Tianyue Zhao Yuanyuan Zhang Hailong He Robert Horton Gang Liu
Abstract
The measurement of thermal properties in partially frozen soil is crucial for global climate models. As the primary method for soil thermal property measurement, the Dual-Probe Heat-Pulse (DPHP) sensor experiences significant errors when used in partially frozen soils. The application of heat pulses leads to ice melting, and the existing DPHP theory, which does not consider phase changes, fails to accurately determine thermal conductivity (k) and heat capacity (C) in the temperature range of − 5 °C to 0 °C. There is a lack of DPHP theory specifically designed for use in partially frozen soils. The existing DPHP theory employs the Infinite Linear Source (ILS) approximation, which does not account for the melting process and the moving ice-liquid interface in transient heat conduction theory. Currently, there is no effective and reliable method to assess DPHP errors associated with measuring the thermal properties of partially frozen soil. To accurately determine k and C in frozen soil, it is essential to perform an error analysis regarding ice melting caused by a DPHP heat pulse input. In this study, (1) we considered the latent heat of ice melting and a moving ice-liquid interface in finite element simulations and compared the results with an analytical solution presented by Paterson (1952); (2) we performed simulations of DPHP measurements based on the temperature-dependent ice content, liquid water content, and melting latent heat of three frozen soils used by Watanabe and Wake (2009); (3) based on COMSOL simulation results for the three frozen soils, we determined the optimal heating parameter combinations (heating duration, t0, and accumulated heating energy, ΔQ) to minimize DPHP measurement errors in frozen soil. The results showed that (1) Simulations that included the melting phase changes were in agreement with the analytical solution by Paterson (1952). (2) Including the ice-liquid moving interface significantly altered the spatial distribution characteristics of temperature, which were not captured by the ILS model in terms of the temperature distribution near the interface. (3) Below a temperature of − 5.5 °C, the simulations that included phase changes were consistent with measured results; (4) For partially frozen soils with initial temperatures ranging from − 0.5 °C to 0 °C, the relative errors in thermal conductivity fitted by the ILS model exceeded 100 %. To mitigate the influence of ice melting, we recommend using 200 < ΔQ < 400 J m−1 for sand, loam, and silt loam soils with 8 s < t0 < 60 s. For a loam soil with t0 = 60 s, ΔQ = 800 J m−1 should be used. For a silt loam soil with t0 = 60 s, we recommend using ΔQ = 600 J m−1. If the ILS model is chosen to calculate soil thermal properties, we recommend using 200 < ΔQ < 600 J m−1 and 30 s < t0 < 60 s for sandy and silt loam soils. For a loam soil, we recommend using 400 < ΔQ < 800 J m−1 and 30 s < t0 < 60 s.
Keywords
Frozen soils; Dual probe Heat pulse method; Finite element simulation; Heat conduction equation; Analytical solution
Optimized measurement of frozen soil thermal properties using a heat-pulse sensor.pdf
