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Time Domain Reflectometry Sensitivity to Lateral Variations in Bulk Soil Electrical Conductivity

^a Dep. of Environmental Engineering, Aalborg Univ., Sohngaardsholmsvej 57, DK-9000 Aalborg, Denmark
^b Dep. of Communication Technology, Aalborg Univ., Fredrik Bajersvej 7, DK-9000 Aalborg, Denmark

View larger version (31K): [in a new window]   Fig. 1. Illustration of (a) the three-rod probe used in this study (all measures are in millimeters) and (b) the relative spatial sensitivity function [G2(X, Y)] as a function of the dimensionless coordinates X and Y in the plane perpendicular to the long axis of the TDR probe rods of a three-rod TDR probe. Note the logarithmic scaling on the relative spatial sensitivity axis.

View larger version (21K): [in a new window]   Fig. 2. Comparison between the cumulative vertical weighting [W(h)] calculated from TDR-measured soil water content () and bulk soil electrical conductivity (ECb) as a function of distance to the soil surface (h) at two different soil water contents: (a) = 0.153 m3 m-3 and (b) = 0.244 m3 m-3. Also shown is the universal cumulative vertical weighting function (Eq. [15]) for the TDR probe shown in Fig. 1a (solid line).

View larger version (24K): [in a new window]   Fig. 3. Example of the relative Cl- concentration measured by extraction of the soil solution at the end of the diffusion experiment (Method II) carried out at = 0.256 m3 m-3 as a function of distance to the interface between the two half-cells.

View larger version (23K): [in a new window]   Fig. 4. Comparison between the actual distribution of relative electrical conductivity (EC), TDR-measured relative bulk soil electrical conductivity (ECb) and the theoretical distribution of TDR-measured relative ECb as a function of distance to the interface between the half-cells at (a) the beginning (t = 0 d) and (b) 5.9 d after the half-cells were assembled in the diffusion experiment (Method I) carried out at = 0.244 m3 m-3.

View larger version (19K): [in a new window]   Fig. 5. Comparison between the actual distribution of relative electrical conductivity (EC), TDR-measured relative bulk soil electrical conductivity ( ECb), and the theoretical distribution of TDR-measured relative ECb as a function of distance to the interface between the two half-cells at the beginning (t = 0 d) of the diffusion experiment (Method II) carried out at = 0.256 m3 m-3.

View larger version (29K): [in a new window]   Fig. 6. Temporal development in absolute difference between the actual relative bulk soil electrical conductivity (ECb) distribution and the theoretical TDR-measured relative ECb distribution (Relative ECb) as a function of distance from the half-cell interface calculated theoretically from the soil data ( and Dp) obtained in the diffusion experiment (Method II) carried out at = 0.256 m3 m-3.

View larger version (20K): [in a new window]   Fig. 7. Time needed to reach the acceptance criterion, the theoretical TDR-measured relative ECb distribution (Relative ECb = 2%), as a function of soil water content () in three different model soils varying in the value of the Cambell parameter, b, where b = 3, 6, and 12 represents a sand, loam, and clay soil, respectively.

View larger version (25K): [in a new window]   Fig. 8. Temporal development in the maximum absolute difference between the actual relative bulk soil electrical conductivity (ECb) distribution and the theoretical TDR-measured relative ECb distribution (Maximum Relative ECb) for (a) the three-rod probe in Fig. 1a compared with two-rod probes with varying probe rod separation (D) and (b) two-rod probes with constant D, but various rod diameter (B). Calculations were based on soil data ( and Dp) obtained in the diffusion experiment (Method II) carried out at = 0.256 m3 m-3.