# Hydraulic Characterization of Green Roof Substrates by Evaporation Experiments
## 3 Results
### Estimation of Soil Hydraulic Functions by Inverse Method
It is worth noting, however, that the worse correspondence observed for the TMT substrate is mostly determined by a single sample (sample TMT 1) that resulted in a very different estimation of \(\lambda\) parameters with the two approaches. The results demonstrated how the two methods of analysis of the evaporation tests yielded similar results both in terms of the estimated water retention curve and unsaturated hydraulic conductivity functions. However, even with the inverse method, the marked tendency to underestimate the near saturated hydraulic conductivity measured with the UHG method was confirmed. The bimodal VGM model was used in order to improve the predictive ability of the inverse Hydrus-1D method at high-pressure head values (Table 6). Due to the increased flexibility of the bimodal hydraulic functions, higher values of \(K_{s}\) were obtained that better approached the independently measured values. At the same time, larger \(\lambda\) values were estimated (Table 6). For the TMT substrate, \(K_{s}\) values estimated by the inverse method and the bimodal VGM model ranged from 54.1 to 473.4 cm h\({}^{-1}\) with an average value of  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Substrate** & **Method** & \begin{tabular}{c} **Averaging** \\ **Method** \\ \end{tabular}  & \(\theta_{s}\) & \(\alpha\) & \(n\) & \(K_{s}\) & \(\lambda\) \\ \hline \hline \multirow{3}{*}{TMT} & \multirow{3}{*}{direct} & \(\theta(h)\) and \(K(h)\) & \multirow{3}{*}{0.47} & [cm\({}^{3}\) cm\({}^{-3}\)] & [cm h\({}^{-1}\)] & \multirow{3}{*}{3.97} \\  & & curves & & & & & \\  & & estimated & & & & & \\  & & parameters & & & & & \\  & inverse & \(\theta(h)\) and \(K(h)\) & \multirow{3}{*}{0.48} & \  
182.4 cm h\({}^{-1}\). For the ATV substrate, estimated \(K_{\mathrm{s}}\) values ranged from 75.3 to 315.7 cm h\({}^{-1}\) with an average value of 235.4 cm h\({}^{-1}\). Finally, for the MIX substrate, the estimated \(K_{\mathrm{s}}\) values were between 135.8 and 315.6 cm h\({}^{-1}\) with an average value of 179.2 cm h\({}^{-1}\). The mean hydraulic conductivity curves obtained by the inverse method considering unimodal and bimodal unsaturated hydraulic conductivity functions are plotted in Figure 5. Compared to the unimodal model, the bimodal model was more effective in fitting the experimental data points obtained with the UHG method at a pressure head close to zero. Figure 4: Comparison between (**a**) volumetric water content \(\theta\) and (**b**) hydraulic conductivity \(K\) values estimated for a given \(h\) value by the direct Wind and inverse Hydrus-1D methods. Symbols in grey represent the individual samples, while symbols in black represent the average values. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Water Retention Curve**} & \multicolumn{4}{c}{**Hydraulic Conductivity Curve**} \\ \hline
**Substrates** & **Sample** & **Slope** & **Intercept** & **R\({}^{2}\)** & **Slope** & **Intercept** & **R\({}^{2}\)** \\  & & & [cm\({}^{3}\) cm\({}^{-3}\)] & & & & [cm h\({}^{-1}\)] & \\ \hline TMT & 1 & 1.03 & \(-\)0.01 & 0.9768 & 0.80 & 0.10 & 0.7453 \\  & 2 & 1.03 & \(-\)0.01 & 0.9997 & 2.63 & 0.00 & 0.9939 \\  & 3 & 1.18 & \(-\)0.02 & 0.9900 & 1.27 & 0.02 & 0.8958 \\  & 4 & 0.99 & 0.00 & 0.9992 & 0.79 & 0.05 & 0.9957 \\  & Avg. & 1.06 & \(-\)0.01 & 0.9943 & 1.22 & 0.03 & 0.9467 \\ \hline ATV & 1 & 1.15 & \(-\)0.01 & 0.9992 & 1.60 & \(-\)0.02 & 0.9767 \\  & 2 & 1.02 & 0.00 & 1.0000 & 0.26 & 0.00 & 0.9993 \\  & 3 & 1.08 & \(-\)0.02 & 0.9889 & 4.72 & \(-\)0.89 & 0.9675 \\  & 4 & 0.99 & 0.00 & 0.9997 & 0.06 & 0.04 & 0.9896 \\  & Avg. & 1.04 & 0.02 & 0.9977 & 0.59 & \(-\)0.03 & 0.9948 \\ \hline MIX & 1 & 1.00 & 0.00 & 0.9986 & 0.31 & 0.01 & 0.9848 \\  & 2 & 0.97 & 0.01 & 0.9976 & 0.76 & 0.02 & 0.9924 \\  & 3 & 1.19 & \(-\)0.05 & 0.9831 & 4.75 & \(-\)0.01 & 0.9924 \\  & 4 & 0.98 & 0.00 & 0.9976 & 0.16 & 0.04 & 0.9758 \\  & Avg. & 1.03 & \(-\)0.01 & 0.9996 & 0.66 & 0.01 & 0.9930 \\ \hline \hline \end{tabular}
\end{table}