Determining Near-Surface Heat Flux Density Using Modeled Soil Thermal Conductivity.

The gradient method determines soil heat flux density (G) from the product of soil thermal conductivity (λ) and temperature (T) gradient at a soil depth below the surface. Heat pulse probes have been used to measure λ, but the accuracy of λ measurements in the near-surface layer is limited, due to the influences of soil-air interface and ambient temperature variation. In this study, we evaluated the potential of estimating near-surface G from measured T gradients and modeled thermal conductivity (λ_m), which was expressed as a function of soil texture, water content (θ), and bulk density. Time domain reflectometry (TDR) probes were inserted at 2, 6, and 10 cm depths to measure θ, which was then used to estimate λ_m with two thermal conductivity models (Lu et al., 2007; Lu et al., 2014). Thermocouples were installed at 1, 3, 4, 8, and 12 cm depths to obtain T gradients, allowing soil heat flux to be measured with the gradient method (G_m) at three soil depths. Heat pulse sensors were also used to determine soil heat flux density (G_HP) from independent temperature (T_HP) and thermal conductivity (λ_HP) measurements. The λ_m and λ_HP values were similar at all three depths, with root mean square errors (RMSE) ranged from 0.05 to 0.09 W m^-1 K^-1. Comparisons between G_m and G_HP yielded RMSEs of 5.7-9.1 W m^-2, indicating that using modeled λ_m and T measurements could produce reliable near-surface heat flux density. Compared to soil sampling θ data, θ estimates from TDR probes performed better for capturing λ_m and G_m dynamics shortly after rainfalls. We also showed that at near-surface depth (e.g., 2 cm), the accuracies of λ_m and G_m estimates could be improved by including the temporal variations of soil bulk density.