## 1. Introduction

[2] Field observations of rapid water table rises indicate that unsaturated-zone preferential flow can contribute substantially to groundwater recharge [*Lee et al*., 2006; *Heppner et al*., 2007; *Gleeson et al*., 2009; *Cuthbert and Tindimugaya*, 2010]. This important process is rarely given physically realistic treatment in mathematical models of flow and transport. In unconfined aquifers, observed water table fluctuations can be used to quantify recharge [*Healy and Cook*, 2002; *Heppner and Nimmo*, 2005; *Cuthbert*, 2010]. These empirical water table fluctuation methods incorporate the impact of both preferential and diffuse flow processes into an area-averaged estimate of unsaturated fluxes. Although sensitive to preferential flow, water table fluctuation methods do not treat it explicitly and generally are not applicable for predicting recharge under a given set of environmental forcing conditions. Explicit treatment of preferential flow in a predictive model would be of great practical value for land and water resources management decisions, especially in the context of dealing with problems of contaminant transport and climate change impacts.

[3] Typical physically based hydrologic models employ numerical solutions for the Darcy-Buckingham formulation of the variably-saturated flow equation to simulate subsurface fluxes, which presents three major problems. First, adequate parameterization and evaluation of this type of model requires substantial data inputs that are essentially never available for operational applications [*Loague and VanderKwaak*, 2004]. Second, when sufficient data are available robust parameter estimation can be computationally expensive and the model user may still struggle with issues related to parameter identifiability, correlation, and heterogeneity [*Vrugt et al*., 2002; *Hill and Tiedeman*, 2007; *Mirus et al*., 2009]. Third, the flow equation relies on the assumption that capillarity dominates unsaturated fluxes, so it represents entirely diffusive flow behavior. The implication of this “diffuse flow” assumption is that even when treated explicitly, preferential flow networks do not activate until the air-entry values of these larger pores are exceeded. Thus, preferential flow is only simulated once the porous medium is nearly or completely saturated. However, numerous observations document preferential flow under far-from-saturated conditions [*Nimmo*, 2012]; as a result, simulations often underestimate unsaturated fluxes of water and the solutes transported by advection. Without full knowledge of heterogeneity in the subsurface, highly parameterized deterministic models present the user with the often insurmountable challenge of being right for the right reasons [*Klemes*, 1986; *Loague and VanderKwaak*, 2004; *Kirchner*, 2006].

[4] The evidence for unsaturated-zone preferential flow is considerable and there is a need to improve quantitative understanding of this important process [*Nimmo*, 2012]. Several alternative mathematical formulations of unsaturated flow have been developed to address the prevalence of nondiffusive, nonequilibrium flow processes observed in natural and laboratory settings [*Rasmussen et al*., 2000; *Ross and Smettem*, 2000; *Nimmo*, 2007, 2010a; *Peters and Durner*, 2008; *Vogel et al*., 2010; *Or and Assouline*, 2011]. Although the need for such paradigm shifts and supplements to the Darcy-Buckingham formulation is becoming more widely accepted, these approaches have not been thoroughly tested for a range of practical applications.

[5] The primary objective of this work is to present the first rigorous testing of the source-responsive fluxes model, which was developed [*Nimmo*, 2007, 2010a] and modified here to provide a parsimonious, but physically realistic treatment of unsaturated preferential flow processes. We use two case studies not considered previously by *Nimmo* [2007, 2010a] to quantitatively evaluate practical applications of the model with limited data. Both case studies are in arid environments with deep vadose zones where simple, low-cost assessments of preferential flow are needed to inform land and water resources management decisions. Previous applications of source-responsive theory have highlighted several areas where the hydrologic realism of the model could be enhanced [*Nimmo*, 2010a, 2010b; *Mirus et al*., 2011], which we now account for in the equations for source-responsive fluxes. A secondary objective of this study is to assess the value of these modifications to the model equations and identify additional data needed to further improve process representation.