## 1. Introduction

[2] Hillslopes are regarded as one of the basic elements of catchments, which are made up of interconnected hillslopes and the channel network [*Troch et al.*, 2007]. There have been considerable advances in our understanding and conceptualizations of hydrological processes at hillslope scale, and our knowledge of hillslope hydrology has improved the understanding of rainfall-runoff mechanisms and provided the theoretical basis for hydrological modeling [*Sivapalan*, 2003]. There have been some attempts to develop hillslope-based models by considering hillslope geometric characteristics. Models such as IHDM [*Beven et al.*, 1987], KINEROS [*Woolhiser et al.*, 1990], WEPP hillslope version [*Flanagan and Nearing*, 1995], CATFLOW [*Maurer*, 1997], and WASA [*Güntner*, 2002] are hydrological models that employ the representative hillslope scheme in a similar manner.

[3] Although modeling hydrological processes of natural hillslope units is considered important, it requires a cumbersome and sophisticated reprocessing of topographic data, and thus is a nontrivial problem [*Bronstert*, 1999; *Bogaart and Troch*, 2006]. For example, the exact procedures for deriving representative hillslopes are actually manually or semimanually determined through an on-screen digitizing technique [*Francke*, 2005]. Moreover, compared with regular grid hydrologic models, the hillslope-based models are difficult to build because of a lack of theories and methods to tailor the discretization scheme to the irregularly topographic characteristics.

[4] Recently developed hillslope storage dynamics models (HSDMs) [*Fan and Bras*, 1998; *Troch et al.*, 2002, 2003] employ low-dimensional approximate equations to represent the essential physical behavior of a natural system. Compared with IHDM or CATFLOW, HSDMs account explicitly for plan shape of hillslopes in an elegant and simple way through using hillslope width functions. HSDMs, as implied by the name, use hillslope width function, *w*(*x*), defined perpendicular to *x* to represent soil moisture storage, *S*.

where *h* is the elevation of the groundwater table, *ε* is the drainable porosity. In the HSDMs, the flow rate is related to the storage *S* through kinematic wave approximation or a more general form of Darcy's equation. Hence the 3-D structure of soil mantle of a hillslope is reduced into a 1-D pore profile, and the 3-D flow problem is transformed into 1-D flow problem.

[5] So far, HSDMs have mainly been applied to theoretical cases using highly idealized hillslope geometries. For example, *Troch et al.* [2002, 2004] applied the hillslope storage kinematic wave (HSKW) and the hillslope storage Boussinesq (HSB) models on nine basic hillslope types with exponential hillslope width functions. The HSDMs which account for landscape geometric complexity have inspired many studies in the field of catchment hydrology. When applying to natural catchment, manually or semimanually determined methods through an on-screen digitizing technique were always used. For instance, *Fan and Bras* [1998], first, applied the HSKW model at a catchment scale and an on-screen digitizing method for partitioning a catchment into the hillslopes was suggested. *Matonse and Kroll,* [2009] further applied the HSKW and HSB models to a headwater portion of the Maimai watershed to simulate low streamflows according to the on-screen digitizing method. This on-screen digitizing method is time consuming and is difficult to derive the required hillslope geometric characteristics, which limits the application of HSDMs to the real-world scenarios.

[6] In this study, the hillslope storage dynamics theories are used to guide the processing and deriving of hillslope geometric characteristics. The goal of this study is to derive hillslope width functions of HSDMs from flow distance field on the basis of grid digital elevation models (DEMs). In section 3, a modified, detailed algorithm based on grid DEMs is presented for automatic derivation of hillslopes, according to the illustrative procedures suggested by *Fan and Bras* [1998]. Then the algorithm based on flow distance transforms for derivation of hillslope width function, which is necessary for running the HSB or HSKW model, is described. Finally, the natural hillslope width functions are fitted by the Gaussian function curve.