# Assessing Water Infiltration and Soil Water Repellency in Brazilian Atlantic Forest Soils

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## Abstract

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## 1. Introduction

_{s}, in the field [12,13]. On the other hand, the mini-disk infiltrometer (MDI) is a routinely used method for measuring infiltration rates under negative pressure head in the field. The MDI is easily transportable and easy to use on hillslopes, thus, it substantially facilitates the replicability of the measurements [10].

## 2. Materials and Methods

#### 2.1. Field Sites and Soil Sampling

^{2}), which belongs to the Piracicaba River basin. The vegetation is classified as seasonal semideciduous forest. The zone is characterized by a complex geology located at the transition between the Atlantic Plateau and the Peripheral Depression geomorphological provinces, with Ultisols and Entisols as main soils [25]. The elevation varies from 600–900 m a.s.l. The climate is classified as Cwa according to the Köppen classification, with annual rainfalls of 1700 mm and mean annual temperature of 20 °C [26].

_{i}(cm

^{3}cm

^{−3}), and the soil bulk density, ρ

_{b}(g cm

^{−3}). Three disturbed soil samples (0–10 cm depth) were also collected to determine the soil texture and the soil organic carbon content (OC). The soil texture was determined by the hydrometer method [27] and the OC was determined by the Walkley-Black method.

#### 2.2. Unsaturated and Saturated Soil Hydraulic Conductivity Measurements

_{s}(mm h

^{−1}), was measured with ponding infiltration experiments of the Beerkan type [13]. At each plot, we performed seven Beerkan tests, for a total of 126 experiments. We used a steel ring with an inner diameter of 16 cm inserted to a depth of about 1 cm into the soil surface (Figure 1). In each infiltration point, a known volume of water (150 mL) was repeatedly poured into the cylinder at a small height above soil surface (i.e., a few cm) and the energy of the water was dissipated with the hand fingers to minimize the soil disturbance. Then, the time needed for each poured volume to complete infiltration was logged. This procedure was repeated until the difference in infiltration time between three consecutives trials became negligible.

_{s}(s), namely the duration of the transient phase of the infiltration process, was estimated according to the suggested criterion by Bagarello et al. [30] for analyzing cumulative infiltration data. More specifically, the t

_{s}value was determined as the first value for which:

_{reg}(t) is estimated from regression analysis considering the last points, and E defines a given threshold to check linearity. Equation (1) is applied from the end of the experiment until finding the first data point that fits the condition $\widehat{E}$ ≤ E [31,32]. An illustrative example of t

_{s}estimation using the commonly used value of E = 2% [30] is shown in Figure 2a. Transient infiltration conditions therefore occur from time 0 until time t

_{s}(i.e., when $\widehat{E}$ > 2), while steady-state conditions establishes for all data points measured after time t

_{s}(i.e., when $\widehat{E}$ ≤ 2).

_{s}(cm

^{3}cm

^{−3}), considering the values of dry bulk density, ρ

_{b}, previously determined.

#### 2.3. Estimating the Saturated Soil Hydraulic Conductivity, K_{s}

_{s}by the Simplified method based on the near Steady-state phase of a Beerkan Infiltration run (SSBI), recently proposed by Bagarello et al. [32]. This method estimates K

_{s}through an infiltration experiment of the Beerkan type [13] and an estimate of the macroscopic capillary length, λ

_{c}(mm), expressing the relative importance of the capillary over gravity forces during water movement in unsaturated soil [33,34,35]. 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 [33]:

_{w}are dimensionless constants [36,37] 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 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 λ

_{c}by the following equation [38]:

^{3}h

^{−1}) are the steady flow rates corresponding to ${h}_{-20}$ and ${h}_{0}$, respectively, and they were estimated as follows:

_{s}values, then plot-dependent λ

_{c}values were estimated by Equation (3) (Table S1).

_{sS}dataset was obtained considering λ

_{c}= 83 mm, since it represents the suggested first approximation value for most soils types [37,39].

_{sB}(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

_{sB}, by the following equation [41]:

_{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 Corey [42] relation and taking into account soil moisture initial conditions as follows [36]:

_{sS}and K

_{sB}in terms of factors of difference, FoD, calculated as the highest value between K

_{sB}and K

_{sS}divided by the lowest value between K

_{sB}and K

_{sS}. Differences between K

_{sS}and K

_{sB}not exceeding a factor of two were considered indicative of satisfactory K

_{s}predictions [33].

#### 2.4. Soil Water Repellency Carachterization

^{0.5}relationship [45,46] (Figure 2b). The persistence of water repellency was measured using the water drop penetration time (WDPT) test. This test is widely used to determine the persistence of water repellency, it is easy to perform in field and presents the hydrological implications of hydrophobicity, because the amount of surface runoff is affected by the time required for the infiltration of droplets [47]. At each plot, we selected five sampling points. The WDPT was carry out by placing 10 drops (0.05 mL) of distilled water on to the soil surface and recording the time for their complete infiltration. Following other investigations [48,49] the infiltration recording was stopped after 3600 s. Moreover, if the drop did not infiltrate after this time interval, the value of 3600 s was assigned for the WDPT [47].

#### 2.5. Data Analysis

_{b}, θ

_{i}, and θ

_{s}were determined for each plot by averaging the measured values. For these soil parameters, we assumed a normal distribution, thus no transformation was performed on these data before statistical analysis. In addition, the K

_{sB}, K

_{sS}, K

_{–}

_{20}, K

_{–5}, K

_{0}, and WDPT data were assumed to be log-normally distributed since the statistical distribution of these data is generally log-normal [50]. Statistical comparison was conducted using two-tailed t-tests, whereas the Tukey Honestly Significant Difference test was applied to compare our data set. The ln-transformed K

_{sS}, K

_{sB}, K

_{–}

_{20}, K

_{–}

_{5}, K

_{0}and WDPT data were used for the statistical treatment. A probability level, α = 0.05, was used for all statistical analyses. It is reasonable to presume that infiltrometer data can also vary depending on the initial soil moisture and its effect on SWR [31], therefore the Spearman’s rank correlation coefficients (r) were used to evaluate the relative influence of the soil properties on the infiltration process. For all the statistical analyses the Minitab© computer program (Minitab Inc., State College, PA, USA) was used.

## 3. Results and Discussion

#### 3.1. Soil Properties

_{b}values were observed in the restored forest R4, where the exposure of the soil and trampling pressure during the land-use history was greater in comparison with restored forest R3. Forest soils were characterized by the lowest ρ

_{b}values, which can be related to the heterogeneous soil structure and higher soil macroporosity in this cover [51,52]. At the time of sampling, the θ

_{i}ranged from 0.12 to 0.32 cm

^{3}cm

^{−3}and the soil was significantly wetter in plots P1U, P2M, R4S, R4M, and F5I (Figure S1).

#### 3.2. Assessing SSBI Estimates

_{s}values). For the first scenario (i.e., λ

_{c}estimated from multi tension experiments), the K

_{sS}values ranged between 5.9 and 1486.8 mm h

^{−1}. The mean FoD was equal to 1.36 (maximum value = 2.74) and the individual values were less than 2 and 1.5 for 89% and 78% of the cases, respectively (Figure 4). For the second scenario (i.e., λ

_{c}= 83 mm), K

_{sS}data ranged between 3.7 and 934.5 mm h

^{−1}. The mean FoD was equal to 1.51 (maximum value = 2.37) and the individual values were less than 2 and 1.5 in the 90% and 53% of the cases, respectively. Therefore, using the estimated λ

_{c}values resulted in a slightly better estimation of K

_{sS}, yielding a lower mean FoD value, thus, only the first scenario was considered in the subsequent analysis.

#### 3.3. Comparing BEST versus SSBI Estimates Under Soil Water Repellency Conditions

_{s}in case of convex-shaped cumulative infiltration curves, which led to negative b

_{s}values and consequently to null K

_{sB}. The K

_{sB}data ranged between 4.5 and 1394 mm h

^{−1}(almost three orders of magnitude). The BEST-steady algorithm yielded physically plausible estimates (i.e., positive K

_{s}values) for 108 of 126 infiltration runs (i.e., 85.7% of cases). The percentage of successful runs was of 95.2% both for the pasture and restored forest (40 of 42 runs). With reference to the remnant forest, BEST led to a failure rate value of 33.3%, leading to lacks of estimates for 14 of 42 infiltration runs. In these cases, cumulative infiltration curves had convex shapes, which are typical for hydrophobia i.e., [42,45,46]. Such hydrophobia may result from significant amounts of organic matter content i.e., [52,53,54], originating from fauna and flora activities [55]. Soil texture also plays a major role on SWR, in particular, SWR is expected to increase for decreasing clay content. In this sense, our plots (i.e., F5U, R3U, R3D, P1M) with more sand content exhibited higher WDPT values. On the other hand, for the forest plots (i.e., F6U, F6M, F6D) the significant amounts of organic matter had a main role in generating relevant WDPT values also on finer textured soils [23,56].

_{s}values, showing that BEST can only be used when the soil does not exhibit hydrophobic effect, as suggested by Lassabatere et al. [57]. As shown in Figure 5, at increasing failure rates of the BEST method corresponded higher WDPT values, suggesting that where hydrophobic condition occurred, mainly in the remnant forest plots, it was the main cause of failure of BEST-steady. More specifically, BEST-steady requires both the slope and the intercept of regression line fitted to the last data points on the I vs. t plot. The magnitude of b

_{s}depends on the entire cumulative infiltration curve (including the transient phase) [58,59], therefore that term is sensitive to SWR that impedes the early wetting phase of the infiltration process. When soil hydrophobicity occurred, the I vs. t

^{0.5}plot exhibited the characteristic “hockey-stick-like” shape [46], hiding the estimation of K

_{s}trough BEST-steady [42]. On the other hand, SSBI differs by the term expressing steady-state condition, considering exclusively the final infiltration rate [13]. The exclusive use of this term allowed to consider only the final stage of the infiltration process, i.e., when the hydrophobicity effect on infiltration was diminished. In this investigation eighteen Beerkan infiltration tests exhibited a clear hockey-stick-like shape, mainly at the remnant forest plots, that allowed calculation of WRCT as the intersection point of two straight lines, representing the initial and the late stages of I vs. t

^{0.5}relationships [45] (Figure 2b).

_{s}values. Therefore, for all the experiments steady-state infiltration rates (i

_{s}) were always reached before the end of the runs and after that the influence of hydrophobicity had ceased, so the K

_{s}values estimated by the use of the SSBI method could be always properly estimated considering the last data points of the infiltration curves. Limiting the hydraulic characterization to the stabilized phase avoided the uncertainties due to specific shape of the cumulative infiltration and a no clear distinction between the early- and late-time infiltration process because soil hydrophobic phenomena [58]. In other words, the results presented in this study suggest that if hydrophobicity affects the first stage of a Beerkan infiltration test, the SSBI estimates should characterize the hydraulic property of the soil properly. We believe that this result has practical importance because the use the SSBI method allowed us to maintain the integrity of the dataset, and to compare the hydraulic behavior of different sites with different land uses, where soil hydrophobicity only occurs in some circumstance.

_{i}and ln(WDPT) was significant (r = −0.67, p = 0.002) (Table 2). This result was in line with the reasoning that the soil water content governs the interaction between soil particles and amphiphilic organic molecules, resulting from degradation of tree tissues, that coat soil particles and may be responsible for SWR [45]. The transition from wettable to hydrophobic status (and vice versa) is generally associated to a critical range of soil moisture [63]. The lower water content of this range defines the condition below which the medium is water repellent, the higher identifies the condition above which the medium is wettable. K

_{s}data were positively correlated to ln(WDPT). This is logical, since both macropore flow (which affects the magnitude of K

_{s}) and water repellency phenomena were relevant at the remnant forest plots. In brief, the correlation between these two variables is not the result of a causal connection but the concomitancy of two processes: hydrophobia and macropore flow, which also lead to mainly subcritical water repellency. In addition, we conclude that hydrophobia had no effect on the estimation of the saturated hydraulic conductivity. Indeed, in opposite case, K

_{sS}and ln(WDPT) would have a negative correlation. Consequently, we assumed that the SSBI method proved efficient for detecting SWR and estimating properly the soil saturated hydraulic conductivity, at the same time. Lastly, K

_{sB}and K

_{sS}had a positive correlation with a value close to unity. The two estimators provide close estimates, as discussed above with the FoD. We then can conclude that soil hydrophobicity only affected the failure rate of the BEST-steady algorithm (Figure 5), without affecting the quality of its estimate when the method worked.

#### 3.4. Unsaturated versus Saturated Soil Hydraulic Conductivity

_{sS}, and near-saturated soil hydraulic conductivity, K

_{–}

_{20}, were 10.7, 21.5, and 118.3, for the pasture, restored forest and remnant forest, respectively. A similar trend was also detected when the K

_{–5}values were considered, with the mean values of the ratios equal to 2.2, 5.6, and 23.7. Similar results were also obtained when K

_{sB}values were considered, with the values of the ratios equal to 10.6, 17.5, 92.0, and 2.2, 4.6, 17.4, for the K

_{–20}and K

_{5}data, respectively. We also noticed a discrepancy between K

_{sS}and K

_{0}data, especially at the Forest site, because only under ponded conditions at the surface the macropores are activated [63]. The increase of the difference between saturated and unsaturated conditions can be explained by the activation of macroporosity at the forest plots [64]. Overall, the soil in the remnant forest is heterogeneous and characterized by a dominance of complex macropores. For example, a higher soil macroporosity and total porosity have been reported in the same forest soil by our previous work [14]. This soil macroporosity resulted from the better soil structure, which is caused by the high amount of biopores, roots, soil fauna activity and greater inputs of organic matter [52,63,64]. Moreover, soil variability at the scale of a few meters could have been less represented by the MDI, due to the small diameter of the infiltrometer (i.e., 4.5 cm).

## 4. Conclusions

_{s}allowed to account for the effect of SWR on water infiltration measurements. In particular, when there are evidences of SWR, our results suggest using the SSBI method instead of BEST-steady to avoid the failure of the analysis in case of string SWR. Indeed, the SSBI method allowed to maintain the integrity of the infiltration dataset, facilitating the hydraulic comparison between different land uses. Tension (MDI) and ponding (Beerkan) infiltration tests provided a complementary information, highlighting a clear increase of the hydraulic conductivity, especially at the remnant forest plots, when moving from near-saturated to saturated conditions. This information is relevant to assess the infiltration recovery after forest restoration, as it signals soil structure heterogeneity and higher soil macroporosity. In addition, measuring the unsaturated soil hydraulic conductivity with different water pressure heads also allowed to estimate λ

_{c}in the field. This approach, in conjunction with Beerkan measurements, allowed to generate better K

_{s}estimates based on field measurements, and also avoided any subjectivity caused by assuming a constant λ

_{c}value, which is often selected based on general descriptions of soil textural and structural characteristics when estimating K

_{s}from ponding infiltration experiments [34]. Nonetheless, developing alternative methods for estimating λ

_{c}is desirable for alleviating the amount of work necessary to accurately estimate K

_{s}.

## Supplementary Materials

^{−1}), dry soil bulk density (ρ

_{b}in g cm

^{−3}), initial volumetric soil water content (θ

_{i}in cm

^{3}cm

^{−3}), and saturated volumetric soil water content (θ

_{s}in cm

^{3}cm

^{−3}), values for the 18 sampled plots. Bars indicate standard deviation. For a given variable and plot, means that do not share a letter are significantly different according to the Tukey honestly significant difference test (P < 0.05). The subscript letter refers to the landscape position (Upslope, Middleslope and Downslope) in each site, Table S1: Mean values for each sampled plot (P1, P2, R3, R4, F5 and F6) of the steady-state infiltration rates, ${i}_{s,{h}_{0}}$ and ${i}_{s,{h}_{-20}}$ (mm h

^{−1}), flow rates, ${Q}_{s,{h}_{0}}$ and ${Q}_{s,{h}_{-20}}$ (mm

^{3}h

^{−1}), obtained from the MDI experiments carried out with a pressure head ${h}_{0}$ = 0 and ${h}_{-20}$ = −20 mm, and macroscopic capillary length, λ

_{c}(mm), estimated by Equation (3).

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Picture in the forest site showing the mini-disk infiltrometer and the steel ring used for the Beerkan infiltration test.

**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).

**Figure 4.**Empirical cumulative distribution function plot of the factors of difference between the saturated soil hydraulic conductivity values estimated by the BEST -steady (K

_{sB}) and SSBI methods (K

_{sS}). K

_{sS}data were estimated considering λ

_{c}= 83 mm (blue solid line) and the mean λ

_{c}values estimated for each sampled plot from the MDI experiments carried out with a suction of 0 and −20 mm (red dashed line).

**Figure 5.**Comparison between the water drop penetration time, WDPT (s), and the failure rate of the BEST-steady algorithm (%). The picture represents water droplets resisting infiltration into forest soil due to the water repellency.

**Figure 6.**Comparison of the mean saturated soil hydraulic conductivity values estimated with BEST-steady, K

_{sB}(mm h

^{−1}), and the SSBI method, K

_{sS}(mm h

^{−1}), and hydraulic conductivity, K

_{0}, K

_{–}

_{5}, and K

_{–}

_{20}(mm h

^{−1}), values measured with the minidisk infiltrometer under a tension of 0, −5, and −20 mm. For a given plot, means that do not share a letter are significantly different according to the Tukey honestly significant difference test (p < 0.05).

**Table 1.**Values of the intercept, b

_{s}(mm) of regression line fitted to the last data points describing the steady-state conditions on the I vs. t plot, total duration, t

_{end}(s), total infiltrated depth, I

_{end}(mm), infiltrated depth at the equilibration time, I(t

_{s}) (mm), equilibration time, t

_{s}(s), and water repellency cessation time, WRCT (s), for the eighteen Beerkan infiltration runs affected by hydrophobicity.

ID | b_{s} (mm) | t_{end} (s) | I_{end} (mm) | I(t_{s}) (mm) | t_{s} (s) | WRCT (s) |
---|---|---|---|---|---|---|

P1M6 | −13.2 | 5053 | 52.7 | 30.1 | 3290 | 93 |

P1M7 | −8.1 | 4601 | 45.2 | 22.5 | 2678 | 89 |

R3U2 | −4.7 | 457 | 52.7 | 30.1 | 277 | 25 |

R3D7 | −2.1 | 327 | 52.7 | 22.5 | 145 | 20 |

F5U1 | −8.4 | 363 | 82.9 | 45.2 | 210 | 23 |

F5U2 | −2.7 | 329 | 82.9 | 7.5 | 39 | 21 |

F5U3 | −6.4 | 325 | 75.3 | 22.5 | 115 | 22 |

F5U4 | −10.4 | 682 | 75.3 | 45.2 | 439 | 33 |

F5M2 | −3.3 | 219 | 75.3 | 22.5 | 72 | 17 |

F5M3 | −3.3 | 160 | 60.2 | 37.6 | 103 | 15 |

F5M4 | −10.7 | 245 | 97.9 | 22.5 | 74 | 19 |

F6U1 | −2.3 | 474 | 67.8 | 22.5 | 166 | 26 |

F6U2 | −3.2 | 207 | 67.8 | 37.6 | 121 | 17 |

F6U5 | −13.3 | 188 | 75.3 | 52.7 | 140 | 18 |

F6M5 | −10.4 | 495 | 82.9 | 37.6 | 253 | 27 |

F6M6 | −4.3 | 208 | 82.9 | 22.5 | 64 | 17 |

F6D2 | −10.1 | 148 | 82.9 | 60.2 | 112 | 14 |

F6D4 | −1.3 | 325 | 75.3 | 52.7 | 229 | 20 |

Variables | θ_{i} | ln(WDPT) | ln(K_{sS}) |
---|---|---|---|

ln(WDPT) | −0.67 | ||

p-Value | 0.002 | ||

ln(K_{sS}) | −0.59 | 0.74 | |

p-Value | 0.009 | <0.001 | |

ln(K_{sB}) | −0.61 | 0.73 | 0.97 |

p-Value | 0.007 | 0.001 | <0.001 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lozano-Baez, S.E.; Cooper, M.; de Barros Ferraz, S.F.; Ribeiro Rodrigues, R.; Lassabatere, L.; Castellini, M.; Di Prima, S. Assessing Water Infiltration and Soil Water Repellency in Brazilian Atlantic Forest Soils. *Appl. Sci.* **2020**, *10*, 1950.
https://doi.org/10.3390/app10061950

**AMA Style**

Lozano-Baez SE, Cooper M, de Barros Ferraz SF, Ribeiro Rodrigues R, Lassabatere L, Castellini M, Di Prima S. Assessing Water Infiltration and Soil Water Repellency in Brazilian Atlantic Forest Soils. *Applied Sciences*. 2020; 10(6):1950.
https://doi.org/10.3390/app10061950

**Chicago/Turabian Style**

Lozano-Baez, Sergio Esteban, Miguel Cooper, Silvio Frosini de Barros Ferraz, Ricardo Ribeiro Rodrigues, Laurent Lassabatere, Mirko Castellini, and Simone Di Prima. 2020. "Assessing Water Infiltration and Soil Water Repellency in Brazilian Atlantic Forest Soils" *Applied Sciences* 10, no. 6: 1950.
https://doi.org/10.3390/app10061950