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National Soil Tilth Lab., 2150 Pammel Dr., Ames, IA 50011
* Corresponding author (logsdon{at}nstl.gov)
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARYNOTESREFERENCES |
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), the macropore fraction (sma), and the half spacing (d) between equivalent parallel fractures. As an example this study used soils in the Des Moines lobe (Mollisols with textures ranging from sandy loam to silty clay). Data used to calculate model parameters included wet-end K--h and K(h), and results from image analysis. For the MACRO model, the parameters fit the equations best when hb was assumed to be 30 mm. For the measured data with assumed hb = 30 mm, n* had a median of 2.1 and a range from 0 to 5.2, median Kb was 15 mm h-1 with a range from 1 to 100 mm h-1, and the median Ks was 122 mm h-1 with a range from 7 to 741 mm h-1. The calculated d ranged from 1 to 847 mm, and sma ranged from 0.001 to 0.053 m3 m-3. Depending on the data available, the various techniques can be used to determine input parameters for preferential flow models. |
INTRODUCTION |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARYNOTESREFERENCES |
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Currently a number of techniques are used to estimate macropore properties (Edwards et al., 1993; McCoy et al., 1994). Techniques have been developed to describe the macropore region in the soil, including infiltration under negative head (Ankeny et al., 1988; Perroux and White, 1988), desorption at the wet-end (McCoy, 1989; Logsdon et al., 1993), image analysis (Protz et al., 1987; Edwards et al., 1988; Moran et al., 1989; Logsdon et al., 1990; Thompson et al., 1992), and multiple-tracer techniques (Jaynes et al., 1995). Measuring soil hydraulic and physical properties for the macropore region should not be an end in itself. Such information should be used for input in preferential flow models, and to test the assumptions of the models. The objectives of this paper were to evaluate methods to independently measure or calculate macropore parameters, and to use this information to test the assumptions of the preferential flow model MACRO.
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THEORY |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARYNOTESREFERENCES |
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b). Within the macropore domain, the relation between h and is assumed to be
 | [1] |
is the water content (L3 L-3) when > b, and s is the saturated water content. The difference, s - b, is also called the macropore fraction (sma), and is influenced by shrinking and swelling (not shown). Hydraulic conductivity is assumed to be related to as
 | [2] |
> b, Kb is the boundary hydraulic conductivity, and n* is an empirical exponent. Water and solute exchange between micropore and macropore domains are inversely related to the square of d, the equivalent half spacing of parallel fractures. Since sma is contributed by hexagonal fracture patterns, biopores, and interpedal voids, as well as parallel fractures, the calculated d is an equivalent fracture spacing.
Literature Parameterization for MACRO Model
Those who have run the MACRO model needed to determine model input parameters. Usually the s was measured, and the b was measured for an assumed or calibrated hb value. Saxena et al. (1994) measured the soil water retention curve for the micropore region, and the smallest h was 100 mm. For one soil, they set the hb at 100 or 150 mm for different depths, but they calibrated hb for the other soil, ending up with hb = 500 mm. Jabro et al. (1994) also measured the soil water retention curve, and the smallest h was 100 mm. They set the hb at 400 mm by defining macropores as those pores smaller than 75 µm. Larsson and Jarvis (1999a)( b) assumed hb = 100 mm, and measured the corresponding from tension table measurements.
Since sma is the difference between s and b, the range of values can be compared. Jabro et al. (1994) had sma values ranging from 0.01 to 0.08 m3 m-3. Saxena et al. (1994) had sma values ranging from 0.02 to 0.13 m3 m-3. Larsson and Jarvis (1999a) measured sma ranging from 0.02 to 0.07 m3 m-3. Based on a different data set (but the same soil), they adjusted these values by calibration to a range of 0.005 to 0.04 m3 m-3 (Larsson and Jarvis, 1999b).
The Ks values were directly measured (Jabro et al., 1994; Saxena et al., 1994), or fitted from tile outflow data (Larsson and Jarvis, 1999a, b). Larsson and Jarvis (1999a)(b) used tension infiltrometer data to get Kb values for the assumed hb of 100 mm, then adjusted the value by calibration. Saxena et al. (1994) obtained Kb through calibration.
How n* was obtained is less clear, but apparently n* was either arbitrarily set or derived through calibration. Jabro et al. (1994) and Larsson and Jarvis (1999a)(b) did not list n* values used, but Saxena et al. (1994) used n* values of 3 or 12 (for different soils). Since n* = 12 is outside of the allowed range, the program was apparently modified to allow a larger n* value. In every case, the d value was calibrated except Jabro et al. (1994) used an earlier version of MACRO that did not have the d value. Saxena et al. (1994) did not list the d values used. Larsson and Jarvis (1999a) calibrated d values ranging from 100 to 300 mm for different depths in the soil. For a different data set (but the same soil), Larsson and Jarvis (1999b) calibrated d values ranging from 50 to 300 mm.
Of key interest is the assumed hb since the chosen value for hb determines the values of Kb and b for a given data set. Those who have used the MACRO model have not evaluated their choices in line with the assumptions of the model (Jabro et al., 1994; Saxena et al., 1994; Larsson and Jarvis, 1999a,b). None had water retention data for h smaller than 100 mm, and none attempted to see if the water retention data fit Eq. [1]. If all the assumed equations given above are true, then these macropore parameters should be interrelated.
Indirect Determination of Macropore Domain Parameters
Based partly on assumptions in the MACRO model, I will now attempt to show how some of the parameters are related to each other. The d value in the MACRO model can be calculated from sma. This assumes that the macropore volume fraction (m3 m-3) is equivalent to the macropore area fraction (m2 m-2). For this set of examples, the possible sma was subdivided into subclasses, and the upper and lower bounds of fracture width (w) and (s - )/sma were determined with the largest w assumed to be 2 mm. Then the mean w was calculated as well as the change in (s - )/sma between the upper and lower bounds for each subclass (Table 1). For a given h, the w can be determined using the capillary equation for parallel fractures,
 | [3] |
is surface tension (kg s-2), a is contact angle, g is acceleration because of gravity (m s-2), 
l and a are densities of water and air (kg m-3), and h is the absolute value of the head within the macropore domain (m). For this set of sample calculations, a was assumed to be 0, but similar calculations could be made for various a values. Assuming parallel fractures in a unit area (A), the fracture length (L) for each subclass can be determined from sma
 | [4] |
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 | [5] |
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sma, or hb values. The calculated d value would decrease as a, sma, or hb increased.
The d value could also be calculated from the mobile/immobile transfer rate exchange coefficient, 
. The calculation used the equation from Gerke and van Genuchten (1993)
 | [6] |
mi is the micropore water content, and D*m is an effective diffusion coefficient for the micropore region calculated from D*m = Dv v + D0 f*
, where Dv is dispersivity, v is pore-water velocity, D0 is diffusion in free water, and f* is an impedance factor equal to 0.5.
In addition, the MACRO equations can be rearranged to show K as a function of h rather than as a function of . Equations [1] and [2] can be combined and rearranged to
 | [7] |
Equation [2] would be used for K() data, whereas Eq. [7] would be used for K(h) data, which are more readily available.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARYNOTESREFERENCES |
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-h, (ii) Wet End K(h), and from (iii) Image Analysis.
Directly Measured Parameters
Wet-end K--h Data
The data discussed for this group contained all three matched factors: K, , h, but not much replication. The significance of this limited data set is that K is matched to , as required by Eq. [2]. The most direct K--h data was from Casey et al. (1998) for a Harps soil. The infiltration rates had been measured at h values of ponded, and at 30, 60, and 150 mm using small-base disk infiltrometers (76-mm diam.; Ankeny et al., 1988). There were ten measurements at each h, and after the infiltration measurements, the soil was sampled for soil water content determination. Because the infiltration data for each h were determined at different locations within the same field plot, the mean infiltration rates were used to determine K using the calculation procedure of Logsdon and Jaynes (1993).
The other data in this group were field K(h) data measured with large-base disk infiltrometers (210-mm diam.; Perroux and White, 1988) again at h values of ponded, 30, 60, and 120 mm. Immediately after the K(h) measurements, soil cores were taken at the each of the K(h) locations to determine (h) in the laboratory by the rotated core procedure (McCoy, 1989; Logsdon et al., 1993). The rotated core procedure drained the samples to h values of 60, 90, and 120 mm. The K value at h = 90 mm was calculated from
 | [8] |
[h] data) for Nicollet clay loam.
Wet-end K(h) Data
These data illustrate direct measurements of K for various h values with many replicates. The significance of this data group is the presence of a large number of replicates, and the large number of h values. To illustrate the use of field-measured K(h), the extensive data set of Logsdon (1999) was used. The K(h) was measured by large-base disk infiltrometers, using the technique of Logsdon and Jaynes (1993). This data group included measurements from four soils (Clarion, Nicollet, Webster, and Okoboji), four depths, two to four replicates per depth, and six
h values (ponded, 30, 60, 90, 120, and 150 mm). Infiltration rates were converted to K using the technique of Logsdon and Jaynes (1993), with two or three sections of unified K(0) and lc (Logsdon, 1999) for each set of six h values. In all there were 55 sets of K(h) data in this group. Medians and ranges were determined for K at each h for the whole data group (55 sets). In addition, medians were determined for each soil and depth.
Image Analysis Data
These data illustrated the use of image analysis to directly measure sma as a function of equivalent w values. Two large undisturbed monoliths (1.5 m deep) of a Nicollet soil were extracted from the field. The extracted monoliths were excavated horizontally for each of seven or eight depths. At each excavated depth, separate plastic sheets were marked to indicate the size and placement of biopores and fractures using the technique of Logsdon et al. (1990). For each horizontal plane, biopore fractional area for a given biopore radius was converted to equivalent fracture area for a given w. For each depth, two or three sheets were used to characterize the excavated horizontal area of almost 1 m2. Video tapes were made of the marked sheets. The image analysis procedure for the biopores is given in the appendix. The fracture L and w were determined by scanning the sheet, and using the ROOTEDGE program (Ewing and Kaspar, 1995). The sma for each w was calculated by summing actual fracture sma and the equivalent sma from biopores.
Because a pit had been dug in the process of extracting the large monoliths, undisturbed soil cores (76 mm long, 74-mm diam.) were taken along the side of the pit, two per depth. The undisturbed cores were taken to the laboratory to measure Ks by the falling head method (Klute and Dirksen, 1986).
Input Parameter Estimation Based on the Experimental Data
Fracture-half Spacing, d
The d value can be independently determined rather than calibrated. The d parameter is critical because Jarvis and Larsson (2001) suggest that a very small d value would be used to predict solute leaching when there is no preferential flow. For these calculations, the largest w was assumed to be 2 mm. Depending on the extent of the data available, intermediate data were interpolated.
For data Group 1, subclasses of h (0–15, 15–30, 30–60, 60–90, 90–120 mm for all, and also 120–150 mm for the Harps data) were used to subdivide the calculated in the macropore region as a function of h, using Eq. [1]. When data were available for a given h, the actual data were used rather than interpolated data. The assumed hb was the largest h in a given data set. The upper and lower bounds of fracture width (w) and (s - )/sma were determined for each subclass. Then the mean w was calculated using Eq. [3], and the change in (s - )/sma between the upper and lower bounds were calculated for each subclass. From w, L, and d were calculated using Eq. [4] and [5]. For the Harps soil of data Group 1 (Casey et al., 1998), the ten values for h = 30 mm were used to determine d using Eq. [6].
For data Group 3, L was measured directly. Additionally, equivalent L from biopores was calculated from the measured sma because of pores, using Eq. [4]. The equivalent subclass h ranges were 0 to 12.5,12.5 to 25, 25 to 50, and 50 to100 mm. For each subclass, L from fractures and equivalent L from biopores were added together. For data Groups 1 and 3, L values for each subclass were summed to get cumulative L for different h values.
Macropore Region (h)
Image analysis results were used to back-calculate (h). Equivalent h values were calculated from Eq. [3], and the values for - b and sma had been determined from the image analysis data. Both the image analysis results (data Group 3) and the desorption data from data Group 1 were compared with the assumptions of Eq. [1].
Exponent of K Relation, n*
Jarvis (1991) showed that MACRO was very sensitive to n*. The exponent n* in Eq. [2] was fitted from the K() data of Group 1. Since at least three points are needed to fit n*, the data were fitted for all four measured K values which would assume that hb = 150 mm for the Harps soil, and 120 mm for the other soils. The data were also fitted for the three wettest K values, which assumed that hb = 60 or 90 mm.
The exponent n* in Eq. [7] was fitted from the K(h) data of Group 2 for each of the four assumed hb values: 150, 120, 90, and 60 mm. For each of the 55 sets, the relationship between assumed hb and n* was approximately linear; therefore, linear regression of n* as a function of assumed hb was used to determine the n* for assumed hb of 30 mm. Figure 1 illustrates this procedure for one of the measurement sets (Clarion soil at 0.35 m, replicate four). Figure 1a shows the data for each assumed hb value. Since at least three points were needed to use Eq. [7], the n* value for assumed hb = 30 mm was determined from the linear regression of n* as a function of hb (Fig. 1b). Then statistical parameters (means, standard deviations, medians, and ranges) were determined for each assumed hb covering all the data (55 sets), and means were calculated for each soil and depth.
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARYNOTESREFERENCES |
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; data Group 2 was a large set of data with K measured as a function of h; whereas, data Group 3 included image analysis estimates of equivalent fracture L and w, and associated Ks measured on soil cores.
Hydraulic Conductivity
Measured hydraulic conductivities at h values of ponded, 30, 60, and 150 mm were 336, 9.1, 5.3, and 1.6 mm h-1 for the Harps soil of data Group 1. The median measured K values at h values of ponded, 60, 90, and 120 mm for the other measurements of Group 1 were 20.4, 9.0, 6.3, and 2.7 mm h-1.
For the larger data Group 2 (Table 3), K values at each h were quite variable. The K decreased greatly as h was decreased from ponded to 30 mm, with smaller decreases in K as h was further increased. The distribution of K values was highly skewed at each h. This type of variability is typical for ponded and tension K data (Logsdon, 1993; Logsdon and Jaynes, 1996).
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Macropore Fraction, sma
For the Harps soil of data in Group 1 (field desorption), the measured sma at assumed hb values of 30, 60, and 150 mm were 0.053, 0.058, and 0.064 m3 m-3. For the rest of data in Group 1 (laboratory desorption) the median sma values at assumed hb values of 60, 90, and 120 mm were 0.008, 0.011, and 0.019 m3 m-3. The median measured sma values for the image analysis results (data Group 3) corresponding to assumed hb values of 12.5, 25, and 50 mm were 0.004, 0.012, and 0.012 m3 m-3. When interpolated to assumed hb of 30 mm by Eq. [1], the sma values ranged from 0.001 to 0.03 m3 m-3 (Table 4), with a median value of 0.01 m3 m-3.
The sma values derived from sampling after steady-state K measurements in the field were higher than sma values from rotated core desorption procedure in the laboratory or from sma measured by image analysis. Since the water might have continued to drain from macropores after completing the K measurements, perhaps the logistics of sampling biased the results. The image analysis results would give total sma, but tortuosity and discontinuities of the observed pores would reduce the effective sma. On the other hand, visual observation probably missed some of the smaller pores.
The choice of sma to use in the MACRO model would depend on the assumed hb value. The sma data were not as variable as K data, but still might necessitate a range of sma input values.
Derived Parameters
Macropore (h)
The (h) from data Group 1 (desorption) and data Group 3 (image analysis) did not always follow the linear relationship assumed in Eq. [1] (Fig. 2)
, in which hb was assumed to be the maximum measured h value. The field desorption measurements and the image analysis results showed high (s - )/sma relative to h/hb, whereas the laboratory desorption suggested the opposite trend. The results were variable, and the data did not match model assumptions of Eq. [1]. Because of this uncertainty, a smaller assumed hb value would be recommended so that the assumptions of Eq. [1] might be met but over a smaller range.
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sma, decreased w, and increased L shown by Eq. [1], [3] to [5]. The decrease in d as assumed hb increased was less pronounced than assuming Eq. [1] would apply over the whole h range (Table 2). This showed that the data did not follow Eq. [1] over a very large range of h.
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The large range for calculated d was highly skewed. The very large d values were calculated from small measured sma values (laboratory desorption of data Group 1 and some of the image analysis data in Group 3). The small d value for field desorption was because of the large sma. The d from field desorption was in the range of the d values calculated from mobile immobile data. Both were calculated for the same Harps soil, but using different procedures. The d value is important because and Jarvis and Larsson (2001) suggest that a very small d value would be used to predict solute leaching when there is no preferential flow.
Calculated n* Values
A range of n* values was calculated. For the Harps sample of K() data of Group 1, if hb was assumed to be 60 mm, the calculated n* was 3.4, and if hb was assumed to be 150 mm, the calculated n* was 2.7. For the other samples (data Group 1), if hb was assumed to be 60 mm, the calculated n* ranged from 2.9 to >6; if hb was assumed to be 120 mm, the calculated n* ranged from 1.4 to >6 (Table 5). The MACRO model restricts the n* value to the range of 1 to 6 (Jarvis and Larsson, 2001) for unspecified reasons.
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The distribution of n* values for a whole data group of 55 measurements was only slightly skewed (Table 6) as shown by medians close to means. This compared with the highly skewed distributions of K and d values. Although some of the calculated n* values were out of the range assumed by the MACRO model, the range of n* values was still small compared with the range of values for K or d. Because the n* value is an exponent, it would be expected to have a greater impact on simulated preferential flow. Jarvis (1991) showed that predicted pesticide leaching using the MACRO model was highly sensitive to the chosen value for n*.
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SUMMARY |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARYNOTESREFERENCES |
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s, and b could be readily determined directly from laboratory and field measurements. The sma would increase and Kb would decrease as hb was increased.
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sma, ranges for these results are also included in Table 7. The data needed to calculate d are often not available. Desorption data might not be available for the wet-end. Only recently has been determined in situ rather than determined using inverse procedures and column effluent data (Clothier et al., 1992; Jaynes et al., 1995). Image analysis is not routinely performed, and specialized software is usually needed to process the data. Very small sma values resulted in very large calculated d values. Conversely, large sma values resulted in very small d values. The fitted n* exponent could be determined either from K() or K(h) data, but K(h) data is often more available. The n* increased as hb increased (Table 6).
In this study, choosing an hb of 30 mm produced the most consistent results. The calculated d values were very small when a larger hb (smaller w) was fitted or selected. Larger assumed hb values resulted in fitted n* values that were >6 (the largest value allowed by MACRO), and the linear relation between h and for gravity flow was not always valid beyond an assumed hb of 30 mm.
In contrast, others have assumed hb values ranging between 100 and 500 mm (Jabro et al., 1994; Saxena et al., 1994; Larsson and Jarvis, 1999a, b). Based on their assumed hb values, they measured sma ranging from 0.01 to 0.13 m3 m-3, Ks ranging from 0.1 to 2040 mm h-1, and Kb ranging from 0.1 to 0.9 mm h-1. They calibrated d values ranging between 50 and 300 mm. These large d values should not occur simultaneously with the large sma values assumed.
The paper described results of several procedures that could be used to independently measure some of the preferential flow parameters for the MACRO model, specifically n*, sma, Kb, and d. Data for Des Moines lobe soils were used as examples. Similar types of analyses could be completed for other soils and for other models, taking into account the assumptions of each preferential flow model. Although the derived data would depend on model assumptions, the measured data would be the same and could include K at a range of h or values near saturation, and a measure of macroporosity from desorption or from image analysis. It is suggested that a data base could be created for macropore region properties, to complement data bases for soil matrix properties.
APPENDIX
List of Variables
, solute exchange coefficient between domains
ß, geometry coefficient
, surface tension
s, saturated soil water content
sma, maximum soil water content in the macropore region
b, boundary soil water content or maximum soil water content in the micropore region
l, density of liquid
a, density of air
a, wetting angle
d, half spacing between equivalent parallel fractures
D0, diffusion in free water
D*m, effective diffusion coefficient
Dv, dispersivity
f*, impedance factor
g, acceleration due to gravity
hb, absolute value of hydraulic head at the boundary between the macropore and micropore domains
Kb, hydraulic conductivity at the boundary between macropore and micropore domains.
Ks, saturated hydraulic conductivity
L, length of fracture
n*, exponent for K- relation in the macropore region
N, number of fractures in cross sectional area
v, pore water velocity
w, mean width of fractures
Image Analysis Procedure
Background description of image analysis terminology and process are discussed in Protz et al. (1987), Moran et al. (1989), and Thompson et al. (1992). For this study the final image was 512 by 480 pixels; therefore, each sheet was analyzed by sections, usually with six to eight sections per plastic sheet. No attempt was made to include the total marked plastic sheet within the combined digitized images, but all the scanned sections were the same size. There were multiple sheets at each depth, so the total number of sections was between 16 and 24 for each depth. Each section was video-taped. The tapes were digitized using a DT-2851 image board1 and IRIS software (Digital Translation). The pixel size was 1 by 0.75 mm because of the aspect ratio of 4:3. The software had callable functions that could be used with C programming language. Segmentation (separating into binary: pore and nonpore) was automated by determining the histogram and delineating between pore and background according to a break in the histogram. This was possible because the original image was good quality, having originated as binary markings on a plastic sheet. All further analysis was done on binary files.
The general automated image analysis procedure used to determine the size of the pores was a scanning routine of the image to find the pore, then finding the eight-connected edge of the pore. The maximum and minimum diameters of the pore were determined, and the area was calculated assuming an oval shape. The x- and y- coordinates of the center of the pore mass were also recorded to join pores divided along edges. After recording data in a file, the pore was changed to background to prevent being scanned again. The scanning was continued until all pores had been measured. Then the pore number and total area were determined by class size.
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NOTES |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARYNOTESREFERENCES |
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Received for publication March 27, 2001.
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