## 1. Introduction

[2] The predictive ability and utility of large-scale distributed hydrologic models heavily relies on a detailed description of the spatial variability of the soil hydraulic properties, namely the water retention function (WRF) and the unsaturated hydraulic conductivity function (HCF). The WRF relates the volumetric water content *θ* (*L*^{3} *L*^{−3}) to the corresponding soil water matric head *h* (*L*). The HCF relates the unsaturated hydraulic conductivity *K* (*L T*^{−1}) to the soil matric head or water content. The spatial distribution of WRF and HCF can be characterized with effective soil hydraulic parameters [*Zhu and Mohanty*, 2002; *Zhu and Mohanty*, 2003; *Vrugt et al*., 2004; *Mohanty and Zhu*, 2007]. Although this approach provides a reasonable description of the lumped behavior of the soil system, it does not accurately characterize the inherent spatially distributed soil water fluxes.

[3] In the past decades, the scaling approach has been developed as an effective method to describe the spatial variability of the soil hydraulic properties in a given study area [*Warrick and Nielsen*, 1980; *Tillotson and Nielsen*, 1984; *Clausnitzer et al*., 1992]. This approach was introduced in soil physics by the seminal paper of *Miller and Miller* [1956] and is based on the assumption that geometrically similar porous media differ only by a characteristic length of their respective pore-size distributions, which in turn provide a good proxy for the soil hydraulic properties. Spatial variability is defined through the statistical distribution of scaling factors that relate the soil hydraulic functions sampled in different locations to the corresponding average hydraulic properties of a reference porous medium (representative for the study area). This geometric scaling approach has been successfully applied for Kosugi's soil hydraulic functions [*Kosugi*, 1996], assuming that scaling factors are lognormally distributed in the sampled soil domain. This includes individual scaling of soil WRFs only [*Kosugi and Hopmans*, 1998; *Hayashi et al*., 2009] or simultaneous scaling of soil water retention and unsaturated HCFs [*Hendrayanto et al*., 2000; *Tuli et al*., 2001].

[4] Notwithstanding this progress made, the inherent spatial variability of soils necessitates a very large number of samples to accurately characterize the hydraulic properties of the considered spatial domain [*Hopmans et al*., 2002a; *Minasny and McBratney*, 2007; *Vereecken et al*., 2007]. Unfortunately, direct measurement of the soil hydraulic properties (hereafter referred to as primary data or PD) is time consuming and tedious [*Hopmans et al*., 2002b]. Alternatively, pedotransfer functions (PTFs) can be used to indirectly estimate the soil hydraulic functions from soil physical and chemical data (hereafter defined as secondary data or SD) that are more readily available because of their ease in collection and simplicity in measurement [*Haverkamp et al*., 2002]. Most PTFs estimate the soil hydraulic functions through mathematical and statistical relations by using oven-dry bulk density, organic carbon content, and soil texture [*Pachepsky and Rawls*, 2004]. We emphasize that PTFs necessitate empirical calibration procedures, and their validity is restricted only for the tested database [*Chirico et al*., 2007]. The majority of PTFs presented in the literature use simple nonlinear regression equations to relate the hydraulic properties to basic soil texture and structure data [*Tietje and Tapkenhinrichs*, 1993; *Weynants et al*., 2009; *Vereecken et al*., 2011]. Such equations are easy to implement and are often favored over more complex fitting methods, such as artificial neural networks [*Schaap and Bouten*, 1996; *Schaap et al*., 1998].

[5] Although PTFs may provide good estimates of the soil hydraulic properties [*Romano*, 2004], they depend on empirical relationships that do not offer physical understanding in the interpretation of their flaws [*Haverkamp et al*., 2002]. Alternatively, physical-empirical PTFs rely on pore-scale physical relationships that are adjusted through empirical calibrations [*Chan and Govindaraju*, 2004; *Hwang and Choi*, 2006; *Nimmo et al*., 2007]. Specifically, *Arya and Paris* [1981] proposed a method (hereinafter defined as AP method) to estimate the soil pore-size distribution by using the soil particle-size distribution (PSD) and oven-dry bulk density. The AP method postulates the fundamental assumption of shape similarity between WRF and PSD. The soil is described as an ideal porous medium with modeled pore spaces created by a cubic packing of uniform spheres. The actual soil matrix geometry is adjusted by an empirical parameter *α* that corrects for the differences in shape and spatial arrangement of solid particles between hypothetical and actual porous medium [*Arya et al*., 1999a, 2008]. Although *Arya and Paris* [1981] assumed a constant *α* value of 1.38 for coarse porous media, others proposed to vary *α* as a function of matric head [*Basile and D'Urso*, 1997], particle size [*Buczko and Gerke*, 2005], or water content [*Vaz et al*., 2005] of the soil. The AP method has subsequently been upgraded by adding the prediction of unsaturated hydraulic conductivity as well [*Arya et al*., 1999b; *Chaudhari and Batta*, 2003; *Hwang and Hong*, 2006; *Blank et al*., 2007; *Arya and Heitman*, 2010]. More recently, *Nasta et al*. [2009] proposed a geometric scaling method of the WRFs estimated with the AP method. This work relaxes experimental effort as the calibration of the parameter *α* requires only a limited number of direct measurements of the WRF of soil samples within the sampled spatial domain.

[6] In this paper we present a hybrid simultaneous scaling approach that complements SD (PSD and oven-dry bulk density) with easily obtainable PD (saturated water content and saturated hydraulic conductivity) to assess the spatial variability of both WRF and HCF. The main purpose of this work is to offer a methodological approach to significantly reduce experimental effort.

[7] The remainder of this paper is organized as follows. In section 'Simultaneous Scaling Using PD', the conventional simultaneous scaling method is described using laboratory measurements of the soil hydraulic properties (PD) to obtain the reference soil WRF (REF-WRF_{PD}) and HCF (REF-HCF_{PD}), respectively, and the corresponding scaling factors *δ*_{PD} [*Tuli et al*., 2001]. Section 'Simultaneous Scaling Using SD' then proceeds with the introduction of our hybrid simultaneous scaling method that uses measurements of the PSD and bulk density (SD) jointly with data of the saturated water content (*θ _{s}*) and saturated hydraulic conductivity (

*K*) (PD) to estimate the reference soil WRF (REF-WRF

_{s}_{SD}) and HCF (REF-HCF

_{SD}), respectively, and the corresponding scaling factors

*δ*

_{SD}. The experimental data are subsequently described in section 'Materials and Methods'. In section 'Results and Discussion', the results of our new hybrid scaling approach are compared against those of the conventional scaling method. Finally, section 'Conclusions' concludes with a summary of the analysis presented herein.