Agricultural Sciences in China
2006, 5(7): 530-538
July 2006
A Fractal Method of Estimating Soil Structure Changes Under Different
Vegetations on Ziwuling Mountains of the Loess Plateau, China
ZHAO Shi-wei1, 2, SU Jing3, YANG Yong-hui2, LIU Na-na3, WU Jin-shui4 and SHANGGUAN Zhou-ping2
1
Institute of Soil and Water Conservation, Northwest A & F University, Yangling 712100, P.R.China
2
State Key Laboratory of Soil Erosion and Dryland Agriculture, Institute of Soil and Water Conservation, the Chinese Academy of Sciences,
3
College of Resources and Environment, Northwest A & F University, Yangling 712100, P.R.China
4
Institute of Subtropical Agriculture, the Chinese Academy of Sciences, Changsha 410125, P.R.China
Yangling 712100, P.R.China
Abstract
Fractal method is a new method to estimate soil structure. It has been shown to be a useful tool in studies related to
physical properties of soil as well as erosion and other hydrological processes. Fractal dimension was used to study the
soil structure in soil at different stages of vegetative succession on the Ziwuling Mountains. The land use and vegetation
types included cultivated land, abandoned land, grassland, two types of shrub land, and three types of forests. The
grassland, shrub land, and forested areas represented a continuum in vegetative succession that had occurred naturally,
as the land was abandoned in 1862. Disturbed and undisturbed soil samples were collected from ten vegetation types from
depths of 0-10, 10-20, and 20-30 cm on the Ziwuling Mountains, at a site with an elevation of about 1 500 m. Particle size
distribution was determined by the pipette method and aggregate size distribution was determined by wet sieving. The
results were used to calculate the particle and aggregate fractal dimension. The results showed that particle and aggregate
fractal dimensions varied between vegetation types. There was a positive correlation between the particle fractal dimension
and the weight of particles with diameter < 0.001 mm, but no relationship between particle fractal dimension and the other
particle size classes. Particle fractal dimension was lower in vegetated soils compared to cropland and there was no
consistent relationship between fractal dimension and vegetation type. Aggregate fractal dimension was positively
correlated with the weight of > 0.25 mm aggregates. Aggregate fractal dimension was lower in vegetated soils compared
with cropland. In contrast to particle fractal dimension, aggregate fractal dimension described changes in soil structure
associated with vegetative succession. The results of this study indicate that aggregate fractal dimension is more
effective in describing soil structure and function compared with particle fractal dimension.
Key words: soil fractal dimension, soil particle, soil aggregate, vegetation type, Ziwuling Mountains
INTRODUCTION
The internal configuration of the soil matrix is called
the soil structure. There is no objective or universally
applicable method to measure soil structure (Niewczas
and Witkowska-Walczak 2004), but soil structure is important because of its relationship with soil function.
The term soil structure is indeed a qualitative concept
rather than a quantifiable property. In general, three
broad categories of soil structure are recognized: single
grained, massive, and aggregated. The last type of struc-
Received 11 November, 2005 Accepted 1 June, 2006
ZHAO Shi-wei, Professor, Tel: +86-29-87011863, Fax: +86-29-87012210, E-mail: [email protected]
© 2006, CAAS. All rights reserved. Published by Elsevier Ltd.
A Fractal Method of Estimating Soil Structure Changes Under Different Vegetations on Ziwuling Mountains of the Loess Plateau
ture is generally the most desirable condition for plant
growth, especially at the early stages of germination
and seedling establishment (Harris et al. 1965; Hillel
1998; Kaczynskij 1963) .
The concept of aggregate stability is usually measured by the destructive action of water on aggregates.
To test aggregate stability, soil physicists generally subject samples of aggregates to artificially induced forces
designed to simulate the phenomena that are likely to
occur in the field. Aggregate stability is usually reported as the proportion of > 0.25 mm diameter water
stable aggregates remaining after wet sieving compared
with the original amount of soil. Of late, researchers
have applied aggregate fractal dimension methods to
determine aggregate stability. The fractal dimension
has been used to estimate the stability of soil structure,
and the results provide additional information that has
not been included in the traditional method for estimating the above-described aggregate stability (Filgueira
and Fournier 1999).
The resistance of soil structure to external stresses
is known as stability. Aggregate stability is especially
important in the hill and slope region of the Loess Plateau where water erosion is severe. Aggregate stability
is an indicator of vital soil function. It can be used to
assess soil quality (Seybold 2001). Aggregate size distribution has been used to analyze aggregate stability.
Other indices that have been used to analyze aggregate
stability include: mean weight diameter (van Bavel 1949),
geometric mean diameter (Mazurak 1950), coefficient
of aggregation, weighted mean diameter, change in mean
weight diameter (Flook 1978), and slaking loss
(Hammond and McCullagh 1978). Gardner reported
that the aggregates of many soils exhibit a logarithmicnormal distribution, which can be characterized by two
parameters, namely, the geometric mean diameter and
the log standard deviation (de Leenheer 1986).
Fractal dimension theory was used by Benoit and
Mandelbrot to describe several aspects of particle morphology (Mandelbrot 1967). Soil has the same
characteristics, so fractal dimension can also be used
to describe soil properties (Yoder 1936). Turcote studied the particle fractal dimensions of 21 soils and showed
that silt and clay contents were low when D > 3 (Gardner
1956). Recently, fractal geometry has become a useful tool in quantifying scale-dependent soil properties
531
such as aggregate mass, particle mass, soil particle
surface, surface roughness, and hydraulic conductivity (de Boer et al. 2000; Turcotte 1986). The heterogeneity of soil structure in relation to aggregate and
particle size distribution has been recently described
on the basis of fractal mathematics (Gime’nez et al.
1997). Literature reviews by Perfect and Kay have
shown that fractal theory has wider application and
acceptability in soil science (Mandelbrot 1977). A common application is to calculate the fragmentation fractal
dimension using aggregate-size distribution or particlesize distribution (Perfect et al. 1992). This is done by
evaluating the slope of a line produced from a double
logarithmic plot of the number of fragments (aggregates
or particles of greater size than the characteristic size
versus the characteristic size (Anderson and McBratney
1995).
The revegetation program in Northwest China has
resulted in changes in soil structure. Fractal dimension
was used as a new technique for analyzing these
changes.
The objectives of this study were: (1) to apply the
fractal method to quantify soil structure, including the
soil particle, and aggregate size distribution under vegetation restoration on Ziwuling Mountains, and (2) to
use these findings as a new method to identify changes
in fractal dimensions of soil aggregates and particles
during vegetative restoration in other parts of the Loess
Plateau, China.
MATERIALS AND METHODS
Soils
Soil samples were collected in May 2002, from 12 vegetation types in Ziwuling, Gansu Province. The area is
located in the Loess Plateau of China (35°03´-36°37´N,
108°10´-109°8´ E). The average annual precipitation is
587.6 mm. The average temperature is 7.4ºC. The soil
in this study has been classified as Huangmian soil
(Calcaric Cambisols, FAO). This soil type covers 23 000
ha in the area around the Ziwuling Mountains. The
area belongs to the hill and gully landform. The original
people had stopped farming and abandoned the region
during the period of 1862-1874. Natural vegetation
© 2006, CAAS. All rights reserved. Published by Elsevier Ltd.
532
ZHAO Shi-wei et al.
has gradually returned according to the succession
sequence: abandoned land, grass, shrub, early forest
community of Populus davidiana or Beula platyphylla,
or Platycladus orientalis, then forest community of
Quercus liaotungensis. The vegetative types are listed
in Tables 1, 2.
W ( δ > di ) = V ( δ > di ) ρ = ρA[1-( di /k) 3-D]
(1)
Where W (δ > di ) is the mass of the weight of > di ,
di is the average of the diameter of di and di+1, δ is the
yard measure, A, k are the constants to describe the
shape, scale of soil, and soil that was omitted, i.e., the
difference of ρi (soil bulk density) and ρi + 1 (soil bulk
Soil aggregate distribution
After air-drying the samples in the laboratory, the aggregate size distribution of the soil was measured using
a modification of the standard wet-sieving method. The
following size fractions were separated: > 5, 2-5, 1-2,
0.5-1, 0.25-0.5, and < 0.25 mm (Savinov 1936). A 50
g sample was placed on a set of sieves in the mechanical wet-sieving apparatus. The samples were sieved
for 10 min. After sieving, the aggregates remaining on
each sieve were washed off into funnels and dried.
density) di of the different soil particle, W0 is the sum
di = 0 from the
of soil weight in different diameter, ilim
→∞
defines, the equation can be expressed in the form:
W (δ > di ) = ρA
W0 = ilim
→∞
(2)
From (1) and (2) draw the equation:
W (δ > di ) /W0 = 1-( di /k)3-D
(3)
Where d max is the largest average diameter, W (δ >
d max ) = 0, substituting this into equation (3), we write:
Soil particle distribution
W (δ > di )/ W0 = 1-( di / d max )3-D
(4)
Soil texture was measured using the pipette method
after dispersion with sodium pyrophosphate Na4P2O7 .
Particle diameter groups were < 0.001, 0.001-0.005,
0.005-0.01, 0.01-0.05, 0.05-0.25, and > 0.25 mm.
log (ρi / p0) = (D-3) log (di / d0)
(5)
Fractal dimension calculation
The fractal dimension of the soil particle and aggregate
D, was estimated from this equation (Yang and Luo
1993; Rieu and Sposito 1991):
Where pi is the bulk density (mg m-3 ) of size class,
p0 is the bulk density of the largest aggregates, di is the
mean aggregate diameter (mm) of size class i, and d0
the mean diameter of the largest aggregates. The scale
dependency of aggregate density increases as the value
of D decreases. The mean aggregate diameter is used
as the arithmetic mean of the upper and lower sieve
sizes.
From (2) and (5) we draw the equation:
Table 1 Vegetation species on the Ziwuling Mountain
Succession
log (
Vegetation
di
d max
) = (D-3) log
W (ä < di )
W0
(6)
Cropland
Five years
Grass
Bothriochloa ischemum
Shrub
Hippophae rhamnoides, Sophora viciifdia,
Early forest
Populus davidiana, forests and shrub
Populus davidiana + Quercus liaotungensis
Quercus liaotungensis
W (ä < di )
was
d max
W0
(3-D). The statistical comparison of parameters was
made using Sigma Stat software from Jandel Scientific.
The level of significance was P < 0.05.
di
Abandoned land
Quercus liaotungensis
The slope of the graph of (
) vs.
Table 2 Basic soil properties
Vegetation succession
Field capacity (%)
Bulk density (g cm-3)
< 0.01 mm (%)
Porosity (%)
Cropland
16.253
1.398
30.956
46.321
Abandoned land
18.918
1.370
31.35
48.30
Grass
22.194
1.260
34.14
52.45
Shrub
23.546
1.138
34.28
57.06
Early forest
24.891
1.090
33.74
58.87
Quercus liaotungensis
25.014
1.035
33.41
60.94
© 2006, CAAS. All rights reserved. Published by Elsevier Ltd.
A Fractal Method of Estimating Soil Structure Changes Under Different Vegetations on Ziwuling Mountains of the Loess Plateau
533
Table 3 The distribution of soil particle (mm) ratio (%) under different vegetation types
Vegetation
1
2
3
4
5
6
7
8
9
Depth (cm)
0-50
5-15
15-25
0-50
5-15
15-25
0-50
5-15
15-25
0-50
5-15
15-25
0-50
5-15
15-25
0-50
5-15
15-25
0-50
5-15
15-25
0-50
5-15
15-25
0-50.0
5-15.0
15-25
0.25-0.05
18.12
13.91
11.17
16.29
12.28
14.83
5.96
17.87
24.00
11.15
7.30
12.79
7.64
17.88
10.17
10.99
14.56
10.53
10.19
9.53
10.02
9.18
13.49
7.60
9.69
12.92
11.92
0.05-0.01
53.51
56.52
60.82
49.89
53.13
50.55
59.90
48.39
41.96
50.54
53.73
52.68
60.25
52.67
63.67
56.38
54.31
61.40
55.93
57.48
61.73
58.04
48.45
64.16
56.89
56.41
60.27
0.01-0.005
7.03
8.09
5.30
8.12
8.03
9.60
9.19
10.19
7.69
10.80
11.10
7.41
8.95
7.32
6.34
6.90
7.68
5.17
6.78
9.36
5.76
4.20
13.75
4.21
3.23
2.43
4.08
0.005-0.001
7.82
7.19
9.26
8.51
9.51
8.32
7.81
5.81
8.02
9.67
9.73
6.93
8.08
8.92
6.96
11.20
10.93
7.73
9.55
9.20
9.19
11.26
8.89
7.80
14.07
12.28
10.89
< 0.001
13.53
14.28
13.43
17.19
17.04
16.68
17.14
17.72
18.33
17.65
16.14
20.17
15.07
13.19
12.85
14.52
12.52
15.17
17.48
14.40
13.29
17.32
15.38
16.21
16.11
15.97
12.83
1, cropland; 2, abandoned land; 3, Bothriochloa ischemum; 4, Sophora viciifdia; 5, Hippophae rhamnoides; 6, forests and shrubs; 7, Populus davidiana; 8, Populus
davidiana + Quercus liaotungensis; 9, Quercus liaotungensi.
RESULTS
The soil particle size distribution
Table 3 showed that the amount of soil particles was
largest in the 0.05-0.01 mm diameter size class. The
second largest amounts were in the < 0.01 mm and
0.25-0.05 mm diameter size classes. The 0.01-0.001
mm diameter size classes contained the least amount of
material. The ratio of < 0.001 mm to 0.005-0.001 mm
diameter particles increased with vegetation succession,
but the ratio of 0.01-0.05 mm to 0.25-0.05 mm diameter
particles decreased with vegetation succession. Soil depth
had no significant effect on the above-described trends.
Particle size distribution was affected by vegetation.
The proportion of clay-sized particles increased and
large particles decreased as vegetative succession
proceeded. Compared to cropland, the ratio of particles with diameter < 0.001 mm was 27.0% higher than
that under abandoned land, 26.7% higher than under
Bothriochloa ischemum, 30.5% higher than under
Sophora viciifdia, 11.3% higher than under Hippophae
rhamnoides, 7.3% higher than under forests and shrubs,
29.2% higher than under Quercus liaotungensis, 28.0%
higher than under Populus davidiana + Quercus
liaotungensis, and 19.1% higher than under Populus
davidiana. Compared with cropland, the ratio of particles with diameter 0.25-0.05 mm was increased by
10% under abandoned land, 67% under Bothriochloa
ischemum, 38% under Sophora viciifdia, 58% under
Hippophae rhamnoides, 39% under forests and shrubs,
44% under Quercus liaotungensis, 49% under Populus
davidiana and Quercus liaotungensis, and 47% under
Populus davidiana.
Soil particle fractal dimension
The results showed that the soil particle fractal dimension under Sophora viciifdia was higher compared
with other vegetation types and cropland. Revegetation led to an increase in the soil particle fractal
dimension. At the same time, the soil particle fractal
dimension was higher when soil texture was finer.
The soil particle fractal dimension in the surface soil
(0-5 cm) was higher than that in the 5-15 and 15-25
cm depths, except for that under cropland. Although
the soil particle fractal dimension increased from 2.66
under cropland to 2.70 under Quercus liaotungensis,
soil particle fractal dimension was not increased obvi-
© 2006, CAAS. All rights reserved. Published by Elsevier Ltd.
534
ously and there was no consistent relationship within
vegetative successions (Fig.1).
The relationship between soil particle size and
fractal dimension
The soil was fractionated into six parts (1-0.25, 0.25-
ZHAO Shi-wei et al.
0.05, 0.05-0.01, 0.01-0.005, 0.005-0.001, < 0.001 mm).
Fig.2 shows the relationship between soil particle fractal
dimension and the fraction weight. There was a positive relationship between soil particle fractal dimension
and the weight of particles with diameter < 0.001 mm,
but there was no relationship between particle fractal
dimension and the other size fractions.
Fig. 1 The fractal dimension of soil particle in different vegetations.
Fig. 2 The correlation of soil particle fractal dimension and particles in different diameters.
© 2006, CAAS. All rights reserved. Published by Elsevier Ltd.
A Fractal Method of Estimating Soil Structure Changes Under Different Vegetations on Ziwuling Mountains of the Loess Plateau
535
Table 4 The distribution of the ratio of soil water stable aggregates (%)
Vegetation
1
2
3
4
5
6
7
8
9
Depth (cm)
>5 mm
5-2 mm
2-1 mm
1-0.5 mm
0.5-0.25 mm
< 0.25 mm
0-50
5-15
15-25
0-50
5-15
15-25
0-50
5-15
15-25
0-50
5-15
15-25
0-50
5-15
15-25
0-50
5-15
15-25
0-50
5-15
15-25
0-50
5-15
15-25
0-50
5-15
15-25
0.21
1.66
0.00
17.10
23.20
12.73
44.84
29.40
12.15
23.51
31.36
8.95
34.01
44.40
14.79
20.00
29.59
23.73
33.20
26.59
10.75
33.68
17.81
22.80
28.63
38.88
40.16
1.47
3.52
0.82
6.84
8.20
3.64
14.29
11.00
10.93
7.57
10.90
6.56
9.51
5.40
3.35
14.65
11.05
7.71
15.91
15.28
9.74
11.50
18.83
6.99
14.72
9.22
8.15
2.53
3.93
2.68
7.04
10.60
8.89
11.31
10.60
11.74
9.76
12.05
7.95
9.11
5.00
5.33
11.88
8.48
7.30
18.07
11.71
9.33
16.63
21.05
9.15
12.88
8.82
7.16
7.16
9.94
8.87
12.47
13.80
15.76
7.14
12.00
12.55
13.35
10.13
14.31
8.70
5.60
6.51
12.28
9.66
8.72
10.41
12.50
20.08
11.91
11.94
12.31
9.82
8.02
8.15
10.32
12.01
14.64
9.46
10.20
12.53
5.36
9.40
11.13
10.76
7.07
13.32
7.29
6.40
7.89
8.91
6.71
10.34
5.11
6.75
11.76
5.54
5.87
7.32
6.95
8.22
6.56
78.32
68.94
72.99
47.08
34.00
46.46
17.06
27.60
41.50
35.06
28.49
48.91
31.38
33.20
62.13
32.28
34.52
42.19
17.29
27.18
38.34
20.74
24.49
41.43
26.99
26.85
29.82
1, cropland; 2, abandoned land; 3, Bothriochloa ischemum; 4, Sophora viciifdia; 5, Hippophae rhamnoides; 6, forests and shrubs; 7, Populus davidiana; 8, Populus
davidiana + Quercus liaotungensis; 9, Quercus liaotungensis.
Soil aggregate fractal dimension
Table 4 shows that the weight of aggregates with diameter < 0.25 mm decrease with vegetative succession,
whereas the weight of aggregates with diameter > 5 mm
increase. There were differences in the soil aggregate
fractal dimension between depths. Compared with
cropland, the ratio of < 0.25 aggregates was reduced
by 39.9% under abandoned land, 78.2% under
Bothriochloa ischemum, 55.2% under Sophora
viciifdia, 59.9% under Hippophae rhamnoides, 58.8%
under forests and shrubs, 77.9% under Populus
davidiana, 73.5% under Populus davidiana + Quercus
liaotungensis, and 65.5% under Quercus liaotungens.
The ratio of 2-5 mm aggregates under Quercus
liaotungensis increased by 899.1% compared with
cropland. The weight of aggregates with diameter > 5
mm increased by an even greater percentage.
The distribution of soil aggregate size is one indicator of soil structure and its ability to resist erosion. Fig.
3 showed that soil aggregate fractal dimension was higher
under cropland compared to forest and shrubs soils.
The soil aggregate fractal dimensions in the surface
soil were smaller than in subsurface soil (5-15 and 1525 cm). At the same time, there was no significant
change in the soil aggregate fractal dimension in the
15-25 cm layers, as vegetative succession preceded
from abandoned land to Quercus liaotungensis. The
results indicated that soil aggregate fractal dimension
decreased with vegetation succession. The soil aggregate fractal dimension decreased from 2.92 under
cropland, to 2.81 under abandoned land, to 2.76 under
grassland, to 2.68 under shrub land, to 2.61 under early
forest, to 2.58 under Quercus liaotungensis.
The relationship between soil aggregate fractal
dimension and the weight of > 0.25 mm aggregates
This is one indicator of soil aggregate stability and the
ability to resist water erosion. The higher value for
weight of > 0.25 mm soil aggregate shows the aggregate is more stable (Filgueira and Fournier 1999). Results in Fig.4 show that there is a negative correlation
between soil aggregate fractal dimension and the weight
of > 0.25 mm aggregates. On the basis of the result
© 2006, CAAS. All rights reserved. Published by Elsevier Ltd.
536
ZHAO Shi-wei et al.
Fig. 3 The soil aggregate fractal dimension in vegetations.
Fig. 4 The relationship between the soil aggregate fractal dimension
and the number of > 0.25 mm soil aggregate.
above, the soil structure stability has improved with
aggregate fractal dimension associated with vegetative
successions.
DISCUSSION
Soil structure exerts a major influence on the physical
processes but its description is still a challenge for
soil scientists. Methods commonly used to describe
soil structure are based on the soil fragmentation. The
application of fractal geometry to describe soil
structure, soil dynamics, and physical processes within
the soil is becoming an increasingly useful tool, which
allows for a better understanding of the performance
of the soil system (Rieu and Sposito 1991; Eghball et
al. 1993; Filgueira et al. 1999) . Our results indicate
that there is a positive relationship between soil particle fractal dimension and the weight of particles with
diameter < 0.001 mm but not with the other particle
size fractions. The study indicates that there is a positive relationship between particle fractal dimension and
soil structure stability (Huang and Zhan 2002). Although
the soil particle fractal dimension increases from 2.66
under cropland to 2.70 under Quercus liaotungensis,
the soil particle fractal dimension does not increase noticeably and there is no consistent relationship between
vegetative successions and soil structure stability,
therefore, particle fractal dimension cannot reflect
changes in soil structure associated with vegetative
succession.
The present study investigated the ability of fractal
dimension to quantify the effect of tillage on soil aggregate stability in calcareous soil in an arid region
(Pirmoradian 2004). Changes in soil structure often
accompany changes in management practices and may
affect the effectiveness of these practices. Parameters
are required to quantify these changes. Soil aggregate
composition has been found to be a good indicator of
the changes in soil structure. The fragmentation fractal
dimension can be inferred from the role of biological
processes in the soil structure formation. Inorganic and
relatively persistent organic binding agents are important for the stabilization of microaggregates (< 0.25 mm
diameter). Microaggregates are subsequently bound
together into macroaggregates (> 0.25 mm in diameter)
by different kinds of mechanisms (Wright and Upadhyaya
1998). In vegetated soils, the soil environment is more
favorable for microbial activity, so there were more
water stable aggregates in the soil with permanent vegetation compared to cropland. An aggregate analysis
indicates the occurrence of fractal fragmentation, which
describes the relationship between aggregate fractal
© 2006, CAAS. All rights reserved. Published by Elsevier Ltd.
A Fractal Method of Estimating Soil Structure Changes Under Different Vegetations on Ziwuling Mountains of the Loess Plateau
dimension and stability (Bartoli et al.1992). Our results show that the weight of < 0.25 mm aggregates
decrease and > 5 mm aggregates increase with vegetation succession. Soil aggregate fractal dimension decreases as vegetative succession progresses, which
shows that aggregate fractal dimension can reflect
changes in soil aggregate stability that occur with vegetative succession on the Ziwuling Mountains.
Soil structure stability is very important for soil
function. Aggregates have a very close relationship
with soil organic carbon that has a significant influence
on soil properties. Organic matter associated with clay
is known to be an important sink for long-term stabilized C, and the amount of C in the aggregate appears
to increase as the aggregate size increases (Balabane
and Balesdent 1992). The results in this article show
that aggregate fractal dimension, but not particle fractal
dimension, can describe the changes in the soil structure associated with the vegetative succession.
537
fractals. Austlian Journal Soil Research, 33, 757-772.
Balabane M, Balesdent J. 1992. Input of fertilizer-derived labelled
n to soil organic matter during a growing season of maize in
the field. Soil Biology and Biochemistry, 24, 89-96.
Bartoli F, Burtin G, Guerif J. 1992. Influence of organic matter
on aggregation in Oxisols rich in gibbsite or in goethite.Ⅱ.
Clay dispersion, aggregate strength and water-stability.
Geoderma, 54, 259-274.
de Boer D H, Stone M, Le vesque L M J. 2000. Fractal
dimensions of individual flocs and floc populations in streams.
Hydrological Process, 14, 653-667.
de Leenheer L. 1967. Varation in time of soil porsity and poresize distribution, general picture of a six years study on a
loam soil. Pedeologie, 17, 123-152.
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 Science Society of American Journal,
57, 1337-1341.
Filgueira R R, Fournier L L. 1999. Sensitivity of fractal parameters
of soil aggregates to different management practices in a
Phaeozem in central Argentina. Soil & Tillage Research, 52,
217-222.
CONCLUSIONS
Filgueira R R, Pachepsky Y A, Fournier L L, Sarli G O, Aragon
A. 1999. Comparison of fractal dimensions estimated from
Our results show that soil particle fractal dimension in
Hippophae rhamnoides, forests and shrubs, Populus
davidiana, Populus davidiana + Quercus liaotungensis,
and Quercus liaotungensis, is lower than that in cropland.
So particle fractal dimension cannot indicate the changes
in soil structure associated with vegetative succession.
In contrast, soil aggregate fractal dimension describes
the changes in soil structure after vegetative restoration.
Thus, soil aggregate fractal dimension is the most effective method for describing soil structure and reflecting soil function.
aggregate mass-size distribution and water retention scaling.
Soil Science, 164, 217-223.
Flook A G. 1978. The use of dilation logic on the Quotient to
achieve fractal dimension characterization of textured and
structured prowls. Powder Technology, 21, 295-298.
Gardner W R. 1956. Representation of soil aggregate size
distribution by a logarithmic-normal distribution. Soil Science
Society of American Journal, 20, 151-153.
Gime´nez D, Perfect E, Rawls W J, Pachepsky Y A. 1997. Fractal
models for predicting soil hydraulic properties: a review.
English Geology, 48, 161-183.
Hammond R, McCullagh P S. 1978. Quantitative Techniques in
Geography: An Introduction, 2nd ed. Oxford University
Acknowledgements
This study was funded by the National Natural Science
Foundation of China (90302001), CAS Knowledge Innovation (KZCX3-SW-421), and the Fund of the State
Key Laboratory of Soil Erosion and Dryland Farming
on the Loess Plateau (10501-152). Thanks are given
to the State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau for providing their
analysis.
Press, Oxford.
Harris R F, Chesters G, Allen O N. 1965. Dynamics of soil
aggregation. Advance in Agronomy, 18, 107-160.
Hillel D. 1998. Environmental Soil Physics. Academic Press,
London. pp. 101-125.
Huang G H, Zhan W H. 2002. Fractal property of soil particle
size distrbution and its application. Acta Pedologica Sinica,
39, 490-497.
Kaczynskij N A. 1963. Soil Structure. MGU Press, Moscow.
(in Russian)
Mandelbrot B B. 1977. Fractals-Form, Chance and Dimension.
References
Anderson A N, McBratney A B. 1995. Soil aggregates as mass
Freeman and Company, San Francisco, California.
Mandelbrot B B. 1967. How long is the coast of Britain? Statistical
© 2006, CAAS. All rights reserved. Published by Elsevier Ltd.
538
ZHAO Shi-wei et al.
self-similarity and fractional dimension. Science, 165, 636638.
Mazurak A P. 1950. Effect of gaseous phase on water-stable
synthetic aggregates. Soil Science, 69, 135-148.
Niewczas J, Witkowska-Walczak B. 2004. The soil aggregates
stability index (ASI) and its extreme values. Soil & Tillage
Research, 57, 369-378.
Perfect E, Rasiah V, Kay B D. 1992. Fractal dimension of soil
aggregate-size distributions calculated by number and mass.
Soil Science Society of American Journal, 56, 1407-1409.
Pirmoradian N. 2004. Application of fractal theory to qualitify
soil aggregates stability as influenced by tillage treatments.
Biosystems Engineering, 90, 227-234.
Rieu M, Sposito G. 1991. Fractal fragmentation, soil porosity,
and soil water properties:Ⅰ. Applications. Soil Science
Society of American Journal, 55, 1231-1238.
Rieu M, Sposito G. 1991. Fractal fragmentation, soil porosity,
and soil water properties:Ⅱ. Applications. Soil Science
Savinov N O. 1936. Soil Physics. Sielchozgiz Press, Moscow.
(in Russian)
Seybold C A. 2001. Aggregate stability kit for soil quality
assessments. Catena, 44, 37-45.
Turcotte D L. 1986. Fractals and fragmentation. Journal of
Geophysical Research, 91, 1921-1926.
van Bavel C H M. 1949. Mean weight-diameter of soil aggregates
as a statistical index of aggregation. Soil Science Society of
American Journal, 14, 20-23.
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.
Yang P L, Luo Y P. 1993. The characteristic of soil fractal
dimension use the weight of diameter distributions. Chinese
Science Bulletin, 38, 1986-1899.
Yoder R. 1936. A direct method of aggregate analysis of soils and
a study of the physical nature of erosion losses. Journal of
American Society Agriculture, 28, 337-351.
Society of American Journal, 55, 1239-1244.
(Edited by ZHAO Qi)
© 2006, CAAS. All rights reserved. Published by Elsevier Ltd.