Alternative approach to calculate soil hydraulic-energy-indices and -functions

Robson André Armindo, Ole Wendroth

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Soil physical quality (SPQ) is related to soil health and many studies have applied these indices manifesting soil structural behavior. A widely used hydraulic function in this analysis is the soil water retention curve (SWRC) and its integration holds important information, which reflects SPQ diversity. Usually, the SWRC is mathematically describing the relationship between volumetric soil water content (θ) and suction head (h) in the functions θ(h) and h(θ), in which h ≥ 0 and 0 < θ < 1. Geometrically, a logic way to describe the SWRC is applying the logarithm to the values of h to build the function θ(log10h) or log10h(θ), however, in this case the graph usually begins at h = 1, since log10(1) = 0. In several studies, the concept of the integral ∫θ(h)dh [or ∫h(θ)dθ] has been presented in the literature since 1978. Unfortunately, the integral ∫log10h(θ)dθ should be used for h ≥ 1 in order to avoid negative results generated from the domain 0 < h < 1, which would be integrated to the final area under the SWRC. Furthermore, since the fitted values of the parameters of the Van Genuchten-Mualem (VGM) equation are different when functions θ(h) and θ(log10h) are used, results of water content at saturation (θs), permanent wilting point (θpwp) and field capacity (θfc) are different as well, questioning the applicability of the integral ∫log10h(θ)dθ. The objective of this study was to develop a novel approach to calculate hydraulic-energy indices and to improve their capacity to reflect SPQ differences. In this approach, the function θ(h) was parameterized in order to find results for θs, θpwp and θfc. Then, the function θ(log10h) was parameterized to obtain results for θs-pF, θpwp-pF and θfc-pF, which were tested against θs, θpwp and θfc. A total of 72 SWRCs were analysed with both functions θ(h) and θ(log10h). Results showed that the limits of integration θs-pF, θpwp-pF and θfc-F remained the same by keeping the same ranges of available water and drainable porosity, as in the case when the function θ(h) was used. This new approach turned out more suitable than the original approach for calculating hydraulic-energy indices, because it was more sensitive to reveal SPQ differences.

Original languageEnglish
Article number113903
StatePublished - Dec 1 2019

Bibliographical note

Publisher Copyright:
© 2019 Elsevier B.V.


  • Integral energy
  • SPQ indices
  • Soil water retention integration

ASJC Scopus subject areas

  • Soil Science


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