Fractal description of soil fragmentation for various tillage methods and crop sequences.

Soil structure has been difficult to quantify and, at best, has been studied semiquantitatively. Fractal representation of soil fragmentation can provide an indication of soil structure. The purpose of our study was to use fractal analysis to quantify soil fragmentation under various tillage and crop sequence tmatments at different times during the growing season. We collected soil samples from four tillage treatments (established 10 yr earlier) of chisel, disk, no-till, and moldboard plow in factorial arrangement with two crop sequences of corn (ZCO m y L.)-soybean [Glycine mar (L.) Merr.]-corn (C-SC), and soybean-cornaoybean, (S-C-S) on a Sharpsburg (fine, montmorillonitic, mesic Typic Argiudoll) soil. Aggregate-size distribution was used to calculate fractal dimension (D) for each treatment. Higher D values indicate greater soil fragmentation and a soil dominated by smaller aggregates. The opposite is true for lower D values. Differences in soil fragmentation observed for tillage treatments after autumn tillage became even greater over winter. Soil fragmentation increased over autumn and winter, with D increasing in the order of plow > chisel > disk > no-till. Formation of larger soil aggregates increased during the growing season for all tillage systems. The D values for C S C were smaller than S-C-S in the no-till, indicating that the previous year's corn in CS-C provided more large aggregates. Soybean appears to have negative effects on large-aggregate formation in no-till. Aggregate densities, averaged across tillage and crop sequence, increased from 1.25 to 1.77 Mg m-' as the aggregate diameter decreased from 6.38 to 0.162 mm. Fractal analysis was found to be useful in determining soil fragmentation differences due to different tillage methods and crop sequences. T" E DISTRIBUTION OF AGGREGATES of different sizes, abbreviated to aggregate-size distribution, is a consequence of soil structure and is a potentially useful way of expressing structure quantitatively. Fractal analysis, which is based on self-similarity (the manner in which variations on one scale are repeated at another), has been applied to soil since soil is both a fragmented material and a porous medium (Mandelbrot, 1983; Tyler and Wheatcraft, 1989; Rieu and Sposito, 1991a). Fractal representation of soil is based on pore-space and particle-size distribution, which are useful ways of quantifying soil structure. In this representation, the fractal dimension is an indicator of soil fragmentation and subsequently of soil structure. Rieu and Sposito (1991a) mathematically developed two fractal dimensions for the soil system based on the degree of soil fragmentation. These are D,, the USDA-ARS, Dep. of Agronom Univ. of Nebraska, Lincoln, NE 68583. Contribution of the ~ D A A R S in cooperation with the Nebraska Exp. Stn., Lincoln, NE, as Paper no. 9909. Received 3 Dec. 1992. 'Corresponding author. Published in Soil Sci. Soc. Am. J. 57:1337-1341 (1993). bulk fractal dimension of an incompletely fragmented soil system, and D, the fractal dimension of a completely fragmented soil or a soil whose aggregate-size distribution is being measured. A soil with clusters of size-scaled, similar partial volumes separated from one another by a network of size-scaled similar fractures is considered to have complete fragmentation (Rieu and Sposito, 1991a). Incomplete fragmentation is the case where there are interaggregate bridges in the fractures holding the aggregates together. According to Rieu and Sposito (1991a), the fractal dimension in soil is expected to be < 3 since a solid volume with no porosity would have a dimension of 3. Perfect and Kay (1991), however, indicated that the D value determined from aggregate-size distribution is a measure of soil fragmentation and showed that it can be as high as 3.5. Generally, improving the structure of a soil would result in the formation of larger aggregates and a decrease in the soil fractal dimension. Soil structure is difficult to quantify and has often been presented and discussed semiquantitatively, i-e., geometric mean diameter (Fahad et al., 1982). The purpose of this study was to quantify soil fragmentation, as an indicator of soil structure, for various tillage methods and crop sequences at different times during the growing season using fractal analysis. MATERLALS AND METHODS Aggregate-Size Distribution A tillagexrop sequence experiment was started in 1978 at the University of Nebraska, Rogers Memorial Farm, near Lincoln, NE, on a Sharpsburg soil. The tillage treatments were chisel, disk, no-till, and plow in a randomized complete block with six replicates. Continuous corn was planted on the experimental area through 1984. In 1985, each tillage plot was divided into four subplots (23 m long by 4.6 m wide each) to which four crop sequences were assigned. The crop sequences were C-C-C, C-S-C, S-C-S, and S-S-S. This made the experiment a split plot in a randomized complete-block design with tillage as the main plot and crop sequence as the subplot. Plow and chisel treatments were applied in the autumn and disk treatment was applied in the spring. All tilled treatments were disked in the spring prior to planting. Corn was planted on 2 May 1988 and 3 May 1989 and soybean was planted on 14 May in both years. Plots were under rainfed conditions. Weeds were controlled by herbicides in the no-till and by herbicides and cultivation in the tilled treatments. In 1988 and 1989, soil samples were collected from the four tillage and two crop sequence (C-S-C and S-C-S) treatments (six replicates) for determination of aggregate-size distribution. SoyAbbreviations: C-S-C, corn-soybean4orn sequence; S-C-S, soybean4orn-soybean; C-C-C, corn-corn-corn; S-S-S, soybean-soybean-soybean. 1338 SOIL SCI. SOC. AM. J., VOL. 57, SEPTEMBER-OCTOBER 1993 bean was growing in C-S-C and corn in S-C-S in 1988 .while these were reversed in 1989. Three soil subsamples were taken from each plot with a bulk hand sampler, 108-mm i-d., to a depth of 80 mm and processed for aggregate-size distribution individually. Soil samples were collected at precultivation (Day 158), flowering (both crops, Day 205), physiological maturity (both crops, Day 256) and post autumn-tillage (Day 303) in 1988 and at prespring-tillage (Day 98), emergence (Day 144), and physiological maturity (Day 265) in 1989. Soil samples were stored in double plastic bags in a cold room at 4 OC constant temperature before determining aggregate-size distribution. The soil samples were spread on a shallow aluminum plate (230-mm diam.) and air dried in a glasshouse. After air drying, =750 g of soil aggregates were separated by shaking the samples on nine sieves with different sized openings (16, 8, 4.76, 4, 2, 1, 0.5, 0.25, and 0.074 mm) for 30 s. This was found to be the best shaking time to ensure passage of aggregates through the sieve openings and to minimize aggregate disruption (Calvo, 1991). Aggregates on each sieve were collected and weighed. Soil samples were taken from three replicates of the tillage and crop sequence treatments in the spring of 1990 and were used to determine the density (u, Mg m-3) of aggregates in different size classes. The samples were sieved to the same size classes as above and the density of each aggregate-size class was determined based on the bulk density method described by Chepil (1950). Aggregate density was determined for all size classes except aggregates of 8 and < 0.074 mm in diameter. Aggregate density was assumed to be similar for all sampling times.