## 1. Introduction

[2] One of the major challenges in hydrological science is the realistic and consistent representation of both hydrographs and water residence times in catchment systems [*Bachmair and Weiler*, 2013; *Beven*, 2010; *Kirchner et al*., 2000; *McDonnell et al*., 2010; *McGuire and McDonnell*, 2006; *Rinaldo et al*., 2011]. It remains a challenge because, while residence times are intrinsically linked to flow pathways and hydrograph responses at hillslope and catchment scales, the flow of water is affected by small-scale heterogeneities in complex, nonstationary and nonlinear ways as a catchment wets and dries. This complexity is compounded by the fact that the hydrograph is controlled by the changing distribution of celerities (pressure wave velocities) in the system, and the residence times by the changing distribution of velocities (water transport velocities). As noted by Beven [*Beven*, 2010, 2012a; *Beven et al*., 1989] for the simplest kinematic case, the celerity or wave speed is an inverse function of local storage *deficits* above the water table, which will be small when the catchment is wet. On the other hand, the distribution of pore water velocities will be a function of local *storage* beneath the water table. Celerities will, therefore, be faster than pore water velocities [see also *Beven*, 2012b, p. 145; *Davies and Beven*, 2012].

[3] Flow pathways also contribute to the complexity and nonstationarity of water residence times. It has been extensively shown throughout the literature of the last 30 years that preferential flow features have an important influence on flow and transport processes [*Abou Najm et al*., 2010; *Anderson et al*., 2008; *Bertolino et al*., 2010; *Beven and Germann*, 1982, 2013; *Bogner et al*., 2012; *Chappell*, 2010; *Frey and Rudolph*, 2011; *Greve et al*., 2010; *Hangen et al*., 2005; *Henderson et al*., 1996; *Holden*, 2004; *Lin*, 2010; *Morales et al*., 2010; *Nobles et al*., 2010; *Sade et al*., 2010; *Weiler and Naef*, 2003; *Weiler and Flühler*, 2004]. Preferential pathway features such as root channels, soil pipes, fissures, and soil fauna burrows allow water to travel at a range of velocities well above those of water traveling through tight matrix pores (note that this was also recognized by Robert Horton in the 1930s, who perceived macropore pathways as important pathways for both water and air during infiltration, see *Beven* [2004]). Dynamic mixing or displacement between preferential features and the soil matrix will also influence residence times.

[4] It is perhaps the complexity of this challenge that has resulted in a lack of progress toward developing integrated representations of water flow and transport that directly incorporate the influence of preferential flows [*Beven and Germann*, 2013]. Where models of flow and transport have been developed, they have tended to be of two types: the first is to rely on the implicit mixing characteristics of conceptual storage elements [e.g., *Christophersen et al*., 1990; *Genereux*, 1998; *Hooper et al*., 1990; *Ogunkoya and Jenkins*, 1993]; and the second is to relate transport to the local mean velocities predicted by a Darcy-Richards continuum approach under the assumptions of local continuity of gradients and homogeneous soil hydraulic characteristics at the calculation element scale [e.g., *Kollet and Maxwell*, 2006; *Qu and Duffy*, 2007; *Ebel et al*., 2008]. In both cases, extension to dual-domain representations have been made [*Beven and Germann*, 1981; *Frey et al*., 2012; *Gerke and Van Genuchten*, 1993; *Haws et al*., 2005; *Hoogmoed and Bouma*, 1980; *Köhne et al*., 2009; *Larsson and Jarvis*, 1999; *Simunek and van Genuchten*, 2008; *Simunek et al*., 2003; *Weiler and McDonnell*, 2007], but have not generally reflected the distributions of potential pathways for water flows.

[5] Typically, transport models are superimposed over these flow solutions in a way that is consistent with local predictions of mean velocities (e.g., the particle transport model SLIM-fast is transposed over ParFlow [*Maxwell and Kastenberg*, 1999], or ModPath over ModFlow [*McDonald and Harbaugh*, 1984] or MOCDENS3D where an advective solution that considers the density of saline waters is imposed over ModFlow [*Oude Essink*, 2001]). Solutions have used analytical or numerical solutions of the Advective-Dispersion equations (ADE) [e.g., *Ahlstrom et al*., 1977; *Prickett et al*., 1981; *Hassan and Mohamed*, 2003; *Frey et al*., 2012; *Ramasomanana et al*., 2013], which in its simplest form implies a symmetric Gaussian distribution of velocities around the local mean velocity. One solution technique is to use particle tracking. Particle tracking methods are flexible and have been used to represent “anomalous” transport [*Haggerty and Gorelick*, 1995], fractional ADEs [*Benson et al*., 2000; *Schumer et al*., 2001], and nonGaussian probability distributions [*Berkowitz et al*., 2006; *Dentz and Berkowitz*, 2003; *Scheibe and Cole*, 1994]. While these transport modeling approaches allow some representation of local heterogeneities, they are dependent on the estimation of local mean velocities from flow models that do not explicitly allow for heterogeneity at the subdiscretization scale.

[6] Thus, there is still a need for a consistent modeling approach. The multiple interacting pathways (MIPs) model is a recently developed methodology that represents flow and transport in an integrated solution, directly acknowledging preferential flow features and their possible interaction. Figure 1 summarizes the MIPs concept. The MIPs model is particle based: water entering the catchment is discretized into water particles/packets (here, the term particles and packets are interchangeable as they refer to a discretized volume of water with specified velocity characteristics, not a single water molecule or contiguous storage volume). The approach is innovative in that, unlike classical implementations of random particle tracking transport solutions, MIPs uses the particles to simulate *both* flow and transport in a completely consistent way, i.e., the movement of water particles according to mechanistic step equations provides the flow, and simultaneously these can be tracked throughout the system to provide water residence times and conservative solute transport. Each particle represents water moving at a certain velocity, regardless of where it might be in the pore space. In this way local heterogeneity, including preferential flow pathways can be simulated using generalized velocity distributions rather than needing to know the detailed soil structure. Water table levels are derived dynamically based on particle densities within discrete sections or grid cells of the catchment. No other approach to the authors' knowledge uses particle tracking at hillslope and catchment scales to represent the water flow directly without a prior solution for the local mean velocities (but see the SAMP model of *Ewen* [1996], for a similar approach including capillarity effects at the profile scale).

[7] In this way, it is possible to represent a whole continuum of flow pathway velocities, which need not be symmetrical, since the distribution will include both relatively immobile water in the soil matrix and water in functioning preferential flow pathways. The distribution will integrate to a flux per unit area analogous to a Darcian velocity. Exchanges between the different velocity pathways are then implemented using transition probabilities. These may be made dependent on current pathway or hydrological conditions.

[8] This combination of particle tracking, velocity distributions, and transition probabilities makes MIPs a highly flexible framework for exploring flow and transport processes, allowing the modeler to think directly in terms of flow pathway velocities and interactions. The methodology has been previously verified against an analytical kinematic wave solution, under shared assumptions [*Davies and Beven*, 2012], and successfully applied to a plot scale tracing experiment [*Davies et al*., 2011] where a 2-D model was used in a hypothesis testing framework to model both discharge and tracer breakthrough. An interesting feature of the presented particle tracking approach is that by making direct use of particle velocities, the length scales of the flow domain are intrinsic to the model predictions. There is no reliance on assumptions of local homogeneity, implicit mixing assumptions, or numerical dispersion.

[9] This paper extends the previous work with MIPs in a number of ways:

[10] 1. A method of formulating 3-D models is detailed that allows MIPs to be applied up to the catchment scale.

[11] 2. The applicability of this 3-D formulation is demonstrated through application to a catchment-scale isotope experiment carried out at Gårdsjön, Sweden (details of which are given in section 'Gårdsjön G1 Catchment Isotope Experiment').

[12] 3. To explore the influence of flow pathways and storage exchanges in determining catchment flow and transport characteristics, several modeling hypotheses regarding flow pathways and pathway exchanges are made and compared to observations. The results demonstrate the importance of preferential flows and exchanges in determining catchment scale residence time distributions, and illustrate that these distributions are nonstationary as the catchment wets and dries.