## 1. Introduction

[2] The unsaturated zone in soil acts as a link between the surface system and the groundwater system and plays a crucial role in water and solute cycling. In semiarid and arid regions where precipitation is low and long-term evaporation is high, soil water is important for its key position in controlling plant growth and other biological processes.

[3] The Richard's equation is the most wildly used model for simulating variably saturated water and solute flow in soil [*Vanclooster et al*., 2004], the solution of which depends greatly on the soil water retention curve (SWRC) *h*(*θ*) and the hydraulic conductivity curve *K*(*h*). However, the commonly used soil hydraulic models that account for capillary forces do not deal well with the flow process that occurs under very dry conditions [e.g., *Rossi and Nimmo*, 1994; *Silva and Grifoll*, 2007]. One important reason for the poor performance in dry conditions is that the common conceptual models for unsaturated hydraulic conductivity on which these flow models rely, e.g., the frequently used model of *Mualem* [1976a], are unsuitable under dry conditions. The Mualem and similar models often rely on oversimplified representation of pore space in a given medium as a bundle of cylindrical capillaries and assume that the matric potential is attributed to capillary forces only [*Tuller and Or*, 2001]. Experimental evidence has shown that the models for *K*(*h*) often underestimate the hydraulic conductivity in the medium to dry range [*Mualem*, 1976b; *Pachepsky et al*., 1984]. *Goss and Madliger* [2007] also noted this phenomenon in field scale.

[4] Pore bundle models may underestimate hydraulic conductivity under dry conditions, because they neglect the flow in thin liquid films, which can be the dominant process at low matric potentials [*Li and Wardlaw*, 1986; *Lenormand*, 1990; *Toledo et al*., 1990]. On the basis of this assumption and previous studies, *Tuller and Or* [2001] proposed a *K*(*h*) model that accounts for both capillary and film flow using hydrodynamic considerations and specific pore geometry assumptions. However, this model, which is meant to be coupled with the retention model developed by *Or and Tuller* [1999], is little used due to its complexity. *Peters and Durner* [2008] presented a model that combines Mualem's capillary flow model with a simple film flow function using film flow conductivity as a function of the effective saturation. The disadvantages of this simple model are that it lacks a physical basis and that it must be coupled with a common SWRC models (e.g., the van Genuchten model used in that paper), which may be invalid at lower water contents [*Nimmo*, 1991; *Rossi and Nimmo*, 1994; *Silva and Grifoll*, 2007]. By combining the film model developed by *Langmuir* [1938] with scaling analysis, *Tokunaga* [2009] developed a formula for estimating hydraulic conductivity that results from film flow in media consisting of smooth uniform spheres. This type of flow is highly dependent on film thickness *f* and accounts for matric potential *h* on a grain scale [*Wan and Tokunaga*, 1997]. *Zhang* [2011] coupled Tokunaga's conductivity model with a modified *van Genuchten* [1980] model and obtained a well-fitted *K*(*h*) curve in very dry ranges by introducing a soil-dependent factor. *Lebeau and Konrad* [2010] proposed a new model, developed from a modified version of *Tokunaga*'s [2009] model, for predicting the hydraulic conductivity of porous media. This model accounts for both capillary and thin film flow processes, and establishes a mathematical relationship between hydraulic conductivity and the water retention function; however, it targets media with smooth spherical grains.

[5] The models developed to date are either mathematically complex or need to be coupled with common SWRC models, which do not perform well in drier ranges. Measured hydraulic conductivity data are often needed to obtain proper parameters and these data are difficult to obtain in dry conditions. In this paper, we discuss how we developed a theoretical model based on Tokunaga's formula and to obtain the parameters needed through traditional evaporation experiments using an inverse method. Finally, we discuss the implications of the different models on water dynamic.