Advanced Search
Article Contents

The Numerical Scheme Development of a Simplified Frozen Soil Model


doi: 10.1007/s00376-009-7174-z

  • In almost all frozen soil models used currently, three variables of temperature, ice content and moisture content are used as prognostic variables and the rate term, accounting for the contribution of the phase change between water and ice, is shown explicitly in both the energy and mass balance equations. The models must be solved by a numerical method with an iterative process, and the rate term of the phase change needs to be pre-estimated at the beginning in each iteration step. Since the rate term of the phase change in the energy equation is closely related to the release or absorption of the great amount of fusion heat, a small error in the rate term estimation will introduce greater error in the energy balance, which will amplify the error in the temperature calculation and in turn, cause problems for the numerical solution convergence. In this work, in order to first reduce the trouble, the methodology of the variable transformation is applied to a simplified frozen soil model used currently, which leads to new frozen soil scheme used in this work. In the new scheme, the enthalpy and the total water equivalent are used as predictive variables in the governing equations to replace temperature, volumetric soil moisture and ice content used in many current models. By doing so, the rate terms of the phase change are not shown explicitly in both the mass and energy equations and its pre-estimation is avoided. Secondly, in order to solve this new scheme more functionally, the development of the numerical scheme to the new scheme is described and a numerical algorithm appropriate to the numerical scheme is developed. In order to evaluate the new scheme of the frozen soil model and its relevant algorithm, a series of model evaluations are conducted by comparing numerical results from the new model scheme with three observational data sets. The comparisons show that the results from the model are in good agreement with these data sets in both the change trend of variables and their magnitude values, and the new scheme, together with the algorithm, is more efficient and saves more computer time.
  • [1] SUN Shufen, YAN Jinfeng, XIA Nan, SUN Changhai, 2007: Development of a Model for Water and Heat Exchange Between the Atmosphere and a Water Body, ADVANCES IN ATMOSPHERIC SCIENCES, 24, 927-938.  doi: 10.1007/s00376-007-0927-7
    [2] Yang Xiaosong, Lin Zhaohui, Dai Yongjiu, Guo Yufu, 2001: Validation of IAP94 Land Surface Model over the Huaihe River Basin with HUBEX Field Experiment Data, ADVANCES IN ATMOSPHERIC SCIENCES, 18, 139-154.  doi: 10.1007/s00376-001-0009-1
    [3] CAO Lijuan, DONG Wenjie, XU Yinlong, ZHANG Yong, Michael SPARROW, 2007: Validating the Runoff from the PRECIS Model Using a Large-Scale Routing Model, ADVANCES IN ATMOSPHERIC SCIENCES, 24, 855-862.  doi: 10.1007/s00376-007-0855-6
    [4] WEN Xinyu, ZHOU Tianjun, WANG Shaowu, WANG Bin, WAN Hui, LI Jian, 2007: Performance of a Reconfigured Atmospheric General Circulation Model at Low Resolution, ADVANCES IN ATMOSPHERIC SCIENCES, 24, 712-728.  doi: 10.1007/s00376-007-0712-7
    [5] Yu Rucong, Li Wei, Zhang Xuehong, LiuYimin, Yu Yongqiang, Liu Hailong, Zhou Tianjun, 2000: Climatic Features Related to Eastern China Summer Rainfalls in the NCAR CCM3, ADVANCES IN ATMOSPHERIC SCIENCES, 17, 503-518.  doi: 10.1007/s00376-000-0014-9
    [6] CHEN Feng, and XIE Zhenghui, 2013: An evaluation of RegCM3_CRES for regional climate modeling in China, ADVANCES IN ATMOSPHERIC SCIENCES, 30, 1187-1200.  doi: 10.1007/s00376-012-2114-8
    [7] Zhang Yu, Lu Shihua, 2002: Development and Validation of a Simple Frozen Soil Parameterization Scheme Used for Climate Model, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 513-527.  doi: 10.1007/s00376-002-0083-z
    [8] Guo Yufu, Chao Jiping, 1984: SIMPLIFIED DYNAMICAL ANOMALY MODEL FOR LONG-RANGE NUMERICAL FORECASTS, ADVANCES IN ATMOSPHERIC SCIENCES, 1, 30-52.  doi: 10.1007/BF03187614
    [9] SUN Lan, XUE Yongkang, 2004: Validation of SSiB Model over Grassland with CHeRES Field Experiment Data in 2001, ADVANCES IN ATMOSPHERIC SCIENCES, 21, 547-556.  doi: 10.1007/BF02915722
    [10] Xia Daqing, Xu Youping, 1998: The Water-Bearing Numerical Model and Its Operational Forecasting Experiments Part I: The Water-Bearing Numerical Model, ADVANCES IN ATMOSPHERIC SCIENCES, 15, 221-232.  doi: 10.1007/s00376-998-0041-5
    [11] DAI Qiudan, SUN Shufen, 2007: A Simplified Scheme of the Generalized Layered Radiative Transfer Model, ADVANCES IN ATMOSPHERIC SCIENCES, 24, 213-226.  doi: 10.1007/s00376-007-0213-8
    [12] Dai Yongjiu, Zeng Qingcun, 1997: A Land Surface Model (IAP94) for Climate Studies Part I: Formulation and Validation in Off-line Experiments, ADVANCES IN ATMOSPHERIC SCIENCES, 14, 433-460.  doi: 10.1007/s00376-997-0063-4
    [13] Ji Zhongzhen, Wang Bin, Zhao Ying, Yang Hongwei, 2002: Total Energy Conservation and the Symplectic Algorithm, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 459-467.  doi: 10.1007/s00376-002-0079-8
    [14] ZHOU Zaixing, ZHENG Xunhua, XIE Baohua, HAN Shenghui, LIU Chunyan, 2010: A process-based model of N2O emission from a rice-winter wheat rotation agroecosystem: structure, validation and sensitivity, ADVANCES IN ATMOSPHERIC SCIENCES, 27, 137-150.  doi: 10.1007/s00376-009-8191-7
    [15] Sun Shufen, Xue Yongkang, 2001: Implementing a New Snow Scheme in Simplified Simple Biosphere Model, ADVANCES IN ATMOSPHERIC SCIENCES, 18, 335-354.  doi: 10.1007/BF02919314
    [16] Xu Youping, Xia Daqing, Qian Yueying, 1998: The Water-Bearing Numerical Model and Its Operational Forecasting Experiments Part II: The Operational Forecasting Experiments, ADVANCES IN ATMOSPHERIC SCIENCES, 15, 321-336.  doi: 10.1007/s00376-998-0004-x
    [17] Guo Weidong, Sun Shufen, Qian Yongfu, 2002: Case Analyses and Numerical Simulation of Soil Thermal Impacts on Land Surface Energy Budget Based on an Off-Line Land Surface Model, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 500-512.  doi: 10.1007/s00376-002-0082-0
    [18] Xie Zhenghui, Dai Yongjiu, Zeng Qingcun, 1999: An Unsaturated Soil Water Flow Problem and Its Numerical Simulation, ADVANCES IN ATMOSPHERIC SCIENCES, 16, 183-196.  doi: 10.1007/BF02973081
    [19] Ji Jinjun, 1986: A SIMPLIFIED MODEL STUDY ON THE SHORT-TERM CLIMATIC EFFECT OF SNOWFALL ANOMALY IN MID-HIGH LATITUDES, ADVANCES IN ATMOSPHERIC SCIENCES, 3, 443-453.  doi: 10.1007/BF02657934
    [20] LIU Shikuo, LIU Shida, FU Zuntao, SUN Lan, 2005: A Nonlinear Coupled Soil Moisture-Vegetation Model, ADVANCES IN ATMOSPHERIC SCIENCES, 22, 337-342.  doi: 10.1007/BF02918747

Get Citation+

Export:  

Share Article

Manuscript History

Manuscript received: 10 September 2009
Manuscript revised: 10 September 2009
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

The Numerical Scheme Development of a Simplified Frozen Soil Model

  • 1. Center for Monsoon System Research, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100190;State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029;State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029

Abstract: In almost all frozen soil models used currently, three variables of temperature, ice content and moisture content are used as prognostic variables and the rate term, accounting for the contribution of the phase change between water and ice, is shown explicitly in both the energy and mass balance equations. The models must be solved by a numerical method with an iterative process, and the rate term of the phase change needs to be pre-estimated at the beginning in each iteration step. Since the rate term of the phase change in the energy equation is closely related to the release or absorption of the great amount of fusion heat, a small error in the rate term estimation will introduce greater error in the energy balance, which will amplify the error in the temperature calculation and in turn, cause problems for the numerical solution convergence. In this work, in order to first reduce the trouble, the methodology of the variable transformation is applied to a simplified frozen soil model used currently, which leads to new frozen soil scheme used in this work. In the new scheme, the enthalpy and the total water equivalent are used as predictive variables in the governing equations to replace temperature, volumetric soil moisture and ice content used in many current models. By doing so, the rate terms of the phase change are not shown explicitly in both the mass and energy equations and its pre-estimation is avoided. Secondly, in order to solve this new scheme more functionally, the development of the numerical scheme to the new scheme is described and a numerical algorithm appropriate to the numerical scheme is developed. In order to evaluate the new scheme of the frozen soil model and its relevant algorithm, a series of model evaluations are conducted by comparing numerical results from the new model scheme with three observational data sets. The comparisons show that the results from the model are in good agreement with these data sets in both the change trend of variables and their magnitude values, and the new scheme, together with the algorithm, is more efficient and saves more computer time.

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return