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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

This paper presents the application of a frequency-domain reflectometry (FDR) sensor designed for soil salinity assessment of sandy mineral soils in a wide range of soil moisture and bulk electrical conductivity, through the determination of soil complex dielectric permittivity spectra in the frequency range 10–500 MHz. The real part of dielectric permittivity was assessed from the 380–440 MHz, while the bulk electrical conductivity was calculated from the 165–325 MHz range. The FDR technique allows determination of bulk electrical conductivity from the imaginary part of the complex dielectric permittivity, without disregarding the dielectric losses. The soil salinity status was determined using the salinity index, defined as a partial derivative of the soil bulk electrical conductivity with respect to the real part of the soil complex dielectric permittivity. The salinity index method enables determining the soil water electrical conductivity value. For the five sandy mineral soils that have been tested, the relationship between bulk electrical conductivity and the real part of dielectric permittivity is essentially linear. As a result, the salinity index method applied for FDR measurements may be adapted to field use after examination of loam and clayey soils.

Accurate and reliable estimation of soil salinity, defined as the electrical conductivity of soil water extract or saturated soil water extract, is a very important issue, especially in arid regions, where salinity of the soil may increase significantly and pose a danger to plants [_{s}_{b}_{b}

Soil bulk dielectric permittivity and electrical conductivity were determined from the velocity of the TDR pulse and its attenuation, respectively, when traveling along the TDR parallel waveguide inserted in the soil [_{s}_{s}

The application of the TDR technique in calculating the salinity index includes simplifications that can affect the final result. The value of _{b}_{b}_{d}_{0}^{−12} F m^{−1} stands for dielectric permittivity of free space.

The dependence of the complex dielectric permittivity of soils on the frequency of the applied electrical field has been discussed in literature; however, the applied frequency was not defined [

It was shown [

The aim of the paper is to determine the bulk electrical conductivity and soil pore water electrical conductivity of selected soil samples based on independent measurements of the real and imaginary parts of the complex dielectric permittivity using the FDR technique in the frequency range of 10 MHz to 500 MHz. The received FDR-based linear salinity index is compared with the Malicki and Walczak [_{b} vs. ε′_{b}

zThe tested material included five mineral soils that were air dried and put through a 2 mm sieve. The basic physical characteristics of these materials are given in ^{3} volume (cylinder; diameter: 4.6 cm, height: 7 cm), which helped to prepare appropriate soil samples with variable water content ranging from approximately 10% to near saturation. The soil material of various moisture levels was packed into the containers in small portions and pressed with a 0.2 kg rubber hammer to achieve homogenous density distribution in the soil sample [

The values of saturation water content by mass for the selected soils were determined using capillary rise. Three samples of each soil of a known dry weight placed in measurement containers with holes at the bottom, were gathered in separate plastic bowls with porous bottom sides. The containers with soil, covered to minimize excessive evaporation, were immersed for 72 hours in distilled water allowing capillary rise to achieve saturation. Then they were weighed to determine the mass of water saturating each soil sample. Finally, after simple calculations it was possible to determine the mass of water for adding to the 120 cm^{3} volume of air-dry soil to achieve soil samples of a desired water content, from 10% to near saturation.

On the basis of generally available conversion tables and pilot measurements of soil electrical conductivity performed by a TDR meter, three KCl solutions and distilled water were prepared for wetting soil samples (_{s}^{−1}, and of soil water content—from air dryness to near saturation. The samples of chosen soils fully filled 120 cm^{3} containers (plastic cylinder 4.6 cm in diameter and 7 cm in height) equipped with a sealed cover, and wetted by distilled water and the KCl solutions.

The material samples in containers were mixed with distilled water and KCl solutions, covered with a sealing cap, weighed and conditioned at 40 °C for 72 hours to ensure uniform water content in the sample volume. Then, after leaving the soil containers for several hours at room temperature, the filled containers were again weighed to make weight corrections caused by possible water evaporation loss. Next, the containers were opened to perform FDR measurements of the complex dielectric permittivity of the material. Each FDR measurement was made three times by inserting the probe rods in various locations of the material in the container. All measurements were made in a laboratory with a controlled temperature 21 ± 1°C.

The applied FDR sensor, measurement details and calibration techniques were described earlier by Skierucha and Wilczek [_{11} of the signal reflected from the probe inserted into the sample. This reflection coefficient is defined as:
_{p}_{11}), which allows determining the complex dielectric permittivity from the measured reflection coefficient for each applied frequency. For calibration purposes, measurements of short circuit, open (air) and acetone were used, which reduced the measurement errors [

The FDR measurement technique allowed determining the real and imaginary parts of the dielectric permittivity directly and independently.

The real part of the dielectric permittivity is strongly related to the soil water content, namely the square root of the real part of the dielectric permittivity (the refractive index) depends linearly [

The imaginary part of the complex dielectric permittivity may be used to infer the bulk electrical conductivity of the sample. According to _{b}

One can multiply both sides of the above equation by the frequency, so that the whole relation is a linear function of

Assuming that _{d}_{b}^{2} and standard error of regression _{d}

This procedure was applied to determine the bulk electrical conductivity _{b}

In order to test the concept of salinity index introduced by Malicki and Walczak [_{b}^{2} and standard error of regression _{b}^{2} (as presented on the graph), it transpires that for all tested samples the relations between _{b}_{b} vs. ε′_{b} vs. ε′_{b}_{d}

The relations between the salinity index and moistening solution conductivity _{s}_{s}_{b}_{s}_{s}_{s}_{s} vs. C_{s}

One may notice that for the samples wetted with distilled water the salinity index is equal to some initial value _{SI}_{r}_{s} vs. C_{s}

Therefore, one may expect that the electrical conductivity of soil water _{w}

This assumption will be tested in a subsequent part of this paper.

To calculate the salinity index using the method presented above, it is necessary to take a series of measurements of the same soil moistened with the same solution to various water contents. Obviously, this procedure has little practical use, since a measure of soil salinity applicable for field conditions should provide an accurate estimate based on a single measurement of a single soil sample. However, similarly to the method shown in [_{b} vs. ε′_{b}_{I}_{I}_{b}

To apply the formula above in the field, it is necessary to know the values of _{I}_{I}_{I}_{I} =^{2} = 0.99, where _{I}_{I}^{2} = 0.89 and clay content given in units from _{I}_{I}_{I}_{I}_{b}_{I}_{I}

To calculate the electrical conductivity of soil water _{w}_{S}_{I}_{I}_{I}^{2} equals only 0.56. It is obvious that in order to minimize the error of _{w}

On the left panel of _{w}_{w}_{b} vs. ε′_{w}_{S}_{w}_{w}_{S}_{S} vs. C_{S}

The data points shown on the left panel of _{w}_{w}_{S}_{w}

The values of _{w}_{S}_{w}_{S}

On the left panel of _{b} vs. ε′_{w}

Even when the dependence _{b} vs. ε′_{b}_{S} vs. C_{S}^{2} = 0.9988 for the worst fit for soil no. 568), which enables calculating _{w}_{w}_{S}_{w}_{w}

The errors of _{w}_{w}_{w}_{b} vs. ε′_{w}

Generally, only the linear field model may exhibit greater errors for _{w}

To further test the linear salinity index model, introduced by Malicki and Walczak in [_{S}_{r}_{w}

The results can be then compared with _{S}_{b} vs. ε′^{2} and the standard errors _{S}_{S}_{w}

The present study deals with the measurement of soil salinity using the FDR technique. It enables directly obtaining real and imaginary parts of complex dielectric permittivity. The obtained

The salinity index method, introduced in [

The linear salinity model by definition gives electrical conductivity of soil pore water independent of the real part of dielectric permittivity and thus of water content. This ignores the possible ion adsorption and desorption processes occurring on the surfaces of the soil solid particles. Even though the chosen soils were sandy, they differed in specific surface area values (as shown in

Real and imaginary parts of the complex dielectric permittivity of a sample of soil no. 601 wetted with distilled water to approximately 50% of saturation water content.

Determination of bulk electrical conductivity of a sample of soil no. 601 wetted with distilled water to 50% of saturation water content; _{b}^{2} and standard error of regression are given on the plot. The standard error of determination of _{b}

On the left: bulk electrical conductivities of all measured soil samples _{S}_{b} vs. ε′_{s}^{2} and standard errors of regressions are given on the plots.

Soil water conductivities _{w}_{w}_{S}_{b} vs. ε′

Conductivities of the moistening solutions calculated from the linear salinity index model

Selected physical characteristics of tested material; RSD stands for relative standard deviation (standard deviation/mean value).

^{−3}) |
^{a}^{2}·g^{−1}) |
^{b} | |||||
---|---|---|---|---|---|---|---|

| |||||||

568 | 1,415 ± 3 | 34 | 37.2 | 0.03 | 58 | 31 | 11 |

589 | 1,697 ± 4 | 10 | 22.4 | 0.04 | 88 | 11 | 1 |

601 | 1,380 ± 4 | 31 | 38.7 | 0.02 | 60 | 34 | 6 |

605 | 1,635 ± 7 | 10 | 23.8 | 0.07 | 95 | 4 | 1 |

loess | 1,382 ± 4 | 30 | 37.6 | 0.01 | 55 | 29 | 16 |

Water vapor adsorption method [

Data taken from Glinski

Parameters of KCl solutions applied for wetting the measured material (values at temperature 21 °C). Assumed _{s}

^{−3}) |
_{S} (mS·m^{−1}) | |
---|---|---|

1 | 0.000 | – |

2 | 0.042 | 490 |

3 | 0.093 | 1,080 |

4 | 0.150 | 1,680 |

Conductivities of water content _{w}

No. of solution | Re( |
_{w} (linear model) (mS m^{−1}) |
_{w} (linear field model) (mS m^{−1}) |
_{w} (quadratic model) (mS m^{−1}) |
|||
---|---|---|---|---|---|---|---|

1 | 13.6 | 263 | 278 | 255 | |||

2 | 13.6 | 758 | 801 | 756 | |||

3 | 13.4 | 1,424 | 1,434 | 1,441 | |||

4 | 13.1 | 1,919 | 1,796 | 1,921 |