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Sciences in Cold and Arid Regions ›› 2017, Vol. 9 ›› Issue (6): 525-533.doi: 10.3724/SP.J.1226.2017.00525

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Comments on thaw-freeze algorithms for multilayered soil, using the Stefan equation

ChangWei Xie1, William A. Gough2   

  1. 1. Cryosphere Research Station on the Qinghai-Tibet Plateau, State Key Laboratory of Cryospheric Sciences, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou, Gansu 730000, China;
    2. Department of Physical and Environmental Sciences, University of Toronto at Scarborough, 1265 Military Trail, Toronto, Ontario, Canada
  • Received:2017-05-06 Online:2017-12-01 Published:2018-11-23
  • Contact: ChangWei Xie, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, No. 320, West Donggang Road, Lanzhou, Gansu 730000, China. E-mail:xiecw@lzb.ac.cn E-mail:xiecw@lzb.ac.cn
  • Supported by:
    This work was supported by grants from the National Natural Science Foundation of China (41671068, 41421061, and 41771040), the State Key Laboratory of Cryospheric Sciences (SKLCS-ZZ-2017), and the Hundred Talents Program of the Chinese Academy of Sciences granted to ChangWei Xie (51Y551831).

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Abstract: The Stefan equation provides a useful and widely used method for predicting the depth of thawing and freezing in a soil where little site-specific information is available. The original Stefan equation was derived for only a homogeneous medium, and some algorithms have been developed for its use in a multilayered system. However, although the Stefan equation was derived more than 100 years ago, there is not a unified understanding for its use in a multilayered system. This paper examines the use of the Stefan equation in multilayered soil, based on comparing three algorithms (JL-algorithm, NM-algorithm, and XG-algorithm). We conclude that the JL and NM algorithms are incorrect, as they arose from flawed mathematical derivations. Both of these algorithms failed to recognize that the thawing depth in a multilayered soil is a piecewise function and not a continuous function of time. This work asserts that the XG-algorithm is a correct and rigorous method to determine the freezing-thawing fronts in multilayered soil.

Key words: Stefan equation, algorithms, thaw depth, multilayered soil

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