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Frequency Domain Analysis for Extending Time Domain Reflectometry Water Content Measurement in Highly Saline Soils

^a Dep. of Plants, Soils, and Biometeorology, Utah State Univ., Logan, UT 84322-4820
^b Dep. of Civil and Environmental Engineering, Univ. of Connecticut, Storrs, CT 06269-2037

View larger version (27K): [in a new window]   Fig. 1. Time domain reflectometry (TDR) waveforms measured in water using a coaxial TDR cell (20 cm) show progressive attenuation of the second reflection point with increasing solution electrical conductivity, w, leading to eventual loss of permittivity (water content) determination.

View larger version (31K): [in a new window]   Fig. 2. Three-rod time domain reflectometry (TDR) probes ranging in size from 15 to 2 cm in length were used to obtain waveforms in Millville silt loam soil. Shorter probes are more effective in maintaining dielectric information based on the second reflection, which preserves critical scatter function features in the frequency domain.

View larger version (20K): [in a new window]   Fig. 3. Different modes of permittivity analysis are outlined in the waveform transformation process. Travel time analysis (TTA) yields permittivities in the time domain using longer probes in non-saline soils. Discrete fast Fourier transform (DFFT) of the input [vo(t)] and response [r(t)] function waveforms provide the scatter function [S11(f)] from the transformed frequency-dependent functions Vo(f) and R(f). Permittivity estimates are obtained from scatter function fitting (SFF) utilizing Debye (1929) model parameterization or from resonant frequency analysis (RFA) giving permittivity estimates based on the resonant or half-wavelength frequency (f*).

View larger version (24K): [in a new window]   Fig. 4. Waveforms derived from TDR measurements using a three-wire probe in air and with no central conductor, vo, in addition to an artificially generated waveform, va. The input function can be represented by the waveform obtained with the central conductor removed or, as an alternative, it may be generated based on the initial rising slope of the waveform in air with a final value of 1.

View larger version (26K): [in a new window]   Fig. 5. Original response function waveform, r(t), of water measured in a coaxial cell compared with the normalized differentiated waveform and the Nicolson ramped waveform. The ramped waveform results from taking the original waveform minus the ramp determined by the magnitude of W(N), the distal point in r(t) (Nicolson, 1973).

View larger version (42K): [in a new window]   Fig. 6. Scatter functions derived from discrete fast Fourier transform (DFFT) of measured waveforms obtained using a three-wire time domain reflectometry (TDR) probe (3-cm) in saturated sand with w = 12 and 24 dS m–1. Lines represent Clarkson (1977)–Debye (1929) modeled scatter functions fit (SFF) to S11 data obtained in the time domain. Static permittivities (s) determined for 12 and 24 dS m–1 were 28 and 29, respectively compared with a TTA measured dielectric of 29 under non-saline conditions.

View larger version (36K): [in a new window]   Fig. 7. Scatter function obtained in saturated Millville silt loam at two different salinity levels using a 3-cm long three-wire probe. Resonant frequency analysis (RFA) of the 48 dS m–1 scatter function using the intersection of two lines drawn through the rising portion of the scatter function data in the first trough yields a permittivity, x, of 30.2 following Eq. [10]. This is comparable with the static permittivity (s = 29.9) obtained from fitting the Debye (1929) model to this data.

View larger version (19K): [in a new window]   Fig. 8. Bulk permittivity of Millville silt loam and sand determined using scatter function fitting (SFF) in the frequency domain and travel time analysis (TTA) in the time domain given as a function of soil solution electrical conductivity. To illustrate the effect of signal attenuation on permittivity determination, probe lengths of 2, 3, 6, 10, and 15 cm were used (note: 10-cm probe was not used in sand).

View larger version (20K): [in a new window]   Fig. 9. One to one comparison between scatter function fitting (SFF) and resonant frequency analysis (RFA) techniques for permittivity determination in the frequency domain. Filled symbols represent determinations in Milville silt loam and empty symbols are for sand.

View larger version (27K): [in a new window]   Fig. 10. Contour lines of resonant frequency-probe length are given as a function of permittivity and suggest bounds for using short probes (i.e., also bounded by maximal TDR frequency and by increasing attenuation). Numbers in parenthesis are computed soil electrical conductivities estimated using Eq. [11] (w = 110 dS–1) and the permittivity-water content relation (Eq. [12]) given by Topp et al. (1980). Reduced permittivity (water content) leads to a commensurate reduction in b suggesting that there may be regions of overlap where TTA and SFF using short probes are applicable.