## 3 Results and Discussion
### Water Infiltration and Application of the BEST Algorithm  
Evidence of the flow dynamics described above, and observed from the 3D diagrams, was also found when analyzing infiltration data. Indeed, all Beerkan infiltration curves showed a sudden decrease in infiltration rate when the wetting front encountered the limestone layer. [PERSON] et al. [51] suggest that water infiltration data should be considered indicative of the hydraulic characteristics of the most impermeable layer. Therefore, characterizing the hydraulic properties of the topsoil required us to discriminate the infiltration process into two different stages: a first stage when water infiltrated only into the surface layer, and a subsequent phase when the wetting front reached the interface between layers. The decline in infiltration rate was not readily discernible from visual examination of the cumulative infiltration curve (Figure 3a) but became apparent upon applying the cumulative linearization method CL, [52] (Figure 3b). More specifically, all the linearized curves showed a convex shape, which is expected in the case of layered soils with an underlying less permeable layer [25]. Conversely, for ideal situations, namely for uniformly unsaturated, rigid, and homogeneous soils, linearized infiltration data are expected to show an increasing trend that is characterized by a practically unique slope [37]. Thus, we characterized all the linearized Beerkan plots (\(I\surd t\) vs. \(\surd t\)) by an initial ascending linear segment, followed, after a knee point, by a more or less distinct reduction in slope. Subsequently, we computed the slope and intercept values for both the early and later phases of the infiltration processes. As shown in Figure 3b, for the case of a single Beerkan test, we also calculated the abscissa (\(\surd t\)) of the intersection point of the two straight lines. This threshold split the infiltration data into two subsets representative of the two stages occurring when water moved across the layering profile: a first stage (first linear portion) when water infiltrated into the upper layer, and a second stage (second liner part) when water started to infiltrate into the underlying limestone layer. The infiltration data corresponding to the first stage were subsequently used for assessing the soil physical quality of the upper soil layer (Figure 3c). The BEST-steady algorithm was employed to derive parameters \(n\), \(m\), \(\alpha\) and \(K_{\mathrm{s}}\) from textural and infiltrometer data (Table 3). Statistical analysis using the Kolmogorov-Smirnov test indicated that \(K_{\mathrm{s}}\) data followed a log-normal distribution. Consequently, the geometric mean and the geometric coefficient of variation were computed for \(K_{\mathrm{s}}\)[41]. Conversely, all other parameters exhibited normal distributions and were synthesized using the average value and its corresponding variability. \(K_{\mathrm{s}}\) values ranged from 192.2 to 1031.0 mm h\({}^{-1}\), with a mean of 424.4 mm h\({}^{-1}\). Additionally, estimates of \(K_{\mathrm{s}}\) were compared with field measurements of unsaturated hydraulic conductivity, \(K_{-30}\), obtained at a pressure head of \(h=-30\) mm (\(K_{-30}\)). Table 3 summarizes the \(K_{-30}\) values measured for the Ottawa site. As expected, the hydraulic conductivity increased dramatically in the proximity of the saturation, i.e., for \(h=0\). The \(K_{-30}\) values ranged between 33.3 and 70.1 mm h\({}^{-1}\). The \(K_{\mathrm{s}}\) values estimated by BEST consistently exceeded the measured \(K_{-30}\) values, indicating that physically realistic estimates of \(K_{\mathrm{s}}\) were obtained across all scenarios, as \(K_{\mathrm{s}}>K_{-30}\). Specifically, for the topsoil, BEST provided a mean \(K_{\mathrm{s}}\) value that was 7.9 times higher than the corresponding \(K_{-30}\), equivalent to an order of magnitude difference. Such substantial differences between saturated and near-saturated hydraulic conductivity are frequently observed under field conditions, e.g., [53].