## 1. Introduction

[2] Because infiltration affects water availability for vegetation, groundwater recharge, overland flow, and solute transport, it has been the focus of considerable study over the previous century [e.g., *Green and Ampt*, 1911; *Philip*, 1957b; *Wooding*, 1968; *Brutsaert*, 1977]. Under normal conditions, gravity and capillarity drive vertical infiltration, whereas capillarity alone drives horizontal infiltration [*Philip*, 1957b].

[3] Under constant head conditions, one- and three-dimensional vertical infiltration into a uniform soil has been adequately described using *Philip*'s [1957b] two-term approximation:

where *I* is cumulative infiltration over time *t* and *S* is the soil sorptivity. For one-dimensional vertical infiltration, *C* is proportional to the soil's saturated hydraulic conductivity (*K*_{s}). The ratio *C*/*K*_{s} is ≤ 1, depending on soil type and soil moisture [*Philip*, 1990], with proposed ranges of 1/3 ≤ *C*/*K*_{s} ≤ 2/3 [*Fuentes et al*., 1992] or 0.3 ≤ *C*/*K*_{s} ≤ 0.4 [*Philip*, 1990]. In the case of three-dimensional infiltration, *C* incorporates both saturated hydraulic conductivity and sorptivity [*Smettem et al*., 1995; *Touma et al*., 2007].

[4] At early times (i.e., *t* << *S*^{2}/*C*^{2}) sorptivity dominates the infiltration behavior, and for very early times (*t* → 0) the second term on the right hand side may be neglected [*White et al*., 1992]. Conversely, the second term dominates as time increases, subject to the limit of *t* = *S*^{2}/C^{2}, when the series expansion from which equation (1) was derived is no longer accurate. Alternate expressions have been developed to describe long-time (steady-state) infiltration behavior [*Philip*, 1957a, 1957b; *Wooding*, 1968; *Haverkamp et al*., 1994], which lend themselves to estimations of *K*_{s}. However, the time required to reach late-time or quasi-steady state conditions may be impractical, particularly for soils with low hydraulic conductivity, and assumptions of homogeneity are typically violated for long infiltration experiments.

[5] Infiltration typically occurs over intermediate or transient timescales (neither exclusively early- nor late-time) and is three-dimensional. One such example is infiltration from an axisymmetric single ring source, which can provide a rapid and low-cost measurement of soil hydraulic properties [*Braud et al*., 2005]. However, interpretation of these infiltration tests often requires that the *S* and *C* terms both be considered. Methods to differentiate between sorptivity and saturated hydraulic conductivity for such infiltration conditions have been proposed [*Smiles and Knight*, 1976; *Smettem et al*., 1995; *Vandervaere et al*., 2000], but may be inadequate for estimating small *K*_{s} values [*Smettem et al*., 1995].

[6] Sorptivity represents the soil's ability to draw water [*Philip*, 1957b; *Touma et al*., 2007], which is a function of the capillarity (the driving force) and the soil's hydraulic conductivity (the dissipation). This dual-dependence is evident in *Parlange* [1975]'s precise solution for sorptivity (as modified for positive ponded conditions by *Haverkamp et al*. [1990]):

where *Θ* is the degree of saturation

[7] *θ*_{0}*, θ*_{s}, and *θ*_{r} are the initial, saturated, and residual volumetric soil water contents, respectively, *K*(*h*) is the hydraulic conductivity as a function of soil matric potential, *h _{0}* is the initial matric potential, and

*h*

_{surf}is the depth of ponding at the surface.

[8] Hydraulic conductivity also appears in the simpler or “traditional” definition of sorptivity provided by the *Green and Ampt* [1911] model:

where *h _{wf}* is the wetting front potential, which is also referred to as the effective capillary drive [

*Morel-Seytoux et al*., 1996], capillary pull, or macroscopic capillary length [

*White and Sully*, 1987]. The correction factor

*φ*accounts for deviations from a sharp wetting front and/or viscous damping effects. For example,

*φ*= 1 for a

*Green and Ampt*[1911] solution, 1.1 for the

*White and Sully*[1987] solution, and 1.1-1.7 for the

*Morel-Seytoux and Khanji*[1974] solution.

[9] Because hydraulic conductivity is embedded in sorptivity, certain measurements of the latter can be used to infer the former. One such approach is to utilize field-based sorptivity measurements in conjunction with variations of the traditional sorptivity model [equation (4)] to quantify *K _{s}* [

*White and Perroux*, 1987, 1989]. However, estimates of initial soil moisture and the soil's wetting front potential are needed for this approach. Solutions exist to quantify wetting front potential in dry soils (when

*Θ*= 0) [

_{0}*Rawls et al*., 1992;

*Morel-Seytoux et al*., 1996], given that the parameters of a water retention function are known. For instance,

*Morel-Seytoux et al*. [1996] approximated the wetting front potential of a dry soil as

where *α* and *m* are parameters of the *Van Genuchten* [1980] water retention curve, based on the *Mualem* [1976] water retention model, for *α* > 0 and 0 *< m <* 1.

[10] *h*_{wf} is recognized to change with the initial moisture state of the soil [*Green and Ampt*, 1911], and the aforementioned solutions for estimating wetting front potential do not include corrections for this variation. In a different approach, *Bouwer* [1964] and *Neuman* [1976] described *h*_{wf} at early infiltration times as a function of soil matric potential, *h*, by

where *K _{r}*(

*h*) is the relative hydraulic conductivity function

*K*(

*h*)/

*K*. While it is possible to put equation (6) in terms of

_{s}*Θ*by using a characteristic curve relationship [

_{0}*Brooks and Corey*, 1964;

*Van Genuchten*, 1980], the resulting equations are cumbersome.

[11] In this paper, we propose an alternative formulation of wetting front potential as a function of initial degree of saturation. This allows for a modification to the traditional (Green and Ampt) sorptivity model so that it better approximates sorptivity throughout the soil moisture range, including nearly saturated soils (*Θ* < 0.96). This modified expression can then be used to interpret short-term constant head infiltration measurements, to quantify the magnitude and variability in time and space of a soil's saturated hydraulic conductivity, even in wet soils.