Saturated hydraulic conductivity (

This heterogeneity parameter can lead to new descriptions of soil PSD, other than the usual clay, silt, and sand, that can describe better different soil physical properties, that are texture-dependent.

Saturated hydraulic conductivity (

The dependence of

A common way to parametrize the PSD for

The heterogeneity of particle size distributions appears to be an important
factor affecting hydraulic parameters of soils, including the saturated
hydraulic conductivity. Values of

The objective of this work was to test the hypothesis that combining two
recent developments – the description of the PSD by different textural
triplets that may represent different soil physical properties dependent on
the particle sizes present in the triplet, and the information entropy, as a
PSD heterogeneity parameter that depends on the triplet used – may linearly
correlate with

For this study we used the USKSAT database, about which detailed information
can be found in

We used all possible triplets formed from seven textural fractions. Triplets consisted of coarse, intermediate, and fine fractions. The symbols for triplet showed how the fractions were grouped. For example the “coarse” fraction for the triplet “3-2-2” included very coarse sand, coarse sand, and medium sand; the “intermediate” fraction included fine sand and very fine sand; and “fine” included silt and clay. The triplet “5-1-1” was the standard one where “coarse” included all five sand fractions, “intermediate” included silt, and “fine” included clay. The amount of possible triplets with 7 textural fractions was 15.

The entropy-based parametrization of textures introduced in

For each soil in this study, we grouped the 7 available textural fractions in
the 15 possible triplet combinations and calculated the respective triplet's
IE using formula (

As we want to compare the linearity (i.e. the proportionality between the
heterogeneity of the particular physical sizes chosen and the hydraulic
behaviour), we used the coefficient of determination,

IE numerical approximation ternary representation: IE is computed for a sample of 5051 evenly distributed soils in the USDA textural triangle using the clay, silt, and sand fractions as input triplet. This distribution of IE is repeated for any textural triangle, when the fractions used for its calculations are the ones at the axes of the triangle. The lowest values for the IE are near the vertex of the triangle, i.e. where one fraction dominates above the others. Biggest values are located towards the centre of the triangle, where the distribution fractions are more balanced.

Linear regressions “bin midpoint vs. average bin

Ternary representations for IE calculated for the soils of the study
but using different triplets. The usual clay, silt, and sand triplet
(“5-1-1”) was used at panel

In order to make some inference on these parameters we employed the bootstrap
method, which has been used in a very similar context by

We took 1000 samples with size equal to the total amount of soils, with
repetition, and calculated, for each sample, the coefficient of
determination (

These regressions were obtained for each of 15 triplets and for those of USDA textural classes that were represented in the selected database by more than 50 samples, i.e. all of them except silty clay loams and silts.

Ternary graphs were used to visually correlate the IE values calculated
with the

Representation in the USDA textural triangle of the 19 193 soils
used in this study.

For each textural class, we did a sensitivity analysis by calculating the
ratio of the range of

Statistical description of

Figure

Table

Linear regressions for

Ternary representations for

The best triplet in terms of highest mean

The standard triplet (“5-1-1”) yielded, for the

Computed mean and standard deviation (SD) for

In this section we show how IE works differently among textural classes: using different triplets we can find that the textural classes are predicted differently; what works for some is for others counterproductive.

Table

Summary of triplets for

Almost all sandy textural classes had the highest regression coefficients.
Table

For the

For the

Furthermore, the best triplet, “1-1-5”, also pointed in this direction: the
fine fraction contains medium sand, fine sand, very fine sand, silt, and sand
particles, while the intermediate fraction contains only the coarse sand,
leaving the coarse fraction with the very coarse sand, thus giving more
importance to the possibly aggregating particles than a triplet, like
“1-4-2”,
which had

In the regressions made with all the soils, the behaviour
of (IE,“3-1-3”) was noteworthy. The average value of all triplets was 0.727, but
(IE,“3-1-3”) gave an exceptionally low

The “3-2-3” triplet groups fine sand with silt and clay, and coarse and very
coarse sand with medium sand.

However, it is also noteworthy that regressions against
(IE,“3-1-3”) were actually quite good (

When all the soils are considered together, then (IE,“3-1-3”) might fail, due to the scaling break, but when we restrict the study to a certain part of the textural triangle, that effect might diminish to a point where this triplet is even useful to predict some texturally derived properties, or maybe the scaling break effect is also restricted to some textural classes and should be further investigated.

As results show, IE is not a powerful

Comparison of parametrizing power of (IE,“5-1-1”) against IE
calculated with other triplets. The ranges of variation of IE calculated with
the different triplets are compared to the ranges of variation of

Table

Textural heterogeneity is a crucial factor affecting soil

This work has limitations, in particular the limited available texture data
of only seven fractions in the database. The boundaries between coarse,
intermediate, and fine fractions can be moved with data from continuous
measurements of texture in the fine sand–silt–clay range of particle sized.
This may bring the improvements in mean bin

Although globally the IE computed from different triplets shows a potential
to reflect the effect of soil texture on the

Overall, the heterogeneity parameter, IE, combined with the different
triplet information, appears to be a strong candidate as an input for the
development of new PTFs to predict

The PSD coarse, intermediate, and fine fractions in soil textural triplets can be redefined from standard “sand–silt–clay” to other fraction size ranges. The textural heterogeneity parameters obtained for some of the new triplets correlate with soil saturated hydraulic conductivity averaged by ranges of the heterogeneity parameters. This approach allows one to quantify the effect of the textural heterogeneity of saturated hydraulic conductivity of soils. Given that size boundaries of sand, silt, and clay fractions have not originally been established for the purposes of prediction of soil hydraulic conductivity, it may be beneficial to look for other size-based subdivisions of particle size distributions that, when used along with other soil properties such as bulk density and organic matter content, may provide better predictions of the saturated hydraulic conductivity.

The data we have used come from the reference

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