Two- and three-parameter calibrations of time domain reflectometry for soil moisture measurement

C. Yu, A. W. Warrick, M. H. Conklin, M. H. Young, M. Zreda

Research output: Contribution to journalArticlepeer-review

42 Scopus citations


Time domain reflectometry (TDR) is widely used to measure and monitor soil water. The commonly used calibration curve is the third-degree 'universal polynomial' of Topp et al. [1980]. The most common refinement is calibration to a specific soil but still using four parameters (coefficients)from fitting a third-degree polynomial. Here we demonstrate that a three-parameter expression, θ(v) = aK(a)/α + b, fits as close as or more closely than the four-parameter polynomial (where the three parameters a, b, and α are determined by fitting water content θ(v) to the dielectric coefficient K(a)). This form is consistent with the well-known mixing model. For an isotropic soil with homogeneous water distribution this expression is further simplified to two parameters by taking α = 0.5. When α is 0.5, its calibration is equivalent to the linear calibration between θ(v) and the travel time along the waveguide. In addition, the simple three-parameter expression can be easily inverted without losing accuracy with regard to the original calibration. The TDR calibration expressed in a three-parameter form not only achieves a good fit but also conveys a physical connotation.

Original languageEnglish (US)
Pages (from-to)2417-2421
Number of pages5
JournalWater Resources Research
Issue number10
StatePublished - Oct 1997

ASJC Scopus subject areas

  • Water Science and Technology


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