| Summary: | Despite the importance of computing soil pore water electrical conductivity (<i>σ<sub>p</sub></i>) from soil bulk electrical conductivity (<i>σ<sub>b</sub></i>) 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 <i>σ<sub>b</sub></i>, and relative dielectric permittivity (<i>ε<sub>b</sub></i>) in moist soil. The reciprocal of pore water electrical conductivity (1/<i>σ<sub>p</sub></i>) appears as a slope of the Hilhorst model and the ordinary least squares (OLS) of this linear relationship yields a single estimate (<inline-formula> <math display="inline"> <semantics> <mrow> <mover accent="true"> <mrow> <mn>1</mn> <mo>/</mo> <msub> <mi>σ</mi> <mi>p</mi> </msub> </mrow> <mo stretchy="true">^</mo> </mover> </mrow> </semantics> </math> </inline-formula>) of the regression parameter vector (<i>σ<sub>p</sub></i>) 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 <i>σ<sub>p</sub></i> over time. A time series of the relative dielectric permittivity (<i>ε<sub>b</sub></i>) and <i>σ<sub>b</sub></i> 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 <i>ε<sub>b</sub></i> and <i>σ<sub>b</sub></i> in order to capture deterministic changes to (1/<i>σ<sub>p</sub></i>). 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 <i>ε<sub>b</sub></i> obtain a much better match and the estimated evolution of <i>σ<sub>p</sub></i> converged to its true value. Moreover, the offset of this linear relation varies for each soil depth.
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