### Abstract

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 language | English (US) |
---|---|

Pages (from-to) | 2417-2421 |

Number of pages | 5 |

Journal | Water Resources Research |

Volume | 33 |

Issue number | 10 |

State | Published - Oct 1997 |

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### ASJC Scopus subject areas

- Aquatic Science
- Environmental Science(all)
- Environmental Chemistry
- Water Science and Technology

### Cite this

*Water Resources Research*,

*33*(10), 2417-2421.

**Two- and three-parameter calibrations of time domain reflectometry for soil moisture measurement.** / Yu, C.; Warrick, A. W.; Conklin, M. H.; Young, M. H.; Zreda, Marek G.

Research output: Contribution to journal › Article

*Water Resources Research*, vol. 33, no. 10, pp. 2417-2421.

}

TY - JOUR

T1 - Two- and three-parameter calibrations of time domain reflectometry for soil moisture measurement

AU - Yu, C.

AU - Warrick, A. W.

AU - Conklin, M. H.

AU - Young, M. H.

AU - Zreda, Marek G

PY - 1997/10

Y1 - 1997/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0030772429&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030772429&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0030772429

VL - 33

SP - 2417

EP - 2421

JO - Water Resources Research

JF - Water Resources Research

SN - 0043-1397

IS - 10

ER -