Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.
OCR for page 149
CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE 5 Uniform and Preferential Flow Mechanisms in the Vadose Zone Jan M.H. Hendrickx1 and Markus Flury2 ABSTRACT The two major flow mechanisms in the vadose zone are uniform flow and preferential flow. Both types of flow occur often simultaneously, but have considerably different consequences for water flow and chemical leaching. The objectives of this paper are to describe and classify flow mechanisms in the subsurface and to present illustrative field and laboratory studies. Since preferential flow occurs at a number of scales, scale is used as the primary classification criterion. Three distinctive scales are recognized on the basis of three different conceptual and physical models for water flow in the vadose zone: pore scale, Darcian scale, and areal scale. A common example of pore-scale preferential flow is saturated and unsaturated flow through macropores and fractures. At the Darcian scale we observe flow through stony soils, unstable flow occurring in water repellent and wettable homogeneous soils, unstable flow in layered soil profiles, preferential flow induced by variability in soil hydraulic properties, and flow through displacement faults. At the areal scale, surface depressions and discontinuous layers with lower or higher permeabilities can cause preferential flow. The paper concludes with a short section on measurement techniques for preferential flow and with guidelines for the formulation of conceptual models for the vadose zone. 1 Department of Earth and Environmental Science, New Mexico Tech, Socorro 2 Department of Crop and Soil Sciences, Washington State University, Pullman
OCR for page 150
CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE INTRODUCTION It has long been recognized that water flow in soils can either be uniform (Green and Ampt, 1911) or non-uniform (Lawes et al., 1881). Uniform flow leads to stable wetting fronts that are parallel to the soil surface; non-uniform flow results in irregular wetting. As a direct consequence of these irregular flow patterns, water moves faster and with increased quantity at certain locations in the vadose zone than at others. This non-uniform movement of water and dissolved solutes is commonly denoted preferential flow. The term preferential flow neither distinguishes between the causes of the non-uniform flow pattern nor differentiates between the types of patterns. As such the term preferential flow comprises all phenomena where water and solutes move along certain pathways, while bypassing a fraction of the porous matrix. The reasons for the non-uniform flow patterns are manifold, and several identified mechanisms have coined an own term: Macropore flow is preferential water movement along root channels, earthworm burrows, fissures, or cracks. It occurs predominantly in fine-textured soils or media with a pronounced structure. Water bypasses the denser and less-permeable soil matrix by using the pathway of least resistance through macropores. Unstable flow is often observed in coarse-textured materials, and may be induced by textural layering, water repellency, air entrapment, or continuous non-ponding infiltration. As in the case of macropore flow, a considerable portion of the porous matrix is bypassed by the infiltrating water. Funnel flow refers to the lateral redirection and funneling of water caused by textural boundaries. Water again moves along the pathway of least resistance and can be redirected through a series of less permeable layers embedded in the soil profile. Each of these types of preferential flow is caused by different physical mechanisms. Often, several mechanisms act simultaneously, which leads to a broad variety of flow patterns. The objectives of this paper are to describe the mechanisms and processes that lead to uniform and preferential flow in the vadose zone, and to elucidate the differences in the types of flow patterns observed. The different types of preferential flow are discussed in terms of three different conceptual and physical models for water flow which are frequently used in vadose zone hydrology and lead to the recognition of three spatial scales. We present illustrative examples and provide the basis for conceptual models to describe preferential flow phenomena. CONCEPTUAL AND PHYSICAL MODELS The physical principles that govern flow and capillary processes in the vadose zone are well understood and many excellent text books are available that deal with this topic at both introductory (Campbell, 1985; Hanks and Ashcroft, 1986; Hillel, 1998; Jury et al., 1991; Koorevaar et al., 1983; Marshall and Holmes, 1979) and advanced levels (Bear, 1972; Childs, 1969; Corey, 1990; Dullien,
OCR for page 151
CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE 1992; Kirkham and Powers, 1972). Flows of incompressible Newtonian fluids such as water are mathematically described by the Navier-Stokes equations, which are nonlinear, second-order, partial differential equations. These equations are related to a conceptual model for the pore scale that is based on the concept of a fluid continuum filling the void space. This approach is valid if the size of the pore diameters is larger than the mean free path of the water molecules. Although the continuum condition is readily met in most flow conditions in the vadose zone, the intricacy of the Navier-Stokes equations allows only a few exact mathematical solutions (Currie, 1993). One of these is the Hagen-Poiseuille equation that describes laminar flow through circular tubes (flow through a pore), between two parallel plates (i.e., flow through a fracture), and over a plate (i.e., film flow). For example, the water flux qfr(m/s) through a saturated parallel, smooth-walled fracture with aperture opening b (m) under laminar flow conditions is (5.1) (Bear et al., 1993; Corey, 1990; Snow, 1969; Streeter et al., 1998), where H is total hydraulic head (m), z is vertical distance (m), and Kfr is the hydraulic conductivity in the fracture (m/s) defined as: (5.2) where ρ is fluid density (kg/m3), g is the acceleration due to gravity (m/s2), and µ is the dynamic viscosity (kg/s · m). The geometrical complexity of porous materials makes it very cumbersome to treat water flow by referring only to the fluid continuum filling the pore space. A solution for this problem is found by moving to a larger spatial scale, which we name in this paper the Darcian scale. Instead of trying to exactly describe pore geometries and corresponding boundary conditions, the actual multiphase porous medium is replaced by a fictitious representative volume consisting of many pores and solids over which an average is performed. This changes the conceptual model from one based on a fluid continuum at the pore scale to one based on the concept of a representative volume at a larger spatial scale. At the Darcian scale, water movement through a one-dimensional, unsaturated, vertical soil column is mathematically expressed by Darcy-Buckingham's equation: (5.3) where q is the water flux (m/s), K(h) the unsaturated hydraulic conductivity (m/s), and H the total hydraulic head:
OCR for page 152
CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE H = h + z (5.4) in which h is the (negative) water pressure (m) and z the elevation head or height above a reference level (m). Equations 5.1 and 5.3 have the same functional form; that is, the flux is proportional to the total hydraulic gradient. However, the proportionality factors in the two flux laws are fundamentally different. The hydraulic conductivity in the fracture Kfr applies to a single aperture whereas the hydraulic conductivity K(h) is defined over a representative volume of the porous medium. As a result K(h) is much more complex than Kfr, which is, for a given fluid, completely defined by a single soil or rock parameter: the aperture width (see Equation 5.2). Only empirical formulations of the hydraulic conductivity K(h) exist. Several mathematical functions have been proposed to represent measured data. The complexity of the unsaturated hydraulic conductivity is apparent in the function proposed by Van Genuchten (1980): (5.5) where Ks is the saturated hydraulic conductivity (m/s); θ is volumetric soil water content (m3/m3); θs is the saturated water content (m3/m3), often taken equal to the soil porosity; θr is residual water content (m3/m3); and the parameters n, m, and λ are empirical constants. The relationship between θ and h, the water retention characteristic, is: (5.6) where α (m−1), n, and m are parameters that determine the water retention curve shape. As it is often assumed that m = 1 − 1/n, the number of parameters needed to describe the hydraulic conductivity as a function of soil water pressure h totals six: Ks, θs, θr, n, λ, and α. The parameter values can be determined from measured θ-h and K-h data pairs using nonlinear curve fitting programs available in statistical software packages and spreadsheets, or by optimization software such as the package RETC developed by Van Genuchten et al. (1991). At the areal scale, application of the Darcy-Buckingham equation is no longer practical since it would require long and expensive field campaigns to characterize and quantify the spatial variability of the vadose zone at the Darcian scale. One approach for the evaluation of water movement at such a big scale is to employ areal mass balance or soil moisture budgeting models (Hendrickx and Walker, 1997). For example, the groundwater recharge over a large area can be assessed by an areal water balance equation:
OCR for page 153
CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE qr = P + R − ET − ΔW (5.7) where qr is the groundwater recharge (m/month), P is precipitation (m/month), R is the net runoff/runon (m/month), ET is actual evapotranspiration (m/month), and ΔW is the change in soil moisture storage in the vadose zone (m/month). Table 5-1 follows previous work by Wagenet (1998), Wagenet et al. (1994), and Wheatcraft and Cushman (1991) to summarize the principal characteristics of the conceptual and physical models discussed above. One immediate observation of great practical significance is the fact that conceptual models at different scales result in different physical models and mathematical equations. Moreover, each of these equations requires a completely different set of input parameters. The complexity of input parameters for physical models increases with the spatial scale. Flow in a fracture requires a measurement of its width; unsaturated flow through a soil profile requires measurements or indirect determination of the six soil parameters Ks, θs, θr, n, λ, and α; evaluation of a regional water balance in the vadose zone requires long-term monitoring of soil water contents, meteorological variables, and groundwater levels. This leads to the observation that the timeframe of a study often will increase if the spatial scale of its conceptual model becomes larger. Although the measurement of fracture widths at depth is no simple matter, it takes less time than the many years of monitoring key environmental parameters needed to assess the water balance of a watershed. Moreover, while measurements of fracture widths and the Van Genuchten soil parameters will yield estimates of their true values within relatively small confidence limits that can be used in a deterministic manner, the nature of environmental parameters often gives studies at areal scales a stochastic character. The results of such studies frequently have to rely more on statistical interpolations of field measurements than on well determined causal and physical relationships. For given weather conditions in a specific soil profile, the changes of soil water fluxes with depth and time can be predicted quite well once the Van Genuchten soil parameters have been determined. However, for the same weather conditions, determination of regional groundwater recharge using Equation 5.7 will become a stochastic exercise using statistical techniques for the interpolation and averaging of soil physical and meteorological measurements. For this reason, areal-scale methods can only yield reliable results if the averaging process does not create havoc with the true flow mechanisms. Our heuristic approach for the discussion of the three different conceptual models and their respective scales suggests an increasing spatial dimension from pore, to Darcian, to areal scale. Although such an increase is a common feature in many vadose zones, there are also hydrological observations that demonstrate at least some overlap between the spatial dimensions of the three distinctive scales. For example, a Darcian approach can be applied to soil volumes as small as a few cubic millimeters, while the Navier-Stokes equations in principle can be used to describe water flow through pores with diameters of centimeters. A Darcian
OCR for page 154
CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE TABLE 5-1 Scales, Conceptual Models, Critical Parameters, and Measurements Relevant to Flow Mechanisms in the Vadose Zone Spatial Scale Domain Conceptual Model Physical Model Critical Parameters Smallest Temporal Measurements Scale Pore Macropores, Fractures Fluid Continuum Hagen-Poisseuille Equation 5.1 Fracture Width Thin sections, NMR Minutes Days Darcian Laboratory, Soil Profiles Representative Volume Darcy-Buckingham Equation 5.3 Hydraulic Properties TDR, Neutron Attenuation, Tensiometers Hours Months Areal Field, Local Depression, Landscape Element Mass Balance Mass Balance Equation 5.7 Weather, Soil Moisture Meteorological Station, TDR, Neutron Attenuation, Remote Sensing, Groundwater Level Days Years
OCR for page 155
CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE approach may be quite appropriate for a large uniform landscape element covering squares of kilometers but fail on a meter scale in a heterogeneous environment. An areal water balance approach can be applied to volumes as small as a flower pot as well as to areas covering an entire continent. For this reason we have chosen names for the spatial scales that reflect their link with a particular physical model rather than a spatial dimension. FLOW MECHANISMS AT DIFFERENT SCALES Water flow in the vadose zone occurs at different spatial and temporal scales under a wide variety of conditions. This makes it problematic to classify vadose zone flow mechanisms in a consistent manner. Another complicating factor is that processes at the pore scale determine processes at larger scales. For these reasons we have selected a practical classification criterion based upon the three conceptual models discussed in the previous section which lead to three typical spatial scales often encountered in vadose zone studies. The pore scale deals with water flow processes described by Hagen-Poiseuille's equations, the Darcian scale with processes considered to take place within fictitious representative volumes and described by Darcy's equation, and the areal scale with processes affected by major landscape elements such as local depressions, faults, and discontinuous layers in the vadose zone. Sometimes processes at the areal scale can be described quantitatively using Darcy's law in numerical models such as HYDRUS2D, while in more complicated situations only a qualitative approach is feasible. Figure 5-1 and Figure 5-2 illustrate the different flow mechanisms and their relation to the spatial scale. On the pore scale, we observe several types of macropore flow and at the Darcian scale, stable wetting as well as funnel and unstable flow (Figure 5-1). On the areal scale, we observe preferential flow due to localized recharge caused by topographic depressions, pipe flow, and funnel flow (Figure 5-2). Pore Scale The lucidity of the Hagen-Poiseuille Equation 5.1 makes the pore scale very attractive for the investigation of water flow through soils and rocks since the only material parameter needed for its application is the pore size. Unfortunately, its application is only practical in materials with a relatively simple pore geometry, such as capillary tube models (Bear, 1972; Scheidegger, 1974), network models (Dullien, 1992; Luxmoore and Ferrand, 1992), fractures (Bear, 1993; Rasmussen, 1987; Schrauf and Evans, 1986), and macropores. There is abundant evidence that many soils are susceptible to rapid water flow through macropores. Macropores are often defined in terms of a specific radius (Luxmoore, 1981; Beven and German, 1982); however, no accepted general definition of a macropore exists. The definition of a specific radius is rather
OCR for page 156
CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE FIGURE 5-1 Schematic showing different preferential flow mechanisms observed at pore and Darcian scales
OCR for page 157
CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE FIGURE 5-2 Schematic showing different preferential flow mechanisms observed at the areal scale
OCR for page 158
CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE arbitrary, and for operational purposes in this paper we consider a macropore to be a pore or fracture considerably larger in radius than the bulk of the pores and fractures in the porous soil or rock. In unsaturated porous media, macropores do not necessarily conduct large amounts of water. Two conditions must be met in order for macropores to contribute to rapid water flow. First, the macropore must be partially or completely filled with water, and, second, the pore needs to continuously extend over a significant portion of the porous medium. Obviously, the definition of a significant distance depends on the system of interest, and therefore the relevance of macropore flow might be very different depending on the spatial and temporal scale of interest. For instance, one common type of macropore flow in soils is flow through earthworm burrows or root channels. Earthworm burrows are typically 1-3 mm in diameter and can extend up to 6 m in vertical length. As such, water and chemicals can bypass the topsoil by traveling in earthworm burrows, and pollutants and pesticides can potentially contaminate shallow groundwater resources. When earthworm burrows end at a certain depth, water and dissolved chemicals will leave the macropore and flow through the porous matrix, thus slowing down vertical migration considerably. It is rather unlikely that continuous vertical flow paths extend over several dozens of meters in unsaturated soil, and therefore macropore flow will stop at a certain depth. The bypass of the topsoil, however, has serious consequences for many contaminants because sorption and degradation processes are usually strongest in the topsoil and cease with increasing soil depth. Several dye tracing studies have demonstrated that macropore flow is rather common in many agricultural soils, particularly in fine-textured soils with a pronounced soil structure (Bouma et al., 1977; Flury et al., 1994; Germann, 1990; Mohanty et al., 1998; Petersen et al., 1997; Stamm et al., 1998). Out of 14 different soils investigated, Flury et al. (1994) found a majority of soils susceptible to macropore flow. Typical flow patterns observed are shown in Figure 5-3. Depending on whether the macropores are more planar or cylindrical in shape, the flow patterns appear more areal or linear, respectively. The process of macropore flow is depicted in Figure 5-4. When the overall water input from precipitation or irrigation, q*(t), exceeds infiltration capacity of the soil, i(t), a horizontal overland flow, o(t), is generated that causes a water flux into the macropores, q(0, t). This flux causes water content inside the macropore, w(z, t), to increase. A fraction of the water, r, that occupies a macropore at a given depth will be absorbed by the soil matrix through the macropore walls. The remainder will percolate downwards into the macropore, q(z, t). The interplay of precipitation or irrigation rates with dynamics of the infiltration rate over time add to the macropore flow mechanism complexity. For example, the infiltration rate of a soil depends not only on the time since infiltration started but also on antecedent water content (Philip, 1969). When the infiltration rate, i(t), decreases with time and with increasing antecedent soil water content, the opportunity for overland flow, o(t), and macropore flow, q(0, t) increases.
OCR for page 159
CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE FIGURE 5-3 Typical macropore flow patterns observed in structured, fine-textured soils. Patterns depict vertical cross sections of soil profiles after sprinkling irrigation of 40 mm dye solution. The horizontal bar in the left graph indicates the maximum excavation depth. After Flury, M., H. Flühler, W. A. Jury, and J. Leuenberger, 1994. Susceptibility of soils to preferential flow of water: A field study. Water Resources Research 30: 1945-1954. Copyright by American Geophysical Union.
OCR for page 178
CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE to long-term persistent preferential flow processes that lead to the formation of observable landscape features. FORMULATION OF CONCEPTUAL MODELS The formulation of criteria for determining whether a conceptual model is an adequate characterization for a specific vadose zone is extremely complicated since there are so many factors that affect flow mechanisms. Nevertheless, the case studies presented in this review have a number of general characteristics in common that can serve as a guideline for the development of conceptual models. All three spatial scales of preferential flow discussed have in common that an initially spatially uniform flux is disturbed and water flow is confined to a smaller cross-sectional area of the vadose zone. Even though the mechanisms that lead to the formation of preferential flow patterns are very different, the phenomenological appearances and the environmental consequences are often very similar. Figure 5-15 depicts a schematic view of different flow regimes that can be distinguished during a preferential flow process: (1) lateral distribution flow in the attractor zone where preferential flow is initiated; (2) downward preferential flow in the transmission zone where water moves along preferential flow pathways and thus bypasses a considerable portion of the porous media matrix; and (3) lateral and downward dispersive flow in the dispersion zone where preferential flow pathways are interrupted and water flow becomes uniform again. The attractor zone can vary considerably in thickness (Figure 5-3), and may even be the soil surface itself when preferential flow is initiated by runon into localized surface depressions. Figure 5-3, Figure 5-4, Figure 5-5, Figure 5-7, and Figure 5-14 clearly show an attractor zone located close to the soil surface. The pipe in Figure 5-14 receives water by lateral collection over the calcic horizon from the surrounding areas. Therefore, it is concluded that an attractor zone at or below the soil surface is a definitive feature of preferential flow at whatever scale it takes place. The dispersion zone can be recognized in Figure 5-7 and Figure 5-11 but is missing in the other figures. It is often not included in graphical presentations of preferential flow when it occurs so deep in the vadose zone that water rarely even reaches this zone (Figure 5-3, Figure 5-4, Figure 5-14). Figure 5-10 shows that the dispersion zone for one layer with preferential flow can be the attractor zone for another deeper layer. Indeed, in a deep vadose zone, finding a sequence of attractor and dispersion zones is expected. Stable flow can be considered as a flow mechanism that did not yet reach the transmission zone (Figure 5-5). This is the case, for example, where the amount of precipitation is not sufficient to wet the attractor zone to a depth that allows unstable wetting to occur (Hendrickx and Yao, 1996). Apparently stable flow can be dealt with as a special case in the general mechanism of preferential flow.
OCR for page 179
CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE FIGURE 5-15 Schematic view of flow processes in the vadose zone. After Geoderma, 70, Flühler, H., W. Durner, and M. Flury, Lateral solute mixing processes: A key for understanding field-scale transport of water and solutes. Pp. 165-183, 1996, with permission from Elsevier Science. FIGURE 5-16 Application of stability criteria for determination of preferential flow caused by unstable wetting fronts. After Geoderma, 70, Hendrickx, J. M. H. and T. Yao, Prediction of wetting front stability in dry field soils using soil and precipitation data, pp. 265-280, 1996, with permission from Elsevier Science.
OCR for page 180
CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE FIGURE 5-17 Flow diagram for evaluation of vadose conditions that will lead to preferential flow.
OCR for page 181
CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE All three spatial scales of preferential flow discussed also have in common that preferential flow can start only after a certain minimum amount of precipitation has fallen at an intensity sufficiently high to cause the attractor zone to feed the transmission zone. Precipitation at a low intensity will infiltrate into the soil surface and result in a stable flow mechanism under a wide variety of conditions, from the fracture at the pore scale to the depression at the areal scale. However, a small amount of rain at a sufficiently high intensity may immediately trigger preferential flow at the pore scale as well as the areal scale. We need also to consider the effect of antecedent soil water content that affects the amount of water that can infiltrate into the soil at the surface or at the walls of a macropore. An example of how precipitation amount, precipitation intensity, and antecedent soil water content affect the occurrence of unstable flow in a wettable sand soil is given in Figure 5-16. In Figure 5-17 we present a flow diagram for the evaluation of vadose zone conditions that will cause preferential flow at different scales as a result of a lateral flow trigger. Since precipitation is spatially uniform, it will result in uniform one-dimensional flow through the vadose zone unless a lateral flow trigger is present. We recognize different lateral flow triggers, such as a precipitation rate that exceeds the infiltration rate, vertical changes in unsaturated hydraulic conductivities where the lower layer has a lower conductivity, water repellency, and other mechanisms that cause unstable flow. Although the principles of the flow diagram are straightforward and will result in a first assessment of the propensity for preferential flow, no evaluation is complete without considering in which manner antecedent soil water content affects the flow processes in the attractor and transmission zones as a function of precipitation amount and intensity. This is the most difficult question but also the most crucial, since the threshold values for the minimum amount of precipitation and the intensity determine the occurrence of preferential flow at any scale. REFERENCES Anderson, M. G., and T. P. Burt, 1990. Subsurface runoff. Chapter 11 in M. G. Anderson and T. P. Burt (eds.). Process Studies in Hillslope Hydrology. Baker, R. S., and D. Hillel, 1972. Laboratory tests of a theory of fingering during infiltration into layered soils. Soil Sci. Soc. Am. J. 54: 20-30. Bear, J., 1972. Dynamics of Fluids in Porous Media. New York: Dover Publications, Inc., 764 pp. Bear, J., 1993. Modeling flow and contaminant transport in fractured rocks. In: J. Bear, C. Tsang, and G. De Marsily, eds. Flow and Contaminant Transport in Fractured Rock. San Diego, Calif.: Academic Press, Inc., pp. 1-37. Bear, J., T. Chin-Fu, and G. De Marsily (eds.), 1993. Flow and Contaminant Transport in Fractured Rock. New York: Academic Press, 560 pp. Beven, K., and P. Germann, 1982. Macropores and water flow in soils. Water Resources Research 18: 1311-1325.
OCR for page 182
CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE Boers, Th. M., 1994. Rainwater harvesting in arid and semi-arid zones. Wageningen, The Netherlands: International Land Reclamation and Improvement Institute (ILRI), 132 pp. Boers, Th. M., M. De Graaf, R. A. Feddes, and J. Ben-Asher, 1986. A linear regression model combined with a soil water balance model to design micro-catchments for water harvesting in add zones. Agricultural Water Management 11: 187-206. Bond, R. D., 1964. The influence of the microflora on the physical properties of soils . II. Field studies on water repellent sands. Australian Journal of Soil Research 2: 123-131. Bouma, J., and L. W. Dekker, 1978. A case study on infiltration into dry clay soil. I. Morphological observations. Geoderma 20: 27-40. 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. Buchter, B., C. Hinz, M. Flury, and H. Fluhler, 1995. Heterogeneous flow and solute transport in an unsaturated stony soil monolith. Soil Sci. Soc. Am. J. 59: 14-21. Campbell, G. S., 1985. Soil Physics with Basic, Transport Models for Soil-Plant Systems. New York: Elsevier, 150 pp. Childs, E. C., 1969. The Physics of Soil Water Phenomena. New York: John Wiley and Sons. Corey, A. T., 1990. Mechanics of Immiscible Fluids in Porous Media. Littleton, Colo.: Water Resources Publications, 255 pp. Currie, I. G., 1993. Fundamental Mechanics of Fluids, 2nd ed. New York: McGraw-Hill, Inc. Darcy, H. 1856. Les Fontaines Publique de la Ville de Dijon. Paris: Dalmont. DeBano, L. F., 1969a. Water movement in water-repellent soils. In: Proc. Symp. on Water-repellent Soils, Riverside, California, 61-89. DeBano, L. F., 1969b. Water-repellent soils: A worldwide concern in management of soil and vegetation. Agric. Sci. Rev. 7: 11-18. DeBano, L. F., 1981. Water-repellent soils: A state of the art. Gen. Tech. Rep. PS-W-46, Pacific Southwest Forest and Range Experiment Station, 21 pp. Deecke, W., 1906. Einige Beobachtungen am Sandstrande. Centralbl. für Mineral. Geol. und Paläont., 721-727. Dekker, L. W., and P. D. Jungerius, 1990. Water repellency in the dunes with special reference to The Netherlands . Catena Suppl. 18: 173-183. Dekker, L. W., and C. J. Ritsema, 1994a. How water moves in a water repellent sandy soil. 1. Potential and actual water repellency. Water Resources Research 30: 2507-2517. Dekker, L. W., and C. J. Ritsema, 1994b. Fingered flow: The creator of sand columns in dune and beach sands . Earth Surface Processes and Landforms 19: 153-164. Diment, G. A., and K. K. Watson, 1985. Stability analysis of water movement in unsaturated porous materials . 3. Experimental studies. Water Resources Research 21: 979-984. Du, X. H., T. Yao, W. D. Stone, and J. M. H. Hendrickx. 2001. Stability analysis of the unsaturated water flow equation, 1. Mathematical derivation. Water Resources Research, in press. Dullien, F. A. L., 1992. Porous media: Fluid transport and pore structure. New York: Academic Press, 574 pp. Edwards, W. M., M. J. Shipitalo, L. B. Owens, and L. D. Norton, 1989. Water and nitrate movement in earthworm burrows within long-term no-till cornfields. J. Soil Water Conserv. 44: 240-243. Emerson, W. W., and R. D. Bond, 1963. The rate of water entry into dry sand and calculation of the advancing contact angle. Australian Journal of Soil Research 1: 9-16. Flühler, H., W. Durner, and M. Flury, 1996. Lateral solute mixing processes: A key for understanding field-scale transport of water and solutes. Geoderma 70: 165-183. Flury, M., H. Flühler, W. A. Jury, and J. Leuenberger, 1994. Susceptibility of soils to preferential flow of water: A field study . Water Resources Research 30: 1945-1954. Forrer, I., R. Kasteel, M. Flury, and H. Flühler, 1999. Longitudinal and lateral dispersion in an unsaturated field soil. Water Resources Research 35(10): 3049-3060.
OCR for page 183
CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE Freeze, R. A., and J. Banner, 1970. The mechanism of natural groundwater recharge and discharge. 2. Laboratory column experiments and field measurements. Water Resources Research 6: 138-155. Gardner, W. H., and J. C. Hsieh, 1959. Water movement in soils. Dept. of Crop and Soil Sciences, Washington State University, [Video], Pullman, Wash. Gee, G. W., and D. Hillel, 1988. Groundwater recharge in arid regions: Review and critique of estimation methods. Hydrological Processes 2: 255-266. Gees, R. A., and A. K. Lyall, 1969. Erosional sand columns in dune sand, Cape Sable Island, Nova Scotia, Canada. Canadian Journal of Earth Sciences 6: 344-347. Germann, P. F., 1986. Rapid drainage response to precipitation. Hydrol. Processes 1: 3-13. Germann, P. F., 1990. Macropores and hydrologic hillslope processes. In: M. G. Anderson and T. P. Burt, eds. Process Studies in Hillslope Hydrology, 327-363. Glass, R. J., T. S. Steenhuis, and J.-Y. Parlange, 1988. Wetting front instability as a rapid and farreaching hydrologic process in the vadose zone. J. Contam. Hydroll. 3: 207-226. Glass, R. J., T. S. Steenhuis, and J.-Y. Parlange, 1989a. Wetting front instability. 1. Theoretical discussion and dimensional analysis. Water Resources Research 25: 1187-1194. Glass, R. J., T. S. Steenhuis, and J.-Y. Parlange, 1989b. Wetting front instability. 2. Experimental determination of relationships between system parameters and two-dimensional unstable flow field behavior in initially dry porous media. Water Resources Research 25: 1195-1207. Glass, R. J., T. S. Steenhuis, and J.-Y. Parlange, 1989c. Mechanism for finger persistence in homogeneous, unsaturated, porous media: Theory and verification. Soil Sci. 148: 60-70. Glass, R. J., J. King, S. Cann, N. Bailey, J.-Y. Parlange, and T. S. Steenhuis, 1990. Wetting front instability in unsaturated porous media: A three-dimensional study. Transp. Porous Media 5: 247-268. Glass, R. J., J.-Y. Parlange, and T. S. Steenhuis, 1991. Immiscible displacement in porous media: Stability analysis of three-dimensional, axisymmetric disturbances with application to gravity-driven wetting front instability. Water Resources Research 27: 1947-1956. Green, W. H., and G. A. Ampt, 1911. Studies on soil physics. I. The flow of water and air through soils. J. Agric. Sci. 4: 1-24. Gripp, K., 1961. Über Werden und Vergehen von Barchanene an der Nordsee-Küste SchleswigHolsteins. Zeitsch. für Geomorphologi, Neue Folge 5: 24-36. Gunn, J., 1983. Point-recharge of limestone aquifers: A model from New Zealand karst . J. Hydrol. 61: 19-29. Hanks, R. J., and G. L. Ashcroft, 1986. Applied Soil Physics: Advanced Series in Agricultural Sciences 8. New York: Springer-Verlag, 159 pp. Heijs, A. W., C. J. Ritsema, and L. W. Dekker, 1996. Three-dimensional visualization of preferential flow patterns in two soils. Geoderma 70: 101-116. Hendrickx, J. M. H., L. W. Dekker, M. H. Bannink, and H. C. van Ommen, 1988. Significance of soil survey for agrohydrological studies. Agricultural Water Management 14: 195-208. Hendrickx, J. M. H., and L. W. Dekker, 1991. Experimental evidence of unstable wetting fronts in non-layered soils . In: Proc. Natl. Symp. on Preferential Flow. Chicago, Ill. 16-17, Dec. 1991, St. Joseph, Mich.: Am. Soc. Agric. Eng., 22-31. Hendrickx, J. M. H., S. Khan, M. H. Bannink, D. Birch, and C. Kidd, 1991. Numerical analysis of groundwater recharge through stony soils using limited data. J. Hydrol. 127: 173-192. Hendrickx, J. M. H., L. W. Dekker, and O. H. Boersma, 1993. Unstable wetting fronts in water repellent field soils. Journal of Environmental Quality 22: 109-118. Hendrickx, J. M. H., and T. Yao, 1996. Prediction of wetting front stability in dry field soils using soil and precipitation data. Geoderma 70: 265-280. Hendrickx, J. M. H., and G. Walker, 1997. Recharge from precipitation. Chapter 2, In: I. Simmers, ed. Recharge of Phreatic Aquifers in (Semi)-Arid Areas. Rotterdam, The Netherlands: Balkema. Hill, D. E., and J.-Y. Parlange, 1972. Wetting front instability in layered soils. Soil Sci. Soc. Am. J. 36: 697-702.
OCR for page 184
CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE Hillel, D., 1998. Environmental Soil Physics. San Diego: Academic Press. Hillel, D., and R. S. Baker, 1988. A descriptive theory of fingering during infiltration into layered soils. Soil Sci. 146: 51-56. Issar, A., and R. Passchier, 1990. Regional hydrogeological concepts. In: D. N. Lerner et al., eds. Groundwater Recharge. International Contributions to Hydrogeology, Vol. 8, Hannover, Germany: Int. Assoc. Hydrogeologists, Verlag Heinz Heise, 21-98. Jamison, V. C., 1969. Wetting resistance under citrus trees in Florida. In: Proc. Symp. on Water Repellent Soils, Riverside, California, 9-15. Jaramillo, D. F., L. W. Dekker, C. J. Ritsema, and J. M. H. Hendrickx. 2000. Occurrence of soil water repellency in arid and humid climates. Journal of Hydrology 231/232: 105-114. Johnston, C. D., 1987. Preferred water flow and localized recharge in a variable regolith . J. Hydrol. 94: 129-142. Jury, W. A., W. R. Gardner, and W. H. Gardner, 1991. Soil Physics, New York: John Wiley and Sons , 328 pp. Kirkham, D., and W. L. Powers, 1972. Advanced Soil Physics. New York: John Wiley and Sons , 534 pp. Koorevaar, P., G. Menelik, and C. Dirksen, 1983. Elements of soil physics. New York: Elsevier, 230 pp. Kung, K.-J. S., 1990. Preferential flow in a sandy vadose zone. 1. Field observation. Geoderma 46: 51-58. Lawes, J. B., J. H. Gilbert, and R. Warington, 1881. On the amount and composition of the rain and drainage-waters collected at Rothamsted, Part I and II. J. Royal Agric. Soc. of England, London 17: 241-279. Lerner, D. N., A. S. Issar, and I. Simmers, 1990. Groundwater Recharge. A Guide to Understanding and Estimating Natural Recharge. International Contributions to Hydrogeology, Vol. 8. Hannover: Internat. Assoc. of Hydrogeologists, Heise. Letey, J., J. F. Osborn, and N. Valoras, 1975. Soil water repellency and the use of nonionic surfactants. Calif. Water Res. Center (Contribution 154) 85 pp. Li, Y., and M. Ghodrati, 1994. Preferential transport of nitrate through soil columns containing root channels. Soil Sci. Soc. Am. J. 94: 653-659. Lopes De Leao, L. R., 1988. Hé. Grondboor en Hamer 3/4: 111-112. Luxmoore, R. J., 1981. Micro-, meso-, and macroporosity of soil. Soil Sci. Soc. Am. J. 45: 671-672. Luxmoore, R. J., and L. A. Ferrand, 1992. Water flow and solute transport in soils: Modeling and applications . In: D. Russo and G. Dagan, eds. New York: Springer Verlag, pp. 45-60. Mallik, A. U., and A. A. Rahman, 1985. Soil water repellency in regularly burned Calluna heathlands: Comparison of three measuring techniques. Journal of Environmental Management 20: 207-218. Marshall, T. J., and J. W. Holmes, 1979. Soil Physics. Cambridge University Press, 345 pp. McGhie, D. A., and A. M. Posner, 1980. Water repellency of a heavy-textured Western Australian surface soil . Aust. J. Soil Res. 18: 309-323. Meeuwig, R. O., 1971. Infiltration and Water Repellency in Granitic Soils. U.S. Dept. of Agriculture Forest Service, Research Paper INT-111, Ogden, Utah, 20 pp. Meyboom, P., 1966. Unsteady groundwater flow near a willow ring in hummocky moraine. J. Hydrol. 4: 38-62. Miller, J. J., D. F. Acton, and R. J. St. Arnaud, 1985. The effect of groundwater on soil formation in a morainal landscape in Saskatchewan. Canadian Journal of Soil Science 65: 293-307. Miyamoto, S., A. Bristol, and W. I. Gould, 1977. Wettability of coal-mine spoils in Northwestern New Mexico. Soil Sci. 123: 258-263. Mohanty, B. P., R. S. Bowman, J. M. H. Hendrickx, J. Simunek, and M. Th. van Genuchten, 1998. Preferential transport of nitrate to a tile drain in an intermittent-flood-irrigated field: Model development and experimental evaluation. Water Resources Research 34: 1061-1076. Mooij, J., 1957. Aeolian destruction forms on a sand beach. Grondboor en Hamer 1: 14-18.
OCR for page 185
CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE Nieber, J. L., C. A. S. Tosomeen, and B. N. Wilson, 1993. A stochastic-mechanistic model of depression-focused recharge. In: Y. Eckstein and A. Zaporozec, eds. Hydrogeologic Inventories and Monitoring and Groundwater Modeling ., 207-229. Parlange, J.-Y., and D. E. Hill, 1976. Theoretical analysis of wetting front instability in soils. Soil Sci. 122: 236-239. Petersen, C. T., S. Hansen, and H. E. Jensen, 1997. Tillage-induced horizontal periodicity of preferential flow in the root zone. Soil Sci. Soc. Am. J. 61: 586-594. Philip, J. R., 1969. Theory of infiltration. Advances in Hydroscience 5: 215-296. Philip, J. R., 1975a. Stability analysis of infiltration. Soil Sci. Soc. Am. Proc. 39: 1042-1049. Philip, J. R., 1975b. The growth of disturbances in unstable infiltration flows. Soil Sci. Soc. Am. Proc. 39: 1049-1053. Raats, P. A. C., 1973. Unstable wetting fronts in uniform and nonuniform soils, Soil Sci. Soc. Am. Proc. 37: 681-685. Raats, P. A. C., 1984. Tracing parcels of water and solutes in unsaturated zones. In: B. Yaron, G. Dagan, and J. Goldshid, eds. Pollutants in Porous Media: The Unsaturated Zone Between Soil Surface and Ground Water. Berlin: Springer, 4-16. Rasmussen, T. C., 1987. Computer simulation model of steady fluid flow and solute transport through three-dimensional networks of variably saturated, discrete fractures. In D. D. Evans and T. J. Nicholson, Flow and Transport Through Unsaturated Fractured Rock. Geophysical Monograph 42, American Geophysical Union, Washington D.C., pp. 107-114. Richardson, J. L., 1984. Field observation and measurement of water repellency for soil surveyors . Soil Survey Horiz. 25: 32-36. Rietveld, J. J., 1978. Soil Nonwettability and Its Relevance as a Contributing Factor to Surface Runoff on Sandy Dune Soils in Mali. Report of project Production primaire au Sahel, Agric. Univ., Wageningen, The Netherlands, 179 pp. Ritsema, C. J., L. W. Dekker, J. M. H. Hendrickx, and W. Hamminga, 1993. Preferential flow mechanism in a water-repellent sandy soil. Water Resources Research 29: 2183-2193. Ritsema, C. J., and L. W. Dekker, 1994. How water moves in a water-repellent sandy soil. 2. Dynamics of fingered flow. Water Resources Research 30: 2517-2531. Roth, K., 1995. Steady state flow in an unsaturated, two-dimensional, macroscopically homogeneous, Miller-similar medium. Water Resources Research 31: 2127-2140. Roth, K., and K. Hammel, 1996. Transport of conservative chemical through an unsaturated two-dimensional Miller-similar medium with steady state flow. Water Resources Research 32: 1653-1663. Scanlon, B. R., 1992. Moisture and solute flux along preferred pathways characterized by fissured sediments in desert soils. J. of Contaminant Hydrol. 10: 19-46. Scheidegger, A. E., 1974. The physics of flow through porous media. Toronto: University of Toronto Press . Schrauf, T. W., and D. D. Evans, 1986. Laboratory studies of gas flow through a single natural fracture. Water Resources Research 19: 1253-1265. Schuddebeurs, A. P, 1957. Cone sand and sandstone. Grondboor en Hamer. 2. 21-25. Selker, J. S., T. S. Steenhuis, and J.-Y. Parlange, 1989. Preferential flow in homogeneous sandy soils without layering. Paper No. 89-2543, Am. Soc. Agric. Eng., Winter Meeting, New Orleans, La., 22 pp. Selker, J. S., T. S. Steenhuis, and J.-Y. Parlange, 1992. Wetting front instability in homogeneous sandy soils under continuous infiltration. Soil Sci. Soc. Am. J. 56: 1346-1350. Sigda, J. M., 1997. Effects of small-displacement faults on the permeability distribution of poorly consolidated Santa Fe Group sands, Rio Grande Rift New Mexico. M.S. thesis, New Mexico Tech, Socorro.
OCR for page 186
CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE Snow, D. T., 1969. Anisotropic permeability of fractured media. Water Resources Research 5: 1273-1289. Stamm, C., H. Flühler, R. Gächter, J. Leuenberger, and H. Wunderli, 1998. Preferential transport of phosphorus in drained grassland soils. J. Environ. Qual. 27: 515-522. 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. 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. Stephens, D. B., 1994. A perspective on diffuse natural recharge mechanisms in areas of low precipitation. Soil Sci. Soc. Am. J. 58: 40-48. Streeter, V. L., E. B. Wylie, and K. W. Bedford, 1988. Fluid Mechanics, 9th ed. Boston: McGraw-Hill. Tabuchi, T., 1961. Infiltration and ensuing percolation in columns of layered glass particles packed in laboratory. Nogyo dobuku kenkyn, Bessatsu. Trans. Agr. Eng. Soc., Japan, 1, 13-19 (in Japanese, with a summary in English). Tamai, N., T. Asaeda, and C. G. Jeevaraj, 1987. Fingering in two-dimensional, homogeneous, unsaturated porous media . Soil Sci. 144: 107-112. Tosomeen, C. A. S., 1991. Modeling the effects of depression focusing on groundwater recharge . M.S. thesis, Dept. of Agricultural Engineering, University of Minnesota. Van As, H., and D. van Dusschoten, 1997. NMR methods for imaging of transport processes in micro-porous systems . Geoderma 80: 389-403. Van Dam, J. C., J. M. H. Hendrickx, H. C. van Ommen, M. H. Bannink, M. Th. Van Genuchten, and L. W. Dekker, 1990. Simulation of water and solute transport through a water-repellent sand soil, J. Hydrol. 120: 139-159. Van Genuchten, M. Th., 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44: 892-898. Van Genuchten, M. Th., F. J. Leij, and S. R. Yates, 1991. The RETC code for quantifying the hydraulic functions of unsaturated soils. EPA/600/2-91/065. R. S. Kerr Environ. Res. Lab., U.S. Environmental Protection Agency, Ada, Okla., 93 pp. Wagenet, R. J., 1998. Scale issues in agroecological research chains. Nutrient Cycling in Agro-ecosystems 50: 23-34. Wagenet, R. J., J. Bouma, and J. L. Hutson, 1994. Modelling water and chemical fluxes as driving forces in pedogenesis . In R. B. Bryant, R. W. Arnold, and M. R. Hoosbeek, eds. Quantitative Modelling of Soil Forming Processes. SSSA Special Publ. 39, ASA/CSSA/SSSA, Madison,Wis., pp. 17-35. Wang, Z., J. Feyen, M. Th. Van Genuchten, and D. R. Nielsen, 1998. Air entrapment effects on infiltration rate and flow instability. Water Resources Research 34: 213-222. Watson, K., and R. J. Luxmoore, 1986. Estimating macroporosity in a watershed by use of a tension infiltrometer . Soil Sci. Soc. Am. J. 50: 578-582. Wheatcraft, S. W., and J. H. Cushman, 1991. Hierarchical approaches to transport in heterogeneous porous media . In: U.S. National Report to International Union of Geodesy and Geophysics, Rev. Geophysics (supplement), pp. 263-269, American Geophysical Union. Washington, D.C. White, I., P. M. Colombera, and J. R. Philip, 1977. Experimental studies of wetting front instability induced by gradual change of pressure gradient and by heterogeneous porous media. Soil Sci. Soc. Am. J. 41: 483-489. Wierenga, P. J., R. G. Hills, and D. B. Hudson, 1991. The Las Cruces trench site: Characterization, experimental results, and one-dimensional flow predictions. Water Resources Research 27: 2695-2705. Winter, T. C., 1986. Effect of ground-water recharge on configuration of the water table beneath sand dunes and on seepage in lakes in the sandhills of Nebraska , USA. J. Hydrol. 86: 221-237.
OCR for page 187
CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE Wood, W. W., and W. E. Sanford, 1995. Chemical and isotopic methods for quantifying groundwater recharge in a regional, semiarid environment. Ground Water 33: 458-468. Yao, T., and J. M. H. Hendrickx, 1996. Stability of wetting fronts in homogeneous soils under low infiltration rates. Soil Science Society of America Journal 60: 20-28. Yao, T., and J. M. H. Hendrickx, 2001. Stability analysis of the unsaturated water flow equation: 2. Experimental Verification. Water Resources Research, in press.
OCR for page 188
CONCEPTUAL MODELS OF FLOW AND TRANSPORT IN THE FRACTURED VADOSE ZONE This page in the original is blank.
Representative terms from entire chapter: