The soil texture representation with the standard textural
fraction triplet “sand–silt–clay” is commonly used to estimate soil
properties. The objective of this work was to test the hypothesis that other
fraction sizes in the triplets may provide a better representation of soil
texture for estimating some soil parameters. We estimated the cumulative
particle size distribution and bulk density from an entropy-based representation
of the textural triplet with experimental data for 6240 soil samples. The results
supported the hypothesis. For example, simulated distributions were not
significantly different from the original ones in 25 and 85 % of cases when
the sand–silt–clay and “very coarse+coarse

The particle size distribution is one of the essential controls of soil structure and functioning. Soil processes, properties and specific features are usually related to these distributions, commonly named soil texture. To express these relationships, the continuous particle size distributions are commonly replaced by their discrete representation with several textural fractions. The fractions are defined as particles within a range of sizes, e.g., medium sand, fine silt, etc. Then the percentages of textural fractions are used as attributes to classify soils and as predictors to the estimate soil properties of parameters.

Different countries have employed different numbers of textural fractions and
different ranges of sizes for each of the fractions.

There were indications that setting the boundaries between textural fractions
might depend on the purpose of further textural data use and on the
specifics of the dataset under consideration.

One application of the data on textural fraction content is the
reconstruction of the particle size distribution from data on a small
number of fractions.

The objective of this work was to test the hypotheses that (a) the reconstruction of the particle size distribution can be more accurate if the textural fraction size boundaries are changed from the USDA sand–silt–clay sizes to other size ranges, and (b) a satisfactory relationship between the information entropy and packing density can be achieved with three textural fractions with boundaries between fraction change sizes other than in the USDA sand–silt–clay triplet.

The USKSAT database is comprised of journal publications and technical
reports containing coupled data on saturated hydraulic conductivity (Ksat),
soil texture, bulk density, and organic matter content obtained across the
United States. Detailed information can be found in

The reconstruction of the particle size distribution (PSD) is based on the
assumption that entropy as the measure of heterogeneity of these
distributions is preserved across the support scales

The reconstruction of distributions was performed using three size fractions:
coarse, intermediate, and fine. The dataset contained experimental data on
seven fractions: very coarse sand, coarse sand, medium sand, fine sand, very
fine sand, silt, and clay. We used all possible triplets formed from seven
textural fractions that were available. The symbols for the triplets show how
the fractions were grouped. For example, the triplet 3–2–2 had
“coarse” and included very coarse sand, coarse sand, and medium sand;
“intermediate” included fine sand and very fine sand, and “fine”
included silt and clay. Triplet 5–1–1 was the standard one in which “coarse”
included all five sand fractions, “intermediate” included silt, and
“fine” included clay. A total of 15 triplets were available, a list of which
can be found in Table

For all textural triplets we generated the PSD and compared experimental particle size distributions (built from seven known fractions) with simulated ones. The Kolmogorov–Smirnov test has been applied to find the probability that the samples are drawn from the same distribution.

Texture of soil samples in the database shown in the standard
USDA

Following Eq. (

Examples of ternary graphs showing the locations of samples in the
“coarse–intermediate–fine” textural fraction content coordinates are shown in
Fig.

The reconstruction of particle size distributions with the iterated function
algorithm showed large difference among the applications of different
triplets. Data on the statistical difference between generated and measured
distributions are shown in Table

Total numbers of samples by ranges of the information entropy for two textural fraction triplets. The 3–2–2 triplet includes very coarse, coarse, and medium sand (fraction 1), fine and very fine sand (fraction 2), and clay and silt (fraction 3); the standard triplet 5–1–1 includes sand (fraction 1), silt (fraction 2), and clay (fraction 3).

Percentage of samples for which simulated and measured particle size distributions are not different at the 0.05 significance level.

Determination of coefficients of regression for the average information entropy versus average bulk density for 10 average entropy bins.

Results of linear regressions of mean information entropy values
versus mean bin bulk density values are shown in Table

The best results by considering both sand and non-sandy samples are obtained with triplets 2–4–1 and 3–3–1, i.e., triplets in which fines are represented only by clays and there is a certain balance between the coarse and the intermediate fractions. Where this balance is not present (1–5–1 and 5–1–1), the separation of clay in the fine fraction does not help. The standard triangle seems to work only for non-sandy soils. Also, this triplet's IE relates well to the BD of sandy clays, sandy loams, and sandy clay loams, but it gives unsatisfactory results for sands.

The triplets having a fine fraction consisting of very fine sand, silt, and
clay appeared to be superior in serving as the input for PSD reconstruction.
One possible explanation is that mass size scaling is not scale invariant
across all particle sizes. Rather it has ranges of particle sizes within which
the power-law scaling dependencies are applied and the boundaries between
these ranges are reflected by the modified textural triplet rather than by
the original 5–1–1 sand–silt–clay triplet. Breaks in particle size
distribution scaling were first highlighted by

Another reason for the better simulations of particle size distributions
could
be the better representation of soil texture, i.e., the distribution of samples by
the ranges of IE in which the majority of soils are found (Table

Scaling in cumulative particle mass of four soils studied by

The large difference between the IE–bulk density relationships developed
for different textural classes indicates that the IE computed for different
triplets has the potential to reflect the effect of soil texture on particle
packing in soils. The theoretical analysis of

The best triplets were different for the reconstruction of the particle size distributions and for establishing relationships between information entropy and bulk density after binning samples. Different triplets may be the most informative to characterize the results of fragmentation and sedimentation that manifest themselves in particle size distributions and the results of packing that manifest themselves in IE–BD relationships. Finally, some processes affecting the particle size distributions and IE–BD relationships may not be elucidated by textural data only; aggregation and weathering are examples.

The utility of textural fractions different from traditional sand–silt–clay
triplet appears to have an application in the development of pedotransfer
functions. The boundary of new fraction sizes can be parameters of pedotransfer
functions along with the regression coefficients.

The usability of triplets other than standard ones indicates the opportunity for a
more efficient use of existing results of textural analysis. Although these
results traditionally consist of seven fractions, including five fractions of
sand, in the majority of applications all sand fractions have been lumped
together. For example, the overwhelming majority of pedotransfer functions in
soil hydrology use the elements of the standard triplet sand–silt–clay

When analyzing the utility of the traditional sand–silt–clay triplet for
classifying soils by their hydraulic properties,

Having three textural size ranges, i.e., coarse, intermediate, and fine particle sizes, undoubtedly appears to be convenient for data presentation and textural class definition. Currently the coarse, intermediate, and fine fractions are identified as sand, silt, and clay, respectively. However, it is not conclusive that current sand, silt, and clay size ranges can provide the best representation of soil texture when these three size ranges are used for estimating soil properties. We hypothesized that the cumulative particle size distribution and soil bulk density can be more accurately estimated from the triplet coarse–intermediate–fine if the boundaries of the coarse, intermediate, and fine size ranges are different from those in the sand–silt–clay triplet. The entropy-based representation of particle size distributions was used to convert the triplet particle size representations into particle size distributions and to define ranges of soil textural heterogeneity. Experimental data on seven size fraction contents and bulk density for 6240 predominantly coarse-textured soil samples were extracted from the USKSAT database

It appears that redefining the triplet coarse–intermediate–fine may lead to a very substantial improvement in soil property estimates from soil textural data. Overall, the drastic improvement in predictions of both cumulative particle size distribution and mean bulk density for heterogeneity ranges occurred when the standard sand–silt–clay triplet was replaced with the modified textural triplet that was defined as very coarse, coarse, medium sand (coarse fraction), fine and very fine sand (intermediate fraction), and clay and silt (fine fraction). The modified triplet apparently provided more information about the particle size heterogeneity and particle packing. Different modified triplets provided the best inputs for different soil textural classes.

Results of this work indicate that detailed information about soil particle size distributions has the potential to enhance estimation of soil properties with soil texture as a predictor. Analyses of both existing and developing soil databases and pedotransfer methodologies may benefit from exploring modifications of textural triangles. The compression of information on textural heterogeneity in textural triangles into a single entropy-based parameter may provide additional advantages.

The data can be obtained from Yakov Pachepsky by email request to yakov.pachepsky@ars.usda.gov.

The authors declare that they have no conflict of interest.

This research work was funded by Spain's Plan Nacional de Investigación Científica, Desarrollo e Innovación Tecnológica (I+D+I) under ref. AGL2015-69697-P. Edited by: Marc Oliva Reviewed by: three anonymous referees