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 (sp) from soil bulk electrical conductivity (sb) 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 sb, and relative dielectric permittivity (eb) in moist soil. The reciprocal of pore water electrical conductivity (1/sp) appears as a slope of the Hilhorst model and the ordinary least squares (OLS) of this linear relationship yields a single estimate ( 1/spˆ ) of the regression parameter vector (sp) 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 sp over time. A time series of the relative dielectric permittivity (eb) and sb 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 eb and sb in order to capture deterministic changes to (1/sp). 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 eb obtain a much better match and the estimated evolution of sp converged to its true value. Moreover, the offset of this linear relation varies for each soil depthPeer Reviewe