Advanced Search
Impact Factor: 5.8

Volume 16 Issue 3

Jul.  1999

Article Contents
Article >  ADVANCES IN ATMOSPHERIC SCIENCES  > 1999 >  16(3): 419-430

Application of Variational Algorithms in Semi-Lagrangian Framework

  • 1.

    Laboratory of Meso-scale Severe Weather, Department of Atmospheric Sciences, Nanjing University, Nanjing 210093,Laboratory of Meso-scale Severe Weather, Department of Atmospheric Sciences, Nanjing University, Nanjing 210093,Laboratory of Meso-scale Severe Weather, Department of Atmospheric Sciences, Nanjing University, Nanjing 210093,Laboratory of Meso-scale Severe Weather, Department of Atmospheric Sciences, Nanjing University, Nanjing 210093


doi: 10.1007/s00376-999-0020-5

  • The variational data assimilation scheme (VAR) is applied to investigating the advective effect and the evolution of the control variables in time splitting semi-Lagrangian framework. Two variational algorithms are used. One is the conjugate code method-direct approach, and another is the numerical backward integration of analytical adjoint equation-indirect approach.Theoretical derivation and sensitivity tests are conducted in order to verify the consistency and inconsistency of the two algorithms under the semi-Lagrangian framework. On the other hand, the sensitivity of the perfect and imperfect initial condition is also tested in both direct and indirect approaches. Our research has shown that the two algorithms are not only identical in theory, but also iden?tical in numerical calculation. Furthermore, the algorithms of the indirect approach are much more feasible and efficient than that of the direct one when both are employed in the semi-Lagrangian framework. Taking advantage of semi-Lagrangian framework, one purpose of this paper is to illustrate when the variational assimilation algorithm is concerned in the computational method of the backward integration, the algorithm is extremely facilitated. Such simplicity in indirect approach should be meaningful for the VAR design in passive model. Indeed, if one can successfully split the diabatic and adiabatic process, the algorithms represented in this paper might be easily used in a more general vision of atmospheric model.
  • [1] WANG Xiaocong, LIU Yimin, WU Guoxiong, Shian-Jiann LIN, BAO Qing, 2013: The Application of Flux-Form Semi-Lagrangian Transport Scheme in a Spectral Atmosphere Model, ADVANCES IN ATMOSPHERIC SCIENCES, 30, 89-100.  doi: 10.1007/s00376-012-2039-2
    [2] Jie TANG, Chungang CHEN, Xueshun SHEN, Feng XIAO, Xingliang LI, 2021: A Positivity-preserving Conservative Semi-Lagrangian Multi-moment Global Transport Model on the Cubed Sphere, ADVANCES IN ATMOSPHERIC SCIENCES, 38, 1460-1473.  doi: 10.1007/s00376-021-0393-7
    [3] HUANG Bo, CHEN Dehui, LI Xingliang, LI Chao, , 2014: Improvement of the Semi-Lagrangian Advection Scheme in the GRAPES Model: Theoretical Analysis and Idealized Tests, ADVANCES IN ATMOSPHERIC SCIENCES, 31, 693-704.  doi: 10.1007/s00376-013-3086-z
    [4] Lucas HARRIS, 2021: A New Semi-Lagrangian Finite Volume Advection Scheme Combines the Best of Both Worlds, ADVANCES IN ATMOSPHERIC SCIENCES, 38, 1608-1609.  doi: 10.1007/s00376-021-1181-0
    [5] Chen Jiabin, Wang Jun, 1996: Studies on Non-interpolating Semi-Lagrangian Scheme and Numerical Solution to KdV Equation, ADVANCES IN ATMOSPHERIC SCIENCES, 13, 265-268.  doi: 10.1007/BF02656869
    [6] LI Xingliang, CHEN Dehui, PENG Xindong, XIAO Feng, CHEN Xiongshan, 2006: Implementation of the Semi-Lagrangian Advection Scheme on a Quasi-Uniform Overset Grid on a Sphere, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 792-801.  doi: 10.1007/s00376-006-0792-9
    [7] WANG Bin, LIU Juanjuan, WANG Shudong, CHENG Wei, LIU Juan, LIU Chengsi, Qingnong XIAO, Ying-Hwa KUO, 2010: An Economical Approach to Four-dimensional Variational Data Assimilation, ADVANCES IN ATMOSPHERIC SCIENCES, 27, 715-727.  doi: 10.1007/s00376-009-9122-3
    [8] Zeinab SALAH, Ahmed SHALABY, Allison L. STEINER, Ashraf S. ZAKEY, Ritesh GAUTAM, Mohamed M. ABDEL WAHAB, 2018: Study of Aerosol Direct and Indirect Effects and Auto-conversion Processes over the West African Monsoon Region Using a Regional Climate Model, ADVANCES IN ATMOSPHERIC SCIENCES, 35, 182-194.  doi: 10.1007/s00376-017-7077-3
    [9] QIAO Fangli, ZHANG Shaoqing, YIN Xunqiang, 2005: Study of Initial Vorticity Forcing for Block Onset by a 4-Dimensional Variational Approach, ADVANCES IN ATMOSPHERIC SCIENCES, 22, 246-259.  doi: 10.1007/BF02918514
    [10] HAN Guijun, LI Wei, HE Zhongjie, LIU Kexiu, MA Jirui, 2006: Assimilated Tidal Results of Tide Gauge and TOPEX/POSEIDON Data over the China Seas Using a Variational Adjoint Approach with a Nonlinear Numerical Model, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 449-460.  doi: 10.1007/s00376-006-0449-8
    [11] FANG Changluan, ZHENG Qin, WU Wenhua, DAI Yi, 2009: Intelligent Optimization Algorithms to VDA of Models with on/off Parameterizations, ADVANCES IN ATMOSPHERIC SCIENCES, 26, 1181-1197.  doi: 10.1007/s00376-009-8084-9
    [12] Ruiyao CHEN, Ralf BENNARTZ, 2021: Rainfall Algorithms Using Oceanic Satellite Observations from MWHS-2, ADVANCES IN ATMOSPHERIC SCIENCES, 38, 1367-1378.  doi: 10.1007/s00376-020-0258-5
    [13] WANG Zhili, ZHANG Hua, SHEN Xueshun, Sunling GONG, ZHANG Xiaoye, 2010: Modeling Study of Aerosol Indirect Effects on Global Climate with an AGCM, ADVANCES IN ATMOSPHERIC SCIENCES, 27, 1064-1077.  doi: 10.1007/s00376-010-9120-5
    [14] XIE Xiaoning, LIU Xiaodong, 2013: Analytical Studies of the Cloud Droplet Spectral Dispersion Influence on the First Indirect Aerosol Effect, ADVANCES IN ATMOSPHERIC SCIENCES, 30, 1313-1319.  doi: 10.1007/s00376-012-2141-5
    [15] Jianjun LIU, Zhanqing LI, 2018: First Surface-based Estimation of the Aerosol Indirect Effect over a Site in Southeastern China, ADVANCES IN ATMOSPHERIC SCIENCES, 35, 169-181.  doi: 10.1007/s00376-017-7106-2
    [16] LI Shu, WANG Tijian, ZHUANG Bingliang, HAN Yong, 2009: Indirect Radiative Forcing and Climatic Effect of the Anthropogenic Nitrate Aerosol on Regional Climate of China, ADVANCES IN ATMOSPHERIC SCIENCES, 26, 543-552.  doi: 10.1007/s00376-009-0543-9
    [17] Zeng Qingcun, 1989: Variational Principle of Instability of Atmospheric Motions, ADVANCES IN ATMOSPHERIC SCIENCES, 6, 137-172.  doi: 10.1007/BF02658013
    [18] Yuejian ZHU, 2005: Ensemble Forecast: A New Approach to Uncertainty and Predictability, ADVANCES IN ATMOSPHERIC SCIENCES, 22, 781-788.  doi: 10.1007/BF02918678
    [19] Ren Shuzhan, 1991: New Approach to Study the Evolution of Rossby Wave Packet, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 79-86.  doi: 10.1007/BF02657366
    [20] LI Hongqi, GUO Weidong, SUN Guodong, ZHANG Yaocun, FU Congbin, 2011: A New Approach for Parameter Optimization in Land Surface Model, ADVANCES IN ATMOSPHERIC SCIENCES, 28, 1056-1066.  doi: 10.1007/s00376-010-0050-z
PDF

Get Citation+

shu
Export:  

Share Article

Article Metrics

Article Views: 1248 Times

PDF downloads: 1084 Times

Cited by: Times
  • 加载中

    • Manuscript History

    Manuscript received: 10 July 1999
    Manuscript revised: 10 July 1999
    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

    Application of Variational Algorithms in Semi-Lagrangian Framework

    • 1. Laboratory of Meso-scale Severe Weather, Department of Atmospheric Sciences, Nanjing University, Nanjing 210093,Laboratory of Meso-scale Severe Weather, Department of Atmospheric Sciences, Nanjing University, Nanjing 210093,Laboratory of Meso-scale Severe Weather, Department of Atmospheric Sciences, Nanjing University, Nanjing 210093,Laboratory of Meso-scale Severe Weather, Department of Atmospheric Sciences, Nanjing University, Nanjing 210093
    • Manuscript received: 1999-07-10
    • Manuscript revised: 1999-07-10

    Abstract: The variational data assimilation scheme (VAR) is applied to investigating the advective effect and the evolution of the control variables in time splitting semi-Lagrangian framework. Two variational algorithms are used. One is the conjugate code method-direct approach, and another is the numerical backward integration of analytical adjoint equation-indirect approach.Theoretical derivation and sensitivity tests are conducted in order to verify the consistency and inconsistency of the two algorithms under the semi-Lagrangian framework. On the other hand, the sensitivity of the perfect and imperfect initial condition is also tested in both direct and indirect approaches. Our research has shown that the two algorithms are not only identical in theory, but also iden?tical in numerical calculation. Furthermore, the algorithms of the indirect approach are much more feasible and efficient than that of the direct one when both are employed in the semi-Lagrangian framework. Taking advantage of semi-Lagrangian framework, one purpose of this paper is to illustrate when the variational assimilation algorithm is concerned in the computational method of the backward integration, the algorithm is extremely facilitated. Such simplicity in indirect approach should be meaningful for the VAR design in passive model. Indeed, if one can successfully split the diabatic and adiabatic process, the algorithms represented in this paper might be easily used in a more general vision of atmospheric model.

      HTML

    Catalog

      Publish with AAS

      Contact us

      Links

      Copyright © 2018-2028 ADVANCES IN ATMOSPHERIC SCIENCES 京ICP备14024088号-7

      Supported by: Beijing Renhe Information Technology Co. Ltd  support: info@rhhz.net  

      /

      DownLoad:  Full-Size Img  PowerPoint
      Return
      Return