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

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