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Volume 19 Issue 2

Mar.  2002

Article Contents
Article >  ADVANCES IN ATMOSPHERIC SCIENCES  > 2002 >  19(2): 255-265

A Proper Time Integration with Split Stepping for the Explicit Free-Surface Modeling

  • 1.

    South China Sea Institute o f Oceanology, Chinese Academy of Sciences, Guangzhou 510301


doi: 10.1007/s00376-002-0020-1

  • Errors due to split time stepping are discussed for an explicit free-surface ocean model. In commonly used split time stepping, the way of time integration for the barotropic momentum equation is not compatible with that of the baroclinic one. The baroclinic equation has three-time-level structure because of leapfrog scheme. The barotropic one, however, has two-time-level structure when represented in terms of the baroclinic time level, on which the baroclinic one is integrated. This incompatibility results in the splitting errors as shown in this paper. The proper split time stepping is therefore proposed in such a way that the compatibility is kept between the barotropic and baroclinic equations. Its splitting errors are shown extremely small, so that it is particularly relevant to long-term integration for climate studies. It is applied to a free-surface model for the North Pacific Ocean.
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    [6] XUE Hai-Le, SHEN Xue-Shun, CHOU Ji-Fan, 2013: A Forecast Error Correction Method in Numerical Weather Prediction by Using Recent Multiple-time Evolution Data, ADVANCES IN ATMOSPHERIC SCIENCES, 30, 1249-1259.  doi: 10.1007/s00376-013-2274-1
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    [9] Bohua Huang, James L. Kinter III, Paul S. Schopf, 2002: Ocean Data Assimilation Using Intermittent Analyses and Continuous Model Error Correction, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 965-992.  doi: 10.1007/s00376-002-0059-z
    [10] 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
    [11] LI Qian, SUN Shufen, DAI Qiudan, 2009: The Numerical Scheme Development of a Simplified Frozen Soil Model, ADVANCES IN ATMOSPHERIC SCIENCES, 26, 940-950.  doi: 10.1007/s00376-009-7174-z
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    [14] XUE Haile, SHEN Xueshun, CHOU Jifan, 2015: An Online Model Correction Method Based on an Inverse Problem: Part I——Model Error Estimation by Iteration, ADVANCES IN ATMOSPHERIC SCIENCES, 32, 1329-1340.  doi: 10.1007/s00376-015-4261-1
    [15] XUE Haile, SHEN Xueshun, CHOU Jifan, 2015: An Online Model Correction Method Based on an Inverse Problem: Part II——Systematic Model Error Correction, ADVANCES IN ATMOSPHERIC SCIENCES, 32, 1493-1503.  doi: 10.1007/s00376-015-4262-0
    [16] DUAN Wansuo, ZHANG Rui, 2010: Is Model Parameter Error Related to a Significant Spring Predictability Barrier for El Nino events? Results from a Theoretical Model, ADVANCES IN ATMOSPHERIC SCIENCES, 27, 1003-1013.  doi: 10.1007/s00376-009-9166-4
    [17] MIN Wenbin, CHEN Zhongming, SUN Linsheng, GAO Wenliang, LUO Xiuling, YANG Tingrong, PU Jian, HUANG Guanglun, YANG Xiurong, 2004: A Scheme for Pixel-Scale Aerodynamic Surface Temperature over Hilly Land, ADVANCES IN ATMOSPHERIC SCIENCES, 21, 125-131.  doi: 10.1007/BF02915686
    [18] Ling-Jiang TAO, Rong-Hua ZHANG, Chuan GAO, 2017: Initial Error-induced Optimal Perturbations in ENSO Predictions, as Derived from an Intermediate Coupled Model, ADVANCES IN ATMOSPHERIC SCIENCES, 34, 791-803.  doi: 10.1007/s00376-017-6266-4
    [19] Xia LIU, Qiang WANG, Mu MU, 2018: Optimal Initial Error Growth in the Prediction of the Kuroshio Large Meander Based on a High-resolution Regional Ocean Model, ADVANCES IN ATMOSPHERIC SCIENCES, 35, 1362-1371.  doi: 10.1007/s00376-018-8003-z
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    • Manuscript History

    Manuscript received: 10 March 2002
    Manuscript revised: 10 March 2002
    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

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    A Proper Time Integration with Split Stepping for the Explicit Free-Surface Modeling

    • 1. South China Sea Institute o f Oceanology, Chinese Academy of Sciences, Guangzhou 510301
    • Manuscript received: 2002-03-10
    • Manuscript revised: 2002-03-10

    Abstract: Errors due to split time stepping are discussed for an explicit free-surface ocean model. In commonly used split time stepping, the way of time integration for the barotropic momentum equation is not compatible with that of the baroclinic one. The baroclinic equation has three-time-level structure because of leapfrog scheme. The barotropic one, however, has two-time-level structure when represented in terms of the baroclinic time level, on which the baroclinic one is integrated. This incompatibility results in the splitting errors as shown in this paper. The proper split time stepping is therefore proposed in such a way that the compatibility is kept between the barotropic and baroclinic equations. Its splitting errors are shown extremely small, so that it is particularly relevant to long-term integration for climate studies. It is applied to a free-surface model for the North Pacific Ocean.

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