INTRODUCTION
Soil water repellency (WR) is a physical phenomenon whereby water is unable to wet the soil surface of mineral particles (Ritsema et al., 2003; Ritsema et al.,1994). This phenomenon is widely distributed across the world (Zavala et al., 2014), with higher WR typically occurring in coarse-textured forest soils (Benito et al., 2019). WR changes the three-dimensional distribution and dynamic characteristics of soil water content, resulting in an uneven distribution of soil moisture (Badía-Villas et al., 2014; S et al., 2015). WR not only affects the soil wettability (Sepehrnia et al., 2017), but also impacts other ecological and hydrological processes, e.g., restraining water infiltration (Sepehrnia et al., 2017), promoting surface runoff (Amiri et al., 2017; Neris et al., 2013), water and soil erosion (Cawson et al., 2016; Fox et al., 2007), wind erosion, accelerating fertilizer loss (Müller et al., 2018a) by influencing preferential flow (Oostindie et al., 2008; Rye and Smettem, 2017), and increasing soil carbon content (Muñoz-Rojas et al., 2018), which may lead to a reduction in crop growth (Li et al., 2019).
The hydraulic properties of water-repellent soil (W-RS) are quite different from those of hydrophilic soils (HS). Ward et al. (2015) concluded that, in W-RS, tillage destroys the existing water entry pathways, and slows the infiltration of water into the soil. Doerr et al. (2003) found that WR can reduce the soil
∗Corresponding author: Department of Hydraulic and Ecological Engineering, Nanchang Institute of Technology, Nanchang 330099, China
E-mail address: 971932670@qq.com
infiltration rate (IR) by 10–40%, while DeBano (2000) showed that the horizontal infiltration of W-RS was 25 times slower than that of HS. Keizer et al. (2005) reported that soil IR can be decreased by reducing the potential gradient of the soil matrix. Many studies show that WR is caused by soil particles and aggregates being coated with hydrophobic materials, which can originate from plant litter and residues, microbes, organic fertilizers, or the application of wastewater and artificial hydrophobic agents (Leelamanie et al., 2009; Subedi et al., 2012). The influence of these factors on the degree of WR reflects the relationship between WR and the contact angle (CA), which enables measurement of the time dependency of CA (Leelamanie et al., 2009). The range of CA attained by wettable soils is less than 90°, whereas W-RS have CA > 90° (Lourenço et al., 2018). Severe hydrophobicity occurs when the CA is greater than 90°. In this case, water does not spontaneously infiltrate. Subcritical repellency occurs when the contact angle is less than 90°, whereby the soil wets spontaneously but with a reduced IR (Tillman et al., 1989). For the same CA, the matrix suction gradually decreases as the volume of the liquid bridge increases (Graber et al., 2009; Hamlett et al., 2011). When the volume of the liquid bridge reaches a certain level, the matrix suction becomes negative. The WR effect of granules then begins to occur (Subedi et al., 2012; Subedi et al., 2013). The CA of hydrophobic media normally decreases with continuous contact with water, eventually allowing water imbibition (Subedi et al., 2013). Arye et al. (2007) investigated the main imbibition relationship between water saturation and capillary pressure using the capillary rise test, and found that organic matter is likely to detach from the soil particles and be dissolved into the soil solution. This, in turn, decreases the equilibrium CA. The effect of WR on infiltration is very complex because of the unstable wetting fronts, which result in finger-pattern preferential flow paths (Rye et al., 2017; Wang et al., 2000a) and hysteresis in soil water retention (Arye et al., 2007). However, WR is a dynamic property (that generally decreases as the soil wets) and, therefore, IR is affected during the process itself, resulting in IR curves that do not correspond to the traditional infiltration theory.
The regulation of surface runoff and infiltration is an important manifestation of the ecological hydrological function of WR (White et al., 2017). Because WR can create unstable water flow within the soil matrix (Jonge et al., 1999), the process of water infiltration is relatively complex. Current understanding of the infiltration process in W-RS is limited to the fact that WR can reduce soil IR (Xiao et al., 2019). In fact, as water infiltration continues, the IR does not decrease monotonously and, contrary to infiltration in wettable soils, can increase with time (Ren et al., 2018; Wang et al., 2000b). This phenomenon generates infiltration curves with a double slope (transient infiltration curve followed by a steady-state section) (Vogelmann et al., 2017). For forest soils with strong WR, water infiltration is not stable (Rye and Smettem, 2017), nor is it strictly in accordance with the three-stage process of HS infiltration. Instead, with continuous water infiltration, the WR gradually disappears and the IR appears to mutate (Burch et al., 1989; Diehl, 2013). The effect of WR is very evident in cumulative infiltration (CI), which exhibits a double-slope curve (Vogelmann et al., 2017). Inaccurate fitting indicates that the Haverkamp model (Haverkamp et al., 1994) should not be applied to such curves.
Leighton et al. (2007) and Pierson et al. (2008) found that, under WR conditions, the IR slope gradually increases with continuous rainfall. Doerr et al. (2000) showed that, during the whole rainfall process, the IR of W-RS first decreases, then increases, and then decreases to the lowest value and remains stable. This phenomenon is particularly obvious in forest soils (Neris et al., 2013; Ritsema et al., 2003). Filipović et al. (2018) used HYDRUS (2D/3D) to invert the hydraulic properties of W-RS under drought conditions. They found that the CI of W-RS exhibits a non-smooth, step-like growth trend, whereas the IR first decreases and then increases. Rye et al. (2017) believe that including only WR in the model enables a correct assessment of the hydrological process. Müller et al. (2018b) considered WR to be an important factor in any hydrological model.
At present, the phenomenon of increasing IR is being ignored and water infiltration is generalized as a monotonously decreasing process. Traditional infiltration models (e.g., those of Green–Ampt, Philip, Kostiakov, and Horton) and piecewise function models are still used to fit the double-slope infiltration process (Almeida et al., 2018; Moret-Fernández et al., 2019) in the model developed by Haverkamp et al. (1994), and the corresponding infiltration curve indicates that the traditional model should not be applied to this kind of curve. A piecewise Kostiakov function (PKF) has been used to calculate the IR, resulting in a discontinuity at the inflection point (Ren et al., 2018). This contradicts the physical phenomenon whereby WR fades away and only one maximum IR exists at the inflection point. Ren et al. (2018) used a Gauss function (GF) and a piecewise Gauss function (PGF) to fit the IR of W-RS. Although the GF reflects the process of the increasing and then decreasing IR in W-RS, it is difficult to describe the gradual decrease in IR after the infiltration starts.
In this study, water infiltration is analyzed in two types of soil using the Kostiakov function (KF), PKF, GF, PGF, Fourier series function (FSF), Gamma function (GMF), Beta function (BF), and piecewise Beta function (PBF). The specific objectives of this study are as follows: (1) investigate the law of W-RS infiltration, and reveal the reasons for the single-peak curve of IR in W-RS; (2) propose a method of dividing the water infiltration stages in W-RS; (3) develop a unified model that demonstrates the monotonous reduction of IR in HS and reflects the single peak IR curve for W-RS; (4) explore the differences and relationship between the proposed models (BF and GMF) and traditional water infiltration models (Philip, Horton, and Kostiakov models).