Different Soil Particle-Size Classiﬁcation Systems for Calculating Volume Fractal Dimension—A Case Study of Pinus sylvestris var. Mongolica in Mu Us Sandy Land, China

: Characterizing changes in the soil particle-size distributions (PSD) are a major issue in environmental research because it has a great impact on soil properties, soil management, and desertiﬁcation. To date, the use of soil volume fractal dimension ( D ) is a feasible approach to describe PSD, and its calculation is mainly dependent on subdivisions of clay, silt, sand fractions as well as different soil particle-size classiﬁcation (PSC) systems. But few studies have developed appropriate research works on how PSC systems affect the calculations of D . Therefore, in this study, topsoil (0–5 cm) across nine forest density gradients of Pinus sylvestris var. mongolica plantations (MPPs) ranging from 900–2700 trees ha –1 were selected in the Mu Us sandy land, China. The D of soil was calculated by measuring soil PSD through fractal model and laser diffraction technique. The experimental results showed that: (1) The predominant PSD was distributed within the sand classiﬁcation followed by clay and silt particle contents, which were far less prevalent in the study area. The general order of D values ( D s) was USDA (1993) > ISO14688 (2002) > ISSS (1929) > Katschinski (1957) > China (1987) > Blott & Pye (2012) PSC systems. (2) D s were signiﬁcantly positively related to the contents of clay and silt, and D s were signiﬁcantly negatively to the sand content. D s were susceptible to the MPPs establishment and forest densities. (3) D s of six PSC systems were signiﬁcantly positive correlated, which indicated that they not only have difference, but also have close connection. (4) According to the fractal model and descriptions of soil fractions under different PSC systems, reﬁning scales of clay and sand fractions could increase D s, while the reﬁning scale of silt fraction could decrease D s. From the conclusions above, it is highly recommended that USDA (1993) and Blott & Pye (2012) PSC systems be used as reliable and practical PSC systems for describing and calculating D of soil PSD. The conclusions

was successful in combating desertification in Yulin City, Shaanxi Province, which is situated on the southern Mu Us Sandy Land since the mid-1950s [19]. Moreover, in these regions, frequent and intense wind erosion drastically changes soil PSD [32]. MPPs protect sand land surfaces, thus soil PSD and D would be affected and also vary with forest densities.
The purposes of this research were: (i) to take examples of MPPs to determine the differences of six PSC systems including China (1987), Katschinski (1957), USDA (1993), ISSS (1929), ISO14688 (2002), and Blott & Pye (2012) of characterizing the PSDs and calculate Ds; (ii) to examine the relationship between six PSC systems; (iii) to determine the sensitivities to the changes of D calculated by six PSC systems in order to discuss the applicability of these PSC systems.

General Situations of Study Region
The study site lies in the Rare Psammophytes Protection Botanical Base which located in Mu Us Sandy Land, has a semi-arid continental monsoons climate ( Figure 1). Average precipitation is 400 mm, annual mean temperature is 8.7 • C and mean evaporation is of 1950 mm [33]. The landscape is characterized by fixed sandy land, soil pH is 7.4 [18]. The natural vegetative cover consists mostly of low shrubs such as Caragana korshinskii and Hedysarum scoparium [19]. The enhanced surface warming in drylands can be explained by surface processes, which are suspected to soil erosion processes [19]. Thereby enabling MPPs to act as a barrier to soil and wind erosion, and have great impact on surface processes. these regions, frequent and intense wind erosion drastically changes soil PSD [32]. MPPs protect sand land surfaces, thus soil PSD and D would be affected and also vary with forest densities. The purposes of this research were: (i) to take examples of MPPs to determine the differences of six PSC systems including China (1987), Katschinski (1957), USDA (1993), ISSS (1929), ISO14688 (2002), and Blott & Pye (2012) of characterizing the PSDs and calculate Ds; (ii) to examine the relationship between six PSC systems; (iii) to determine the sensitivities to the changes of D calculated by six PSC systems in order to discuss the applicability of these PSC systems.

General Situations of Study Region
The study site lies in the Rare Psammophytes Protection Botanical Base which located in Mu Us Sandy Land, has a semi-arid continental monsoons climate ( Figure 1). Average precipitation is 400 mm, annual mean temperature is 8.7 °C and mean evaporation is of 1950 mm [33]. The landscape is characterized by fixed sandy land, soil pH is 7.4 [18]. The natural vegetative cover consists mostly of low shrubs such as Caragana korshinskii and Hedysarum scoparium [19]. The enhanced surface warming in drylands can be explained by surface processes, which are suspected to soil erosion processes [19]. Thereby enabling MPPs to act as a barrier to soil and wind erosion, and have great impact on surface processes.

Sample Plots Investigation
This study was carried out from June to August 2013. A total of 9 MPPs sample plots of 20 m × 20 m with a stand density of 900-2700 trees·ha −1 were chosen, and initial planting time was in the year of 1989. These plots were intact and thus having no human impact and interference. Within these plots, the dominant vegetation species was P. sylvestris, and understory species comprised a sparse grass-shrub layer. General information of surveyed MPP plots is presented in Table 1. For each plot, 3 topsoil samples (as reduplicates) were collected at a depth of 0-5 cm (avoid the plot edge). Additionally, sampling positions were all on the flat tops of sand dunes to eliminate the effects of microphysiognomy. Soil samples were also collected in the uncovered sandy area referred as CK.

Sample Plots Investigation
This study was carried out from June to August 2013. A total of 9 MPPs sample plots of 20 m × 20 m with a stand density of 900-2700 trees·ha −1 were chosen, and initial planting time was in the year of 1989. These plots were intact and thus having no human impact and interference. Within these plots, the dominant vegetation species was P. sylvestris, and understory species comprised a sparse grass-shrub layer. General information of surveyed MPP plots is presented in Table 1. For each plot, 3 topsoil samples (as reduplicates) were collected at a depth of 0-5 cm (avoid the plot edge). Additionally, sampling positions were all on the flat tops of sand dunes to eliminate the effects of microphysiognomy. Soil samples were also collected in the uncovered sandy area referred as CK.

Soil Fractal Model Descriptions
To identify topsoil PSD information and fractal characteristics, all soil samples were treated following the procedures which were described in the references [8,10]. Soil PSD data was generated with a laser diffraction technique by using a Malvern Instrument MS 2000 (Malvern, UK) with a measurement range of 0.01-2000 µm and a margin of error of 2%.
Tyler & Wheatacraft (1992) [5] put forward a fractal model of PSD expressed with the relationship between the cumulative volume and particle-size of the soil, the calculation of singular fractal dimension D as follows (Equation (1)): where r-soil particle-size, R i -soil particle-size of grade i, R max -greatest value of soil particle-size, V(r < R i )-volume of R i more than soil particle-size, and V T -general volume of soil particles [34,35]. The measured data have linear relationships bewteen Lg value of (V/V T ) and (R i /R max ) and carrying out linear regression analysis, the slope (k) is obtained, and D = 3 − k. The parameters of Lg value of (V/V T ) and (R i /R max ), and D were used in this study.

Soil Fractal Model Descriptions
To identify topsoil PSD information and fractal characteristics, all soil samples were treated following the procedures which were described in the references [8,10]. Soil PSD data was generated with a laser diffraction technique by using a Malvern Instrument MS 2000 (Malvern, UK) with a measurement range of 0.01-2000 μm and a margin of error of 2%.
Tyler & Wheatacraft (1992) [5] put forward a fractal model of PSD expressed with the relationship between the cumulative volume and particle-size of the soil, the calculation of singular fractal dimension D as follows (Equation (1)): where r-soil particle-size, Ri-soil particle-size of grade i, Rmax-greatest value of soil particle-size, V(r < Ri)-volume of Ri more than soil particle-size, and VT-general volume of soil particles [34,35]. The measured data have linear relationships bewteen Lg value of (V/VT) and (Ri/Rmax) and carrying out linear regression analysis, the slope (k) is obtained, and D = 3 − k. The parameters of Lg value of (V/VT) and (Ri/Rmax), and D were used in this study.

Data Processing and Statistical Analysis
All data presented in the figures and tables are average values. The One-way analysis of variance procedures (ANOVA) and Duncan test (at p < 0.05) was used to compare means of soil PSD and Ds among surveyed plots represented by different capital letters. Pearson's correlation coefficients, employing a 2-tailed test, were used to detect the relations between Ds under different PSC systems (at p < 0.01). Linear regression was used to identify the relations between Ds and soil particle fractions. Statistical analysis by using SPSS software version 21.0 (IBM Inc., Amok, NC, USA). Plotting was completed using OriginLab OriginPro 2018 software (OriginLab Inc., Northampton, MA, USA).

Soil PSD and Ds under Different PSC Systems
Soil PSD of surveyed plots under six PSC systems were classified (as shown in . In the surveyed plots, the prevailing soil PSC was the size of sand particles (>70.000%) followed by silt and clay (<4.000%) contents. Soil of this nature is classified as quartisamment (U.S. Soil Taxonomy), which is identified in semiarid regions of China.   Amount of variability as observed in P I and other plots. From P I (2700 trees·ha -1 ) to P IX (900 trees·ha -1 ), the content of clay and silt decreased, while sand content gradually increased with forest density. Compared with CK (0.000 ± 0.000%, 11.000 ± 0.000%, and 89.000 ± 0.000% for clay, silt, and sand contents under USDA (1993) PSC system), from P I (4.667 ± 1.155%, 20.000 ± 1.732%, and 75.333 ± 2.887%) to P IX (0.000 ± 0.000%, 11.333 ± 0.577%, and 88.667 ± 0.577%), clay contents were increased by 466.700% and 0.000%. Silt contents were increased by 81.819% and 3.0273%. Sand contents were decreased by 15.356% and 0.374%. Clay and silt content differed greatly between MPPs and CK.   Moreover, there were obviously differences between these two PSC systems and other four PSC systems in calculating the content of sand fractions in plots of P II , P III , P V , P VI , P VIII , and CK (p < 0.05).
Based .504, respectively. The highest D was found in P I with clay and silt contents of 4.667 ± 1.155% and 20.000 ± 1.732% and sand content of 75.333 ± 2.887% (USDA (1993) PSC system). The lowest D value corresponded to CK with clay and silt contents of 0.000 ± 0.000% and 11.000 ± 0.000% and higher sand content (89.000 ± 0.000%) (

The Relations between Ds and PSD of Sample Contents under Different PSC Systems
The results of Soil PSD and Ds under different PSC systems were specified, and linear regression analysis was applied to identify correlations between Ds and PSD of sample contents (in Figure 7). Results indicated that a positive linear correlation existed between Ds and clay as well as silt contents with R 2 range from 0.721 to 0.964 and 0.740 to 0.987. By contrast, Figure 7 showed a

The Relations between Ds and PSD of Sample Contents under Different PSC Systems
The results of Soil PSD and Ds under different PSC systems were specified, and linear regression analysis was applied to identify correlations between Ds and PSD of sample contents (in Figure 7). Results indicated that a positive linear correlation existed between Ds and clay as well as silt contents with R 2 range from 0.721 to 0.964 and 0.740 to 0.987. By contrast, Figure 7

Relationships between Soil Fractal Dimensions under Different PSC Systems
In order to compare these PSC systems, Pearson correlation method was applied. Soil  (Table 2). Correlation coefficients were above 0.970 (p < 0.01), which means these six PSC systems were highly correlated.

Relationships between Soil Fractal Dimensions under Different PSC Systems
In order to compare these PSC systems, Pearson correlation method was applied. Soil  (Table 2). Correlation coefficients were above 0.970 (p < 0.01), which means these six PSC systems were highly correlated.

Relationships between Forest Densities and Soil Fractal Dimensions under Different PSC Systems
To test the application of

Relationships between Forest Densities and Soil Fractal Dimensions under Different PSC Systems
To test the application of

Sensitivities of Calculation of Soil Fractal Dimensions to Different Soil PSC
To further analyze the effects of PSC systems on calculating volume fractal dimensions, results of Lg (V/VT) and Lg (Ri/Rmax) change under different PSC systems were analyzed. The variation trend indicated that refining clay and sand scales could lower slope (k) of the regression equation, then Ds increased (in Figure 9). Accordingly, Ds decreased while silt scales were refined. Among all PSC systems, Blott & Pye (2012) PSC system contained the most information comparing to the other five PSC systems.

Sensitivities of Calculation of Soil Fractal Dimensions to Different Soil PSC
To further analyze the effects of PSC systems on calculating volume fractal dimensions, results of Lg (V/V T ) and Lg (R i /R max ) change under different PSC systems were analyzed. The variation trend indicated that refining clay and sand scales could lower slope (k) of the regression equation, then Ds increased (in Figure 9). Accordingly, Ds decreased while silt scales were refined. Among all PSC systems, Blott & Pye (2012) PSC system contained the most information comparing to the other five PSC systems.

Discussion
The main approach for soil PSD analysis, textural triangle is limited by the arbitrary classification of PSD scales [36][37][38]. To date, there remains no general agreement about what PSD of sediments and other soils types attributes should be monitored and described based on different PSD scales and PSC systems, worldwide [28]. However, Katschinski (1957) PSC system has a larger range of clay scale, while ISSS (1929) PSC system has a larger range of sand scale. Apparently, fully dividing the soil fractions like clay, silt, and sand could display the most information of integrated indicators and of soil property characteristics, but the existing schemes do not contribute to a completely true logical or sufficient basis for description and comparison of soil PSD. For example, Katschinski (1957) PSC system divides the <1 μm particle into colloidal, fine, and coarse clay fraction, while USDA (1993) PSC system divides the >50 μm particle into fraction into very fine, fine, medium, coarse and very coarse sand fraction. In this study, Blott & Pye (2012) PSC system is recommended due to its sufficient subdivisions of clay, silt, and sand classes.

Discussion
The main approach for soil PSD analysis, textural triangle is limited by the arbitrary classification of PSD scales [36][37][38]. To date, there remains no general agreement about what PSD of sediments and other soils types attributes should be monitored and described based on different PSD scales and PSC systems, worldwide [28]. However, Katschinski (1957) PSC system has a larger range of clay scale, while ISSS (1929) PSC system has a larger range of sand scale. Apparently, fully dividing the soil fractions like clay, silt, and sand could display the most information of integrated indicators and of soil property characteristics, but the existing schemes do not contribute to a completely true logical or sufficient basis for description and comparison of soil PSD. For example, Katschinski (1957) PSC system divides the <1 µm particle into colloidal, fine, and coarse clay fraction, while USDA (1993) PSC system divides the >50 µm particle into fraction into very fine, fine, medium, coarse and very coarse sand fraction. In this study, Blott & Pye (2012) PSC system is recommended due to its sufficient subdivisions of clay, silt, and sand classes.
Fractal method can be applied for various disciplines like soil science, computer science and network, etc. [39][40][41][42][43][44][45][46][47]. Fractal analysis associate with laser diffraction could provide opportunity of revealing soil information [13,38,40]. Recent studies showed the Ds increased with clay and silt fractions but decreased with sand fractions following a linear trend [32,41,43], and our research results agree with the mentioned studies above. Moreover, in the previous studies, topsoil profile of vegetation solutions could obviously prevent land desertification and thus the clay and silt contents would be increased, then it usually had higher Ds [8,44]. Since accumulative fine particles like clay and silt fractions can be rapidly eroded and lost than sand fraction [18,45]. In our study, anti-desertification solutions like MPPs establishment had a considerable effect in the increase of the clay and silt fractions, also with the forest densities of MPPs increased.
Though Ds calculated by China (1987), Katschinski (1957), USDA (1993), ISSS (1929), ISO14688 (2002), and Blott & Pye (2012) PSC systems varied differently, they were highly correlated with correlation coefficients above 0.970 (p < 0.01), and great strength of correlations between Ds and forest densities (p < 0.01). The PSD prediction has been used for comparing and converting texture measurements from diverse PSC systems [2,21,27]. For instance, in the Second National Soil Surveys of China, soil textures were measured by ISSS (1929) and Katschinski (1957) PSC systems, in which the conversion from ISSS and Katschinski's to the widely used USDA (1993) PSC system [48,49]. In this study, PSD characteristics which are described by fractal method were investigated because of its simplicity and effectiveness to compare the different PSC systems. To our knowledge, a few studies have been performed with such the purpose. Therefore, the fractal method can provide a feasible way to describe the PSD and to convert the data or texture measurements from China (1987), Katschinski (1957), and ISSS (1929) schemes to the USDA (1993) and ISO14688 (2002) standards or vice versa.
Previous studies have found more clay and silt contents associated with higher fractal dimensions of PSD [1,35,36]. However, subdividing the clay, silt, and sand fractions more specifically could not simply increase or decrease D values. During our research, curve of Lg (V/V T ) and Lg (R i /R max ) changes under different PSC systems indicated that refining clay and sand scales could lower slope (k) of regression equation, then Ds became larger. Such a tendency is more obvious in Katschinski (1957) and Blott & Pye (2012) PSC systems.
In conclusion, Ds of soil PSD could provide fully information related to desertification processes and anti-desertification methods. Thus, a general consensus is urgently needed to define the proper PSC system that can more adequately describe the PSD attributes of sediments and soils and thus estimate fractal dimensions of soil PSD. By comparing among all the PSC systems, the highest significant correlations between Ds and clay, silt, and sand fractions in USDA (1993) PSC system. Blott & Pye (2012) PSC system had the most complete information regarding the subdivision of PSD, and in both of these PSC systems, Ds were still sensitive to the desertification combating processes by MPPs establishment and associated forest densities. Thus, USDA (1993) and Blott & Pye (2012) PSC systems are recommended in estimating soil structure and calculating soil fractal dimensions to keep the consistency and enhance the comparability and applicability of the relevant research results.
Ecological systems are complex, soil fractal dimensions vary because scientists chose different PSC systems, it remains a challenge to examine soil PSD information with fractal methods under different PSC systems from a larger field-scale are needed. Besides, further studies should focus on the range of particle size correlated with Ds by using networks analysis or other methods.

Conclusions
To evaluate effects of different PSC systems on calculating D. Mongolian pine plantations composed of Pinus sylvestris var. mongolica were used. By comparing top (0-5 cm) soil PSD across nine forest densities of Pinus sylvestris var. mongolica ranging from 900-2700 trees ha - (1) The major soil particle-size was distributed within the sand classification, which accounted for more than 90% of the total volume. Clay and silt particle contents were much less prevalent. Blott