Dynamic Harmonic Regression Approach for Soil Water Flux Estimation and Temperature Prediction Under Non-Stationary Temperature Forcing

Analytical temperature-based methods commonly assume stationary sinusoidal forcing, limiting their applicability under natural non-stationary conditions. This study couples Dynamic Harmonic Regression (DHR) with a one-dimensional conductive–advective heat transport solution to estimate time-varying thermal diffusivity and water flux and to predict subsurface temperature in the semi-arid Hailiutu River catchment. DHR captured the temporally varying amplitude and phase and reduced the representation RMSE by 44.8–81.9% relative to a stationary harmonic method. Predicted temperatures agreed well with observations, with R2 values of 0.962–0.994 and RMSE values of 0.2–0.7 °C across depths of 0.10–0.40 m; 84.5–100% of the predictions differed from the corresponding observations by no more than the nominal ±1 °C reference based on the manufacturer-stated temperature sensor precision. Thermal diffusivity and water flux showed substantial temporal variability and weak monotonic relationships with soil water content. The framework extends physically based temperature methods to non-stationary field forcing while retaining an explicit analytical interpretation.