A scarcity of information exists on how physical processes govern the movement of liquid manure, or other viscous fluids, through layered macroporous soils. To elucidate these complex flow and transport phenomena, a viscosity dependent, two-dimensional dual-permeability model that considers macropore anisotropy is employed to simulate field experiments where liquid swine manure (LSM) was applied to silt loam with both a soil crust and plowpan layer present. Using data from the field experiment as a benchmark, the model was used to predict nutrient (NH4-N and total P) breakthrough to tile drains; and to assess the influence of reduced permeability crust and plowpan layers, and fluid viscosity, on solute movement within 48 h of LSM application. Results demonstrate the importance of viscosity on flow and transport in macroporous soils. By increasing LSM viscosity, nutrient breakthrough to tile drains can be greatly reduced, and near surface nutrient retention can increase. The presence of a nonmacroporous soil crust layer can also lead to reduced nutrient concentrations in tile discharge by reducing pressure heads in the underlying A-horizon soil matrix, resulting in reduced macropore flow; whereas a low permeability plowpan layer at the base of the A horizon can increase pressure heads in the A-horizon soil matrix and lead to increased macropore flow. Multiple target point parameter sensitivity analysis revealed that relative parameter sensitivity can be a transient characteristic, and that hydraulic properties of the A and B horizon tend to exhibit their greatest influence over the respective early and late time solute breakthrough characteristics.
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 Liquid swine manure (LSM) is a large source of nonpoint pollution across the agricultural landscape. In 2006 it was estimated that over 15 million swine in Canada produced approximately 16 million tons of manure [Hofmann, 2008], of which approximately 85% [Statistics Canada, 2002] could be expected to have been in liquid form. While the nutrients contained in the LSM (e.g., nitrogen, phosphorus) have appreciable agronomic value if they can be utilized for crop growth, they also pose significant risk to water resources, which is exemplified in the numerous studies conducted around the world that have shown that nutrient constituents of LSM are often detected in tile drainage water following LSM land application [Stamm et al., 2002; Hoorman and Shipitalo, 2006; Ball Coelho et al., 2007].
 In shallow water table, tile-drained agricultural settings with structured soil, preferential flow pathways (macropores) such as biopores, root holes, and desiccation cracks [Beven and Germann, 1982], serve as conduits for rapid downward movement of LSM [Shipitalo and Gibbs, 2000]. Because macropores are not typically hydraulically active until soil water pressure head exceeds the range of −10 to −6 cm [Jarvis, 2007], it might be concluded that LSM application on relatively dry soil does not pose an environmental risk with respect to preferential flow. In practice however, LSM is applied at such high rates that localized ponding often develops on the application surfaces, which can readily initiate macropore flow if macropores vent in the vicinity of the pond. Once LSM enters a macropore its movement into the soil matrix can be impeded by low permeability skin layers that line the walls of the macropores [Gerke and Köhne, 2002].
 In addition to preferential flow pathways, the presence of discrete low permeability layers can also be envisioned to influence LSM movement in soil. Highly compacted crusts formed on the soil surface from water droplet impact forces have been found to have a hydraulic conductivity up to four orders of magnitude less than the underlying soil [McIntyre, 1958], and when present they can significantly reduce infiltration rates [Assouline, 2004]. Low permeability plowpan layers are also common in structured soil. In previous dye infiltration studies, plowpans have been found to inhibit the vertical migration of dyed water through the soil matrix, and have resulted in lateral dye dispersal [Shipitalo et al., 2004; Frey and Rudolph, 2011]. In these cases, the movement of dye into the B horizon is facilitated by macropores that are vertically continuous through the plowpan layer. While soil crust and plowpan layers are not commonly incorporated into infiltration analysis, some past numerical studies have found the need to incorporate discrete, low permeability layers, in order to more accurately emulate field observations [Abbaspour et al., 2000; Rosenbom et al., 2009].
 The predominantly vertical nature of macropore features [Bouma et al., 1982; Edwards et al., 1988; Mohanty et al., 1998; Cey and Rudolph, 2009; Frey and Rudolph, 2011] infers that vertical fluxes will be much greater than horizontal fluxes in macropore networks. Past field experiments have shown that preferential flow intercepted by tile drains has originated at the soil surface and in close proximity to the drain [Mohanty et al., 1998; Shipitalo and Gibbs, 2000], which infers that the anisotropic nature of the macropores is an important factor in governing the lateral distribution of infiltrating water and solutes. Failure to properly account for macropore flow direction poses a serious conceptual problem for multidimensional numerical analysis of time dependent tile drain flow and solute capture; however, as of yet, the directional nature of macropore networks, and the associated influence on bulk flow direction, has not been carefully considered.
 While tile drainage systems can act to integrate the effects of spatial variability in soil composition and structure, and allow tile drained fields to effectively serve as field scale lysimeters [Richard and Steenhuis, 1988], they can also induce relatively steep localized hydraulic gradients that necessitate the use of two-dimensional (2-D) models for realistic preferential flow and transport analysis [Köhne and Gerke, 2005]. When the soil of interest also contains macropores, dual-continuum numerical models that account for a preferential flow domain are well known to have superior performance over their single-continuum counterparts [Vogel et al., 2000; Gärdenäs et al., 2006; Gerke et al., 2007]. In recent past work [Haws et al., 2005; Gerke et al., 2007], 2-D dual-permeability models have been employed to analyze preferential flow and transport in tile drained, macroporous soil; however, application of dual-continuum models to field scenarios is complicated by the parameter intensiveness of the governing equations [Šimůnek et al., 2003], and by the impracticality of obtaining estimates for some of the most critical parameters at the plot and field scale. For comprehensive review of dual permeability modeling concepts and application, readers are referred to Šimůnek et al. , Gerke, , and Köhne et al. .
 When investigating movement of LSM through soil it is important to note that the dynamic viscosity of LSM is well correlated with its dry matter content, and can be significantly greater than water [Landry et al., 2004; Keener et al., 2006]; and that manure slurries with less than 5% total solids behave as Newtonian fluids [Kumar et al., 1972]. Work by Keener et al.  found that a 5% LSM dry matter content resulted in approximately a one order of magnitude increase in the viscosity of the LSM, which would result in a one order of magnitude reduction in hydraulic conductivity (K) according to ; where k (L2) is intrinsic permeability, ρ (M L−3) is fluid density, g (L T−2) is acceleration due to gravity, and μ (M L−1T−1) is fluid dynamic viscosity. While previous work has demonstrated the importance of considering viscosity influences when simulating variably saturated flow of saltwater through one-dimensional columns [Forkel and Celia, 1992], and saturated flow through density stratified deep geological cross sections [Ophori, 1998], little progress has been made on understanding the influence of viscosity on the flow of LSM through macroporous soil, even though it is quite clear that the movement of LSM through soil will be impeded in comparison to water.
 To increase our knowledge of the environmental risks associated with the land application of LSM, and of potential impact abatement measures, we must increase our understanding of the processes that control the movement of LSM through the soil. This goal is complicated by the large number of factors that may potentially affect the movement of LSM, and is therefore well suited for an investigative numerical analysis [Beven, 1989; Ebel and Loague, 2006]. Accordingly, this study addresses quantitative aspects of LSM movement in structured, layered soil; with specific focus given to the following:
 1. Modification of an existing dual-permeability model to account for variable fluid viscosity, and application of the new model to field based scenarios that consider the unique hydraulic conditions imposed by different LSM application methods (i.e., surface banding and subsurface injection).
 2. Determining the relative sensitivity of the simulated tile drain discharge rates and nutrient concentrations to variations in LSM viscosity, and the presence or absence of soil crust and plowpan layers.
 3. Numerical assessment of residual nutrient distribution in soil profiles with and without crust and plowpan layers, and with consideration of viscosity effects, following LSM application using surface banding and subsurface injection application methods.
 This work advances the modeling tools available for investigating the fate of LSM in structured, layered, tile drained soil; and for determining the influence that unique boundary conditions imposed by different LSM application methods, fluid viscosity, and low permeability soil layers, have on associated nutrient movement. In addition, new light is shed on the dynamic nature of parameter sensitivity in dual permeability models that provides basis for future work focused on reducing equifinality issues currently associated with preferential flow simulations.
2.1. Field Experiments
 The numerical experimentation here is based on field experiments that were designed to evaluate the effects of LSM application methods and loading rates on corn yield, nitrogen recovery, and tile effluent water quality [Ball Coelho et al., 2005]. These studies were conducted in late June to early July of 2000, 2001, and 2002, at a generally flat-lying agricultural field near Sebringville, in southwestern Ontario, Canada (see Figures S1–S4 in the auxiliary material). Soil at the site is classified as Huron silt loam, for which selected properties are provided in Table 1. Tile drains at the site were installed in the early 1980s and are 10 cm in diameter, systematically spaced approximately 9 m apart, and positioned at a depth of about 70 cm.
Table 1. Physical Soil Properties (From Ball Coelho et al., 2007; Used With Permission From the Journal of Environmental Quality) From the Liquid Swine Manure Injection (INJ), and Surface Banding (SB), Experiment Site
 During the experiments, LSM was applied to standing corn using either surface banding (SB) or subsurface injection (INJ) application methods. Following LSM application, NH4-N (hereafter referred to as NH4) and total phosphorus (P) were monitored in the tile effluent. Of the three years when field experiments were conducted, data from 2002 has the greatest temporal resolution for nutrient breakthrough at the tile drain, and of the four different LSM application rates (0, 28.1, 37.4, 56.1, and 74.8 m3 ha−1) employed during the field experiments, the 56.1 m3 ha−1 application provides the data set with the greatest resolution for the combination of both application methods. Accordingly, 56.1 m3 ha−1 field data from 2002, when the LSM contained 2.5% dry matter, is used as the benchmark for this work. As shown by Ball Coelho et al. , tile effluent NH4 and P concentrations returned to background levels within one week of LSM application each year; as a result, residual nutrient concentrations are deemed to have little year over year cumulative effect. For INJ, the application depth was targeted at 10 to 15 cm below surface. Two replicates of each application method – loading rate combination were applied to individual plots that were 9.0 m wide (12 corn rows) by 206 m long, and centered over individual tiles. Not all tile drains were flowing at the time of the experiments in 2002; therefore, concentration data does not exist for all application method – loading rate scenarios. Because of considerable rainfall prior to the 2002 field experiments, there was an agronomically significant soil crust present.
2.2. Model Description
 The numerical model utilized in this study was HydroGeoSphere (HGS) [Therrien et al., 2009]. HGS is an integrated surface – subsurface flow and transport model that includes a three-dimensional extension of the original one-dimensional, dual-permeability model of Gerke and van Genuchten [1993a]. For realistic simulation of flow and transport in dual-permeability media with anisotropic hydraulic conductivity, HGS allows individual hydraulic conductivity values to be specified for the X, Y, and Z directions for both continua, therefore making the model well suited for the conjunctive simulation of flow and transport within the predominantly vertical soil macropores and the relatively isotropic soil matrix. For the purpose of this study, where the infiltrating fluid is known to have a viscosity that is dependent on the concentration of a specific component, HGS has been modified to include continuously variable relative viscosity as a function of solute (i.e., dry matter) concentration. A conceptual overview of the modified model and the associated partial differential equations which govern flow and transport is given below. For further information on the HGS model, and the numerical solution of the dual-permeability flow and transport governing equations, the reader is referred to Therrien et al. .
 Dual-permeability porous media are considered to be a superposition of primary and secondary pore systems over the same volume. In the description that follows, the subscripts m and f are used to denote the respective primary (soil matrix) and secondary (macropore) pore systems. The dual-permeability, variably saturated flow solution is obtained by simultaneously solving two modified Richards equations for each grid node in the model domain that contains macropores in addition to the ubiquitous soil matrix. The pair of coupled equations is defined as follows:
where ∇ is the gradient operator; K (L T−1) is the saturated hydraulic conductivity tensor; h (L) is the pressure head; z (L) is the elevation head; wf is the macroporosity volumetric fraction; θm and (L3L−3) are the water contents in the matrix and macropores, respectively; and kr is relative permeability described with the van Genuchten  unsaturated soil hydraulic property model. The saturation – pressure head relationship is considered to be nonhysteretic.
 A simultaneous solution to the set of flow equations is obtained by coupling the two equations via (T−1) which is a water transfer term [Gerke and van Genuchten, 1993b] and is defined as , where (L−2) is a first-order mass transfer coefficient for water and Ka (L T−1) is the effective hydraulic conductivity of the matrix – macropore interface, which is defined as , where Ka (h) is also described with the van Genuchten  model. Although has previously been defined as [Gerke and van Genuchten, 1993a; Gerke and van Genuchten, 1996], where β is a geometry factor, is the distance from the center of a fictitious soil matrix block to the fracture edge and λw is an empirical coefficient; the difficulty in quantifying these parameters led to the decision that it would be prudent in this work to consider as an empirical fitting coefficient that can be adjusted during the model calibration process, and as noted by Gerke and van Genuchten , is a common practice.
 Viscosity dependence is incorporated into the flow governing equations through the (–) and (–) terms, which represent the relative viscosity of fluid in the respective soil matrix and macropores. The method employed here to incorporate variable fluid viscosity is generally applicable for any solute that has a predictable concentration – viscosity relationship. In our case, where LSM is the fluid of interest, μr is calculated according to , where is the dynamic viscosity of water at 20°C and is the calculated viscosity of the LSM mixture based on the moisture content – viscosity relationships presented by Keener et al. , which are approximated here as and , where CDM is the percentage of dry matter content (DM) in the LSM mixture as calculated with the transport solution described below. Accordingly, LSM with 2.5% DM would be predicted to have a relative viscosity 3 times greater than water at 20°C.
 As described by Therrien et al. , fluid exchange between the surface and soil matrix flow domains is controlled with a first-order relationship that assumes the existence of a thin boundary layer to allow calculation of a vertical gradient. For the purpose of this work, where the surface water zone serves only as a temporary reservoir for infiltrating fluid and lateral overland flow is neglected, the exchange equation can be given as
where is exchange flux, h and ho (L) are the soil matrix pressure head and water depth in the surface domain, respectively, and lexch (L) is the thickness of the boundary layer, which is set to 0.1 cm.
 The dual-permeability transport solution utilized by HGS solves a pair of advection-dispersion equations that are coupled by an exchange term that accounts for solute mass flux between the primary and secondary porosity continua. Advective and dispersive transport controls the mass flux between the surface and subsurface domains. The governing equations for subsurface transport are based on the description given by Gerke and van Genuchten [1993a], and are given as follows:
where C (M L−3) is solute concentration; λ (T−1) is a first-order decay coefficient; q (L T−1) is the Darcy flux; R (–) is a retardation factor that is calculated using a linear equilibrium distribution coefficient, K′ (L3M−1); D (L2T−1) is the hydrodynamic dispersion coefficient [Bear, 1972] that is itself a function of longitudinal ( ) and transverse ( ) dispersivity; and Γs (M L−3T−1) is a solute mass transfer term defined by Gerke and van Genuchten [1993a] as
where d (–) determines the transfer direction according to
and (–) and (–) are solute concentration relation terms defined as
where θbulk is the water content of the bulk soil. In the solute mass transfer equation (T−1) is a solute mass transfer coefficient defined as , where Dfree is the free solution diffusion coefficient. Similar to the approach taken with , αs is treated here as an empirical fitting coefficient that is adjusted during the model calibration process. For the purposes of this work, NH4 and P are subject to first-order decay and linear sorption, respectively, with the associated values determined during model calibration; while DM is considered to be a conservative species.
 The simulation domains (Figure 1) represent two-dimensional, unit thickness, cross sections of the INJ and SB LSM application field test plots. The 150 cm high soil profiles have been subdivided into five distinct layers (Figure 1a) that consist of: (1) a nonmacroporous soil crust layer, (2) a macroporous A horizon, (3) a macroporous plowpan layer, (4) a macroporous B horizon, and (5) a nonmacroporous B horizon below the tile drain elevation, in the permanently saturated region of the domain, where previous local work on silt loam soil with a shallow water table has found minimal macroporosity [Frey and Rudolph, 2011]. Both the INJ (Figure 1b) and SB (Figure 1c) domains represent one half of the symmetrical, 900 cm wide, field test plots. Both sides and the bottom of the domains are considered no-flow boundaries. A constant head boundary condition with the head fixed at atmospheric pressure was assigned to the exterior nodes located at a depth of 70 cm on the right side of the domain to represent the tile drains.
 Steady state initial conditions were developed by applying a constant water flux of 0.007 cm d−1 to the top surfaces prior to introducing LSM into the domain, resulting in a steady state water table that gently slopes toward the tile drain with about 2 cm of vertical relief across the width of the domain, a constant tile discharge rate of 3.15 cm3 d−1; and a near surface θm of 0.39 (m3 m−3), to closely represent conditions observed during the field experiments when near-surface moisture content was in the range of 0.40 to 0.42 [Ball Coelho et al., 2007].
 LSM is applied to the domain via surface water zones that allow for advective flux of LSM into the soil matrix to vary as a function of both surface water depth and soil matrix pressure head. The surface water zones are not directly coupled to the macropore zones in either of the application method scenarios. In SB, the soil crust was assumed to seal the macropores at the surface [Ela et al., 1992] to reflect the observed soil conditions at the time of the 2002′ field experiments. In INJ, tillage action is assumed to minimize the direct connection between macropores and the LSM [Turpin et al., 2007b]. Both the INJ and SB domains contain six individual surface water zones, spaced 75 cm apart and configured to reflect the physical reality of the two application methods, in order to optimize model predictions [Dusek et al., 2008]. For INJ (Figure 1b), the surface water zones are each 10 cm wide and recessed 10 cm into the top surface of the domain; whereas for SB (Figure 1c), they are each 50 cm wide and located on the top surface of the domain. Initial depth of LSM in the surface water zones is proportional to the manure application rate. For an application rate of 56.1 m3 ha−1, the initial LSM depth was 4.3 cm in the INJ scenario, and 0.9 cm in the BRD scenario. The horizontal distance between the tile drains and the vertical centerlines of the surface water zones located nearest to the tile drains is 37.5 cm.
 The control volume finite difference method was used to perform the numerical solution. Vertical grid spacing was 1 cm above the tile drain elevation and graded from 1 to 15 cm from tile drain elevation to the base of the domain. Horizontal grid spacing increased from 1 cm along the right side of the domain, to 7.5 cm along the left side of the domain.
2.4. Hydraulic Property Derivation
 Soil hydraulic properties required for the parameterization of the dual-permeability numerical model were primarily derived using a combination of (1) field measured bulk hydraulic conductivity measured with a single ring pressure infiltrometer [Ball Coelho et al., 2007], (2) soil physical properties in conjunction with the Rosetta pedotransfer-function based hydraulic property estimation program [Schaap et al., 2001], (3) macropore-area-fraction estimates reported by Frey and Rudolph  for similar soil located 35 km away, (4) manual model calibration, and (5) the constitutive relationship described by Gerke and van Genuchten [1993a], which relates Km and Kf to bulk soil saturated hydraulic conductivity (Kbulk) according to
2.4.1. Soil Matrix
 Soil composition and bulk density data given for the 0–20 and 20–40 cm depth intervals in Table 1 were used in conjunction with Rosetta [Schaap et al. 2001] to derive the A and B layer soil matrix hydraulic properties presented in Table 2. For the soil crust and plowpan layers, the hydraulic conductivities (Km) were determined during model calibration, while the residual ( ) and saturated ( ) soil moisture contents, and the and empirical coefficients of the van Genuchten  soil water retention function, were set equivalent to those of the A layer.
Table 2. Base Case Hydraulic Properties Assigned to the Soil Matrix Zones
 Macropore hydraulic properties are presented in Table 3. The macroporosity weighting factor coefficient (wf) was held constant at 0.006 for the A and B layers of the SB scenario, and the B layer of the INJ scenario. Because tillage associated with subsurface manure injection creates additional macroporosity [Turpin et al., 2007a], wf for the A layer of the INJ scenario was determined during model calibration.
Table 3. Base Case Hydraulic Properties Assigned to the Macroporous Zones
 The vertical, saturated hydraulic conductivity (Kf,z) for macropores in the A and B layers of both the INJ and SB scenarios was individually calculated using equation (9) in combination with the following: (1) bulk field saturated hydraulic conductivity (Kfs) values given in Table 1, where values from the 0–20 cm and 20–40 cm depth intervals are used to represent the A and B layers, respectively; (2) estimated soil matrix saturated hydraulic conductivities (Km); and (3) wf. For the A layer of the INJ scenario, a new value of Kf was calculated for each value of wf that was tested in the model calibration process.
 The horizontal/vertical macropore saturated hydraulic conductivity ratios (Kf,x/Kf,z) were determined during model calibration. While it was assumed that Kf,x/Kf,z for the macropores in the B layer of both LSM application scenarios would be equal, application scenario specific Kf,x/Kf,z ratios were determined for the A layers.
 Based on the assumption that the majority of the macropore zone is open pore space, θs was set to 0.9 for all of the macropore flow zones. θr was set to 0.05, which in combination with the respective values for and , of 0.1 cm−1 and 2.0, lead to relatively dry macropores in the simulated soil profile when it is in a freely drained state.
 The water ( ) and solute ( ) exchange parameters for the A and B layers were determined individually for both the INJ and SB scenarios during model calibration, with the constraint that B layer values are common. The saturated hydraulic conductivity of the matrix-macropore interface (Ka) was set to 0.08 times that of the soil matrix in the corresponding layer and is based on work conducted by Gerke and Köhne .
2.4.3. Transport Parameters
 Transport parameters used in the simulations are presented in Table 4. The longitudinal ( ) and transverse ( ) dispersivity values required to calculate D in equations (4) and (5) were set to 1.0 and 0.1 cm, respectively; and were taken from data presented by Neuman  for tracer tests conducted at a similar size scale, and from work by Sudicky  that showed transverse dispersion is generally small when compared to longitudinal dispersion. A first order decay coefficient of 0.3 d−1 for NH4 transport and an equilibrium distribution coefficient of 0.2 cm3 kg−1 for P transport were both determined during model calibration.
Table 4. Base Case Transport Parameters Applied in the Simulations
 Viscosity dependent models for the two application scenarios were primarily calibrated to field data for NH4 and P concentrations in tile drain effluent using results from the 56.1 m3 ha−1 LSM application experiments. Tile discharge was of limited focus during model calibration because of sparse field data; therefore, attempts were not made to estimate the total nutrient mass transmitted to the tile drains. The manual calibration process involved successive iterations of parameter updating followed by model execution and results analysis. The goal of the calibration process was to enable the models for both the INJ and SB scenarios to predict the shape of the NH4 and P breakthrough curves (BTC) at the tile drain outlet with respect to: arrival time, peak concentration, and late time (24–48 h after application) concentration. Because of the large variation in the tile effluent concentration data; and our interest in evaluating the important and information rich, early time breakthrough characteristics [Larsbo and Jarvis, 2006], the BTC are plotted using log-log scales.
 In addition to the detailed mechanistic assessment of viscosity, soil crust, and plowpan influences on LSM movement, a parameter sensitivity test was conducted in order to determine the relative sensitivity of short term tile discharge and solute breakthrough (model response) characteristics to perturbations in the model parameters listed in Table 5. Recognizing that parameter sensitivity can be temporally [Vrugt et al., 2002; Reusser et al., 2011], as well as boundary condition specific [Mertens et al., 2006], the following discrete target points (Figure 2) along the model response curves for both the INJ and SB scenarios were selected for analysis: peak tile flow (QMAX), time of peak flow (T [QMAX]), time associated with the leading and trailing edge of the flow peak (T [Q0.5]), where the 0.5 subscript represents one half the MAX value, maximum solute concentration (CMAX), time of peak concentration (T [CMAX]), and time associated with the leading and trailing edge of the solute breakthrough (T [C0.5]). The magnitude of the parameter perturbation was equal to one half the base case parameter value (b) used in the calibrated model, and the relative sensitivity of the model response to the parameter perturbation (Λ), normalized with respect to the base case model response ( fb), was calculated according to Λ = ( fb+1/4b – fb−1/4b)/fb for all of the parameters except KfA and KfB, where the effect was calculated according to Λ = ( fb – fb−1/2b)/fb in order to maintain a stable numerical solution. Note that the magnitude of the anisotropy perturbation described in Table 5 reflects the ratio of Kfx/Kfz which was altered by adjusting Kfx while Kfz was held constant.
Table 5. Hydraulic Properties and Transport Parameters, and Their Associated Values, Evaluated in the Sensitivity Tests
 While great care was taken to ensure that the parameter values derived through calibration are physically realistic, and well suited to the field scenarios under consideration, it should be noted that complex hydrologic models are inherently nonunique [Beven, 2006; Gupta et al., 1998]. As such, the nonunique nature of hydrologic models does not preclude their use as tools for developing an understanding of complex physical processes [Beven, 1989; Ebel and Loague, 2006], which is the theme of this work.
3. Results and Discussion
3.1. Parameter Estimation/Model Calibration
 Although the calibrated INJ model does a somewhat better job than the calibrated SB model (Figure 3), both models are generally able to reproduce the observed NH4 and P concentrations to within an order of magnitude, and the peak concentration arrival times to within approximately 30 min.
3.1.1. Soil Matrix
 The final set of calibrated hydraulic parameters for the soil matrix zones are presented in Table 2. Using Rosetta, Km is estimated to be 13.4 and 4.4 cm d−1 for the respective A and B soil layers. During model calibration, Km of the soil crust was reduced by a factor of 8 relative to Km of the underlying A layer soil matrix. Km of the 10 cm thick plowpan layer, with its base located at a depth of 30 cm, was reduced by a factor of 335 and 110, relative to Km of the A and B layer soil matrix, respectively.
 The final set of calibrated hydraulic parameters for the macropore zones are presented in Table 3. Using the method described in section 2.4.2, Kf,z values range from 13,600 to 69,700 cm d−1. While it may seem that these Kf,z values are quite large, it is important to note that the resulting flow velocities are generally within an order of magnitude of those reported in past field studies; such as Cey and Rudolph  who report that flow velocity in partially saturated vertical macropores was approximately 4000 cm d−1; and Nimmo  who calculated that the field experiments of Kung et al.  that were conducted under relatively wet conditions on a tile drained loam soil, yielded preferential flow velocities of 10,000 cm d−1.
 While acceptable model calibration for the SB scenario was achieved by using mean wf values obtained from similar soil, calibration of the INJ scenario model was improved by accounting for local tillage effects on soil structure, which resulted in the A layer wf being increased by a factor of 8 relative to that of the SB scenario. The B layer wf in the INJ scenario did not require compensation, which highlights the obvious fact that tillage influences on soil structure are strongest in the A layer.
 During model calibration, Kf,x of the B layer macropores in both application scenarios were reduced by a factor of 50 relative to Kf,z. For the macropores in the A layer of the SB scenario, Kf,x was reduced by a factor of 10 relative to Kf,z; while Kf,x was equal to Kf,z in the A layer of the INJ scenario. Consideration of macropore anisotropy was imperative for acceptable simulation of the NH4 and P peak concentrations, and the peak concentration arrival time at the tile drain. The Kf,x/Kf,z ratios obtained here correspond well with field observations that have shown wormholes become increasingly vertical with increased depth [McKenzie and Dexter, 1993], and that fractures and root holes (which could both readily facilitate lateral flow) tend to be greater near surface [Cey and Rudolph, 2009]. Different anisotropy ratios for the two LSM application methods highlight the fact that tillage can disrupt existing macropores while at the same time also create new fractures in the A layer [Turpin et al., 2007a] that lead to an increase in Kf,x.
3.1.3. Water and Solute Exchange Coefficients
 Individual (Table 3) and (Table 4) values were determined for the A and B layers of both the INJ and SB scenarios. Optimal values of in the A layers were 10 and 5 cm−2, for the INJ and SB scenarios, respectively; while in the B layer, a value of 0.005 cm−2 worked well for both scenarios. The parameter was finalized at values of 100 and 0.01 d−1, in the A layers of the respective INJ and SB scenarios, while in the B layer, a value of 0.1 d−1 worked well for both scenarios.
 Although and have both been treated as fitting coefficients, their relative magnitudes can be explained in terms of the underlying physical processes, which supports their presence in a physically based model [Ebel et al., 2009]. This perspective is adopted in the following discussion in order to provide insight on water and solute exchange processes between the soil matrix and macropore zones in layered macroporous soils, which employs the principle that larger values of promote greater water exchange and related advective mass flux, and larger values of promote greater diffusive mass flux, between the two continua. It is also important to note that the β coefficient employed in the theoretical description of the exchange coefficients (outlined in section 2.2) has been shown to be closely related to surface area available to support mass transfer [Gerke and van Genuchten, 1996] which supports the suggestion that the exchange parameters are influenced by tillage practices, and, as suggested by Schwartz et al. , soil structure. Accordingly, the three order of magnitude difference in the values between the A and B layers may reflect on the differences in the soil structure between the two layers. While the A layer consists of features that could be expected to undergo annual cycles of generation and destruction, such as interpedal voids, root holes, worm burrows, and tillage induced fractures; macropore features in the B layer primarily consist of root holes and worm burrows that could be expected to survive over a number of annual cycles, and develop organic rich linings that inhibit exchange [Gerke and Köhne, 2002]. Also, the fractures that have been observed to be most abundant in the A layer of similar soils [Cey and Rudolph, 2009; Frey and Rudolph, 2011] could potentially provide more surface area for intercontinuum exchange to occur than cylindrical macropore features of equivalent volume.
 Hydraulic conditions in the soil are strongly influenced by the magnitude of . The relatively low value of the B layer parameter facilitates the development of nonequilibrium conditions between the macropores and the soil matrix that exist for up to a day after LSM application, and lead to the steep lateral pressure head gradients within the macropore zone in the vicinity of the tile observed in Figure 4. These gradients exist because macropores near the tile are in effect freely drained by the tile; whereas away from the tile, macropore drainage occurs via lateral flow toward the tile (which is controlled by macropore Kf,x), and through water movement into the soil matrix (which is restricted by relatively low matrix hydraulic conductivity and values). It is the steep pressure head gradients in the macropore zone that allow the model to simulate the rapid movement of water and solutes, through a continuum with strong anisotropy, to the tile drain from a surface position that is horizontally displaced relative to the tile drain.
 In comparison to the B layer, the relatively large A layer values reduce both the magnitude and the duration of the pressure head nonequilibrium. Also, because the conceptual model assumes that LSM first moves from the surface water zone into the soil matrix and then from the soil matrix into the macropores, the easy intercontinuum exchange of water and solutes near the LSM application surface that is facilitated by large values leads to increased infiltration rates as a result of reduced pressure head buildup in the soil matrix.
 While there is not a clear layer dependent trend in the value of for the two LSM application scenarios, the A layer is four orders of magnitude larger for INJ than for SB, which can be at least partially explained by the presence of new, tillage induced fracture surfaces that could promote more diffusive mass exchange between the macropores and the soil matrix than the surfaces of the preexisting macropore features in the SB scenario, which may have developed surface skins that restrict diffusive mass exchange [Köhne et al., 2002].
3.2. Hydraulic Conditions and Nutrient Movement to the Tile Drain
 Simulation results from the calibrated models (Figure 3) show that tile effluent NH4 concentrations are predicted to peak 0.08 d, and 0.16 d after LSM application for the two 56.1 m3 ha−1 application scenarios. When tile concentrations peak, the single LSM application surfaces located closest to the tile drain are the sole source of the tile effluent NH4 for both the INJ (Figure 4a) and SB (Figure 4b) scenarios, and NH4 remains centered beneath the other five application surfaces. When the tile effluent NH4 concentrations peak, the water table in the macropore zone is near its maximum, at which time water levels at a position 75 cm from the tile drain have risen by approximately 18 cm in the two scenarios, relative to the initial position, and are considerably higher than the corresponding water tables in the soil matrix zones, which have risen approximately 7 cm. The relatively large water table rise in the macropores induces steep lateral pressure head gradients in the vicinity of the tile drains. When tile effluent NH4 concentrations peak, the water table slope (cm cm−1) in the macropore zone across the 75 cm interval nearest the tile is 0.25 and 0.23, in the respective INJ and SB scenarios; and the concurrent water table slope in the soil matrix are 0.091 and 0.135. For both scenarios, water table elevation in the soil matrix does not peak until approximately 0.8 d after LSM application, when maximum water table slopes of 0.119 and 0.143 are observed in the respective INJ and SB scenarios across the 75 cm interval nearest the tile; and at which time pressure heads in the macropore and soil matrix have nearly equilibrated.
 Away from the tile drain the lateral hydraulic head gradients in both the soil matrix and macropore zones remain relatively low throughout the simulation interval. At its peak 0.8 d after LSM application, the water table slope in the soil matrix across the 75 cm horizontal interval located furthest from the tile drain is approximately 0.0025 for both the INJ and SB scenarios.
3.3. Viscosity Sensitivity
 Sensitivity tests for both the INJ and SB scenarios, using an LSM application rate of 56.1 m3 ha−1, were conducted in order to determine the importance of considering the DM – viscosity relationship when predicting LSM movement in the soil profile. LSM dry matter contents of 0%, 1.25%, 2.5%, and 5% were considered in the evaluation, which according to the relationships presented in section 2.2.1, would lead to relative permeability multiplication factors of 1, 0.6, 0.3, and 0.1, respectively. The same LSM dry matter content values were also used to assess viscosity influences on both residual NH4 distribution within the soil matrix and LSM infiltration rates from the soil surface, for both application scenarios. Flow and transport parameters established during the calibration process were used in the viscosity sensitivity scenarios.
 Predicted tile effluent NH4 concentrations relative to LSM dry matter content are shown in Figure 5. When the viscosity effects associated with a LSM dry matter content of 1.25% are compared to the scenario where viscosity is not considered, peak concentrations decrease by 30% and 60%, and arrival times decrease by 12 and 35 min, for INJ (Figure 5a) and SB (Figure 5d), respectively. As would be expected, viscosity influences increase as DM content increases. When 5% DM is considered in the INJ scenario (Figure 5c), viscosity effects are responsible for a 60 min delay in the arrival of NH4 at the tile drain, and an 86% reduction in peak concentration. For the SB scenario, 5% DM content (Figure 5f) induces a 160 min delay in the arrival of NH4 at the tile drain, and a two order of magnitude reduction in peak concentration.
 Simulated residual soil matrix NH4 distributions beneath single LSM application surfaces adjacent to the tile drain, 24 h after LSM application, are shown in Figure 6. With LSM dry matter content of 1.25%, there is very little difference in residual NH4 distribution between simulations that do, and do not, consider viscosity effects for both the INJ (Figures 6a and 6b) and the SB (Figures 6e and 6f) scenarios. As DM content increases, NH4 is progressively retained higher in the soil profile in both scenarios; with results suggesting that increasing viscosity has a stronger influence on SB than INJ. With a DM content of 5%, very little NH4 is predicted to move below the base of the A layer in the SB scenario (Figure 6h), whereas for the INJ scenario (Figure 6d), NH4 does move into the B layer, albeit with lower spatial distribution than in the simulations where DM content was lower.
 Simulated infiltration rates for LSM to move into the soil profile, from a single application surface, are shown in Figure 7. Increased DM content reduces the infiltration rate and extends the associated infiltration time for both the INJ (Figure 7a) and SB (Figure 7b) scenarios. In the INJ scenario, the maximum infiltration rate of LSM with 5% DM is reduced by approximately 50%, and the time required for infiltration is approximately 3 times longer, than for the simulation where viscosity influence is not considered. In the SB scenario, the time required for infiltration of LSM with 5% DM is again extended by a factor of approximately 3 relative to the simulation where the influence of viscosity is not considered. However, the influence of viscosity on maximum infiltration rate is slightly less than in the INJ scenario, and viscosity effects associated with 5% DM content reduce the maximum infiltration rate by approximately 30% relative to the case where viscosity effects are not considered. For SB application of LSM with 2.5% DM applied at 56.1 m3 ha−1, the time required for complete infiltration is predicted to be approximately 80 min; which corresponds well to observations made during the field experiments that showed 60 to 120 min was required for complete infiltration.
 As shown in Figure 8, slower infiltration rates associated with 5% LSM dry matter content lead to reduced pressure heads in the soil matrix below the LSM application surface, and to delayed rise in pressure heads for both application scenarios; however, the relative reduction in pressure heads is greater for the SB scenario because of the additional dampening effect of the soil crust layer. Lower soil matrix pressure head leads to a reduction in the magnitude of pressure head nonequilibrium between the matrix and macropores, which in turn reduces LSM movement into the macropores (Figure 9). Because macropore flow is the mechanism for rapid vertical movement of LSM to the tile drain, a reduction in LSM movement into the A layer macropores also leads to delayed arrival of LSM at the tile drain and lower nutrient concentrations in the tile effluent.
 It is important to note that the viscosity influences investigated here only address the influence of DM content and not those of temperature. While previous work has concluded that temperature influences on manure viscosity are small in field conditions [Schofield, 1984], it should not be discounted that the dynamic viscosity of water increases by approximately 30% as its temperature declines from 20 to 10°C; or conversely, it decreases by approximately 26% as temperature increases from 0 to 10°C [Bear, 1972]. Accordingly, it is reasonable to expect similar differential changes in manure viscosity over equivalent temperature intervals, and as shown by Carson and Moses , temperature differences of this magnitude can exist over short depth intervals in shallow soils, in the region where preferential flow could readily facilitate rapid downward manure movement. As a result, the viscosity of LSM (or any other fluid for that matter) infiltrating macroporous soil may well be considered as a dynamic function of temperature, in addition to being a function of DM or solute content.
3.4. Plowpan and Soil Crust Sensitivity
 To determine the influence of the plowpan layer on the movement of LSM in the soil profile, results from simulations that included a plowpan were compared to results from simulations that did not include a plowpan for both application scenarios. Similarly, to determine the influence of the soil crust layer on LSM movement, results from a SB simulation that included the soil crust layer were compared to results from a simulation that did not include the soil crust. LSM movement in the INJ scenario is not influenced by the presence of a soil crust layer. Soil hydraulic properties established in the model calibration process were used for both the plowpan and the soil crust sensitivity tests; however, properties of the A layer soil matrix were extended to a depth of 30 cm for the simulations that did not include the plowpan; and in the simulation that did not include the soil crust, properties of both the A layer macropore and soil matrix continua were extended to the surface. An LSM application rate of 56.1 m3 ha−1, and viscosity dependency in conjunction with a manure DM content of 2.5%, was used in all of the plowpan and soil crust sensitivity simulations. In the results, the magnitude of nonequilibrium (NE) between the macropore and soil matrix zones for pressure head (hf − hm), and NH4 concentration (Cf − Cm), are reported for commonly located grid nodes that are horizontally centered beneath the leftmost LSM application surfaces (Figure 1), and located at depths of 15 and 40 cm, to represent hydraulic conditions in the A and B layers, respectively.
 Removing the plowpan in the INJ simulation caused a 50% reduction in peak tile discharge (Figure 10a), a 75% reduction in peak NH4 concentration in the tile effluent (Figure 10b), and also delayed both the hydraulic response, and NH4 arrival at the tile drain by approximately 15 min. The effect of removing the plowpan is greater for the SB scenario. Results from the SB simulation with the plowpan removed show: peak tile discharge is reduced by 57% (Figure 10c), peak NH4 concentration is reduced by over three orders of magnitude (Figure 10d), the hydraulic response of the tile drain is delayed by approximately 30 min, and NH4 arrival at the tile drain is delayed by 8 h.
 Removing the plowpan layer also changes characteristics of both the pressure head and NH4 concentration NE conditions, with more pronounced effects observed for SB as compared to INJ. When the plowpan is removed from the INJ simulation there is minimal change in both the NH4 concentration (Figure 11a) and the pressure head (Figure 11b) NE conditions in the A layer at a depth of 15 cm; whereas in the B layer, the development of NH4 concentration NE conditions is only slightly delayed and the magnitude of the peak pressure head NE condition is reduced by 55%. In the A layer of the SB scenario, at a depth of 15 cm, removing the plowpan causes a 30% reduction in peak NH4 concentration NE (Figure 11c), and delays the development of NH4 concentration NE conditions by 15 min; whereas pressure head equilibrium is not noticeably affected by the removal of the plowpan (Figure 11d). In the B layer of the SB scenario, NH4 concentration NE conditions are effectively eliminated when the plowpan layer is removed and peak pressure head NE conditions are reduced by 95%.
 The residual NH4 distribution is also affected by the removal of the plowpan. For the INJ scenario, removal of the plowpan causes a slight reduction in the width of the NH4 distribution profile (Figures 12a and 12b) and leads to more retention of NH4 in the A layer. The plowpan has a much more pronounced effect on residual NH4 distribution in the SB scenario, where practically all of the NH4 gets retained in the A layer when the plowpan is removed (Figures 12c and 12d).
 By restricting downward flow in the soil matrix, the plowpan can lead to increased A layer pressure head conditions during infiltration that promotes increased shallow lateral distribution of LSM, and increased LSM movement into the A layer macropores. Because the models consider macropores to be vertically continuous, increased macropore flow in the A layer also leads to increased macropore flow in the B layer; as a result, inclusion of a plowpan also increases both the B layer pressure head NE conditions, and vertical LSM distribution.
3.4.2. Soil Crust
 Removing the soil crust layer from the SB scenario increases the peak tile discharge rate by approximately 15% (Figure 13a), increases the peak NH4 concentration by 95% (Figure 13b), decreases the time required for the tile to exhibit a hydraulic response to LSM application by approximately 40 min, and decreases the time required for NH4 to reach the tile drain by approximately 75 min.
 Removing the soil crust layer from the SB simulations also changes the NH4 concentration and pressure head NE conditions between the macropore and soil matrix zones. When the soil crust is removed, peak NH4 concentration NE (Figure 14a) increases by factors of approximately 3 and 10 for the A and B layers, respectively; and the associated NE conditions are established 40 min earlier in the A layer and 50 min earlier in the B layer. Little change is observed in the A layer pressure head NE conditions (Figure 14b) when the soil crust is removed since pressure head equilibrium conditions exist for both cases (with and without soil crust) throughout the simulation time at a depth of 15 cm below the LSM application surface. However, at a depth of 40 cm, in the B layer, pressure head NE increases by 20%, and pressure head NE conditions are established approximately 30 min earlier, when the soil crust is removed.
 Residual NH4 distribution in the soil profile also changes in response to removal of the soil crust layer from the SB simulation. Removal of the crust (Figure 12e) promotes both deeper movement of NH4 into the soil profile, and B layer NH4 concentrations that are an order of magnitude greater than when the crust is included (Figure 12c). By slowing down the infiltration rate of LSM from the surface, the presence of a soil crust reduces the pressure head in the A layer soil matrix which in turn reduces LSM movement into the macropores and increases LSM retention near surface.
3.5. Parameter Sensitivity
 Of the four parameters included in the sensitivity analysis that were established a priori (i.e., Kf A, Kf B, KmA, and KmB) and held constant during calibration, values associated with Kf A, Kf B, and KmA tend to be larger than for KmB, for both the Q and C target points (Figure 15). Of the eight different target points assessed, CMAX tends to be the most sensitive (Figure 15h). The Λ values are also notably different for the two different LSM application scenarios. For INJ, Kf B is consistently the most sensitive parameter for all target points except T [QMAX] and T [Q0.5] Leading Edge, where KmA is the most sensitive, while for SB, KmA is the most sensitive parameter for CMAX; and Kf B and Km crust alternate as the most sensitive parameters for the other target points. The large values associated with SB Km crust support the results given in section 3.4.2 that show the crust to be an important structural feature for flow and transport characteristics. In contrast, for Km plowpan is consistently low for both INJ and SB even though results given in section 3.4.1 demonstrate the strong effect that the plowpan has on tile discharge and solute concentrations. These confounding observations for the plowpan demonstrate the importance of having a conceptual understanding of the potential role of in situ soil structural features on flow and transport processes, and that such an understanding can complement a formalized parameter sensitivity analyses when assessing how these features will influence simulation endpoints.
 While the values associated with the λ (NH4) and K′(P) parameters are effectively 0 for the target points identified in Figure 2, the relative influence of these two parameters increases as time elapses, and by 48 h after LSM application (data not shown) the respective Λ values for the λ and K′ influence on C have reached −0.25 and −0.44 for INJ scenario, and −0.27 and −0.59 for the BRD scenario. Of the two macropore anisotropy ratios incorporated into the models, was consistently greatest for Kfx/Kfz of the B horizon for the both the INJ and BRD scenarios; while associated with Kfx/Kfz in the A horizon was comparably low for the BRD scenario, and with the exception of the CMAX target point, also tended to be low for the INJ scenario.
 Based on the magnitude of the parameter perturbations employed, the values associated with the mass exchange parameters ( and ) tend to be low in relation to for the more influential hydraulic parameters, with the exception of A for the INJ CMAX target point (Figure 15h), where the magnitude of is on par with that of the A and B horizon anisotropy, and Kf B. In comparison, for BRD A is consistently low; although, it should be noted that A differs by four orders of magnitude between INJ and SB, and as a result, there was a similar difference in the magnitude of the parameter perturbation. A was also much more sensitive for INJ than SB, even though there is little difference in the magnitude of A parameter values employed in the two scenarios. In contrast, for the B horizon mass exchange parameters (which were held constant between INJ and SB) was more consistent between the INJ and SB scenarios.
 It is also apparent that Λ can exhibit temporal variability. For instance, in the INJ scenario, associated with select A horizon properties (anisotropy, Kf, and Km) tends to progressively decrease from T[C0.5] Leading Edge to T[C0.5] Trailing Edge; whereas the opposite trend exists for B horizon anisotropy and Kf. Noting that the same trend is not apparent for Λ associated with the tile discharge data, the results infer that for multi-soil-layer model calibration purposes, the information content of the tile drain concentration data is greater than the discharge data. Incorporating parameter temporal response dynamics into the calibration scheme (which was inherently applied with the multitarget point method applied here) can provide an opportunity to reduce dual permeability model nonuniqueness [e.g., Šimůnek et al., 2003], by associating parameters with the segments of the model response curve for which they have the greatest influence, during model calibration.
 Physical and hydraulic property data from a macroporous silt loam soil were used to parameterize a pair of 2-D dual-permeability models that were successfully able to simulate the observed movement of nutrients to tile drains in a variably saturated soil profile over a 2 day period following surface banding (SB) and injection (INJ) application of liquid swine manure (LSM). Soil crust and plowpan layer hydraulic conductivity, macropore anisotropy ratios, and LSM application method specific values for the water and mass exchange coefficients in the A and B layers were incorporated into the conceptual model and the associated parameters were determined through model calibration. Modeling results emphasize that fluid viscosity is an important factor for flow and transport in macroporous soil, and by increasing liquid manure viscosity during the application of liquid manure, nutrient movement to tile drains over the 2 day time period following manure application can be greatly reduced. When liquid manure has an initial viscosity that is not significantly greater than that of water, modeling suggests that it may be advantageous to take steps to increase the viscosity at some stage prior to field application in order to reduce nutrient transmission to tile drains. The modeling results also suggest that the risk of rapid nutrient movement to tile drains will be most pronounced within approximately 0.75 m of the tile (horizontal distance). Awareness and inclusion of soil features such as crusts and plowpans is demonstrated here to be very important in the context of simulating subsurface movement of liquid manure and associated nutrients in macroporous soil because of the strong influence that these low permeability layers have on soil matrix pressure heads, and the associated macropore hydraulic activity, in the A and B horizons. Negating the potential for increased surface runoff, the presence of a uniform soil crust can reduce nutrient movement to tile drains following SB liquid manure application; whereas the presence of a low permeability plowpan layer perforated by vertical macropores can increase nutrient movement to tile drains following both SB and INJ manure application.
 Multiple target point parameter sensitivity analysis revealed that the relative influence on solute breakthrough characteristics from the soil matrix and macropore hydraulic conductivity, macropore anisotropy, and intercontinuum exchange coefficients, tend to exhibit temporal variability. The influence of the first order decay (for NH4) and linear sorption (for P) coefficients on tile effluent solute concentrations also increased with time, which demonstrates that reaction characteristics (as well as weather and crop factors) become increasingly important when assessing nutrient fate as the simulation time extends beyond the time period where the effects of preferential flow are strongest.
 This work demonstrates that dual-permeability models can effectively simulate liquid manure application and rapid, short term nutrient movement in macroporous soils, and can also be used to elucidate the underlying physical processes; as a result, these models can aid in the design of soil-specific liquid manure delivery techniques that minimize potential contamination of water resources while concurrently maximizing nutrient availability for crops.
 The authors would like to thank Rob McLaren, Young Jin Park, and Ed Sudicky for their consultation and technical support, and the three anonymous reviewers who all provided constructive comments for an improved final version of this manuscript.