Tracing lateral subsurface flow in layered soils by undisturbed monolith sampling, targeted laboratory experiments, and model-based analysis

Abstract

Lateral subsurface flow (LSF) is a phenomenon frequently occurring in the field induced by local water saturation along horizon boundaries under nonequilibrium conditions. However, observations of LSF in undisturbed soils under controlled irrigation in the laboratory are limited but needed for model improvement, prediction, and quantification of LSF. We present a method for extracting an undisturbed soil monolith along a soil horizon boundary and introduce an experimental setup for the measurement of LSF and an irrigation device for simulating rainfall. An experimental test run was simulated using HYDRUS 2D. Water infiltrating into the monolith and flowing either laterally along the horizon boundary or vertically through the bottom horizon could be separately captured by suction discs at the side and the bottom. Thus, a clear distinction between lateral and vertical flow was possible. Pressure heads and water contents were recorded by tensiometers and frequency domain reflectometry (FDR) sensors distributed across the monolith in a regular two-dimensional, vertical, cross-sectional pattern. Sensor readings indicated the presence of nonequilibrium conditions within the monolith. Modeling results could reproduce the lateral and vertical outflow of the monolith under constant irrigation, thus showing that water flow within the monolith under steady-state conditions can be explained by the Richards equation and the van Genuchten–Mualem model. The presented method can be used to improve and verify models designed for the prediction of the onset of LSF including that induced by local nonequilibrium conditions.

Abbreviations

FDR

frequency domain reflectometry

LSF

lateral subsurface flow

1D

one dimensional

PVC

polyvinyl chloride

SWC

soil water content

2D

two dimensional

3D

three dimensional

1 INTRODUCTION

A lateral redirection of water flow can occur along textural and other boundaries in the subsoil of sloping landscapes (Guo & Lin, 2018) or as interflow in forested hillslopes (Sidle et al., 2001). The lateral subsurface flow (LSF) can be a highly efficient shortcut for the movement of water and solutes such as plant nutrients and pesticides (Julich et al., 2017; Kahl et al., 2008; Potter et al., 2015). Despite ample evidence (H. H. Gerke et al., 2010; K. M. Gerke et al., 2015; Hardie et al., 2012; Laine-Kaulio et al., 2014; Liu & Lin, 2015; McNamara et al., 2005; Schwärzel et al., 2012; Wienhöfer & Zehe, 2014; Wöhling et al., 2012), observation and modeling of LSF are challenging due to the highly nonlinear, threshold-like onset of LSF, especially when based on local changes in the water potential (Filipović et al., 2018; Lv et al., 2013).

Water infiltration in unsaturated soil is mainly vertical (Hillel, 1987), because the hydraulic gradient is composed of nondirectional capillary forces and gravity pointing downwards. When the soil gets saturated (pressure heads approaching zero), capillary forces vanish and lateral downslope flows may be initiated above waterlogging layers (Lin et al., 2006). Because of preferential flow and local hydraulic nonequilibrium conditions, the critical point of zero water potential might be reached well before the soil is completely water saturated (Hannes et al., 2016).

Previous studies assumed that preferential flow along macropores (e.g., H. H. Gerke, 2006; Jarvis, 2007) could lead to local water saturation in regions where these pores were ending, and thus, such nonequilibrium flow conditions may initiate higher saturation above impeding soil horizons (Newman et al., 2004; Noguchi et al., 1999; Redding & Devito, 2010). The resulting transient local saturations in these soil regions could initiate LSF when located in sloping soil landscapes (Lin et al., 2006).

Experimental verifications are still limited because the subsurface flow field cannot easily be detected in situ (e.g., Allaire et al., 2009; Ehrhardt et al., 2021). Attempts made by geophysical approaches to identify LSF are limited in the spatial resolution to identify the onset (Di Prima et al., 2020; Guo et al., 2014; Leslie & Heinse, 2013; Nyquist et al., 2018). Also, the scale of observation needs to be accounted for: despite LSF occurring in hillslopes at the field scale (Buttle & McDonald, 2002; Lin et al., 2006; Redding & Devito, 2010; Wöhling et al., 2012), the onset of LSF was only observed in the laboratory at smaller scales (Lv et al., 2013; Sinai & Dirksen, 2006). Lateral subsurface flow may occur at various scales; however, capturing it experimentally seems to be more challenging, especially for the larger scales that are difficult to reproduce in the laboratory.

In the laboratory, several problems are strongly limiting the observation of LSF. For sampling of intact soil samples of the relevant size, special extraction equipment and encasings need to be constructed (Germer & Braun, 2015). One of the main issues is the separate collection of vertically and laterally moving soil water. The design of a laboratory setup for the model-based analyses requires a controllable irrigation system for water and tracer solutions (e.g., Sobotkova & Snehota, 2014) together with special spatial arrangements and sensor resolutions to be able to identify the local nonequilibrium conditions and separately control and quantify the vertical and lateral soil water fluxes (Fox et al., 2018).

Core Ideas

• A Laboratory method to induce and quantify lateral subsurface flow (LSF) is presented.
• The experimental setup is verified by modeling with HYDRUS 2D.
• Sampling of rectangular soil monoliths for 2D flow experiments is improved.
• Lateral subsurface flow and hydraulic nonequilibrium conditions are observed.
• The experimental data allow for improving models on the onset of LSF.

In several studies, samples consisting of artificially compacted soil of homogeneous grain size have been used to observe LSF under controlled conditions in the laboratory (Fox et al., 2018; Guertault & Fox, 2020; Miyazaki, 1988; Sakaki et al., 2011). Miyazaki (1988) proved the occurrence of LSF along textural boundaries in layered, sloped, and artificially compacted sandy loam soil samples with a layer of less compacted plant material. Evidence for LSF in artificially packed unsaturated sands was observed by Sinai and Dirksen (2006). Guertault and Fox (2020) observed LSF induced by artificial macropores in a homogeneous soil over a gravel layer. Percolation experiments using soil columns with artificial macropores have also been conducted by Köhne and Mohanty (2005) and Castiglione et al. (2003) to quantify macropore and matrix flow, as well as the interdomain water transfer. Macropore induced flow along texture contrasting layers (Lin et al., 2006) was observed in the field (Noguchi et al., 1999) and has also been observed in laboratory experiments after drilling artificial macropores down to the horizon boundary (Guertault & Fox, 2020). Sakaki et al. (2011) developed an experimental scheme to simultaneously determine the two-dimensional (2D) distribution of soil water content (SWC) and soil water potential in a soil monolith to assess water retention during wetting and drainage cycles. As presented above, most of the experimental studies focusing on LSF quantification have been done on artificially constructed soils, which certainly affect soil pore network and architecture that play an important role under field conditions, especially in arable soils.

For quantifying LSF dynamics, numerical models have been developed and applied. Guo et al. (2019) studied preferential flow in unsaturated saprock in forested hillslopes and proposed a three-dimensional (3D) fill-and-spill model that described the importance of subsurface flow. These authors identified shallow saprock and concave hillslopes as essential controls governing the hillslope subsurface flow. Dušek and Vogel (2014) presented two modeling approaches (one-dimensional [1D] vs. 2D) for quantification of hillslope discharge data (subsurface runoff) collected in an experimental trench. The two model approaches resulted in similar hillslope discharge hydrographs, characterized by short-term runoff peaks followed by zero-discharge periods, but the 2D model showed closer agreement between observed and simulated soil water pressure heads near the trench (subsurface runoff collection system). In a similar study, Dušek et al. (2012) studied preferential subsurface flow on a hillslope scale by combining a 1D vertical dual-continuum approach with a 1D Boussinesq-type lateral flow equation. They concluded that the physically based combined modeling allows for a reliable description of both preferential flow in a 1D vertical soil profile and lateral subsurface hillslope flow. In their study, Filipović et al. (2018) used HYDRUS 2D to quantify the potential for subsurface lateral flow depending on the erosion-affected spatial hydropedological complexity. It was shown that lateral flow was increasing with decreasing solum thickness, indicating an erosion-induced feedback on LSF, which was sensitive to the soil moisture regime prior to rainstorms during which LSF occurred. These modeling examples proved the necessity to design experiments for LSF quantification, which could help understanding of LSF in arable fields and improving modeling capabilities in reproducing LSF numerically.

An experimental setup that allows generating LSF in natural soil monoliths under local nonequilibrium conditions is still needed because data are missing to parameterize and test models that incorporate nonequilibrium conditions. Such conditions could be induced by macropores continuing vertically through compacted layers in the subsurface.

The objectives of the present study were to develop and test an experimental 2D setup that allows a quantitative investigation of LSF in intact unsaturated soil monoliths with particular emphasis on the initiation of local nonequilibrium conditions to provide datasets for model-based analysis under controlled conditions. The idea of the novel experimental setup was to combine the bottom suction plate with a suction-plate drainage system at the expected lateral flow side, and an irrigation system complemented by a relatively dense arrangement of water content and pressure head sensors (c.f., Sakaki et al., 2011) to obtain spatially distributed information about local soil hydraulic properties. The setup required extraction of intact soil monolith samples with contrasting soil horizons in sloping field soil and the transfer of the monolith into transparent casings without disturbance of the pore structure. The experimental data of LSF should allow the simulation with a 2D numerical model to verify the experimental setup. With this measurement setup, we want to determine whether it is possible to measure and visualize LSF in undisturbed soil monoliths under equilibrium and nonequilibrium conditions. Modeling with HYDRUS 2D is carried out in order to test the experimental setup under steady-state flow.

2 MATERIALS AND METHODS

2.1 Soil sampling

The soil was extracted at the CarboZalf-D experimental field of the Leibniz-Centre for Agricultural Landscape Research (ZALF), Müncheberg (Sommer et al., 2016), as a subsequent study of Filipović et al. (2018). The field site is located in a hummocky ground moraine soil landscape (53°23′ N, 13°47′ E; 50–60 m asl). The horizon boundary from a CBkg to a Bgk1 horizon of a Haplic Regosol (calcaric) was chosen for the analysis of LSF because of higher vertical and horizontal hydraulic conductivities in the CBkg horizon in contrast with the Bgk1-horizon, as we noted that on this specific boundary LSF could occur in specific conditions (Filipović et al., 2018).

The soil in both horizons was classified as a loamy sand (Rieckh et al., 2012). The horizontal hydraulic conductivity, K_h (cm d⁻¹), at a pressure head, h (cm), of h = −1 cm, close to saturation was 18.4 cm d⁻¹ for the CBkg horizon (26-to-48-cm depth). The value was about three times larger than that of the Bgk1 horizon (48-to-85-cm depth). The K_h values were larger in both horizons than those of their respective vertical hydraulic conductivity, K_v (cm d⁻¹) (Table 1). The hydraulic conductivities were determined by throughflow experiments with tension disc infiltrometers.

TABLE 1. Soil physical characteristics of the sampled horizons of the Haplic Regosol (calcaric): classification according to FAO classification (IUSS, 2006); equivalent particle size of organic carbon-free and carbonate-free sieved (<2 mm) soil for sand (2–0.063 mm), silt (0.063–0.002 mm), and clay (<0.002 mm) (Rieckh et al., 2012); soil bulk density, ρ_b; soil hydraulic conductivity in vertical, K_v, and horizontal, K_h, direction measured at pressure head of h = −1 cm; and anisotropy ratio K_v/K_h

Horizon	Depth	Sand	Silt	Clay	ρb	Kh	Kv	Kv/Kh
	cm	g kg^−1			g cm^−^3	cm d^−1
CBkg	26–48	614	267	118	1.76 (0.06)	18.4 (19.5)	11.0 (10.3)	0.59
Bgk1	48–85	612	270	118	1.73 (0.07)	5.9 (9.5)	2.7 (0.8)	0.36

• Note. Mean values from five replicates. The standard deviation is given in parentheses.

2.2 Soil monolith extraction procedure

For the soil monolith extraction procedure a 12-cm × 24-cm × 10-cm steel frame was constructed with sharpened chamfered edges at the bottom. A carbonate glass box was attached on top of the steel frame with metal angles and screws. Between the metal frame and the carbonate glass box, a 6-mm space was left with a bold nut for insertion of a bottom plate (Figure 1a).

FIGURE 1

Extraction procedure of the soil monolith: (a) pressing of the carbonate glass box (1) on top of the metal frame (2) into the ground; (b) carbonate glass box filled with soil but still attached at the bottom to the ground with the horizon boundary (3); (c) cutting of the soil from the ground at the bottom of the carbonate glass box with the bottom plate (4); (d) exchanging of the side walls for sensor installation

The sample was taken on 19 Oct. 2019 at 22-to-72-cm depth below the ground surface. A 3-m-long, 1.5-m-wide, and 1-m-deep pit was dug at the edge of the adjacent agricultural field. At the 3-m-long edge of the pit, the upper 22 cm of soil was removed to capture the horizon boundary approximately in the middle of the carbonate glass box. The soil around the soil monolith sample was excavated manually at the three sides, and the fourth side was the soil pit (already open). The metal frame with the attached carbonate glass box was carefully pressed vertically downwards (Figure 1a), such that the intact soil monolith progressively entered the 24-cm × 25-cm × 12-cm box (Figure 1b). After reaching the targeted depth, the soil monolith was cut at the bottom from the intact soil by inserting a chamfered steel plate (Figure 1c) that was then tightly attached to the monolith in the box using a strap.

In addition, three intact 100-cm³ soil cores (5-cm diam.) were sampled in the two soil horizons to gravimetrically determine the volumetric SWC at the time of extraction, θ (cm³ cm⁻³), and the soil bulk density, ρ_b (cm d⁻¹), after oven drying for 24 h at 105 °C.

In the laboratory, the final positions for installing the sensors were determined after checking the proposed, regularly spaced locations for stones or other obstructions (e.g., at tensiometers between artificial macropores in the upper and lower row, stones were found so that the sensors had to be moved). Then, carbonate glass plates with holes for the sensors were prepared according to the scheme and the location of the soil horizons (i.e., CBkg and Bgk1). Finally, the carbonate glass plates at the sides were replaced by those with the holes for the sensors by carefully sliding the old plate downwards and at the same time inserting the new plate from the top (Figure 1d).

2.3 Monolith setup

After the monolith was transferred into the carbonate glass box, it was placed on a bottom tension disc (inner edges: 15 cm × 30 cm × 0.6 cm) to drain the soil monolith (Supplemental Figure S1). At the left side, a second tension disc (inner edges: 10 cm × 10 cm × 1.0 cm) was attached in a distance of 6 cm from the bottom near the horizon boundary in order to drain water flowing laterally (Figure 2). This tension disc was used to capture the LSF above the CBkg/Bgk1 horizon boundary. The tension discs (Walter Weissig) covered a total area of 100 cm² and were connected via silicon pipes to leveling vessels that allowed for the adjustment of soil water pressure head at the side and the bottom of the monolith. The leveling vessels could be moved upward and downward by laboratory lifting tables. Water was removed from the leveling vessels via a side outlet and pipes to containers placed on scales to measure the rate of water drained from the monolith (Figure 2). The measurements were recorded in 3-min intervals by a DELTA data logger (DN Meßtechnik).

FIGURE 2

Scheme of the monolith measurement setup. The soil monolith is supplied with water via a capillary rainfall simulator connected to a water reservoir and a pump. The water is drained from the soil at the side and at the bottom by tension discs. Tension is adjusted by the leveling vessels. The amount of the drained water is captured with a container placed on the scale. PVC, polyvinyl chloride

The tension discs consisted of a Plexiglas disc with a rectangular Plexiglas frame glued on top. Within this frame, a gridded polyvinyl chloride (PVC) mesh similar to a fly screen was laid in several layers (later proven to be problematic due to the flexible structure, see Section 3). The tension discs were sealed on top of the Plexiglas frame by a fine gaze material (Saatifil polyamide, PA31/21, mesh size = 31 μm, air permeability [20-mm water column] = 2,300.l m⁻² s⁻¹). The gaze material was glued to the Plexiglas frame with epoxy resin. Both Plexiglas discs contained two holes: one in the middle of the disc for filling the disc with water and discharging the water from the monolith, and a second hole in one corner of the Plexiglas disc to remove the air from the disc while it was drained (Figure 2). The air entry point of the plates is dependent on the pore size of the gaze material and lies between −30 and −50 cm. The construction of the tension discs was carried out, which were similar to the tension disc infiltrometer described by Cook (2006), who used a Buchner funnel to apply a certain pressure head at the bottom of a soil core.

Twelve tensiometers (T5, METER Group) with a shaft length of 7 cm, a shaft diameter o of 0.5 cm, and a ceramic tip surface area of 0.5 cm² were installed horizontally at one side of the monolith by carefully drilling the holes (diameter = 0.5 cm, depth = 6 cm) in the soil monolith, so the sensor tips were placed in the middle of the monolith (Supplemental Figure S1). Three rows of tensiometers were installed with four tensiometers in each row. The upper row was located above the horizon boundary and the other two rows below the horizon boundary (Figure 3). On the opposite side of the monolith, six frequency domain reflectometry (FDR) sensors (ECH₂O EC-5 volumetric water content sensors, METER Group; length = 8.9 cm, width = 1.8 cm, height = 0.7 cm) were installed horizontally with the narrow side up in the spaces between the tensiometers (see Figure 3 for the exact positions). The sensor placement was carried out in order to avoid the disruption of vertical flow as minimal as possible and to fit more tensiometers between the FDR sensors (Supplemental Figure S1). The number of tensiometers installed at the horizon boundary (four) was constrained by the space required for FDR sensor placement while minimizing the disturbance of the soil structure. In addition, the space for the artificial macropore had to be reserved in the monolith. Both, FDR sensors and tensiometers were connected to a DT80 Series 4 data logger (dataTaker). Measurements were recorded at 1-min intervals.

FIGURE 3

Scheme of the exact sensor placement in the soil monolith for the tensiometers (T5) (left) and the frequency domain reflectometry (FDR) sensors (EC5, right)

To supply the soil monolith with water, a rainfall simulator was constructed, similar to the one proposed by Sobotkova and Snehota (2014). It consisted of a distributor vessel that was connected to a water reservoir. “Heidelberg” elongations with capillary needles (diameter = 0.4 mm, length = 25 mm) were screwed into the 35 openings of the distributor vessel with a Luer-lock system. The needles were placed into holes in a regular grid in a carbonate glass plate mounted on top of the soil monolith. The distance between the lower end of the needles and the monolith was 5.5 cm. The water was pumped from the water reservoir into the distributor vessel by a peristaltic pump (LAMBDA MAXIFLOW, LAMBDA CZ, s.r.o.).

2.4 Sensor calibration procedures

The ECH₂O EC-5 volumetric water content sensors (EC5 sensors) were calibrated by installing the sensors horizontally into sieved, air-dried soil from the two soil layers, where the monolith was extracted (PVC cylinder volume = 424.74 cm³; height = 5 cm; inner diameter = 10.4 cm). The soil was saturated for 6 d and exposed to evaporation on a scale CP 2202 S (Satorius; precision = 0.01 g) to determine the gravimetric water content. The FDR sensor readings and gravimetric volumetric water content were related in a quadratic relationship to derive the sensor calibration curve.

The T5 tensiometers were calibrated by applying well defined pressures in the range from 0 to −100 cm using a calibration unit. Applied pressures and sensor readings were used to determine the offset between the actual pressure and the values measured by the tensiometers and used for bias correction.

2.5 Experimental procedures and data analysis

First, the monolith was subjected to a constant precipitation rate of 1,200 ml d⁻¹ (41.7 L m⁻² d⁻¹). The rainfall rate was adjusted, so the vertical and horizontal saturated conductivity of the lower horizon was reached. In the long run, this should lead to water saturation in the lower layer and lateral flux on top of it. The constant rate of rainfall was applied until steady state (the sensor readings did not change anymore for 24 h).

The water level of the bottom tension disc was adjusted to −5 cm with the leveling vessel (Figure 2). The side tension disc was set to −20 cm in order to create a sufficient gradient that would lead to the discharge of water flow laterally along the soil horizon boundary. This pressure was determined experimentally. It corresponds to the value at which the first lateral water flow could be measured in our experimental setup. This experiment should demonstrate the ability of the measurement setup to discharge LSF along the horizon boundary.

In a second experiment, two holes (diameter = 0.8 cm) were drilled into the monolith from above representing earthworm burrows reaching down to the horizon boundary (Figure 3) similar to Guertault and Fox (2020). By only filling the holes with water, an artificial local saturation was created, possibly leading to LSF. The macropores had a length of 9–9.5 cm and were located in the middle of the monolith (9.3–9.5 cm from each end). The distance between the macropores was approximately 3.6 cm. Before the experiment, the soil was close to saturation, with pressure heads around −11 to −12 cm in the lower part of the monolith (close to bottom suction plate) and −15 to −17 cm in the uppermost row of the tensiometers. Contour plots of the hydraulic potential were calculated from the measurements of pressure head indicating the direction of water flow. In each hole, 7 ml of 5 g L⁻¹ Brilliant Blue dye was inserted and flushed with 48 ml of deionized water to facilitate the propagation of the dye while the rainfall simulator was turned off. The monolith was cut afterwards in 5-mm slices from the top to −11.5 cm to document the distribution of the dye. The cutting was performed with a diamond cutting wire (diameter = 0.2 mm) fastened in a clamping device. To make sure that even slices of 0.5-cm thickness were cut in every step, PVC discs with the size of the monolith cross-section and a height of 0.5 cm were inserted from the bottom of the monolith. Thus, the monolith was pushed 0.5 cm up and above the upper edge of the carbonate glass box, which served as a frame for cutting the soil evenly. To verify the calibration of the FDR sensors, small (4 cm × 5 cm × 0.5 cm) samples in the layer where the FDR sensors were installed were analyzed for the SWC of the upper row of FDR sensors.

After each slice was removed, a photo was taken with Canon EOS 1000D (10 MPx and 72 dpi). Photos were taken on an illuminated desk with the camera adjusted in a frame to achieve for each photo similar illumination conditions and a similar distance from the camera to the monolith surface. From each slice, a defined volume of the soil was cut and dried at 105 °C to analyze the SWC.

Data analysis and visualization of the contour plots and gradients was carried out with the software R version 3.6.2 (R Core Team, 2019). The hydraulic head was calculated from the sum of the pressure heads and the gravitational potential. Interpolation between the 12 points of the hydraulic potential was performed by bivariate interpolation according to Akima (1978) available in R in the akima package version 0.6-2.1. To visualize the flow direction, gradients of the hydraulic potentials were calculated in x and z direction and plotted as arrows with the ggplot2 package version 3.3.2. The evaluation of the tracer experiment pictures were downsized from 10 to 1 MPx with FastStone Photo Resizer version 4.3 (FastStone Corporation, 2019). The images were loaded into the image processing tool Fiji (ImageJ 1.53c, National Institutes of Health; Schindelin et al., 2012). Pixels in the images were classified into three classes: noncolored soil, colored soil, and pore system (i.e., holes and cracks in order to separate the colored soil from the noncolored areas). The images were scaled, and the blue-stained area was reconstructed as a 3D representation with the 3D Viewer plugin.

2.6 Numerical modeling

Simulation of water flow was performed using the HYDRUS-2D software (Šimůnek et al., 2016; version 2.04.0580, released April 2015). Water flow was simulated according to the Richards equation:

$$\begin{equation}\frac{{\partial {{\theta}}}}{{\partial t}} = \frac{\partial }{{\partial {x_i}}}\left[ {K\left( h \right)\left( {K_{i,j}^{\rm{A}}\frac{{\partial h}}{{\partial {x_j}}} + K_{i,z}^{\rm{A}}} \right)} \right]\end{equation}$$(1)

with θ as the volumetric water content [L³ L⁻³], t as time [T], h as the pressure head [L], x_i (i = 1, 2) as the spatial coordinates [L] with x₁ = x and x₂ = z (vertical), $$K_{i,j}^{\rm{A}}$$ are components of the dimensionless hydraulic conductivity anisotropy tensor, K^A, K(h) is the unsaturated hydraulic conductivity function [L T⁻¹]. The single porosity model according to van Genuchten–Mualem with an air-entry value of −2 cm was chosen. As demonstrated by Ippisch et al. (2006), such a modification is required for the application of the van Genuchten–Mualem model in case the n parameter is <2, as is the case here. This modification is a very minor change in the shape of the water retention curve near saturation but significantly affects the shape of the conductivity function close to water saturation, leading to an improved stability of the numerical solution of Richards equation as demonstrated by Vogel et al. (2001). Hysteresis was neglected in the simulation scenarios, and root water uptake was set to zero as no plants were involved in the experiment.

Because the hydraulic conductivity anisotropy tensor, K^A, is assumed to be symmetric, it is possible to define at any point in the flow domain a local coordinate system for which the tensor K^A is diagonal. The diagonal entries $$K_1^{\rm{A}}$$ and $$K_2^{\rm{A}}$$ of K^A are referred to as the principal components of K^A and represent scaling factors for the hydraulic conductivity in the x and z direction.

The soil hydraulic functions θ(h) and K(h) are described with the constraint single porosity van Genuchten–Mualem model with air entry of h_a = −2 cm as

$$\begin{equation} \def\eqcellsep{&}\begin{array}{@{}*{1}{l}@{}} {{{\theta}}\left( h \right) = {{{\theta}}_{\rm{r}}} + \frac{{{{{\theta}}_{\rm{s}}} - {{{\theta}}_{\rm{r}}}}}{{{{\left( {1 + {{\left| {{{\alpha}}h} \right|}^n}} \right)}^m}}}{\rm{ for h}} &lt; {h_{\rm{a}}}}\\ {{{\theta}}\left( h \right) = {{{\theta}}_{\rm{s}}}{\rm{ for }}h \ge {h_{\rm{a}}}} \end{array} \end{equation}$$(2)

$$\begin{equation}K\left( h \right) = {K_{\rm{s}}}K_{\rm{r}}^l{\left[ {1 - {{\left( {1 - S_{\rm{e}}^{\frac{1}{m}}} \right)}^m}} \right]^2}\end{equation}$$(3)

$$\begin{equation}{S_{\rm{e}}} = \frac{{{{\theta}} - {{{\theta}}_{\rm{r}}}}}{{{{{\theta}}_{\rm{s}}} - {{{\theta}}_{\rm{r}}}}}\end{equation}$$(4)

$$\begin{equation}m = 1 - \frac{1}{n}{\rm{; }}n &gt; 1\end{equation}$$(5)

where θ_r and θ_s denote residual and saturated volumetric water content [L³ L⁻³], respectively, K_s is the saturated hydraulic conductivity [L T⁻¹], as stated above, S_e is the effective saturation, α [L⁻¹] and n [–] are shape parameters, and the preconnectivity parameter is l = 0.5.

The two layers of the monolith were parametrized as shown in Table 2. Parameter estimates (θ_r, θ_s, α, and n) were derived from soil textural information using a neural-network-based pedotransfer function approach (i.e., Rosetta Lite DLL implemented into HYDRUS code; Schaap et al., 2001) with few parameters optimized throughout the model adaption (i.e., θ_s). $$K_1^{\rm{A}}$$ was derived from the ratio of hydraulic conductivities in the horizontal and vertical direction experimentally determined (Table 1).

TABLE 2. Manually adjusted soil hydraulic model parameters for the water flow simulation scenarios

Horizon	θr	θs	α	n	Ks	$${\bm{K}}_{{\bf 1}}^{{\bf A}}$$
	cm^3 cm^−3		cm^−1		cm d^−1
CBkg	0.037	0.26	0.0431	1.3	11.0	1.670
Bgk1	0.033	0.21	0.0552	1.2	2.7	2.185

• Note. $$K_1^{\rm{A}}$$, the first principal component of the dimensionless conductivity tensor K^A; K_s, the saturated hydraulic conductivity; α and n, van Genuchten's shape parameters; θ_r, the residual water content; θ_s, the saturated water content.

At the top soil surface of the monolith, an atmospheric surface boundary condition was assumed. A rainfall rate of 4.17 cm d⁻¹ was applied similar to the laboratory experiments. At the bottom, a seepage face condition was applied. No-flow boundary conditions were imposed at the left and right sides of the monolith except for the location of suction disc where a variable flux condition with a pressure head of −20 cm was applied. The initial conditions for the hydraulic potential were set to −5 cm at the bottom with a hydrostatic equilibrium distribution along the soil profile. The simulation was carried out until approaching steady-state flow conditions in the soil, which was after 24 h.

3 RESULTS AND DISCUSSION

3.1 Infiltration under constant precipitation

For the constant irrigation rate of 1,200 ml d⁻¹, the steady-state amount of water drained by the side tension disc was 935 ml d⁻¹, whereas 278 ml d⁻¹ were discharged by the bottom tension disc resulting in a balanced water budget (the difference between in- and outflow was only 13 ml; Table 3).

TABLE 3. Comparison of measured and simulated outflow (HYDRUS 2D) from the monolith during steady-state infiltration

Source	Inflow	Outflow (side)		Outflow (bottom)		Difference error
	ml d^−1		%	ml d^−1	%	ml d^−1
Data	1,200	935	77.9	278	23.2	13
Model	1,200	872	72.7	327.6	27.3	0

• Note. Percentages are given as the share of the total outflow. The difference error is defined as the discrepancy between the inflow and outflow.

The contour plot of the hydraulic potential shows a relatively homogeneous downward infiltration of the water indicated by the little blue arrows in the gradient plot (Figure 4b). This is similar to the observations of Sinai and Dirksen (2006), who found that under constant precipitation (infiltration), the flow is directed vertically downward, however, for a homogeneous sand soil. Only at the left side where the side tension disc is located, lateral movement of water is observed. This shows that the installation of a lateral tension disc and the application of a pressure head in a modified setup according to Sakaki et al. (2011) induced a suction that was sufficient to drain and quantify water moving laterally due to the applied lateral pressure gradients. Also, in the upper right part of the monolith, a lateral flow direction is observed, possibly caused by stones that were found after cutting the monolith. The magnitude of the gradient in hydraulic potential decreases from top to bottom and increases towards the side suction disc.

FIGURE 4

Contour plots of the (a) pressure head (cm) and (b) hydraulic potential (cm) with correspondent gradients under constant rain (1,200 ml d⁻¹). The length of the arrow in Plot b indicates the magnitude of the gradient. The red line indicates the horizon boundary, and the blue structure on the left indicates the position of the side tension disc

Unlike in the experiments of Miyazaki (1988), no clear deviation of flow along the horizon boundary is observed, which was evident from the hydraulic potential and SWC profiles. Miyazaki (1988) found an increase in water content and suction just along the boundary of a sandy loam layer over a gravel–plant layer that led to a lateral subsurface downhill flow on top of the coarser layer. In our experiment, the horizontal conductivity of the upper layer was three times higher in the upper layer than in the lower layer (Table 1). Also, secondary cracks during sensor installation (Figure 1) might have led to allow for vertical flow in the monolith. These cracks could only be observed due to the use of a transparent encasement of the monolith facilitating the monitoring of the occurrence of such cracks during or after sensor installation instead of a wooden box (Germer & Braun, 2015). The transparent encasement was useful also for the identification of the horizon boundary and the resulting placement of the sensors (Figure 1). Thus, the vertical hydraulic conductivity K_s might have been larger than 2.7 cm d⁻¹ due to these cracks or heterogeneity during sampling and measurement of K_s, preventing the lower layer from being saturated and leading to lateral flow on top of it.

The pressure head of the side tension disc was set to −20 cm. This pressure head was experimentally derived as to where to first lateral flow would occur. It is assumed that this rather low pressure head was needed, because the contact between the soil and the side tension disc was poor. The side tension disc is filled with a flexible PVC mesh that will be dented towards the Plexiglas-encasing of the plate, if low pressure heads are applied. Thus, a high resistance must be overcome before the water can enter the plate. In the future, this might be avoided by using a less flexible filling material for the plate, like sinter glass plates that will not be dented by low pressure heads. Also, the size of the side suction plate is rather large in comparison with the size of the monolith. Thus, the pressure field within the box might be disturbed. To counteract this effect, the size of the monolith could be increased or the size of the side suction plate could be reduced. Because the size of the monolith is defined by the steel frame, it is handier to reduce the size of the side suction plate. This would also help to minimize the vertical gradient within the plate.

3.2 Comparison of steady-state infiltration to model

Simulated and measured outflow at the bottom and at the side have the same ratio of ∼75% of the outflow leaving the monolith via the side suction plate and 25 % of the outflow being discharged via the bottom suction plate (Table 3). The higher discharge at the side suction disc indicates a strong lateral component of the flow along the horizon boundary. This is also observed in the direction of the velocity vectors (model, Figure 5a) and gradients (measurement, Figure 4b). Infiltration is mainly directed vertical in the upper and lower part of the monolith, whereas along the horizon boundary close to the side suction disc, water is flowing laterally. Below the horizon boundary, vertical flow is observed, similar to the hillslope study of Dušek and Vogel (2014).

FIGURE 5

Modeling results using HYDRUS 2D showing (a) flow direction, (b) pressure head (cm), and (c) soil water content; circles within Plots b and c indicate the measured values (same color range as modeled values), and white circles indicate no difference between modeled and measured values. Figures show the steady state conditions 96 h after simulation start under constant rain (1,200 ml d⁻¹)

A decrease in pressure heads towards the side suction disc is observed in the model (Figure 5b). The highest observed pressure heads are found in the upper left part that decrease towards the side suction disc (Figure 4a), similar to the model. Modeled and observed pressure heads (colored dots at the sensor positions in Figure 5b) are almost similar. Only the right sensor in the middle row of the tensiometers differs strongly from the simulated value, possibly due to a crack.

For the water content, a clear distinction between the upper and the lower layer is observed, with higher water contents of around 25% (v/v) in the CBkg horizon as compared with the lower layer, with water contents around 19% (v/v) (Figure 5 c). In the measurements, no such boundary is found. Still, the water content is higher in the upper layer as compared with the lower layer, with values reaching 40% (v/v) in the upper left corner (colored dots in Figure 5c).

The idea of the model setup was to show that the observed water flow within the monolith under steady-state conditions can be explained by established models like the Richards equation and the van Genuchten–Mualem model. The model matched the observed outflow at the side and bottom suction discs reasonably well. The local pressure heads and the water contents in the two soil horizons were also reproduced by the model. These modeling results successfully evaluated the experimental setup for the quantification of LSF under steady-state conditions.

3.3 Reproducing preferential flow: Infiltration into macropores

To induce local saturation conditions, two artificial macropores were supplied with 7 ml of Brilliant Blue and 48 ml of water (total fluid application = 110 ml) within 30 h. Within the time of the tracer and the water application, 93 ml was drained via the side tension disc. The discrepancy between input and output might be attributed to evaporation during the fluid application.

The contour plots clearly show the position of the two macropores by an elevated hydraulic potential (Figure 6b). The water infiltrates laterally around the holes into the matrix (blue strings in the middle top of the monolith in Figure 6), similar to what was observed by Buttle and McDonald (2002) and Noguchi et al. (1999) and proposed by Lin et al. (2006) in a sloped forest soil. Also, below the holes, a sideward movement of water is observed towards the edge of the monolith, especially next to the right hole (Figure 6b). Below the horizon boundary, the water flows vertically downwards to bottom tension disc. The lateral movement towards the side tension disc is much stronger than towards the bottom tension disc, as indicated by the larger magnitude of the gradient towards the left (longer arrows in Figure 6b). This is in accordance with the observation that all water leached from the monolith via the side tension disc throughout the tracer experiment. Due to the installation of the small tensiometers according to Sakaki et al. (2011), a fine resolution in the visualization of the gradients in the hydraulic potential was achieved, especially in the areas around the macropores. Placing a tensiometer closer to the side tension disc would probably give further insights about the flow passages of such small amounts of water added to the macropores.

FIGURE 6

Contour plots of the (a) pressure head (cm) and (b) hydraulic potential (cm) with correspondent gradients when only the macropores are infiltrated. The length of the arrow in Plot b indicates the magnitude of the gradient. The red line indicates the horizon boundary, the blue structure on the left indicates the position of the side tension disc, and the blue strings in the middle top of the monolith show the position of the macropores

3.4 Verification of flow direction with tracer experiment

To verify the flow behavior observed by the tensiometers and FDR sensors, 7 ml of the tracer Brilliant Blue were inserted into each hole followed by 48 ml of deionized water to spread the tracer. The dye was laterally distributed around the holes (3D visualization of dye spread in Figure 7), as already observed in the contour plots (Figure 6). At the top of the monolith, the dye was spread widely due to ponding during the water application. At the left hole, the dye was concentrated around the upper part of the hole. In contrast, the right hole showed a lateral spread of the tracer at the lower end of the hole that was also observed in the contour plots (Figure 6b). Despite infiltrating vertically the Brilliant Blue was also distributed laterally around the right macropore indicating the LSF occurrence. The dye was also spread at the bottom of the right macropore further to the left in the direction of the side tension disc. This can be attributed to LSF of water along the horizon boundary as observed by Redding and Devito (2010) and Buttle and McDonald (2002) for the soil–bedrock interface. This supports the conceptual model, proposed by Lin et al. (2006), of LSF also occurring along soil horizon boundaries as found by Noguchi et al. (1999) in a forest soil and by Hardie et al. (2012) in texture-contrast soils in Australia.

FIGURE 7

Three-dimensional representation of the dye stained areas after the Brilliant Blue tracer was applied. The holes representing macropores where the tracer was applied are marked in yellow. The side tension disc (1) is located at left side of the cuboid. The horizon boundary (2) is marked by two white lines

The SWC was overestimated by the left and the middle sensor, whereas the sensor on the right underestimated the water content (Table 4) compared with the gravimetric water content. The middle sensor showed the highest SWC in both cases, whereas the left sensor had higher SWC than the right sensor in case of the FDR measurement and vice versa in the gravimetrical SWC measurement. Thus, despite the calibration of the sensors, deviations of 2–6% (v/v) were still found between the two measurement procedures. As for the gravimetric method, possible sources for errors are the time gap between FDR sensor removal and sampling and the small volume of the sample. Samples from the layer were taken ∼24 h after the FDR sensors were removed and infiltration was stopped. The volume of the samples was only 10 cm³, such that small measurement errors could have already affected the value of the volumetric SWC. Also the EC5 sensor readings were sensitive to temperature and electrical conductivity of the soil water (Rosenbaum et al., 2011), not accounted for during the calibration procedure.

TABLE 4. Comparison of the soil water content measured by the frequency domain reflectometry sensors (SWC_FDR) in the upper part of the monolith and the mean and SD of the soil water content determined gravimetrically (FDR_grav) during the cutting of the monolith in the depths from 3 to 7 cm

Sensor location	SWCFDR	SWCgrav	SD (SWCgrav)
	% (v/v)
Left	28.8	26.6	3.4
Middle	31.3	27.6	1.7
Right	23.1	27.0	0

3.5 Interrelation between experiments and nonequilibrium conditions

The experimental setup as presented above was capable of draining LSF from the monolith as well as vertical flow. Lateral subsurface flow occurred under constant rainfall and macropore infiltration. It was assumed that equilibrium conditions were present in the monolith under constant rainfall. The water retention curves of the CBkg and Bgk1 horizons under equilibrium conditions according to the laboratory measurements of Rieckh et al. (2012) and the model results of this study are presented in Figure 8. The water retention curves measured in the monolith during a wetting process vary according to the sensor position within the monolith, indicating a heterogeneous soil structure of the soil monolith. The curves were extracted at the FDR sensor positions by interpolation of the measured pressure heads of the tensiometers surrounding each FDR sensor (for time series of sensors, see Supplemental Figures S2 and S3). In particular, the measured water retention curves of the CBkg horizon differ in their inclination as compared with the equilibrium curves. This might indicate the presence of nonequilibrium conditions within the monolith, because the steeper curves show that the water content lags behind the pressure head increase during irrigation (Hannes et al., 2016). For the water retention curve and timeseries of pressure head and water content under drying of the monolith, see Supplemental Figures S4–S6. These findings show the ability of the measurement setup to capture nonequilibrium conditions and thus provide data for model improvement and verification of nonequilibrium models.

FIGURE 8

Modeled curves of the CBkg (blue) and the Bgk1 (orange) horizons from this paper (broken lines) and from Rieckh et al. (2012) (solid lines), and the measured values from the monolith experiment under irrigation (short curves). Eqn., equation; FDR, frequency domain reflectometry

3.6 Experimental setup to enhance the understanding of the mechanisms of LSF

According to Hardie et al. (2012), the mechanisms of LSF occurrence along texture-contrast soils are still poorly understood. So far structural variability (McNamara et al., 2005; Wöhling et al., 2012), vertical preferential flow through macropores (Guertault & Fox, 2020; Schwärzel et al., 2012), hydraulic gradients in highly permeable layers beneath kettleholes (H. H. Gerke et al., 2010), and connected flow paths within hillslopes (Guo et al., 2014; Laine-Kaulio et al., 2014; Wienhöfer & Zehe, 2014) have been reported as possible triggers for the onset of LSF. In particular, the widespread phenomenon of vertical preferential flow (K. M. Gerke et al., 2015; Liu & Lin, 2015; Newman et al., 2004) is an important mechanism for the onset of LSF even before the soil is water saturated (Guo et al., 2018), and that needs more detailed investigation. A better understanding of the processes leading to the onset of LSF due to vertical preferential flow will improve the prediction and modeling of agrochemical leaching from agricultural areas into the groundwater (Janssen et al., 2010) and adjacent streams (Kahl et al., 2008).

The presented experimental setup provides the means to further explore the onset of LSF along texture-contrast soil horizon boundaries. The transparent encasing allows for the visual inspection of heterogeneities that might be responsible for LSF (McNamara et al., 2005; Wöhling et al., 2012). Additionally, by installing artificial macropores or capturing natural macropores, the effects of local saturation and hydraulic nonequilibrium on the onset of LSF can be investigated.

4 CONCLUSIONS

With the experimental setup for the detection of LSF, it was possible to visualize and quantify the water movement within an undisturbed soil monolith sampled from a Haplic Regosol (calcaric). We could distinguish between lateral flow along horizon boundaries and vertical flow. With sensors for measuring the water contents and pressure heads in regular spatial intervals within the monolith, it was possible to capture water flow under local nonequilibrium conditions that could occur at impeding soil horizons (e.g., during macropore infiltration). Thus the measurement setup could be useful to provide data for the verification of modeling results.

Under constant rainfall, an equilibrium model could reproduce the flow diversion within the monolith, with the amount of outflow at the bottom and at the side of the sample proving the successful operation of the experimental setup. In comparison with the model predictions, the measured water content and pressure heads varied greatly and indicated the presence of heterogeneities within the monolith that were not implemented in the model.

The observed LSF that was experimentally induced by local pressure head nonequilibrium during preferential flow through artificial macropores proved that the experimental setup was able to capture assumed flow phenomena. The data provided could be used to explore water dynamics under transient conditions for the development of improved model concepts including nonequilibrium phenomena that allow to predict the onset of LSF in macroscopically unsaturated soil.

ACKNOWLEDGMENTS

This study was financially supported by the Deutsche Forschungsgemeinschaft (DFG), Bonn, Germany, under grants GE 990/13-1 “Vadose Zone Modelling of water flow in hillslope soil (VAMOS).” The authors thank Norber Wypler (ZALF, Müncheberg) for technical support in constructing the experimental setup and Dr. Christoph Haas (Christian-Albrechts-Universität zu Kiel) for his help with soil monolith sampling. We are grateful for technical support during the analysis of the Brilliant Blue tracer experiment by Dr. Martin Leue (ZALF, Müncheberg) and Dr. Luis Barbosa (ZALF, Müncheberg). We thank Prof. Dr. Michael Sommer (ZALF, Müncheberg) for providing access to soil physical and soil chemical data.

AUTHOR CONTRIBUTIONS

Annelie Ehrhardt: Data curation; Formal analysis; Investigation; Methodology; Resources; Software; Visualization; Writing – original draft. Kristian Berger: Investigation; Methodology. Vilim Filipović: Investigation; Software; Validation; Visualization; Writing – original draft; Writing – review & editing. Hans-Jörg Vogel: Conceptualization; Funding acquisition; Project administration; Supervision; Writing – review & editing. Thomas Wöhling: Conceptualization; Writing – review & editing. Horst H. Gerke: Conceptualization; Funding acquisition; Investigation; Methodology; Project administration; Supervision; Writing – original draft; Writing – review & editing.

CONFLICT OF INTEREST

The authors declare no conflict of interest.