Estimating Pore Water Electrical Conductivity of Sandy Soil from Time Domain Reflectometry Records Using a...

Despite the importance of computing soil pore water electrical conductivity (σ) from soil bulk electrical conductivity (σ) 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 σ, and relative dielectric permittivity (ε) in moist soil. The reciprocal of pore water electrical conductivity (1/σ) 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 (σ) 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 σ over time. A time series of the relative dielectric permittivity (ε) and σ 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 ε and σ in order to capture deterministic changes to (1/σ). 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 ε obtain a much better match and the estimated evolution of σ converged to its true value. Moreover, the offset of this linear relation varies for each soil depth.