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Comments on thaw-freeze algorithms for multilayered soil, using the Stefan equation
Received:May 06, 2017    Click here to download the full text
Citation of this paper:ChangWei Xie,William A. Gough,2017.Comments on thaw-freeze algorithms for multilayered soil, using the Stefan equation.Sciences in Cold and Arid Regions,9(6):525~533.
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Author NameAffiliationE-mail
ChangWei Xie 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 xiecw@lzb.ac.cn 
William A. Gough Department of Physical and Environmental Sciences, University of Toronto at Scarborough, 1265 Military Trail, Toronto, Ontario, Canada  
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.
keywords:Stefan equation  algorithms  thaw depth  multilayered soil
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