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 ([Formula: see text]) 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.