Plant and Soil

, Volume 419, Issue 1–2, pp 237–256 | Cite as

An improved formula for evaluating electrical capacitance using the dissipation factor

  • Imre Cseresnyés
  • Sándor Kabos
  • Tünde Takács
  • Krisztina R. Végh
  • Eszter Vozáry
  • Kálmán Rajkai
Regular Article


Background and aims

The measurement of electrical capacitance in root–soil system (CR) is a useful method for estimating the root system size (RSS) in situ; however, CR–RSS regressions are often poor. It was hypothesized that this weak relationships could be partly due to the variable energy-loss rate, indicated by the dissipation factor (DF).


The values of CR and the associated DF were measured in six plant species grown in quasi-hydroponic pumice medium, arenosol and chernozem soil. The dielectric properties of the plant growth media were also recorded. A modified root–soil capacitance, CDF, was calculated from each CR/DF pair according to the formula CDF = CR·(DF/DFmean)α by estimating α with a standard nonlinear minimization of the sum of squared residuals for CDF–RSS regressions.


The capacitive behavior of the medium improved (mean DF decreased) but fluctuated increasingly as the substrate became more complex. The mean DF values in plant–substrate systems were chiefly determined by the plant and were the most variable in chernozem soil. This strengthening substrate effect on CR measurements appeared as a decreasing trend in the R2 values obtained for the CR–RSS regressions. The regression slope was influenced by plant species and medium, while the y-intercept differed only between substrate types. The proposed use of CDF in place of CR could significantly improve the R2 of CDF–RSS regressions, particularly in chernozem soil (R2 increased by 0.07–0.31).


The application of CDF will provide more reliable and accurate RSS estimations and more efficient statistical comparisons. The findings are worth considering in future investigations using the root capacitance method.


Complex permittivity Dissipation factor Plant–soil system Root electrical capacitance Root system size Soil dielectric 



Akaike’s Information Criterion


Electrical capacitance


Electrical capacitance of the planting substrate


Electrical capacitance of the root–soil system


Electrical capacitance of the root–soil system corrected with dissipation factor


Dissipation factor


Number of model parameters


Root dry mass


Root length


Root surface area


Root system size



This research was funded by the Hungarian National Research, Development and Innovation Office (Project No. K-115714). The authors thank Dr. Tapani Repo for valuable remarks and the anonymous reviewers for their helpful and constructive comments.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Imre Cseresnyés
    • 1
  • Sándor Kabos
    • 2
  • Tünde Takács
    • 1
  • Krisztina R. Végh
    • 1
  • Eszter Vozáry
    • 3
  • Kálmán Rajkai
    • 1
  1. 1.Institute for Soil Sciences and Agricultural Chemistry, Centre for Agricultural ResearchHungarian Academy of SciencesBudapestHungary
  2. 2.Department of StatisticsEötvös Loránd UniversityBudapestHungary
  3. 3.Department of Physics and ControlSzent István UniversityBudapestHungary

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