A data assimilation-based heat pulse method for monitoring soil hydraulic and thermal parameters in root zones

Abstract

Continuous measurements of soil physical properties in root zones are crucial for understanding soilplant interactions and sustainable agriculture. Traditional heat pulse (HP) methods are based on analytical solutions with the assumption of a homogeneous porous medium. The interpretation of HP signals obtained in soils with nonuniform soil thermal properties, such as HP measurements in root zones, is an ongoing problem. According to Bayes’ theorem, data assimilation methods can estimate model parameters and characterize their heterogeneity by integrating measurements with numerical models in a statistical manner. This paper introduces a novel data assimilation-based HP method that uses the iterative local updating ensemble smoother (ILUES) algorithm to solve this problem. The ILUES is implemented with three steps. First, generating a large volume of prior ensemble. Second, updating local ensembles of each sample with ensemble smoother to explore parameters distributions. Finally, inversion results of parameters to be estimated can be obtained by statistical analysis of these samples. It was evaluated theoretically on synthetic data and in practical applications, i.e., laboratory experiments in sandy soil with root fragments included. Then, the ILUES was further applied to infer the water content (θ) and bulk density (ρ_b) in laboratory experiments. The results demonstrate significant improvements in the estimation accuracy for soil thermal properties, θ, and ρ_b. Compared with those of the traditional method, the average values of the root mean square error (RMSE) decreased from 1.20 to 0.10 MJ m⁻³ K⁻¹ for the volumetric heat capacity (C) estimates and from 0.4 to 0.3 W m⁻¹ K⁻¹ for the thermal conductivity (λ) estimates. Furthermore, the accuracies of the θ and ρ_b values also improved significantly, with the RMSEs decreasing from 0.20 to 0.05 m³ m^-3 and 0.60–0.10 g cm⁻³, respectively. This research provides a powerful tool for the in-situ monitoring of soil physical properties in root zones, providing deeper insights into soilplant interactions and contributing to sustainable agricultural and environmental management practices.