Hydrol. Earth Syst. Sci., 22, 3923–3932, 2018 https://doi.org/10.5194/hess-22-3923-2018 © Author(s) 2018. This work is distributed under the Creative Commons Attribution 4.0 License. Technical note: Saturated hydraulic conductivity and textural heterogeneity of soils Carlos García-Gutiérrez1, Yakov Pachepsky2, and Miguel Ángel Martín1 1Department of Applied Mathematics, Universidad Politécnica de Madrid, Madrid, Spain 2USDA-ARS Environmental Microbial and Food Safety Laboratory, Beltsville, MD 20705, USA Correspondence: Carlos García-Gutiérrez ([email protected]) Received: 1 December 2017 – Discussion started: 5 December 2017 Revised: 14 May 2018 – Accepted: 28 June 2018 – Published: 20 July 2018 Abstract. Saturated hydraulic conductivity (Ksat) is an im- ues of soil Ksat appears to be essential in designing man- portant soil parameter that highly depends on soil’s particle agement actions and practices, such as irrigation scheduling, size distribution (PSD). The nature of this dependency is ex- drainage, flood protection, and erosion control. plored in this work in two ways, (1) by using the informa- The dependence of Ksat on soil texture has been well docu- tion entropy as a heterogeneity parameter of the PSD and mented (Hillel, 1980). Different parametrizations of particle (2) using descriptions of PSD in forms of textural triplets, size distributions (PSDs) were suggested to relate Ksat and different than the usual description in terms of the triplet of soil texture. It was proposed that d10, d20, and d50 particle sand, silt, and clay contents. The power of this parameter, as diameters (Chapuis, 2004; Odong, 2007) or slope and inter- a descriptor of lnKsat, was tested on a database larger than cept of the particle size distribution curve (Arya and Paris, 19 000 soils. Bootstrap analysis yielded coefficients of deter- 1980; Alyamani and Sen, 1993) could be used. Also, various mination of up to 0.977 for lnKsat using a triplet that com- functions were fitted to PSDs, and the fitting parameters were bines very coarse, coarse, medium, and fine sand as coarse related to Ksat. For example, Chapuis et al.(2015) proposed particles; very fine sand, and silt as intermediate particles; using two lognormal distributions to fit the detailed particle and clay as fine particles. The power of the correlation was size distribution and to use the lognormal distribution param- analysed for different textural classes and different triplets eters to predict the Ksat. using a bootstrap approach. Also, it is noteworthy that soils A common way to parametrize the PSD for Ksat estima- with finer textures had worse correlations, as their hydraulic tion purposes is using the textural triplet that provides the properties are not solely dependent on soil PSD. percentage of coarse particles (sand), intermediate particles This heterogeneity parameter can lead to new descriptions (silt), and fine particles (clay). Ksat values are estimated us- of soil PSD, other than the usual clay, silt, and sand, that ing the contents of one or two triplet fractions or just the tex- can describe better different soil physical properties, that are tural class (Rawls et al., 1998). Representing PSD by textural texture-dependent. triplets is the common way to estimate a large number of soil parameters (Pachepsky and Rawls, 2004). The coarse, inter- mediate, and fine fractions need not be sand, silt, and clay. Martín et al.(2018) showed that different definitions of the 1 Introduction triplet (e.g. coarse sand, sand, and medium sand as coarse; fine sand and very fine sand as intermediate; and silt and Saturated hydraulic conductivity (Ksat) is the measure of clay as fine triplet fractions) provide much better inputs for soil’s ability to conduct water under saturation conditions bulk density estimation compared with the standard textural (Klute and Dirksen, 1986). It is an essential parameter of triplet. These different parametrizations of soil texture might soil hydrology. Soil Ksat affects many aspects of soil func- put the focus on different soil physical properties, depending tioning and soil ecological services, like infiltration, runoff, on the different particle sizes represented in the triplet. groundwater recharge, and nutrient transport. Knowing val- Published by Copernicus Publications on behalf of the European Geosciences Union. 3924 C. García-Gutiérrez et al.: Saturated hydraulic conductivity and textural heterogeneity of soils The heterogeneity of particle size distributions appears 2 Materials and methods to be an important factor affecting hydraulic parameters of soils, including the saturated hydraulic conductivity. Values 2.1 Database description and textural triplet selection of Ksat depend on both distribution of sizes of soil particles, i.e. soil texture, and the spatial arrangement of these parti- For this study we used the USKSAT database, about which cles, i.e. soil structure. Soil structure can be to some extent detailed information can be found in Pachepsky and Park controlled by soil texture, since packing of particles is af- (2015). This database consists of soils from different loca- fected by the particle size distributions (e.g. Gupta and Lar- tions of the USA and contains soils from 45 different sources. son, 1979; Assouline and Rouault, 1997; Horn et al., 1994; We selected only those sources which (a) had data on both Jorda et al., 2015). Recent studies proposed using the infor- Ksat and on the seven textural fractions and (b) presented mation entropy as the parameter of the PSD heterogeneity measurements of Ksat made in laboratory with the constant for predicting soil water retention (Martín et al., 2005) and head method. From those, we subset those soils whose sum soil bulk density (Martín et al., 2018). Previously, informa- of mass in the seven textural fractions, i.e. (1) very coarse tion entropy was used, together with other predictor variables sand, (2) coarse sand, (3) medium sand, (4) fine sand, (5) very to estimate Ksat, using multivariate analysis (Boadu, 2000). fine sand, (6) silt, and (7) clay ranged from 98 to 102 %. The objective of this work was to test the hypothesis that The final number of soils considered was 19 121. By USDA combining two recent developments – the description of the textural classes the total number of soils are 12 068 sands, PSD by different textural triplets that may represent differ- 1780 loamy sands, 2123 sandy loams, 104 loams, 135 silt ent soil physical properties dependent on the particle sizes loams, 36 silts, 2004 sandy clay loams, 78 clay loams, 41 silt present in the triplet, and the information entropy, as a PSD clay loams, 345 sandy clays, 0 silty clays, and 407 clays. All heterogeneity parameter that depends on the triplet used – the samples in the database used are undisturbed soil sam- may linearly correlate with lnKsat and may be seen as a step ples. forward to study the effect of heterogeneity widely recog- We used all possible triplets formed from seven textu- nized in the majority of works that studied the particle size– ral fractions. Triplets consisted of coarse, intermediate, and hydraulic-conductivity relationships. By describing the PSD fine fractions. The symbols for triplet showed how the frac- in terms of different triplets, the input information would tions were grouped. For example the “coarse” fraction for possibly have different physical interpretations. We wanted the triplet “3-2-2” included very coarse sand, coarse sand, to link the heterogeneity of this physical information to the and medium sand; the “intermediate” fraction included fine hydraulic behaviour of the soil. Therefore, we explored the sand and very fine sand; and “fine” included silt and clay. possible relationships between lnKsat values and an entropy The triplet “5-1-1” was the standard one where “coarse” in- metric of soil texture heterogeneity using different size lim- cluded all five sand fractions, “intermediate” included silt, its of coarse intermediate and fine fractions, using the large and “fine” included clay. The amount of possible triplets with USKSAT database on laboratory-measured Ksat, which con- 7 textural fractions was 15. tains more than 19 000 samples. The triplets with highest cor- relations will be understood as the physical sizes that influ- 2.2 Heterogeneity metric calculation ence the most in the packing of particles yielding the particu- The entropy-based parametrization of textures introduced in lar hydraulic behaviour. While pedotransfer functions (PTFs) Martín et al.(2001) is a central concept in the information are a useful tool to predict difficult-to-measure soil proper- entropy (IE) (Shannon, 1948). Assuming the texture inter- ties, they sometimes exhibit highly non-linear relationships val divided into k textural size ranges and that the respective that are difficult to interpret. While the objective of this pa- textural fraction contents are p ;p ;:::;p , 1 ≤ i ≤ k , with per was the exploration of the physical relation of the new 1 2 k Pk p D 1, the Shannon IE (Shannon, 1948) is defined by tools and the saturated hydraulic conductivity, the future de- iD1 i velopment of PTFs for prediction purposes is a promising k avenue for expanding this research. We note that research X IE D − pilog2pi; (1) in this work is descriptive. It does not include an explana- iD1 tion of what we have observed. However, any explanatory research with mechanisms, models, etc. was historically pre- where pilog2pi D 0 if pi D 0. The IE is a widely accepted ceded with the descriptive research. measure of the heterogeneity of distributions (Khinchin, 1957). In the case of three fractions, the minimum value of IE is zero when only one fraction is present, and the maxi- mum value is 1.57 when three fractions are present in equal amounts (see Fig.1). For each soil in this study, we grouped the 7 available tex- tural fractions in the 15 possible triplet combinations and cal- culated the respective triplet’s IE using formula (1).