A Century of Denial: Preferential and Nonequilibrium Water Flow in

Published December 20, 2018

Special Section: Nonuniform Flow across Vadose Zone Scales Core Ideas • In the 20th century there was a general denial of the evidence for preferential flow. • The development of models of preferential flow is reviewed. • Some critical areas for future research in this field are identified.

A Century of Denial: Preferential and Nonequilibrium Water Flow in Soils, 1864-1984 Keith Beven* This review provides a historical summary of the development of knowledge on preferential and non-equilibrium flows in soils, particularly in the period 1864 to 1984. It is pointed out that preferential flows were recognized long before the equilibrium concepts of Edgar Buckingham and Lorenzo A. Richards were developed and became the dominant underpinnings of soil physics in the 20th century, effectively in denial of all the evidence that the Buckingham–Richards theory was inadequate to deal with water flows in field soils. Summaries of evidence from soil microscopy, tracing and breakthrough curve experiments, infiltration and throughflow observations, and studies of natural pipes are presented. Approaches to modeling preferential flows at soil profile and hillslope responses are also reviewed, including viscous flow theory and particle tracking methods. Further research is required into the integration of viscosity and capillarity-dominated flows, into nonlaminar flows in larger pores, and into upscaling from core and profile experiments to larger hillslope scales. Also, more rigorous hypothesis testing is required in soil physics and hillslope hydrology using both flow and tracer data. This might lead to a new paradigm in representing the detail complexity of flow in soils in applications at larger scales. Abbreviations: ADE, advection–dispersion equation; B-R, Buckingham–Richards.

The starting point for most studies of water flow in soils is the memoir by Henry

Lancaster Environment Centre, Lancaster Univ., Lancaster LA1 4YQ, UK. *Corresponding author ([email protected]). Received 8 Aug. 2018. Accepted 18 Oct. 2018. Citation: Beven, K. 2018. A century of denial: Preferential and nonequilibrium water flow in soils, 1864–1984. Vadose Zone J. 17:180153. doi:10.2136/vzj2018.08.0153

© Soil Science Society of America. This is an open access article distributed under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-ncnd/4.0/).

Philibert Gaspard Darcy (1803–1858), published in 1856. Darcy showed that, for steady saturated flow in repacked sand columns, the flux rate was linearly related to the applied pressure gradient (Darcy, 1856). The constant of proportionality is what we now know as the hydraulic conductivity of the soil. A long time later, Davis et al. (1992) showed that Darcy’s original data set was not strictly linear but only closely approximated a linear relationship. The relationship is still widely used, however, and is commonly referred to as Darcy’s Law. It was extended to the realm of unsaturated flow in 1907 by the work of the physicist Edgar Buckingham (1867–1940), who apparently did not know of the work of Darcy but who drew directly on analogy with Ohm’s law and Fourier’s law to define water flow through unsaturated soil in terms of a gradient of attraction and a constant of proportionality that he called “capillary conductivity” (Buckingham, 1907). He also suggested that capillary conductivity would be a function of capillary potential (see also Sposito, 1987). In 1931, Lorenzo Richards (1904–1993), in a paper published in Volume 1 of the journal Physics, did similar experiments to those of Darcy, looking at steady unsaturated flows in repacked columns of sand and soil. He used applied positive air pressure to ensure that the soil would remain unsaturated. Flux rates were measured when the sample had come into equilibrium with the air pressure and pressure gradient across the end of the sample. The higher the air pressure, the smaller the remaining moisture content and the smaller the pores through which the water would be flowing. He showed that the hydraulic conductivity was a nonlinear function of water content or average pressure, but at a given water content the flux rate is approximately linearly related to the pressure gradient. This much is presented in most hydrological textbooks. It is perhaps less well known that Fig. 6 of the Richards (1931) paper shows that the hydraulic conductivity is also a function of whether the soil sample is wetting or drying (i.e., that there is hysteresis in the hydraulic

Vadose Zone Journal | Advancing Critical Zone Science

conductivity relationship). Richards showed both primary and secondary scanning curves. In doing so, he reinforced the conclusions of Haines (1930) in a paper published the previous year that showed hysteretic effects in experiments on columns of glass beads. The steady nature of the flow, and the air pressure in the case of the Richards experiments, imposed an equilibrium condition on the experiments, albeit different for wetting and drying. There were good reasons to do so: As in any physics experiment, you should start by learning from the simplest controlled boundary conditions. The question is whether the resulting knowledge is usefully applied to more general cases. From the hydrological perspective, the more general case means unsteady flow in undisturbed heterogeneous soils that have been subject to weathering and other soil formation processes, bioturbation, and land management practices at field scales. In these cases, it would seem that the Buckingham–Richards (B-R) approach to flow in unsaturated soils is not generally applicable at any useful scale for good physical reasons. Although there have been attempts to provide (theoretical) criteria for the validity of the equilibrium approach (e.g., Sposito, 1980), even if water pressures were changing in ways that allowed an assumption of local equilibrium to be valid, the nonlinearity of the flux–gradient relationship would mean that the same equation cannot be valid at larger scales if there is any heterogeneity in local hydraulic conductivities. The fluxes in any chosen direction necessarily average linearly, but pressure gradients and hydraulic conductivities cannot. Some averaged effective gradient and averaged effective conductivity values will not therefore be sufficient. Attempts to allow for heterogeneities within equilibrium flow theory have proven complex and subject to strong assumptions (e.g., Yeh et al., 1985), and it is now appreciated that nonequilibrium effects, such as different types of preferential flows, can be common in undisturbed soils (see other papers in this issue). We can conclude that, for wider applications of flow in soils, the experimental set-up of Richards (1931) was the wrong experiment (see also Beven, 2014). But the importance of preferential flows has been recognized for a very long time. We can look back at least to Schumacher (1864), who wrote: the permeability of a soil during infiltration is mainly controlled by big pores, in which the water is not held under the influence of capillary forces (quoted in Beven and Germann, 1982). A similar inference was made from early research at what became known as the Rothamsted Experimental Station. Rothamsted dates from 1843 when John Bennet Lawes (1814–1900), the owner of the Rothamsted Estate, appointed Joseph Henry Gilbert (1817–1901), a chemist, as his scientific collaborator with the aim of improving agricultural practice and productivity. Lawes was a classic gentleman scientist, who in 1842 was granted a patent for the production of superphosphate fertilizer and created the world’s first factory for artificial manures. In Lawes et al. (1882), the first results from the Rothamsted drainage plots or lysimeters, which are

VZJ | Advancing Critical Zone Science

still being monitored today, were presented. From analysis of the chemical composition of the drainage waters, they stated that The drainage water of a soil may thus be of two kinds: it may consist (1) of rainwater that has passed with but little change in composition down the open channels of the soil; or (2) of the water discharged from the pores of a saturated soil. They also noted that In a heavy soil, channel drainage will in most cases precede general drainage; a portion of the water escaping by the open channels before the body of the soil has become saturated; this will especially be the case if the rain fell rapidly, and water accumulates on the surface. Statements about non-equilibrium flows in unsaturated soils therefore preceded the equilibrium “soil physics” description by some decades. Both Lawes and Gilbert were later elected as Fellows of the Royal Society. There were other sources of evidence. Soil thin sections were being examined in the laboratory under microscopes since the early years of the 20th Century. The book by Kubiena (1938) summarized a large body of work (see also FitzPatrick, 1984). One of the features of such sections that was commonly found was the layering of clay particles around larger soil pores. These were called cutans (see, for example, Banse and Graff [1968] and Brewer [1960]). The inference was that some cutans were the result of translocation of clay particles by flowing water, which would then suggest a nonlaminar flow regime. There is, of course, no shortage of mechanisms for producing macropores and open channels in the soil, where water will be less subject to capillary forces. Beven and Germann (1982) list pores formed by soil fauna, pores formed by plant roots, cracks and fissures, and natural soil pipes formed either in dispersive soils or peat soils. In addition, there is the possibility of the creation of non-equilibrium fingers of wetting in unsaturated soil by different mechanisms. Indeed, it would appear that non-equilibrium or preferential flow can be considered ubiquitous in field soils and may dominate during infiltration and redistribution, whereas capillary-dominated equilibrium flow might be important only during extended periods of drainage (e.g., Germann, 2014). Despite this evidence and practical experience, preferential or non-equilibrium flows in soils were generally ignored during this period. Even as late as 1990 there were hydrology texts that made no mention of macropore flows, preferential flows, or nonequilibrium flows in soils (e.g., Bras, 1990). The seminal book edited by Mike Kirkby on Hillslope Hydrology (Kirkby, 1978) mentions pipeflows (which were also of interest to geomorphologists in terms of channel development) but no other forms of non-equilibrium flow. My own personal experience also suggests that it was difficult to get a positive review of papers on preferential p. 2 of 17

flow from a whole generation of soil physicists during this period. There was either denial that this was a significant problem or criticism of any alternative theory that it did not represent soil physics. Sposito (1987), in his review of the physics of soil physics, makes no mention of any study involving non-equilibrium flows. His concerns, as expressed in four fundamental questions at the end of his paper, are concerned with issues of similarity of soil characteristics, relating the Richards formulation to internal energy balance, the physics of coupled heat and water flows, and relating microscopic (equilibrium) behavior to macroscopic flows in a more rigorous way. These questions have rightly continued to occupy soil physicists to the present day, but the difficulty of developing a “physics” of non-equilibrium flows in soils with arbitrary structure remains. It is also interesting that the review of preferential flows by Liu and Lin (2015) does not cite a single paper prior to 1990 (not even the important early review of Thomas and Phillips [1979]), even though the literature on preferential and non-equilibrium flows has expanded enormously since then. The review of Jarvis (2007) is better in this respect, but it is important that some of the earlier contributions should be properly recognized. There are undoubtedly many other observations of preferential and non-equilibrium flows of water in soils that did not get published in this period. Luxmoore et al. (1981), for example, discuss the problems involved deriving unsaturated hydraulic conductivities from field observations of capillary potential and water content profiles over time. Cases where infiltration resulted in wetting at depth while the gradient of potential remained upward (inferring a negative conductivity value) were common. In that particular case, this led to some later work on preferential flows (e.g., Watson and Luxmoore, 1986); in many other cases, such values were simply excluded as “outliers” or anomalies. Such was the power of the B-R paradigm.

66More Evidence for Preferential Flows As noted above, the recognition of preferential water flow through soil goes back a long way. Many of the early references to such flows were qualitative or conceptual in nature. The American hydrologist Robert Elmer Horton (1875–1945) was aware of both vertical preferential flows during infiltration, including the potential impacts of entrapped air (see Fig. 1, taken from Beven, 2004a) and downslope preferential flow in soils with “sun cracks” that he called “concealed surface runoff” (Horton, 1942). He also had an interesting interpretation of his empirical infiltration equation, which has a functional form that produces an exponential decline from an initial rate to a final constant capacity. This is similar in shape to the analytical infiltration equations derived from the Darcy–Richards equation under different assumptions about the soil moisture characteristics from Green and Ampt (1911) to Philip (1957) and others. Horton, however, suggested that the exponential form was due not to a soil profile control of the wetting front (as implied by B-R theory) but due to “extinction phenomena” at the soil surface, such as the packing of the surface by raindrop impact, the swelling of the soil at the surface closing cracks, and

VZJ | Advancing Critical Zone Science

Fig. 1. Robert Horton’s sketch for Fig. 13 of his unpublished Infiltration of Rainfall monograph. He notes: “Apparently the manner in which air escapes and water enters a natural or cultivated soil surface with numerous alternate depressions and summits is somewhat as shown in Fig. 13. Dark areas indicate water flowing down the slopes of micro-basins or accumulated in depressions. Arrows flying upward indicate escaping air and those flying downward indicate infiltration. A, B and C are earthworm holes or other soil perforations. Water is flowing down A, while air is escaping freely from B and C, the latter forming the only outlet for air between two depressions, one of which is overflowing into the other.” Original drawing in pencil, with erasures, held in the US National Archives, College Park, MD, reproduced in Beven (2004a).

the blocking of larger pores by fine particles mobilized by rainsplash (Horton 1933). In particular, he notes: This is the principal reason why soils free to drain are not seldom if ever fully saturated during rain, however intense or prolonged. Another reason is the necessity for escape of air as fast as the water enters the soil. This reduces the pore space available for water within the soil (Horton, 1933). At much the same time, Charles Hursh (1895–1988), working on the forested high-infiltration capacity catchments at Coweeta in North Carolina, noted that, ...in considering flow through upper soil horizons, the formulas of soil mechanics do not generally apply. Here porosity is not a factor of individual soil particle size but rather of structure determined by soil aggregates which form a three-dimensional lattice pattern. This structure is permeated throughout by biological channels which in themselves also function as hydraulic pathways. A single dead-root channel, worm-hole or insect burrow may govern both the draining of water and escape of air through a considerable block of soil (Hursh, 1944). Such factors are, of course, much more difficult to treat theoretically. There were no methods available for adequately characterizing the soil structure (and even now we cannot do so at other p. 3 of 17

than laboratory core scales), the changes that take place at the soil surface during infiltration, or the physical, biotic, and land management processes that might operate to alter infiltration capacity after rainfall events. Soil structural voids are often recorded in soil surveys in qualitative ways, but the relationship between voids and water fluxes can be complex. It was much easier to theorize and quantify infiltration rates based on the B-R theory (and, indeed, it still is, hence the use of dual-permeability models as a way of representing preferential flows within an equilibrium gradient framework). And yet, some of the most persuasive evidence that nonequilibrium flows might be important comes from tracer evidence. One of the first studies to demonstrate this was that of Reynolds (1966). He demonstrated, by detecting sorbed pyranine using ultraviolet light, lateral movements of water in the organic layer and deeper penetration of infiltrating water close to tree trunks. Tracers and destructive sampling have been used to demonstrate preferential flows at both laboratory soil core (e.g., Hornberger et al., 1991; Kissel et al., 1973; Omoti and Wild, 1979; Seyfried and Rao, 1987; and Fig. 2, taken from Beven et al., 1993) and field plot scales (e.g., Fig. 3, taken from Flury et al. [1994], Quisenberry and Phillips [1976], and the 1979 experiment reported in Beven and Germann [2013]). Other terms were also used in these tracer studies, such as by-passing flows (e.g., Smettem and Trudgill, 1983) or short-circuiting (e.g., Bouma and Dekker, 1978) and channeling flow (e.g., Beven and Germann, 1982). Other evidence came from work on tracer breakthrough curve experiments on (mostly saturated) undisturbed soil cores (e.g., Anderson and Bouma, 1977a, 1977b; Bouma, 1981a; Bouma and Wösten, 1979; Jury, 1982; Kanchanasut et al., 1978; Rao et al., 1980; Scotter, 1978; Smettem, 1984; White et al., 1984) and in lysimeters and field experiments (e.g., Blake et al., 1973; Smettem et al., 1983; Trudgill et al., 1983; Tyler and Thomas, 1977). Such studies were driven by a concern with understanding the transport of nutrients, biocides, and pathogens in the field. The later Lancaster work on transport in undisturbed cores using multiple tracers (e.g., Abdulkabir et al., 1996; Henderson et al., 1996; and Fig. 2) was performed in the context of the mixing of subsurface sources of radionuclides in the near surface soil. Many such studies showed the early breakthrough of tracer, far faster than would be expected by the accepted theory of transport in porous media based on the advection–dispersion equation (ADE). The ADE predicts a symmetrical Gaussian distribution of solute concentrations in space in the direction of travel, which is slightly skewed when concentration measurements are made at a single depth as the solute cloud passes, reflecting the effects of greater dispersion at later times. Observed breakthrough curves in undisturbed cores are generally highly skewed toward the origin with much longer tails and often with significant amounts of tracer being retained even after many pore volumes of water are added after the tracer pulse. The interpretation of the greater skew and longer tails was that the initial early breakthrough was the result of transport in larger-pore pathways that was effectively bypassing much of the soil matrix. The transport could also depend on the nature of the

VZJ | Advancing Critical Zone Science

macropores (e.g., Bouma et al., 1977), and the mixing of multiple sources could be even more complex (e.g., Henderson et al., 1996). Some extreme cases of preferential flow were reported at this time. Rahe et al. (1978), for example, suggested that Escherichia coli could move downslope through a forest soil away from a septic tank at rates of 15 m h–1, suggesting connected flow pathways over significant length scales.

66Infiltration and Soil Air Pressure A quite separate strand of research concerned with the effects of larger pores in the soil on water flows stemmed from concerns regarding the effects of internal soil air pressure on infiltration and consequently on overland flow. Figure 1 shows that as early as the 1940s Robert Horton was aware of air pressure effects on infiltration and the role of larger voids in allowing air to escape back to the surface. He performed some detailed experimental work on repacked soil cores under ponded infiltration to examine this in more detail (Beven, 2004a) but recognized that the effects might not be as great under field conditions with lower rainfall intensities. Later, the role of air pressure in infiltration became a concern of agricultural engineers concerned with land management measures to mitigate overland flow. Dixon and Linden (1972) and Linden and Dixon (1973) reported that an internal air pressure of about 2.0 kPa (20 mbar) decreased infiltration rates by a factor of 3, whereas Linden and Dixon (1976) found even greater reductions with air pressure excess of only 0.5 kPa (5 mbar). Dixon and Peterson (1971) suggested that air would escape most easily though larger channels in the soil, and agricultural equipment was designed with a view to enhancing the potential for air to escape during infiltration. The effects of air pressure on the nature of soil water flows are still not very well understood for the case of field soils.

66Quantitative Studies of Preferential

and Nonequilibrium Flows

An early study of the role of larger pores on f low was performed by Burger (1922) and Burger (1940) (summarized in Germann and Beven [1981]) on over 70 different Swiss soil horizons, some of which had up to 10 replicate measurements, although only averages were reported for each horizon. The study involved the measurement of permeability using a ring permeameter together with an estimate of the freely drained porosity derived from allowing slowly saturated samples to drain for 24 h to reach what Burger called the “air capacity” of the soil. Analysis of the data in Germann and Beven (1981) reveals a power law relationship between flux and drained porosity with a power of 2.419. That is somewhat greater than the theoretical value that might be expected for laminar flow through systems of cylindrical tubes (a power of 2 on macroporosity) and less than that for film flow in planar cracks (a power of 3). A similar analysis of the data from Ehlers (1975) on flow into individual wormholes provides a p. 4 of 17

Fig. 2. Core sections showing dye staining, Lancaster University soil core. Distances are from the base of the core. Black indicates recognizable macropores with dye staining; hatched areas indicate dye staining in areas without obvious macropores (from Beven et al., 1993).

VZJ | Advancing Critical Zone Science

p. 5 of 17

Fig. 3. Variability of the vertical flow pattern between two profiles within the same plot after a sprinkling application of 40 mm of colored water with wet initial conditions. The solid bar at Obermumpf indicates the maximum depth of excavation (from Flury et al., 1994).

power of 4.138 on pore radius, slightly greater than the theoretical value for laminar flow in saturated cylindrical pores of 4 (Childs, 1969). Ehlers recognizes that the resulting volumes are affected by flow rates, storage volume of the channels, and percolation away from the channels into the matrix. There is one point on the plot that is a distinct outlier (at a diameter of 6 mm but with a very low flow rate). Excavation at this point after the experiment revealed that the earthworm was still in its burrow (Germann and Beven, 1981). More recently, Germann (2014, and citations therein) has argued that the exponent can be fixed at 3 for film flows based on viscous flow theory and Stokes Law, whereas Jarvis et al. (2017) suggest a range from 1 to 3 in fitting field data. Gaiser (1952) also suggested that the high density of root channels in a forest soil under deciduous trees in Ohio would have an important impact on water flows. Hoover (1962) noted that abundant plant and animal channels in surface soil layers increases their lateral permeability so that water movement may take place downslope before the underlying soils are completely wet. Green

VZJ | Advancing Critical Zone Science

and Askew (1965) studied the macropore networks produced by ants down to depths of 1 m; whereas Williams and Allman (1969) found cylindrical macropores to depths of at least 10 m in a loess soil, they were unsure what had produced them. Ehlers (1975) found that the macropores produced by earthworms increased in frequency down to a depth of 0.6 m in both tilled and untilled soils at his site, although frequencies were generally less in the tilled soil. Aubertin (1971) studied the role of root channels in downslope flow through Piedmont soils and found that they could make up to 35% of the soil volume. However, most studies by soil hydrologists remained firmly within the B-R equilibrium framework. The challenge at that time was not to question the theoretical concepts but to try and characterize the soil structure in quantitative ways (e.g., Bullock and Murphy, 1980) so that it could then be related to the hydraulic conductivity for both saturated and unsaturated conditions. The first theories of unsaturated hydraulic conductivity were “bundled capillary tube” models and depended p. 6 of 17

on knowledge of soil pore size distributions (e.g., Childs and Collis‐George, 1950; Millington and Quirk, 1961; Mualem, 1976; Wyllie and Gardner, 1958). Thus, attempts were made to characterize pore size distributions directly from microscopic thin sections rather than indirectly from more classical suction plate methods. In doing so, sorbing colored tracers were also used to try and distinguish active from inactive pores (see Fig. 4). Pore sizes could be quantified using techniques such as the Quantimet, and Bouma et al. (1977) produced a classification of pores based on size and shape based on this type of microscopic analysis (Fig. 4) (Bouma and Dekker, 1978; Bouma et al., 1979; Bullock and Thomasson, 1979; Murphy et al., 1977; Walker and Trudgill, 1983). What this revealed was that some rather large well-connected pores (i.e., macropores) could be actively involved in water movement through the soil, with pore sizes such that capillary potential effects could be considered negligible (Fig. 2 and 4) This led to some questioning of the B-R concept of local equilibration of pressures and gradients, including discussions of just what should be considered a macropore initiated by Bob Luxmoore of Oak Ridge Laboratory (Beven, 1981; Bouma, 1981b; Luxmoore, 1981; Skopp, 1981). It also led to some of the first models of water flow through macroporous soils (see below). Omoti and Wild (1979), however, showed that channeling of water flows and bypassing parts of the soil matrix could take place in pores smaller than what would be considered as macropores. This period was also when studies of hillslope runoff processes using throughflow troughs were becoming more widespread. Whipkey (1965a) installed collectors for a number of different depths in the soil down to a depth of 1.5 m at a site in Ohio. He noted that the soil profile was “well-permeated with roots, root channels, small animal and earthworm burrows, and structural cracks” Whipkey (1965b). He looked at subsurface runoff as a nonDarcy flow, noting the importance of the antecedent conditions in the generation of runoff. This was one of the first studies to support the earlier work of Hursh in suggesting that overland flow could, in such circumstances, provide only a minimal contribution to the stream hydrograph. Aubertin (1971) later dissected the lower part of Whipkey’s plot to investigate the network of root channels and showed that water would move through soil macropores without the matrix being saturated. He suggested that, In many, if not most, forested areas, the soil mass is honeycombed with a complex network of intricately connected old root channels, animal passages and other microvoids. Strong arguments can be advanced to support the contention that, under these conditions, the complex network is always open to the atmosphere at numerous points and that truly dead-end isolated channels, or macrovoids, are rare and of little consequence. Beasley (1976), at a slope plot in northern Mississippi, also concluded that the best explanation of the fast response of the plot is that

VZJ | Advancing Critical Zone Science

Fig. 4. Examples of thin sections of soil showing dyed cylindrical, planar, and vugh macropores (dark color) where infiltrated water has passed as well as many undyed macropores (from Bouma et al., 1977).

“…water travels through macrochannels formed by decayed roots. During several storms that occurred before the trenches were filled with gravel I observed water gushing from such openings... . Depressions formed by uprooted trees or decayed stumps provide a place for water to concentrate. Decayed roots spreading outward from the depressions provide natural pathways for water to flow freely though the soil toward the stream channels. Stem flow accumulating at the bases of trees is another possible source of significant quantities of subsurface flow.” De Vries and Chow (1978) came to similar conclusions for a forest site in British Columbia but also showed how the nature of the partitioning between flow in the root channels and soil matrix could be modified by removing the organic forest floor material. This led to an increase in matrix flow, which they suggested was a result of the larger channels being filled at the surface. Pilgrim et al. (1978) showed a high degree of variability in subsurface runoff p. 7 of 17

in a plot-tracing study near Stanford, CA, and, with some element of surprise, how fine sediments in the narrow range of 4 to 8 mm could move through subsurface pathways. They inferred, from atomic testing fallout 137Cs measurements, that the sediment particles had been mobilized in near surface soil before being transported to their collection troughs. Other early throughflow trough experiments include those of Dunne and Black (1970), Knapp (1970), Ragan (1968), and Weyman (1970, 1973). Atkinson (1978) provides a summary of throughflow trough techniques, including how the installation can affect the flow pathways depending on saturation. These studies mainly interpret flow rates in terms of the depths of upslope soil saturation. Only Weyman (1970) makes any reference to preferential flows. He notes that the rates of flow measured at the throughflow troughs could not support the total inflow to the stream reach under study and that the bulk of the input came from small seeps: The supply area for these seeps is indeterminate but in terms of bank length is certainly not more than 1 m because seep spacing is often less than that distance. The seeps also show the same variation through time as the soil plot outputs and control section hydrograph. Weyman also notes that the main flood peak for the small East Twin catchment in the Mendips UK is produced in the podzols of the headwater part of the rather than the brown earth side slopes of the control section where the throughflow troughs were sited as a result of channel extension and “an extensive network of natural soil pipes (5-cm diameter) at the base of the peat.” The element of surprise has often been a feature of hillslope plot studies. Aubertin (1971) for example noted that free water can move rapidly substantial distances through relatively dry soil was demonstrated by an observation of seepage occurring from a pit face some 30 feet obliquely downslope from the pit under study. The seepage commenced between 30 and 45 min after starting to wet the forest floor above the observation pit. Beven (2002) records a USDA plot sprinkling experiment on a mine reclamation site at Steamboat Springs, CO, performed in 1981. The installation was set up to observe surface runoff from the sprinkled plots, but narrow percolines of subsurface runoff appeared both beneath the surface flow collector and in two distinct lines to either side appearing at a stream channel several meters downslope. In the plot experiments of Hornberger et al. (1991), excavation of the sides of the plot revealed a cross-slope pipe feature. They do not mention this in their paper; they only note that a separate collector (the “east inside tube”) was installed to collect runoff from this feature. There are undoubtedly many other examples of such complexity during this period that are not necessarily recorded in the literature.

VZJ | Advancing Critical Zone Science

66Early Work

on Nonequilibrium Fingering

Some of the earliest work on non-equilibrium and preferential flows in soils was concerned with the instability of wetting fronts to form fingers of wetting at greater depths (Glass et al., 1988; Hill and Parlange, 1972; Hillel, 1987). Irregular wetting had been observed in laboratory experiments with soils since at least the 1960s (e.g., Miller and Gardner, 1962; Smith, 1967), but it was not until the 1970s that it was considered in terms of instabilities within the B-R framework. Analysis of the conditions for fingering built on the work of the physicist G.I. Taylor (Taylor, 1950) and were first developed in the context of the displacement of oil in rock reservoirs (e.g., Chuoke et al., 1959). During the 1970s, some of the best soil physicists around turned their attention to this problem, including John Philip (Philip, 1975a, 1975b; White et al., 1978), Jean-Yves Parlange (Hill and Parlange, 1972; Parlange and Hill, 1976), and Peter Raats (Raats, 1973), including both experimental (e.g., Diment and Watson, 1985; Starr et al., 1978, 1986) and later analytical work (Diment and Watson, 1983; Diment et al., 1982; Glass et al., 1989). The mathematical challenges of this type of analysis of non-equilibrium flows have resulted in continuing work in the area, including the effects of soil layering and hydrophobicity on fingering. However, the value is surely limited to conditions where the underlying B-R assumptions are valid, which might not be the case, for example, where viscosity dominates capillarity (see Germann, 2014).

66Early Work on Models

of Macropore Flows

There is also a history to the modeling of preferential flows and transport. In the saturated domain, this dates back at least to Muskat (1946), who analyzed the effects of fractures on transport in Darcian groundwater flow. In partially saturated soils, it could be argued that the first attempt to study a form of preferential flow is that of Philip (1968), who looked at the effect on infiltration rates of the interaction of a B-R flow domain and soil aggregates using analytical approximations. It was not until the late 1970s, however, that a surge in trying to quantify the effects of macropores on preferential flows occurred. These approaches were generally based on a dual-porosity approach, differentiating between the matrix and macropore domains, with a particular concern on representing transport processes. Thus, Addiscott et al. (1978), working with data from the same experimental site of Lawes et al. (1882) a century earlier, tried to predict the transport of chloride using a rather conceptual discrete-layer, dual-porosity model. Scotter (1978) was also concerned with transport but used laminar flow theory to predict expected velocities in the pore size distribution of a soil. Edwards et al. (1979) produced a model for infiltration away from a single cylindrical vertical macropore, based on how quickly a macropore of limited depth would fill but predicting infiltration into the matrix using B-R theory. They looked at the sensitivity to macropore size and depth of penetration and some simple upscaling

p. 8 of 17

to distributions of such macropores over an area, but their model was not tested against any observational data (see also the later analytical work of Beven and Clarke [1986]). Another approach to upscaling was that of Hoogmoed and Bouma (1980), who modeled the effects of macropores on surface infiltration. In their model, infiltration into the matrix was predicted using B-R theory, with initiation of macropore flow once a certain threshold of surface water storage had been reached. Infiltration away from the macropores was also predicted using B-R theory applied across a defined contact area or wall length. A more explicit account of flow rates within the macropore system was included in the model of Beven and Germann (1981). Starting with the theory of laminar flow in planar cracks and cylindrical channels, they suggested that a power law relationship between flux rate and macropore storage could be derived (see also their analysis of the data sets of Burger and Ehlers in Germann and Beven [1981]). This leads naturally to a simple kinematic wave model for flow in the macropores in which the coefficients of the power law can be calibrated to represent any distribution of preferential flow pathways up to the constraint of the fully saturated case. Their model also generalized losses to the matrix, making this a function of filled storage in the macropores (which varies in depth and time) and thereby avoiding the need to specify some gradient of potential in the matrix. They extended this work to model distributions of macropores (Beven and Germann, 1985; Germann and Beven, 1986). Later developments of this approach (particularly the MACRO model of Jarvis et al. [1991, 1994, 1997], Larsson and Jarvis [1999], and Larsson et al. [1999]) have combined the kinematic approach with a B-R model of flows in the matrix. Modeling preferential transport through macropores was mostly performed using a non-equilibrium modification of the ADE that allowed for exchange between mobile and immobile zones (e.g., Skopp et al., 1981). Calibration of the mean pore water velocity, dispersion, and exchange parameters would often allow a good fit to the data (e.g., using the nonlinear least squares CXTFIT program of Parker and van Genuchten [1984]). An alternative approach was to formulate the transport directly as a linear transfer function (e.g., Jury, 1982; Jury et al., 1982; White et al., 1984). Defining the transfer function in terms of volume of water rather than time allowed a simple extrapolation to other flow rates, at least for the saturated case. A wider range of approaches to modeling preferential flows have been reviewed more recently by Allaire et al. (2009), Beven and Germann (2013), Gerke (2006), Jarvis et al. (2016), and Šimůnek et al. (2003). There is a related line of research on preferential flow through fractured rocks, which has been reviewed by Bear et al. (1993), Berkowitz (2002), and Sahimi (1995).

66Early Work on Pipes and Piping The difference between soil macropores and soil pipes can be defined in terms of the way flow pathways are formed. In the

VZJ | Advancing Critical Zone Science

former, the macropores are the result of processes such as cracking or biological activity (e.g., roots, worms, burrowing animals). They may be modified to some extent by water flows but are not formed by water flows. In the case of pipes, however, networks are formed and shaped by water flows, even if the initiation of a pipe might be due to some other agency. Work on water flows through natural pipes and pipe networks has been predominantly associated with two types of processes: those associated with piping in dispersive soils and those where pipes have developed in peats and the organic horizons of peaty podzols in humid temperate uplands. Early work on the former includes that of Terzaghi (1922, 1943), Fletcher et al. (1954), and Zasłavsky and Kassiff (1965). The process was put into a wider hydrological context by Zaslavsky and Sinai (1981) but has primarily been a concern from the point of view of soil mechanics and slope stability (e.g., Hencher, 2010). Work on upland peat pipe networks started in the 1970s in mid-Wales with the work of Knapp (1970), Gilman (1971), Newson (1976), and Gilman and Newson (1980) in the Wye catchment, and Jones (1971, 1978, 1981) in the Maesnant catchment just over the divide formed by the summit of Plynlimon. It is thought that pipes in this region are of two types: first-order bedrock channels that have been overgrown by peat forming tunnels up to 1 m in diameter and networks of much smaller pipes in the peat, or near-surface organic horizons that result from the preferential development of desiccation cracks in the (rare) dry summers in Wales. Pipe networks of this type were explored by Newson (1976) (Fig. 5, taken from that paper), McCaig (1983) (see also the later work of Holden [2004, 2005]), and Gilman and Newson (1980). Similar pipes were found in the headwater podzols of the East Twin catchment in the Mendips, England, by Weyman (1970), who also reported concentrated inputs along the stream channel in the brown earth soils (Cambisols/Inceptisols) of the lower catchment, analogous to what Bunting (1961) had called “percolines.” Such pipes would be expected to have an effect both on hydrograph response times and transit time distributions of water in a catchment, with the latter also affecting the stream hydrochemical response. The latter was studied with respect to acidification of stream waters by Jones (2004), although an interesting result from Sklash et al. (1996), based on environmental isotope measurements, suggested that the outflows from an ephemeral pipe in the peat at the Plynlimon site, with a time to peak of the order of 15 min, was dominated by pre-event stored water. This was a particularly interesting result because it suggested that such fast responses could be generated without having continuous preferential flow pathways from the surface to the pipe. The question of continuity of pipe pathways and hillslope hydrological connectivity more generally has been the subject of much more research since (e.g., Chappell, 2010; Holden, 2004; Jencso et al., 2009; McGuire and McDonnell, 2010; Smart et al., 2013; Wienhöfer and Zehe, 2014). There have been few attempts to model the hydrological response of pipe networks, in part because of the difficulty of p. 9 of 17

Fig. 5. Mapped soil pipe networks showing complex patterns of connections and reconnections in the Cerrig-y-wyn catchment (Upper Wye, Plynlimon, Wales). Contours in meters (from Newson, 1976).

knowing the form and structure of the networks (Fig. 5) (Newson, 1976; Jones and Crane, 1982). Exceptions are the attempts of Gilman and Newson (1980) in the upper Wye catchment, Wilson and Smart (1984) in the Brecon Beacons, Jones and Connelly (2002) at Maesnant, and the more hypothetical approach of Weiler and McDonnell (2007). A recent review of pipes and soil hydrology is given by Jones (2010), who also reviews the extensive, somewhat later work on pipe systems in Japan (e.g., Kitahara and Nakai, 1992; Kitahara et al., 1988; Noguchi et al., 1999; Sidle et al., 1995, 2001; Uchida et al., 1999 and studies elsewhere).

66Preferential Flow and Flood Runoff

Generation

A continuing question in hydrology is how preferential flows might influence runoff generation. This has been given renewed impetus by the current interest in “natural flood management,”

VZJ | Advancing Critical Zone Science

which involves tree planting and other soil management techniques to encourage infiltration and to “slow the flow” from headwater hillslopes (e.g., Dadson et al., 2017; Lane, 2017). There is a growing body of evidence that tree planting and stock exclusion can promote infiltration because of longer retention times and the development of better connected structural voids (e.g., Marshall et al., 2014). In this respect there is a link back to the much earlier studies of Horton (Fig. 1) and the channel concepts of Dixon and Peterson (1971). The latter expressed the importance of land management on the structural flow pathways by considering the flow of infiltrating water and the escape of air with and without connectivity of the structural flow pathways in the soil. This will have significance in terms of the effective infiltration capacity of the soil as affected by the blocking of large pores and the build-up or escape of air pressure (see also Dixon and Linden [1972] and Linden and Dixon [1976]). The concentration on infiltration rates in these cases was a reflection of the long dominance of the infiltration excess or the Hortonian concept of runoff generation as the source of flood hydrographs; a dominance encouraged by the simplicity with which flood responses could be predicted in the days before digital computers. However, there was also always an undercurrent of views suggesting an alternative dominance of subsurface processes in stream runoff generation (e.g., Hewlett, 1961, 1974; Hewlett and Hibbert, 1967; Hursh and Brater, 1941; Weyman, 1970, 1973) and in controlling saturation excess overland flow (e.g., Cappus, 1960; Dunne and Black, 1970; Dunne et al., 1975). Subsurface controls on runoff received greater recognition once tracer data started to show that in many catchments storm hydrographs were dominated by “old” or “pre-event” waters displaced from storage by rainfall and snowmelt inputs (e.g., Pinder and Jones, 1969; Sklash and Farvolden, 1979; Sklash et al., 1976). This was called “translatory flow” by Hewlett and Hibbert (1967), although concerns about displacement and rapid rises of groundwater tables go back much earlier (see the discussion in Beven [2004b]). The example of rapid runoff responses in pipes in peat of Sklash et al. (1996) mentioned earlier is a good example. Consequently, subsurface and preferential flow processes are now widely accepted in conceptualizations of hillslope storm responses (e.g., McDonnell, 2003), but there remain significant issues to resolve concerning the role of preferential flow pathways in rapid subsurface responses and displacement or translatory flow processes. The connectivity of preferential flow pathways is critical in generating fast subsurface responses in terms of both the source of water for different pathways and the spatial extent of individual pathways. We can perhaps distinguish fingering (including Stokes flow in laminar viscous films) from discrete macropore flows. In both cases, part of the water storage in the matrix can be bypassed after infiltration at the soil surface. In the case of fingering, we can be sure that part, and perhaps a major part, of the water involved in the preferential flow will be mobilized from storage even if the mechanisms involved may not be too clear (note that there is an p. 10 of 17

implication then that not all preferential flows might be revealed by the dye tracing experiments discussed earlier because mobilized pre-event water will not necessary mix with the added dyed water). An exception are the documented cases of fingering in very dry soils, where there is little storage to be mobilized and where fingering might be encouraged by hydrophobicity effects. In the case of macropore flows, where these are connected to a surface supply of water, then they might rapidly transfer event water to depth (as revealed, for example, in the dyed macropores shown in Fig. 2–4). Continued flow in macropores might be encouraged by limited connectivity to the matrix (e.g., because of cutans) and hydrophobic organic coatings on some macropore boundaries. However, the flow might also be limited in the depths to which individual macropores penetrate. If this is the case, then water collecting at the end of a macropore can produce a positive pressure to induce infiltration into the surrounding matrix and possible a source of water for flow in a nearby macropore. Some of that water might then be displaced from pre-event storage. However, many macropores might not be connected to a supply and might not then be active in flow processes except when the soil becomes saturated, as also illustrated in Fig. 2 to 4. So how does this then play out in terms of flood runoff generation and natural flood management? We can infer from past research that increased infiltration rates as the result of tree planting or improved agricultural soil management will tend to also increase the potential for preferential flows in the upper soil. Where pipe networks exist, either natural or through artificial drainage, then the response might very much depend on the antecedent conditions prior to an event and the state of hydrophobicity of the soil. Under dry antecedent conditions, preferential flows might be exacerbated by hydrophobicity, or in the case of nonhydrophobic soil the infiltration will be more evenly distributed through the depth of the soil. There will be some potential for rapid transmission of input or displaced water to depth and to shallow water tables, but celerities for the subsurface response will be slower with a greater soil moisture deficit (e.g., Beven, 1989; McDonnell and Beven, 2014). Under wet antecedent conditions, it is more likely that infiltrating water, or resulting displaced water, will penetrate to depth, and celerities for subsurface responses might be very fast with small water deficits, including for water entering into extensive pipe systems. Evidence suggests that not all pipe systems have response times that are faster than the characteristic peak timing in a catchment (e.g., Chappell, 2010). The connectivity of saturated areas with the pipe and stream networks might lead to significant spatial variability in the hillslope responses (e.g., Jencso et al., 2009). Thus, even this qualitative conceptualization reveals significant complexity leading to time-variable nonlinear responses that will be difficult to quantify. In addition, under very wet antecedent conditions and in areas of poorly drained soils, natural flood management measures might have little effect because the available storage for reducing overland flow on the hillslopes will be minimal. Thus, the impact on reducing peaks in wet antecedent conditions might be small.

VZJ | Advancing Critical Zone Science

66Progress and Problems after 1984 The year 1984 was a rather arbitrary cut-off date for this review: a convenient 120 yr after the Schumacher paper of 1864 and just before the rapid expansion of the literature on different types of preferential and non-equilibrium flows. A turning point in a more widespread appreciation for some of the issues involved was, perhaps, the meeting on preferential flows organized by Gish and Shirmohammadi (1991) in Detroit as part of the American Society of Agricultural Engineers meeting. There some 400 people attended the talks, at least in part driven by the increasing concentrations of nutrients and biocides being found in groundwater samples, when neither the chemistry nor the Darcian flow analysis would suggest that this should be the case. There have certainly been advances in observational techniques in terms of tracing water flow pathways at laboratory, field, and catchment scales; in the visualization of pore structures using X-ray tomography; and in alternative modeling strategies. However, as Beven and Germann (2013) note, one of the surprises of the last 30 yr has been the survival of the B-R theory in models based on “soil physics.” Certainly, there have been dualcontinuum, dual-porosity, or dual-permeability modifications to allow for some preferential flows (e.g., Beven and Germann, 2013; Jarvis et al., 2016), but there has been little recognition of the fundamental theoretical problem of using effective values of the B-R parameters at scales of interest in heterogeneous and structured soils. The theory itself suggests that this will not work; it has also been demonstrated numerically, as long ago as Binley et al. (1989). The problem is surely exacerbated when parameters are derived from pedotransfer functions that have been based on measurements on small soil samples or when macroporosity and preferential flows are important (but see Moeys et al. [2012] for the use of pedotransfer functions with the MACRO model). The few studies that have suggested that alternative approaches (the Stokes flow of Germann [2014] and the particle tracking of Davies et al. [2011, 2013]) can provide integrated ways of incorporating preferential flows at larger scales but at the expense of neglecting capillarity. This avoids any need to assume local equilibration of potentials and potential gradients in heterogeneous structured soils but results in models that will be less credible under drier conditions when capillarity becomes important. The particlebased SAMP model of Ewen (1996a, 1996b) and the Lagrangian particle tracking model of Zehe and Jackisch (2016) are attempts to integrate capillarity with velocity distributions. What is lacking in all these studies is any rigorous testing of the available models as hypotheses about how the soil water flow system functions under field conditions. Potential, but rather general, hypotheses to be tested are discussed by Beven (2010) in terms of both preferential water flows and travel time distributions. He points out that statistical hypothesis testing is not necessarily appropriate when both models and observations are subject to epistemic and commensurability errors and shows that not all the hypotheses that might be posed are testable. He suggests a “limits p. 11 of 17

of acceptability” approach, where the limits are set independently of any model run, as an alternative to a statistical approach. It is surely the case that the available models of preferential flows could be tested as hypotheses more explicitly in this way even if decisions about what type of observations should be used in model evaluation require significant further research. However, for the science to advance it is necessary to require more rigorous testing, and potential falsification, of models (Beven, 2018). An exception to this limited hypothesis testing is the Stokes flow approach of Germann (2014). This developed from the original assumptions about steady laminar film flow in unsaturated macropores in Beven and Germann (1981) that led to a more general kinematic description of viscous flow under gravity (e.g., Germann, 1985). In this viscous flow regime, flux rates can be represented in terms of an effective equivalent film thickness of laminar flow that leads to specific predictions about the rate of propagation of wetting and drying fronts. In a series of papers (e.g., Germann and al Hagrey, 2008; Germann and Hensel, 2006; Germann and Karlen, 2016; Germann and Prasuhn, 2018), these predictions have been tested against observations of wetting and drying fronts and shown to provide acceptable representations of preferential flow without requiring any knowledge of pore structures, relative conductivities, or macroporosity. Certainly, once drying fronts have passed, capillarity and B-R theory might dominate, and, given a sufficient source of water, nonlaminar flows in larger pores might be important in flow and transport, but the (essentially scale free) viscous flow approach would appear to be worth pursuing further as a description of preferential flows. For the case of preferential flows, adequate hypothesis testing will require better estimates of patterns of water storage, coupled to tracer information about travel times (Davies et al. [2011, 2013] provide examples of qualitative hypothesis testing against flow and tracer data). The continued use of B-R models, however, does not suggest that the community is open to this type of testing. In that case, if a model based on B-R theory satisfactorily reproduces field scale observations it will be in spite of, rather than because of, the theoretical basis of the model, however good is the numerical implementation. Should we really be satisfied with that? Should functionality dominate the theoretical (non-)acceptability of equilibrium assumptions at field or model grid scales in a heterogeneous soil? Of course, some important issues remain to be resolved for both model formulation and testing: (i) how to integrate viscosity and capillarity dominated flows, (ii) how to assess and represent the effects of air pressure on the initiation and development of preferential flows, (iii) how to go beyond the viscous flow description of preferential flow into nonlaminar flows in larger pores when the secondary structure is generally unknowable at any useful scales, (iv) how to allow for commensurability and sampling errors in model evaluation at field scales, (v) and how to upscale from core and profile experiments to larger hillslope scales and surface and subsurface runoff responses. It is to be hoped that studies that address these issues will appear in the future and finally close this long period of denial and self-delusion in the application of soil physics.

VZJ | Advancing Critical Zone Science

Except that, as two referees on this paper have pointed out, there is no denial now. Soil physicists and hydrologists, especially the early career researchers, do indeed recognize that preferential and non-equilibrium flows are important for both flow and transport. The need for research on the topic has also been recognized as the first key challenge in Vereecken et al. (2016). We do indeed have in hand a number of (inconsistent) modeling concepts (the dualcontinuum, dual-porosity, dual-permeability, Stoke’s flow, and particle tracking concepts mentioned above) to make predictions that take some account of preferential flows, and even where we have little knowledge of actual subsurface structures we can use fineresolution modeling with assumptions about heterogeneities and “virtual soils” to learn about problems of scaling up from the pore to scales of interest in real applications (e.g., Schlüter et al., 2012). And yet there are still many applications of both profile and larger scale hillslope and catchment models that are based directly on B-R concepts, even if dual-continuum and dualpermeability options might be available in the packages used. The B-R paradigm is still fundamental to the teaching of soil physics and soil hydrology, and it remains the dominant paradigm for subsurface flows in hydrological texts, even if preferential flows are also mentioned. In this sense there is still denial going on (at least implicitly from a lack of any deeper thinking). The major questions remain: Why are we still using continuum partial differential equation approaches to represent processes that are clearly not continuous at scales of interest, and why are we still using physics that is based on the wrong experiment and that evidently fails in the face of heterogeneity of unsaturated soil properties? Direct numerical solution of the Navier–Stokes equations or finer and finer solutions of the B-R equations might be used for virtual experiments but cannot be a solution for real applications. I would suggest that a new paradigm to modeling soil water flows and transport is necessary. I cannot suggest I am happy with the alternatives that I have tried myself, although clearly the kinematic wave analogy still has some resonance (see Jarvis et al. [2017]), and the Multiple Interacting Pathways particle tracking model might still hold some promise at larger scales. What is clear is that there is much for the next generation to think deeply about.

Acknowledgments

This history depends on past reviews, notably Chorley (1978), Thomas and Phillips (1979), Bouma (1981a), Beven and Germann (1982, 2013), White (1985), Bonell (1993), Gerke (2006), Jarvis (2007), Allaire et al. (2009), Köhne et al. (2009), Chappell (2010), Hencher (2010), Jones (2010), Liu and Lin (2015), Vereecken et al. (2016), and Jarvis et al. (2016). I have long discussed the issues of macropore and preferential flow with Peter Germann, ever since his arrival as a post doc at the Institute of Hydrology in Wallingford in 1978. His comments on a draft of this paper have helped to improve it. The preparation of this paper has been supported by the NERC Q-NFM project led by Dr. Nick Chappell of Lancaster University (Grant NE/R004722/1), who also helped with comments and the figures. The comments of two anonymous referees helped improve the paper but also seemed to reflect some continuing denial about the need for an improved soil physics.

References Abdulkabir, M.O., K.J. Beven, and A.D. Reeves. 1996. Flow separation in undisturbed soil using multiple anionic tracers (3) unsteady core scale infiltration experiments. Hydrol. Processes 10:1467–1482.

p. 12 of 17

Addiscott, T.M., D.A. Rose, and J. Bolton. 1978. Chloride leaching in the Rothamsted drain gauges: Influence of rainfall pattern and soil structure. J. Soil Sci. 29:305–314. doi:10.1111/j.1365-2389.1978.tb00778.x

Beven, K.J., D.E. Henderson, and A.D. Reeves. 1993. Dispersion parameters for undisturbed partially saturated soil. J. Hydrol. 143:19–43. doi:10.1016/0022-1694(93)90087-P

Allaire, S.E., S. Roulier, and A.J. Cessna. 2009. Quantifying preferential flow in soils: A review of different techniques. J. Hydrol. 378:179–204. doi:10.1016/j.jhydrol.2009.08.013

Binley, A.M., K.J. Beven, and J. Elgy. 1989. A physically-based model of heterogeneous hillslopes: II. Effective hydraulic conductivities. Water Resour. Res. 25:1227–1233. doi:10.1029/WR025i006p01227

Anderson, J.L., and J. Bouma. 1977a. Water movement through pedal soils: I. Saturated flow. Soil Sci. Soc. Am. J. 41:413–418. doi:10.2136/sssaj1977.03615995004100020049x

Blake, G., E. Schlichting, and U. Zimmermann. 1973. Water recharge in a soil with shrinkage cracks. Soil Sci. Soc. Am. J. 37:669–672. doi:10.2136/sssaj1973.03615995003700050014x

Anderson, J.L., and J. Bouma. 1977b. Water movement through pedal soils: II. Unsaturated flow. Soil Sci. Soc. Am. J. 41:419–423. doi:10.2136/sssaj1977.03615995004100020050x

Bonell, M. 1993. Progress in the understanding of runoff generation dynamics in forests. J. Hydrol. 150:217–275. doi:10.1016/0022-1694(93)90112-M

Atkinson, T.C. 1978. Techniques for measuring subsurface flow on hillslopes. In: M.J. Kirkby, editor, Hillslope hydrology. John Wiley & Sons, Chichester, UK. p. 73–120. Aubertin, G.M. 1971. Nature and extent of macropores in forest soils and their influence on subsurface water movement. Res. Pap. NE-192. US For. Serv., Northeast. For. Exp. Stn., Upper Darby, PA. Banse, H.T., and O.Z. Graff. 1968. Tonverlagerung in den Underboden entlang von Regenwurmröhren. Mitt. Dtsch. Bodenkd. Ges. 8:223–225. Bear, J., C.F. Tsang, and G. de Marsily, editors. 1993. Flow and contaminant transport in fractured rock. Academic Press, San Diego. doi:10.1016/B978-0-12-083980-3.50005-X Beasley, R.S. 1976. Contribution of subsurface flow from the upper slopes of forested watersheds to channel flow. Soil Sci. Soc. Am. J. 40:955– 957. doi:10.2136/sssaj1976.03615995004000060039x Berkowitz, B. 2002. Characterizing flow and transport in fractured geological media: A review. Adv. Water Resour. 25:861–884. doi:10.1016/S0309-1708(02)00042-8 Beven, K.J. 1981. Micro-, meso-, macroporosity and channeling flow phenomena in soils. Soil Sci. Soc. Am. J. 45:1245. doi:10.2136/sssaj1981.03615995004500060051x Beven, K.J. 1989. Interflow. In: H.J. Morel-Seytoux, editor, Unsaturated flow in hydrological modelling. Kluwer, Dordrecht, the Netherlands. p. 191–219. doi:10.1007/978-94-009-2352-2_7

Bouma, J. 1981a. Soil morphology and preferential flow along macropores. Agric. Water Manage. 3:235–250. doi:10.1016/0378-3774(81)90009-3 Bouma, J. 1981b. Comment on ‘Micro-, meso- and macroporosity of Soil’. Soil Sci. Soc. Am. J. 45:1244–1245. doi:10.2136/sssaj1981.03615995004500060050x Bouma, J., and L.W. Dekker. 1978. A case study on infiltration into dry clay soil: I. Morphological observations. Geoderma 20:27–40. doi:10.1016/0016-7061(78)90047-2 Bouma, J., A. Jongerius, O. Boersma, A. Jager, and D. Schoonderbeek. 1977. The function of different types of macropores during saturated flow through four swelling soil horizons. Soil Sci. Soc. Am. J. 41:945–950. doi:10.2136/sssaj1977.03615995004100050028x Bouma, J., A. Jongerius, and D. Schoonderbeek. 1979. Calculation of saturated hydraulic conductivity of some pedal clay soils using micromorphometric data. Soil Sci. Soc. Am. J. 43:261–264. doi:10.2136/sssaj1979.03615995004300020002x Bouma, J., and J.H.M. Wösten. 1979. Flow patterns during extended saturated flow in two, undisturbed swelling clay soils with different macrostructures. Soil Sci. Soc. Am. J. 43:16–22. doi:10.2136/sssaj1979.03615995004300010003x Bras, R.L. 1990. Hydrology: An introduction to hydrological science. Academic Press, New York. Brewer, R. 1960. Cutans: Their definition, recognition, and interpretation. Eur. J. Soil Sci. 11:280–292. doi:10.1111/j.1365-2389.1960.tb01085.x

Beven, K.J. 2002. Runoff generation in semi-arid areas. In: L.J. Bull and M.J. Kirkby, editors, Dryland rivers. John Wiley & Sons, Chichester, UK. p. 57–106.

Buckingham, E. 1907. Studies on the movement of soil moisture. Bureau of Soils Bull. 38. US Gov. Print. Office, Washington, DC.

Beven, K.J. 2004a. Robert Horton’s perceptual model of infiltration. Hydrol. Processes 18:3447–3460. doi:10.1002/hyp.5740

Bullock, P., and A.J. Thomasson. 1979. Rothamsted studies of soil structure 2: Measurement and characterisation of macroporosity by image analysis and comparison with data from water retention measurements. J. Soil Sci. 30:391–413. doi:10.1111/j.1365-2389.1979.tb00997.x

Beven, K.J. 2004b. Robert Horton and abrupt rises of groundwater. Hydrol. Processes 18:3687–3696. doi:10.1002/hyp.5741 Beven, K.J. 2010. Preferential flows and travel time distributions: Defining adequate hypothesis tests for hydrological process models. Hydrol. Processes 24:1537–1547. doi:10.1002/hyp.7718 Beven, K.J. 2014. Penman lecture: “Here we have a system in which liquid water is moving; let’s just get at the physics of it” (Penman 1965). Hydrol. Res. 45:727–736. doi:10.2166/nh.2014.130 Beven, K.J. 2018. On hypothesis testing in hydrology: Why falsification of models is still a really good idea. Wiley Interdiscip. Rev.: Water 5:e1278. doi:10.1002/wat2.1278 Beven, K.J., and R.T. Clarke. 1986. On the variation of infiltration into a homogeneous soil matrix containing a population of macropores. Water Resour. Res. 22:383–388. doi:10.1029/WR022i003p00383 Beven, K.J., and P.F. Germann. 1981. Water flow in soil macropores: II. A combined flow model. J. Soil Sci. 32:15–29. doi:10.1111/j.1365-2389.1981.tb01682.x Beven, K.J., and P. Germann. 1982. Macropores and water flow in soils. Water Resour. Res. 18:1311–1325. doi:10.1029/WR018i005p01311 Beven, K.J., and P.F. Germann. 1985. A distribution function model of channelling flow in soils based on kinematic wave theory. In: J. Bouma and P.A.C. Raats, editors, Proceedings of the International Symposium on Water and Solute Movement in Heavy Clay Soils, Wageningen, The Netherlands. 27–31 Aug. 1984. Int. Inst. for Land Reclam. and Improve., Wageningen, the Netherlands. p. 89–100. Beven, K.J., and P.F. Germann. 2013. Macropores and water flow in soils revisited. Water Resour. Res. 49:3071–3092. doi:10.1002/wrcr.20156

VZJ | Advancing Critical Zone Science

Bullock, P., and C.P. Murphy. 1980. Towards the quantification of soil structure. J. Microsc. 120(3):317–328. doi:10.1111/j.1365-2818.1980.tb04151.x Bunting, B.T. 1961. The role of seepage moisture in soil formation, slope development, and stream initiation. Am. J. Sci. 259:503–518. doi:10.2475/ajs.259.7.503 Burger, H. 1922. Physikalische Eigenschaften von Wald-und Freiland boden. Mitt. Schweiz. Anst. Forst. Versuchswes. 13:1–221. Burger, H. 1940. Physikalische Eigenschaften von Wald-und Freilandböden: VI. Mitteilung: Der Wald als Erholungsstätte und der Waldboden. Mitt. Schweiz. Anst. Forst. Versuchswes. 21(2):223–249. Cappus, P. 1960. Bassin expérimental d’Alrance: Etude des lois de l’écoulement: Application au calcul et à la prévision des debits. La Houille Blanche A:493–520. Chappell, N.A. 2010. Soil pipe distribution and hydrological functioning within the humid tropics: A synthesis. Hydrol. Processes 24:1567–1581. doi:10.1002/hyp.7579 Childs, E.C. 1969. An introduction to the physical bases of soil water phenomena. John Wiley & Sons, Chichester, UK. Childs, E.C., and N. Collis-George. 1950. The permeability of porous materials. Proc. R. Soc. London, Ser. A 201:392–405. doi:10.1098/rspa.1950.0068 Chorley, R.J. 1978. The hillslope hydrological cycle. In: M.J. Kirkby, editor, Hillslope hydrology. John Wiley & Sons, Chichester, UK. Chuoke, R.L., P. van Meurs, and C. van der Poel. 1959. The instability of slow, immiscible, viscous liquid-liquid displacements in permeable media. Trans. Am. Inst. Min. Metall. Pet. Eng. 216:188–194.

p. 13 of 17

Dadson, S.J., J.W. Hall, A. Murgatroyd, M. Acreman, P. Bates, K.J. Beven, et al. 2017. A restatement of the natural science evidence concerning catchment-based “natural” flood management in the United Kingdom. Proc. R. Soc., Ser. A 473:20160706. doi:10.1098/rspa.2016.0706 Darcy, H.P.G. 1856. Les fontaines publiques de la ville de Dijon. Dalmont, Paris. Davies, J., K.J. Beven, L. Nyberg, and A. Rodhe. 2011. A discrete particle representation of hillslope hydrology: Hypothesis testing in reproducing a tracer experiment at Gårdsjön, Sweden. Hydrol. Processes 25:3602–3612. doi:10.1002/hyp.8085 Davies, J., K.J. Beven, A. Rodhe, L. Nyberg, and K. Bishop. 2013. Integrated modelling of flow and residence times at the catchment scale with multiple interacting pathways. Water Resour. Res. 49:4738–4750. doi:10.1002/wrcr.20377 Davis, P.A., N.E. Olague, and M.T. Goodrich. 1992. Application of a validation strategy to Darcy’s experiment. Adv. Water Resour. 15:175– 180. doi:10.1016/0309-1708(92)90022-T De Vries, J., and T.L. Chow. 1978. Hydrologic behavior of a forested mountain soil in coastal British Columbia. Water Resour. Res. 14:935– 942. doi:10.1029/WR014i005p00935 Diment, G.A., K.K. Watson, and P.J. Blennerhassett. 1982. Stability analysis of water movement in unsaturated porous materials: 1. Theoretical considerations. Water Resour. Res. 18:1248–1254. doi:10.1029/WR018i004p01248 Diment, G.A., and K.K. Watson. 1983. Stability analysis of water movement in unsaturated porous materials 2: Numerical studies. Water Resour. Res. 19:1002–1010. doi:10.1029/WR019i004p01002 Diment, G.A., and K.K. Watson. 1985. Stability analysis of water movement in unsaturated porous materials 3: Experimental studies. Water Resour. Res. 21:979–984. doi:10.1029/WR021i007p00979 Dixon, R.M., and D.R. Linden. 1972. Soil air pressure and water infiltration under border irrigation. Soil Sci. Soc. Am. Proc. 36:948–953. doi:10.2136/sssaj1972.03615995003600060032x Dixon, D.M., and A.E. Peterson. 1971. Water infiltration control: A channel system concept. Soil Sci. Soc. Am. Proc. 35:968–973. doi:10.2136/sssaj1971.03615995003500060033x

Germann, P.F. 2014. Preferential flow: Stokes approach to infiltration and drainage. Geographica Bernensia, Bern, Switzerland Germann, P.F., and K.J. Beven. 1981. Water flow in soil macropores: III. A statistical approach. J. Soil Sci. 32:29–31. Germann, P.F., and K.J. Beven. 1986. A distribution function approach to water flow in soil macropores based on kinematic wave theory. J. Hydrol. 83:173–183. doi:10.1016/0022-1694(86)90191-5 Germann, P.F., and S.A. al Hagrey. 2008. Gravity-driven and viscosity dominated infiltration in a full-scale sand model. Vadose Zone J. 7:1160–1169. doi:10.2136/vzj2007.0172 Germann, P.F., and D. Hensel. 2006. Poiseuille flow inferred from velocities of wetting fronts in soils. Vadose Zone J. 5:867–876. doi:10.2136/vzj2005.0080 Germann, P.F., and M. Karlen. 2016. Viscous-flow approach to in situ infiltration and in vitro hydraulic conductivity determination. Vadose Zone J. 15(2). doi:10.2136/vzj2015.05.0065 Germann, P.F., and V. Prasuhn. 2018. Viscous flow approach to rapid infiltration and drainage in a weighing lysimeter. Vadose Zone J. 17:170020. doi:10.2136/vzj2017.01.0020 Gilman, K. 1971. A semi-quantitative study of the flow of natural pipes in the Nant Gerig sub-catchment. NERC Institute of Hydrology, Subsurface Section, internal report No. 50. Inst. Hydrol., Wallingford, UK. Gilman, K., and M.D. Newson. 1980. Soil pipes and pipeflow: A hydrological study in Upland Wales. Geo Books, Norwich, UK. Gish, T.J., and A. Shirmohammadi, editors. 1991. Preferential flow. Am. Soc. Agric. Eng., St Joseph, MI. Glass, R.J., T.S. Steenhuis, and J.Y. Parlange. 1988. Wetting front instability as a rapid and far-reaching hydrologic process in the vadose zone. J. Contam. Hydrol. 3:207–226. doi:10.1016/0169-7722(88)90032-0 Glass, R.J., J.-Y. Parlange, and T.S. Steenhuis. 1989. Wetting front instability: 1. Theoretical discussion and dimensional analysis. Water Resour. Res. 25:1187–1194. doi:10.1029/WR025i006p01187 Green, W.H., and C.A. Ampt. 1911. Studies on soil physics: 1. Flow of air and water through soils. J. Agric. Sci. 41:1–24.

Dunne, T., and R.D. Black. 1970. Partial area contributions to storm runoff in a small New England watershed. Water Resour. Res. 6:1296–1311. doi:10.1029/WR006i005p01296

Green, R.D., and G.P. Askew. 1965. Observations on the biological development of macropores in soils of Romney Marsh. J. Soil Sci. 6:342–344. doi:10.1111/j.1365-2389.1965.tb01446.x

Dunne, T., T.R. Moore, and C.H. Taylor. 1975. Recognition and prediction of runoff producing zones in humid regions. Hydrol. Sci. Bull. 20:305–327.

Haines, W.B. 1930. Studies in the physical properties of soil: V. The hysteresis effect in capillary properties and the modes of moisture distribution associated therewith. J. Agric. Sci. 20:97–116. doi:10.1017/S002185960008864X

Edwards, W.M., R.R. van der Ploeg, and W. Ehlers. 1979. A numerical study of the effects of non-capillary-sized pores upon infiltration. Soil Sci. Soc. Am. J. 43:851–856. doi:10.2136/sssaj1979.03615995004300050007x Ehlers, W. 1975. Observation on earthworm channels and infiltration on tilled and untilled loess soil. Soil Sci. 119:242–249. doi:10.1097/00010694-197503000-00010 Ewen, J. 1996a. ‘SAMP’ model for water and solute movement in unsaturated porous media involving thermodynamic subsystems and moving packets: 1. Theory. J. Hydrol. 182:175–194. Ewen, J. 1996b. ‘SAMP’ model for water and solute movement in unsaturated porous media involving thermodynamic subsystems and moving packets: 2. Design and application. J. Hydrol. 182:195–207. FitzPatrick, E.A. 1984. Micromorphology of soils. Chapman and Hall, London. doi:10.1007/978-94-009-5544-8 Fletcher, J.E., K. Harris, H.B. Peterson, and Y.N. Chandler. 1954. Piping. Trans. Am. Geophys. Union 35:258–262. doi:10.1029/TR035i002p00258 Flury, M., H. Flühler, W.A. Jury, and J. Leuenberger. 1994. Susceptibility of soils to preferential flow of water: A field study. Water Resour. Res. 7:1945–1954. doi:10.1029/94WR00871 Gaiser, R.N. 1952. Root channels and roots in forest soils 1. Soil Sci. Soc. Am. J. 16:62–65. doi:10.2136/sssaj1952.03615995001600010019x

Hencher, S.R. 2010. Preferential flow paths through soil and rock and their association with landslides. Hydrol. Processes 24:1610–1630. doi:10.1002/hyp.7721 Henderson, D.E., A.D. Reeves, and K.J. Beven. 1996. Flow separation in undisturbed soil using multiple anionic tracers (2) steady state core scale rainfall and return flows. Hydrol. Processes 10:1451– 1465. doi:10.1002/(SICI)1099-1085(199611)10:113.0.CO;2-C Hewlett, J.D. 1961. Soil moisture as a source of base flow from steep mountain watersheds. Stn. Pap. 132. US For. Serv., Southeast. For. Exp. Stn., Asheville, NC. Hewlett, J.D. 1974. Comments on letters relating to ‘Role of subsurface flow in generating surface runoff: 2, Upstream source areas’ by R. Allan Freeze. Water Resour. Res. 10:605–607. doi:10.1029/WR010i003p00605 Hewlett, J.D., and A.R. Hibbert. 1967. Factors affecting the response of small watersheds to precipitation in humid areas. In: W.E. Sopper and H.W. Lull, editors, Proceedings of International Symposium on Forest Hydrology, State College, PA. 29 Aug.–10 Sept. 1965. Pergamon Press, New York. p. 275–290.

Gerke, H.H. 2006. Preferential flow descriptions for structured soils. J. Plant Nutr. Soil Sci. 169:382–400.

Hill, D.E., and J.-Y. Parlange. 1972. Wetting front instability in layered soils. Soil Sci. Soc. Am. Proc. 36:697–702. doi:10.2136/sssaj1972.03615995003600050010x

Germann, P.F. 1985. Kinematic wave approach to infiltration and rainage into and from soil macropores. Trans. ASAE 28:745–749. doi:10.13031/2013.32331

Holden, J. 2004. Hydrological connectivity of soil pipes determined by

VZJ | Advancing Critical Zone Science

Hillel, D. 1987. Unstable flow in layered soils: A review. Hydrol. Processes 1(2):143–147. doi:10.1002/hyp.3360010203

p. 14 of 17

ground penetrating radar tracer detection. Earth Surf. Processes Landforms 29:437–442. doi:10.1002/esp.1039 Holden, J. 2005. Controls on soil pipe frequency in upland blanket peat. J. Geophys. Res. 110(F1):F02010. doi:10.1029/2004JF000143 Hoogmoed, W.D., and J. Bouma. 1980. A simulation model for predicting infiltration into cracked clay soil. Soil Sci. Soc. Am. J. 44:458–461. doi:10.2136/sssaj1980.03615995004400030003x Hoover, M.D. 1962. Water action and water movement in the forest. In: Forest influences. Forest. For. Prod. Stud. 15. FAO, Rome, Italy. p. 31–80. Hornberger, G.M., P.F. Germann, and K.J. Beven. 1991. Throughflow and solute transport in an isolated sloping soil block in a forested catchment. J. Hydrol. 124:81–99. doi:10.1016/0022-1694(91)90007-5 Horton, R.E. 1933. The role of infiltration in the hydrologic cycle. Eos Trans. AGU 14:446–460. doi:10.1029/TR014i001p00446 Horton, R.E. 1942. Remarks on hydrologic terminology. Eos Trans. AGU 23:479–482. doi:10.1029/TR023i002p00479 Hursh, C.R. 1944. Report of the subcommittee on subsurface flow. Eos Trans. AGU 25:743–746. doi:10.1029/TR025i005p00743 Hursh, C.R., and E.F. Brater. 1941. Separating storm hydrographs from small drainage areas into surface and subsurface flow. Eos Trans. AGU 22:862–870. Jarvis, N.J. 2007. A review of non-equilibrium water flow and solute transport in soil macropores: Principles, controlling factors and consequences for water quality. Eur. J. Soil Sci. 58:523–546. doi:10.1111/j.1365-2389.2007.00915.x

Jury, W.A. 1982. Simulation of solute transport using a transfer function model. Water Resour. Res. 18:363–368. doi:10.1029/WR018i002p00363 Jury, W.A., L.H. Stolzy, and P. Shouse. 1982. A field test of the transfer function model for predicting solute transport. Water Resour. Res. 18:369–375. doi:10.1029/WR018i002p00369 Kanchanasut, P., D.R. Scotter, and R.W. Tillman. 1978. Preferential solute movement through larger soil voids: II. Experiments with saturated soil. Soil Res. 16:269–276. doi:10.1071/SR9780269 Kissel, D.E., J.T. Ritchie, and E. Burnett. 1973. Chloride movement in undisturbed swelling clay soil. Soil Sci. Soc. Am. Proc. 37:21–24. doi:10.2136/sssaj1973.03615995003700010012x Kirkby, M.J., editor. 1978. Hillslope hydrology. John Wiley & Sons, Chichester, UK. Kitahara, H., A. Shimizu, and Y. Mashima. 1988. Characteristics of pipe flow in a subsurface soil layer of a gentle hillside. Jpn. For. Soc. 70:318–323. Kitahara, H., and Y. Nakai. 1992. Relationship of pipe flow to streamflow on a first order watershed. Jpn. For. Soc. 74:49–54. Knapp, B.J. 1970. A note on throughflow and overland flow on steep mountain watersheds. Reading Geogr. 1:40–43. Köhne, J.M., S. Köhne, and J. Šimůnek. 2009. A review of model applications for structured soils: A. Water flow and tracer transport. J. Contam. Hydrol. 104:4–35. doi:10.1016/j.jconhyd.2008.10.002 Kubiena, W. 1938. Micropedology. Collegiate Press, Ames, IA. Lane, S.N., 2017. Natural flood management. Wiley Interdiscip. Rev. Water 4:e1211. doi:10.1002/wat2.1211

Jarvis, N.J., P.E. Jansson, P.E. Dick, and I. Messing. 1991. Modelling water and solute transport in macroporous soils: I. Model description and sensitivity analysis. J. Soil Sci. 42:59–70. doi:10.1111/j.1365-2389.1991.tb00091.x

Larsson, M.H., and N.J. Jarvis. 1999. Evaluation of a dual-porosity model to predict field scale solute transport in a macroporous soil. J. Hydrol. 215:153–171. doi:10.1016/S0022-1694(98)00267-4

Jarvis, N.J., M. Stahli, L. Bergstrom, and H. Johnsson. 1994. Simulation of dichlorprop and bentazon leaching in soils of contrasting texture using the MACRO model. J. Environ. Sci. Health A 29:1255–1277. doi:10.1080/10934529409376106

Larsson, M.H., N.J. Jarvis, G. Torstensson, and R. Kasteel. 1999. Quantifying the impact of preferential flow on solute transport to tile drains in a sandy field soil. J. Hydrol. 215:116–134. doi:10.1016/S0022-1694(98)00265-0

Jarvis, N.J., J.M. Hollis, P.H. Nicholls, T. Mayr, and S.P. Evans. 1997. MACRO_DB: A decision-support tool to assess the fate and mobility of pesticides in soils. Environ. Model. Softw. 12:251–265. doi:10.1016/S1364-8152(97)00147-3 Jarvis, N., J. Koestel, and M. Larsbo. 2016. Understanding preferential flow in the vadose zone: Recent advances and future prospects. Vadose Zone J. 15(12). doi:10.2136/vzj2016.09.0075 Jarvis, N., J. Koestel, and M. Larsbo. 2017. Reply to ‘Comment on “Understanding preferential flow in the vadose zone: Recent advances and future prospects” by N. Jarvis et al.’ Vadose Zone J. 16(5). doi:10.2136/vzj2017.01.0034r Jencso, K.G., B.L. McGlynn, M.N. Gooseff, S.M. Wondzell, K.E. Bencala, and L.A. Marshall. 2009. Hydrologic connectivity between landscapes and streams: Transferring reach‐ and plot‐scale understanding to the catchment scale. Water Resour. Res. 45:W04428. doi:10.1029/2008WR007225 Jones, J.A.A. 1971. Soil piping and stream channel initiation. Water Resour. Res. 7:602–610. doi:10.1029/WR007i003p00602 Jones J.A.A. 1978. Soil pipe networks: Distribution and discharge. Cambria 5:1–21. Jones, J.A.A. 1981. The nature of soil piping: A review of research. British Geomorphological Research Group Res. Monogr. 3. Geo Books, Norwich, UK. Jones, J.A.A. 2004. Implications of natural soil piping for basin management in the British uplands. Land Degrad. Dev. 15:325–349. doi:10.1002/ldr.618 Jones, J.A.A. 2010. Soil piping and catchment response. Hydrol. Processes 24:1548–1566. doi:10.1002/hyp.7634 Jones, J.A.A., and F.G. Crane. 1982. New evidence for rapid interflow contributions to the streamflow hydrograph. Beitr. Hydrol. Sonderh. 3:219–232. Jones, J.A.A., and L.J. Connelly. 2002. A semi-distributed simulation model for natural pipeflow. J. Hydrol. 262:28–49. doi:10.1016/S0022-1694(02)00018-5

VZJ | Advancing Critical Zone Science

Lawes, J.B., J.H. Gilbert, and R. Warington. 1882. On the amount and composition of the rain and drainage water collected at Rothamsted. Williams, Clowes and Sons, London. Linden, D.R., and R.M. Dixon. 1973. Infiltration and water table effects of soil air pressure under border irrigation. Soil Sci. Soc. Am. J. 37:94–98. doi:10.2136/sssaj1973.03615995003700010030x Linden, D.R., and R.M. Dixon. 1976. Soil air pressure effects on volume and rate of infiltration. Soil Sci. Soc. Am. J. 40:963–965. doi:10.2136/sssaj1976.03615995004000060042x Liu, H., and H. Lin. 2015. Frequency and control of subsurface preferential flow: From pedon to catchment scales. Soil Sci. Soc. Am. J. 79:362–377. doi:10.2136/sssaj2014.08.0330 Luxmoore, R.J. 1981. Micro-, meso-, and macroporosity of soil. Soil Sci. Soc. Am. J. 45:671–672. doi:10.2136/sssaj1981.03615995004500030051x Luxmoore, R.J., T. Grizzard, and M.R. Patterson. 1981. Hydraulic properties of Fullerton cherty silt loam. Soil Sci. Soc. Am. J. 45:692–698. doi:10.2136/sssaj1981.03615995004500040004x Marshall, M.R., C.E. Ballard, Z.L. Frogbrook, I. Solloway, N. McIntyre, B. Reynolds, and H.S. Wheater. 2014. The impact of rural land management changes on soil hydraulic properties and runoff processes: Results from experimental plots in upland UK. Hydrol. Processes 28:2617–2629. doi:10.1002/hyp.9826 McCaig, M. 1983. Contributions to storm quickflow in a small headwater catchment: The role of natural pipes and soil macropores. Earth Surf. Processes Landforms 8:239–252. doi:10.1002/esp.3290080306 McDonnell, J.J. 2003. Where does water go when it rains? Moving beyond the variable source area concept of rainfall‐runoff response. Hydrol. Processes 17:1869–1875. doi:10.1002/hyp.5132 McDonnell, J.J., and K.J. Beven. 2014. Debates: The future of hydrological sciences: A (common) path forward? A call to action aimed at understanding velocities, celerities, and residence time distributions of the headwater hydrograph. Water Resour. Res. 50:5342–5350. doi:10.1002/2013WR015141 McGuire, K.J., and J.J. McDonnell. 2010. Hydrological connectivity of hillslopes and streams: Characteristic time scales and nonlinearities.

p. 15 of 17

Water Resour. Res. 46:W10543. doi:10.1029/2010WR009341 Miller, D.E., and W.H. Gardner. 1962. Water infiltration into stratified soil. Soil Sci. Soc. Am. Proc. 26:115–119. doi:10.2136/sssaj1962.03615995002600020007x Millington, R.J., and J.P. Quirk. 1961. Permeability of porous solids. Trans. Faraday Soc. 57:1200–1207. doi:10.1039/tf9615701200 Moeys, J., M. Larsbo, L. Bergström, C.D. Brown, Y. Coquet, and N.J. Jarvis. 2012. Functional test of pedotransfer functions to predict water flow and solute transport with the dual-permeability model macro. Hydrol. Earth Syst. Sci. 16:2069–2083. doi:10.5194/hess-16-2069-2012 Mualem, Y. 1976. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res. 12:513–522. Murphy, C.P., P. Bullock, and R.H. Turner. 1977. The measurement and characterisation of voids in soil thin sections by image analysis: I. Principles and techniques. J. Soil Sci. 28:498–508. doi:10.1111/j.1365-2389.1977.tb02258.x Muskat, M. 1946. The flow of homogeneous fluids through porous media. J.W. Edwards, Ann Arbor, MI. Newson, M.D. 1976. Soil piping in upland Wales: A call for more information. Cambria 3:33–39. Noguchi, S., Y. Tsuboyama, R.C. Sidle, and I. Hosoda. 1999. Morphological characteristics of macropores and the distribution of preferential flow pathways in a forested slope segment. Soil Sci. Soc. Am. J. 63:1413– 1423. doi:10.2136/sssaj1999.6351413x

Reynolds, E.R.C. 1966. The percolation of rainwater through soil demonstrated by fluorescent dyes. J. Soil Sci. 17:127–132. doi:10.1111/j.1365-2389.1966.tb01459.x Richards, L.A. 1931. Capillary conduction of liquids through porous mediums. Physics 1:318–333. doi:10.1063/1.1745010 Sahimi, M. 1995. Flow and transport in porous media and fractured rock: From classical methods to modern approaches. VCH, Weinheim, Germany. Schlüter, S., H.-J. Vogel, O. Ippisch, P. Bastian, K. Roth, H. Schelle, W. Durner, R. Kasteel, and J. Vanderborght. 2012. Virtual soils: Assessment of the effects of soil structure on the hydraulic behavior of cultivated soils. Vadose Zone J. 11(4). doi:10.2136/vzj2011.0174 Schumacher, W. 1864. Die physik des bodens. Wiegandt & Hempel, Berlin. Scotter, D.R. 1978. Preferential solute movement through larger soil voids: I. Some computations using simple theory. Soil Res. 16:257–267. doi:10.1071/SR9780257 Seyfried, M.S., and P.S.C. Rao. 1987. Solute transport in undisturbed columns of an aggregated tropical soil: Preferential flow effects. Soil Sci. Soc. Am. J. 51:1434–1444. doi:10.2136/sssaj1987.03615995005100060008x Sidle, R.C., H. Kitahara, T. Terajima, and Y. Nakai. 1995. Experimental studies on the effects of pipeflow and throughflow partitioning. J. Hydrol. 165:207–219. doi:10.1016/0022-1694(94)02563-Q Sidle, R.C., S. Noguchi, Y. Tsuboyama, and K. Laursen. 2001. A conceptual model of preferential flow systems in forested hillslopes: Evidence of self‐organization. Hydrol. Processes 15:1675–1692. doi:10.1002/hyp.233

Omoti, U., and A. Wild. 1979. Use of fluorescent dyes to mark the pathways of solute movement through soils under leaching conditions: 2. Field experiments. Soil Sci. 128:98–104. doi:10.1097/00010694-197908000-00006

Šimůnek, J., N.J. Jarvis, M.Th. van Genuchten, and A. Gärdenäs. 2003. Review and comparison of models describing non-equilibrium and preferential flow and transport in the vadose zone. J. Hydrol. 272:14– 35. doi:10.1016/S0022-1694(02)00252-4

Parker, J.C., and M.Th. van Genuchten. 1984. Determining transport parameters from laboratory and field tracing experiments. Virginia Tech. Exp. Stn. Rep. 84-3. Virginia Tech., Blacksburg.

Sklash, M.G., K.J. Beven, K. Gilman, and W.G. Darling. 1996. Isotope studies of pipeflow at Plynlimon, Wales, UK. Hydrol. Processes 10:921–944.

Parlange, J.-Y., and D.E. Hill. 1976. Theoretical analysis of wetting front instability in soils. Soil Sci. 122:236–239. doi:10.1097/00010694-197610000-00008

Sklash, M.G., and R.N. Farvolden. 1979. The role of groundwater in storm runoff. J. Hydrol. 43:45–65. doi:10.1016/0022-1694(79)90164-1

Philip, J.R. 1957. The theory of infiltration: 1. The infiltration equation and its solution. Soil Sci. 83:345–358. doi:10.1097/00010694-195705000-00002

Sklash, M.G., R.N. Farvolden, and P. Fritz. 1976. A conceptual model of watershed response to rainfall, developed through the use of oxygen-18 as a natural tracer. Can. J. Earth Sci. 13:271–283. doi:10.1139/e76-029

Philip, J.R. 1968. The theory of absorption in aggregated media. Soil Res. 6:1–19. doi:10.1071/SR9680001

Skopp, J. 1981. Comment on ‘Micro-, meso- and macroporosity of soil’. Soil Sci. Soc. Am. J. 45:1246. doi:10.2136/sssaj1981.03615995004500060052x

Philip, J.R. 1975a. Stability analysis of infiltration. Soil Sci. Soc. Am. J. 39:1042–1049. doi:10.2136/sssaj1975.03615995003900060013x

Skopp, J., W.R. Gardner, and E.J. Tyler. 1981. Solute movement in structured soils: Two-region model with small interaction. Soil Sci. Soc. Am. J. 45:837–842. doi:10.2136/sssaj1981.03615995004500050002x

Philip, J.R. 1975b. The growth of disturbances in unstable infiltration flows. Soil Sci. Soc. Am. J. 39:1049–1053. doi:10.2136/sssaj1975.03615995003900060014x Pilgrim, D.H., D.D. Huff, and T.D. Steel. 1978. A field evaluation of subsurface and surface runoff: 2. Runoff processes. J. Hydrol. 38:319– 341. doi:10.1016/0022-1694(78)90077-X Pinder, G.F., and J.F. Jones. 1969. Determination of the ground‐water component of peak discharge from the chemistry of total runoff. Water Resour. Res. 5:438–445. doi:10.1029/WR005i002p00438 Quisenberry, V.L., and R.E. Phillips. 1976. Percolation of surfaceapplied water in the field. Soil Sci. Soc. Am. J. 40:484–489. doi:10.2136/sssaj1976.03615995004000040013x Rao, P.S.C., D.E. Rolston, R.E. Jessup, and J.M. Davidson. 1980. Solute transport in aggregated porous media: Theoretical and experimental evaluation. Soil Sci. Soc. Am. J. 44:1139–1146. doi:10.2136/sssaj1980.03615995004400060003x

Smart, R.P., J. Holden, K.J. Dinsmore, A.J. Baird, M.F. Billett, P.J. Chapman, and R. Grayson. 2013. The dynamics of natural pipe hydrological behaviour in blanket peat. Hydrol. Processes 27:1523–1534. doi:10.1002/hyp.9242 Smettem, K.R.J. 1984. Soil-water residence time and solute uptake: 3. Mass transfer under simulated winter rainfall conditions in undisturbed soil cores. J. Hydrol. 67:235–248. doi:10.1016/0022-1694(84)90243-9 Smettem, K.R.J., and S.T. Trudgill. 1983. An evaluation of some fluorescent and non‐fluorescent dyes in the identification of water transmission routes in soils. J. Soil Sci. 34:45–56. doi:10.1111/j.1365-2389.1983.tb00811.x Smettem, K.R.J., S.T. Trudgill, and A.M. Pickles. 1983. Nitrate loss in soil drainage waters in relation to by‐passing flow and discharge on an arable site. J. Soil Sci. 34:499–509. doi:10.1111/j.1365-2389.1983.tb01051.x Smith, W.O. 1967. Infiltration in sand and its relation to ground water recharge. Water Resour. Res. 3:539–555. doi:10.1029/WR003i002p00539

Raats, P.A.C. 1973. Unstable wetting fronts in uniform and nonuniform soils. Soil Sci. Soc. Am. J. 37:681–685. doi:10.2136/sssaj1973.03615995003700050017x

Sposito, G. 1980. General criteria for the validity of the Buckingham–Darcy flow law. Soil Sci. Soc. Am. J. 44:1159–1168. doi:10.2136/sssaj1980.03615995004400060006x

Ragan, R.M. 1968. An experimental investigation of partial area contributions. IAHS Publ. 76:241–249.

Sposito, G. 1987. The “physics” of soil physics. In: E.R. Landa and S. Ince, editors, History of geophysics. Vol. 3: The history of hydrology. Am. Geophys. Union, Washington, DC. p. 93–98.

Rahe, T.M., C. Hagedorn, E.L. McCoy, and G.F. Kling. 1978. Transport of antibiotic-resistant Escherichia coli through a western Oregon hillslope soil under conditions of saturated flow. J. Environ. Qual. 7:487–494. doi:10.2134/jeq1978.00472425000700040005x

VZJ | Advancing Critical Zone Science

Starr, J.L., H.C. DeRoo, C.R. Frink, and J.-Y. Parlange. 1978. Leaching characteristics of a layered field soil. Soil Sci. Soc. Am. J. 42:386–391. doi:10.2136/sssaj1978.03615995004200030002x

p. 16 of 17

Starr, J.L., J.-Y. Parlange, and C.R. Frink. 1986. Water and chloride movement through a layered field soil. Soil Sci. Soc. Am. J. 50:1384– 1390. doi:10.2136/sssaj1986.03615995005000060003x

Wienhöfer, J., and E. Zehe. 2014. Predicting subsurface stormflow response of a forested hillslope: The role of connected flow paths. Hydrol. Earth Syst. Sci. 18:121–138. doi:10.5194/hess-18-121-2014

Taylor, G.I. 1950. The instability of liquid surfaces when accelerated in a direction perpendicular to their plane. Proc. R. Soc. London, Ser. A 201:192–196. doi:10.1098/rspa.1950.0052

Whipkey, R.Z. 1965a. Theory and mechanics of subsurface stormflow. In: W.E. Sopper and H.W. Lull, editors, Proceedings of the International Symposium on Forest Hydrology, State College, PA. 29 Aug.–10 Sept. 1965. Pergamon Press, New York. p. 255–260.

Terzaghi K. 1922. Der Grundbruch an Stauwerken und seine Verhütung. Die Wasserkraft 17:445–449. Terzaghi, K. 1943. Theoretical soil mechanics. Chapman and Hall, London. doi:10.1002/9780470172766 Thomas, G.W., and R.E. Phillips. 1979. Consequences of water movement in macropores. J. Environ. Qual. 8:149–156. doi:10.2134/jeq1979.00472425000800020002x Trudgill, S.T., A.M. Pickles, K.R.J. Smettem, and R.W. Crabtree. 1983. Soilwater residence time and solute uptake: 1. Dye tracing and rainfall events. J. Hydrol. 60:257–279. doi:10.1016/0022-1694(83)90026-4 Tyler, D.D., and G.W. Thomas. 1977. Lysimeter measurements of nitrate and chloride losses from soil under conventional and no-tillage corn. J. Environ. Qual. 6:63–66. doi:10.2134/jeq1977.00472425000600010014x Uchida, T., K. Kosugi, and T. Mizuyama. 1999. Runoff characteristics of pipeflow and effects of pipeflow on rainfall-runoff phenomena in a mountainous watershed. J. Hydrol. 222:18–36. doi:10.1016/S0022-1694(99)00090-6 Vereecken, V., A. Schnepf, J.W. Hopmans, M. Javaux, D. Or, T. Roose, et al. 2016. Modeling soil processes: Review, key challenges, and new perspectives. Vadose Zone J. 15(5). doi:10.2136/vzj2015.09.0131 Walker, P.J.C., and S.T. Trudgill. 1983. Quantimet image analysis of soil pore geometry: Comparison with tracer breakthrough curves. Earth Surf. Processes Landforms 8:465–472. doi:10.1002/esp.3290080507 Watson, K.W., and R.J. Luxmoore. 1986. Estimating macroporosity in a forest watershed by use of a tension infiltrometer. Soil Sci. Soc. Am. J. 50:578–582. doi:10.2136/sssaj1986.03615995005000030007x Weiler, M., and J.J. McDonnell. 2007. Conceptualizing lateral preferential flow and flow networks and simulating the effects on gauged and ungauged hillslopes. Water Resour. Res. 43:W03403. doi:10.1029/2006WR004867 Weyman, D.R. 1970. Throughflow on hillslopes and its relation to the stream hydrograph. Bull. lnt. Assoc. Hydrol. Sci. 15:25–33. doi:10.1080/02626667009493969 Weyman, D.R. 1973. Measurements of the downslope flow of water in a soil. J. Hydrol. 20:267–288. doi:10.1016/0022-1694(73)90065-6

VZJ | Advancing Critical Zone Science

Whipkey, R.Z. 1965b. Subsurface stormflow from forested slopes. Int. Assoc. Sci. Hydrol. Bull 10(2):74–85. doi:10.1080/02626666509493392 White, R.E. 1985. The influence of macropores on the transport of dissolved and suspended matter through soil. Adv. Soil Sci. 3:95–120. doi:10.1007/978-1-4612-5090-6_3 White, I., P.M. Colombera, and J.R. Philip. 1978. Experimental studies of wetting front instability induced by sudden changes of pressure gradient. Soil Sci. Soc. Am. Proc. 40:824–829. doi:10.2136/sssaj1976.03615995004000060012x White, R.E., G.W. Thomas, and M.S. Smith. 1984. Modelling water flow through undisturbed soil cores using a transfer function model derived from 3HOH and Cl transport. J. Soil Sci. 35:159–168. doi:10.1111/j.1365-2389.1984.tb00271.x Williams, R.E., and D.W. Allman. 1969. Factors affecting infiltration and recharge in a loess covered basin. J. Hydrol. 8:265–281. doi:10.1016/0022-1694(69)90002-X Wilson, C.M., and P.L. Smart. 1984. Pipes and pipe flow process in an upland catchment, Wales. Catena 11:145–158. doi:10.1016/0341-8162(84)90004-3 Wyllie, M.R.J., and G.H.F. Gardner. 1958. The generalized Kozeny-Carman equation. World Oil 146(4):121–128. Yeh, T.C.J., L.W. Gelhar, and A.L. Gutjahr. 1985. Stochastic-analysis of unsaturated flow in heterogeneous soils: 2. Statistically anisotropic media with variable alpha. Water Resour. Res. 21:457–464. doi:10.1029/WR021i004p00457 Zasłavsky, D., and G. Kassiff. 1965. Theoretical formulation of piping mechanism in cohesive soils. Geotechnique 15:305–316. doi:10.1680/geot.1965.15.3.305 Zaslavsky, D., and G. Sinai. 1981. Surface hydrology: I. Explanation of phenomena. J. Hydraul. Div. Am. Soc. Civ. Eng. 107:1–16. Zehe, E., and C. Jackisch. 2016. A Lagrangian model for soil water dynamics during rainfall-driven conditions. Hydrol. Earth Syst. Sci. 20:3511–3526. doi:10.5194/hess-20-3511-2016

p. 17 of 17