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a USDA-ARS-NPA, Great Plains Systems Research Unit, P.O. Box E, 301 S. Howes St., Fort Collins, CO 80522
b USDA-ARS-NPA, Central Great Plains Research Unit, Akron, CO 80720
Corresponding author (ruan{at}gpsr.colostate.edu)
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Abbreviations: Prc, percentage residue cover • Kc, saturated hydraulic conductivity of the surface seal • Ks, saturated hydraulic conductivity of bulk soil • Kce, spatially averaged saturated hydraulic conductivity • R1, radius of the residue patch • R2, radius of the cylinder
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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The impact of raindrops on a bare soil surface forms a thin layer known as a surface seal on the soil surface due to a combination of physical and chemical processes. The surface seal is denser and has a lower saturated hydraulic conductivity than that of the bulk soil (Tackett and Pearson, 1965). Water infiltration into the bare soil is most often determined by the surface seal (Duley, 1939; Ellison and Slater, 1945; McIntyre, 1958; Ahuja, 1974; Morin and Benyamini, 1977; Ahuja, 1983; Eigel and Moore, 1983; Smith et al., 1999). Crop residues protect the soil surface from physical raindrop impact, which can reduce the formation of surface seals and increase the infiltration rate (Unger and Stewart, 1983). On the other hand, rainfall interception by residue cover may decrease infiltration (Savabi and Stott, 1994) and is an issue we do not consider in this study.
The relationship between the mass or extent of residue cover and the increase in infiltration is an important issue in dealing with the surface-sealing problem. Baumhardt and Lascano (1996) conducted a field experiment near Lubbock, TX. Simulated rain was applied at 65 mm h-1 for 1 h on a bare and residue-covered Olton clay loam soil. They found that cumulative infiltration was lowest (28.7 mm) on bare soil, and increased curvilinearly with increasing residue amounts, leveling off to a limit (49.0 mm). The leveling off (asymptotic limit) occurred at a residue amount of 2.4 ton ha-1. Increases in infiltration were related to the residue amount and not influenced by residue geometry, or their location on the bed or furrow. Lang and Mallett (1984) compared six levels of maize stover, expressed as a percentage ground cover (0, 10, 20, 30, 45, and 75%) under a rainfall simulator (rainfall intensity of 63.5 mm h-1) to assess the effect of surface residues on infiltration and soil loss on a clay loam soil with a 3.5% slope. The increase of infiltration was curvilinearly related to the ground-cover percentage, and the infiltration was 54% greater with 45% residue cover than without residue cover.
It would be extremely useful to know what level of residue cover would be adequate to achieve maximum infiltration, or perhaps 95% of the maximum. This infiltration would be especially important in arid and semiarid regions, where water is the most limiting factor for crop production. It is surprising that only a few studies have been conducted to quantify the residue-cover efficiency.
A number of modeling studies on infiltration into surface-sealed soils have been reported (e.g., Mualem and Assouline, 1989; Baumhardt et al., 1990). Without residues, surface seals are formed uniformly over the soil surface and the water infiltration and redistribution in soils are in one dimension, if the soil is otherwise homogeneous and flat. Several other studies have modeled the water infiltration into the surface-sealed or crusted soil using one-dimensional methods (Ahuja, 1973; Ahuja, 1983; Ahuja and Swartzendruber, 1992; Mualem et al., 1993; Philip, 1998; Smith et al., 1999). Most models such as the RZWQM (RZWQM Development Team, 1998) use one-dimensional approaches.
Infiltration into soil partially covered by crop residues is a two-dimensional problem for which we need to use a two-dimensional model. However, if we can determine an effective saturated hydraulic conductivity for the soil surface that allows the same amount of infiltration as an actually distributed surface seal, we could use one-dimensional methods instead of two-dimensional methods to simulate the infiltration. The effective saturated hydraulic conductivity for a nonuniform or patchy surface seal (Kce) could be formulated with the saturated hydraulic conductivities of the surface seal and the non-sealed soil and the Prc. For practical purposes, it would be very useful to evaluate this effective one-dimensional approach.
Objectives of this theoretical study were (i) to quantify rain infiltration in two typical soil textures (clay loam and loamy sand) as a function of percentage residue cover (residue-cover efficiency); (ii) to examine the sensitivity of residue-cover efficiency to the surface-seal hydraulic conductivity (Kc), the residue-patch size, and the rainfall intensity; and (iii) to evaluate the use of an effective saturated hydraulic conductivity of the nonuniform surface seal (Kce) so that the infiltration can be simplified as a one-dimensional problem.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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As an upper boundary condition, we used rainfall intensities of 25 mm h-1, 65 mm h-1, or 250 mm h-1 for a 1-h duration. The evaporation in this short time period was assumed to be negligible compared with the rainfall. The value 250 mm h-1 was arbitrarily selected as an extreme limit. The rainfall intensity value of 25 mm h-1, which was slightly greater than the saturated hydraulic conductivity of the clay loam soil, was selected because at lower rainfall intensities, all water will infiltrate. Similarly, the rainfall intensity value of 65 mm h-1 was slightly greater than the Ks of the loamy sand soil. The rainfall intensity of 65 mm h-1 was the same as the rainfall intensity that was used by Baumhardt and Lascano (1996) and was only 1.5 mm h-1 greater than that used by Lang and Mallett (1984). Both Baumhardt and Lascano (1996) and Lang and Mallett (1984) used a 1-h duration. These conditions allowed a better comparison of our research with theirs. At the bottom of the domain, the soil was assumed to be free-draining.
Residue-Patch Geometry
We assumed a flat soil condition and that the portion of the soil surface covered by residues had no surface seal. In nature, the residues and bare areas on the soil surface may be distributed in a variety of ways. To model infiltration into a soil that was partially residue-covered, we assumed two simplified geometrical distributions of residue cover. The first type (Type I) was a simple residue distribution (Fig. 1)
, that is, residues were in circular patches surrounded by concentric bare spaces. In this case, we could choose one residue patch, plus the concentric bare space, as the representative unit. The second type (Type II) was the same as the first, except that the circular bare spaces were surrounded by concentric residues. Another type of geometrical distribution of residue cover that we could have considered was residues placed in strips. We hope to simulate this special geometry of residue distribution in a future study.
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50, 100, or 200 mm. In method (ii), R2 was set to one of the same three sizes as above (50, 100, or 200 mm), and Prc was set to change with R1, once R2 was selected. Here, R1 
50, 100, or 200 mm.
Two-Dimensional Infiltration and Redistribution Model
The governing equation is given by the following modified cylindrical form of Richards' equation (Bruggeman and Mostaghimi, 1991):
 | (1) |
is the water content, h is the hydraulic pressure head, and K is the hydraulic conductivity, which is a function of h or .
The relationship between and h is the key hydraulic property. Van Genuchten's model (van Genuchten, 1980) was used to relate these two hydraulic variables:
 | (2) |
r is the residual water content, s is the saturated water content, and 
and n are the fitted parameters that control the shape of the (h) curve.
The hydraulic conductivity function we used is the equation presented by Corey (1994):
 | (3) |
We used SWMS_2D (Simunek et al., 1994), a two-dimensional finite element model, to solve Eq. [1]. The surface boundary conditions of SWMS_2D were modified to deal with the surface seal. The boundary condition at r = R2 was a zero flux boundary. The boundary at z = D was a flux boundary that was equal to a unit hydraulic gradient multiplied by the hydraulic conductivity. In the residue-covered area, it was a flux boundary (rainfall plus run-on from the surface-sealed area) before runoff occurred and was a zero head boundary after runoff occurred (when the soil surface was saturated).
In the surface-sealed area, we separated the surface-seal layer from the flow domain of the finite element mesh. We assumed that the surface seal developed very rapidly after the start of rainfall or the seal existed before the infiltration event. As a result, the change of water content in the surface seal was negligible, and the surface-seal hydraulic conductivity was constant and equal to Kc (Ahuja, 1983). Mualem et al. (1993) also set the seal to be saturated at the very beginning of rainfall. We simplified the hydraulic pressure head within the surface seal to linearly change from the top to the bottom of the surface seal. At the top of the surface seal, the hydraulic pressure head was zero when there was excess rainwater and a negative value determined by the dynamics of the simulation when all rainfall water had infiltrated into the surface seal. At the bottom of the surface seal, the hydraulic pressure head was equal to the hydraulic pressure head of the soil below the surface seal.
The surface-seal layer controlled the flux at the soil surface that was the flux admitted to soil beneath the surface seal. This flux was used as the flux boundary condition in the surface-sealed area of the flow domain of the finite element mesh. To find the flux entering the surface seal, we set the pressure head at the top of the surface seal to zero and set the pressure head at the bottom of the surface seal to the pressure head of the previous time step at the boundary of the flow domain below the surface seal. The flux was then obtained using the hydraulic gradient and the saturated hydraulic conductivity of the surface seal (Kc). If the flux was less than the rainfall, the flux was used as the flux boundary condition in the surface-sealed area. If the flux was greater than the rainfall, the rainfall was used as the flux boundary condition in the surface-sealed area. Generally, the flux through the surface seal was controlled by the rainfall intensity in early stages (no ponding) and by the hydraulic gradient within the surface seal later (ponding).
When infiltration was controlled by the infiltration capacity (the hydraulic gradient multiplied by the saturated hydraulic conductivity of the surface seal), the excess rainwater from the surface-sealed area was instantaneously redistributed over the residue-covered area where the infiltration capacity was greater. When the excess water from the surface-sealed area, plus the rainwater directly applied on the residue-covered area, exceeded the infiltration capacity of the residue-covered area, runoff occurred. The runoff was removed instantaneously.
One-Dimensional Model Using an Effective Surface Seal
Water infiltration and redistribution in soils were simplified as a one-dimensional problem by assuming that a uniform effective surface seal covered the entire soil surface including residue-covered and uncovered areas. The effective surface seal had an effective saturated hydraulic conductivity (Kce) and the same thickness as the surface seal in the surface-sealed areas. The value of Kce must be greater than Kc of the surface-sealed areas and less than Ks of the residue-covered areas. A linear interpolation was a simple method to obtain Kce:
 | (4) |
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Cases with Simple Residue-Cover Efficiency
Model-simulated results of 96 cases (of 216 cases total) were outside the scope of surface-seal effects. With the combination of the loamy sand soil and a rainfall intensity of 25 mm h-1 (36 cases), and the combination of the loamy sand soil, a rainfall intensity of 65 mm h-1, and Kc 0.1Ks (24 cases), all rainwater infiltrated. When rainfall intensity was small relative to Ks, residue cover was not needed. With the combination of the clay loam soil and a rainfall intensity of 250 mm h-1 (36 cases), the simulated infiltration was not significantly different from the infiltration at the rainfall intensity of 65 mm h-1. This was because residue cover can, at most, prevent surface sealing due to physical processes, and there is a limit of infiltration that is controlled by the soil itself.
Sensitivity of Residue-Cover Efficiency for Type I Residue Geometrical Distribution
Sensitivity of Residue-Cover Efficiency to the Way the Residue-Patch Size Changes
The simulated results of all other combinations (60 cases) for Type I residue geometrical distribution were summarized in Fig. 3 and 4
. Each curve in the two figures represents the change of relative infiltration with the Prc for a specific combination of soil type, Ks, residue-patch size, and rainfall intensity. Infiltration was normalized with the infiltration at a full residue cover (Prc = 100%) to get the relative infiltration for easy comparison of residue-cover efficiency.
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Sensitivity of Residue-Cover Efficiency to Soil Type
Figure 3 shows the relationships between the residue-cover efficiency and each of the four factors we selected earlier. Considering the soil type, the residue-cover efficiency for the loamy sand was greater than for the clay loam with Kc = 0, and similar with Kc = 0.1Ks or Kc = 0.3Ks. The differences were caused not only by the soil type but also by the rainfall intensity values relative to the saturated hydraulic conductivity of the soil. With greater K or infiltration capacity in the residue-covered areas, the residue-cover efficiency was greater.
Sensitivity of Residue-Cover Efficiency to Kc
Considering the saturated hydraulic conductivity of the surface seal, the residue covers were more efficient with Kc = 0 than with Kc = 0.1Ks or Kc = 0.3Ks (see Fig. 3). This is obvious because with Kc = 0, residue cover increased the infiltration capacity from 0 to >Ks in the residue-covered areas rather than from 0.1Ks or 0.3Ks to >Ks. The relationship was not linear. From Kc = 0.1Ks to Kc = 0.3Ks, the residue-cover efficiency did not increase as much as from Kc = 0 to Kc = 0.1Ks.
Sensitivity of Residue-Cover Efficiency to Residue-Patch Size
Small residue patches had greater residue-cover efficiency than large residue patches at the same percent residue cover (see Fig. 3). With small residue-patch sizes and thus small surface-seal areas (at the same values of Prc), water was more easily and evenly redistributed laterally in the soil after entering the residue-covered areas, increasing the hydraulic gradient beneath small patches relative to large patches. Consequently, the infiltration capacity was greater for smaller residue patches. The decrease of infiltration capacity in the surface-sealed areas due to the redistributed water from residue-covered areas was much less because the original capacity was much less than in the residue-covered areas.
Sensitivity of Residue-Cover Efficiency to Rainfall Intensity
At high rainfall intensities, residue-cover efficiency was greater than at low rainfall intensities, except when Kc = 0 (Fig. 3). The increase of residue-cover efficiency with rainfall intensity was curvilinear and could reach an asymptotic limit. At Kc = 0, residue cover increased the infiltration capacity from zero to a number near the rainfall intensity more easily at low rainfall intensities than at high rainfall intensities. At Kc = 0.1Ks or Kc = 0.3Ks, the infiltration capacity of surface seals was relatively high compared with low rainfall intensities and relatively low compared with high rainfall intensities. Therefore, the residue cover did not increase the infiltration as much at low rainfall intensities as at high rainfall intensities.
The Leveling-Off Values of Prc
We used the infiltration without surface sealing (100% residue cover) as the maximum infiltration (100%). For different cases, the maximum infiltration changed. At 95% of the maximum infiltration, the value of Prc was considered optimal (i.e., leveling off). Increasing Prc value beyond 95% maximum infiltration was considered to not increase the infiltration efficiently, relative to the increase of residues. We examined how this optimal Prc changed with rainfall intensity, residue size, the surface-seal saturated hydraulic conductivity, and soil type.
The leveling-off values of Prc are plotted against rainfall intensity with different combinations of factors in Fig. 5
. For loamy sand, the leveling-off values of Prc increased from 0% (no residue-cover efficiency) at a rainfall intensity of 25 mm h-1 to 
57% at a rainfall intensity of 250 mm h-1. It did not reach a limit at a rainfall intensity of 250 mm h-1, but we assumed rainfall intensities >250 mm h-1 were not practical. For clay loam, the leveling-off values of Prc increased from 60% at a rainfall intensity of 25 mm h-1 to 70% at a rainfall intensity of 250 mm h-1. It reached a limit at a rainfall intensity of 65 mm h-1.
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Figure 6 shows the leveling-off values of Prc against the residue-patch size. The leveling-off values of Prc increased curvilinearly with residue-patch size. At R1 = 200 mm, the leveling-off values of Prc for both soils did not reach a limit but increased less. The loamy sand had smaller leveling-off values of Prc than the clay loam.
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Residue-Cover Efficiency for Type II Residue Geometrical Distribution
The simulated results for Type II distribution were similar to the results of Type I distribution. We omitted further discussions on Type II residue cover distribution.
One-Dimensional Solutions
The results of one-dimensional simulations are compared with those of the two-dimensional simulations in Fig. 7
for the residue-patch size of 50 mm. To better understand the differences between the one-dimensional and two-dimensional methods, we also simulated four extra cases using Kc = 0.05Ks. If Kc 0.05Ks, there were no significant differences between one-dimensional and two-dimensional results. When Kc = 0, the one-dimensional infiltration was much greater than the two-dimensional infiltration. For most practical conditions, Kc 0.05Ks; it is seldom equal to zero. Therefore the one-dimensional method with Eq. [4] will give adequate estimates of the two-dimensional water infiltration and redistribution under partial residue-cover conditions.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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With the model for effective hydraulic conductivity of surface seal that we proposed, one-dimensional approaches can be used to simulate infiltration for soils that are partially and not severely surface sealed. If soils are severely surface sealed, the one-dimensional infiltration is much greater than the two-dimensional infiltration, making the present two-dimensional simulations necessary to realistically model field behavior for this extreme scenario.
The good agreements between the results of numerical simulations and the two independent experimental observations indicate that the numerical model that we proposed well represents the real system under complicated conditions. In the future, we will test (i) the residue geometrical distribution in strips to see its differences from a circular type, and (ii) layered soil profiles.
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ACKNOWLEDGMENTS |
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Received for publication March 15, 1999.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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This article has been cited by other articles:
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  L. R. Ahuja, L. Ma, and D. J. Timlin Trans-Disciplinary Soil Physics Research Critical to Synthesis and Modeling of Agricultural Systems Soil Sci. Soc. Am. J., February 2, 2006; 70(2): 311 - 326. [Abstract] [Full Text] [PDF]
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