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Open AccessArticle

Estimating Pore Water Electrical Conductivity of Sandy Soil from Time Domain Reflectometry Records Using a Time-Varying Dynamic Linear Model

1
Department of Ecology, Ecohydrology and Landscape Evaluation, Technische Universität Berlin Ernst-Reuter Platz 1, 10587 Berlin, Germany
2
Department of Statistical and Operational Research, Universitat Politècnica de Catalunya (UPC), Jordi Girona, 31, 08034 Barcelona, Spain
3
Department of Ecology, Technische Universität Berlin Ernst-Reuter Platz 1, 10587 Berlin, Germany
*
Author to whom correspondence should be addressed.
Sensors 2018, 18(12), 4403; https://doi.org/10.3390/s18124403
Received: 8 November 2018 / Revised: 7 December 2018 / Accepted: 10 December 2018 / Published: 13 December 2018
(This article belongs to the Special Issue Selected Papers from ISEMA 2018)
Despite the importance of computing soil pore water electrical conductivity (σp) from soil bulk electrical conductivity (σb) in ecological and hydrological applications, a good method of doing so remains elusive. The Hilhorst concept offers a theoretical model describing a linear relationship between σb, and relative dielectric permittivity (εb) in moist soil. The reciprocal of pore water electrical conductivity (1/σp) appears as a slope of the Hilhorst model and the ordinary least squares (OLS) of this linear relationship yields a single estimate ( 1 / σ p ^ ) of the regression parameter vector (σp) for the entire data. This study was carried out on a sandy soil under laboratory conditions. We used a time-varying dynamic linear model (DLM) and the Kalman filter (Kf) to estimate the evolution of σp over time. A time series of the relative dielectric permittivity (εb) and σb of the soil were measured using time domain reflectometry (TDR) at different depths in a soil column to transform the deterministic Hilhorst model into a stochastic model and evaluate the linear relationship between εb and σb in order to capture deterministic changes to (1/σp). Applying the Hilhorst model, strong positive autocorrelations between the residuals could be found. By using and modifying them to DLM, the observed and modeled data of εb obtain a much better match and the estimated evolution of σp converged to its true value. Moreover, the offset of this linear relation varies for each soil depth. View Full-Text
Keywords: electrical conductivity; relative dielectric permittivity; time domain reflectometry; kalman filter; dynamic linear model electrical conductivity; relative dielectric permittivity; time domain reflectometry; kalman filter; dynamic linear model
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Aljoumani, B.; Sanchez-Espigares, J.A.; Wessolek, G. Estimating Pore Water Electrical Conductivity of Sandy Soil from Time Domain Reflectometry Records Using a Time-Varying Dynamic Linear Model. Sensors 2018, 18, 4403.

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