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# Comparison of Six Algorithms to Determine the Soil Apparent Thermal Diffusivity at a Site in the Loess Plateau of China

Wang, Linlin1; Gao, Zhiqiu1; Horton, Robert2

doi: 10.1097/SS.0b013e3181cdda3f
Technical Article

Soil apparent thermal diffusivity is a crucial physical parameter that affects soil temperature. Six prevalent algorithms to calculate soil apparent thermal diffusivity are intercompared by using soil temperature data collected at the depths of 0.05 m and 0.10 m at a bare site in the China Loess Plateau from day of year 201 through day of year 207 in 2005. Five (i.e., Amplitude, Phase, Arctangent, Logarithm, and Harmonic [HM] algorithms) of the six algorithms are developed from the traditional one-dimensional heat conduction equation. The other algorithm is based on the one-dimensional heat conduction-convection equation that considers the vertical heterogeneity of thermal diffusivity in soil and couples thermal conduction and convection processes (hereinafter referred to as the Conduction-convection algorithm). To assess these six algorithms, we (i) calculate the soil apparent thermal diffusivities by using each of the algorithms, (ii) use the soil apparent thermal diffusivities to predict soil temperature at the 0.10-m depth, and (iii) compare the estimated soil temperature against direct measurements. Results show that (i) HM algorithm gives the most reliable estimates among the traditional five algorithms; and (ii) generally, the Conduction-convection algorithm provides the second-best estimates. Among all of the algorithms, the HM algorithm has the best description of the upper boundary temperature with time, but it only includes conduction heat transfer in the soil. Compared with the HM algorithm, the Conduction-convection algorithm has a less accurate description of the upper boundary temperature, but by accounting for the vertical gradient of soil diffusivity and the water flux density, it includes more physics in the soil heat transfer process. The Conduction-convection algorithm has potential application within land surface models, but future effort should be made to combine the HM and Conduction-convection algorithms to make use of the advantages of each.

1State Key Laboratory of Atmospheric Boundary Layer Physics and Atmospheric Chemistry, Institute of Atmospheric Physics, CAS, Beijing, China. Mr. Zhiqiu Gao is corresponding author. E-mail: zgao@mail.iap.ac.cn

2Department of Agronomy, Iowa State University, Ames, IA.