# Hydraulic Characterization of Green Roof Substrates by Evaporation Experiments
## 3 Results  
### Estimation of Soil Hydraulic Functions by Direct Wind Method  
The retention curves obtained for the different replicated samples of the three considered substrates are plotted in Figure 2. For both conditions (\(\theta_{r}\) fitted or fixed at \(\theta_{150}\)), the estimated retention curves effectively reproduced the measured \(\theta\)_(\(h\))_ values and the two curves mostly overlapped in the measurement range. The estimated values of the volumetric water content at saturation, \(\theta_{s}\), ranged from 0.46 to 0.48 cm\({}^{3}\)cm\({}^{-3}\) and from 0.53 to 0.59 cm\({}^{3}\)cm\({}^{-3}\) for the TMT and MIX substrates, respectively. For these substrates, the differences in \(\theta_{s}\) estimated with the two procedures were the most equal to 0.01 cm\({}^{3}\)cm\({}^{-3}\). It was concluded that a close estimation of \(\theta_{s}\) can be obtained independently of the considered estimation strategy. The only exception was for two samples of the ATV substrate in which the difference between the two estimated \(\theta_{s}\) values reached 0.09 cm\({}^{3}\)cm\({}^{-3}\). For all the considered experiments (\(n=12\)), when \(\theta_{r}\) was estimated (\(\theta_{r}=\) fit), the iterative Wind procedure yielded \(\theta_{r}=0\) as the best solution and, therefore, \(\theta_{r}\) was fixed at zero. Compared to the \(\theta_{r}=\theta_{150}\) strategy, this resulted in a systematic underestimation of \(\theta\)(\(h\)) in the dry range of the water retention curve. The goodness of fit for both strategies is indicated by the low RMSE values and the NSE value close to one. Specifically, the RMSE values ranged from a minimum of 0.002 to a maximum of 0.013 cm\({}^{3}\)cm\({}^{-3}\), whereas the NSE index was always higher than 0.97. Figure 2: Retention curves obtained for each sample of the three substrates (TMT, ATV and MIX) by assuming \(\theta_{r}\) was fitted (\(\theta_{r}=\) fit) or fixed at \(\theta_{150}\) (\(\theta_{r}=\) fix). The grey dots represent the measured values. For the TMT and ATV substrates, no clear preference for a specific estimation strategy could be claimed. For the MIX substrate, fixing the residual water content at the value measured for \(h=\theta_{150}\) m generally yielded better estimates of the water retention curve (Table 1). From these findings, it can be deduced that the estimation of the retention curve carried out with the direct Wind method is more accurate if an appropriate choice of the \(\theta_{r}\) parameter is made. The measured values of unsaturated soil hydraulics showed a large dispersion at higher pressure heads (\(h>-30\) cm) particularly for the two commercial substrates (TMT and ATV) (Figure 3). The uncertainty in \(K(h)\) measurements close to saturation is a known drawback of the evaporation method due to the influence of measurement errors when the hydraulic gradients are low. In the case of the commercial substrate, the measurement error influence is probably emphasized by the coarser nature of the material that makes the hydraulic contact with the ceramic cup of the tensiometers more problematic. For both the considered conditions (\(\lambda\) fitted or fixed at 0.5), the estimated hydraulic conductivity curves overlapped the experimental \(K(h)\) values in the measured range of pressure heads (Figure 3). The two estimated \(K(h)\) relationships diverged for drier conditions (i.e., low \(h\) values). In this range, fitting of the \(\lambda\) parameter generally resulted in an underestimation of the unsaturated hydraulic conductivity function. This was the case for TMT, for which \(\lambda\) ranged from 1.51 to 6.57, sample 1 of ATV (\(\lambda=3.0\)) and samples 1, 2 and 3 of MIX (\(\lambda=1.32\)-1.77). Conversely, overestimated \(K(h)\) functions in the dry range corresponded to fitted values of \(\lambda\) lower than 0.5 (samples 2, 3 and 4 of ATV and sample 4 of MIX).