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Archives of Agronomy and Soil Science

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Response of soil multifractal characteristics anderodibility to 15-year fertilization on cropland inthe Loess Plateau, China

Caili Sun, Guobin Liu & Sha Xue

To cite this article: Caili Sun, Guobin Liu & Sha Xue (2016): Response of soil multifractalcharacteristics and erodibility to 15-year fertilization on cropland in the Loess Plateau, China,Archives of Agronomy and Soil Science, DOI: 10.1080/03650340.2016.1249476

To link to this article: http://dx.doi.org/10.1080/03650340.2016.1249476

Accepted author version posted online: 18Oct 2016.Published online: 02 Nov 2016.

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Response of soilmultifractal characteristics and erodibility to 15-yearfertilization on cropland in the Loess Plateau, ChinaCaili Suna, Guobin Liua,b and Sha Xuea

aState Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau of Northwest, A & F University,Yangling, China; bInstitute of Soil and Water Conservation, Chinese Academy of Sciences and Ministry ofEducation, Yangling, China

ABSTRACTUnderstanding the influence of long-term fertilization on the multifractalcharacteristics and erodibility of soil of cultivated land on the LoessPlateau of China could help prevent soil erosion and promote thesustainable development of agriculture. We collected 27 soil samplesfrom 0 to20 cm layers of nine fertilizer treatments. Rényi spectrum (Dq)and singularity spectrum (ƒ(α)) were applied to characterize soil particle-size distribution (PSD). The multifractal parameters of capacity dimension(D0), entropy dimension (D1), Hölder exponent of order zero (α0), anderodibility K and anti-erodibility indices (aggregate state and degree)were used to determine the effect of fertilization on soil properties anderodibility. The multifractal models could characterize the PSDs in thevarious fertilizer treatments well. Treatments receiving manure hadhigher D0, D1, α0, soil organic carbon (SOC) content, aggregate stateand degree and lower erodibility. It was concluded that D0, D1, and α0could clearly discriminate among the various treatments, and the com-bined application of mineral fertilizers and organic manure greatlyimproved soil quality and structure of the cultivated land in the LoessPlateau. Furthermore, changes of multifractal parameters D0, D1, and α0,especially D1, was mainly due to the reduced soil erosion and theincrease of SOC.

ARTICLE HISTORYReceived 15 November 2015Accepted 12 October 2016

KEYWORDSFertilizer treatment;multifractal analysis;erodibility; anti-erodibility

Introduction

The Loess Plateau of China covers approximately 62.4 × 104 km2 and is known for its longagricultural history and serious soil erosion (Sun et al. 2016). China initiated the state-fundedGrain for Green project in 1999 to reduce soil erosion, and croplands with slopes greater than15° have been converted to undisturbed green land (Chen et al. 2007). Much of the area on gentleslopes, however, remains cultivated (>1.3 × 105 km2), and the soil on these cultivated lands stillerodes during the rainy season (Wei et al. 2014). The soil on the Loess Plateau is a silty loamdeveloped over loess and is classified as a Calcic Cambisol. This soil has low fertility and watercontent, and small particles can be easily eroded by water (Wang et al. 2008; Zhu et al. 2010).

Soil particle-size distribution (PSD) and aggregate-size distribution are important physical attri-butes influencing hydraulic characteristics, solution transportation, and soil erosion (Segal et al.2009; Yu et al. 2015). Characterizing the variation of soil PSD is accordingly important for under-standing and quantifying soil structure and dynamics. Soil PSD can be well characterized bymultifractal analysis (Grout et al. 1998; Paz-Ferreiro et al. 2010), and the Rényi (Dq) and singularity

CONTACT Sha Xue xuesha100@163.com State Key Laboratory of Soil Erosion and Dryland Farming on the LoessPlateau of Northwest, A & F University, Yangling, Shaanxi, China

ARCHIVES OF AGRONOMY AND SOIL SCIENCE, 2016http://dx.doi.org/10.1080/03650340.2016.1249476

© 2016 Informa UK Limited, trading as Taylor & Francis Group

(ƒ(α)) spectra are useful for obtaining precise information from PSDs (Montero 2005; Paz-Ferreiroet al. 2010; Lyu et al. 2015). The multifractal features of soil PSDs may be correlated with soilerodibility. This correlation was demonstrated by Wang et al. (2008), who reported that the rankseries of multifractal parameters (capacity dimension (D0), entropy dimension (D1) and D1/D0)among land uses were nearly opposite to that of the degree of soil erosion on the LoessPlateau. The specific study of the relationship between multifractals and soil erosion, however, israre.

Soil erodibility (K factor) can be predicted from a multi-regression equation that correlates soilproperties, including percentages of sand, silt, clay, and organic matter, for regions without naturalrunoff areas (Römkens et al. 1977). Zhang et al. (2008) pointed out that measured K and estimatedK from data of soil properties in China were strongly linearly correlated, although the calculatedvalues were systematically higher than the measured values. Anti-erodibility indices are calculatedaccording to soil particles and aggregate distributions, which are also suitable for the soil of theLoess Plateau (Xiao et al. 2014).

Multifractal characteristics and soil erodibility are associated with soil fertility (Xu et al. 2013; Lyuet al. 2015). Long-term application of organic fertilizer facilitates the accumulation of soil organicmatter, which can improve soil structure and reduce soil erodibility, content of micro-aggregateand fine-particle fractions was thus increased (Xu et al. 2013; Lyu et al. 2015), and the multifractalfeatures of soil PSDs changed. Studies of fractals and soil erosion on the Loess Plateau have mainlyfocused on changes of land use and the restoration of vegetation (Chen et al. 2007; Sun et al.2014), but information on fertilization is unavailable. We analyzed the response of the multifractalcharacteristics of soil PSD and erodibility to 15 years of fertilization on cultivated land of the LoessPlateau. The objectives were to: (1) analyze the multifractal characteristics of the PSD, (2) examinethe effects of fertilizer treatments on multifractal characteristics, soil organic carbon (SOC), anderodibility.

Materials and methods

Experimental site

This study was part of an ongoing long-term field experiment of fertilization established in 1998in the ‘Ansai National Field Scientific Observation and Research Station for FarmlandEcosystems’, Shaanxi province, China (109°19′23″E, 36°51′30″N). The station is at an altitude of1068–1309 m a.s.l. with a temperate semiarid climate, a mean annual temperature of 8.8°C andan average annual rainfall of 500 mm. The Huangmian soil, classified as a Calcic Cambisol (FAO/UNESCO/ISRIC 1988), originated from wind-deposited loessial parental material and is charac-terized by yellow particles, an absence of bedding, a silty texture, looseness, macroporosity, andwetness-induced collapsibility (Zhu et al. 2010). The initial soil properties were: SOC content of9.03 g kg−1, total N content of 0.57 g kg−1, total phosphorus (P) content of 0.63 g kg−1,available N content of 28.99 mg kg−1, available P content of 2.49 mg kg−1, rapidly availablepotassium content of 84.86 mg kg−1, pH 8.6, and soil bulk weight of 1.25 g cm−3. All of thesenutrients were determined using common method, that is, SOC was determined by the Walkleyand Black dichromate oxidation method (Nelson & Sommers 1982), total N was determinedusing the Kjeldahl method (Bremner & Mulvaney 1982), total P was determined using themolybdenum antimony blue colorimetry (Murphy & Riley 1962). Available N was alkalineKMnO4 method (Subbiah & Asija 1956), available P was extracted with 0.5 M NaHCO3 (pH 8.5)(Olsen & Sommers 1982), and available potassium was extracted with neutral 1N NH4OAc(Knudsen et al. 1982). pH was determined in water and 1N KCl (1:2.5 w/v) using an electronicpH meter with a glass electrode (WTW pH 330, WTW, Weilheim, Germany).

2 C. SUN ET AL.

Field experiment

The long-term experiment had a triplicate randomized complete block design with area for eachplot of 14 m2. Each replicate had nine treatments, including mineral fertilizers (N and P), organicmanure, different combinations of mineral fertilizers and organic manure, unfertilized bare land(BL), and an unfertilized control (CK) (Figure 1). BL had not been sowed or fertilized, and the controlplots were sowed but not fertilized. We did these various experiments in order to explore the effectof chemical and organic fertilizers applied alone or in mixture on soil properties and erodibility. It isnoteworthy that treatment with potassium fertilizer was not included in this experiment, becausethe soil on the Loess Plateau is rich in potassium content (Huang et al. 2003; Fan et al. 2005; Wuet al. 2011). N was added as urea and P as superphosphate, and the farmyard manure containedthe faeces and urine from domestic sheep. The amounts of the fertilizers applied in the treatmentsare presented in Table 1, which was recommended by local farmers could satisfy the crop growth.The experiment was under a 3-year rotation, with a sequence of Glycine max – Z. mays – Z. mays,

Figure 1. Arrangement of the three replicates of the fertilizer treatments. Mineral fertilizers were nitrogen (N) and phosphorus(P) and the organic fertilizer was farmyard manure (M). Treatments were mineral fertilizers, organic manure, differentcombinations of mineral fertilizers and organic manure, unfertilized bare land (BL), and an unfertilized control (CK).

Table 1. The amounts of fertilizer (kg ha−1) applied in the long-term experiment.

Treatments Manure N fertilizer P fertilizer

BL 0 0 0CK 0 0 0M 7500 0 0MN 7500 211.95 0MNP 7500 211.95 166.65MP 7500 0 166.65N 0 211.95 0NP 0 211.95 166.65P 0 0 166.65

N was added as urea and P as superphosphate, and the farmyard manure contained thefeces and urine from domestic sheep. The contents of organic matter, N and P in thefeces were 25.7, 0.75, and 0.54%, respectively, and the contents of N and P in the urinewere 1.4 and 0.45%, respectively.

ARCHIVES OF AGRONOMY AND SOIL SCIENCE 3

beginning with G. max in the autumn of 1998. The last crops of Z. mays (QiangSheng 101) wereseeded on 29 April 2012 at a rate of 52.5 kg hm−2. These crops were manually harvested, and theaboveground crop residues were removed in October. Other agricultural practices, such as tillingand weeding, were all conducted according to the traditional and regular practices of fieldmanagement and the methods of local farmers. Generally, mechanized tillage and soil preparationwere conducted before sowing, and manual weeding was proceeded after raining in summer.

Sampling

The soil was sampled in October 2012. Three columns from the 0–20 cm layer were randomlyexcavated at each plot using a soil drill (diameter, 4 cm) and then mixed to produce a compositesample, and finally 27 composite samples were collected. Visible plant residues were removed,and the samples were broken by hand into fragments <10 mm and air-dried at room tempera-ture. Each sample was passed through a 1-mm sieve for PSD and aggregate determination, andan aliquot was then ground to pass through a 0.25-mm sieve for the determination of SOCcontent.

Analysis of particle-size and aggregate-size distributions

Soil PSDs and aggregates were analyzed by laser diffraction using a Longbench Mastersizer 2000(Malvern Instruments, Malvern, England). For PSD determination, soil samples were pretreated with10 mL of 30% H2O2 at 72°C to destroy the organic matter and with 10 mL of 10% HCL to removecarbonates and oxides and were then soaked in distilled water for 12 h. After the distilled waterwas removed, the samples were chemically dispersed by sodium hexametaphosphate and weremechanically dispersed by ultrasonication for 30 s. For aggregate-size determination, soil sampleswere soaked in distilled water for 24 h and mechanically dispersed by ultrasonication for 5 min(Xiao et al. 2014).

Determination of SOC content

SOC content was determined by the Walkley and Black dichromate oxidation method (Nelson &Sommers 1982).

Multifractal analysis

Multifractal analysis of particle distributions over an interval of sizes I commonly uses successivepartitions of the interval in dyadic scaling down (Evertsz & Mandelbrot 1992). With a diameter L ofinterval I, dyadic partitions in k stages (k = 1, 2, 3, . . .) generate a number of cells N(ε) = 2k withdiameter ε = L × 2−k that cover the initial interval I. At every size scale ε, a number N(ε) = 2k of cellsare considered, and their respective measures, μi(ε), are supplied by the available data. The data

should also be normalized, that is,PNε

i¼1μi εð Þ¼ 1, to provide a measurement of probability. For PSDs,

μi (ε) in each subinterval of sizes was calculated from the diffraction grain-size analyzer andrepresented the relative volume of soil particles of characteristic size in the subinterval (Montero2005).

This study considered the array of particle sizes of I = [0.12, 724.44 μm], which was subdividedinto 64 subintervals Ii = [ϕi, ϕi+1], i = 1, 2, 3, . . . 64. The length of the subintervals follows alogarithmic scale, and log(ϕi+1 /ϕi) is constant, that is, the first subinterval is I1 = [0.12, 0.137], andthe last subinterval is I64 = [632.30, 724.44]. For constructing a new measure where multifractaltechniques can be applied to take advantage of the data potential, a transformation such as

4 C. SUN ET AL.

φj = log(ϕi+1 /ϕ1), for j = 1, 2, . . . 65, can create a new dimensionless interval J = [0, 3.78] partitionedinto 64 subintervals of equal length (Martı́n & Montero 2002; Wang et al. 2008). ε then has a valueof J × 2−k for k ranging from 1 to 6, that is, ε = 1.89–0.06.

The Rényi dimension, Dq, can be calculated by Hentschel and Procaccia (1983):

DðqÞ¼ 1q-1

limε!0

log½PNðεÞi¼1 μqi ðεÞ�log ε

ðq�1Þ (1)

and

D1¼ limε!0

PN εð Þi¼1 μiðεÞlog μi εð Þ

log εðq ¼ 1Þ: (2)

For multifractal measures, Dq is a decreasing function with respect to q. The most frequentlyused generalized dimensions are D0 for q = 0 and D1 for q = 1, which are termed the capacity andentropy (information) dimensions, respectively (Posadas et al. 2001; Montero 2005). D0 providesgeneral information of the PSD system; when D0 = 1, all intervals or cells would have someabundance of particle volume under successively finer partitions, whereas all subintervals areempty when D0 = 0 (Posadas et al. 2001). D1 is directly associated with the entropy of the systemand is also a measure of the heterogeneity of a PSD. A higher D1 indicates higher heterogeneity ofthe PSD (Montero 2005).

Following Chhabra and Jensen (1989), the singularity spectrum can be calculated through a setof real numbers q by:

α qð Þ¼ limε!0

PN εð Þi¼1 μiðq; εÞlog μi εð Þ

log ε(3)

and

f αð Þ¼ limε!0

PN εð Þi¼1 μi q; εð Þlog μi q; εð Þ

log ε; (4)

where μi q; εð Þ¼μi εð Þq= PN εð Þ

i¼1μiðεÞq (Evertsz & Mandelbrot 1992).

Hölder exponents of order zero (α0) quantifies the average scale of local mass density, that is, α0is the average of the singularity strength of the PSDs (Miranda et al. 2006). A high value of α0corresponds to PSDs exhibiting, on average, a low degree of volume concentration, and theopposite is also true.

The singularity spectrum, ƒ(α) provides the entropy dimension of the distorted measure μ(q, ε)and characterizes the original measure μ by analyzing the variation under successive distortionsdriven by q (Martı́n & Montero 2002). ƒ(α) is maximum when q = 0 and typically has a parabolicshape around this point.

Estimation of erodibility factor K and anti-erodibility indices

We used the K factor in the universal soil loss equation (Rejman et al. 1998) to determine soilerodibility and used the anti-erodibility indices (aggregate state and degree) proposed by Baverand Rhoades (1932) to determine soil susceptibility to water erosion.

K is calculated using SOC and soil PSD in the EPIC model (Williams et al. 1984) as:

K ¼ 0:2þ 0:3 exp½�0:0256SAN 1� 0:01SILð Þ�f g�½SIL=ðCLAþ SILÞ�0:3�1:0� 0:25C=½Cþ exp 3:72� 2:95Cð Þ�f g� 1:0� 0:7SNI=½SNIþ expð�5:51þ 22:9SNIÞ�f g; (5)

ARCHIVES OF AGRONOMY AND SOIL SCIENCE 5

where SAN, SIL, and CLA are the sand (%), silt (%), and clay (%) fractions, respectively. C is the SOCcontent (%), and SNI = 1-SAN/100.

Baver and Rhoades (1932) proposed the concept of aggregate state and degree toevaluate soil structure via the following equations:

Aggregate stateð%Þ ¼ content of > 0:05 mm micro-aggregates � content of > 0:05 mm particles

Aggregate degree ð%Þ ¼ aggregate statecontent of > 0:05 mm micro-aggregates

�100% (6)

Statistical analyses

A one-way analysis of variation (ANOVAs) was used to compare the effects of the various fertilizertreatments on the soil multifractal parameters, SOC contents, K, and anti-erodibility indices. Duncantests separated the means of these variables at P < 0.05. Redundancy analysis (RDA) was used toanalyze the relationship between multifractal parameters and soil properties and erodibility. Allstatistical analyses were conducted using R version 3.2.3 (R Core Team 2015).

Results and discussion

Multifractal analysis

The Rényi dimension spectrum, Dq, is a constant for scale-invariant distributions but changes with qfor multifractal measures (Paz-Ferreiro et al. 2010). Selected samples from three replicates of ninetreatments were calculated for −10 ≤ q ≤ 10 at steps of 0.2q (Figure 2). Dq decreased monotonicallywith a left-hand branch much more developed than the right branch, and the difference (D0 – Dq)notably increased as the absolute q grew, indicating that the PSDs were not monofractal butexhibited singular behavior.

The first and one of the most important steps in multifractal analysis is to verify the linearbehavior when fitting Equiation (3) and (4). We considered a coefficient of determination ofR2 = 0.90 as the threshold. The multifractality was consequently expressed only for a limitedrange of q moments when the ƒ(α) spectra of 27 PSDs were calculated in the range of−10 ≤ q ≤ 10 for successive 0.2 steps. The range of positive moments, Δq+, varied from 4.8 to5.6, but the range of negative moments was very narrow, Δq- = −0.8 for 1 sample, Δq- = −0.6 for 11samples, and Δq- = −0.4 for 15 samples (data not shown). The degree of multifractal scaling for thePSDs thus differed among the fertilizer treatments even though they belonged to the same class ofsoil texture.

The shape and symmetry of the ƒ(α) spectra allowed the assessment of the heterogeneity of thePSDs (Martı́n & Montero 2002; Miranda et al. 2006; Paz-Ferreiro et al. 2010). An asymmetricalspectrum corresponds to samples displaying different heterogeneities for high and low data(Martı́n & Montero 2002; Paz-Ferreiro et al. 2013). ƒ(α) spectra for nine selected samples werecharacterized by a typical concave parabolic shape but exhibited very different features of sym-metry, with high variability among the right parts of the spectra (Figure 3). ƒ(α) spectra wereasymmetrically long on the right part in M, MN, MNP, and MP and shot on the right part in BL, CK,N, and NP. The right part of a spectrum describes the distribution of low data, and the left partdescribes the distribution of high data (Paz-Ferreiro et al. 2010). The volume of soil PSDs in thevarious fertilizer treatments differed mostly in low data, and the high volume tended to be similar.The ƒ(α) spectra in M, MN, MNP, and MP had strongly asymmetrically long right parts, indicatinghigh heterogeneity in the low data of the PSDs for these treatments. The symmetry/asymmetry of amultifractal system can be indicated by the apertures of the two branches of the ƒ(α) spectrum,that is, (α0–αq+) and (αq–α0) (Montero 2005; Miranda et al. 2006). The right parts of all ƒ(α) spectra,(αq–α0), have a greater width or aperture than the left parts, (α0–αq+), and the differences between

6 C. SUN ET AL.

Figure 2. Rényi spectra Dq of 9 randomly selected samples from one of the three replicates of each treatment.

Figure 3. Singularity spectra f(α) of 9 randomly selected samples from one of the three replicates of each treatment. Points ofthe spectrum (α, f(α)) are drawn with their coefficients of determination R2 ≥ 0.90.

ARCHIVES OF AGRONOMY AND SOIL SCIENCE 7

these two parts were larger for samples from M, MN, MNP, MP, and P compared to the othertreatments, indicating that the ƒ(α) spectra in these treatments were more asymmetric, which canbe illustrated by a plot of ƒ(α)- α (Figure 3). The PSDs were thus more heterogeneous in these thanthe other treatments.

The meaning of D0, D1, and α0 was previously stated, and they represent different informationfor soil PSDs. For the 27 samples in the present study, D0 ranged from 0.88 to 0.95 (Table 2),indicating that several subintervals in the range of 0.12–724.44 μm were empty. D1 in the currentstudy was close to 1 and had a narrow range of 0.86–0.88, indicating a high degree of hetero-geneity for the PSD in all treatments (Table 2). The value of α0 in our study ranged from 0.95 to 1.12(Table 2), indicating that the volume of the PSDs was not concentrated and that the singularitybehavior of the PSDs changed after long-term fertilization.

Effects of fertilization on multifractal parameters, SOC, K, and anti-erodibility indices

Treatments of M and MNP signficantly increased D0, D1, and α0 and treatments of MN and MP alsoincreased D0, D1, and α0, but not significantly compared to CK. Soil texture, however, did not differsignificantly among the various fertilizer treatments (Table 3). Multifractal parameters were thusmore sensitive to the effect of fertilization on the PSDs than soil texture. Higher values of D0, D1,and α0 in the treatments with added manure suggested a high degree of heterogeneity and a widerange of the distribution of soil particles and indicated larger quantities of fine particles comparedto the other treatments. The quantities of fine particles were associated with soil organic matterand erosion (Wang et al. 2008; Lyu et al. 2015). High concentrations of soil organic matter and lowsoil erosion generally facilitate the improvement of soil structure and the increase of micro-aggregates and fine particles (Lyu et al. 2015) and correspondingly increase the value of multi-fractal parameters (D0, D1, and α0). This deduction can be illustrated by the significantly lower K andhigher content of SOC in M, MN, MP, and MNP compared to CK (Table 3). The content of 0.05–1 mm aggregates was significantly higher and the aggregate state was better in M than CK(Table 4).

The combined application of mineral fertilizers and organic manure facilitated the reduction ofsoil erodibility. The lower soil erodibility in M, MN, MP, and MNP was mainly ascribed to theaddition of manure. Over the long term, the application of manure significantly enhanced thelevels of soil organic matter, which in turn affected the factors that influence soil erodibility, such assoil nutrient levels, porosity, infiltration, and aggregate stability (Chen et al. 2010; Zhu et al. 2010).An et al. (2008) demonstrated that increased SOC could bind soil particles, provide a ‘spring’against mechanical deformation within and between soil aggregates and provide a matrix forhigher water absorption, which increased the soil shear strength at a given soil-water potential onthe Loess Plateau. In contrast, the long-term application of chemical fertilizer (N and P) alone

Table 2. Minimum, maximum, and mean values of selected variables for all 27 samples.

Variables Minimum Maximum Mean

Clay (%) 5.4 6.6 5.8Silt (%) 62.1 66.2 64.2Sand (%) 27.5 32.4 30.0<0.002 mm aggregate (%) 3.7 4.56 4.120.002–0.05 mm aggregate (%) 54.6 62.8 57.40.05–1 mm aggregate (%) 32.7 41.8 38.5D0 0.88 0.95 0.90D1 0.86 0.88 0.86α0 0.95 1.12 0.99Organic carbon (g kg−1) 0.5 1.1 0.8K 0.38 0.42 0.40Aggregate state (%) 3.5 13.0 8.5Aggregate degree (%) 10.7 31.7 21.9

8 C. SUN ET AL.

Table3.

Soiltexture,multifractalparameters,SO

Ccontent,andKof

thefertilizertreatm

ents.

Treatm

ents

Clay

(%)

Silt(%

)Sand

(%)

D0

D1

α0

SOC(g

kg−1 )

K

BL6.1±0.2

65.1

±1.2

28.8

±1.4

0.89

±0.00b

0.86

±0.00b

0.96

±0.00c

5.77

±0.05d

0.41

±0.00a

CK5.9±0.2

64.9

±1.1

29.2

±1.2

0.88

±0.00b

0.86

±0.00b

0.96

±0.00c

6.47

±0.03

cd0.41

±0.00a

M5.9±0.6

63.9

±1.4

30.2

±2.0

0.92

±0.03a

0.87

±0.01a

1.03

±0.08ab

9.74

±0.08a

0.39

±0.01d

MN

5.7±0.1

64.1

±0.3

30.3

±0.4

0.89

±0.01ab

0.86

±0.00ab

0.98

±0.01abc

8.98

±0.01ab

0.39

±0.00c

MNP

5.7±0.2

63.3

±1.1

31.1

±1.2

0.92

±0.03a

0.87

±0.00ab

1.05

±0.08a

8.73

±0.03b

0.39

±0.00c

MP

5.7±0.5

64.1

±1.3

30.1

±1.8

0.89

±0.01ab

0.86

±0.00ab

0.98

±0.02abc

9.32

±0.06ab

0.39

±0.01

cdN

5.7±0.2

64.4

±0.3

29.9

±0.5

0.89

±0.00b

0.86

±0.00b

0.96

±0.00c

6.27

±0.04

cd0.40

±0.00a

NP

5.8±0.1

64.8

±0.3

29.4

±0.2

0.89

±0.00b

0.86

±0.00b

0.96

±0.01bc

0.67

±0.05c

0.40

±0.00a

P5.6±0.2

63.4

±0.9

31.0

±1.0

0.89

±0.01ab

0.86

±0.00ab

0.98

±0.02abc

0.67

±0.02c

0.40

±0.01b

Differentletterswith

inacolumnindicate

sign

ificant

differencesat

P<0.05.

ARCHIVES OF AGRONOMY AND SOIL SCIENCE 9

cannot effectively improve soil structure and increase soil SOC sequestration even though it has asignificant effect on plant yield (Edmeades 2003), which may be the main reason why K was higherin N, NP, and P compared to the treatments receiving manure.

Correlation analysis of soil properties and erosion

The eigenvalues of the RDA indicated that 91.5 and 7.8% of the total variance within the responseparameters was explained by the first and second ordination axes, respectively. Factors of clay, silt,sand, erodibility, and SOC were the most influential factors driving the changes of multifractalparameters. The vectors on the RDA ordination plot suggested D0 and D1 were positively correlatedwith clay, SOC, and aggregate state and degree, α0 was positively correlated with sand and 0.05–1 mm aggregate, all multifractal parameters were negatively correlated with soil erodibility(Figure 4). The quantitative relationship between the multifractal parameters and the SOC anderodibility/anti-erodibility indices were analyzed by linear regression (Figure 5). Erodibility waslinearly correlated negatively with D0, D1, and α0 (P < 0.05). Aggregate state and degree alsopositively correlated with D1 but not significantly (P > 0.05). D0, D1, and α0 were also linearlypositively correlated with SOC (P = 0.01, 0.00 and 0.02, respectively) (Figure 6). These resultsindicated that the multifractal parameters, especially D1, were sensitive to the variability of soilerodibility and SOC in the fertilizer treatments. Many studies have proved that long-term applica-tion of organic fertilizer facilitates the improvement of soil structure and reduction of soil

Table 4. Aggregate-size distribution and anti-erodibility indices of the fertilizer treatments.

Treatments < 0.002 mm (%) 0.002–0.05 mm (%) 0.05–1 mm (%) Aggregate state (%) Aggregate degree (%)

BL 4.4 ± 0.0 59.2 ± 0.3ab 36.4 ± 0.2bc 7.7 ± 1.6ab 21.0 ± 4.3CK 4.1 ± 0.3 57.3 ± 2.2abc 38.6 ± 2.5abc 9.4 ± 3.6ab 24.0 ± 7.9M 4.0 ± 0.3 55.4 ± 0.7c 40.6 ± 1.0a 10.4 ± 1.2a 25.7 ± 3.5MN 4.1 ± 0.4 57.4 ± 2.0abc 38.6 ± 2.4abc 8.3 ± 1.9ab 21.4 ± 3.7MNP 4.0 ± 0.2 56.6 ± 0.6bc 39.4 ± 0.7ab 8.3 ± 1.0ab 21.1 ± 2.5MP 4.0 ± 0.2 56.5 ± 1.1bc 39.5 ± 1.3ab 9.4 ± 0.8ab 23.8 ± 2.4N 4.1 ± 0.4 57.8 ± 1.8abc 38.1 ± 2.2abc 8.1 ± 2.0ab 21.2 ± 4.3NP 4.3 ± 0.2 59.9 ± 2.5a 35.8 ± 2.7c 6.4 ± 2.5a 17.5 ± 6.0P 4.0 ± 0.3 56.4 ± 1.3bc 39.5 ± 1.5ab 8.6 ± 1.3ab 21.6 ± 2.8

<0.002 mm, 0.002–0.05 mm and 0.05–1 mm means <0.002 mm aggregate, 0.002–0.05 mm aggregate and 0.05–1 mmaggregate, respectively. Different letters within a column indicate significant differences at P < 0.05.

Figure 4. Biplot of the first two RDA axes between the multifractal parameters and soil texture, aggregate-size distribution,SOC, erodibility K factor and anti-erodibility indices. <0.002 mm, 0.002–0.05 mm and 0.05–1 mm means <0.002 mm aggregate,0.002–0.05 mm aggregate and 0.05–1 mm aggregate, respectively.

10 C. SUN ET AL.

Figure 5. Relationships between the multifractal parameters and erodibility, aggregate state and aggregate degree.

Figure 6. Relationships between the multifractal parameters and soil organic carbon.

ARCHIVES OF AGRONOMY AND SOIL SCIENCE 11

erodibility due to the accumulation of organic matter (Reganold et al. 1987; Edmeades 2003; Fanet al. 2005). Combining with the above discussion, changes of multifractal feature were related tothe improvement of soil structure and quality after application of manure.

Conclusions

Multifractal models could characterize the soil PSDs in the various fertilizer treatments well. Theasymmetric shapes of the ƒ(α) spectra indicated the heterogeneity of the PSDs, and long-termapplication of manure increased the heterogeneity of the PSDs. The treatments with manure hadsignificantly higher D0, D1, α0, and SOC contents but lower soil erodibility compared to the othertreatments, suggesting that the combined application of mineral fertilizers and organic manure canchange multifractal features of PSDs and improve soil quality and anti-erodibility on cropland inthe Loess Plateau of China, by contrast, application of mere mechanical fertilizer cannot. Changesof multifractal parameters D0, D1, and α0, especially D1, was mainly due to the reduced soil erosionand the improvement of SOC.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This work was supported by the National Natural Science Foundation of China [41371510,41371508,41471438]; theFoundation for Western Young Scholars, Chinese Academy of Sciences [XAB2015A05];

References

An SS, Huang YM, Zheng FL, Yang JG. 2008. Aggregate characteristics during natural revegetation on the LoessPlateau. Pedosphere. 18:809–816.

Baver L, Rhoades H. 1932. Aggregate analysis as an aid in the study of soil structure relationships. J Am Soc Agron.24:920–930.

Bremner JM, Mulvaney CS. 1982. Nitrogen-total. Methods of soil analysis, part 2, chemical and microbial properties.Madison (WI): American Society of Agronomy; p. 595–624.

Chen L, Huang Z, Gong J, Fu B, Huang Y. 2007. The effect of land cover/vegetation on soil water dynamic in the hillyarea of the loess plateau, China. Catena. 70:200–208.

Chen Y, Zhang XD, He HB, Xie HT, Yan Y, Zhu P, Ren J, Wang LC. 2010. Carbon and nitrogen pools in differentaggregates of a Chinese Mollisol as influenced by long-term fertilization. J Soil Sediment. 10:1018–1026.

Chhabra A, Jensen RV. 1989. Direct determination of the f (α) singularity spectrum. Phys Rev Lett. 62:1327–1330.Edmeades DC. 2003. The long-term effects of manures and fertilisers on soil productivity and quality: a review. Nutr

Cycl Agroecosys. 66:165–180.Evertsz CJG, Mandelbrot BB. 1992. Multifractal measures, in Chaos and fractals. New York: SpringerVerlag. New

Frontiers of Science; p. 921–953.Fan T, Stewart BA, Yong W, Junjie L, Guangye Z. 2005. Long-term fertilization effects on grain yield, water-use

efficiency and soil fertility in the dryland of Loess Plateau in China. Agr Ecosyst Environ. 106:313–329.FAO/UNESCO/ISRIC. 1988. Soil map of the world; revised legend. World Soil Resource Report, vol.60. Rome: FAO.Grout H, Tarquis AM, Wiesner MR. 1998. Multifractal analysis of particle size distributions in soil. Environ Sci Technol.

32:1176–1182.Hentschel HGE, Procaccia I. 1983. The infinite number of generalized dimensions of fractals and strange attractors.

Physica D. 8:435–444.Huang M, Shao M, Zhang L, Li Y. 2003. Water use efficiency and sustainability of different long-term crop rotation

systems in the Loess Plateau of China. Soil Till Res. 72:95–104.Knudsen D, Peterson GA, Pratt PF. 1982. Lithium, sodium, and potassium. Methods of soil analysis Part 2 Chemical and

microbiological properties. Madison (WI): American Society of Agronomy; p. 225–246.Lyu X, Yu J, Zhou M, Ma B, Wang G, Zhan C, Han G, Guan B, Wu H, Li Y, et al. 2015. Changes of soil particle size

distribution in tidal flats in the yellow river delta. PLoS ONE. 10:e0121368.

12 C. SUN ET AL.

Má M, Montero ES. 2002. Laser diffraction and multifractal analysis for the characterization of dry soil volume-sizedistributions. Soil Till Res. 64:113–123.

Miranda JGV, Montero E, Alves MC, Paz González A, Vidal Vázquez E. 2006. Multifractal characterization of saproliteparticle-size distributions after topsoil removal. Geoderma. 134:373–385.

Montero E. 2005. Rényi dimensions analysis of soil particle-size distributions. Ecol Model. 182:305–315.Murphy J, Riley JP. 1962. A modified single solution method for the determination of phosphate in natural waters.

Anal Chim Acta. 27:31–36.Nelson DW, Sommers LE. 1982. Total carbon, organic carbon and organic matter. Wisconsin: Agronomy Society of

America Madiso, Methods of Soil Analysis, Part 2. Chemical and Microbial Properties; p. 539–552.Olsen SR, Sommers LE. 1982. Phosphorus. Methods of soil analysis. Part 2. Chemical and microbiological properties.

2nd ed. Madison (WI): American Society of Agronomy; p. 403–430.Paz-Ferreiro J, Marinho MD, da Silva LFS, Motoshima ST, Dias RD. 2013. The effects of bulk density and water potential

on multifractal characteristics of soil penetration resistance microprofiles measured on disturbed soil samples.Vadose Zone J. 12:1–13.

Paz-Ferreiro J, Vázquez EV, Miranda JGV. 2010. Assessing soil particle-size distribution on experimental plots withsimilar texture under different management systems using multifractal parameters. Geoderma. 160:47–56.

Posadas AND, Giménez D, Bittelli M, Vaz CMP, Flury M. 2001. Multifractal characterization of soil particle-sizedistributions. Soil Sci Soc Am J. 65:1361–1367.

R Core Team. 2015. R: a language and environment for statistical computing. Vienna: R Foundation for StatisticalComputing. Available from: http://www.R-project.org/.

Reganold JP, Elliott LF, Unger YL. 1987. Long-term effects of organic and conventional farming on soil erosion. Nature.330:370–372.

Rejman J, Turski R, Paluszek J. 1998. Spatial and temporal variations in erodibility of loess soil. Soil Till Res. 46:61–68.Römkens M, Roth C, Nelson D. 1977. Erodibility of selected clay subsoils in relation to physical and chemical

properties. Soil Sci Soc Am J. 41:954–960.Segal E, Shouse PJ, Bradford SA, Skaggs TH, Corwin DL. 2009. Measuring particle size distribution using laser

diffraction: Implications for predicting soil hydraulic properties. Soil Sci. 174:639–645.Subbiah B, Asija G. 1956. A rapid procedure for the estimation of available nitrogen in soils. Curr Sci India. 25:259–260.Sun C, Xue S, Chai Z, Zhang C, Liu G. 2016. Effects of land-use types on the vertical distribution of fractions of

oxidizable organic carbon on the Loess Plateau, China. J Arid Land. 8:221–231.Sun W, Shao Q, Liu J, Zhai J. 2014. Assessing the effects of land use and topography on soil erosion on the Loess

Plateau in China. Catena. 121:151–163.Wang D, Fu BJ, Zhao WW, Hu HF, Wang YF. 2008. Multifractal characteristics of soil particle size distribution under

different land-use types on the Loess Plateau, China. Catena. 72:29–36.Wei W, Chen L, Zhang H, Yang L, Yu Y, Chen J. 2014. Effects of crop rotation and rainfall on water erosion on a gentle

slope in the hilly loess area, China. Catena. 123:205–214.Williams JR, Jones CA, Dyke PT. 1984. A modeling approach to determining the relationship between erosion and

productivity. T ASAE. 27:129–144.Wu F, Dong M, Liu Y, Ma X, An L, Young JPW, Feng H. 2011. Effects of long-term fertilization on AM fungal community

structure and Glomalin-related soil protein in the Loess Plateau of China. Plant Soil. 342:233–247.Xiao L, Xue S, Liu G, Zhang C. 2014. Fractal features of soil profiles under different land use patterns on the Loess

Plateau, China. J Arid Land. 6:550–560.Xu G, Li Z, Li P. 2013. Fractal features of soil particle-size distribution and total soil nitrogen distribution in a typical

watershed in the source area of the middle Dan River, China. Catena. 101:17–23.Yu JB, Lv XF, Bin M, Wu HF, Du SY, Zhou M, Yang YM, Han GX. 2015. Fractal features of soil particle size distribution in

newly formed wetlands in the Yellow River Delta. Sci Rep-UK. 5:10540.Zhang KL, Shu AP, Xu XL, Yang QK, Yu B. 2008. Soil erodibility and its estimation for agricultural soils in China. J Arid

Environ. 72:1002–1011.Zhu BB, Li ZB, Li P, Liu GB, Xue S. 2010. Soil erodibility, microbial biomass, and physical-chemical property changes

during long-term natural vegetation restoration: a case study in the Loess Plateau, China. Ecol Res. 25:531–541.

ARCHIVES OF AGRONOMY AND SOIL SCIENCE 13