Technical Notes
Variance of Aggregate Size Distribution as a Criterion for Soil Similarity Bhabani Sankar Das,* Hitesh Bhogilal Vasava, Madathiparambil Chandran Sarathjith, and Biswajita Mohanty
The finding of this study provides a practical guideline to identify similar soils. The aggregate size distribution data from different soils are used to create such a guideline.
Identification of similar soils is an important step in different branches of soil hydrology. Generally, a characteristic length in porous media is used for estimating scaling factors in a similarity analysis. Such an approach amounts to the use of the first moment of the pore size distribution (PSD). Previous research has suggested that the s of PSD of similar soils should also be similar. Authors of this research proposed a new criterion in terms of the CV for s (CVs) with the suggestion that the “geometrically similar” soils should satisfy the condition of CVs < 10%. Here, we validate this result using the aggregate size distribution (ASD) data of 1375 soils collected from 10 different zones with varying scale and properties. The lognormal distribution function and the physically based scaling (PBS) approach were used to scale the ASD datasets. The effectiveness of scaling was determined by the RMSE between the scaled ASD curve and the reference ASD curve. Four out of 10 soil datasets had CVs < 12%, and their corresponding RMSE values were an order of magnitude lower than those for the remaining soil groups. A plot between the RMSE and CVs values showed that CVs < 10% may be used as a practical limit for identifying similar soils. Abbreviations: ASD, aggregate size distribution; CVs, coefficient of variation among standard deviations; EC, electrical conductivity; KBS, black soils of Karnataka, KRS; red soils of Karnataka; MSSD, mean sum of squared deviations; ODS, surface soils of Odisha; OWBS, depth samples of Odisha and West Bengal; PBS, physically based scaling; Plot, plot-scale data; PSD, pore size distribution; SOC, soil organic carbon; WBS, surface soils of West Bengal; WRC, water retention curve; WS1S, watershed 1 soils; WS2S, watershed 2 soils; WS3S, watershed 3 soils.
Identification of similar soils is an important step in soil mapping and classification, soil physics, and hydrology. Miller and Miller (1956) proposed that the microscopic structures of two geometrically similar soils differ only by a characteristic length, l (Warrick et al., 1977). The soil pore radius (r) is generally used as a proxy for l (Tuli et al., 2001) such that soil water retention curves (WRCs) provide necessary data to test a specific scaling approach (Warrick et al., 1977; Claustnizer et al., 1992; Pachepsky et al., 1995; Kosugi and Hopmans, 1998). Specifically, l, r, and matric potential heads (h) are related through the scaling relationship: B.S. Das, H.B. Vasava, M.C. Sarathjith, and B. Mohanty, Agricultural and Food Engineering Department, Indian Institute of Technology Kharagpur, WB 721302, India. *Corresponding author (
[email protected]). Vadose Zone J. doi:10.2136/vzj2015.05.0072 Received 13 May 2015. Accepted 24 June 2015.
© Soil Science Society of America
5585 Guilford Rd., Madison, WI 53711 USA. All rights reserved.
l 1 / r1 = l 2 / r2 =×××= l i / ri = l * / r* = l i hi = l * h* [1]
where the numbered subscripts denote the ith WRC and the * subscript refers to the reference WRC (Miller and Miller, 1956). A scaling factor for the ith soil (a i = l i/l*) may be computed either by minimizing the mean sum of squared deviations (MSSD) between the observed and an assumed reference WRC data (Warrick et al., 1977) or by using a PBS approach (Kosugi and Hopmans, 1998). In the PBS approach, a lognormal probability distribution function ( f ) is used for describing PSD: f (ln r ) =
é ( ln r - ln r )2 ù 1 m ú [2] exp êê ú s 2p 2s 2 êë úû
Vadose Zone Journal | Advancing Critical Zone Science
where rm is the median pore size and s is the standard deviation of f. Equation [2] may be used to represent the PSD for the reference WRC by substituting rm and s with rm,* (the median pore size of the reference WRC) and s * (standard deviation of the reference WRC), respectively, and the reference WRC parameters may be estimated as follows:
ln rm,* = 2 (s * ) =
1 n å ln(r ) [3] n i=1 m,i
1 n 2 å s i [4] n i=1
Thus, Kosugi and Hopmans (1998) used rm to compute a i: a i = l i / l * = rm,i / rm,* Þ ln(a i ) = ln(rm,i )- ln(rm,* ) [5]
The PBS approach has been used by several workers to test the effectiveness of scaling soil WRCs (Tuli et al., 2001) and ASD functions (Nasta et al., 2009, 2013a, 2013b). A fundamental feature of the PBS approach is the assumption of lognormal PSD that allows Eq. [5] to be used for translating all the sample PSDs by their respective scaling length such that the scaled PSDs have the same mean as that of reference PSD. In other words, this scaling approach ensures that the first moment of the scaled PSD is indeed the first moment of the reference PSD. However, it does not explain if the variance parameter (second moment) of PSDs for samples in a pool of similar soils (as defined by the scaling of median pore size alone) has any role on the effectiveness of scaling procedure. Recently, Das et al. (2005) showed that the MSSD values indeed were high (lack of similarity) when the s values across the scaled datasets were variable. They proposed that the CV for the s values (CVs) of geometrically similar soils should be less than 10% (i.e., CVs < 10% as an additional criterion for defining similar soils). This result was obtained through a numerical experiment of generating a subset of WRCs from 247 WRCs because no experimental data on soil hydraulic properties at multiple scales of observation were available. Here, we test the CVs < 10% criterion using 1375 soil samples collected from different parts of India at different sample-to-sample distance. The PBS scaling approach was applied on the ASD parameters in this study instead of WRC data. Several studies have shown that the pore sizes and aggregate sizes are inherently linked (Assouline and Or, 2013). The diameters of soil aggregates (and soil particles) are often used as substitutes for r in scaling relationships (Nasta et al., 2009). Thus, the ASD data may be used in the PBS scaling framework to test this second-moment criterion of CVs < 10%.
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66Materials
and Methods
Experimental Datasets
Table 1 shows the summary of 10 datasets collected from three different states (West Bengal, Odisha, and Karnataka) of India (figures shown in supplementary material) with varying total sampling area, average distance between two consecutive sampling points, and five important physicochemical properties. The Trench data consisted of 11 soil profile data collected at 10- to 20-cm depth intervals from the exposed face of 25-m-long and 2-m-deep trench excavated on a rice (Oryza sativa L.) field. Total 106 soil samples representing four different soil layers in a rice field were collected from this Trench site (Patil and Das, 2013). The depth samples of Odisha and West Bengal (OWBS dataset) were compiled from 261 soil samples collected from 87 locations across Odisha and West Bengal states of eastern India, each from three different soil depths (0–20 cm, 20–40 cm, and 40–60 cm). This dataset may be treated as one of the most heterogeneous datasets having large spatial extent and three different soil horizons for each sample. The remaining datasets were collected from the top 0- to 20-cm soil depths. The plot-scale data (Plot) was collected from 30 plots (5 by 6 m) in an experimental site where rice has been grown for over five decades (Garg et al., 2009; Patil et al., 2011). Because of puddling year after year, the surface soil in these plots get disturbed and homogenized every year; therefore, soils from this smallest (horizontal) scale of our measurement showed the least variation in soil properties. With the total area of about 1612 m2 , the surface soils of this experimental site may be treated as more or less similar. The black soils of Karnataka (KBS) and red soils of Karnataka (KRS) are Vertisols and Alfisols, respectively (Sarathjith et al., 2014). Ten soils were collected each from 25 contiguous villages to generate about 250 soil samples for the KBS and KRS datasets. With the total area of 9839 km2 for KBS and 2602 km2 for KRS, these soils may be treated as representative of catchment-scale soils. Two datasets that are more large-scale than catchments are the soil samples collected from Odisha (ODS dataset) and West Bengal (WBS dataset) that had a mean sampleto-sample distance of about 40 to 90 km. Soil samples were also collected from three watersheds (WS1S, WS2S, WS3S) that drain to the Chilika Lake located in the eastern part of Odisha. These three watersheds form the major component of Chilika’s western catchment, which is a part of the Eastern Ghats mountain range that runs north–south along eastern India. With hillslope hydrology, these three watersheds show large variations in soil properties even if their total area is small. The soil textural components such as sand, silt, and clay fractions in the 2-mm-sieved soils were analyzed using the pipette method (Gee and Bauder, 1986), and the soil organic carbon (SOC) content was determined using the chromic acid digestion method (Walkley and Black, 1934). Soil pH and electrical conductivity (EC) were determined in a 1:2.5 soil–water slurry. Soil ASD was determined by dry sieving a 100- to 200-g soil sample in a stack of p. 2 of 5
eight sieves (1.18-, 0.3-, 0.2-, 0.18-, 0.125-, 0.09-, 0.075-, and 0.053mm nominal diameter). Soil samples retained in each sieve and pan were weighed to estimate the mass fraction of soil aggregates corresponding to the ith sieve diameter. Samples passing through the bottom-most sieve were assigned an aggregate diameter of 0.005 mm. Buchan (1989) proposed the lognormal probability distribution function (g) for ASD similar to Eq. [2]:
g (ln d ) =
é ( ln d - ln d )2 ù 1 m ú exp êê ú s 2p 2s 2 êë úû
[6]
where d is the aggregate diameter, dm is the median aggregate diameter, and s is the standard deviation of the frequency distribution, g. Corresponding cumulative aggregate mass fraction G may be expressed as (Buchan et al., 1993; Hwang and Choi, 2006):
é ln(d / d m ) ù ú G (ln d ) = 0.5erfc ê ëê s 2 ûú
[7]
where erfc is the complementary error function. Equation [7] was fitted to the ASD data for estimating dm and s in the MATLAB (MathWorks) environment. Equivalent forms of Eq. [3–5] were then used for estimating scaling parameters. Thus, the PBS approach was applied to ASD data instead of soil hydraulic properties with the presumption that dm may serve as a proxy for the “characteristic length scale” in the similarity framework. However, it may be noted that direct conversion of ASD data into soil hydraulic properties may not be possible (Nasta et al., 2009).
66Results
and Discussion
Variability in Selected Datasets
Table 1 shows average and CV values for sand content, clay content, SOC content, pH, and EC values. While the textural components along with SOC form the fundamental fabric of soil, pH and EC are overall reflections of chemical characteristics of soils. Together, these properties influence soil structure. Table 1 also shows that most of these soils have high sand contents and soils are mostly acidic except for the Vertisols of the KBS group. However, the CV values for sand and clay contents are high, suggesting that many of the individual soils may have high clay content. For example, 58 out of 261 OWBS soils had clay contents more than 40%, with the highest clay content of 74% clays observed in this soil group. As expected, the Plot dataset showed the least variability and the OWBS soils were generally the most variable among the listed parameters. Soil pH is the smallest variable soil property, while EC appears to have the most variability across different soil groups. Because of the smaller extent (total area sampled) of observations, the Plot and Trench datasets are expected to be similar. The watershed-scale datasets may not show similarity even though their sampling area is small because of large variability in soil properties
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and large elevational difference (data not shown). The remaining datasets are expected to show dissimilarity as they represent datasets that are larger than catchment scale. Thus, these 10 datasets represent soils at a variety of scales in terms of sampled area, sample-to-sample distance, topography, agroecological settings, and inherent soil variability and, therefore, may be ideal to examine how the scaling parameters depend on their scale of assessment.
Scaling of Aggregate Size Distribution Functions Results of the PBS scaling on ASD datasets for different soil groups are summarized in Table 2. The RMSE between the scaled ASD datasets within a soil group and its reference ASD function ranged from 0.067 for the Vertisols soil group of KBS to 0.204 for the surface soils of West Bengal (WBS group), suggesting that the ASD datasets for the KBS and WBS groups were the most and least effectively scaled datasets, respectively. Figure 1 shows the effectiveness of scaling for these two soil groups. The spread of the ASD data in the KBS group (Fig. 1c and 1d) is less than the WBS group (Fig. 1a and 1b). A comparison of scaled ASD datasets in Fig. 1b Table 1. Area, average distance between two sampling points, and average values for basic soil properties of selected datasets.† Soil group‡
Area
Distance Sand
km2
km
Clay
Soil organic carbon pH
————— % ————
Electrical conductivity mS/cm
Profile-based soil data Trench 50§ (n = 106)
0.012
60.3 (11)
19.9 (26)
0.14 (72)
5.6 (6)
23.4 (42)
OWBS (n = 261)
96,382
48.6
47.5 (40)
29.5 (47)
0.63 (59)
6.4 (16)
244.3 (115)
Plot (n = 30)
1,612§
Surface soil data 0.008
73.1 (6)
9.8 (11)
0.57 (18)
6.4 (10)
149.7 (24)
KBS 9,839 (n = 249)
8.4
65.6 (15)
14.6 (36)
0.40 (38)
KRS 2,602 (n = 248)
4.5
78.1 (10)
12.4 0.38 6.7 (53) (36) (21)
WS1S 425 (n = 107)
1.5
50.7 (29)
28.4 (35)
0.97 6.4 940.9 (41) (14) (270)
WS2S (n = 61)
139
1.3
43.5 (41)
29.3 (48)
0.99 6.5 (30) (14)
WS3S (n = 30)
515
3.8
50.5 (32)
27.3 (46)
0.76 (23)
5.9 486.1 (15) (102)
ODS 65,774 (n = 177)
92.8
55.0 (34)
25.1 (44)
0.74 (42)
5.8 744.3 (15) (613)
WBS 46,186 (n = 107)
37.3
46.7 (41)
26.6 (51)
1.02 5.9 403.8 (38) (15) (215)
8.5 581.2 (6) (318) 414.2 (67)
527.3 (79)
† The values in parentheses show the CVs expressed in percentage. ‡ KBS, black soils of Karnataka, KRS; red soils of Karnataka; ODS, surface soils of Odisha; OWBS, depth samples of Odisha and West Bengal; Plot, plot-scale data; WBS, surface soils of West Bengal; WS1S, watershed 1 soils; WS2S, watershed 2 soils; WS3S, watershed 3 soils. § Total area of sampling for the Plot and Trench datasets are given in square meters.
p. 3 of 5
Table 2. Reference soil parameters for the aggregate size distribution, corresponding RMSEs from scaling and estimated CV values for dm and s. † Soil group
dm,ref
sref
RMSE
mm
CVdm
CVs
———— % ————— Profile-based soil data
Trench (n = 106)
0.27
0.98
0.073
25.0
6.6
OWBS (n = 261)
0.28
1.08
0.159
32.3
23.2
Plot (n = 30)
0.18
0.86
0.079
6.5
6.5
KBS (n = 249)
0.51
1.00
0.067
34.9
12.2
KRS (n = 248)
0.31
0.99
0.080
35.1
11.9
WS1S (n = 107)
0.24
1.06
0.148
29.1
22.1
WS2S (n = 61)
0.32
1.11
0.147
37.8
22.1
WS3S (n = 30)
0.25
1.06
0.159
41.1
26.0
ODS (n = 177)
0.25
0.98
0.166
32.4
24.2
WBS (n = 107)
0.21
1.11
0.204
44.9
30.7
Surface soil data
† dm, median aggregate diameter; dm,ref, dm for reference soil; sref, s for reference soil; CVdm, coefficient of variation among dm values; CVs , coefficient of variation among standard deviations; KBS, black soils of Karnataka, KRS; red soils of Karnataka; ODS, surface soils of Odisha; OWBS, depth samples of Odisha and West Bengal; Plot, plot-scale data; WBS, surface soils of West Bengal; WS1S, watershed 1 soils; WS2S, watershed 2 soils; WS3S, watershed 3 soils.
and 1d shows that the KBS group of ASD data is more effectively scaled. Interestingly, the RMSE values for the Plot, Trench, KBS, and KRS groups were all an order of magnitude smaller than those of the remaining soils. Smaller RMSE and smaller CVs in KBS and KRS soils similar to those of smaller-scale Plot and Trench soils suggest that these two soil groups may be treated as geometrically similar soils despite their catchment-scale occurrence. In contrast, the three watershed soil groups show large variability and larger RMSE similar to the catchment and larger-scale soil groups (OWBS, ODS, WBS). The hilly terrain of these watersheds may have contributed to the dissimilarity in watershed soils. A similar variability was observed in a 41-km2 microwatershed in the western catchment of Chilika by Santra and Das (2008). Resulting scaling parameters for the reference soils for each of the 10 soil datasets reflect broad characteristics of individual soil groups. The lowest median aggregate size for the Plot soils (dm,ref = 0.18 mm) may have been a result of its loamy sand soil textural class and low SOC contents promoting very little soil aggregation. Besides, these soils are disturbed twice a year during puddling
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Fig. 1. Unscaled and scaled aggregate size distribution curves for the surface soils of West Bengal (WBS) and Vertisols of Karnataka (KBS) datasets.
operations as part of two rice crops grown every year; hence, structural development in such soils should not be expected. The largest value of dm,ref = 0.51 mm for the KBS group is clearly a result of inherently bigger aggregates observed in Vertisols. Similarly, a moderate median aggregate size for the WS2S group may be a result of the greater proportion of finer size fractions than similar soils from Odisha and West Bengal. The reference soil s values varied from 0.86 to 1.11 with the CV for s across different soil groups varying from 6.5 to 30.7%. Corresponding variations for dm values ranged from 6.5 to 44.9%. Interestingly, the variation in the ASD parameter s appears to be small compared with CV values for the basic physicochemical properties. Being a structural attribute, ASD reflects an integrated response (outcome) of individual components such as sand, clay, and SOC contents; therefore, the ASD parameter s may be showing less variability even with such large spatial extents of sampling. Table 2 also shows that 4 out of 10 soil datasets had a CVs value less than 12% and their corresponding RMSE values were an order of magnitude lower than those for the remaining soil groups. Figure 2 shows the relationship between the variations in s with the effectiveness of scaling as determined by the RMSE for 10 different soil groups. The RMSE values remain constant for low CVs values and thereafter linearly increase as sCV values increase. Such a pattern was observed in the numerical experiments with the modeling of water retention behavior (Das et al., 2005). Low RMSE values suggest that the scaled ASD datasets coalesce around the reference ASD data estimated through the PBS approach, which supports p. 4 of 5
Reference
Assouline, S., and D. Or. 2013. Conceptual and parametric representation of soil hydraulic properties: A review. Vadose Zone J. 12:1–20. Buchan, G.D. 1989. Applicability of the simple lognormal model to particle size distribution in soils. Soil Sci. 147:155–161. Buchan, G.D., K.S. Grewal, and A.B. Robson. 1993. Improved models of particle-size distribution: An illustration of model comparison techniques. Soil Sci. Soc. Am. J. 57:901–908. doi:10.2136/ sssaj1993.03615995005700040004x Claustnizer, V., J.W. Hopmans, and D.R. Nielsen. 1992. Simultaneous scaling of soil water retention and hydraulic conductivity curves. Water Resourc. Res. 28(1):19–31. Das, B.S., N.W. Haws, and P.S.C. Rao. 2005. Defining geometric similarity in soils. Vadose Zone J. 4:264–270. doi:10.2136/vzj2004.0113 Garg, K.K., B.S. Das, M. Safeeq, and P.B.S. Bhadoria. 2009. Measurement and modeling of soil water regime in a lowland paddy field showing preferential transport. Agric. Water Manage. 96:1705–1714. doi:10.1016/j.agwat.2009.06.018 Gee, G.W., and J.W. Bauder. 1986. Particle-size analysis. In: A. Klute, editor, Methods of soil analysis. Part 1. 2nd ed. Agron. Monogr. 9. ASA and SSSA, Madison, WI. p. 383–412. Hwang, S., and S. Choi. 2006. Use of a lognormal distribution model for estimating soil water retention curves from particle-size distribution data. J. Hydrol. 323:325–334. doi:10.1016/j.jhydrol.2005.09.005 Kosugi, K., and J.W. Hopmans. 1998. Scaling water retention curves for soils with lognormal pore-size distribution. Soil Sci. Soc. Am. J. 62:1496– 1505. doi:10.2136/sssaj1998.03615995006200060004x
Fig. 2. Coefficient of variation of sample standard deviations (CVs) for the aggregate size distribution function and the RMSE for different soil groups.
effective scaling of ASD datasets. Similar to Das et al. (2005), this graph also suggests that soils with CVs values less than 10% may be treated as geometrically similar.
66Summary
The PBS approach proposed by Kosugi and Hopmans (1998) was applied to ASD data for 1375 soil samples collected from 10 different zones with varying scale and properties. Although the PBS approach was meant for the water retention data, Nasta et al. (2009) have shown that the same approach may be applied to ASD data. As has been noticed earlier, the PBS approach works well for scaling of ASD data as long as there is less variation in the standard deviation parameters of the ASD function. The critical value of CVs < 10% for geometrically similar soils is an experimentally determined observation in this study and supports the earlier findings of Das et al. (2005).
Acknowledgments
Sincere appreciation is expressed to the Department of Science and Technology, New Delhi for providing financial support for collecting soil samples. Sincere thanks are also given to Dr. S.P. Wani of the International Crops Research Institute for the Semi-Arid Tropics, Patancheru, Telengana for providing soils from Karnataka. The assistance of Mr. Biplab Dutta in collecting aggregate size data is also appreciated.
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