User-derived calibration equation

A quadratic equation or third order polynomial can describe the relationship between soil permittivity and volumetric water content. In many applications, a linear equation similar to Ledieu et al (1986) gives required accuracy.

Quadratic form:

θ_v(K_a) = C₀ + C₁•K_a + C₂•K_a²

with θ_v the volumetric water content, K_a the bulk dielectric permittivity of the soil, and Cn, the calibration coefficient.

Third-degree polynomial form:

θ_v(K_a) = C₀ + C₁•K_a + C₂•K_a² + C₃•K_a³

with θ_v the volumetric water content, K_a the bulk dielectric permittivity of the soil, and Cn, the calibration coefficient.

Linear form:

θ_v(K_a) = C₀ + C₁•K_a^0.5

with θ_v the volumetric water content, K_a the bulk dielectric permittivity of the soil, and Cn, the calibration coefficient.

Two data points from careful measurements sometimes are enough to derive a linear calibration. Use at least three data points for a quadratic calibration. With three evenly spaced water contents covering the expected range, the middle water content data point indicates whether a linear or polynomial calibration equation is needed.

Use at least four data points for the derivation of a third-degree polynomial. Space the data points as evenly as practical over the expected range of water content and include the wettest and driest expected values.

FAQ(s)

How was the general calibration performed for the CS650 and the CS655?

Period average and electrical conductivity readings were taken with several sensors in solutions of varying permittivity and varying electrical conductivity at constant temperature. Coefficients were determined for a best fit of the data. The equation is of the form

K_a(σ,τ) = C₀*σ³*τ² + C₁*σ²*τ² + C₂*σ*τ² + C₃*τ² + C₄*σ³*τ + C₅*σ²*τ + C₆*σ*τ + C₇*τ + C₈*σ³ + C₉*σ² + C₁₀*σ + C₁₁

where Ka is apparent dielectric permittivity, σ is bulk electrical conductivity (dS/m), τ is period average (μS), and C₁ to C₁₁ are constants.

With regard to the CS650 and the CS655, is there a generic calibration equation for artificial or organic soil?

No. The equation used to determine volumetric water content in the firmware for the CS650 and the CS655 is the Topp et al. (1980) equation, which works for a wide range of mineral soils but not necessarily for artificial or organic soils that typically have high organic matter content and high clay content. In this type of soil, the standard equations in the firmware will overestimate water content.

When using a CS650 or a CS655 in artificial or organic soil, it is best to perform a soil-specific calibration. A linear or quadratic equation that relates period average to volumetric water content will work well.

Using a CS650 or a CS655, when should a soil-specific calibration be performed?

To get accurate water content readings, a soil-specific calibration is probably required if any of the following are true:

The soil has more than 5% organic matter content.
The soil has more than 20% clay content.
The soil is derived from volcanic parent material.
The soil has porosity greater than 0.5.