# Horizontal and Vertical Variability of Soil Hydraulic Properties in Roadside Sustainable Drainage Systems (SuDS)—Nature and Implications for Hydrological Performance Evaluation

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## Abstract

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_{s}(up to 160% coefficient of variation), which is dominant relative to uncertainties in PTFs predictions and those induced by experimental errors. Many specific factors might be responsible for this variability, especially in the urban context, such as construction techniques, CaCO

_{3}precipitation, and vegetation development. In order to evaluate the effects of this variability on hydrological performance, a hydrological model of a bioretention cell was tested. Simulations revealed that peak flows and volumes are highly affected by the spatial variability of soil hydraulic properties; notably, vertical variability increases the overflow by 50%. The number of infiltration measurements required to evaluate a representative average K

_{s}with an uncertainty of a factor of two or less was found to be four/eight, depending on the studied site. This study provides considerable insight into the spatial variability of soil hydraulic properties and its implications for hydrological performance of roadside SuDS, as it is based on a sound understanding of both theory and practice.

## 1. Introduction

_{s}, are more complex to evaluate. They can be predicted from the soil physical properties via pedotransfer functions (PTFs), derived from laboratory experiments, or measured in the field [9,10]. Although field techniques are more difficult to implement, they are often considered more accurate than other methods, because soil hydraulic properties are generally site-specific [11,12].

_{s}obtained by a large number of measurements? To what extent could a limited number of measurements, pedotransfer function predicted values, and the intrinsic spatial variability affect the predictions of the hydrological processes at the scale of an infiltration system?

## 2. Material and Methods

#### 2.1. Study Sites

#### 2.2. Soil Hydraulic Properties

_{r}, and θ

_{s}[cm

^{3}·cm

^{−3}] are respectively the residual and saturated volumetric water contents; K(h) is the hydraulic conductivity at the suction h, and K

_{s}[m·s

^{−1}] is the saturated hydraulic conductivity; $\mathrm{n}$, $\mathrm{m}$ and $\mathsf{\mu}$ are shape parameters; $\mathrm{m}$ can be calculated either as $\mathrm{m}=1-1/\mathrm{n}$ (Mualem’s condition [22]), or $\mathrm{m}=1-2/\mathrm{n}$ (Burdine’s condition [24]), and $\mathsf{\mu}=3+2/\left(\mathrm{n}-2\right)\text{}$ [24]; h

_{g}[cm] is a scale parameter which corresponds approximately to the air entry bubbling pressure [25].

_{r}, θ

_{s}, K

_{s}, h

_{g}, $\mathrm{n}$), several pedotransfer functions may be found in the literature [26], such as the “Rosetta” software, based on the hierarchical relationships proposed by Schaap et al. [27]. Rosetta offers different options for the estimation of hydraulic soil properties, based on different levels of input data with increasing precision (1 = soil textural class only, 2 = soil texture, 3 = 2 + bulk density, 4 = 3 + one or two point(s) of the water retention curve corresponding to the field capacity and the wilting point) to predict the parameters of the van Genuchten-Mualem equations (Equations (1) and (2)). However, given the fact that soil hydraulic properties are affected by site-specific conditions like soil structure, macropores, and preferential flow paths [28], the applicability of pedotransfer functions which are based on a finite sample set may be limited. This is why field measurements are often recommended for more reliable and representative values.

#### 2.3. Infiltration Tests

#### 2.3.1. Type and Number of Infiltration Measurements

_{s}in the sub-surface was performed with the mean of the Guelph permeameter [30].

#### 2.3.2. Beerkan Infiltration Test and BEST Algorithm

#### “Beerkan” In-Situ Infiltration Test

^{3}undisturbed soil samples were collected at each measurement point with soil sample rings; the first served to determine the soil bulk density and the initial volumetric water content (θ

_{0}), and the other (taken at the end of the experiment) to estimate the saturated volumetric water content (θ

_{s}) through a gravimetric method [34].

#### “BEST” Algorithm

_{r}= 0. Hydraulic shape parameters (n, m, and μ) derive from the analysis of both soil porosity and particle size distribution [32], while the scale parameters h

_{g}and K

_{s}are estimated from the inverse analysis of cumulative infiltration using the two-term equations developed by Haverkamp et al. [35]. Three algorithms can be used, referred to as “BEST-Slope”, “BEST-Intercept”, and “BEST-Steady” [36,37] which are different in defining the mathematical constraint between the sorptivity—capacity of the soil to absorb water by capillarity [38]—and the saturated hydraulic conductivity. The “BEST-Steady” was retained for the present analysis because it was proven to be a robust algorithm which always provides a proper estimate of K

_{s}when the steady state infiltration regime could be reached [39].

_{+}

_{∞}) and the intercept (b

_{+}

_{∞}) of the steady-state model (Equation (4)) fitted to the I(t) data at steady state conditions.

_{s}and S are then defined based on the slope (Equation (5)) and intercept (Equation (6)) as follow:

_{s}can be derived using either Equation (5) or (6).

#### 2.3.3. Guelph Permeameter

_{s}, measurements were conducted at a depth of 20 cm using a Guelph permeameter. This method consists of measuring the steady-state infiltration rate in a small hole having a diameter-height of 6–20 cm, where a constant depth of water H is maintained [40]. The calculation method to evaluate K

_{s}is fully described by Reynolds and Elrick [30], and the basic equation is given below (Equation (8)). At each measurement point, two ponding-depths H

_{1}(5 cm) and H

_{2}(10 cm) were established subsequently, for which two steady state infiltration rates, Q

_{1}and Q

_{2}respectively, were measured. Then, the two K

_{s}values calculated using the single-height approach [41] were averaged.

#### 2.4. Data Analysis

_{s}) was tested by the means of Lilliefors test [45]. The null hypothesis of this test is that the data comes from a normal distribution. Results indicate the acceptance of the null hypothesis at a 5% significance level for the three sites. Thus, the K

_{s}values of the sites A, B and C were fitted to a log-normal distribution. Fitting parameters obtained by the maximum likelihood estimation method are given in Figure A1, Appendix B.

#### 2.5. Effect of K_{s} Variability on Hydrological Performance Modelling

_{s}varies as a function of the number of measurements, an analysis was performed on the three sites. For each number of measurements N from 1 to 20, 1000 subsamples of size N were randomly sampled from the fitted log-normal distribution. Subsequently, the arithmetic mean of each subsample was computed, and the quantiles Q

_{0.1}and Q

_{0.9}of the latter 1000 means were determined. These quantiles were then normalized by the mean $m$ of the population. It should be noted that the mean $m$ of the population is calculated via the adjusted distribution for each site.

_{s}, which account (or not) for its horizontal and/or vertical variability on the hydrological processes (focusing both on dynamical and cumulative aspects of the water balance).

_{s}variability is considered on the one hand, and when the vertical variability is included on the other. In the first case, the considered K

_{s}values are: (1) the mean m of the surface measurements; (2) the Rosetta predicted value; and lastly (3) the calculated quantiles Q

_{0.1}and Q

_{0.9}for a chosen N number of measurements. The vertical variability is accounted for with two additional approaches; firstly, a two-layered structure with different K

_{s}, i.e., equal to the arithmetic mean of the total number of measurements at each layer; and secondly, a homogenous domain whose K

_{s}is calculated as the harmonic mean of each layer’s K

_{s}(Equation (9)), as suggested by Freeze and Cherry [46].

_{s}value, which depended on the modelling option.

## 3. Results and Discussion

#### 3.1. Horizontal and Vertical Variability of Soil Characteristics

_{s}, 𝜌, and K

_{s}measured at each point of the four sites are provided as Supplementary data (Appendix A); further developments are based on standard statistics (Table 2). Figure 2 illustrates the variability of these three parameters for the three sites. A comparison between the measurements and “typical” literature values (based on the texture class) of these soil properties is also presented. Literature data originate from more than 30 states in the USA [48]. The factors at the origin of the intra-site variability were discussed in this section, based on visual inspections as well as measurements.

_{s}in sites A and C is 5.8 × 10

^{−6}and 4.8 × 10

^{−6}m·s

^{−1}, respectively, which is also consistent with literature data. Site B, which is formed of a loamy soil, has a lower density, and higher saturated water content and hydraulic conductivity than the two former sites. The mean K

_{s}value is 2.1 × 10

^{−5}m·s

^{−1}, while “typical” values are one order of magnitude lower. This difference may be attributed to the types of vegetation present (trees and clumps) and their growth (10 years), so that the development of roots and biological activity may create macropores [49], which tend to increase the saturated hydraulic conductivity. The two latter examples suggest that soil texture may be an insufficient for a reliable estimation of soil hydraulic properties, since other factors such as construction technique, vegetation cover, and biological activity constitute additional sources of variability. To confirm these hypotheses, it would be of interest to undertake studies comparing sites with the same characteristics and their evolution over time.

_{s}parameter (at the surface) was found to be much higher, with a coefficient of variation ranging from 64% in site C to 134% in site A. In the latter case, there was visual evidence of an uneven distribution of the vegetation, which explain this higher variability [51]. The present results should be put into perspective with the findings of Mulla et al. and Vauclin et al. [52,53] who reported a coefficient of variation ranging from 48 to 352% for K

_{s}; additionally Warrick [54] pointed out low variability of the bulk density and saturated water content (<15%) and high variability of saturated hydraulic conductivity (>50%).

_{s}parameter at the surface, it should be noted that no spatial trend was visible with respect to the longitudinal location within the swales or the filter strip. Contrariwise, the measurements at a depth of 20 cm were more than one order of magnitude lower than at the surface (Table 2), evidencing a vertical variability of K

_{s}; this difference could be induced by the different infiltration test methods (Beerkan at the surface, Guelph at 20 cm). While Guelph was found to produce lower K

_{s}measurements than other infiltration tests that explore a larger soil volume [55,56], no comparison was found in the literature to the Beerkan test, which explores a similar soil volume. The lower infiltration rates at 20 cm are consistent with other field observations. Firstly, a difference of compaction between the two layers was noted, as shown by the vertical increase in bulk density (from 1.70 to 1.94 g·cm

^{−3}) with depth. As for this cause, Pitt et al. [57] have demonstrated that the saturated hydraulic conductivity of soil is highly affected by the degree of compaction. In the latter study, a sandy loam soil with a bulk density of 2 g·cm

^{−3}was found to have a saturated hydraulic conductivity of 8 × 10

^{−8}m·s

^{−1}. The construction techniques may induce this level of compaction since for site A, the filter media was placed on a smooth geomembrane. Actually, a smooth underlying layer causes a significant decrease in saturated water content, as tested by Brown and Hunt [58]. In addition, the filter media was implemented in wet conditions, which may also have a strong impact on the degree of compaction, and subsequently, on the steady-state infiltration rate of the soil.

_{s}with increasing depth, 3 soil samples were composited from 6 subsamples collected respectively at the surface, 20 cm, and 30 cm depth in the bioretention swale; these samples were then analyzed for both their particle size distribution and their total calcium carbonate content. The results revealed no significant difference in particle size distribution with depth, negating the hypothesis of downward migration of fine particles. Conversely, the CaCO

_{3}increased with increasing depth, from 214 g/kg at the surface to 252 and 265 g/kg at 20 and 30 cm, respectively. As the sand used in the filter media mixture is basically calcareous, the decrease in saturated hydraulic conductivity and the increase in the bulk density might be due to CaCO

_{3}precipitation that “plugs” soil pores [59].

#### 3.2. Measurement Uncertainties

_{0}, bulk density ρ, and particle size distribution) when the experimental conditions are respected, but considering the possible occurrence of experimental errors. For example, a wrong estimation of θ

_{0}and ρ may be the consequence of a non-complete cylinder taken at the beginning of the test. Additionally, these two parameters might show “local” variability, i.e., at a very small scale, inducing differences between the point where infiltration was conducted and the adjacent point where the cylinder was taken. This spatial variability was quantified during this study by collecting 5 samples at a small scale. It was found to be equal to ±0.05 cm

^{3}∙cm

^{−3}and ±0.1 g∙cm

^{−3}for θ

_{0}and ρ, respectively. Assuming that the soil texture does not vary at this scale and that the cumulated infiltration curve (Figure 3) was assessed precisely, the two remaining sources of experimental errors are θ

_{0}and ρ, the effects of which will be discussed in the following developments.

_{0}and ρ for four tests (carried out in sites A, B, and C) with different initial conditions. Tests B3 and C1 were conducted in a soil with relatively low bulk density (1.28 and 1.38 g·cm

^{−3}, respectively), at different initial water contents (19% and 28.5% respectively), while for the other two tests, A6 and C6, the bulk density was higher (1.72 and 1.70 g·cm

^{−3}, respectively) and the initial water content was equal to 8.1% and 27.3% respectively.

_{s}upon the soil parameters, but the dependency of the estimation method (i.e., the “BEST-steady” algorithm) on its measured input data. Hence, for a given infiltration curve, the predicted K

_{s}decreases with increasing θ

_{0}and ρ. Results show that for the four measurement points, the error in the predicted hydraulic conductivity due to a ±0.05 cm

^{3}∙cm

^{−3}variation in θ

_{0}is larger than the error induced by ±0.1 g∙cm

^{−3}variation in ρ. For example, for point B3, these errors represent 13% and 9.5% of the K

_{s}measurement value, respectively. For tests A6 and B3, an error of ±0.05 cm

^{3}∙cm

^{−3}in the initial water content causes an error of 12% and 13% of the K

_{s}measurement values, respectively. With regards to the points C1 and C6, which display the highest bulk densities and the lowest hydraulic conductivities among these four examples, the potential bias induced by a ±0.05 cm

^{3}∙cm

^{−3}error in the initial water content corresponds respectively to 23% and 32% of the calculated K

_{s}value.

_{0}or ρ is lower than the coefficient of variation of K

_{s}within each site.

#### 3.3. The Accuracy of the Pedotransfer Functions

^{−6}and 1.5 × 10

^{−6}m·s

^{−1}, respectively, which falls within the measured spatial variability of this parameter in these two devices, but is higher than the experimental bias evaluated in Section 3.2. In site B, where pedotransfer functions underestimate K

_{s}, the maximum difference is 1.9 × 10

^{−5}m·s

^{−1}, while the standard deviation of the measurements is 1.5 × 10

^{−5}m·s

^{−1}. In this site, the development of vegetation roots over time may have caused modifications in the soil structure that were not taken into consideration in the PTFs functions [61]. Yet, it appears that the accuracy of Rosetta predictions does not necessarily increase with increasing precision of the input data (e.g., in site A, the mean K

_{s}is better predicted without adding the bulk density, and in site C, it is better predicted with the textural class only). Following a similar approach (based on laboratory measurements of K

_{s}on undisturbed soil samples from an agricultural field), [62] came to the same conclusion—as long as the 4th hierarchical level of input data (i.e., including textural class, soil texture, bulk density and the water content at field capacity) was not reached.

_{s}and θ (2.5 pF) for sites B and C; however, the measured values in site A are significantly lower than the Rosetta prediction, whatever the input data. This observation is a probable consequence of the unusually high bulk density in this infiltration system (1.7–1.9 g·cm

^{−3}), which significantly decreased the soil’s porosity. In order to further assess the predictive capacity of the Rosetta model, the comparison was realized based on effective saturation θ/θ

_{s}(%). The latter measure expresses the shape parameter n and scale parameter h

_{g}of the van Genuchten model. At 2.5 pF, the maximum differences in effective saturation between Rosetta and BEST for the three sites are equal to 5% to 7%. However, at 4 pF, the two estimation methods lead to different values and higher differences in effective saturation (11% to 15%), which may be related to intrinsic differences between the van Genuchten-Mualem and the van Genuchten with Burdine’s condition models, resulting in non-overlaying curves at high-pressure heads.

_{s}when the natural variability of this parameter is not important and the structure of the soil is marginally affected by either long-term factors such as vegetation growth or short-term conditions as a construction technique.

#### 3.4. Effect of Horizontal and Vertical Variability of Soil Hydraulic Properties on the Hydrological Performance

#### 3.4.1. Number of Infiltration Measurements Needed for a Representative Value of K_{s}

_{0.1}and Q

_{0.9}normalized by the mean $m$ of the population are plotted as a function of the sample size for the three sites A, B, and C in Figure 5. These quantiles constitute an empirical 80% confidence interval which represents the uncertainty in the estimation of K

_{s}mean value from N measurements.

_{s}arithmetic mean decreases with an increasing number of measurements. For example, considering a small number of measurements n = 2, it is equal to a factor of 2–3. Yet, with a larger number of measurement n = 8, this uncertainty decreases to a factor <2, for all three sites. Additionally, the quantiles intervals show an asymptotic behavior, starting from a certain number of measurements. Thus, an increase in infiltration measurements beyond this certain number does not necessarily yield a better evaluation of K

_{s}.

_{s}was 134%, while this variation was <70% for sites B and C. Hence the uncertainty on K

_{s}mean associated with N measurements for the latter two sites is lower than for site A. This variation from one site to another is due to the dispersion parameters of the log-normal distribution that derive directly from spatial variability of K

_{s}within each site.

_{s}evaluation and the studied site. For an uncertainty of a factor of two or less, which is operationally acceptable, this number is equal to 4 (resp. 8) measurements for sites B and C (resp. site A). This brings into question the consequence of this level of uncertainty on the hydrological modelling of SuDS.

#### 3.4.2. Effect of the Horizontal and Vertical Variability of Soil Hydraulic Properties on the Hydrological Modelling

_{s}values in the different scenarios are equal to (1) the mean m of the surface measurements (6.1 × 10

^{−6}m∙s

^{−1}); (2) the Rosetta predicted value based on the particle size distribution (5.8 × 10

^{−6}m∙s

^{−1}); and lastly (3) the quantiles calculated in Section 3.4.1 (Q

_{0.1}(3 × 10

^{−6}m∙s

^{−1}) and Q

_{0.9}(1 × 10

^{−5}m∙s

^{−1}) for n = 8, corresponding to an uncertainty of a factor of two for site A). With regards to the vertical variability, the average K

_{s}value at 20 cm and the harmonic mean are equal to 2.9 × 10

^{−7}m∙s

^{−1}and 4.8 × 10

^{−7}m∙s

^{−1}, respectively.

_{s}values vary. The peaks and troughs corresponding to the mean of the population and Rosetta prediction (referred to as Mean 1 L and Rosetta 1 L, respectively) are very similar: their peaks are around 400 L∙h

^{−1}. However, these peaks decrease (resp. increase) by a factor of 2 when K

_{s}value is equal to the quantile Q

_{0.1}(resp. Q

_{0.9}). Although an increase in K

_{s}value by a factor of 1.6 results in a notable increase in peak fluxes, it does not necessarily induce a remarkable increase in the cumulated drained volume, which amounts to ∼4 × 10

^{4}L at the end of the simulation period for the mean, Rosetta, and Q

_{0.9}. In contrast, a decrease in K

_{s}value as for Q

_{0.1}has an impact on the cumulated drained volume, since it allows more water accumulation on the surface, leading to the generation of runoff (overflow) when the depth of water exceeds the available ponding depth. Therefore, a threshold is observed in the impact of K

_{s}on the outputs, corresponding to the moment where the surface water exceeds the available ponding-depth.

_{s}for each layer is referred to as Mean 2 L, while the homogeneous layer with a harmonic mean K

_{s}is referred to as Harmonic mean 1 L. At first, the results revealed no significant differences in dynamics and fluxes between the two-layered model and the homogeneous layer model. However, when comparing, the latter two approaches that account for vertical variability to the previous approaches that consider only the surface horizontal variability, large gaps in their outputs are identified. For instance, the inclusion of vertical variability in the model either by a two-layered or one layer domain sharply reduces the peak drained flux by a factor of 12. Additionally, the infiltration dynamics are completely smoothed and the drainage time is no longer comparable. The latter increased from several hours to several days (7 to 10 days) for the Mean 1L and the Mean 2 L/Harmonic mean 1 L, respectively. The vertical variability also has implications on the water balance. To illustrate this statement, the drained volumes constitute >80% of the water volumes and the runoff <20% if only the surface measurements are considered, whereas their relative importance is inverted when the vertical variability is considered (30% and 70%, respectively).

_{s}is better accounted for by a harmonic mean of each layer’s K

_{s}than by a simple arithmetic mean. Thus, a homogenous domain whose K

_{s}is equal to a harmonic mean could replace a two-layered system. Consequently, factors causing this variability, such as construction techniques inducing high compaction level in addition to the type of sand used in the media (as discussed in Section 3.1), may cause an important variation in the SuDS’ hydrologic performance. This prevents the facility from mimicking the pre-development conditions in order to mitigate peaks inflow without producing overflow.

## 4. Conclusions

_{s}with an uncertainty of a factor of two or less and at 80% confidence level was found to be four/eight, depending on the studied site.

_{s}value on the predicted hydrologic performance of a bioretention cell was assessed using the HYDRUS-1D software. The results clearly highlight the significant impact of K

_{s}on the simulated water dynamics, including drained flux and volume. In addition, the vertical variability was found to be the most impacting relative to the horizontal variability of K

_{s}and its assessment method. This vertical variability could modify the long-term hydrologic performance of SuDS and the flow apportionment by decreasing infiltration into the soil and increasing the overland flow. Consequently, to effectively represent the spatial variability when modeling an infiltration SuDS, soil measurements should be conducted at the surface, and vertically as well. A harmonic mean value of each layer’s K

_{s}applied to a homogenous domain could be an alternative to a two-layered domain with two different K

_{s}.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

Bulk Density ρ (g·cm^{3}) | Initial Water Content θ_{0} (%) | Saturated Water Content θ_{s} Calculated (%) | Saturated Water Content θ_{s} Measured (%) | Saturated Hydraulic Conductivity K_{s} (m·s^{−1}) | ||
---|---|---|---|---|---|---|

Site A (Surface) | A1 | 1.72 | 16.1 | 35.3 | 21.4 | 1.8 × 10^{−6} |

A2 | 1.37 | 5.7 | 48.3 | 27.8 | 2.6 × 10^{−5} | |

A3 | 1.83 | 13.2 | 30.9 | 26.6 | 7.7 × 10^{−6} | |

A4 | 1.81 | 10.4 | 31.9 | 20.2 | 3.0 × 10^{−6} | |

A5 | 1.72 | 11.6 | 35.3 | 20.7 | 2.9 × 10^{−6} | |

A6 | 1.72 | 8.1 | 35.7 | 18.2 | 2.2 × 10^{−6} | |

A7 | 1.75 | 12.4 | 34.2 | 27 | 6.7 × 10^{−6} | |

A8 | 1.72 | 16.3 | 35.1 | 24.2 | 4.8 × 10^{−7} | |

A9 | 1.77 | 8.7 | 33.2 | 26 | 1.8 × 10^{−6} | |

Site A (20 cm depth) | A2–20 | - | - | - | - | 6.1 × 10^{−8} |

A4–20 | 2 | - | - | - | 3.6 × 10^{−7} | |

A5–20 | - | - | - | - | 4.5 × 10^{−8} | |

A7–20 | 2.1 | - | - | - | 3.3 × 10^{−8} | |

A8–20 | - | - | - | - | 1.5 × 10^{−8} | |

A9–20 | 1.74 | - | - | - | 1.2 × 10^{−6} | |

Site B | B1 | 1.21 | 39 | 54.3 | 46 | 4.0 × 10^{−5} |

B2 | 1.04 | 14 | 60.8 | 50 | 3.2 × 10^{−5} | |

B3 | 1.28 | 19 | 51.7 | 43 | 4.4 × 10^{−6} | |

B4 | 1.24 | 23 | 53.2 | 45 | 4.9 × 10^{−5} | |

B5 | 1.11 | 24 | 58.1 | 47 | 2.3 × 10^{−5} | |

B6 | 1.16 | 30 | 56.2 | 48 | 1.0 × 10^{−5} | |

B7 | 1.42 | 31 | 46.4 | 39 | 2.5 × 10^{−5} | |

B8 | 1.33 | 29 | 49.8 | 39 | 1.4 × 10^{−5} | |

B9 | 1.18 | 32 | 55.5 | 40 | 6.9 × 10^{−6} | |

B10 | 1.19 | 26 | 55.1 | 39 | 1.0 × 10^{−5} | |

Site C | C1 | 1.38 | 28.5 | 47.9 | 41.5 | 1.5 × 10^{−6} |

C2 | 1.41 | 26.5 | 47.0 | 36.2 | 7.2 × 10^{−6} | |

C3 | 1.72 | 21.8 | 35.3 | 41.4 | 4.9 × 10^{−6} | |

C4 | 1.61 | 22.0 | 39.2 | 24.3 | 3.6 × 10^{−6} | |

C5 | 1.57 | 16.8 | 40.8 | 31.5 | 3.8 × 10^{−6} | |

C6 | 1.7 | 27.3 | 35.8 | 32.2 | 1.1 × 10^{−6} | |

C7 | 1.71 | 18.4 | 35.5 | 28.2 | 3.8 × 10^{−6} | |

C8 | 1.38 | 22.2 | 47.9 | 35.8 | 5.9 × 10^{−6} | |

C9 | 1.41 | 27.4 | 46.8 | 50 | 1.1 × 10^{−5} |

## Appendix B

**Figure A1.**Density histogram and probability density function (PDF) of the log-normal distribution Lognormal ($\mu ,\sigma )$ of K

_{s}values for sites A, B and C. With $\mu $ and $\sigma $ the mean and standard deviation of the normal distribution of ln(K

_{s}), and $m$ and $v$ the mean and the variance of the population.

## Appendix C

Van Genuchten Parameters | θ_{r} (cm^{3}·cm^{−3}) | θ_{s} (cm^{3}·cm^{−3}) | 1/h_{g} (cm^{−1}) | n |
---|---|---|---|---|

At the surface | 0.0395 | 0.23 | 0.044 | 1.4128 |

At 20 cm depth | 0.0354 | 0.275 | 0.0552 | 1.2775 |

## References

- Coombes, P.J.; Kuczera, G.; Kalma, J.D.; Argue, J.R. An evaluation of the benefits of source control measures at the regional scale. Urban Water
**2002**, 4, 307–320. [Google Scholar] [CrossRef] - Liu, A.; Goonetilleke, A.; Egodawatta, P. Taxonomy for rainfall events based on pollutant wash-off potential in urban areas. Ecol. Eng.
**2012**, 47, 110–114. [Google Scholar] [CrossRef] [Green Version] - Davis, A.P. Green Engineering Promote Low-Impact Development. Environ. Sci. Technol.
**2005**, 39, 338A–344A. [Google Scholar] [CrossRef] [PubMed] - Davis, A.P. Field Performance of Bioretention: Hydrology Impacts. J. Hydrol. Eng.
**2008**, 13, 90–95. [Google Scholar] [CrossRef] [Green Version] - Bäckström, M.; Viklander, M.; Malmqvist, P.-A. Transport of stormwater pollutants through a roadside grassed swale. Urban Water J.
**2006**, 3, 55–67. [Google Scholar] [CrossRef] - Barrett, M.E.; Walsh, P.M.; Malina, J.F., Jr.; Charbeneau, R.J. Performance of Vegetative Controls for Treating Highway Runoff. J. Environ. Eng.
**1998**, 124, 1121–1128. [Google Scholar] [CrossRef] - Deletic, A.; Fletcher, T.D. Performance of grass filters used for stormwater treatment—A field and modelling study. J. Hydrol.
**2006**, 317, 261–275. [Google Scholar] [CrossRef] - Rezaei, M.; Seuntjens, P.; Joris, I.; Boënne, W.; Van Hoey, S.; Campling, P.; Cornelis, W.M. Sensitivity of water stress in a two-layered sandy grassland soil to variations in groundwater depth and soil hydraulic parameters. Hydrol. Earth Syst. Sci. Discuss.
**2015**, 12, 6881–6920. [Google Scholar] [CrossRef] - Clothier, B.E.; Smettem, K.R.J. Combining laboratory and field measurements to define the hydraulic properties of soil. Soil Sci. Soc. Am. J.
**1990**, 54, 299–304. [Google Scholar] [CrossRef] - Jhorar, R.K.; Van Dam, J.C.; Bastiaanssen, W.G.M.; Feddes, R.A. Calibration of effective soil hydraulic parameters of heterogeneous soil profiles. J. Hydrol.
**2004**, 285, 233–247. [Google Scholar] [CrossRef] - Angulo-Jaramillo, R.; Vandervaere, J.-P.; Roulier, S.; Thony, J.-L.; Gaudet, J.-P.; Vauclin, M. Field measurement of soil surface hydraulic properties by disc and ring infiltrometers: A review and recent developments. Soil Tillage Res.
**2000**, 55, 1–29. [Google Scholar] [CrossRef] - Reynolds, W.D.; Elrick, D.E.; Youngs, E.G.; Booltink, H.W.G.; Bouma, J.; Dane, J.H. Saturated and Field-Saturated Water Flow Parameters: Laboratory methods. In Methods of Soil Analysis; Soil Science Society of America: Madison, WI, USA, 2002; pp. 688–690. [Google Scholar]
- Ahmed, F.; Gulliver, J.S.; Nieber, J.L. Field infiltration measurements in grassed roadside drainage ditches: Spatial and temporal variability. J. Hydrol.
**2015**, 530, 604–611. [Google Scholar] [CrossRef] - Weiss, P.T.; Gulliver, J.S. Effective saturated hydraulic conductivity of an infiltration-based stormwater control measure. J. Sustain. Water Built Environ.
**2015**, 1, 04015005. [Google Scholar] [CrossRef] - Jabro, J.D.; Iversen, W.M.; Stevens, W.B.; Evans, R.G.; Mikha, M.M.; Allen, B.L. Physical and hydraulic properties of a sandy loam soil under zero, shallow and deep tillage practices. Soil Tillage Res.
**2016**, 159, 67–72. [Google Scholar] [CrossRef] - Logsdon, S.D. CS616 Calibration: Field versus Laboratory. Soil Sci. Soc. Am. J.
**2009**, 73, 1. [Google Scholar] [CrossRef] - Marín-Castro, B.E.; Geissert, D.; Negrete-Yankelevich, S.; Gómez-Tagle Chávez, A. Spatial distribution of hydraulic conductivity in soils of secondary tropical montane cloud forests and shade coffee agroecosystems. Geoderma
**2016**, 283, 57–67. [Google Scholar] [CrossRef] - Sobieraj, J.A.; Elsenbeer, H.; Coelho, R.M.; Newton, B. Spatial variability of soil hydraulic conductivity along a tropical rainforest catena. Geoderma
**2002**, 108, 79–90. [Google Scholar] [CrossRef] - Mubarak, I.; Angulo-Jaramillo, R.; Mailhol, J.C.; Ruelle, P.; Khaledian, M.; Vauclin, M. Spatial analysis of soil surface hydraulic properties: Is infiltration method dependent? Agric. Water Manag.
**2010**, 97, 1517–1526. [Google Scholar] [CrossRef] - Rienzner, M.; Gandolfi, C. Investigation of spatial and temporal variability of saturated soil hydraulic conductivity at the field-scale. Soil Tillage Res.
**2014**, 135, 28–40. [Google Scholar] [CrossRef] - Brooks, R.; Corey, T. Hydraulic Properties of Porous Media; Hydrology Papers Colorado State University: Fort Collins, CO, USA, 1964. [Google Scholar]
- Mualem, Y. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res.
**1976**, 12, 513–522. [Google Scholar] [CrossRef] - van Genuchten, M.T. A Closed-form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils1. Soil Sci. Soc. Am. J.
**1980**, 44, 892. [Google Scholar] [CrossRef] - Burdine, N. Relative permeability calculations from pore size distribution data. J. Pet. Technol.
**1953**, 5, 71–78. [Google Scholar] [CrossRef] - Bouwer, H. Rapid field measurement of air entry value and hydraulic conductivity of soil as significant parameters in flow system analysis. Water Resour Res
**1966**, 2, 729–738. [Google Scholar] [CrossRef] - McBratney, A.B.; Minasny, B.; Cattle, S.R.; Vervoort, R.W. From pedotransfer functions to soil inference systems. Geoderma
**2002**, 109, 41–73. [Google Scholar] [CrossRef] - Schaap, M.G.; Leij, F.J.; Van Genuchten, M.T. ROSETTA: A computer program for estimating soil hydraulic parameters with hierarchical pedotransfer functions. J. Hydrol.
**2001**, 251, 163–176. [Google Scholar] [CrossRef] - Lin, H.S.; McInnes, K.J.; Wilding, L.P.; Hallmark, C.T. Effects of Soil Morphology on Hydraulic Properties. Soil Sci. Soc. Am. J.
**1999**, 63, 955. [Google Scholar] [CrossRef] - Lassabatère, L.; Angulo-Jaramillo, R.; Winiarski, T.; Yilmaz, D. Advances in Unsaturated Soils. In BEST Method: Characterization of Soil Unsaturated Hydraulic Properties; CRC Press Taylor and Francis Group: London, UK, 2013. [Google Scholar]
- Reynolds, W.D.; Elrick, D.E. In situ measurement of field-saturated hydraulic conductivity, sorptivity, and the α-parameter using the Guelph permeameter. Soil Sci.
**1985**, 140, 292–302. [Google Scholar] [CrossRef] - Cannavo, P.; Coulon, A.; Charpentier, S.; Béchet, B.; Vidal-Beaudet, L. Water balance prediction in stormwater infiltration basins using 2-D modeling: An application to evaluate the clogging process. Int. J. Sediment Res.
**2018**. [Google Scholar] [CrossRef] - Lassabatère, L.; Angulo-Jaramillo, R.; Soria Ugalde, J.M.; Cuenca, R.; Braud, I.; Haverkamp, R. Beerkan Estimation of Soil Transfer Parameters through Infiltration Experiments—BEST. Soil Sci. Soc. Am. J.
**2006**, 70, 521. [Google Scholar] [CrossRef] - Reynolds, W.D.; Elrick, D.E. Ponded infiltration from a single ring: I. Analysis of steady flow. Soil Sci. Soc. Am. J.
**1990**. [Google Scholar] [CrossRef] - Topp, G.C.; Ferré, P.A. 3.1 Water content. In Methods of Soil Analysis; Soil Science Society of America: Madison, WI, USA, 2002; pp. 417–545. [Google Scholar]
- Haverkamp, R.; Ross, P.J.; Smettem, K.R.J.; Parlange, J.Y. Three-dimensional analysis of infiltration from the disc infiltrometer: 2. Physically based infiltration equation. Water Resour. Res.
**1994**, 30, 2931–2935. [Google Scholar] [CrossRef] [Green Version] - Bagarello, V.; Di Prima, S.; Iovino, M. Comparing Alternative Algorithms to Analyze the Beerkan Infiltration Experiment. Soil Sci. Soc. Am. J.
**2014**, 78, 724. [Google Scholar] [CrossRef] - Yilmaz, D.; Lassabatere, L.; Angulo-Jaramillo, R.; Deneele, D.; Legret, M. Hydrodynamic Characterization of Basic Oxygen Furnace Slag through an Adapted BEST Method. Vadose Zone J.
**2010**, 9, 107. [Google Scholar] [CrossRef] - Philip, J.R. The theory of infiltration: 4. Sorptivity and algebraic infiltration equations. Soil Sci.
**1957**, 84, 257–264. [Google Scholar] [CrossRef] - Di Prima, S.; Lassabatere, L.; Bagarello, V.; Iovino, M.; Angulo-Jaramillo, R. Testing a new automated single ring infiltrometer for Beerkan infiltration experiments. Geoderma
**2016**, 262, 20–34. [Google Scholar] [CrossRef] - Eijkelkamp Guelph Permeameter—Operating Instructions; Eijkelkamp: Giesbeek, The Netherlands, 2011.
- Elrick, D.E.; Reynolds, W.D. Methods for Analyzing Constant-Head Well Permeameter Data. Soil Sci. Soc. Am. J.
**1992**, 56, 320. [Google Scholar] [CrossRef] - Gardner, W.R. Some steady-state solutions of the unsaturated moisture flow equation with application to evaporation from a water table. Soil Sci.
**1958**, 85, 228–232. [Google Scholar] [CrossRef] - Bresler, E.; Dagan, G. Unsaturated flow in spatially variable fields: 2. Application of water flow models to various fields. Water Resour. Res.
**1983**, 19, 421–428. [Google Scholar] [CrossRef] - Muñoz-Carpena, R.; Regalado, C.M.; Álvarez-Benedi, J.; Bartoli, F. Field evaluation of the new Philip-Dunne permeameter for measuring saturated hydraulic conductivity. Soil Sci.
**2002**, 167, 9–24. [Google Scholar] [CrossRef] - Lilliefors, H.W. On the Kolmogorov-Smirnov test for normality with mean and variance unknown. J. Am. Stat. Assoc.
**1967**, 62, 399–402. [Google Scholar] [CrossRef] - Freeze, R.A.; Cherry, J.A. Groundwater; Prentice-Hall: Englewood Cliffs, NJ, USA, 1979; p. 604. [Google Scholar]
- Simunek, J.; Sejna, M.; Saito, H.; Sakai, M.; Van Genuchten, M.T. The Hydrus-1D Software Package for Simulating the Movement of Water, Heat, and Multiple Solutes in Variably Saturated Media; Department of Environmental Sciences, University of California Riverside: Riverside, CA, USA, 2013; p. 342. [Google Scholar]
- Rawls, W.J.; Brakensiek, D.L.; Saxton, K.E. Estimation of soil water properties. Trans. ASAE
**1982**, 25, 1316–1320. [Google Scholar] [CrossRef] - Archer, N.A.L.; Quinton, J.N.; Hess, T.M. Below-ground relationships of soil texture, roots and hydraulic conductivity in two-phase mosaic vegetation in South-east Spain. J. Arid Environ.
**2002**, 52, 535–553. [Google Scholar] [CrossRef] - Nielsen, D.; Biggar, J.W.; Erh, K.T. Spatial variability of field-measured soil-water properties. Calif. Agric.
**1973**, 42, 215–259. [Google Scholar] [Green Version] - Wang, C.; Zhao, C.; Xu, Z.; Wang, Y.; Peng, H. Effect of vegetation on soil water retention and storage in a semi-arid alpine forest catchment. J. Arid Land
**2013**, 5, 207–219. [Google Scholar] [CrossRef] - Mulla, D.J.; McBratney, A.B.; Warrick, A.W. Soil spatial variability. In Soil Physics Companion; CRC Press: Boca Raton, FL, USA; 2002; pp. 343–373. [Google Scholar]
- Vauclin, M.; Vieira, S.R.; Bernard, R.; Hatfield, J.L. Spatial variability of surface temperature along two transects of a bare soil. Water Resour. Res.
**1982**, 18, 1677–1686. [Google Scholar] [CrossRef] - Hillel, D. Spatial variability. In Environmental Soil Physics; Academic Press: San Diego, CA, USA, 1998; pp. 655–675. [Google Scholar]
- Mohanty, B.P.; Kanwar, R.S.; Everts, C.J. Comparison of saturated hydraulic conductivity measurement methods for a glacial-till soil. Soil Sci. Soc. Am. J.
**1994**, 58, 672–677. [Google Scholar] [CrossRef] - Gupta, R.K.; Rudra, R.P.; Dickinson, W.T.; Patni, N.K.; Wall, G.J. Comparison of saturated hydraulic conductivity measured by various field methods. Trans. ASAE
**1993**, 36, 51–55. [Google Scholar] [CrossRef] - Pitt, R.; Chen, S.-E.; Clark, S.E.; Swenson, J.; Ong, C.K. Compaction’s impacts on urban storm-water infiltration. J. Irrig. Drain. Eng.
**2008**, 134, 652–658. [Google Scholar] [CrossRef] - Brown, R.A.; Hunt, W.F., III. Impacts of construction activity on bioretention performance. J. Hydrol. Eng.
**2009**, 15, 386–394. [Google Scholar] [CrossRef] - Zamanian, K.; Pustovoytov, K.; Kuzyakov, Y. Pedogenic carbonates: Forms and formation processes. Earth-Sci. Rev.
**2016**, 157, 1–17. [Google Scholar] [CrossRef] - Mermoud, A. Cours de Physique du Sol; Ecole Polytechnique Fédérale de Lausanne: Lausanne, Switzerland, 2001. [Google Scholar]
- Lewis, C.; Albertson, J.; Xu, X.; Kiely, G. Spatial variability of hydraulic conductivity and bulk density along a blanket peatland hillslope. Hydrol. Process.
**2012**, 26, 1527–1537. [Google Scholar] [CrossRef] - Alvarez-Acosta, C.; Lascano, R.J.; Stroosnijder, L. Test of the Rosetta Pedotransfer Function for Saturated Hydraulic Conductivity. Open J. Soil Sci.
**2012**, 02, 203–212. [Google Scholar] [CrossRef]

**Figure 2.**Scatter plot of saturated hydraulic conductivity K

_{s}(m·s

^{−1}), bulk density 𝜌 (g∙cm

^{−3}), and saturated water content θ

_{s}(%). The K

_{s}literature value corresponds to the data mean value, while the two values for 𝜌 and θ

_{s}correspond to ±standard deviation about the mean.

**Figure 3.**Example of the cumulative infiltration curve I(t) from site A. The slope and intercept of the steady state model are also represented.

**Figure 4.**K

_{s}sensitivity to θ

_{0}and ρ in four typical examples from sites A, B, and C. The corresponding results of each individual measurement can be found in Table A1 (Appendix A).

**Figure 5.**The quantiles Q

_{0.1}and Q

_{0.9}of K

_{s}arithmetic mean as a function of a number of measurements for sites A, B, and C (normalized by the mean m of the population).

**Figure 6.**Simulation results: drained flux (L∙h

^{−1}) and cumulated drained/runoff volumes (L) over one month period.

**Table 1.**Particle size distribution and soil texture class of each site (results are given in % w/w).

Site A (Surface) | Site A (20 cm) | Site B | Site C | |
---|---|---|---|---|

Clay (<2 μm) | 9.7 | 10.5 | 14.8 | 11.1 |

Fine silt (2–20 μm) | 9.0 | 8.8 | 18.2 | 9.6 |

Coarse silt (20–50 μm) | 9.2 | 11.1 | 21.9 | 18.6 |

Fine sand (50–200 μm) | 15.4 | 18.2 | 17.6 | 13.5 |

Coarse sand (200–2000 μm) | 56.7 | 51.4 | 27.5 | 47.2 |

Soil texture class (USDA) | Sandy Loam | Sandy Loam | Loam | Sandy Loam |

**Table 2.**Statistics of the measured saturated water content θ

_{s}, bulk density ρ, and saturated hydraulic conductivity K

_{s}for the three sites.

n | Min | Max | Median | SD | CV [%] | Arithmetic Mean | ||
---|---|---|---|---|---|---|---|---|

Site A Surface | θ_{s} [%] | 9 | 18.2 | 27.8 | 24.2 | 3.5 | 15 | 23.6 |

ρ [g·cm^{−3}] | 9 | 1.37 | 1.83 | 1.72 | 0.13 | 8 | 1.70 | |

K_{s} [m·s^{−1}] | 9 | 4.8 × 10^{−7} | 2.6 × 10^{−5} | 2.9 × 10^{−6} | 7.9 × 10^{−6} | 134 | 5.8 × 10^{−6} | |

Site A (20 cm) | ρ [g·cm^{−3}] | 3 | 1.74 | 2.10 | 2.00 | 0.19 | 10 | 1.94 |

K_{s} [m·s^{−1}] | 6 | 1.5 × 10^{−8} | 1.2 × 10^{−6} | 5.3 × 10^{−8} | 4.7 × 10^{−7} | 163 | 2.9 × 10^{−7} | |

Site B | θ_{s} [%] | 10 | 39 | 50 | 44 | 4.2 | 10 | 43.6 |

ρ [g·cm^{−3}] | 10 | 1.04 | 1.42 | 1.20 | 0.10 | 9 | 1.22 | |

K_{s} [m·s^{−1}] | 10 | 4.4 × 10^{−6} | 4.9 × 10^{−5} | 1.9 × 10^{−5} | 1.5 × 10^{−5} | 70 | 2.1 × 10^{−5} | |

Site C | θ_{s} [%] | 9 | 24.3 | 50 | 35.8 | 7.8 | 22 | 35.7 |

ρ [g·cm^{−3}] | 9 | 1.38 | 1.72 | 1.57 | 0.15 | 10 | 1.54 | |

K_{s} [m·s^{−1}] | 9 | 1.1 × 10^{−6} | 1.1 × 10^{−5} | 3.8 × 10^{−6} | 3 × 10^{−6} | 64 | 4.8 × 10^{−6} |

**Table 3.**Comparison between Rosetta estimations and experimental measurements of the curves K (h) and θ (h) (mean (standard deviation) of all the measurements carried out in each site).

Permeability Curve K(h) (m·s^{−1}) | Retention Curve θ(h) (%) | ||||||
---|---|---|---|---|---|---|---|

K_{s} | K (2.5 pF) | K (4 pF) | θ_{s} | θ (2.5 pF) θ/θ _{s} (%) | θ (4 pF) θ/θ _{s} (%) | ||

Site A | Rosetta (Textural class) | 4.4 × 10^{−6} | 5.1 × 10^{−10} | 1.1 × 10^{−14} | 38.7 | 14.7 38 | 3.2 8 |

Rosetta (%Sand, Silt, Clay) | 5.8 × 10^{−6} | 2.6 × 10^{−10} | 5.7 × 10^{−15} | 38.4 | 12.7 33 | 2.7 7 | |

Rosetta (%Sand, Silt, Clay + ρ) | 2.9 × 10^{−6} | 8.0 × 10^{−11} | 2.5 × 10^{−15} | 33.0 | 11.2 34 | 2.8 8 | |

Mean BEST values | 5.9 × 10^{−6}(7.9 × 10 ^{−6}) | 3.4 × 10^{−10}(5.8 × 10 ^{−10}) | 3.0 × 10^{−14}(5.1 × 10 ^{−14}) | 23.5 (3.5) | 9.6 (1.9) 40 | 4.2 (0.9) 18 | |

Site B | Rosetta (Textural class) | 1.4 × 10^{−6} | 2.1 × 10^{−9} | 4.4 × 10^{−14} | 39.9 | 21.0 53 | 4.3 10 |

Rosetta (%Sand, Silt, Clay) | 1.7 × 10^{−6} | 3.0 × 10^{−9} | 5.3 × 10^{−14} | 39.6 | 20.7 52 | 4.0 10 | |

Rosetta (%Sand, Silt, Clay + ρ) | 4.8 × 10^{−6} | 1.5 × 10^{−8} | 1.7 × 10^{−13} | 42.5 | 22.7 53 | 3.6 8 | |

Mean BEST values | 2.1 × 10^{−5}(1.5 × 10 ^{−5}) | 4.0 × 10^{−9}(7.1 × 10 ^{−9}) | 4.6 × 10^{−13}(8.0 × 10 ^{−13}) | 43.6 (4.2) | 20.4 (2.8) 47 | 9.9 (1.4) 23 | |

Site C | Rosetta (Textural class) | 4.4 × 10^{−6} | 5.1 × 10^{−10} | 1.1 × 10^{−14} | 38.7 | 14.7 38 | 3.2 8 |

Rosetta (%Sand, Silt, Clay) | 3.9 × 10^{−6} | 5.7 × 10^{−10} | 1.9 × 10^{−14} | 38.7 | 16.543 | 4.2 10 | |

Rosetta (%Sand, Silt, Clay + ρ) | 3.3 × 10^{−6} | 3.7 × 10^{−10} | 1.1 × 10^{−14} | 36.6 | 14.8 40 | 3.6 10 | |

Mean BEST values | 4.8 × 10^{−6}(3.0 × 10 ^{−6}) | 5.9 × 10^{−10}(9.4 × 10 ^{−10}) | 5.5 × 10^{−14}(8.8 × 10 ^{−14}) | 35.7 (7.8) | 16.0 (4.4) 45 | 7.3 (2.0) 20 |

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## Share and Cite

**MDPI and ACS Style**

Kanso, T.; Tedoldi, D.; Gromaire, M.-C.; Ramier, D.; Saad, M.; Chebbo, G.
Horizontal and Vertical Variability of Soil Hydraulic Properties in Roadside Sustainable Drainage Systems (SuDS)—Nature and Implications for Hydrological Performance Evaluation. *Water* **2018**, *10*, 987.
https://doi.org/10.3390/w10080987

**AMA Style**

Kanso T, Tedoldi D, Gromaire M-C, Ramier D, Saad M, Chebbo G.
Horizontal and Vertical Variability of Soil Hydraulic Properties in Roadside Sustainable Drainage Systems (SuDS)—Nature and Implications for Hydrological Performance Evaluation. *Water*. 2018; 10(8):987.
https://doi.org/10.3390/w10080987

**Chicago/Turabian Style**

Kanso, Tala, Damien Tedoldi, Marie-Christine Gromaire, David Ramier, Mohamed Saad, and Ghassan Chebbo.
2018. "Horizontal and Vertical Variability of Soil Hydraulic Properties in Roadside Sustainable Drainage Systems (SuDS)—Nature and Implications for Hydrological Performance Evaluation" *Water* 10, no. 8: 987.
https://doi.org/10.3390/w10080987