## 1. Introduction

[2] Describing and quantifying flow and transport in the vadose zone requires knowledge of the soil water retention function which relates soil water pressure head with volumetric soil water content, and the conductivity function which relates hydraulic conductivity with soil water content or pressure head. Here, we focus on the description of the water retention function.

[3] Many different equations have been proposed to parameterize water retention data [e.g., *Gardner*, 1958; *Brooks and Corey*, 1964; *Brutsaert*, 1966; *Haverkamp et al.*, 1977; *van Genuchten*, 1980; *Kosugi*, 1994; *Assouline et al.*, 1998]. We consider one of the most popular among them for this study, i.e., the van Genuchten equation:

where θ* is the degree of saturation, θ is the volumetric soil water content [L^{3}/L^{3}], and θ_{S} and θ_{r} [L^{3}/L^{3}] are water content scaling parameters that denote the (maximum) saturated and (minimum) residual volumetric soil water content, respectively. The soil water pressure head *h* [L] is taken to be negative for unsaturated conditions and is expressed in centimeters of water. The parameter *h*_{g} [L] is the van Genuchten pressure head scale parameter.

[4] Equation (1) contains two dimensionless shape parameters, *m* [−] and *n* [−] usually related through

where the parameter *k*_{m} is referred to as the user index [*Haverkamp et al.*, 2005; *Leij et al.*, 2005]. Even though *k*_{m} may take any positive value, integer values are often chosen in order to accommodate closed form analytical expressions selected by the user for the hydraulic conductivity. The user index *k*_{m} = 1 (*n* > 1) corresponds to the conductivity model of *Mualem* [1976] while *k*_{m} = 2 with *n* > 2 gives the conductivity model of *Burdine* [1953].

[5] The use of equations (1) and (2) for the description of water transfer processes, requires a priori determination of five unknown water retention system parameters, i.e., two shape parameters *m* and *n*, and three scale parameters θ_{S}, θ_{r} and *h*_{g}. Both shape parameters are strongly linked to the textural soil properties, whereas the scale parameters are related to soil structure [*Haverkamp et al.*, 2002a]. The parameters are generally estimated by fitting the water retention equation to measured *h*(θ) data points and should result in a unique parameter set for a particular retention function, independent of the choice of optimization method. It may also be necessary to impose constraints during the optimization of the system parameters to either ensure that retention function reproduces the actual data, or to minimize the number of parameters. Classically, constraints are imposed on the shape parameter *m* and the scale parameter θ_{r} [*van Genuchten et al.*, 1991].

[6] Using a prefixed value of *k*_{m} (e.g., *k*_{m} = 1 or *k*_{m} = 2) the number of shape parameters is reduced to one (either *m* or *n*) without affecting a priori the fitting abilities of the van Genuchten model (equation (1)) [*Leij et al.*, 1997]. The case of the scale parameter θ_{r} is more delicate. Conceptually, the residual water content may be associated with the immobile water held (by adsorptive forces) within in a dry soil profile in films on particle surfaces, in interstices between particles, and within soil pores. In practice however, its value is generally estimated by fitting the water retention equation to measured data points reducing θ_{r} to an empirical fitting parameter valid for the range of data points used. It may well give doubtful results when applied beyond this range of data points (e.g., for the simulation of evaporation). For this reason, various authors set its value equal to zero, θ_{r} = 0 [e.g., *Kool et al.*, 1987; *van Genuchten et al.*, 1991; *Leij et al.*, 1996].

[7] In this study, the value of θ_{r} is related to the wetting and drying history prior to the measurement of the *h*(θ) data points in line with the hysteresis model of *Haverkamp et al.* [2002b]. Setting θ_{r} = 0 for the main hysteresis loop, the scanning curves will have nonzero θ_{r}-values. The nonzero θ_{r}-value is then attributed to a wetting or drying curve of a higher scanning order rather than to the main wetting or drying curve. This eliminates θ_{r} as a soil characteristic parameter (at least for soils with unimodal behavior) to be estimated through fitting.

[8] Several conceptual and empirical models of varying complexity have been introduced in the literature to describe the hysteretic behavior of the water retention θ(*h*)-relationship [e.g., *Poulovassilis*, 1962; *Mualem*, 1973, 1974; *Parlange*, 1976; *Kool and Parker*, 1987; *Hogarth et al.*, 1988; *Jaynes*, 1992; *Braddock et al.*, 2001; *Haverkamp et al.*, 2002b].

[9] Under field conditions, hysteresis is usually ignored because its influence is often masked by heterogeneities and spatial variability. However, many authors [e.g., *Nielsen et al.*, 1986; *Parker and Lenhard*, 1987; *Russo et al.*, 1989; *Heinen and Raats*, 1997; *Otten et al.*, 1997; *Whitmore and Heinen*, 1999; *Si and Kachanoski*, 2000; *Brutsaert*, 2005] have shown it to be important in simulations of water transfer, solute transport, multiphase flow and/or microbial activities, and to disregard it leads to significant errors in predicted fluid distributions with concomitant effects on solute transport and contaminant concentrations [e.g., *Gilham et al.*, 1976; *Hoa et al.*, 1977; *Kool and Parker*, 1987; *Kaluarachchi and Parker*, 1987; *Mitchel and Mayer*, 1998].

[10] Besides its effect on the flow behavior of water transfer, another aspect of hysteresis is nearly completely overlooked in the literature. Neglecting hysteresis and, hence, the history of drying and wetting cycles prior to measurement of the water retention data points, may well introduce an uncertainty in the choice of the appropriate equation to be used for the parameter identification. When equation (1) is chosen to represent the main loop of hysteresis, then all intermediate curves are described either by equations different from equation (1) or by equation (1) but with different system parameters. This is, what ever the hysteresis model used. As field measurements generally do not belong to the main loop, the use of equation (1) may often lead to a wrong interpretation of field measurements for the estimation of water retention system parameters with unreliable parameter values. In practice, users are rarely aware of this difficulty since generally only one set of drying data is measured making comparison impossible. Such erratic interpretation of water retention field data in the literature will probably be far more common than expected. As soil system parameters are generally compiled in soil databases for establishing statistical correlations of the type of pedotransfer functions [e.g., *Rawls and Brakensiek*, 1985; *Vereecken*, 1992; *Schaap and Leij*, 1998; *Schaap et al.*, 1998], one easily understands the difficulties that may cause the wrong interpretation of field data.

[11] The objective of this paper is to illustrate potential pitfalls with the estimation and use of retention parameters for field studies when hysteresis is neglected. The results will be illustrated with three examples, two taken from the literature and one from a recent field experiment. The purpose is not to validate the particular hysteresis model used for this study (as that is already presented elsewhere), but rather to draw the reader's attention to the fact that soil system parameters often presented in the literature to four significant figures, should be considered with precaution. Especially when only one set of data is measured without the possibility of comparison, the lack of information on the history of drying and wetting prior to the measurements is an important source of errors. Some guidelines to avoid possible pitfalls are addressed.