# Hydraulic Characterization of Green Roof Substrates by Evaporation Experiments
## 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 \(\theta_{r}\) 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 \(\lambda\) 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 \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Substrate** & **Sample** & \(\theta_{r}\) & \(\theta_{s}\) & \(\alpha_{1}\) & \(n_{1}\) & \(K_{s}\) & \(\lambda\) & \(\omega_{2}\) & \(\alpha_{2}\) & \(n_{2}\) \\ \hline  & & [cm\({}^{3}\) cm\({}^{-3}\)] & [cm\({}^{3}\) cm\({}^{-3}\)] & [cm\({}^{-1}\)] & & [cm h\({}^{-1}\)] & & & [cm\({}^{-1}\)] & \\ \hline TMT & 1 & 0.04 & 0.50 & 0.062 & 3.07 & 54.12 & 2.15 & 0.168 & 0.003 & 1.100 \\  & 2 & 0.04 & 0.47 & 0.086 & 1.29 & 473.40 & 9.52 & 0.730 & 0.030 & 1.340 \\  & 3 & 0.04 & 0.46 & 0.010 & 1.30 & 121.30 & 5.44 & 0.105 & 0.010 & 1.100 \\  & 4 & 0.04 & 0.48 & 0.021 & 1.65 & 80.89 & 3.31 & 0.099 & 0.115 & 3.762 \\  & Avg. & 0.044 & 0.476 & 0.045 & 1.83 & 182.43 & 5.10 & 0.275 & 0.040 & 1.826 \\ \hline ATV & 1 & 0.11 & 0.45 & 0.070 & 2.02 & 286.20 & 5.13 & 0.360 & 0.044 & 1.110 \\  & 2 & 0.11 & 0.60 & 0.075 & 2.08 & 263.10 & 3.67 & 0.380 & 0.058 & 1.300 \\  & 3 & 0.11 & 0.67 & 0.080 & 3.97 & 75.25 & 3.18 & 0.575 & 0.019 & 1.714 \\  & 4 & 0.11 & 0.66 & 0.031 & 1.42 & 315.70 & 6.09 & 0.392 & 0.090 & 1.877 \\  & Avg. & 0.106 & 0.595 & 0.064 & 2.37 & 235.06 & 4.52 & 0.427 & 0.052 & 1.500 \\ \hline MIX & 1 & 0.07 & 0.55 & 0.068 & 5.54 & 135.80 & 7.74 & 0.894 & 0.030 & 1.519 \\  & 2 & 0.07 & 0.60 & 0.046 & 1.10 & 315.60 & 4.75 & 0.579 & 0.048 & 1.977 \\  & 3 & 0.07 & 0.46 & 0.013 & 2.38 & 155.30 & 10.11 & 0.067 & 0.072 & 5.000 \\  & 4 & 0.07 & 0.58 & 0.057 & 2.99 & 110.00 & 4.68 & 0.609 & 0.017 & 1.332 \\  & Avg. & 0.070 & 0.546 & 0.046 & 3.00 & 179.18 & 6.82 & 0.537 & 0.042 & 2.457 \\ \hline \end{tabular}
\end{table} 
Table 6: Parameters of the van Genuchten bimodal water retention (Equation (7)) and hydraulic conductivity (Equation (8)) functions obtained by the inverse method. Figure 5: Hydraulic conductivity curves obtained by the inverse method considering unimodal (Equations (5) and (6), dot line) and bimodal (Equations (7) and (8), continuous line) VGM models. Lines represent the average of four replicated samples. Grey crosses and dots represent the measured \(K(h)\) values of individual samples measured by direct Wind and UGH methods, respectively. conducting UHG and evaporation experiments in succession on the same sample [20,27].