# Hydraulic Characterization of Green Roof Substrates by Evaporation Experiments
## 3 Results
### Estimation of Soil Hydraulic Functions by Direct Wind Method
Due to the direct correlation existing between \(K_{s}\) and \(\lambda\)[32; 46], higher estimated saturated hydraulic conductivity values corresponded to higher \(\lambda\) values (Table 2). Fitting a \(\lambda\) parameter greater than 0.5 resulted in an overestimation of \(K_{s}\) by a mean factor of  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Substrates** & **Sample** & \(\theta_{r}\) & \(\theta_{s}\) & \(\alpha\) & \(n\) & \(m\) & **RMSE** & **NSE** \\ \hline  & & [cm\({}^{3}\) cm\({}^{-3}\)] & [cm\({}^{3}\) cm\({}^{-3}\)] & [-cm\({}^{-1}\)] & & & [cm\  
When fitted \(\lambda\) was lower than 0.5, \(K_{\rm s}\) was underestimated by a mean factor of 0.87. Therefore, overestimation of \(K_{\rm s}\) when \(\lambda\) was left unconstrained was a more frequent and relevant outcome than the opposite one (underestimation of \(K_{\rm s}\)). It is worth noting that even an overestimation of \(K_{\rm s}\) up to a factor of 2 was not able to fit the near saturated hydraulic conductivity values estimated from UHG experiments (Figure 3). The only exception was for sample 4 of TMT, for which \(K_{\rm s}\) estimated with unconstrained \(\lambda\) was a factor of 12.4 larger than the one estimated with \(\lambda\) = 0.5. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Substrate** & **Sample** & \(K_{\rm s}\) & \(\lambda\) & **RMSE** & **NSE** & **AIC** \\ \hline  & & [cm\({}^{3}\) h\({}^{-1}\)] & & [cm\({}^{3}\) cm\({}^{-3}\)] & & \\ \hline TMT & 1 & 1.08 & 1.51 & 0.18 & \(-\)1.64 & 0.04 \\  & 1 & 0.58 & 0.50 * & 0.17 & \(-\)1.50 & 0.02 \\  & 2 & 1.12 & 6.57 & 0.01 & 0.92 & \(-\)0.38 \\  & 2 & 0.61 & 0.50 * & 0.01 & 0.84 & \(-\)0.17 \\  & 3 & 0.40 & 2.22 & 0.03 & 0.63 & \(-\)0.22 \\  & 3 & 0.34 & 0.50 * & 0.03 & 0.61 & \(-\)0.11 \\  & 4 & 43.34 & 4.60 & 0.00 & 0.97 & \(-\)0.44 \\  & 4 & 3.50 & 0.50 * & 0.00 & 0.89 & \(-\)0.19 \\ \hline ATV & 1 & 10.74 & 3.30 & 0.03 & 0.53 & \(-\)0.06 \\  & 1 & 4.52 & 0.50 * & 0.03 & 0.51 & \(-\)0.03 \\  & 2 & 1.94 & 0 & 0.03 & 0.35 & \(-\)0.06 \\  & 2 & 2.30 & 0.50 * & 0.03 & 0.34 & \(-\)0.03 \\  & 3 & 48.11 & 0.00 & 0.14 & 0.46 & 0.03 \\  & 3 & 59.39 & 0.50 * & 0.14 & 0.44 & 0.01 \\  & 4 & 4.62 & 0.00 & 0.07 & 0.54 & \(-\)0.02 \\  & 4 & 5.11 & 0.50 * & 0.07 & 0.53 & \(-\)0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of hydraulic conductivity curves obtained with the Wind iterative approach by assuming \(\lambda\) fitted or fixed at 0.5. Figure 3: Hydraulic conductivity curves obtained for each sample of the three substrates by considering \(\lambda\) fitted (\(\lambda\) = fit) or fixed at 0.5 (\(\lambda\) = fix). The grey crosses and dots represent the values measured by direct Wind and UGH methods, respectively. The RMSE and NSE values indicated a very good estimation performance for the MIX substrate and a relatively good performance for the other two substrates (Table 2). Only sample 1 of TMT showed negative values of NSE and high values of RMSE. In terms of RMSE and NSE, the two considered estimation strategies (\(\lambda\) fitted or fixed at 0.5) were practically equivalent. For 10 out of 12 samples, the AIC values for fitted \(\lambda\) were lower than those for fixed \(\lambda\). The two exceptions were sample 1 of TMT and sample 3 of ATV that showed poor RMSE and NSE values. Therefore, the strategy involving fitting of the \(\lambda\) parameter was considered preferable to that assuming a constrained \(\lambda\) value equal to 0.5.