## 1. Introduction

[2] Modeling fluxes of water and solutes in soils are an essential means to address many problems in applied soil science, such as water, nutrient, and salinity management research. Typically, the Richards equation is used in order to model the behavior of water in unsaturated soils. An accurate knowledge of the soil hydraulic functions is required to solve this equation, i.e., the soil water retention function *θ*(*h*) and the hydraulic conductivity function *K*(*h*), where *θ* is the volumetric water content, *h* (L) is the suction, and *K* (L T^{−1}) is the hydraulic conductivity. This knowledge implies both the appropriate soil hydraulic models and the correct parameterization of these models.

[3] The selection of the correct model combination is of crucial importance. In many cases, the well-established retention functions of *Brooks and Corey* [1964], *van Genuchten* [1980], or more recently *Kosugi* [1996] in combination with the capillary bundle models of *Mualem* [1976a] or *Burdine* [1953] for conductivity prediction are used and well suited for specific problems. However, a lot of studies show that other model combinations are of great benefit for specific soils or boundary conditions. Soils with structural elements are often better described by bimodal, multimodal [*Ross and Smettem*, 1993; *Durner*, 1994] or, for the most flexible description, free from spline retention functions [*Iden and Durner*, 2007].

[4] Usually, the water retention functions assume a distinct residual water content, *θ*_{r}, which is asymptotically reached at very high suctions. The residual water content is either interpreted as the water held by adsorptive forces [*Corey and Brooks*, 1999] or as a mere fitting parameter. In the very dry range, even the adsorptive water content finally reaches a value of 0 and thus the concept of residual water content is inappropriate. Several retention models have been proposed to account for this fact [*Campbell and Shiozawa*, 1992; *Fredlund and Xing*, 1994; *Rossi and Nimmo*, 1994; *Fayer and Simmons*, 1995; *Khlosi et al*., 2006]. Since the measured water contents are usually based on oven drying, it is conventional to assign a finite suction, at which the water content becomes zero (herein denoted as *h*_{0}), to a value corresponding to oven dry conditions at 105°C. This yields a suction of ≈ 6.3 × 10^{6} to 10^{7} cm depending on laboratory conditions.

[5] The frequently used retention models of *Fayer and Simmons* [1995] or *Khlosi et al*. [2006], which account for water adsorption in the medium to dry range, fail for soils with wide pore-size distributions, because in these models *θ* does not reach 0 at *h*_{0}. The same applies to the *Zhang* [2011] retention model. *Fredlund and Xing* [1994] developed a retention model, where *θ* equals 0 at *h*_{0}, regardless of pore-size distribution. Unfortunately, their model does not allow a partition of capillary and adsorptive water. Moreover, *Peters et al*. [2011] showed that the models of the type introduced by *Fayer and Simmons* [1995] (including the model of *Khlosi et al*. [2006]) can lead to the physically unrealistic case of increasing water content with increasing suction. They solved this problem by introducing a slight modification together with appropriate parameter constraints.

[6] The capillary bundle models often fail to express hydraulic conductivity in the medium to dry range, because they neglect film and corner flow [*Tuller and Or*, 2001]. Extensions of the capillary models accounting for film flow can improve hydraulic conductivity prediction [*Peters and Durner*, 2008a; *Lebeau and Konrad*, 2010; *Zhang*, 2011]. In the very dry range, liquid water flow might completely cease, but water can still be conducted by vapor flow [*Philip and de Vries*, 1957; *Saito et al*., 2006]. An accurate description of *θ*(*h*) and *K*(*h*) in the medium to dry range is of great importance for simulating evaporation or root water uptake processes.

[7] *Peters and Durner* [2008a] described liquid conductivity in the complete moisture range with a weighted sum of capillary and film conductivity. In their model, capillary conductivity is described by a capillary bundle model [e.g., *Mualem*, 1976a] and film conductivity is given by a simple empirical power function of saturation. They showed that their film conductivity model is well suited to describe the measured conductivity data. However, both capillary and film conductivity depend on the capillary retention characteristics with residual water content. Thus, their film conductivity part is coupled with an inappropriate retention model. This conceptual inconsistency was first overcome by *Lebeau and Konrad* [2010]. They developed a more consistent model, where the retention model of *Khlosi et al*. [2006] is partitioned into a capillary and an adsorptive part. The capillary and film conductivities are linked to the capillary and adsorptive retention characteristics, respectively. In their model, capillary conductivity is again given by a capillary bundle model, whereas the film conductivity is described by a more complex hydrodynamic model. The same applies to the *Zhang* [2011] conductivity model. He also partitioned his slightly modified version of the *Fayer and Simmons* [1995] retention function into capillary and adsorptive water and linked capillary and film conductivity to the according retention parts.

[8] The physically based film conductivity in the model of *Lebeau and Konrad* [2010] is further partitioned into thick and thin film conductivity, accounting for different viscosities in the vicinity of solid surfaces. However, their model is difficult to implement due to its mathematical complexity. Furthermore, the used physical constants might differ from the literature values because of heterogeneities of mineral and organic matter surfaces as well as the usually unknown composition of the fluid.

[9] The film conductivity model of *Zhang* [2011] also uses a number of physical constants, which might differ from the literature values. Moreover, it is coupled to his retention function, which is difficult to use with regard to the determination procedure of the critical point distinguishing between capillary and adsorptive retention.

[10] Summarizing, the models accounting for water adsorption and film conductivity are either difficult to use or physically inconsistent. Up to now no physically consistent and easy-to-use hydraulic models for the complete moisture range exist.

[11] In this paper, a new retention model is presented allowing a direct partition of the capillary and adsorptive water and guaranteeing that *θ* = 0 at *h*_{0}. A new empirical conductivity model is introduced, which links the capillary and film conductivity to capillary and adsorptive water retention. Both models are easy to use. Thus, the gap between simple straightforward-to-use models with physical inconsistencies on the one hand and physically consistent but more cumbersome-to-use models on the other hand is closed.

[12] The new liquid conductivity model is coupled with an existing vapor conductivity model to describe conductivity in the complete moisture range. The new models are tested with literature data reaching dry to very dry conditions. Finally, the contributions of capillary, film, and vapor conductivity to total flow are exemplarily shown in a steady-state simulation study.