Abstract
Grain size is a fundamental physical property of sediments, and its parameters are crucial indicators of the provenance, transport processes, and depositional environments. However, owing to the availability of graphic and moment method choices for the determination of grain size parameters, the associated data are characterized by inconsistencies, and these issues restrict the utilization of such data. Compared to other regions, comparative analyses of grain size parameters determined using the graphic and moment methods for aeolian sediments in the Tibetan Plateau are scant. To obtain more accurate information and optimize and integrate historical data, in the present study, sediments in the Yahecun section of the Menyuan Basin in the northeastern Tibetan Plateau were investigated. Data for the Menyuan loess show that the mean grain size, sorting, skewness, and kurtosis data obtained from the two methods can be converted using linear equations. However, differences in the descriptions following the establishment of relationships should be considered. Owing to its sedimentary characteristics, the moment method is more suitable for determining grain size parameters for the Menyuan loess. The results from the moment method indicate that the Menyuan loess originated from multiple sources involving varying dynamics, and the sediments recorded changes from a cold, dry to a warm climate.
1 Introduction
Grain size refers to the dimensions of a particle, and it is a fundamental physical property of sediments [1,2]. The grain size parameters are indicators for elucidation of the origin, transport, and environments of deposition of sediments [3,4]. Consequently, grain size parameters are widely used to characterize and distinguish sediments associated with different environments, including the aeolian, lacustrine, fluvial, and marine. For example, the 22–225 μm grain size fraction of wind-derived loess is considered the East Asian winter monsoon index [5], whereas the clay fraction reflects the extent of pedogenesis [4,6,7]. Relatedly, the mean grain size (10–63 μm) highlights the flow speed in marine sediments [8], whereas the sand content can indicate the contribution of aeolian activity to lacustrine sediments [9]. Among grain size parameters, the mean grain size (M Z), sorting (σ I), skewness (SkI), and kurtosis (K G) are most commonly utilized for the characterization of sediments. These parameters are conventionally determined using graphic and moment methods [10]. However, these methods yield data that show disparities, which limits their integration and utilization [11].
The graphic method is based on the cumulative grain size distribution curve of a sediment sample. Representative points are used to highlight cumulative percentages of defined parameters, and others are calculated using simple expressions [12]. Conversely, in the moment method, the grain size distribution frequency curves of a deposit for different grain size groups are used to synthesize central moments of variables. These enable the definition of first-, second-, third-, and fourth-order moment functions of grain size parameters, such as M Z, σ I, SkI, and K G [10]. The calculation of parameters is simpler using the graphic than the moment method, and thus, the former has been utilized more frequently in previous studies. Currently, owing to advances in computer technology, the moment method is indispensable for calculating grain size parameters in the research community because of its high sensitivity [11].
Grain size parameters for aeolian sediments from the Chinese Loess Plateau and marine sediments from the inland sea in China’s continental shelf have been compared in previous studies [11,13]. These studies revealed disparities between data for grain size parameters computed using the two methods for different environments and sediment types [1]. However, a comparative analysis of the results of grain size parameters of sediments in the Tibetan Plateau determined using the graphic and moment methods is unavailable. The Tibetan Plateau, which covers parts of Central and Southern Asia, is called “the Third Pole” because of its peculiar physical geography characteristics [14,15]. In fact, it significantly influenced the natural environment in the surrounding areas. The abundant materials transported by wind circulation and rivers across the plateau provided prominent sources of sediments for the surrounding regions [16,17,18].
The Menyuan Basin, which is in the northeastern Tibetan Plateau, is a base for the dust transportation from Central Asia and the Tibetan Plateau to the Chinese Loess Plateau and eastern plains. Thick aeolian sediments in the basin retain records on the dust transportation and wind circulation in the region [19]. In the present study, 200 loess samples from the Yahecun (YHC) section in the Menyuan Basin were analyzed. The associated data were used to explore differences and similarities between the grain size parameters of Menyuan aeolian sediments determined using the graphic and moment methods. The most appropriate method for computing grain size parameters for the sediments is highlighted, and the significance of these parameters is discussed. The present study provides an approach for highlighting the significance of grain size data for loess in the Tibetan Plateau.
2 Environmental background
The Menyuan Basin (37.05–37.99°N, 100.92–102.69°E) is located at the northeastern Tibetan Plateau (Figure 1). It extends for 172.44 km from east to west and 103.99 km from north to south, covering an area of 6,902 km2. It is partially cut across by the Qilian Mountains, and its altitude varies between 2,388 and 5,255 m, with mountains for its boundaries on three sides.
![Figure 1
Maps showing the study area and sampling locations. (a) The blue area is the extent of the Tibetan Plateau (after [42]); the yellow and orange areas represent the locations of loess deposits and deserts, respectively (modified from [43,44]); the black dashed line represents the edge of the modern summer monsoon (after [45]); the purple square is the main study area of this article, the Menyuan Basin; the image in the upper right corner is modified from [46], EAWM: East Asian Winter Monsoon; EASM: East Asian Summer Monsoon; SH: Siberian High; the base map is based on data from https://tiles.arcgis.com/tiles/P3ePLMYs2RVChkJx/arcgis/rest/services/NatGeoStyleBase/MapServer. (b) The gray area with a black line is the extent of the Menyuan Basin; the pinkish area represents the Menyuan loess; Dem data from https://srtm.csi.cgiar.org/.](/document/doi/10.1515/geo-2022-0474/asset/graphic/j_geo-2022-0474_fig_001.jpg)
Maps showing the study area and sampling locations. (a) The blue area is the extent of the Tibetan Plateau (after [42]); the yellow and orange areas represent the locations of loess deposits and deserts, respectively (modified from [43,44]); the black dashed line represents the edge of the modern summer monsoon (after [45]); the purple square is the main study area of this article, the Menyuan Basin; the image in the upper right corner is modified from [46], EAWM: East Asian Winter Monsoon; EASM: East Asian Summer Monsoon; SH: Siberian High; the base map is based on data from https://tiles.arcgis.com/tiles/P3ePLMYs2RVChkJx/arcgis/rest/services/NatGeoStyleBase/MapServer. (b) The gray area with a black line is the extent of the Menyuan Basin; the pinkish area represents the Menyuan loess; Dem data from https://srtm.csi.cgiar.org/.
The Chinese Loess Plateau, Xining Basin, Qilian Mountains, and Jiuquan-Zhangye Basin are correspondingly present in the east, south, west, and north of the basin. The Menyuan Basin is an onshore basin at the junction between the mid-latitude westerly area and the East Asian monsoon zone. The climate in the area covered by the basin is continental [19], with an average yearly precipitation of 520 mm (concentrated in July and August) and an average annual temperature of 0.5°C [20]. The basin contains wide valleys and flat areas, and its drainage is primarily linked to the Datong River, which flows from northwest to southeast. Owing to fluvial and glacial activities, numerous alluvial fans and glacial terraces were formed in the basin [21]. These alluvial fans and river and glacial terraces are covered by abundant loess deposits, and thus, the Menyuan Basin comprises diverse environments of deposition [19].
According to field observations, the Menyuan loess is concentrated in the Datong River terrace, where its thickness reaches tens of meters, and its formation is attributed to the Middle Pleistocene [19]. The YHC profile (101.70°E and 37.38°N; altitude 2,891 m) represents a typical sequence of sediments in the Menyuan Basin, and thus, it was chosen for the analysis of grain size parameters. This profile is located on a secondary terrace of the Datong River, north of the Yahecun Village, and this hand-excavated area is approximately 400 cm high (not bottomed out). The delineation of lithologies in the YHC profile is based on the structural characteristics of the sediments (Table 1, Figure 2).
Stratigraphic delineation of the YHC profile
| Depth (cm) | Stratigraphic divisions | Stratigraphic features |
|---|---|---|
| 0–82 | Topsoil (TS) | Modern brown soil with a porous structure containing a large number of plant roots and overlying vegetation of thread leaf tarragon and small tarragon |
| 82–96 | Top loess (L0) | Light brown silty soil, homogeneous structure, weakly cemented |
| 96–154 | Paleosol (S0) | Brownish-black paleosol zone, strong loamy layer, agglomerate structure, dense, and compact |
| 154–176 | Transition (LT) | Light brown weakly loamy layer with agglomerate structure and relatively firm texture |
| 176–400 | Lower loess (L1) | Light brown silty soil, uniform in texture, with obvious vertical joints, occasional white calcium nodules |
Scheme of the YHC loess-paleosol sequence. The abbreviation of the different layers is explained in Table 1.
3 Materials and methods
The top 20–30 cm of soil was removed first in the vertical direction from the surface of the YHC profile. Samples for grain size analysis were then collected from the cleaned surface to the bottom at 2 cm intervals, yielding a total of 200 samples.
Preprocessing and determination of grain sizes of samples were performed in the Qinghai Province Key Laboratory of Physical Geography and Environmental Process, Qinghai Normal University, Xining, China. A Mastersizer 2000 laser diffraction grain size analyzer (Malvern Panalytical Ltd., United Kingdom) with a range of 0.02–2,000 μm was used for the measurements. The pre-treatment process included the following [22,23]: the air-dried bulk sample was passed through a 20-mesh sieve to remove gravel; 0.3–0.5 g of the sample was then placed in a beaker, 20 mL of 10% H2O2 was added, and the mixture was boiled to remove all organic matter. Subsequently, 10 mL of 10% HCl was added to the beaker, and the mixture was heated to eliminate carbonates. The beaker was then filled with ultrapure water and kept for 12 h, and after removal of the supernatant, 10 mL of dispersant (0.05 mol/L of (NaPO3)6 solution) was added. The beaker was placed in an ultrasonic shaker for 10 min, and the retrieved sample was tested in triplicate to obtain an average using the Mastersizer 2000 analyzer.
In the present study, GRADISAT 9.1 software developed by Blott and Pye [1] was used to calculate grain size parameters using both the graphic and moment methods. The two datasets were then compared using statistical methods, such as correlation analysis, to highlight similarities and differences.
In the graphic method, φ values (Figure 3) corresponding to representative points in the cumulative grain size distribution curve (i.e., 5, 16, 25, 50, 75, 84, and 95%) are selected and used to calculate grain size parameters according to the Folk–Word equation [12] (Table 2). In contrast to the graphic method in which an incomplete range of grain size components is utilized, the overall grain size information is considered in the moment method. Consequently, in the latter, data are grouped according to grain size, and data for each component are combined to conduct a comprehensive statistical analysis [10] (Figure 3). In the present study, the Friedman moment formula (Table 2) was used to group all grains’ sizes to calculate parameters. Considering that grain sizes of sediments are commonly >0.3 μm in the YHC profile, the grain size data output was set to range from 0.3 to 2,000 μm, and the grain size group spacing was 0.127φ, yielding 100 grain sizes. Classification criteria associated with the results for the two methods are presented in Table 3 [1].
Schematic diagram of the principle of the graphic and moment methods for calculating grain size parameters (YHC100 sample as an example).
Equations for grain size parameters calculated by the graphic and moment methods
| Grain size parameter | Graphic method | Moment method |
|---|---|---|
| M Z |
|
|
| σ I |
|
|
| SkI |
|
|
| K G |
|
|
Note: φ n is the grain size at n% on the cumulative grain size distribution curve; m φi and f i are the median and frequency percentages within the grain size fraction of group i of the grain size frequency distribution curve.
Comparison of the qualitative descriptions of grain size parameters for the graphic and moment methods
| σ I | SkI | K G | |||||
|---|---|---|---|---|---|---|---|
| Physical descriptive term | Graphic method and moment method | Physical descriptive term | Graphic method | Moment method | Physical descriptive term | Graphic method | Moment method |
| Very well sorted | <0.35 | Very coarse skewed | −0.3 to −1.0 | <−1.30 | Very platykurtic | <0.67 | <1.70 |
| Well sorted | 0.35–0.50 | Coarse skewed | −1.0 to −0.3 | −1.30 to −0.43 | Platykurtic | 0.67–0.90 | 1.70–2.55 |
| Moderately well sorted | 0.50–0.70 | Symmetrical | −0.1 to 0.1 | −0.43 to 0.43 | Mesokurtic | 0.90–1.11 | 2.55–3.70 |
| Moderately sorted | 0.70–1.00 | Fine skewed | 0.1–0.3 | 0.43–1.30 | Leptokurtic | 1.11–1.50 | 3.70–7.40 |
| Poorly sorted | 1.00–2.00 | Very fine skewed | 0.3–1.0 | >1.30 | Very leptokurtic | 1.50–3.00 | >7.40 |
| Very poorly sorted | 2.00–4.00 | Extremely leptokurtic | >3.00 | — | |||
| Extremely poorly sorted | >4.00 | ||||||
Four grain size parameters, including mean grain size, sorting, skewness, and kurtosis, were determined using the graphic and moment methods. The mean grain size represents the average sediment grain size distribution, which reflects the sediment concentration trend and depositional dynamics [24]. Sorting highlights the deviation of sediment around the concentration trend, reflecting the degree of homogeneity of sediment particles, and is closely related to sediment transport dynamics conditions [25,26]. The skewness indicates the symmetry of the frequency curve, suggesting the proportion of the sediment occupied by coarse and fine particles [27]. The skewness provides a measure of the degree of concentration of each part of the sediment, i.e., the degree of peak convexity of the grain size frequency curve, concerning the source area; a low K G value indicates that the deposit has recently entered a new environment and has not been significantly altered by the new environment [28].
4 Results
4.1 Sediment grain size grouping
Samples from the YHC profile are characterized based on the Udden–Wentworth grain size classification standard for Quaternary sediments [29,30] into the following: sand (<4φ), silt (4–8φ), and clay (>8φ). The Shepard triangle [31] (Figure 4) shows that, overall, the Menyuan loess is dominated by silt-sized particles. The proportion of silt in samples ranges from 61.64 to 82.21% (mean = 75.78%), the clay content varies between 7.11 and 21.68% (mean = 14.03%), and sand particles range from 3.42 to 28.87% (mean = 10.19%). The TS layer sediments are concentrated in the clayey silt zone; the L0, S0, LT, and majority of the L1 layers sediments are condensed in the silt zone; and some of the L1 samples are in the sandy silt zone. Lithological variations in the strata are minor, suggesting relatively uniform sources of materials in the profile.
![Figure 4
Lithological triangulation of sediments from YHC profiles. The base of the picture is from ref. [31].](/document/doi/10.1515/geo-2022-0474/asset/graphic/j_geo-2022-0474_fig_004.jpg)
Lithological triangulation of sediments from YHC profiles. The base of the picture is from ref. [31].
4.2 Grain size frequency distribution characteristics
Grain size frequency curves can indicate the status and concentration of different sizes in a distribution, and thus, these are crucial for the characterization of depositional environments and distinguishing sources of sediments [32]. As depicted in Figure 5a, the grain size frequency curves of samples from layers in the YHC profile exhibit essentially asymmetric bimodal distributions with “fine tail” characteristics, and this “fine tail” is associated with the fine grain size side. The curves reveal evident primary and secondary peaks, but the concentration of primary peaks in the 4–5φ range indicates the dominance of silt particles. In these bimodal curves, the occurrence of secondary peaks near 10° reflects the contribution of clay-sized particles. The presence of weak peaks at 7φ in the curves for most samples highlights fine silt deposits.
The distribution frequency curves (a) and cumulative curves (b) of grain size in Menyuan loess.
Therefore, sediments in the YHC profile contain mainly silt particles, and the associated frequency curves exhibit asymmetric bimodal distributions involving “fine tail.” A comparison of grain size characteristics of lacustrine, fluvial, and aeolian sediments from different regions [3,32,33,34,35,36] and results from field investigations suggest that sediments in the YHC profile are aeolian.
Probabilistic cumulative curves are used to infer transport processes associated with sediments and their relationships to the grain size distribution, thereby highlighting the depositional environment [37]. Figure 5a shows comparable probability accumulation curves for different layers across the YHC profile, with grain sizes varying mostly from 2 to 11φ. The curves are dominantly bipartite, and the φ cut-off is approximately 7.5. Excluding a few samples from the L1 layer with curves that are steeper from 2.5φ, most samples from the Menyuan loess are markedly steeper from 3φ, and the significant increase in coarse sediments indicates that the deposit mainly contains 3–7.5φ particles. The curves exhibit increases until 80% and then flatten, and the distinct and extended associated tails indicate that fine-grained particles contributed significantly to the Menyuan loess. This observation is consistent with the results from the grain size frequency plots. In addition, the probability accumulation curves reveal the following transport processes for the sediments: low- and high-suspension. According to frequency accumulation curves for the YHC profile, strata exhibit minor differences. In fact, data for all horizons indicate that the sediments were mainly transported through a low suspension, followed by a high suspension, with a minor proportion linked to saltation.
4.3 Grain size characterization parameters
Two datasets comprising four indicators for grain size characterization (M Z, σ I, SkI, and K G) were generated following analyses and calculations. Results in Figure 6 demonstrate variations in grain-size parameters based on depths, and average data for various parameters for each layer are presented in Table 4.
Comparison of grain size parameters with depth calculated by the graphic and moment methods.
Grain size parameters for the graphic and moment methods of YHC loess sediments
| Strata | M Z | σ I | SkI | K G | ||||
|---|---|---|---|---|---|---|---|---|
| Graphic method | Moment method | Graphic method | Moment method | Graphic method | Moment method | Graphic method | Moment method | |
| TS (n = 41) | 5.63–6.31 | 5.57–6.24 | 1.64–1.95 | 1.65–1.92 | 0.22–0.33 | 0.58–0.85 | 0.91–0.99 | 2.60–3.21 |
| 6.04(0.18) | 5.98(0.18) | 1.80(0.07) | 1.78(0.06) | 0.27(0.02) | 0.67(0.06) | 0.94(0.01) | 2.81(0.16) | |
| L0 (n = 7) | 5.87–6.47 | 5.82–6.40 | 1.62–1.82 | 1.63–1.79 | 0.16–0.26 | 0.46–0.67 | 0.89–0.96 | 2.49–3.01 |
| 6.21(0.18) | 6.15(0.17) | 1.75(0.06) | 1.73(0.05) | 0.22(0.03) | 0.60(0.06) | 0.94(0.02) | 2.75(0.15) | |
| S0 (n = 29) | 6.00–6.50 | 5.94–6.43 | 1.56–1.84 | 1.57–1.80 | 0.15–0.25 | 0.48–0.67 | 0.91–0.99 | 2.57–3.02 |
| 6.33(0.12) | 6.27(0.12) | 1.76(0.05) | 1.73(0.04) | 0.21(0.02) | 0.59(0.05) | 0.95(0.02) | 2.74(0.10) | |
| LT (n = 11) | 5.54–6.15 | 5.48–6.09 | 1.68–1.81 | 1.69–1.80 | 0.24–0.36 | 0.65–0.92 | 0.94–0.99 | 2.87–3.34 |
| 5.80(0.22) | 5.75(0.22) | 1.72(0.04) | 1.72(0.03) | 0.29(0.04) | 0.78(0.11) | 0.97(0.02) | 3.09(0.18) | |
| L1 (n = 112) | 5.03–6.05 | 4.96–6.00 | 1.50–1.91 | 1.55–1.93 | 0.26–0.42 | 0.64–1.18 | 0.91–1.15 | 2.75–4.36 |
| 5.66(0.23) | 5.61(0.23) | 1.68(0.09) | 1.70(0.08) | 0.34(0.03) | 0.91(0.10) | 0.99(0.04) | 3.32(0.30) | |
| All (n = 200) | 5.03–6.50 | 4.96–6.43 | 1.50–1.95 | 1.55–1.93 | 0.15–0.42 | 0.46–1.18 | 0.89–1.15 | 2.49–4.36 |
| 5.86(0.33) | 5.81(0.33) | 1.72(0.09) | 1.72(0.07) | 0.30(0.06) | 0.80(0.16) | 0.97(0.04) | 3.10(0.36) | |
| Note: | Min–Max | |||||||
| Mean(standard deviation) | ||||||||
4.3.1 Mean grain size
Mean grain size values calculated using the graphic (M Z-graphic) and moment (M Z-moment) methods correspondingly range between 5.03 and 6.50φ (mean = 5.86φ) and between 4.96 and 6.43φ (mean = 5.81φ), and the associated two standard deviations are equal (Table 4). The M Z data calculated using both methods exhibit similar trends with depth in the profile, which involve considerable vertical variations (Figure 6a). In the lower part of the L1 layer (400–300 cm), the M z values are essentially stable, but these slowly decrease between 300 and 245 cm, reaching a minimum of 248 cm. The values then fluctuate and slowly increase in the upper part of the L1 layer, followed by a rapid increase in the LT layer. This increase continued gradually into the S0 layer, reaching the maximum of the profile at 140 cm. Subsequently, these data display fluctuations, followed by a decrease from the bottom of the L0 layer to the surface (96–0 cm).
4.3.2 Sorting
The calculated sorting values based on the two methods are comparable. Results based on the graphic (σ I-graphic) and moment (σ I-moment) methods vary between 1.50 and 1.95 and between 1.55 and 1.93, respectively, with identical mean values of 1.72 (Table 4). Even though the standard deviation of data associated with the graphic method is slightly higher than that for the moment method, both sorting datasets revealed that the samples are poorly sorted. In addition, both datasets exhibit no significant variation with depth (Figure 6b); the maximum values are associated with the TS layer, whereas the lowest value was yielded by a sample from the L1 layer. Both datasets are characterized by fluctuations from poorly sorted to very poorly sorted from the base to the top of the profile, and the most intense variations are linked with depths of 275–175 cm in the L1 layer.
4.3.3 Skewness
The calculated skewness values based on the graphic (SkI-graphic) and moment (SkI-moment) methods vary from 0.15 to 0.42 (mean = 0.30) and from 0.46 to 1.18 (mean = 0.80), respectively (Table 4). The SkI-graphic data produced a lower standard deviation relative to the SkI-moment data. According to the classification criteria, skewness data from both methods differ significantly. The SkI-graphic data indicate that the samples are very fine-skewed, whereas the SkI-moment data suggest that the sediments are fine-skewed. Even though the skewness data vary considerably, data for both methods exhibit similar trends with depth in the profile (Figure 6c). Notably, the skewness data vary more significantly with stratigraphy compared with the mean grain size data, and the highest value is associated with the L1 layer, whereas the minimum value is yielded by a sample obtained from the S0 layer. The skewness curves demonstrate stable values in the lower part of the L1 layer (400–300 cm), followed by fluctuation and an increase in the L1 layer from 300 to 178 cm. The values then decrease rapidly in the LT layer, and the decrease continues at a lower intensity in the S0 layer, reaching a minimum for the entire profile at 106 cm. Subsequently, the values fluctuate and increase from the L0 layer to the surface (96–0 cm).
4.3.4 Kurtosis
The calculated kurtosis data based on the graphic (K G-graphic) and moment (K G-moment) methods range from 0.89 to 1.15 (mean = 0.97) and from 2.49 to 4.36 (mean = 3.10), respectively (Table 4). Even though data for both methods significantly differ, these data reveal that the samples are dominantly mesokurtic, with a few leptokurtic samples from the L1 layer. The K G-graphic data produced a lower standard deviation compared to the K G-moment data. However, the kurtosis curves display comparable trends with depth in the YHC profile (Figure 6d). Similar to the skewness data, the K G data are essentially steady at the bottom (400–280 cm) and top (140–0 cm) portions of the profile, whereas the 280–180 cm interval is characterized by substantial variations, and a rapid decline occurs between 180 and 140 cm.
In summary, grain size parameters calculated for different strata using the graphic and moment methods involve some variations (especially for the loess and paleosol layers). Therefore, even though trends in the curves of both datasets are consistent, the values and associated descriptions differ. Subsequently, the relationships between grain-size parameter data from the graphic and moment methods are discussed.
5 Discussion
5.1 Correlation analysis of grain size parameters from different methods
The scatter plot of the mean grain size data (Figure 7a) reveals a good fit (0.99) of the linear regression between data obtained using the moment and graphic methods, and the associated slope is approximately 1. These results suggest that data calculated using the two methods can be interchanged; however, overall, the M Z-moment (φ) values are slightly lower. A significant positive correlation exists between the difference between data for the two methods and the mean grain size (φ), and this disparity increases as the mean grain size decreases (Figure 8a). This difference is attributed to the neglected 5% of grain proportions at each grain size end in graphic methods, especially the tail data representing a fine particle fraction. Therefore, the higher the proportion of the neglected fraction, the more evident the difference between the data from the two methods.
Correlation analysis of grain size parameters between the graphic and moment methods. (a), (b), (c), and (d) correspond to M Z, σ I, SkI, and K G, respectively.
Scatterplot of the M Z-moment and difference between parameters of graphic and moment methods. (a) and (b) represent M Z and σ I, respectively.
Compared to the mean grain size distribution, sorting data for the methods is relatively more discrete, but these are also characterized by linear relationships that can be expressed as y = x. In fact, the goodness-of-fit values associated with data for both methods are up to 0.96 (Figure 7b). Notably, for the Menyuan loess, the σ I-moment values are higher than the σ I-graphic values, whereas an opposite trend is observed for other strata (especially the paleosol layer). The numerical relationship of sorting for both methods is closely related to the mean grain size. A plot of differences between the value for sorting obtained from the two methods and the mean grain size (Figure 8b) reveals that the σ I-moment is equal to the σ I-graphic at approximately 5.7φ. Overall, the graphic method demonstrated higher sorting values for finer grain sizes, whereas the moment method yielded higher values for coarse grain sizes. However, the differences associated with diverse strata are minor, and both methods characterize the sediments as poorly sorted. Therefore, the σ I-moment and σ I-graphic data for the Menyuan Basin can be converted to each other by a linear equation.
As shown in Figure 7c, the distributions of skewness values associated with the graphic and moment methods deviate significantly from a straight line (y = x), and overall, the SkI-graphic values are approximately 38% of the SkI-moment values. Compared to other grain size parameters, the SkI-moment and SkI-graphic data are more discrete; however, a linear relationship remains evident. The linear goodness-of-fit coefficient of 0.81 highlights a strong positive correlation (Figure 7c). However, even though the skewness data from both methods display a strong linear relationship, because of description differences, the interconversion of data for two methods using linear relationships requires attention to taxonomic descriptions to prevent confusion in the data reported.
Similar to skewness, the distribution of kurtosis values calculated using the graphic and moment methods deviated significantly from a linear relationship (Figure 7d). Relatively, the K G-moment and degree of dispersion values were considerably larger than those for the K G-graphic method. Nevertheless, kurtosis values obtained from the two methods produced a correlation coefficient of 0.84, and the relationship between the two datasets can be expressed as follows: y(K G-moment) = 8.16 × (K G-graphic) − 4.85. The results for most of the samples converted altered in value; the associated descriptions or classifications were unaltered. Notably, kurtosis values for the sediments tended to shift from mesokurtic to leptokurtic following conversion from the graphic to the moment method data. Overall, kurtosis for samples from the Menyuan Basin can be determined using a linear relationship obtained from data associated with the graphic and moment methods. However, attention should be paid to ensure that descriptions change.
In summary, linear equations can be used to convert mean grain size, sorting, skewness, and kurtosis data for samples from the Menyuan loess from the graphic and moment methods. However, because of description differences, attention is required to ensure that the conversion does not alter the original classification. Data for grain size parameters calculated using the moment and graphic methods for aeolian loess in the Chinese Loess Plateau and for continental shelf sediments from previous studies were jointly analyzed [11,13]. It was found that there is a clear linear transformation relationship for the mean grain size of all sediments; except for some marine sediments in certain regions, the sorting parameters of other sediments can also be interchanged by formula; there is no universal linear transformation pattern for the skewness and kurtosis, only aeolian sediments and few marine sediments meet the conditions. Linear relationships between grain size parameters based on the two methods are possibly influenced by the mixing of sediments from multiple source areas and the associated transport dynamics. Grain size frequency curves for marine sediments are often multi-modal [38], and these highlight diverse sources and complex transport dynamics. Such complexities limit the linear relationship established between data from the graphic and moment methods. Relatedly, grain size frequency curves of aeolian loess are commonly bimodal [39], which highlights fewer sources and simpler transport dynamics. Therefore, grain size parameters of the two methods are suitable for linear transformation; however, data for skewness and kurtosis often require corrections.
5.2 Discrepancies in grain size parameters between the methods
Discrepancies between grain size parameter data calculated using the graphic and moment methods are commonly attributed to the following reasons: first, the methods are based on different principles; second, the sediments have differentiated characteristics.
The difference in the principle is the fundamental reason for the variance between data for grain size parameters from the graphic and moment methods [1]. Through the Folk–Ward formula, grain size characteristics are calculated based on a subsample of the entire sample (cumulative content from 5 to 95%). Therefore, the <5 and >95% fractions (extremes of both ends), which are correspondingly referred to as tail and head, are neglected, thereby causing the loss of some detail [11,12]. Therefore, for complex deposits associated with multi-modal characteristics, the graphic method can rarely be used to adequately characterize samples. Conversely, the moment method is based on statistical principles. In the moment method, descriptive statistics are used to display trends and patterns in data based on primary, secondary, tertiary, and quadratic moments of distribution [10]. In theory, relevant statistical parameters can be obtained for any discrete random variable with convergence characteristics, and thus, the moment method is widely used. In the moment method, all data are utilized, and the overall features of granularity and proportions of samples at ends, which are neglected in the graphic method, are considered. Thus, the moment method data are more accurate and closer to actual values [1]. The more pronounced the tail characteristics, the higher the discrepancy between values computed using the two methods. In most cases, 90% of the subsamples are consistent with the overall characteristics. In calculating the mean grain size and sorting, the moment method operates at low power, similar to the graphic method, and thus, it is a low-order function expression. Consequently, discrepancies between the calculated values are insignificant, and the correlation between data from the two methods is significant for most sediments. Regarding skewness and kurtosis, the graphic method involves first-order expressions, whereas the moment method is associated with higher orders, and this amplifies errors during complex calculations. This explains the higher discrepancies between data from the two methods.
In both the graphic and moment methods, a log-normal distribution is assumed for the grain size. Therefore, similarities and differences between data from the two methods are linked to the extent to which the actual sediment deviates from a log-normal distribution [10,12]. If sediments conform strictly to a log-normal distribution, calculations using both methods produce identical results, whereas these differ if the deposit deviates from a log-normal distribution. The tendency to shift increases as the order increases. Characteristics of sediments, such as the type and distribution, also influence the magnitude of differences between results of grain size parameters calculated using different methods. Therefore, regarding some sediments, the removal of 5% of the sample from each end of a multi-modal grain size probability curve increases the deviation between data obtained using the two methods. In fact, the discrepancy increases as peaks increase, such as marine sediments [11]. Sediments from the YHC profile exhibit bimodal grain size frequency curves, and secondary peaks represent approximately 2.18–7.71% (Figure 5a). Therefore, tails minimally influence grain size parameters (especially the higher order indices) for these sediments. Accordingly, the four grain size parameters that were calculated using the two methods in the present study can be converted using linear equations, Luochuan loess in the Chinese Loess Plateau has similar characteristics [13]. However, in the graphic method, nearly all of the fine particles transported in suspension aloft in the sub-peak section are disregarded. Therefore, some information on dust transported by westerly wind is lost, and this explains discrepancies between grain size parameters for the Menyuan loess that were calculated using the two methods. Therefore, the moment method enables the calculation of more comprehensive grain size parameters and better reflects conditions during the deposition of loess in the study area. So, regarding the calculation of grain size parameters for the Menyuan loess, the moment method is preferable.
5.3 Significances of Menyuan loess grain size parameters via moment method
According to the analysis in Section 5.2, the moment method is considered most appropriate for the calculation of grain size parameters for the YHC profile. Data from this method reflect the depositional characteristics of the Menyuan loess, and these are essential for the reconstruction of the source, transport dynamics, and environments of deposition of sediments in the study area.
The mean grain size of sediments is mainly influenced by the mean kinetic energy factor [24]. In the YHC profile, the mean grain size is relatively stable in the paleosol layer, whereas it fluctuates significantly in the loess layer (Figure 6a). These results indicate that the study area involved stable and low-energy deposition of sediments during the development of the paleosol, whereas the loess was deposited under complex, high-energy conditions. The mean grain size of the Menyuan loess changed significantly in the LT layer because of the corresponding changed kinetic energy during the transportation of sediments, and this suggests a remarkable alteration in the climate. According to the C–M diagram of the YHC profile, the Menyuan loess is concentrated in the lower portion of the S-shaped in the N–O–P–R–S figure (Figure 9) [37,40]. Overall, the sediments are dominated by fine grains, which indicate deposition controlled by low kinetic energy. The low average kinetic energy associated with the transportation of the sediments and the unique transportation mode dominated by suspension is consistent with the observation derived from the analysis of data in Figure 5b.
![Figure 9
C–M plot for the loess deposit of the study area. C and M represent the grain size at 1 and 50% content, respectively. The base of the picture is from [37,40].](/document/doi/10.1515/geo-2022-0474/asset/graphic/j_geo-2022-0474_fig_009.jpg)
Sorting is closely related to conditions during the transportation of sediments [25,26]. The poorly sorted sediments in the YHC profile indicate a scattered grain size distribution, and the Menyuan loess is likely associated with a complicated provenance and transport (Figure 6b). Recently, Shi et al. [19] analyzed the Menyuan loess using rare earth elements and reported that these aeolian sediments originated primarily from the Qaidam Desert within the Tibetan Plateau and other deserts in arid Central Asia, with transportation dominantly through the westerly wind. Strong winter monsoon also transported dust from the Badain Jaran Desert and Tengger Desert to the Menyuan Basin. These observations are consistent with the suggestion that the Menyuan loess is associated with several sources and dynamic interactions.
Skewness can indicate the symmetry of a grain size frequency curve. It reflects the symmetry of the distribution, shows the relative positions of the plural, median, and mean, and highlights the type and strength of the transportation medium [27]. Skewness values from the YHC profile were fine skewed or very fine skewed, and these results are consistent with the characteristics of aeolian sediments [41]. In fact, these results suggest that the Menyuan loess was formed mainly via the transportation of fine sediments from other areas by the wind. Relatedly, kurtosis represents the height and width of peaks in the grain size distribution curves of sediments. Loess samples from the YHC profile generally produced higher kurtosis values than samples from the paleosol layer (Figure 6d). These results indicate that the loess contained a higher proportion of coarse-grained materials and that the original sediments had been altered by post-depositional processes in the paleosol layer, such as pedogenesis [28].
The data generated in the present study revealed that changes from a cold, dry to a warm, humid climate in the Menyuan Basin were recorded in the YHC profile (Figure 6). During the cold, dry age, coarse particles transported by westerly wind and winter monsoon were deposited as dust in the basin. Therefore, abundant loess is characterized by a high mean grain size accumulated in the basin, and these highlight the implication of intense transport dynamics. Subsequently, significant fluctuations in climate and changes in the source of sediment produced poor sorting for aeolian sediments in Menyuan loess. Following the change to a warm, humid climate, increasingly finer particles were deposited, and pedogenesis increased. The proportion of clay increased accordingly, thereby decreasing the skewness and kurtosis indexes of the sediments.
A comparative study of grain size parameters calculated using the graphic and moment methods improves understanding of the utility of these parameters for the characterization of sediments. The present study highlights an avenue for optimizing and integrating grain size data on aeolian sediments in the Tibetan Plateau. A systematic study of the Tibetan Plateau is also needed for a more comprehensive understanding of the grain size characteristics and patterns of the Tibetan Plateau loess.
6 Conclusion
In the present study, grain size parameters calculated using graphic and moment methods for samples from the YHC section of the Menyuan Basin were compared, and the main findings are summarized as follows:
In Menyuan loess, the M Z, σ I, SkI, and K G calculated by the two methods can be converted using linear equations. Attention to possible differences between descriptions is necessary.
Owing to its characteristics, the calculation of grain size parameters for the Menyuan loess is better using the moment method than the graphic method.
The grain size analysis results based on the moment method revealed that the Menyuan loess originated from multiple sources involving diverse dynamics. These sediments recorded changes in the climate from cold, dry to warm, wet conditions.
Acknowledgments
This work was jointly supported by the National Natural Science Foundation of China (Nos 42171011, 41761042, and 41361047), the Natural Science Foundation of Qinghai Provincial Science and Technology Department (2021-ZJ-918), and the free exploration research project of the Key Laboratory of Tibetan Plateau Land Surface Processes and Ecological Conservation (Ministry of Education) (TGEZT-2022-03). The authors sincerely thank the anonymous reviewers for their constructive comments and suggestions. We also thank the editor, who has been extremely helpful. We would like to thank Editage (www.editage.cn) for English language editing.
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Author contributions: YS: designed the study, formal analysis, investigation, writing, and editing. CE: conceptualization, funding acquisition, investigation, and writing. ZZ and QP: investigation and writing. JZ: investigation and formal analysis. WY and CX: experimental treatment and formal analysis.
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Conflict of interest: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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Data availability statement: The data supporting the findings of this study are available within the article.
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