# Assessing Water Infiltration and Soil Water Repellency in Brazilian Atlantic Forest Soils
## 2 Materials and Methods
### Estimating the Saturated Soil Hydraulic Conductivity, \(K_{s}\)  
We estimated \(K_{s}\) by the Simplified method based on the near Steady-state phase of a Beerkan Infiltration run (SSBI), recently proposed by [PERSON] et al. (2018). This method estimates \(K_{s}\) through an infiltration experiment of the Beerkan type ([PERSON] et al., 2018) and an estimate of the macroscopic capillary length, \(\lambda_{c}\) (mm), expressing the relative importance of the capillary over gravity forces during water movement in unsaturated soil ([PERSON] et al., 2018; [PERSON] et al., 2018; [PERSON] et al., 2018). Firstly, the experimental steady-state infiltration rate, \(i_{s}\) (mm h\({}^{-1}\)), is estimated by linear regression analysis of the last data points of the cumulative infiltration, \(I\) (mm), versus time, \(t\) (h), plot, describing the near steady-state condition. Then, SSBI estimates the saturated soil hydraulic conductivity, \(K_{sS}\) (mm h\({}^{-1}\)) (the subscript S is used to indicate SSBI), as follows ([PERSON] et al., 2018):  
\[K_{sS}=\frac{i_{s}}{\frac{\gamma\gamma_{w}\lambda_{c}}{r_{d}}+1} \tag{2}\]  
where \(\gamma\) and \(\gamma_{w}\) are dimensionless constants ([PERSON] et al., 2018; [PERSON] et al., 2018) related to the infiltration front shape, that are commonly set at 0.75 and 1.818, and \(r_{d}\) (mm) is the radius of the containment ring. Two different scenarios  
Figure 2: (**a**) Example of estimation of the equilibration time, \(t_{s}\) (s), and infiltrated depth at the equilibration time, \(I(t_{s})\) (mm) from cumulative infiltration and (**b**) water repellency cessation time, WRCT (s), as the intersection point of two straight lines, representing the initial (hydrophobic) and the late (wettable) stages of the \(I\) vs. \(t^{0.5}\) plot of a Beerkan infiltration run affected by soil water repellency (SWR). were considered to apply the SSBI method. The first scenario considered the MDI experiments, carried out with pressure heads of \(h_{-20}=-20\) mm and \(h_{0}=0\), to estimate \(\lambda_{c}\) by the following equation [38]:  
\[\lambda_{c}=\frac{h_{-20}-h_{0}}{ln\left(Q_{s,h_{-20}}/Q_{s,h_{0}}\right)} \tag{3}\]  
where \(Q_{s,h_{-20}}\) and \(Q_{s,h_{0}}\) (mm\({}^{3}\) h\({}^{-1}\)) are the steady flow rates corresponding to \(h_{-20}\) and \(h_{0}\), respectively, and they were estimated as follows:  
\[Q_{s}=\mathrm{i}_{s}\pi\mathrm{r_{d}}^{2} \tag{4}\]  
For this scenario, we firstly averaged for each plot the individual \(i_{s}\) values, then plot-dependent \(\lambda_{c}\) values were estimated by Equation (3) (Table S1). The second \(K_{\mathrm{s}S}\) dataset was obtained considering \(\lambda_{c}=83\) mm, since it represents the suggested first approximation value for most soils types [37; 39]. The Beerkan Estimation of Soil Transfer parameters (BEST) method [11] was also applied to estimate the saturated soil hydraulic conductivity, \(K_{\mathrm{s}B}\) (mm h\({}^{-1}\)) (the subscript B is used to indicate BEST). More specifically, among the three existing BEST algorithms, we used the BEST-steady algorithm [40], that estimates \(K_{\mathrm{s}B}\), by the following equation [41]:  
\[K_{\mathrm{s}B}=\frac{\mathrm{C}\ \mathrm{i}_{s}}{\mathrm{A}\ \mathrm{b}_{s}+ \mathrm{C}} \tag{5}\]  
where \(b_{s}\) (mm) is the intercept of the regression line fitted to the last data points of the \(I\) versus \(t\) plot. The \(A\) (mm\({}^{-1}\)) and \(C\) constants are defined for the specific case of the Brooks and [PERSON] [42] relation and taking into account soil moisture initial conditions as follows [36]:  
\[A=\frac{\gamma}{\mathrm{r_{d}}(\mathrm{\theta_{s}-\mathrm{\theta_{i}}})} \tag{6}\]  
\[C=\frac{1}{2\left[1-\left(\frac{\mathrm{\theta_{i}}}{\mathrm{\theta_{s}}} \right)^{\mathrm{n}}\right](1-\beta)}\ln\left(\frac{1}{\beta}\right) \tag{7}\]  
where \(\beta\) is a coefficient commonly set at 0.6, and \(\mathrm{\eta}\) is a shape parameter that is estimated from the analysis of the particle size data with the pedotransfer function included in the BEST procedure [11].