| Stefan方程在土壤冻融过程模拟中的应用 |
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| 引用本文： | 刘文惠,谢昌卫,刘海瑞,庞强强,王武,刘广岳,杨雨昆,王铭,张琪.Stefan方程在土壤冻融过程模拟中的应用[J].冰川冻土,2022,44(1):327-339. |
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| 作者姓名： | 刘文惠 谢昌卫 刘海瑞 庞强强 王武 刘广岳 杨雨昆 王铭 张琪 |
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| 作者单位： | 1.青海大学 地质工程系，青海 西宁 810016;2.中国科学院 西北生态环境资源研究院 冰冻圈科学国家重点实验室 藏北高原 冰冻圈特殊环境与灾害国家野外科学观测研究站，甘肃 兰州 730000;3.青海大学 生态环境工程学院，青海 西宁 810016 |
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| 基金项目： | 国家自然科学基金项目（41671068）资助； |
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| 摘 要： | 多年冻土与大气间的相互作用主要是通过活动层中的水热动态变化过程而实现。气候变化背景下的多年冻土活动层冻融过程模拟、多年冻土厚度制图和变化预测是研究冻土区生态环境、水文、工程以及碳循环的基础。根据国内外研究进展，总结了不同修正形式的Stefan方程在多年冻土活动层冻融过程和活动层厚度模拟中的应用进展，对将Stefan方程应用到分层堆积土壤中的不同算法进行了简要介绍，并指出了其在应用过程中存在的问题。Stefan方程首次将地表（或者大气）温度的变化与冰层（或者土层）的冻结融化过程以简单公式的形式联系起来，极大地简化了土壤冻结融化过程的分析计算。由于其输入参数少、形式简单、模拟效果可靠，成为常用模拟土壤冻融过程的方法之一，将其耦合到气候模型、陆面模型和水文模型中的研究也越来越多。Stefan方程最初在研究北极地区湖冰形成过程时提出，在应用到冻土学中后，不同学者在考虑土壤含水量、不同下垫面地气温差、地形和降水等因素后对方程进行了改进，并有多种算法试图将这一方程应用到非均质土壤中，取得了较好的模拟效果。但是，Stefan方程在国内的应用更多地用于简单模拟均质土壤多年冻土活动层厚度的空间分布状况，其应用到非均质土壤中的研究却较少。因此，未来需更深入研究Stefan方程模拟分层土壤的冻融过程，为准确掌握多年冻土对气候变化的响应研究提供最基本的方法。
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| 关 键 词： | Stefan方程 冻融过程 活动层厚度 含水量 |
| 收稿时间： | 2020-12-11 |
| 修稿时间： | 2021-03-27 |
Application of Stefan equation on simulating freezing-thawing process of permafrost |
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| LIU Wenhui,XIE Changwei,LIU Hairui,PANG Qiangqiang,WANG Wu,LIU Guangyue,YANG Yukun,WANG Ming,ZHANG Qi.Application of Stefan equation on simulating freezing-thawing process of permafrost[J].Journal of Glaciology and Geocryology,2022,44(1):327-339. |
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| Authors: | LIU Wenhui XIE Changwei LIU Hairui PANG Qiangqiang WANG Wu LIU Guangyue YANG Yukun WANG Ming ZHANG Qi |
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| Institution: | 1.Department of Geological Engineering，Qinghai University，Xining 810016，China;2.Cryosphere Research Station on the Qinghai-Tibet Plateau，State Key Laboratory of Cryospheric Science，Northwest Institute of Eco-Environment and Resources，Chinese Academy of Sciences，Lanzhou 730000，China;3.College of Eco-Environmental Engineering，Qinghai University，Xining 810016，China |
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| Abstract: | The interaction between permafrost and atmosphere is mainly accomplished through the thermal and hydro-dynamics in the active layer. In background of climate change， the simulation of freezing-thawing process， active layer thickness map and variation-prediction are the basis of studying ecological environment， hydrology， engineering and carbon cycle of permafrost regions. For this paper， we summarize the application of different revised Stefan equations in simulating freezing-thawing process and active layer thickness， as well as its significant application in multi-layer soil， and then discuss the possible questions in its implication. Stefan equation revealed the linkage between change of surface temperature （or air temperature） and freezing-thawing process of ice （or soil） in a simple form， which significantly simplified the analysis and calculation of freezing-thawing process of soil. Stefan equation， with less parameters， simple form and reliable simulation results， is widely used to simulate freezing-thawing process. Also， more and more studies focusing on coupled it to climate model， land surface model and hydrological model. Stefan equation was originally proposed in the study of lake ice formation in the Arctic region and later widely used in permafrost. It was improved by considering soil water content， difference between ground and air temperature on different underlying， topography， precipitation and other factors， and even was applied to simulate freezing-thawing process of heterogeneous soil. However， on the Qinghai-Tibet Plateau， Stefan equation is widely used for simulating spatial distribution of active layer thickness of permafrost for homogeneous soil but rarely applied to heterogeneous soils. Therefore， it is necessary to further study that Stefan equation simulated freezing-thawing process for multilayer soil in the future， which will provide a basic method for accurately studying the response of permafrost to climate change. |
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| Keywords: | Stefan equation freezing-thawing process active layer thickness water content |
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