## 1. Introduction

[2] Subsurface water flows play a fundamental role in determining the partition between surface and subsurface water flows. In the past, parameterizations of groundwater flows in hillslope and catchment hydrology were often developed on the basis of conceptualized approaches [*Beven and Kirkby*, 1979; *Barling et al*., 1994; *Troch et al*., 2003, 2004; *Akylas and Koussis*, 2007; *Harman and Sivapalan*, 2009, and references therein] which were mainly aimed at the identification of runoff source areas and the estimation of discharge at the hillslope toe. In these studies, steady-state approaches were often used, but they have proven to be insufficient for many purposes, especially revealing the real patterns of soil moisture distribution [*Western and Grayson*, 1998]. Therefore, in subsequent researches, these have been modified to introduce more dynamic conditions [e.g., *Barling et al*., 1994; *Chirico et al*., 2003] and/or effects due to the downslope topography [e.g., *Hjerdt et al*., 2004; *Lanni et al*., 2011]. Eventually, these latter studies also proved to be of interest in determining hillslope stability [e.g., *Dietrich and Montgomery*, 1994; *Iverson*, 2000; *D'Odorico et al*., 2005] by coupling the simplified hydrology with geomechanics.

[3] In the more traditional contexts of groundwater analysis, analytical solutions for unconfined groundwater flow have been produced for suitably simplified conditions and simple geometries [*Hantush*, 1967; *Barenblatt et al*., 1990; *Fan and Bras*, 1998; *Lockington et al*., 2000; *Parlange et al*., 2000; *Kim and Ann*, 2001; *Rai et al*., 2006; *Song et al*., 2007; *Telyakovskiy et al*., 2010]. These studies have been a valuable reference in understanding the processes dynamics; however, they have been less useful in exploiting the information generated by the growing knowledge of catchment topography.

[4] Very rarely do hillslope hydrologists use complete three-dimensional (3-D) numerical models [e.g., as those in *Harbaugh et al*., 2000; *Panday and Huyakorn*, 2004], developed in mainstream groundwater studies, and they have always looked for the greatest algorithmic simplicity. In hillslope literature, the search for conceptualized or analytical methods has been justified by the avoiding the computational burden of solving the complete 3-D form of the groundwater equations, which seemed too great, but also by the perception that hillslopes water table dynamics has different characteristics than in aquifers, and, therefore, requires a special care. In fact, soils can more frequently dry than large-scale aquifers, and the presence of rugged bedrocks and shallow perched water tables can bring to disconnected patterns of soil moisture [*Tromp-van Meerveld and McDonnell*, 2006]. This is called wetting-and-drying phenomenon and has been studied thoroughly in surface water literature [*Stelling and Duynmeyer*, 2003]. However, it has been less investigated in groundwater literature, and, for instance MODFLOW [*Harbaugh et al*., 2000] has been shown to fail to in modeling it [*Doherty*, 2001; *Werner et al*., 2006; *Sokrut et al*., 2007; *Painter et al*., 2008].

[5] Overall, considering the various approaches, it can be verified that there is a gap in literature: there are many 3-D solvers for the scopes of groundwater analysis, which are possibly unsuitable to model hillslope problems; there are contributions that investigate the one-dimensional (1-D) version of the groundwater equation, in which the lateral width of a hillslope is appropriately parameterized [e.g., *Troch et al*., 2003, 2004, and references therein]. But much fewer, and much more recent, are the two-dimensional (2-D) solvers [*Rocha et al*., 2007; *Harman and Sivapalan*, 2009; *Cayar and Kavvas*, 2009; *Dehotin et al*., 2011].

[6] This paper tries to support the statement that a 2-D simplification of groundwater flow, based on a new numerical method, can answer the needs of spatial information for hillslope hydrology (in relation to hillslope-toe discharge and soil saturation patterns—therefore contributing also to some hillslope stability problems) and for modern catchment hydrology.

[7] To obtain this result, the paper implements a new and clean numerical method that merges the achievements of *Brugnano and Casulli* [2008] and *Casulli* [2009], and, in particular, extends the latter (which deals with free surface waters) to the case of Darcian flow.

[8] The paper is organized as follows: in section 2, the form of the Boussinesq equation and its terms are discussed; in section 3, the equation is discretized according to the new conservative scheme; in section 4, the effect of boundary conditions on the structure of the solver is presented; in section 5, the model is validated against appropriate analytical and numerical solutions, and the model is applied to the Panola experimental site to confirm its behavior at the presence of rugged terrain. In the same section the model's results are also compared to those of GEOtop.