Comparison of Different “S-index” Expressions to Evaluate the State of Physical Soil Properties

The S-index describes the absolute value of slope at the inflection point of the water retention curve (WRC) and it is a popular tool for the indirect description of the soil physical-hydraulic conditions. It can be calculated as a function of van Genuchten (VG) parameters by four different expressions based on (a) the use of arithmetic or ln-transformed axis of pressure head h and (b) the use of volumetric θ or gravimetric W soil water content [the four expressions are obtained from the dθ/dh, dW/dh, dθ/d(lnh) and dW/d(lnh) derivatives]. The aim of the study is to test the ability of the four S-index expressions to rank soil physical-hydraulic (SPH) indicators such as fractions of porosity, bulk density and saturated hydraulic conductivity. WRCs of an artificial soil, which was subjected to flooding and extensive destruction of macroporosity, and WRCs from the twelve USDA soil classes were used in the analysis. The results showed that the expressions of dθ/dh and dW/dh display higher correlations versus the SPH indicators in comparison to dθ/d(lnh) and dW/d(lnh). The expressions based on the gravimetric approach such as dW/dh and dW/d(lnh) do not contain the parameter of bulk density while the expressions based on the ln-transformed axis of h do not contain the parameter a of VG model. Even though dθ/dh and dW/dh showed similar performance, the first one is suggested as the safest approach to describe SPH indicators for non-deformable soils because its theoretical background is more consistent and more relevant to porosity attributes which are always described in terms of volume and not of mass, whereas the second one is suggested for the case of deformable soils in order to avoid errors introduced by the changes of bulk density.