1. Introduction
Green roofs are low-impact development measures aimed at mitigating the effects of flooding in urban areas [
1]. Green roofs are able to reduce and delay the peak rate into the sewage system through two mechanisms: (i) the retention of rainfall and (ii) the detention of runoff. The retention capacity is the volume of rainfall that is stored by the growing medium and lost via evapotranspiration. Detention refers to the temporal delay occurring between rainfall that is not retained and emerges as runoff [
2]. Considering that roofs may represent a large portion of the total impervious surfaces in urban areas, green roofs are one of the key options for hydrologic restoration and stormwater management [
3].
Conceptual models for green roof hydrologic functioning, e.g., [
4], include lumped parameters that are case sensitive and need to be calibrated against experimental data, thus limiting their general applicability [
5,
6]. Physically based models such as Environmental Protection Agency (EPA)’s Storm Water Management Model (SWMM) [
6,
7], Soil Water Atmosphere and Plant (SWAP) model [
8] and Hydrus model [
9,
10,
11,
12] in either one-dimensional [
13,
14], two-dimensional [
15,
16] and three-dimensional versions [
5] were successfully applied to simulate the water balance and the hydrologic response of a vegetated roof. Knowledge of the hydraulic properties, i.e., the relationships between the soil water pressure head, h, the volumetric water content,
θ, and the soil hydraulic conductivity,
K, is necessary to apply simulation models based on the numerical solution of the Richards equation [
8,
14]. However, few studies have provided a comprehensive hydraulic characterization of green roof substrates. In most cases, the hydraulic properties of green roofs were highly simplified or limited to some specific soil characteristics (e.g., field capacity, wilting point, or particle size distribution) and generally focused only on the soil water retention curves. For example, in [
13], only field capacity and wilting point were measured. These data, in conjunction with the bulk density and particle size distribution, were used to estimate the hydraulic properties of substrates using a pedotransfer function. Similarly, Refs. [
8,
17] assumed water retention parameters from the literature. Li and Babcock [
15] acquired the shape parameters (α and
n) of the van Genuchten model for water retention [
18] from the hanging water column and saturated hydraulic conductivity from laboratory falling head experiments. A comprehensive estimation of both
θ(h) and
K(h) functions for a mineral green roof substrate was conducted by [
5] and [
14] who used a simplified version of the evaporation method with an extended measurement range [
19,
20]. However, they assumed the saturated soil hydraulic conductivity,
Ks, as a fitting parameter and their estimations of soil hydraulic conductivity function basically relies on measurements conducted in the dry range between 10 and 30% of volumetric water content.
In the range of θ values near to soil saturation, an accurate determination of K(h) (or K(θ)) is critically important for highly permeable porous media, like green roof substrates, given they must ensure rapid drainage and avoid water ponding on the surface even during intense precipitation. However, the high non-linearity of hydraulic functions represents a major difficulty as a small change in θ may change K by several orders of magnitude.
A very effective and rapid transient laboratory method for simultaneous determination of both
θ(h) and
K(h) relationships for the same sample is the evaporation method, firstly proposed by Wind [
21]. The water retention characteristic
θ(h) is first estimated from the average water content and pressure head readings at several locations of the soil sample by an iterative procedure. Then, the unsaturated hydraulic conductivity function is determined from the pressure head profile and the changes in water content distribution. A simplified version of Wind’s method was proposed by [
22] in which tensiometers are installed at only two depths within a short soil column. However, the linearizing assumptions of the simplified method with respect to time, space and the water content–pressure head relationship could result in marked deviations from the true hydraulic properties for the coarse-textured pore media that are commonly used for green roof design [
23].
Apart from this, other limitations may affect the evaporation method. Water cavitation in the tensiometers, typically occurring around −70 to −90 kPa, limits the measurement range on the dry end [
19,
20]. On the wet end, the major limitations arise from the inability to obtain accurate estimates of the hydraulic conductivity because the hydraulic gradients are too small and subject to uncertainties in tensiometric readings [
19,
24]. However, many hydrologic and agronomic studies require soil hydraulic property measurements at both lower and higher tensions. Therefore, the integration of evaporation data with independent measurements conducted for both the wet and/or the dry ends seems a valuable solution to improve the soil hydraulic functions’ reliability. Water retention data at low pressure head values can be readily obtained by the pressure plate apparatus [
25] whereas measurements of near-saturated hydraulic conductivity may be obtained from steady-state head-controlled infiltration experiments, like the unit hydraulic gradient (UHG) [
26]. Although the combination of these two techniques is attractive, to our knowledge, measurements of near-saturated hydraulic conductivity on the same sample used for evaporation experiments were conducted only by [
19,
27]. Furthermore, provided that
θ(h) and
K(h) data collected from the evaporation method are generally fitted by closed-form empirical functions like the van Genuchten–Mualem (VGM) model [
18], the consistency between modelled functions and additional steady-state measurements (pressure plate and UGH data) may be problematic and need to be specifically assessed. This is particularly true close to saturation where, due to the influence of the macropore domain, unimodal functions may be inappropriate to describe the hydraulic properties of green roof substrates [
3,
28,
29,
30].
Parameter optimization based on an inverse solution of the Richards equation has been largely used for soil hydraulic characterization (e.g., [
31,
32]). One of the advantages of the inverse method is the flexibility in modelling the hydraulic properties of the porous media. Though numerically more expensive, inverse modelling was considered preferable to simplified evaporation methods for coarse media with narrow pore-size distribution [
33]. The optimization module of the Hydrus-1D model [
9] was used to estimate the water retention curve and the hydraulic conductivity function of green roof substrates from simulated rainfall experiments [
34,
35,
36,
37] but the feasibility of estimating the parameters of the bimodal VGM [
28] from an inverse approach was not explored.
The present study was performed with the main objective of developing a laboratory procedure for the hydraulic characterization of green roof artificial substrates based on evaporation and steady-state UHG experiments. The hydraulic properties of the substrates obtained with the direct Wind method were compared with those obtained by numerical inversion of the evaporation transient experiments performed by Hydrus-1D software. The agreement with independent near-saturated K measurements was assessed with the aim of establishing the reliability of unimodal and bimodal VGM models to describe the hydraulic properties of the considered artificial substrates. Specific aims were addressed, including the following: (i) evaluating the influence of fixing the parameters related to the dry portion of θ(h) and K(h) functions, namely the residual volumetric water content θr and the shape parameter λ, and (ii) establishing the best approach to obtain mean θ(h) and K(h) functions representative of several replicate samples.
4. Discussion
The direct Wind [
21] evaporation method with a pressure head measured at three heights allowed an accurate description of the unimodal water retention curve of the three considered substrates, provided the
θr parameter is fixed at the water content value measured at
h = −150 m. Despite showing a relative larger dispersion at high
h values, the measured unsaturated hydraulic conductivity data were adequately fitted by the unimodal VGM model when the λ parameter was left unconstrained. The direct Wind and the inverse Hydrus-1D methods yielded estimations of the water retention data that were practically coincident and highly correlated (R
2 > 0.97) estimations of
K(h). The experimental setup consisting of three tensiometers at 4 cm intervals seemed adequate to estimate the hydraulic properties of coarse green roof substrates that may be problematic with the simplified evaporation method, making use of only two tensiometers [
23,
33]. A very good estimation performance for the MIX substrate and a relatively good performance for the coarser TMT and ATV substrates was obtained, thus confirming that this sample schematization improved identification of the non-linearity of
h(
t) profiles in the initial stage of the transient process and reduced errors caused by linearization and quasi steady-state assumptions [
24]. However, for pressure heads higher than −30 cm, direct measurement of
K(
h) was inaccessible due to the estimates of the hydraulic gradient that become too small. This is a well-known limitation of the evaporation method that can be overcome by conducting UHG and evaporation experiments in succession on the same sample [
20,
27]. However, our results showed that this strategy was not enough in the case of green roof substrates that present a heterogeneous composition with a double order of pores of different sizes, i.e., micropores and macropores [
30]. Indeed, the independently measured hydraulic conductivity values close to saturation were always underestimated.
When the inverse method with the hydraulic properties expressed by the bimodal VGM model was used, a close description of the
K(
h) function in the range from saturation to the lower limit of the evaporation method was obtained. The effective benefit of using the bimodal VGM model was sometimes questioned. Peng et al. [
3] and Liu and Fassman-Beck [
29] showed that the bimodal VGM model improved the description of substrates’ water retention but the hydraulic conductivity was effectively improved only when a three-modal function was considered. Turco et al. [
30] showed that although the substrate could have a bimodal behavior, the differences between uni- and bimodal soil hydraulic characteristics had minimal effects on the hydrological functioning of a green roof, given the error in simulated runoff volume is less than 1%. They concluded that the unimodal model must be preferred instead of the bimodal due to the lower number of estimated parameters.
5. Conclusions
The knowledge of the substrate hydraulic properties, i.e., the relationships between the water pressure head, h, the volumetric water content, θ, and the hydraulic conductivity, K, of the porous medium, is crucial for the simulation of water fluxes in green roofs by mechanistic models. The evaporation method could be a very effective and rapid transient laboratory method for simultaneous determination of θ(h) and K(h) relationships. In this study, we applied the Wind evaporation method supplemented by steady-state independent measurements of K(h) conducted close to saturation to estimate the hydraulic properties of artificial substrates designed for green roof preparation. The results confirmed that the evaporation method, either direct or inverse, is inadequate to estimate the near saturated hydraulic conductivity of heterogeneous pore media like the substrates under study. A much better description of the K(h) function could be obtained only when the inverse method with the bimodal VGM model was used. Therefore, this approach could be recommended as an effective strategy for green roof substrate characterization.
However, further investigation is necessary to assess the effectiveness of the bimodal models in improving the simulation of the hydraulic processes that occur in extensive green roofs subjected to natural rainfall and evapotranspiration.