Model-based exploration of hydrological connectivity and solute transport in a forested hillslope

1 INTRODUCTION

Preferential flowpaths in soil are networks of large pores, soil pipes, and other void spaces that are formed by soil fauna, rooting activities, erosion related to soil water flow, and swelling and shrinking processes, including those caused by freezing–thawing phenomena (Aubertin, 1971; Beven & Germann, 1982; Laine-Kaulio, Backnäs, Koivusalo, & Laurén, 2015). Individual preferential flowpaths, often less than 50 cm in length, form connected, larger flow systems when the soil saturates, and thus preferential flow mechanisms control the run-off generation and solute transport in forested hillslopes (Laine-Kaulio et al., 2015; Sidle, Noguchi, Tsuboyama, & Laursen, 2001). Connectivity of subsurface saturation is a unifying descriptor of hydrological behaviour across different types of forested hillslopes (Hopp & McDonnell, 2009).

Two pore domain models provide means to investigate subsurface flow formation and solute transport in and between the preferential flow domain (PFD) and the soil matrix (SM) at forested hillslopes (Laine-Kaulio, Backnäs, Karvonen, Koivusalo, & McDonnell, 2014). Despite the current abundance of two pore domain models (e.g., Gerke, 2006; Šimůnek, Jarvis, van Genuchten, & Gärdenäs, 2003) and the evident two pore domain nature of forest soils (e.g., Laine-Kaulio et al., 2015; McDonnell, 1990), two pore domain models have not been systematically used at forest sites (James, McDonnell, Tromp-van Meerveld, & Peters, 2010; Laine-Kaulio, 2011). The limited availability of data for parameterizing and evaluating complex models is the major limitation of their applications (Arora, Mohanty, & McGuire, 2012; Faeh, Scherrer, & Naef, 1997; Kirchner, Feng, Neal, & Robson, 2004).

Data on solute concentrations in soil water, such as tracer data from specifically designed irrigation experiments, are important for identifying parameter values and appropriate structural features of two pore domain models (e.g., Kirchner, 2006; Laine-Kaulio et al., 2014). Combining field experiments with modelling exercises is a way towards a more comprehensive assessment of flow process representations in models (McGuire, Weiler, & McDonnell, 2007). Model applications with varying structure and parameterization can be considered hypotheses of how a hydrological system works (Beven, 2008). Joint simulations of water flow and tracer concentrations, as well as use of high-frequency data, should belong to the highest priorities of modern hydrological research (McDonnell & Beven, 2014).

Laine-Kaulio et al. (2014) utilized high-frequency field data from a specifically designed ion-tracer experiment to develop and evaluate a modifiable, 3D two pore domain model. The study exemplified how run-off generation in a shallow till soil profile at a boreal forest hillslope was controlled by preferential flow mechanisms, in particular by lateral by-pass flow. Even though the main flow and transport mechanisms were appropriately simulated by the model, the internal concentration dynamics of the observed tracer plume was not satisfyingly simulated at all measurement locations within the hillslope. The main reason for this was that spatial heterogeneity of soil properties was not explicitly presented in the model, as the model was only parameterized depth wise. As a consequence, lateral by-pass flow within the PFD dominated over water and solute exchange between the pore domains near and at saturation within the entire modelled hillslope section, without any local exceptions.

The exact nature of subsurface flow and solute transport is controlled by the hydraulic conductivity of soil, permeability of fractures in the underlying bedrock, existence of soil layers differing in hydraulic properties and macropore content, soil depth, and the local slope angle (Lehmann, Hinz, McGrath, Tromp-van Meerveld, & McDonnell, 2007). As a result of these soil properties, spatial connections and disconnections of individual preferential flowpaths are an important factor in flowpath development within hillslopes (Anderson, Weiler, Alila, & Hudson, 2009). By observing the breakthrough of a fluorescent dye in a forested hillslope, Wilson, Rigby, Ursic, and Dabney (2016) found that flow velocities in the PFD were in the same range with streamflow velocities and that continuous soil pipe networks connected the uppermost reaches of hillslopes with catchment outlets. The term “hydrological connectivity” generally refers to the passage of water from one part of the landscape to another and is expected to generate a run-off response (Bracken & Croke, 2007). We define hydrological connectivity within a forested hillslope as the formation of continuous lateral flow and transport patterns due to dynamic linkages between preferential flowpaths.

A quantitative description of rapid flow processes in connected preferential flowpaths is a challenge in hydrological research (Wienhöfer & Zehe, 2014). Water fluxes in and between the PFD and SM, and the resulting hydrological connectivity within hillslopes may have a decisive influence on solute transport from hillslopes. This is emphasized by geochemical differences between the PFD and SM (e.g., Backnäs, Laine-Kaulio, & Kløve, 2012). Wienhöfer and Zehe (2014) incorporated preferential flowpaths in a 2D, traditional one-pore domain model of flow and solute transport by allocating the model grid cells to either SM or PFD. As the explicit configuration of preferential flowpaths at their steep, forested hillslope was not known, different realizations of preferential flowpath networks were tested with the model. Successful model set-ups suggested that connected preferential flowpaths were a first-order control on the hydrology of the study hillslope. To further investigate the formation of connected preferential flow systems, and to quantify flow and transport within and from hillslopes, a 3D two pore domain modelling approach with exchange processes between the PFD and SM is required (Laine-Kaulio et al., 2014; Wienhöfer & Zehe, 2014).

In the present study, we identify possible (dis)connections between preferential flowpaths within a forested hillslope section using dye tracer data and incorporate them in a 3D two pore domain model of water flow and solute transport. The model is used to simulate the observed migration velocity and concentration status of an ion tracer plume during the different stages of an irrigation experiment. The main hypothesis is that the identified (dis)connections control the observed transport pattern, as well as the model performance. The objectives are to describe preferential flowpaths and hydrological connectivity within the hillslope and quantify their impacts on lateral subsurface stormflow and pollutant transport. To ease the use of the complex two pore domain model in further solute transport simulations, we test, at the end, whether a simplified presentation of selected model parameters is possible without compromising the validity of simulation results.

2 MATERIAL AND METHODS

2.1 Study site

The forested experimental hillslope in Kangaslampi, Finland (Figure 1a), belongs to the middle boreal forest zone and is classified as Vaccinium-Myrtillus type according to the Finnish forest-type classification (Cajander, 1949; Mikola, 1982). This study concentrates on the midslope area where the mean slope angle is 15%, and the mean thickness of the mineral soil profile above bedrock is about 85 cm. The soil type is haplic podzol with sandy till as the parent material (Food and Agriculture Organization (FAO), 1988) and with a high stone content of over 30% within the uppermost 23 cm of soil. The podzol profile consists of eluvial (E), illuvial (B), transitional (BC), and subsoil (C) horizons, and the forest floor consists of a 10-cm thick organic litter and mor humus layer (O). The mean thickness of the E-horizon is 9 cm, B 14 cm, BC 17 cm, and C is 45 cm. The nearly impervious bedrock is formed of gneiss granite and granodiorite.

Run-off generation within the midslope area is characterized by preferential flow and the transmissivity feedback phenomenon (Bishop, 1991; Bishop, Seibert, Nyberg, & Rodhe, 2011) with no surface run-off and with nonlinearly increasing lateral flow volumes when the soil saturates and watertable rises towards the soil surface. About half of the annual precipitation (600–700 mm during 1981–2010) generates run-off, and the main yearly run-off event is induced by spring snowmelt (late March snow depth 60–80 cm during 1981–2010; Finnish Meteorological Institute, 2015).

2.2 Tracer data

2.2.1 Chloride transport during an irrigation experiment

Data from a chloride irrigation experiment performed in September 2005 (Laine-Kaulio, 2011; Laine-Kaulio et al., 2014) were used to simulate run-off generation and solute transport in this study. In the experiment, a 3.6 m long, line-type irrigation source (i.e., a perforated tube) was placed upslope from a field of observation wells that were used to observe watertable levels and chloride concentrations (Figure 1b). The observation wells were screened at their entire height with a vertical spacing of 2 mm; the screen holes were 0.3 mm high and 30–40 mm wide. The screening enabled a rapid inflow/outflow to/from the wells, and water observed in the wells during the experiment was predominantly water flowing in the PFD, as demonstrated by Laine-Kaulio (2011).

The experiment consisted of two parts: The study area was first irrigated with 1.4 m³ of tracer-free water during a period of 2 hr. The next day, after a break of 19 hr, the area was irrigated with 0.8 m³ of 698 mg l⁻¹ chloride solution during 1 hr and 20 min, followed by 1.3 m³ of unchlorinated water during 2 hr and 10 min. Chloride concentrations were recorded at two depths in the wells, that is, at a level corresponding to the E-B-horizons and at a level corresponding to the BC-C-horizons. The depth distribution of chloride concentration in an observation well reflected the vertical concentration distribution in the PFD of the surrounding soil profile under saturation due to the fast inflow/ouflow to/from the wells. The stratification was hard to mix, as a clear depth distribution prevailed in wells even after stirring. The concentration values also returned to the same values within few minutes as recorded prior to stirring (Laine-Kaulio, 2011).

Figure 2a–f shows the measured chloride concentration and water table along the centre line of the studied hillslope section at six different time points. Every subfigure represents tracer concentrations and watertable levels in the vertical and lateral directions along the hillslope, that is, perpendicularly downslope from the midpoint of the horizontal, line-type irrigation source. The presented watertable levels are as measured in the observation wells; the chloride plume is interpolated from the measured values (Laine-Kaulio, 2011; Laine-Kaulio et al., 2014).

The following facts are to be kept in mind when examining the data:

The soil profile was dry before the initial irrigation was started (measured pressure head values varied from −396 to −144 cm). Also at the beginning of the actual tracer experiment, the soil profile was not saturated, and no watertable prevailed above the bedrock even though the soil profile was moistened until a distance of about 3.5 m from the irrigation source due to the initial irrigation a day before.

The data (Figure 2a–f) describe tracer concentrations in the PFD. Tracer concentrations as high as the concentration in the irrigated water were recorded during the tracer irrigation (Figure 2a,b). After changing the irrigation to tracer-free water, tracer concentrations along the slope dropped quickly, but at a distance of about 2 m from the irrigation source, dilution of the concentration was slower than upslope and downslope from this point (Figure 2c,d).

Lateral movement of the saturation front and tracer plume slowed down remarkably when the front had crossed a distance of about 4 m (cf. Figure 2a,b with 2c,d). This was mainly due to the fact that at this time point, the front had reached the drier section of the hillslope that had not been moistened a day before.

Tracer concentrations above the watertable at 16:30 and 18:50 (Figure 2e,f) are estimates calculated from the observed dilution velocity between 13:00 and 15:10. This is because watertable had already started to withdraw down, and concentrations could no longer be measured in the upper half of the soil profile. In addition, draining of soil increased the share of matrix flow in the total lateral flow, whereby a larger share of matrix water also entered the observation wells. Thus, concentrations at 16:30 and 18:50 were not used as primary data in model evaluations.

2.2.2 Dye patterns in saturated soil

Data from a dye tracer experiment performed in June 2006 (Laine-Kaulio et al., 2015) were used to explore soil properties, and connections and disconnections of preferential flowpaths in the hillslope. It is noteworthy that the dye tracer experiment was performed within the field of observation wells of the earlier ion tracer studies with chloride (Figure 1b). In the dye tracer experiment, 10 L of 1.0 g l⁻¹ dye solution were infiltrated into soil from a 1.0 m wide, shallow trench (Figures 1b and 2g). As the soil had been locally saturated using artificial irrigation, a 1 m wide dye pulse was sent downslope above a watertable that was located in the B-horizon. The study area was excavated into vertical cross sections the next day; Figure 2h shows the horizontal continuity of the line-type dye pulse in the B-horizon at different cross sections downslope from the dye source trench.

While migrating downslope, the dye pulse spread to the sides in the horizontal direction, and became discontinuous (Figure 2h). For the current study, it is most noteworthy that no dye was detected upslope from the point [0 m, 2.1 m] (Figure 2h). This corresponds to the 2 m distance of the ion tracer experiment, that is, the point where the dilution of chloride concentration was slow (Figure 2c,d and 2h). The absence of dye indicated local discontinuity of preferential flow. Instead, the B-horizon was observed to be thick and cemented with strong, dark reddish-brown mineralizations upslope from [0 m, 2.1 m], as well as elsewhere within the excavated area as shown with dark grey squares in Figure 1b. The width of the cemented clumps/lenses varied approximately between 0.15 and 0.7 m. Cemented areas were considered probable for disconnecting preferential flow. Moreover, many large stones (ca. 20–40 in the largest diameter) were found accumulated close to each other in the E and B-horizon within the black area marked on Figure 1b.

According to further dye tracer studies performed at the site (Laine-Kaulio, 2011; Laine-Kaulio et al., 2015), preferential flowpaths in the Kangaslampi hillslope are formed by rooting activities, erosion related to soil water flow, freezing–thawing phenomena, and soil fauna. Roots alter the pore size distribution of soil, and subsurface water flow and soil frost create voids around stone surfaces. As roots grow around and between stones, and water and solutes accumulate below stones, preferential flowpaths related to roots are connected to the voids around stones (Backnäs et al., 2012; Laine-Kaulio et al., 2015). These connections would then facilitate the self-organization of individual preferential flowpaths into larger preferential flow networks when the soil saturates.

2.3 Two pore domain model

2.3.1 Equations and model implementation

The two pore domain model used in this study (Laine-Kaulio, 2011; Laine-Kaulio et al., 2014) is a distributed, dual-permeability type, 3-D flow and solute transport model where flow is described in both the SM and PFD following Gerke and van Genuchten (1993):

(1)

where C^d is the differential moisture capacity [L⁻¹], h is the pressure head [L], t is the time [T], K is the unsaturated hydraulic conductivity function [LT⁻¹], H is the hydraulic head [L], S is the sink/source from/into the system [L³ L⁻³ T⁻¹], and Γ_w is the exchange of water between the two pore domains [L³ L⁻³ T⁻¹]. The sign of Γ_w is positive when calculating flow in the SM with Equation 1 and negative when using the equation for the PFD. Γ_w is calculated following Gerke & van Genuchten (1993) and Ray, Ellsworth, Valocchi, & Boast (1997) and is determined as

(2)

where α_wl is the lumped water transfer coefficient between the pore domains [L⁻²], K_a is the effective hydraulic conductivity at the PFD–M interface [LT⁻¹], and H_p and H_m are the hydraulic heads in the PFD and SM [L], respectively. K_a is calculated as the arithmetic mean of hydraulic conductivities in the PFD and SM. Arithmetic mean is also used within both pore domains in calculating hydraulic conductivity between model grid cells.

The relationship between hydraulic head and soil moisture is defined in both pore domains following van Genuchten (1980):

(3)

where θ is the volumetric soil moisture [L³ L⁻³]; θ_S and θ_R are the saturated and residual water contents [L³ L⁻³], respectively; and α [L⁻¹] and β [−] are the shape parameters of the model. For K applies:

(4)

where K_S is the saturated hydraulic conductivity [LT⁻¹] and S_e is the degree of saturation [−].

Solute transport mechanisms include advection, dispersion, and diffusion according to

(5)

where C is the solute concentration [ML⁻³], D is the dispersion coefficient [L² T⁻¹], v is the pore water velocity [LT⁻¹], S_s is the sink/source of solute from/into the system [ML⁻³ T⁻¹], and Г_s is the term that describes the solute exchange between the pore domains [ML⁻³ T⁻¹]. For D applies

(6)

where α* is the diffusion term [L² T⁻¹], α_L is the longitudinal and α_T1 and α_T2 are the transverse dispersivities [L], v_L is the longitudinal and v_T1 and v_T2 are the transverse flow velocities [LT⁻¹], and |v| is the flow velocity magnitude [LT⁻¹]. The sign of Γ_s is positive when calculating transport in the SM with Equation 5 and negative when using the equation for the PFD. Γ_s is calculated following Gerke & van Genuchten, 1993, and it is determined as

(7)

where d is the flow direction switch [−]; C_p and C_m are the concentrations in the PFD and SM [ML⁻³], respectively; α_s is the first-order solute mass transfer coefficient [T⁻¹]; and θ_m is the soil moisture in SM [L³ L⁻³].

The partial differential equations for flow and solute transport are solved implicitly in the model, using the control volume method (e.g., Rausch, Schäfer, Therrien, & Wagner, 2005). The computation time step is 1 min. The grid spacing is 20 cm in the lateral and horizontal directions (i.e., along the slope in y-direction and across the slope in x-direction, respectively), and about 9–20 cm in the vertical direction (i.e., z-direction). The uppermost four vertical layers in the model directly correspond to the mean observed thicknesses of the E-BC horizons, but the subsoil horizon C is split in two layers in the model, and the thickness of these layers varies following the variations in the total thickness of the mineral soil profile. The calculation grid is 45 cells long (y-direction), 25 cells wide (x-direction), and 5 cells high (z-direction). It is noteworthy that calculations are performed directly in the actual pore volumes allocated for the two pore domains, using parameter values that directly represent these domains (Table 1). Thus, unlike in Gerke and van Genuchten (1993), no scaling factor is needed in Equations 1 and 5. Calculations are started from the beginning of the initial irrigation, using measured pressure head values as initial state.

Table 1. Initial (H0) and final (H3) model parameterization; values that are different for H3 as compared to H0 are highlighted in bolda

Soil horizon	θS (cm3 cm−3)	θR (cm3 cm−3)	α (cm−1)	β (−)	KS (cms−1)	α* (cm2 s−1)	αL (cm)	αT (cm)	αwl (cm−2)	αs (s−1)
H0
ESM	0.178	0	0.013	1.861	6.2E-04	1.0E-06	5	0.5	0.01	1.0E-06
BSM	0.207	0.02	0.008	1.600	9.8E-04	1.0E-06	5	0.5	0.01	1.0E-06
BCSM	0.216	0.008	0.012	1.990	6.0E-04	1.0E-06	5	0.5	0.01	1.0E-06
CSM	0.203	0	0.012	1.898	6.0E-04	1.0E-06	5	0.5	0.01	1.0E-06
EPFD	0.070	0	0.080	1.380	8.0E-02	1.0E-06	50	5	0.01	1.0E-06
BPFD	0.035	0	0.039	1.375	3.0E-02	1.0E-06	50	5	0.01	1.0E-06
BCPFD	0.020	0	0.032	1.440	3.0E-03	1.0E-06	50	5	0.01	1.0E-06
CPFD	0.015	0	0.025	1.544	1.0E-03	1.0E-06	50	5	0.01	1.0E-06
H3
ESM	0.178	0.01	0.01	1.9	6.0E-04	1.0E-06	5	0.5	0.01	1.0E-06
BSM	0.207	0.01	0.01	1.9	6.0E-04	1.0E-06	5	0.5	0.01	1.0E-06
BCSM	0.216	0.01	0.01	1.9	6.0E-04	1.0E-06	5	0.5	0.01	1.0E-06
CSM	0.203	0.01	0.01	1.9	6.0E-04	1.0E-06	5	0.5	0.01	1.0E-06
EPFD	0.070	0	0.08	1.4	1.3E-01	1.0E-06	50	5	0.01	1.0E-06
BPFD	0.035	0	0.08	1.4	4.8E-02	1.0E-06	50	5	0.01	1.0E-06
BCPFD	0.020	0	0.08	1.4	4.8E-03	1.0E-06	50	5	0.01	1.0E-06
CPFD	0.015	0	0.08	1.4	1.6E-03	1.0E-06	50	5	0.01	1.0E-06

• ^a Observed stoniness of each soil horizon is taken into account in θ_S and θ_R.

2.3.2 Parameterization, hypotheses, and model evaluation

The initial model parameterization (H0 in Table 1) directly followed Laine-Kaulio et al. (2014), who calibrated the values of α_wl, K_S in the PFD, and θ_S in the PFD and SM. Running the two pore domain model against the ion tracer experiment data facilitated the identification of these parameter values. It is noteworthy that the site had a high stone content, and the effect of stones on the hillslope section–scale saturable pore volume was taken into account in the θ_S values (Laine-Kaulio et al., 2014). Values of K_S in the SM and α, β, and θ_R in both pore domains were fixed to their measured values. Parameters related to the calculation of dispersion were derived from literature. Parameter values changed depth wise. The bedrock had a horizontal fracture at the distance of 4.5 m from the irrigation source (Figure 1b), and it was taken into account by a sink in the corresponding horizontal row of model grid cells directly above bedrock, that is, in one horizontal row of grid cells in the lowest modelled mineral soil layer. By comparing the observed and simulated water levels at this distance, a value of 10% of the PFD water volume at each time step was set for the sink. In an hour, a water volume corresponding to 0.4% of the total pore volume of subsoil (i.e., the C-horizon) was removed through the sink. Thus, the amount of water removed from the soil profile into bedrock was small.

The main hypothesis was that the probable (dis)connections identified in the dye tracer studies control the observed ion tracer transport and its simulation. To test the main hypothesis, two contradictory hypotheses were tested with the model. The first hypothesis (H1) was that the accumulation of large stones found in the E and B horizon at the distance of about 1–3 m from the ion tracer irrigation source (Figure 1b) block lateral flow and thereby delay the migration velocity of the saturation front, as well as the dilution of tracer concentrations after changing the irrigation to tracer-free water. Thus, H1 aimed at invalidating the conception that stone surfaces would function as preferential flowpaths, and that these flowpaths would be connected to other types of preferential flowpaths so that continuous lateral preferential flow passes between stones in soil at the 1- to 3-m distance.

H1 was implemented in the model by setting the K_S values of E and B-horizons to zero in both pore domains within an area approximating the stone accumulations (Figure 3a). As the H0 model had been calibrated to produce the observed migration velocity of the saturation front, as well as to capture the observed chloride concentrations outside the 2-m measurement point (Laine-Kaulio et al., 2014), introducing locally zero K_S values to the model reduced the average migration velocity. To maintain the simulated migration velocity at the observed level, the PDF K_S had to be increased outside the noflow area. The model was run several times with gradually higher K_S values until the observed velocity was reached, that is, the simulated watertable levels corresponded to the observed levels. The resulting factor for the original PFD K_S was approximately 1.5. The marked, 18 grid cells with K_S = 0 corresponded to an area of 0.72 m². However, as the hydraulic conductivity between model grid cells was calculated as arithmetic mean, the extent of the entirely impermeable area was 0.24 m². Acknowledging the fact that defining exact locations and extents of stone accumulations is uncertain, the model was run with two alternative realizations of the accumulation that differ in shape and extent (H1a1 and H1a2 in Figure 3a).

The second hypothesis (H2) was that large soil pores do not exist, or they are not connected to each other and do not thereby contribute to the continuous, preferential flowpath network where cemented soil material was observed in a well-developed, thick B-horizon (Figure 1b). H2 was implemented in the model by lowering the K_S values in PFD to the level of the K_S values of SM within the areas marked on Figure 3b. Similarly to H1, higher values for the PFD K_S were calibrated outside the low-flow areas to maintain the average migration velocity of the saturation front at the observed level. The resulting factor for the original PFD K_S was 1.6. Again, two alternative realizations of the affected area were tested (H2a1 and H2a2 in Figure 3b). The default low-flow area along the centre line consisted of 24 grid cells that corresponded to a total affected area of 0.96 m²; Due to using arithmetic mean for hydraulic conductivity between grid cells, the area of the lowest conductivity covered 0.56 m². Because cemented soil was observed around R1 and to the right from L1 (Figure 1b), and because the observed watertable levels were similar in L1 and R1 (Figure 4a and 4c), the average width of the low-flow area was set equal for L1 and R1. L2 and R2, for their part, had clearly different watertable levels. Because almost no water entered L2, the left-side cemented area was expanded to cover its surroundings (Figure 3b). Because R2 received a high watertable, its surroundings were set to belong to the high-flow area.

Parameterization of distributed two pore domain models is generally considered challenging because measurements of soil hydraulic properties seldom cover the large number of model parameters, or the measurements are not representative for the two separate pore domains. On the other hand, identification of a large number of parameter values by calibration can result in equifinality of various value combinations (e.g., Beven & Binley, 1992). As an alternative way to tackle the parameterization problem, we tested, at the end, a third hypothesis (H3) that constant values can be used for a subset of model parameters without compromising the goodness of fit of the simulation results.

Dual-permeability models have been found to be least sensitive to K_S in the SM, and to α, β, and θ_R both in the PFD and SM (e.g., Dohnal, Vogel, Sanda, & Jelínková, 2012). Our measured, average values for K_S, α, β, and θ_R in the SM were very similar in all soil horizons (Table 1). In addition, these average values of each soil horizon were within the range of variation of all measured values of the other soil horizons (Laine-Kaulio, 2011). Thus, we set the values of K_S, α, β, and θ_R in the SM to average values of the entire soil profile (Table 1). In most studies on two pore domain models, constant values have been used for the water retention parameters of the PFD or even for all parameters of the PFD (e.g., Gärdenäs, Šimůnek, Jarvis, & van Genuchten, 2006; Vogel, Lichner, Dusek, & Cipakova, 2007). Assuming that the water retention capacity of an arbitrary, default preferential flowpath is weak and clearly differs from that of the SM, we applied α, β, and θ_R values of the PFD of the E-horizon to the PFD in all soil horizons (Table 1). Compared to the selected default values (α = 0.08, β = 1.4), the effect of a stronger water retention capacity (α = 0.07, β = 1.5) and a weaker water retention capacity (α = 0.09, β = 1.3) on the model outcome were tested.

The H0 model was calibrated by Laine-Kaulio et al. (2014) against observed chloride concentrations in the PFD at the end of tracer irrigation (i.e., at 13:00; Figure 2b) and at the end of tracer-free irrigation (i.e., at 15:10; Figure 2d). The remaining concentration data (Figure 2a, 2c, and 2e,f), as well as watertable data at all six time points (Figure 2a–f) were used for the model validation. Similarly to Laine-Kaulio et al. (2014), we analysed the performance of the H0–H3 models with the Nash–Sutcliffe model efficiency coefficient, E, (Nash & Sutcliffe, 1970) and the coefficient of determination, R². However, we did not divide the data into calibration and validation time points, but the goodness of fit values were evaluated at all time points presented in Figure 2a–f. At the end, the best performing model was validated against data from the left and right side wells (Figures 1b and 4). Because the watertable did not rise as fast and as high in these wells as in the centre line wells, these data consisted of fewer values, and interpolation of plumes was not possible (Laine-Kaulio, 2011). Therefore the observed and simulated watertable levels, as well as average chloride concentrations, were directly compared at locations L1, L2, R1, and R2 (Figure 1b).

3 RESULTS

3.1 Simulated tracer concentrations and watertable levels along the centre line

Figures 5 and 6 (unlike Figure 2a–f) show the difference between the observed and simulated chloride concentrations in the PFD. The greener the colour, the better the correspondence between the observed and simulated plumes; blue, yellow, and red denote clear differences. Figure 5a–f presents the results obtained by the H0 model with a good correspondence between the observed and simulated concentrations in the PFD during the tracer irrigation period, but an overestimated dilution velocity at the distance of about 2 m from the irrigation source. The overestimation is particularly clear in the highly conductive soil horizons near the soil surface directly after changing the irrigation to tracer-free water (Figure 5c).

Damming lateral flow by impervious model grid cells, assuming stones do not have a crucial role in the formation of preferential flowpaths and in their connectivity (H1), changed the simulated chloride concentrations of PFD at 14:00, 15:10, and 16:30 (cf. Figure 5c–e and 5i–k). Concentrations at the other time points, as well as watertable levels throughout the simulation period, remained similar as in the H0 run. Change in the simulated dilution was unfavourable: The impervious grid cells increased the simulated dilution in the PFD from before, and the goodness of fit between the observed and simulated chloride concentrations became even lower (cf. Figure 5c–e and 5i–k). The use of deviated impervious areas in the model produced similar results as the default area (Figure 7a–d). The simulated chloride concentrations did not correspond to the observed ones during the dilution period. Thus, the results did not support H1.

Restraining flow due to disconnections of preferential flowpaths (H2) led to favourable changes in the simulated dilution (Figure 6c,d). The use of small disconnected areas (H2a1), compared to the default areas (H2), slightly improved the simulated water levels at 14:00 and 18:50 (Figure 7e,f) but led to a clearly lower correspondence between the observed and simulated concentrations (Figure 7g,h). Using large disconnected areas produced low water levels after 12:00, which led to low goodness of fits for both the water levels and the concentrations (Figure 7e–h). The closest correspondence to the observed dilution was obtained using the midsized disconnected area in the model. Due to the good correspondence between observed and simulated water levels and chloride concentrations, the results supported H2. Thus, the low-conductivity area of H2 was included in the model also when testing the effect of simplified parameterization on simulation results (H3).

In H3, we formulated a conception of generally applicable SM and PFD domains with default water retention properties; water flow varied in the different soil horizons only due to spatially different K_S values in the PFD and with-depth changing θ_s values in both pore domains. The H3 parameterization caused small improvements in the goodness of fit values (Figure 6) by slightly accelerating the soil saturation at the leading edge of the tracer plume. For the H3 model, the minimum goodness of fit value between the observed and simulated watertable levels was as high as 0.88 (Figure 6g–l). As for the dilution dynamics of the tracer plume directly after changing the irrigation to tracer-free water, the goodness of fit between the observed and simulated chloride concentration was as high as 0.80 (Figure 6i). Deviating the default values of α and β in the PFD did not cause considerable changes in the goodness of fit values (Figure 7 i–l). The results supported H3.

3.2 Validation of the H3 model with data outside the centre line

The H3 model could satisfyingly reproduce the observed watertable levels (Figure 4). The low goodness of fits at L2 were due to low water table levels (Figure 4b) whereby a few centimetres difference between observed and simulated values was proportionally high. As for the chloride concentrations, the goodness of fits between observed and simulated values (Figure 4) were calculated using weighted means of PFD and SM concentrations as simulated values; simulated proportions of PFD lateral flow and SM lateral flow in the total lateral flow at the different locations L1, L2, R1, and R2 were used as weighting factors. This was because lateral flow in the PFD did not dominate over lateral flow in the SM outside the centre line area. At/close to the centre line, practically all water entering the observation wells during irrigations was water from the PDF (Figure 8b–d).

The model performed satisfactory for the chloride concentrations at R1-R2 (Figure 4c,d). At L2, the model captured the right concentration level, but the goodness of fits were low as they were for the water table levels (Figure 4b). For the concentrations at L1, the model did not perform satisfactory. Laine-Kaulio (2011) reported the largest stone (ca. 60 cm in diameter) peaking out from the soil surface between the irrigation source and L1. The stone prevented direct lateral flow to L1. The stone, as well as the unknown, exact local soil properties around it, and around L1, were not adequately represented by the model. Excluding L1, model evaluation outside the centre line supported the selected model set-up.

4 DISCUSSION

Earlier studies (e.g., Anderson et al., 2009; Wienhöfer & Zehe, 2014) have acknowledged the importance of (dis)connections between individual preferential flowpaths in the formation of the dominant lateral flowpath in forested hillslopes. We explored the finding further by establishing a description of connections and disconnections between different types of preferential flowpaths, and by quantifying water flow and solute transport in the PFD and SM within a typical boreal forest hillslope section. The study was enabled by a variety of field data to set up and run a complex 3D two pore domain model. Conservative tracers (such as chloride) alone give direct information about transport velocities in soil, but the actual flow pathways and velocities between observation points remain unknown (Beven & Germann, 2013). For this reason, dye tracer experiments and excavations were performed at the Kangaslampi site. Placing observed (dis)connections of preferential flowpaths in the 3D model let us test hypotheses about the flowpath network, and to quantify discharge and solute transport in the dominant lateral flowpath. As expected, subsurface stormflow and tracer transport at our site were most accurately simulated when local disconnections of preferential flowpaths were explicitly taken into account. The local disconnections were located there where strong mineralizations were observed in the soil material in the B-horizon.

Earlier studies (e.g., Leslie, Heinse, Alistair, & Mcdaniel, 2014) have addressed the role of decayed tree roots as preferential flowpaths in forest soils. The role of stones in the formation of preferential flowpaths has not been commonly addressed. According to our simulations, stones did not restrain preferential flow. Instead, connected preferential flow was required in the model within the area where an accumulation of stones was observed. This supported the conception that stones can contribute to the formation of continuous preferential flow routes in soil. Whereas roots alter the pore size distribution of soil, subsurface water flow and soil frost create voids around stone surfaces. Soil pipe formation and distribution are influenced by tree root growth, decay, slope gradient, and root limiting soil horizons (Leslie et al., 2014). As roots grow in the vicinity of stones, where also water and solutes accumulate, preferential flowpaths related to roots can be connected to the voids around stones (Backnäs et al., 2012; Laine-Kaulio et al., 2015).

Introducing spatial changes in the K_S of the PFD made it possible to mimic with the 3D model the effect of local disconnections in lateral preferential flow on the actual dominant flowpath. Because the disconnections restrained lateral flow, the dominant lateral flowpath was tortuous instead of being directly lateral along the centre line, demonstrating how difficult water and solute transport patterns in sloping terrains can be to predict (cf. McGlynn, McDonnell, & Brammer, 2002). It is noteworthy that spatial reductions in the θ_S of the PFD would only have caused a reduction in the total volume of large soil pores but would not have disconnected preferential flow. In addition, lateral preferential by-pass flow dominated over all other flow processes, thus tracer was rapidly washed away from the PFD after changing the irrigation to tracer-free water. This happens despite the calculation routine or parameter values used for the water and solute exchange between the pore domains (Laine-Kaulio et al., 2014), whereby local changes in the exchange also did not provide means to disconnect preferential flow in the model.

As comprehensive data are often not available to parameterize complex models (e.g., Arora et al., 2012), and as calibration of a large number of parameter values generally result in equifinality of different value combinations (e.g., Beven & Binley, 1992), finding ways to simplify the model parameterization are important. In the present study, simplifying the complex model parameterization by using constant values for water retention parameters and the SM K_S similarly to earlier studies (e.g., Gärdenäs et al., 2006) caused minor changes to the simulation results. This was because our constant values were of same magnitude than the original measured values, and because the simulation results were mainly controlled by the PFD K_S. Justifying the simplification in other studies will require further sensitivity analyses.

Despite encouraging examples of modelling subsurface water movement and solute transport in forested hillslopes (e.g., Dohnal et al., 2012; Wienhöfer & Zehe, 2014), finding widely applicable models that can take into account the effect of flowpath connectivities on solute transport remains a challenge. This was exemplified by the limitations of our study approach. First, any assumptions on local deviations in soil properties outside the very limited excavated area (Figure 1b) cannot be confirmed. Second, models are approximations of the reality. For instance, calculating preferential flow in heterogeneous soils with Richards' equation is an extension outside the equations' original scope of laminar flow and homogeneous porous medium (e.g., Beven & Germann, 2013; Gerke, 2006). Soils may exhibit a wide range of flow velocities in a wide range of pore sizes (Beven & Germann, 2013). Spatially varying values of the Ks in PFD exhibited the most important features in terms of simulating subsurface stormflow and solute transport in our hillslope, and heterogeneity of soil was hereby taken into account to a larger degree than earlier. Yet the real extent of heterogeneity was not known even within this small, intensively investigated area and could thereby not be presented in the model. Furthermore, preferential flowpaths are distinct structures in soil that cannot not be treated as a uniform, continuous flow domain at the scale of our model grid cells. Considering our modelling approach, continuity of preferential flow within and between all model grid cells would require using large grid cells, which was not realisable in our detailed, hillslope section–scale case study. To mimic subsurface pore structures in another way calls for a different modelling approach. Non-invasive X-ray imaging techniques have provided detailed 3D data on subsurface pore structures at soil column–scale, and flow within these small-scale structures can be simulated with Navier–Stokes-based approaches of laminar, viscous fluid flow (e.g., Jarvis, Koestel, & Larsbo, 2016). Considering hillslope scale flow and transport investigations, a promising model based on particle tracking has been tested for heterogeneous forest soil in Sweden (Davies, Beven, Nyberg, & Rodhe, 2011). None of the currently available models fully reflect, however, the prevailing process understanding and empirical knowledge of preferential flow (Jarvis et al., 2016).

At the end, estimations of subsurface water flow without consideration for preferential flowpaths are likely underestimated (e.g., Leslie et al., 2014). However, several studies have suggested that as important as it is to include preferential flow in hillslope hydrological models, the exact configuration of subsurface flowpaths does not need to be known explicitly to correctly simulate the total run-off from hillslopes (e.g., Weiler & McDonnell, 2007; Wienhöfer & Zehe, 2014). Simulations performed at our site do not invalidate this conception as average lateral flow can be satisfyingly simulated without an explicit representation of flowpath (dis)connections in the model, as demonstrated by Laine-Kaulio et al. (2014). On the basis of the present study, we note, however, that hillslope internal features of the PFD have a decisive influence on solute transport from hillslopes. At our site, the average simulated tracer flux within the dominant tortuous lateral flowpath was 1.7-fold compared to the originally modelled straight flowpath. A correct simulation of the average migration velocity of a pollutant plume in a hillslope does not directly guarantee a correct simulation of a released pollutant load. When also keeping in mind the geochemical differences between the PFD and SM (e.g., Backnäs et al., 2012), consideration of flowpath connectivities within hillslopes is essential for a reliable simulation of pollutant transport.

5 CONCLUSIONS

This study demonstrates how complex two pore domain models can be used in explaining observed transport patterns and in quantifying solute transport within forested hillslopes as response to hydrological forcing. The results emphasize the role of local disconnections of preferential flowpaths, and the resulting local reductions in their hydraulic conductivity, in the formation of the dominant lateral flow pathway, and the related pollutant load. At our site, continuous preferential flowpaths were formed by rooting activities, erosion caused by subsurface flow, freezing–thawing cycles, and soil fauna, but they were locally disconnected due to, for example, cemented soil material. Adding disconnections to dual-permeability models increases the complexity of parameterizing the saturated hydraulic conductivity of preferential flowpaths. Whereas increased complexity of parameterization can be justified by the observed heterogeneities in soil, finding ways to simplify the parameterization of distributed two pore domains models is important for their broader use. The consequence of the discovered disconnections of preferential flowpaths is that flow formation and solute transport within a typical boreal forest hillslope can be even more preferential than modelled earlier. Even if the exact configuration of subsurface preferential flowpaths would not need to be known in calculating the total run-off from hillslopes, the degree of flowpath connectivity within hillslopes can have a notable effect on pollutant transport.