Sensitivity of fractal parameters of soil aggregates to different
management practices in a Phaeozem in central Argentina
R.R. Filgueira
a,*, L.L. Fournier
a, G.O. Sarli
a, A. AragoÂn
a, W.J. Rawls
baFacultad de Ciencias Agrarias y Forestales, Universidad Nacional de La Plata, Calles 60 y 119, 1900 La Plata, Argentina bUSDA/ARS/NRI/HL, Bldg. 007, Rm. 108, BARC-West, Beltsville, MD 20705, USA
Received 12 November 1998; received in revised form 1 July 1999; accepted 25 August 1999
Abstract
Changes in soil structure often accompany changes in management practices and may affect the effectiveness of these practices. Parameters are needed to quantify these changes. Our objective was to see if fractal dimensions derived from `aggregate bulk density±aggregate size' and `aggregate number±aggregate size' relationships could be applied to quantify such changes. The study was conducted at the Experimental Farm of the School of Agronomy and Forestry Engineering, National University of La Plata, Argentina. A Vertic Phaeozem soil was sampled at seven locations differing in long-term management practices. The `aggregate bulk density±aggregate size' and `number of aggregates±aggregate size' data were obtained for seven ranges of aggregate sizes. Differences in treatments were re¯ected by the fragmentation fractal dimension but not the mass fractal dimension. The lowest fragmentation fractal dimensions corresponded to plots under long-term no-tillage and the highest to plots with a history of cultivation of rice (Oryza sativaL.) under water. The fragmentation fractal dimension re¯ected the differences in soil management whereas the mass fractal dimension appeared to be insensitive to those differences.#1999 Elsevier Science B.V. All rights reserved.
Keywords:Soils; Structure; Fractal dimension; Fragmentation; Aggregation; Tillage
1. Introduction
Changes in soil structure often accompany changes in management practices and may affect the effec-tiveness of these practices. Parameters are needed to quantify these changes. Soil aggregate composition has been found to be a good indicator of changes in soil structure. Several parameters were proposed to
condense information on aggregate mass or numbers distributions. Van Bavel (1949) and Mazurak (1950) used the mean weight diameter (MWD) and the geo-metric mean diameter (GMD), respectively. The use of GMD was supported by the observation that many dry aggregate size distributions gave a straight line when plotted on log probability paper (Gardner, 1956).
Recently, fractal geometry has become a useful tool in quantifying scale-dependent soil properties such as aggregate mass, particle mass, soil particle surface, surface roughness, hydraulic conductivity, etc. (GimeÂ-*Corresponding author. Tel.: 54-21-833658; fax:
54-21-252346
E-mail address: [email protected] (R.R. Filgueira)
nez et al., 1997; Baveye et al., 1998). Fractal geometry recognizes that natural objects often have similar features at different scales and that measures of these features, such as number, mass, length, and surface area, depend on the scale of observation and measure-ment. The power laws express these dependencies.
Two types of power law scaling dependencies have been documented for soil aggregate compositions. Dependencies of aggregate bulk density on the aggre-gate size were shown to obey a power law between mass,M,and size,x:MkmxDm (0Dm3)
(Che-pil, 1950; Wittmuss and Mazurak, 1958; Baldock and Kay, 1987; Bartoli et al., 1991; Young and Craw-ford, 1991). HereDmandkmare mass fractal
dimen-sion and mass of an aggregate of unit length, respectively. The smaller the value ofDm, the greater
the scale dependency of aggregate density. Models of a fractal porous media were employed to interpret these dependencies, and the researchers concluded that the observed power laws mean that soil solid matrix is fractal (Rieu and Sposito, 1991b; Anderson and McBratney, 1995; Filgueira et al., 1997). Hence, the exponent in such power law dependencies was interpreted as the difference between 3 and the mass fractal dimensionDm.
Another power law dependence was found for the number of aggregates larger than a particular size as related to this size. Such dependence was predicted by the model of fractal fragmentation (Mandelbrot, 1982), and the fractal fragmentation was assumed to happen in soil undergoing the aggregate analysis (Bartoli et al., 1991; Perfect et al., 1992). Conse-quently, the exponent in this power law dependence was interpreted as the fragmentation fractal dimension Df.
The fractal model of Rieu and Sposito (1991a) explicitly describes the soil fragmentation as a fractal process along with formation of fractal aggregates. They proposed two fractal dimensions to characterize the fragmentation process,Dm, mass fractal dimension
of an incompletely fragmented soil, andDf, the fractal
dimension of a completely fragmented soil. In this theoretical framework, the difference among the frac-tal dimensionsDmandDfshould re¯ect the degree of
fragmentation of a soil. Recently, Perfect (1997)
developed a relationship between Dm and Df:
DfDmlog(P)/log(b), wherePis the scale
invar-iant probability of failure, andbthe scaling factor >1.
WhenP!1 the fragmentation of the soil tends to be complete andDf!Dm.
Both fractal dimensions,DfandDm, were used as
indicators of effects of soil management on soil structure. Young and Crawford (1991) explored the applicability of mass fractal dimension to quantify heterogeneity in soil as affected by tillage. They found that Dm for a soil increased from 2.75 (fallow site,
prior to cultivation) to 2.95 (same site, after rotary cultivation). Eghball et al. (1993) studied aggregate size distributions for soils subjected to four different tillage techniques (chisel, disc, no-till and plow) and two different crop sequences:corn (Zea mays L.)±
soybean (Glycine max (L.) Merr.)±corn and
soy-bean±corn±soybean. Fragmentation fractal dimension from aggregate size distributions was used to quantify differences between tillage treatments and crop
sequences. Values of Df ranged from 2.281 to
3.306. Perfect and Blevins (1997) estimated fractal parameters from ped mass-size and number-size dis-tributions for a soil with two different treatments; long-term conventional tillage and no-till. They found values of fragmentation fractal dimension,Df, varying
from 2.02 (no-till) to 2.55 (moldboard plow), and mass fractal dimension ranging from 2.88 (no-till) to 2.99 (moldboard plow followed by two passes with a disk harrow). They found signi®cant tillage effects on both mass and fragmentation fractal dimensions, and sug-gested similar studies on other soils to test the general applicability of fractal relations to soil structure.
Although both mass and fragmentation fractal dimensions were used to distinguish between soil structure under different tillage practices, no attempt was made to compare the two dimensions by their ability to re¯ect differences in long-term (decade or more) soil management. The objective of this paper was to compare the sensitivity of mass and fragmenta-tion fractal dimensions to changes in soil structure induced by the differences in crop sequences after 20 years of management.
2. Materials and methods
2.1. Experimental sites
National University of La Plata, Argentina, located at 348540S latitude and 578570W longitude. All culti-vated plots were moldboard plowed and disk har-rowed, at least twice a year. Tillage depth was around 20020 mm. The soil sample sites distances varied from around 50 m between T5 and T6, to several hundred meters apart for the others. Data on management practices, soil texture, and total organic carbon content are reported in Table 1. The T1 treatment was the least disturbed soil sample after 20 years uncultivated under natural grasses. The T2 treatment sample was taken from a border of a plot, with minor tillage disturbance, but with some traf®c of machinery. Treatment T4 underwent the following sequence: 15 years uncultivated under natural grasses, during 1992/1993 conventional tillage and cultivated with oats (Avena sativaL.) and 2 years fallow. Treat-ment T5 spent 14 years uncultivated, 1 year with oats and 3 years with corn. Treatment T6, a plot adjacent to T5, had 15 years uncultivated under grasses and 3 years corn. Treatment T7 included two periods with the following sequence: 1 year fallow, 1 year corn, and 1 year rice innundated. Shortly before sampling time it was plowed and withstood one pass with a tandem disk harrow. Treatment T3 included several years with the following sequence: 1 year rice innundated, and 2 years fallow. The last period was rice. Shortly before the sampling time, it was plowed and withstood two passes with a tandem disk harrow.
2.2. Soil samples
Soil cores (three at each location) were taken with cylinders, 75 mm in diameter, to a depth of 85 mm in the A horizon from a Vertic Phaeozem (WRB, 1994) with different long-term management practices. All
samples were allowed to dry at room temperature (258C).
Dry soil samples were sieved mechanically in a nest of sieves, in the same condition, with mesh openings of 16, 8, 4, 2, 1, 0.5, and 0.25 mm. Aggregate size distribution was determined based on the weight of soil in each class with respect to the total soil sample weight. Each fraction was weighed, and the aggregate bulk density was determined by the method of Chepil (1950). The soil fractions were poured in test tubes, and an automatic tapping device was used in order to compact them to a ®nal density. The bulk density of each fraction was calculated by multiplying by a coef®cient. The entire procedure was performed in triplicate.
2.3. Estimation of fractal parameters
The fractal dimension of soil solid matrix,Dm, was
estimated from the following equation (Rieu and Sposito, 1991a):
log i=0 Dmÿ3log di=d0; (1)
whereiis the bulk density (Mg mÿ3) of theith size class,0the bulk density of the largest aggregates,di the mean aggregate diameter (mm) of the ith size class, andd0the mean diameter of the largest
aggre-gate, respectively. The smaller the value of Dm, the
greater the scale dependency of aggregate density. The mean aggregate diameter was taken as the arithmetic mean of the upper and lower sieve sizes. To estimate the fractal dimension of the aggregate size distribu-tion, a quantity proportional to the number of aggre-gates of each size class was calculated with the equation (Rieu and Sposito, 1991b):
N di M di= di3i; (2)
Table 1
Long-term management practices, particle size distribution (g kgÿ1) and organic carbon (g kgÿ1) content of soil samples under study
Sample Management practice Clay Silt Sand Organic carbon T1 20 years uncultivated soil 242 508 250 30.1
whereM(di) is the mass (kg) of class i, i the bulk density of the aggregates of size classi,dithe mean aggregate diameter of size classi. Size class 0 contains the largest aggregates. The number of aggregates were then accumulated from the largest class to the kth class, by the following equation:
Nk
Xk
i0
N di: (3)
Finally, the fractal dimension was estimated from the equation:
NkAdÿkDf: (4)
The slope of the graph of logNkvs. logdkwasÿDf.
The statistical comparison of parameters was made using SigmaStat software from Jandel Scienti®c. The 0.05 signi®cance level was used.
3. Results and discussion
3.1. Dry aggregate distribution
Bulk densities of the aggregate classes vs. its mean diameter are reported in Table 2. As expected from the fractal theory of a soil, the general trend was the increase in bulk density of aggregates with the decrease in their mean diameter. The density increase rate is higher for the smallest aggregates. Some incon-sistency in the bulk densities values obtained in the mean diameter range 0.375±1.5 mm could be attrib-uted to an experimental error of the Chepil's method. This will be further studied in the future.
3.2. Fractal dimensions
Table 3 contains fractal dimensions found when Eqs. (1) and (4) have been applied to each soil data set. Fragmentation fractal dimensions were signi®cantly affected by the treatments. The lowest Df
corre-sponded to the site T1 which was uncultivated for 20 years and had well-developed soil structure. Next was the T2 treatment, a soil site seldom disturbed and only occasionally traf®cked by tractors. In the T4 treatment, 2 years of conventional tillage and cultiva-tion after 15 years of no cultivacultiva-tion seemed to destroy the structure to a major extent. The structure was not recovered after 2 years fallow. Sites T5 and T6 had similar treatments; 3 years conventional tillage and cultivation of corn, with T5, having one additional year of oats. Fractal dimensions estimated for these
Table 2
Bulk density (Mg mÿ3) of aggregate size classes and mean aggregate diameter (mm) at long-term management sitesa
Site Mean aggregate diameter (mm)
12 6 3 1.5 0.75 0.375 0.125
T1 1.01 (4.10) 1.11 (6.31) 1.15 (8.38) 1.18 (0.69) 1.21 (3.42) 1.21 (2.56) 1.45 (3.48) T2 0.97 (1.60) 1.09 (10.10) 1.19 (4.18) 1.26 (10.70) 1.23 (7.50) 1.27 (13.36) 1.51 (3.94) T3 1.08 (10.26) 1.25 (2.40) 1.22 (1.25) 1.35 (2.59) 1.32 (0.44) 1.34 (1.73) 1.67 (3.80) T4 1.08 (4.90) 1.16 (1.25) 1.14 (7.59) 1.25 (6.82) 1.29 (2.05) 1.31 (3.43) 1.64 (0.46) T5 1.16 (6.80) 1.24 (1.67) 1.28 (3.92) 1.38 (1.87) 1.32 (1.32) 1.33 (3.86) 1.59 (1.70) T6 1.16 (1.83) 1.29 (4.60) 1.33 (6.93) 1.42 (7.76) 1.38 (9.79) 1.41 (9.05) 1.61 (3.33) T7 1.09 (2.86) 1.23 (3.68) 1.24 (3.42) 1.34 (1.93) 1.36 (2.90) 1.41 (5.33) 1.65 (3.49)
aSee Table 1 for treatment descriptions. Coefficients of variation are in parentheses.
Table 3
Results of the fractal scaling application to the data on aggregate bulk density and number of aggregates for soils from seven sites under different long-term managementa
Treatment Mass fractal dimension (Dm)
Fragmentation fractal dimension (Df)
Difference (DmÿDf)
T1 2.935a 2.284a 0.651 T2 2.918a 2.494b 0.424 T3 2.924a 2.854c 0.070 T4 2.919a 2.633b,d 0.286 T5 2.944a 2.736c,d 0.208 T6 2.941a 2.653b,d 0.288 T7 2.921a 2.849c 0.072
aSee Table 1 for treatment descriptions. Parameters followed by
sites had similar values. Sites T3 and T7 were innun-dated several times and had the largest values ofDf.
The determination coef®cients, R2, of the linear regressions (from Eq. (4)) were high and ranged between 0.992 and 0.998. This indicates that power law scaling is appropriate for number-size distribution data, and that the applicability of a fractal model is possible.
Mass fractal dimensions were not good indica-tors of changes in soil structure due to imposed differences in management. They varied in narrow ranges and did not differ signi®cantly. We obtained similar results using data of Eghball et al. (1993). Values ofDmvaried in the narrow range from 2.894
to 2.907 although treatments were distinctly different. Filgueira et al. (1997) found values of mass fractal
dimension, Dm, that varied in a similar narrow
range, from 2.919 in no-till to 2.955 in conventional tillage.
It is possible that the relationships betweenDmand
aggregate size are not close enough, and the variance of the values ofDmis too large to observe differences.
Indeed, R2 values for log(aggregate bulk density)± log(size) regressions ranged from 0.810 to 0.945. This range is similar to ranges found by other authors. Rieu and Sposito (1991b) determined the fractal dimension, Dm, using Eq. (1), with data reported by Chepil (1950),
and found that theR2varied between 0.78 and 0.92. We estimated values ofDmfrom the data of Eghball et
al. (1993) and foundR2values ranging from 0.79 to 0.88. Values of the aggregate bulk density varied moderately. Variation coef®cients of bulk density values for the same aggregate size were between 0.5% and 13% (Table 2) and did not show any relation to the aggregate size. Therefore, the variability of bulk density should not be a reason for the aforementioned relatively low correlations. It is possible that the theoretical framework developed by Rieu and Sposito (1991a) is not accurate enough to explain the distribu-tion of bulk density of aggregate fracdistribu-tions vs. size of the aggregates.
Mass fractal dimensions were shown to be affected by the soil texture. Rieu and Sposito (1991b) found Dmvalues of 2.95, 2.91, and 2.88 for soils having clay,
silt loam, and ®ne sandy loam, respectively. Brake-nsiek and Rawls (1992) and Rasiah et al. (1993) demonstrated that the content of clay and sand parti-cles in soil could be used to predict fractal dimensions
in pore number vs. size and aggregate mass vs. size dependencies. Although we observed signi®cant dif-ferences in texture among the treatments (Table 1), our values ofDmwere in the narrow range from 2.918
to 2.944 with no clear trends related to the texture (Table 3). It is possible that long term soil manage-ment affects aggregate mass scaling more than soil texture does.
The differences between mass fractal dimension and fragmentation fractal dimension indicate the degree of fragmentation. When the difference is lower the degree of fragmentation is higher (Rieu and Spo-sito, 1991b; Perfect, 1997). Table 3 shows that the largest differences were found at the 20 years uncul-tivated site, T1, with a well developed structure and at the T2 treatment, a soil site seldom disturbed. The more disturbance introduced by the soil management, the more complete is the fragmentation process, revealed by an increasing value ofDf.
The differences in the values of the fragmentation fractal dimension can be inferred from the role of biological processes in soil structure formation. Inor-ganic and relatively persistent orInor-ganic binding agents are important for the stabilization of
microag-gregates (<0.25 mm diameter). Microaggregates
subsequently are bounded together into macroaggre-gates (>0.25 mm in diameter) by a variety of primary organic mechanisms (e.g., Muneer and Oades, 1989; Miller and Jastrow, 1992). The hyphae of both mycor-rhizal and saprophytic fungi are important agents that, along with ®brous roots, bind soil particles and micro-aggregates into larger, aggregated units. Recent dis-coveries of copious production of glycoprotein (glomalin) by arbuscular mycorrhizal fungi led to the comparison between concentration of glomalin and aggregate stability (Wright and Upadhyaya, 1998). After total or partial destruction by innundation or mechanical agents, the hyphae, and fungi colonies themselves, may take several years to recover and improve again the structure of the soil (Miller and Jastrow, 1992). This might be the case in our experi-ments, since the higher fragmentation fractal dimen-sion corresponded to soil sites cultivated with innundated rice in which the destruction of fungi colonies was presumably complete. On the opposite, the lowerDfvalues were found in soils with no-till or
4. Conclusions
Estimates of the mass fractal and the fragmentation fractal dimensions were made from soil aggregate composition data. The sensitivity of these dimensions were compared with differences in long-term manage-ment of the same soil. The fragmanage-mentation fractal dimension re¯ected the differences in soil manage-ment whereas the mass fractal dimension appeared to be insensitive to those differences.
Acknowledgements
The National Research Council of Argentina (CONICET), the National University of La Plata (UNLP), CampodoÂnico Foundation (La Plata) and ARS-USDA supported this study. Discussions with Dr. Ya. Pachepsky were helpful during the preparation of the manuscript.
References
Anderson, A.N., McBratney, A.B., 1995. Soil aggregates as mass fractals. Aust. J. Soil Res. 33, 757±772.
Baldock, J.A., Kay, B.D., 1987. Influence of cropping history and chemical treatments on the water-stable aggregation of a silt loam soil. Can. J. Soil Sci. 67, 501±511.
Bartoli, F., Philippy, R., Doirisse, M., Niquet, S., Dubuit, M., 1991. Structure and self-similarity in silty and sandy soils: The fractal approach. J. Soil Sci. 42, 167±185.
Baveye, P., Parlange, J.Y., Stewart, B.A. (Eds.), 1998. Fractals in Soil Science. Adv. in Soil Sci. CRC Press, Boca Raton, FL, 377 pp.
Brakensiek, D.L., Rawls, W.J., 1992. Comment on fractal processes in soil water retention. Water Resour. Res. 28, 601±602. Chepil, W.S., 1950. Methods of estimating apparent density of
discrete soil grains and aggregates. Soil Sci. 70, 351±362. Eghball, B., Mielke, L.N., Calvo, G.A., Wilhelm, W.W., 1993. Fractal
description of soil fragmentation for various tillage methods and crop sequences. Soil. Sci. Soc. Am. J. 57, 1337±1341. Filgueira, R.R., Fournier, L.L., Sarli, G.O., Piro, A., AragoÂn, A.,
1997. AplicacioÂn de la matemaÂtica fractal a la fragmentacion de un suelo. Ciencia del Suelo (Argentina) 15, 33±36.
Gardner, W.R., 1956. Representation of soil aggregate size distribution by a logarithmic-normal distribution. Soil Sci. Soc. Am. Proc. 20, 151±153.
GimeÂnez, D., Perfect, E., Rawls, W.J., Pachepsky, Ya., 1997. Fractal models for predicting soil hydraulic properties: a review. Engineering Geology 48, 161±183.
Mandelbrot, B.B., 1982. The Fractal Geometry of Nature. W.H. Freeman, San Francisco, CA, 468 pp.
Mazurak, A.P., 1950. Effect of gaseous phase on water-stable synthetic aggregates. Soil Sci. 69, 135±148.
Miller, R.M., Jastrow, J.D., 1992. The role of mycorrhizal fungi in soil conservation. In: Mycorrhizae in Sustainable Agriculture, ASA Special Publication No. 54. Madison, WI 53711, USA, pp. 29±44.
Muneer, M., Oades, J.M., 1989. The role of Ca±organic interac-tions in soil aggregate stability: III. Mechanisms and models. Aust. J. Soil Res. 27, 411±423.
Perfect, E., Rasiah, V., Kay, B.D., 1992. Fractal dimensions of soil aggregate size distributions calculated by number and mass. Soil Sci. Soc. Am. J. 56, 1407±1409.
Perfect, E., 1997. On the relationship between mass and fragmentation fractal dimensions. In: Proc. Int. Multidiscipl. Conf. 4th World Scientific Publ., River Edge, NJ, pp. 349± 357.
Perfect, E., Blevins, R.L., 1997. Fractal characterization of soil aggregation and fragmentation as influenced by tillage treat-ment. Soil Sci. Soc. Am. J. 61, 896±900.
Rasiah, V., Kay, B.D., Perfect, E., 1993. New mass-based model for estimating fractal dimensions of soil aggregates. Soil Sci. Soc. Am. J. 57, 891±895.
Rieu, M., Sposito, G., 1991a. Fractal fragmentation, soil porosity, and soil water properties: I. Theory. Soil Sci. Soc. Am. J. 55, 1231±1238.
Rieu, M., Sposito, G., 1991b. Fractal fragmentation, soil porosity, and soil water properties: II. Applications. Soil Sci. Soc. Am. J. 55, 1239±1244.
Van Bavel, C.H.M., 1949. Mean weight-diameter of soil aggregates as a statistical index of aggregation. Soil Sci. Soc. Am. Proc. 14, 20±23.
Wittmuss, H.D., Mazurak, A.P., 1958. Physical and chemical properties of soil aggregates in a Brunizem soil. Soil Sci. Soc. Am. Proc. 22, 1±5.
WRB, 1994. World Reference Base for Soil Resources. ISSS, ISRIC, FAO.
Wright, S.F., Upadhyaya, A., 1998. A survey of soils for aggregate stability and glomalin, a glycoprotein produced by hyphae of arbuscular mycorrhizal fungi. Plant and Soil 198, 97±107. Young, I.M., Crawford, J.W., 1991. The fractal structure of soil
