# Analysis of Preferential Flow in Artificial Substrates with Sedum Roots for Green Roofs: Experiments and Modeling

^{1}

^{2}

^{3}

^{4}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Plants and Substrates

_{s})) and chemical properties of PAS and VAS are shown in Table 1 [39]. For each artificial substrate, both plant species were propagated by stem cuttings in monoculture at three depths (6 cm, 10 cm, and 14 cm) in 10 cm-diameter acrylic cylinders and grown in an artificial climate chest for 103 days to ensure an excellent plant coverage [39]. Thereafter, plant root characteristics, such as root volume density, and K

_{s}of these 12 vegetated substrates of varying depths (Table 2) were measured [39].

#### 2.2. Solute Breakthrough Experiments

_{s}values (Table 1 and Table 2) of different plant–substrate combinations were notably larger than the applied rainfall intensities, neither ponding nor overflow occurred in all experiments, and the measured outflow was equal to runoff. The cumulative outflow mass [g] was first converted into outflow volume [L] by assuming a water density of 1 g/cm

^{3}, and was then converted into water depth [cm] by dividing the column surface area of 10 cm diameter. Taking PAS1 as an example (Figure 1), the cumulative outflow process is shown in Figure 3a. The negative values represent the outflow direction vertical downward. The result of the related solute breakthrough curve is also shown in Figure 3b. The C and C

_{0}[g/L] are the outflow and inflow solute concentration, respectively. V [L] is the cumulative outflow volume with time. V

_{0}[L] is the infiltrated water volume within the substrate pores, equal to the volume of rainfall minus the volume of outflow in the same time.

#### 2.3. Preferential Flow Detection

_{0}; $c\left(Z,T\right)$ and ${c}_{0}$ are the time-dependent outflow and the initial solute concentrations [g/L], respectively; and Z is the dimensionless spatial coordinate.

#### 2.4. Determination of Substrate Hydraulic Parameters

#### 2.4.1. Calculation of Substrate Hydraulic Parameters

_{r}, θ

_{s}, a, n, K

_{s}, and l) defining water retention curves and hydraulic conductivity functions were needed, and the van Genuchten–Mualem formula [46] was used to fit these parameters.

^{3}·cm

^{−3}]; t is the simulation time [min]; z is the vertical coordinate positive upward [cm]; ${S}_{f}$ and ${S}_{m}$ are the plant water uptake rates of the preferential flow domain and matrix domain, respectively [min

^{−1}]; ${K}_{f}$ and ${K}_{m}$ are the unsaturated hydraulic conductivity of the preferential flow domain and the matrix domain, respectively [cm·min

^{−1}]; ${h}_{f}$ and ${h}_{m}$ are the matric potential of the preferential flow domain and the matrix domain, respectively [kPa]; $\omega $ is the proportion of the preferential flow domain to the whole domain [dimensionless]; ${\Gamma}_{w}$ is the water exchange rate between the two domains [min

^{−1}]; ${\alpha}_{w}$ is the first-order mass transfer coefficient for water [cm

^{−1}·min

^{−1}]; $\beta $ is a dimensionless geometry-dependent shape factor; $\gamma $ is a dimensionless scaling factor;$a$ is the distance between the center of the matrix domain and the boundary of the preferential flow domain [cm]; and ${K}_{a}$ is the effective hydraulic conductivity of the fracture-matrix interface [cm·min

^{−1}].

_{rm}(taking the value of 0), θ

_{sm}, a

_{m}, n

_{m}, K

_{sm}, l

_{m}(pore curvature, generally taking the value of 0.5)), hydraulic parameters of the preferential flow domain (${\theta}_{rf}{\left(\mathrm{t}\mathrm{a}\mathrm{k}\mathrm{i}\mathrm{n}\mathrm{g}\hspace{0.17em}\mathrm{t}\mathrm{h}\mathrm{e}\hspace{0.17em}\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\hspace{0.17em}\mathrm{o}\mathrm{f}\hspace{0.17em}0.5\right),\hspace{0.17em}\theta}_{sf}$, ${\alpha}_{f}$, ${n}_{f}$, ${K}_{sf}$, ${l}_{f}$(taking the value of 0.5)), the parameter of the interface (${K}_{a}$), and the dimensionless factor ($\omega $). Constraints on those unspecified parameters were given to ensure an overall unique solution and convergence in the parameter optimization [51]. Based on substrate physical properties (Table 2), the constraint of saturated water content (that is, the sum of ${\theta}_{sm}$ and ${\theta}_{sf}$) of PAS was set as <0.90, and the constraint of saturated water content of VAS was set as <0.78. Since ${\alpha}_{m},{\alpha}_{f}{,n}_{m},{n}_{f}$ were related to the physical properties of the particles, and the empirical parameter range was set as $\alpha \in \left(\mathrm{0.001,0.01}\right),n\in \left(\mathrm{2,5}\right)$ [52]. The constraint of hydraulic conductivities of the two domains was set as ${{K}_{sm}+K}_{sf}\le {K}_{s}$. The empirical range of ${K}_{a}$ was 10

^{−7}–10

^{−4}when preferential flow occurred [47]. Based on the measured and modeled values of the objective function, the coefficient of determination R

^{2}(Equation (10), [52]) and the Nash–Sutcliffe efficiency coefficient NSE (Equation (11), [53]) were calculated to determine the optimal parameters.

^{2}values close to 1 indicate that variations of the observed values can be captured well in the modeling. NSE can range from −∞ to 1, with a closer value of 1 representing a more perfect match [52,53].

#### 2.4.2. Validation of Substrate Hydraulic Parameters

^{−3}]; ρ is the bulk density of the substrate [g·cm

^{−3}];${D}_{f},{D}_{m}\hspace{0.17em}\mathrm{a}\mathrm{r}\mathrm{e}\hspace{0.17em}\mathrm{t}\mathrm{h}\mathrm{e}$ sorbed concentrations of the preferential flow domain and the matrix domain [g·g

^{−1}]; ${q}_{f}$,${q}_{m}$ are the volumetric fluid flux densities of the preferential flow domain and the matrix domain [cm·s

^{−1}];${\varphi}_{f}$,${\varphi}_{m}$ are sink-source terms that account for various zero- and first-order or other reactions in both domains [g·cm

^{−3}·s

^{−1}];${\Gamma}_{s}$ is the solute mass transfer term [g·cm

^{−3}·min

^{−1}]; ${\omega}_{dp}$ is the first-order solute mass transfer coefficient [min

^{−1}]; and ${c}^{*}$= ${c}_{f}$ for ${\Gamma}_{w}$> 0 and ${c}^{*}$ = ${c}_{m}$ for ${\Gamma}_{w}$< 0.

_{w}for Cl

^{−}was 1.7 cm

^{2}/day, and the dispersion coefficient D

_{L}was 1/10 of the corresponding substrate depth (Figure 1). Substrate bulk densities are given in Table 1. The incoming solute concentration was 1 g/L, and the solute dosing time was 60 min (Section 2.2). The forward modeling predicted solute concentrations at different moments, and based on modeled and observed concentrations, R

^{2}and NSE were calculated to assess the rationality of the substrate hydraulic parameters.

#### 2.5. Preferential Flow and Influential Factors

_{v}[54], was used to describe the variance of preferential outflow and PFI among simulation conditions [55]. According to Nielsen’s classification criteria [56], C

_{v}≤ 10% indicates a weak coefficient of variation, 10% < C

_{v}< 100% indicates a medium coefficient of variation, and C

_{v}≥ 100% indicates a strong coefficient of variation.

## 3. Results and Discussion

#### 3.1. Preferential Flow Detection

#### 3.2. Substrate Hydraulic Parameters

#### 3.2.1. Results

^{2}(Equation (10)) are in the range of 0.998–0.999, and NSE (Equation (11)) are in the range of 0.741–0.997. Figure 5 shows the predicted outflow concentrations from the forward modeling and the corresponding measured concentrations. It shows that R

^{2}are in the range of 0.937–0.993, and NSE are in the range of 0.741–0.973. These data indicate that the substrate hydraulic parameters (Table 4) obtained from the inverse modeling are validated for the forward modeling and can be further used for the preferential flow simulation of different plant–substrates combinations (Section 3.3). In Table 4, the hydraulic parameters of the matrix domain remain constant for each substrate, irrespective of plant–substrate combinations, as the dual permeability model assumes that the root system only make changes to the preferential flow domain [59]. Considering the significant effect of plant root traits on K

_{s}of PAS [60], the hydraulic parameters of the preferential flow domain of PAS are varied. However, since there was no insignificant difference in K

_{s}of VAS due to the root system [60], hydraulic properties of the preferential flow domain of VAS can be viewed as the same.

#### 3.2.2. Implications

^{−4}N/cm at room temperature), r

_{0}denotes the capillary radius, and D denotes the capillary diameter (i.e., equivalent pore diameter, D = 2r

_{0}). The relationship between the equivalent pore diameter and the matric potential is D = 4σ/S. When the matric potential is S

_{1}, the corresponding equivalent pore diameter is D

_{1}. Only in the pore diameter less than D

_{1}are capillary pores filled with water, and the water content is θ

_{1}. When the matric potential is S

_{2}(S

_{1}< S

_{2}), D

_{2}, θ

_{2}are obtained in the same way. The ratio of the pore volume occupied by pores with an equivalent pore size between D

_{2}and D

_{1}to the total volume of substrate pores is called the equivalent pore volume ratio (θ

_{1}–θ

_{2}). Based on the above theory, equivalent pore volume ratios of PAS between 0–−10 kPa, −10–−100 kPa, −100–−1000 kPa were calculated (Table 5). As can be seen from Table 5, compared to vegetated PAS, pure PAS has greater volume ratios of pores, with diameters > 0.03 mm and between 0.003–0.03 mm, but lower ratios of pores with diameters <0.003 mm. According to the agronomic criteria, pores larger than 0.03 mm in diameter tend to act as macropores for water permeable and aeration, and water in pores between 0.003–0.03 mm are most easily accessible to plants [35]. The differences in pore structure between vegetated PAS and pure PAS reflect that the presence of roots in PAS can effectively block its macropores. Further analysis combined with the root characteristics (Table 2) reveal that the volume ratio of pores > 0.03 mm in diameter is linearly correlated (correlation coefficient r = 0.92) with the root volume density of 0.2–0.4 mm roots [39]. This indicates that for vegetated PAS, although shallow-rooted Sedums with a large portion of fine roots often lead to a reduction of macropores, the presence of 0.2–0.4 mm roots can effectively offset the reduction. The root characteristics, in turn, are associated with interactions between plant species, substrate type, and substrate depth [60]. The relatively high (28.48–30.63%) macropores are present in 6 cm-PAS-SS, 10 cm-PAS-SS, and 6 cm-PAS-SL (Table 5). It is noted that a deeper PAS does not promote the development of 0.2–0.4 mm roots (Table 2); on the contrary, it will foster a root system resulting in macropore blockage and K

_{s}reduction [60].

#### 3.3. Preferential Flow and Influential Factors

#### 3.3.1. Perlite-Based Substrate (PAS)

_{v}(≤2.97%) are present in non-vegetated PAS, 6 cm- and 10 cm-PAS with SS, and 6 cm-PAS with SL. Table 5 reveals that these plant–substrate combinations have high portions of macropores (28.48–41.63%), comprising pore networks favoring preferential flow development [34]. Therefore, preferential flow development in these plant–substrates is mainly influenced by internal pore structure and less correlated with rainfall intensity, resulting in high mean PFI, but low C

_{v}values. In contrast, for 14 cm-PAS with SS, and 10 and 14 cm-PAS with SL, small portions of macropores (0.99–4.30%, Table 5) provide few preferential paths, and therefore, the related preferential flow development can be influenced by both internal pore structure and rainfall intensity. Correspondingly, the associated mean PFI are 57.51–82.50%, 36.04–51.06%, and 33.00–65.68%, respectively, and the C

_{v}values are 17.77%, 17.47%, and 38.63%, all showing considerable degrees of variability (Table 8).

_{v}values from 6 cm-PAS subject to various rainfalls were less than 10%, while those from 10 cm-PAS and 14 cm-PAS subject to various rainfalls were greater than 20%. Considering the secondary importance of plant species for preferential outflow (Table 7), the change in preferential outflow C

_{v}can be attributed to plant species, and the effect of plant species on preferential outflow becomes more prominent for deeper substrates. In addition, for any three simulations of varying plant species, but fixed other factors (Table 9), non-vegetated PAS had the largest preferential outflow (Table 6). This may be due to a high volume ratio of macropores (>0.03 mm) in the non-vegetated PAS (41.63%, Table 5), which was 1.36–42.05 times larger than that in the vegetated PAS, and since macropores are potential preferential flow paths, eventually the largest preferential outflow occurred in non-vegetated PAS. Table 7 also shows that plant species have the greatest effect on PFI (F = 84.98). Similar to preferential outflow, based on changes in PFI C

_{v}values for simulations of varying plant species, it can be concluded that the effect of plant species on PFI also becomes more prominent for deeper substrates. As plants make changes to the pore structures of PAS (Table 5), further analysis for the 27 simulation conditions shows a positive (correlation coefficient r = 0.92) linear correlation between macropore volume ratio and PFI. Since the macropore volume ratio is also significantly and positively correlated with the root volume density of 0.2–0.4 mm roots (Section 3.2.2), it indicates that Sedum roots of 0.2–0.4 mm diameter promote the development of preferential flow.

_{v}values from non-vegetated PAS subject to various rainfalls were less than 1%, followed by less than 20% from PAS with SS, and greater than 27% from PAS with SL (Table 10). This indicates that PAS with SL is more influenced by substrate depth in terms of preferential outflow, compared to non-vegetated PAS and PAS with SS. In addition, for any three simulations of varying substrate depth, but fixed other factors (Table 10), 6 cm-vegetated PAS had the largest preferential outflow (Table 6). Similar to preferential outflow, the effect of substrate depth on PFI was the smallest (F = 23.94, Table 7), and based on PFI C

_{v}changes, it is concluded that PAS with SL is more influenced by substrate depth in terms of PFI, compared to non-vegetated PAS and PAS with SS. Likewise, for any three simulations of varying substrate depth, but fixed other factors (Table 10), 6 cm-vegetated PAS had the largest PFI (Table 6). The 6 cm depth of vegetated PAS is associated with high root volume densities of 0.2–0.4 mm roots (0.33 mm

^{3}/cm

^{3}for 6 cm-PAS-SS and 0.31 mm

^{3}/cm

^{3}for 6 cm-PAS-SL, Table 2) that can play positive roles for preferential flow development.

#### 3.3.2. Vermiculite-Based Substrate (VAS)

_{v}values are extremely low (≤0.1%).

_{v}values of preferential outflow were small (<3%, Table 14). The PFI was only influenced by the VAS depth (Table 12), and its variation pattern, along with different substrate depths, was consistent with that of the preferential outflow (e.g., 6 cm-VAS had the largest PFI, and the C

_{v}values had limited variations (Table 14)).

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Apparatus for solute breakthrough experiments. 1—Mariotte bottle, 2—rainfall device, 3—acrylic column, 4—outflow collection container, 5—automatic weighing scale.

Characteristics | Substrate Type | |
---|---|---|

PAS | VAS | |

Components (% by volume) | 90% perlite (<6 mm) 10% chicken manure | 90% vermiculite (<5 mm) 10% chicken manure |

Bulk density (g/cm^{3}) | 0.21 (0.01) | 0.34 (0.01) |

Total porosity (%) | 91.40 (0.01) | 78.80 (0.02) |

WHC (%) | 36.65 (1.33) | 64.05 (1.55) |

Organic matter content (g/kg) | 31.15 (2.72) | 38.64 (2.60) |

K_{s} (cm/min) | 54.45 (0.19) | 18.48 (1.39) |

Substrate Depth-Substrate Type-Plant Species | Root Volume Density /(mm ^{3}/cm^{3}) | Root Volume Density of 0.2–0.4 mm Roots/(mm ^{3}/cm^{3}) | K_{s}/(cm/min) |
---|---|---|---|

6 cm-PAS-SS | 0.63 (0.00) | 0.33 (0.00) | 2.12 (0.17) |

10 cm-PAS-SS | 0.42 (0.01) | 0.33 (0.01) | 1.97 (0.19) |

14 cm-PAS-SS | 1.37 (0.02) | 0.20 (0.01) | 0.56 (0.00) |

6 cm-PAS-SL | 0.71 (0.03) | 0.31 (0.01) | 2.64 (0.09) |

10 cm-PAS-SL | 0.02 (0.00) | 0.01 (0.00) | 0.68 (0.06) |

14 cm-PAS-SL | 1.13 (0.02) | 0.15 (0.00) | 0.74 (0.05) |

6 cm-VAS-SS | 2.46 (0.04) | 0.37 (0.02) | 19.19 (0.54) |

10 cm-VAS-SS | 0.16 (0.00) | 0.09 (0.00) | 14.14 (1.31) |

14 cm-VAS-SS | 5.66 (0.06) | 0.14 (0.01) | 12.77 (0.57) |

6 cm-VAS-SL | 1.59 (0.02) | 0.59 (0.01) | 16.94 (1.28) |

10 cm-VAS-SL | 1.31 (0.02) | 0.44 (0.01) | 15.44 (0.67) |

14 cm-VAS-SL | 8.98 (0.24) | 0.15 (0.01) | 13.60 (0.67) |

Experimental No. | M_{0} | M_{1} | ${\mathbf{\mu}}_{1}^{\mathbf{\prime}}$ | ${\mathbf{\mu}}_{2}$ | ${\mathbf{\mu}}_{3}$ | S | Experimental No. | M_{0} | M_{1} | ${\mathbf{\mu}}_{1}^{\mathbf{\prime}}$ | ${\mathbf{\mu}}_{2}$ | ${\mathbf{\mu}}_{3}$ | S |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

PAS1 | 2.34 | 0.53 | 0.23 | 1.61 | −0.12 | −0.06 | VAS1 | 1.28 | 0.58 | 0.5 | 0.41 | 0.01 | 0.05 |

PAS2 | 1.18 | 0.48 | 0.41 | 0.47 | 0.09 | 0.27 | VAS2 | 0.79 | 0.49 | 0.62 | 0.22 | 0.01 | 0.06 |

PAS3 | 0.81 | 0.35 | 0.43 | 0.29 | 0.05 | 0.34 | VAS3 | 0.45 | 0.47 | 1.05 | 0.07 | 0.01 | 0.30 |

PAS4 | 1.13 | 0.42 | 0.37 | 0.57 | 0.16 | 0.37 | VAS4 | 0.87 | 0.51 | 0.58 | 0.24 | 0.01 | 0.05 |

PAS5 | 1.26 | 0.48 | 0.38 | 0.57 | 0.16 | 0.37 | VAS5 | 0.94 | 0.52 | 0.55 | 0.26 | 0.03 | 0.23 |

PAS6 | 1.25 | 0.50 | 0.40 | 0.49 | 0.07 | 0.22 | VAS6 | 0.87 | 0.50 | 0.58 | 0.25 | 0.00 | 0.01 |

PAS7 | 3.39 | 0.62 | 0.18 | 2.46 | 0.44 | 0.11 | VAS7 | 1.90 | 0.48 | 0.25 | 1.37 | 0.98 | 0.61 |

PAS8 | 0.77 | 0.40 | 0.52 | 0.31 | 0.00 | 0.01 | VAS8 | 0.62 | 0.39 | 0.63 | 0.18 | 0.01 | 0.17 |

PAS9 | 0.76 | 0.37 | 0.49 | 0.26 | 0.03 | 0.21 | VAS9 | 0.57 | 0.37 | 0.64 | 0.17 | 0.02 | 0.26 |

Name | Matrix Domain | Preferential Flow Domain | $\mathit{\omega}$ | ${\mathit{K}}_{\mathit{a}}$/ (cm·min ^{−1})
| ||||||
---|---|---|---|---|---|---|---|---|---|---|

${\mathit{\theta}}_{\mathit{s}\mathit{m}}$/ (cm ^{3}·cm^{−3})
| ${\mathit{\alpha}}_{\mathit{m}}$
/ (cm ^{−1})
| ${\mathit{n}}_{\mathit{m}}$ | ${\mathit{K}}_{\mathit{s}\mathit{m}}$
/ (cm·min ^{−1})
| ${\mathit{\theta}}_{\mathit{s}\mathit{f}}$
/ (cm ^{3}·cm^{−3})
| ${\mathit{\alpha}}_{\mathit{f}}$
/ (cm ^{−1})
| ${\mathit{n}}_{\mathit{f}}$ | ${\mathit{K}}_{\mathit{s}\mathit{f}}$
/ (cm·min ^{−1})
| |||

6 cm-PAS-SS | 0.150 | 0.008 | 2.50 | 0.100 | 0.33 | 0.050 | 2.1 | 2.0 | 0.12 | 0.75 × 10^{–6} |

10 cm-PAS-SS | 0.35 | 0.050 | 2.1 | 1.8 | 0.11 | |||||

14 cm-PAS-SS | 0.27 | 0.002 | 1.5 | 0.4 | 0.05 | |||||

6 cm-PAS-SL | 0.36 | 0.054 | 2.0 | 2.5 | 0.14 | |||||

10 cm-PAS-SL | 0.30 | 0.005 | 1.8 | 0.5 | 0.07 | |||||

14 cm-PAS-SL | 0.30 | 0.005 | 1.8 | 0.6 | 0.07 | |||||

pure PAS | 0.75 | 0.009 | 3.8 | 54.4 | 0.60 | 0.16 × 10^{–6} | ||||

6 cm-VAS-SS | 0.131 | 0.011 | 2.41 | 0.105 | 0.60 | 0.008 | 2.618 | 19.1 | 0.026 | 0.75 × 10^{–6} |

10 cm-VAS-SS | 14.1 | |||||||||

14 cm-VAS-SS | 12.7 | |||||||||

6 cm-VAS-SL | 16.9 | |||||||||

10 cm-VAS-SL | 15.4 | |||||||||

14 cm-VAS-SL | 13.6 | |||||||||

pure VAS | 18.8 |

Name | Range of Equivalent Pore Sizes (Corresponding Matric Potentials) | ||
---|---|---|---|

>0.03 mm (0–−10 kPa) | 0.003–0.03 mm (−10–−100 kPa) | 0.0003–0.003 mm (−100–−1000 kPa) | |

6 cm-PAS-SS | 28.48% | 5.34% | 0.42% |

10 cm-PAS-SS | 30.60% | 6.34% | 0.61% |

14 cm-PAS-SS | 0.99% | 12.47% | 12.30% |

6 cm-PAS-SL | 30.63% | 6.12% | 0.60% |

10 cm-PAS-SL | 4.18% | 18.80% | 6.92% |

14 cm-PAS-SL | 4.30% | 21.05% | 5.42% |

pure PAS | 41.63% | 48.41% | 0.11% |

Simulation No. | Plant Species | Substrate Depth/(cm) | Rainfall Intensity/(a) | Initial Water Content/(%) | S | Preferential Outflow/(cm) | PFI/(%) |
---|---|---|---|---|---|---|---|

1 | Sedum sarmentosum | 6 | 2 | WHC | −0.35 | 6.38 | 84.29 |

2 | MDC | −0.35 | 6.38 | 84.29 | |||

3 | 5 | WHC | −0.06 | 9.01 | 83.43 | ||

4 | MDC | −0.06 | 9.01 | 83.43 | |||

5 | 10 | WHC | −0.31 | 11.05 | 83.65 | ||

6 | MDC | −0.31 | 11.05 | 83.65 | |||

7 | 10 | 2 | WHC | 0.64 | 5.08 | 67.19 | |

8 | MDC | 0.64 | 5.08 | 67.19 | |||

9 | 5 | WHC | 0.04 | 7.59 | 70.32 | ||

10 | MDC | 0.04 | 7.59 | 70.32 | |||

11 | 10 | WHC | 0.27 | 9.37 | 70.77 | ||

12 | MDC | 0.04 | 9.37 | 70.77 | |||

13 | 14 | 2 | WHC | 0.34 | 4.35 | 57.51 | |

14 | MDC | 0.34 | 4.35 | 57.51 | |||

15 | 5 | WHC | 0.12 | 7.71 | 71.43 | ||

16 | MDC | 0.12 | 7.71 | 71.43 | |||

17 | 10 | WHC | 0.56 | 10.89 | 82.50 | ||

18 | MDC | 0.56 | 10.89 | 82.50 | |||

19 | Sedum lineare | 6 | 2 | WHC | 0.37 | 6.73 | 89.00 |

20 | MDC | 0.37 | 6.73 | 89.00 | |||

21 | 5 | WHC | −0.27 | 9.56 | 88.55 | ||

22 | MDC | −0.27 | 9.56 | 88.55 | |||

23 | 10 | WHC | −0.39 | 11.58 | 87.73 | ||

24 | MDC | 0.39 | 11.58 | 87.73 | |||

25 | 10 | 2 | WHC | 0.88 | 2.72 | 36.04 | |

26 | MDC | 0.88 | 2.72 | 36.04 | |||

27 | 5 | WHC | 0.37 | 4.61 | 42.37 | ||

28 | MDC | 0.37 | 4.61 | 42.37 | |||

29 | 10 | WHC | −0.52 | 6.74 | 51.06 | ||

30 | MDC | −0.52 | 6.74 | 51.06 | |||

31 | 14 | 2 | WHC | 0.07 | 2.49 | 33.00 | |

32 | MDC | 0.07 | 2.49 | 33.00 | |||

33 | 5 | WHC | 0.18 | 4.09 | 38.01 | ||

34 | MDC | 0.18 | 4.09 | 38.01 | |||

35 | 10 | WHC | 0.22 | 8.66 | 65.68 | ||

36 | MDC | 0.22 | 8.66 | 65.68 | |||

37 | No-plants | 6 | 2 | WHC | 0.09 | 7.59 | 99.97 |

38 | MDC | 0.09 | 7.59 | 99.97 | |||

39 | 5 | WHC | 0.10 | 10.85 | 100.0 | ||

40 | MDC | 0.10 | 10.85 | 100.0 | |||

41 | 10 | WHC | 0.11 | 13.21 | 99.92 | ||

42 | MDC | 0.11 | 13.21 | 99.92 | |||

43 | 10 | 2 | WHC | 0.01 | 7.56 | 99.89 | |

44 | MDC | 0.01 | 7.56 | 99.89 | |||

45 | 5 | WHC | 0.59 | 10.73 | 99.91 | ||

46 | MDC | 0.59 | 10.73 | 99.91 | |||

47 | 10 | WHC | 0.63 | 13.08 | 99.92 | ||

48 | MDC | 0.63 | 13.08 | 99.92 | |||

49 | 14 | 2 | WHC | 0.18 | 7.59 | 99.87 | |

50 | MDC | 0.18 | 7.59 | 99.87 | |||

51 | 5 | WHC | 0.21 | 10.76 | 99.91 | ||

52 | MDC | 0.21 | 10.76 | 99.91 | |||

53 | 10 | WHC | 0.46 | 13.19 | 99.77 | ||

54 | MDC | 0.46 | 13.19 | 99.77 |

Sources of Variance | F Values | |
---|---|---|

Preferential Outflow | PFI | |

Plant species | 118.54 ** | 84.98 ** |

Substrate depth | 31.66 ** | 23.94 ** |

Plant species × Substrate depth | 13.96 ** | 10.55 ** |

Rainfall intensity | 268.98 ** | 8.175 * |

Initial water content | 0.00 | 0.00 |

**Table 8.**Mean values and C

_{v}of PAS preferential outflow and PFI for different rainfall intensities.

Simulation No. (Rainfall Intensity Varying) | Fixed Variables: Plant Species, Substrate Depth, Initial Water Content | Preferential Outflow | PFI | ||
---|---|---|---|---|---|

Mean Values /(cm) | C_{v}/(%) | Mean Values /(cm) | C_{v}/(%) | ||

2, 4, 6 | SS, 6 cm, MDC | 8.81 | 26.56 | 83.79 | 0.53 |

20, 22, 24 | SL, 6 cm, MDC | 9.29 | 26.22 | 88.43 | 0.73 |

38, 40, 42 | No-plants, 6 cm, MDC | 10.55 | 26.75 | 99.96 | 0.04 |

8, 10, 12 | SS, 10 cm, MDC | 7.35 | 29.30 | 69.36 | 2.97 |

26, 28, 30 | SL, 10 cm, MDC | 4.69 | 42.88 | 43.16 | 17.47 |

44, 46, 48 | No-plants, 10 cm, MDC | 10.46 | 26.49 | 99.91 | 0.02 |

14, 16, 18 | SS, 14 cm, MDC | 7.65 | 42.75 | 70.48 | 17.77 |

32, 34, 36 | SL, 14 cm, MDC | 3.20 | 63.03 | 45.56 | 38.63 |

50, 52, 54 | No-plants, 14 cm, MDC | 10.51 | 26.71 | 99.85 | 0.07 |

Simulation No. (Plant Species Varying) | Fixed Variables: Substrate Depth, Rainfall Intensity, Initial Water Content | Preferential Outflow | PFI | ||
---|---|---|---|---|---|

Mean Values /(cm) | C_{v}/(%) | Mean Values /(cm) | C_{v}/(%) | ||

2, 20, 38 | 6 cm, 2 a, MDC | 6.90 | 9.02 | 91.09 | 8.83 |

4, 22, 40 | 6 cm, 5 a, MDC | 9.81 | 9.63 | 90.66 | 9.36 |

6, 24, 42 | 6 cm, 10 a, MDC | 11.95 | 9.42 | 90.43 | 9.36 |

8, 26, 44 | 10 cm, 2 a, MDC | 5.12 | 47.26 | 67.71 | 47.16 |

10, 28, 46 | 10 cm, 5 a, MDC | 7.64 | 40.04 | 70.87 | 40.60 |

12, 30, 48 | 10 cm, 10 a, MDC | 9.73 | 32.74 | 73.92 | 33.26 |

14, 32, 50 | 14 cm, 2 a, MDC | 4.81 | 53.66 | 63.46 | 53.31 |

16, 34, 52 | 14 cm, 5 a, MDC | 7.52 | 44.40 | 69.78 | 44.40 |

18, 36, 54 | 14 cm, 10 a, MDC | 10.91 | 20.76 | 82.65 | 20.62 |

Simulation No. (Substrate Depth Varying) | Fixed Variables: Plant Species, Rainfall Intensity, Initial Water Content | Preferential Outflow | PFI | ||
---|---|---|---|---|---|

Mean Values /(cm) | C_{v}/(%) | Mean Values /(cm) | C_{v}/(%) | ||

2, 8, 14 | SS, 2 a, MDC | 5.08 | 20.01 | 67.19 | 19.98 |

4, 10, 16 | SS, 5 a, MDC | 8.10 | 9.72 | 75.06 | 9.69 |

6, 12, 18 | SS, 10 a, MDC | 10.44 | 8.88 | 78.97 | 9.03 |

20, 26, 32 | SL, 2 a, MDC | 3.98 | 59.91 | 52.68 | 59.78 |

22, 28, 34 | SL, 5 a, MDC | 6.09 | 49.60 | 56.31 | 49.73 |

24, 30, 36 | SL, 10 a, MDC | 8.99 | 27.10 | 68.16 | 27.08 |

38, 44, 50 | No-plants, 2 a, MDC | 7.58 | 0.23 | 99.91 | 0.05 |

40, 46, 52 | No-plants, 5 a, MDC | 10.78 | 0.58 | 99.94 | 0.05 |

42, 48, 54 | No-plants, 10 a, MDC | 13.16 | 0.53 | 99.87 | 0.09 |

Simulation Conditions | Substrate Depth /(cm) | Rainfall Intensity /(a) | Initial Water Content /(%) | S | Preferential Outflow /(cm) | PFI /(%) |
---|---|---|---|---|---|---|

1 | 6 | 2 | WHC | 0.05 | 7.42 | 98.27 |

2 | MDC | 0.05 | 7.42 | 98.27 | ||

3 | 5 | WHC | 0.06 | 10.62 | 98.33 | |

4 | MDC | 0.06 | 10.62 | 98.33 | ||

5 | 10 | WHC | 0.30 | 13.01 | 98.26 | |

6 | MDC | 0.30 | 13.01 | 98.26 | ||

7 | 10 | 2 | WHC | 0.05 | 7.24 | 95.81 |

8 | MDC | 0.05 | 7.24 | 95.81 | ||

9 | 5 | WHC | 0.23 | 10.36 | 95.84 | |

10 | MDC | 0.23 | 10.36 | 95.84 | ||

11 | 10 | WHC | 0.01 | 12.67 | 95.84 | |

12 | MDC | 0.01 | 12.67 | 95.84 | ||

13 | 14 | 2 | WHC | –0.61 | 7.04 | 93.09 |

14 | MDC | –0.61 | 7.04 | 93.09 | ||

15 | 5 | WHC | 0.17 | 10.05 | 93.06 | |

16 | MDC | 0.17 | 10.05 | 93.06 | ||

17 | 10 | WHC | 0.26 | 12.31 | 93.12 | |

18 | MDC | 0.26 | 12.31 | 93.12 |

Sources of Variance | F Values | |
---|---|---|

Preferential Outflow | PFI | |

Substrate depth | 104.095 ** | 50,845.585 ** |

Rainfall intensity | 10,207.964 ** | 1.098 |

Initial water content | 0.000 | 0.000 |

**Table 13.**Mean values and C

_{v}of VAS preferential outflow and PFI for different rainfall intensities.

Simulation No. (Rainfall Intensity Varying) | Fixed Variables: Substrate Depth, Plant Species, Initial Water Content | Preferential Outflow | PFI | ||
---|---|---|---|---|---|

Mean Values /(cm) | C_{v}/(%) | Mean Values /(cm) | C_{v}/(%) | ||

2, 4, 6 | 6 cm, no-plants, MDC | 10.35 | 27.09 | 98.29 | 0.04 |

8, 10, 12 | 10 cm, no-plants, MDC | 10.09 | 26.98 | 95.83 | 0.02 |

14, 16, 18 | 14 cm, no-plants, MDC | 9.80 | 26.97 | 93.09 | 0.03 |

Simulation No. (Substrate Depth Varying) | Fixed Variables: Rainfall Intensity, Plant Species, Initial Water Content | Preferential Out-flow | PFI | ||
---|---|---|---|---|---|

Mean Values /(cm) | C_{v}/(%) | Mean Values /(cm) | C_{v}/(%) | ||

2, 8, 14 | 2 a, no-plants, MDC | 7.24 | 2.62 | 95.72 | 2.71 |

4, 10, 16 | 5 a, no-plants, MDC | 10.34 | 2.76 | 95.74 | 2.75 |

6, 12, 18 | 10 a, no-plants, MDC | 12.66 | 2.76 | 95.74 | 2.69 |

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## Share and Cite

**MDPI and ACS Style**

Chen, X.; Liu, R.; Liu, D.; Xin, X.
Analysis of Preferential Flow in Artificial Substrates with *Sedum* Roots for Green Roofs: Experiments and Modeling. *Water* **2023**, *15*, 914.
https://doi.org/10.3390/w15050914

**AMA Style**

Chen X, Liu R, Liu D, Xin X.
Analysis of Preferential Flow in Artificial Substrates with *Sedum* Roots for Green Roofs: Experiments and Modeling. *Water*. 2023; 15(5):914.
https://doi.org/10.3390/w15050914

**Chicago/Turabian Style**

Chen, Xuan, Ruifen Liu, Defu Liu, and Xiaokang Xin.
2023. "Analysis of Preferential Flow in Artificial Substrates with *Sedum* Roots for Green Roofs: Experiments and Modeling" *Water* 15, no. 5: 914.
https://doi.org/10.3390/w15050914