) 0.782
3.2 Mathematical Equations
A mathematical equation model for the output variable was generated by Minitab and by changing the input values, the model will forecast the hydrological properties of green roofs.
The formulas used to forecast the recession value are Eqn. (2), (3), and (4) for peak runoff, peak attenuation, and water retention, respectively.
𝑃𝑒𝑎𝑘 𝑟𝑢𝑛𝑜𝑓𝑓 = −29.4 + 2.016A − 0.541B + 0.282C − 0.0992𝐴2 + 0.0729𝐵2− 0.000588𝐶2 + 0.00230AB
− 0.00434AC − 0.00027BC (2)
𝑃𝑒𝑎𝑘 𝑎𝑡𝑡𝑒𝑛𝑢𝑎𝑡𝑖𝑜𝑛 = 35.7 − 2.053A − 0.033B − 0.139C + 0.0632𝐴2 − 0.0847𝐵2 + 0.000137𝐶2 − 0.0050AB + 0.00586AC + 0.00413BC
(3)
𝑊𝑎𝑡𝑒𝑟 𝑟𝑒𝑡𝑒𝑛𝑡𝑖𝑜𝑛 = −213 + 7.05𝐴 − 2.30𝐵 + 2.07𝐶 − 0.536𝐴2 + 0.3222𝐵2− 0.00457𝐶2 + 0.0079𝐴𝐵 − 0.00960𝐴𝐶 − 0.00194𝐵𝐶
(4)
Table 6 shows that the highest error in the predicted response from the equation for peak runoff is 0.6141% which is when rubber crumb and sugarcane fibre (RCSF) were used as drainage and filter layer, respectively, at a slope of 2%. On the other hand, the lowest error is -0.8242%
which is when rubber crumb and coconut fibre (RCCF) were used as materials for the drainage layer and filter layer in the green roof system, at a slope of 2%.
Table 6: Comparison of predicted and actual value for peak runoff Materials Slope
(%)
Water absorption of waste material (%)
Water absorption of natural fibres (%)
Peak runoff (mm)
Error (%) Actual Predicted
OPSSF 0 8.87 215.00 4.04 4.4908 -0.4508
OPSOPF 0 8.87 185.50 2.95 3.1872 -0.2372
OPSCF 0 8.87 176.00 2.72 2.5494 0.1706
PFSF 0 0.38 215.00 3.89 3.8548 0.0352
PFOPF 0 0.38 185.50 2.56 2.4828 0.0772
PFCF 0 0.38 176.00 2.41 1.8230 0.5870
RCSF 0 3.37 215.00 3.11 2.8800 0.2300
RCOPF 0 3.37 185.50 1.09 1.5321 -0.4421
RCCF 0 3.37 176.00 0.91 0.8800 0.0300
OPSSF 2 8.87 215.00 6.29 6.3020 -0.0120
OPSOPF 2 8.87 185.50 5.75 5.2543 0.4957
OPSCF 2 8.87 176.00 5.05 4.6989 0.3511
PFSF 2 0.38 215.00 5.44 5.6269 -0.1869
PFOPF 2 0.38 185.50 4.04 4.5107 -0.4707
PFCF 2 0.38 176.00 3.65 3.9333 -0.2833
RCSF 2 3.37 215.00 5.28 4.6659 0.6141
RCOPF 2 3.37 185.50 3.89 3.5738 0.3162
RCCF 2 3.37 176.00 2.18 3.0042 -0.8242
OPSSF 6 8.87 215.00 7.77 7.5433 0.2267
OPSOPF 6 8.87 185.50 6.76 7.0074 -0.2474
OPSCF 6 8.87 176.00 6.32 6.6168 -0.2968
PFSF 6 0.38 215.00 6.60 6.7899 -0.1899
PFOPF 6 0.38 185.50 6.22 6.1856 0.0344
PFCF 6 0.38 176.00 6.17 5.7730 0.3970
RCSF 6 3.37 215.00 5.59 5.8565 -0.2665
RCOPF 6 3.37 185.50 5.75 5.2762 0.4738
RCCF 6 3.37 176.00 4.74 4.8714 -0.1314
Table 7 shows that the highest error in the predicted response from the equation for peak attenuation is 1.1590% which is when the materials used for waste material and natural fibre in green roof system are polyfoam and sugarcane fibre (PFSF), respectively, at a slope of 2%. The lowest error is -0.9572%, which is when polyfoam and sugarcane fibre (PFSF) were used as materials for the drainage layer and filter layer in the green roof system at slope of 0%.
Table 7: Comparison of predicted and actual value for peak attenuation Materials Slope
(%)
Water absorption of waste material (%)
Water absorption of natural fibres (%)
Peak attenuation (mm)
Error (%) Actual Predicted
OPSSF 0 8.87 215.00 13.56 12.9420 0.6180
OPSOPF 0 8.87 185.50 14.65 14.3541 0.2959
OPSCF 0 8.87 176.00 14.88 14.8597 0.0203
PFSF 0 0.38 215.00 11.38 12.3372 -0.9572
PFOPF 0 0.38 185.50 15.04 14.7832 0.2568
PFCF 0 0.38 176.00 15.19 15.6218 -0.4318
RCSF 0 3.37 215.00 13.71 13.9423 -0.2323
RCOPF 0 3.37 185.50 16.51 16.0242 0.4858
RCCF 0 3.37 176.00 16.69 16.7455 -0.0555
OPSSF 2 8.87 215.00 11.31 11.5207 -0.2107
OPSOPF 2 8.87 185.50 11.85 12.5870 -0.7370
OPSCF 2 8.87 176.00 12.55 12.9812 -0.4312
PFSF 2 0.38 215.00 12.16 11.0010 1.1590
PFOPF 2 0.38 185.50 13.56 13.1012 0.4588
PFCF 2 0.38 176.00 13.95 13.8284 0.1216
RCSF 2 3.37 215.00 12.32 12.5761 -0.2561
RCOPF 2 3.37 185.50 13.71 14.3122 -0.6022
RCCF 2 3.37 176.00 15.42 14.9221 0.4979
OPSSF 6 8.87 215.00 9.83 10.1949 -0.3649
OPSOPF 6 8.87 185.50 10.84 10.5694 0.2706
OPSCF 6 8.87 176.00 11.28 10.7409 0.5391
PFSF 6 0.38 215.00 9.44 9.84529 -0.4053
PFOPF 6 0.38 185.50 11.38 11.2538 0.1262
PFCF 6 0.38 176.00 11.43 11.7582 -0.3282
RCSF 6 3.37 215.00 12.01 11.3605 0.6495
RCOPF 6 3.37 185.50 11.85 12.4049 -0.5549
RCCF 6 3.37 176.00 12.86 12.7921 0.0679
Table 8 shows that the highest error in the predicted response from the equation for water retention is 3.1132% which is when the materials used for waste material and natural fibre in green roof system are oil palm shell and coconut fibre (OPSCF), respectively, at a slope of 6%. The lowest error is -2.4320%, which is when oil palm shell and oil palm fibre (OPSOPF) were used as materials for the drainage layer and filter layer in the green roof system at slope of 6%.
Table 8: Comparison of predicted and actual value for water retention Materials Slope
(%)
Water absorption of waste material (%)
Water absorption of natural fibres (%)
Water retention (mm)
Error (%) Actual Predicted
OPSSF 0 8.87 215.00 26.07 28.1512 -2.0812
OPSOPF 0 8.87 185.50 36.32 34.7426 1.5774
OPSCF 0 8.87 176.00 38.34 38.5542 -0.2142
PFSF 0 0.38 215.00 28.06 30.3904 -2.3304
PFOPF 0 0.38 185.50 40.01 37.4612 2.5488
PFCF 0 0.38 176.00 41.39 41.4272 -0.0372
RCSF 0 3.37 215.00 36.22 34.9026 1.3174
RCOPF 0 3.37 185.50 43.2 41.8045 1.3955
RCCF 0 3.37 176.00 43.54 45.7161 -2.1761
OPSSF 2 8.87 215.00 22.97 20.1815 2.7885
OPSOPF 2 8.87 185.50 26.3 26.2069 0.0931
OPSCF 2 8.87 176.00 28.14 29.8362 -1.6962
PFSF 2 0.38 215.00 23.68 22.5564 1.1236
PFOPF 2 0.38 185.50 29.05 29.0611 -0.0111
PFCF 2 0.38 176.00 31.66 32.8448 -1.1848
RCSF 2 3.37 215.00 26.15 27.0207 -0.8707
RCOPF 2 3.37 185.50 31.56 33.3566 -1.7966
RCCF 2 3.37 176.00 38.64 37.0859 1.5541
OPSSF 6 8.87 215.00 15.96 17.1087 -1.1487
OPSOPF 6 8.87 185.50 19.57 22.0020 -2.4320
OPSCF 6 8.87 176.00 28.38 25.2668 3.1132
PFSF 6 0.38 215.00 18.99 19.7548 -0.7648
PFOPF 6 0.38 185.50 25.95 25.1275 0.8225
PFCF 6 0.38 176.00 28.38 28.5466 -0.1666
RCSF 6 3.37 215.00 26.09 24.1237 1.9663
RCOPF 6 3.37 185.50 27.13 29.3275 -2.1975
RCCF 6 3.37 176.00 33.5 32.6923 0.8077
3.3 Regression Analysis
A displayed fitted line graph from the regression analysis was developed after determining projected peak runoff, peak attenuation, and water retention using the equation derived by ANOVA. Fig. 1, Fig. 2, and Fig. 3 each depicts a plotted fitted line for estimated peak runoff against experimental peak runoff, plotted fitted line for estimated peak attenuation against experimental peak attenuation and plotted fitted line for estimated water retention against experimental water retention, respectively. The R-squared value was calculated using the graph.
The better the model, the closer the R-squared number is to 1. The summary model of regression analysis for all models is shown in Table 9.
Figure 1: Fitted line plot for predicted and actual peak runoff
Figure 2: Fitted line plot for predicted and actual peak attenuation
Figure 3: Fitted line plot for predicted and actual water retention
Table 9: Regression analysis for green roof hydrological performance Hydrological properties R-squared value
Peak runoff 0.960
Peak Attenuation 0.932 Water retention 0.948
3.4 Hydrological Performance a. Peak runoff
Based on Fig. 4, the minimum peak runoff is achieved when the slope is at a range of 0% to 0.8%
and WA(WM) is within the range of 0.5% to 7.5%. The maximum of peak runoff is achieved when slope is within the range of 4.5% to 6% and WA(WM) value is >8%. Based on Fig. 5, the minimum peak runoff is achieved when both slope and WA(NF) at a value of 0% while the maximum value is obtained when slope is at the range of 2.7% to 6% and WA(NF) is at the range of 180% to 215%. Based on Fig. 6, the minimum value of peak runoff is obtained when the value of WA(WM) is within the range of 2% to 6% and value of WA(NF) is <180%. Peak runoff achieved its maximum value when WA(WM) is <1% or >8% and, WA(NF) is within the range of 200% to 215%. This finding tally with the experimental done by Asman (2018), that stated the slope factors shows a linear relationship where the peak runoff increases as the slope are higher.
Figure 4: Contour peak runoff vs WA(WM), slope Figure 5: Contour peak runoff vs WA(NF), slope
Figure 6: Contour peak runoff vs WA(NF), WA(WM)
b. Peak attenuation
Based on Fig. 7, peak attenuation is at its highest when value of slope is at 0% until 4% and WA(WM) is within the range of 2.5% to 6.5%. Nevertheless, the lowest peak attenuation is achieved when slope is within the range of 4.5% to 6% and WA(WM) value is ≤1% or ≥8%. As can be seen in the contour data in Fig. 8, peak attenuation is at its lowest when slope value is at a range of 3.8% to 6% and WA(NF) is at a range of 200% to 215%, while the highest value of peak attenuation is achieved when slope is at a value of 0% until 0.8% and WA(NF) is within the range of 0% until 185%. Based on Fig. 9, peak attenuation is at its highest when WA(WM) is at a range of 2.5% to 5.5% and WA(NF) value is >180%. The lowest value of peak attenuation is obtained when WA(WM) value is ≤1% or ≥180% and WA(NF) is within the range of 200% until 215%.
As a result, when the slope increases, peak attenuation decreases with it, and water absorption for natural fibres, is lower compared to waste materials. This finding supported by experimental done by Asman (2018), where it was discovered that slope of green roof influences by the peak attenuation performances as the slopes increases, the peak attenuation is decreases. Meanwhile the different in water absorption for both materials is because natural fibres have maximum water absorption with more than 100 per cent and minimum water absorption with less than 10 per cent for all three waste materials (Asman, 2018).
Figure 7: Contour peak attenuation vs WA(WM), Figure 8: Contour peak attenuation vs WA(NF), slope slope
Figure 9: Contour peak attenuation vs WA(NF), WA(WM)
c. Water retention
Fig. 10 indicates that water retention is at its highest when slope is at 0% until 0.5% and WA(WM) at a range of 1.5% to 6.5%. The lowest value of water retention obtained when slope is at a range of 2.8% to 6% and value of WA(WM) is at ≤1.5% or >8% on the contour plot. The contour data in Fig. 11 shows the highest value of water retention achieved when both slope and WA(NF) at 0% while the lowest value of water retention achieved when value of slope is at a range of 3% until 6% and value of WA(NF) is at a range of 200% until 215%. Fig. 12 indicates that the water retention is at its highest when WA(WM) is at a range of 1.8% to 6.5% and WA(NF) at <180%. The lowest value of water retention is obtained when value of WA(WM) is
>8% and WA(NF) is within the range of 200% until 215%. Based on Asman (2018) experimental result, it was observed that water retention capacity and runoff dynamics of green roof depend on roof slope which tally with the results in this study where there is reduction in water retention capacity as the slope are increased. It also being found that in response to the density of materials (WM and NF), size of materials and effect of green roof slope can result in significant increasing in the total runoff rate thus reduced the water retention. Based on Asman (2018) findings, the density is correlated with the size of materials whereas the density is proportional to the sizes of materials and water absorption. Meanwhile, it is proven that the size of materials used in green roof drainage and filter layers played a significant role in water retention performance. This is because the grain size of materials influences the water flowing and hydraulic conductivity (permeability) of drainage layer which indicates that the ability of water passing through the filter and drainage materials without being susceptible to clogging. It was also discovered lower water retention having a bigger size of materials used in green roof layer and lower value in water retention indicates the high ability to drain water (Asman, 2018). This had also proved through the findings by Shahid et al. (2015) and Pérez et al. (2012), shows the ability to drain water is proportionate to the size of materials which is the bigger particles size will give a higher value of hydraulic conductivity. Even though, this study specific the size of materials, the result obtained is tally with experimental study done by Asman (2018).
Figure 10: Contour water retention vs WA(WM), Figure 11: Contour water retention vs WA(NF), slope slope
Figure 12: Contour plot peak attenuation vs WA(NF), WA(WM)
3.5 Optimization of Slope, Water Absorption of Waste Material and Natural Fibre on Hydrological Performance of Green Roof
The results were used to calculate the maximum and minimum hydrological parameters of a green roof system by determining the optimal slope, water absorption of waste materials, and water absorption of natural fibre. The Minitab software can calculate the maximum and minimum values for any hydrological attribute. The optimization results for each hydrological performance which are peak runoff (PR), peak attenuation (PA) and water retention (WR) were summarised in Table 4. Fig. 10, Fig. 11, and Fig. 12 depicts a graph of optimal data of hydrological performance of a green roof developed by Minitab.
(a) (b)
Figure 13: Optimization for (a) Minimum and (b) Maximum peak runoff
(a) (b)
Figure 14: Optimization for (a) Minimum and (b) Maximum peak attenuation
(a) (b)
Figure 15: Optimization for (a) Minimum and (b) Maximum water retention
According to Table 10, it shows that, the greater the slope, water absorption of waste materials, and water absorption of natural fibre, the greater the peak runoff value of the green roof system.
However, as the slope, water absorption of waste materials, and water absorption of natural fibre increases, water retention also decreases. It can also be observed when the water absorption of waste material increases, the peak attenuation value increases. As a result, the hydrological performance is influence by slope and water absorption (for waste and natural fibre materials).
Table 10: Optimization result for green roof hydrological performance.
Input parameters Optimization PR PA WR
Slope Minimum 0 6 4.719
Maximum 5.5758 0 0
WA(WM) Minimum 4.0676 0.38 8.87
Maximum 8.87 4.0676 4.0676
WA(NF) Minimum 176 215 215
Maximum 215 176 176
4. Conclusion
In conclusion, the hydrological performance of green roof (peak runoff, peak attenuation, and water retention) can be determined using computational analysis of RSM model. Based on its
intended input parameters, the generated mathematical equation from analysis of variance (ANOVA) can be applied to forecast the output variables (peak runoff, peak attenuation, and water retention) of green roof. For peak runoff, peak attenuation and water retention, the percentage error or variations between the output variables and real experimental results are within a tolerance of 15%. The R-Squared values from the regression analysis are greater than 0.900. The models created in this study are acceptable because the model is relevant when the value for R – squared is considered close to 1.0 (the closer the R-squared value is to 1, the better the model).
The RSM model's 2D contours was used to determine the input parameters that have a major effect on the hydrological performance of a green roof. It can be concluded that all the input parameters are the main factors that contribute to the peak runoff, peak attenuation, and water retention of green roof. Based on the optimization data generated by RSM model, maximum value of slope (5.578%), water absorption of waste materials (8.87%), and water absorption of natural fibre (215%), contributed to a maximum peak runoff value of a green roof system. However, maximum value of slope (4.179%), water absorption of waste materials (8.87%), and water absorption of natural fibre (215%) would cause a minimum value of water retention. In addition, minimum value of peak attenuation would be obtained when maximum value of slope (6%) and water absorption of natural fibre (215%) are used. Nevertheless, maximum value of water absorption of waste material (4.0676%) would produce a maximum value of peak attenuation of green roof system.
Acknowledgements
The authors would like to thank the Research and Innovation Management Centre, University Malaysia Sabah for providing the financial support under the Acculturation Grant Scheme (SGA), grant number SGA0098-2019, is deeply appreciated.
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