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Volume 26 Issue 3

May  2009

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Article >  ADVANCES IN ATMOSPHERIC SCIENCES  > 2009 >  26(3): 373-380

Ensemble-based Kalman Filters in Strongly Nonlinear Dynamics

  • 1.

    Department of Atmospheric Sciences, University of Utah, USA;National Center for Atmospheric Research, USA


doi: 10.1007/s00376-009-0373-9

  • This study examines the effectiveness of ensemble Kalman filters in data assimilation with the strongly nonlinear dynamics of the Lorenz-63 model, and in particular their use in predicting the regime transition that occurs when the model jumps from one basin of attraction to the other. Four configurations of the ensemble-based Kalman filtering data assimilation techniques, including the ensemble Kalman filter, ensemble adjustment Kalman filter, ensemble square root filter and ensemble transform Kalman filter, are evaluated with their ability in predicting the regime transition (also called phase transition) and also are compared in terms of their sensitivity to both observational and sampling errors. The sensitivity of each ensemble-based filter to the size of the ensemble is also examined.
  • [1] Fuqing ZHANG, Meng ZHANG, James A. HANSEN, 2009: Coupling Ensemble Kalman Filter with Four-dimensional Variational Data Assimilation, ADVANCES IN ATMOSPHERIC SCIENCES, 26, 1-8.  doi: 10.1007/s00376-009-0001-8
    [2] ZHENG Xiaogu, WU Guocan, ZHANG Shupeng, LIANG Xiao, DAI Yongjiu, LI Yong, , 2013: Using Analysis State to Construct a Forecast Error Covariance Matrix in Ensemble Kalman Filter Assimilation, ADVANCES IN ATMOSPHERIC SCIENCES, 30, 1303-1312.  doi: 10.1007/s00376-012-2133-5
    [3] Yong LI, Siming LI, Yao SHENG, Luheng WANG, 2018: Data Assimilation Method Based on the Constraints of Confidence Region, ADVANCES IN ATMOSPHERIC SCIENCES, 35, 334-345.  doi: 10.1007/s00376-017-7045-y
    [4] LIU Zhengyu, WU Shu, ZHANG Shaoqing, LIU Yun, RONG Xinyao, , 2013: Ensemble Data Assimilation in a Simple Coupled Climate Model: The Role of Ocean-Atmosphere Interaction, ADVANCES IN ATMOSPHERIC SCIENCES, 30, 1235-1248.  doi: 10.1007/s00376-013-2268-z
    [5] Youmin TANG, Jaison AMBANDAN, Dake CHEN, , , 2014: Nonlinear Measurement Function in the Ensemble Kalman Filter, ADVANCES IN ATMOSPHERIC SCIENCES, 31, 551-558.  doi: 10.1007/s00376-013-3117-9
    [6] Xinrong WU, Shaoqing ZHANG, Zhengyu LIU, 2016: Implementation of a One-Dimensional Enthalpy Sea-Ice Model in a Simple Pycnocline Prediction Model for Sea-Ice Data Assimilation Studies, ADVANCES IN ATMOSPHERIC SCIENCES, 33, 193-207.  doi: 10.1007/s00376-015-5099-2
    [7] Jian YUE, Zhiyong MENG, Cheng-Ku YU, Lin-Wen CHENG, 2017: Impact of Coastal Radar Observability on the Forecast of the Track and Rainfall of Typhoon Morakot (2009) Using WRF-based Ensemble Kalman Filter Data Assimilation, ADVANCES IN ATMOSPHERIC SCIENCES, 34, 66-78.  doi: 10.1007/s00376-016-6028-8
    [8] Li Chongyin, Liao Qinghai, 1996: Behaviour of Coupled Modes in a Simple Nonlinear Air-Sea Interaction Model, ADVANCES IN ATMOSPHERIC SCIENCES, 13, 183-195.  doi: 10.1007/BF02656861
    [9] Lili LEI, Yangjinxi GE, Zhe-Min TAN, Yi ZHANG, Kekuan CHU, Xin QIU, Qifeng QIAN, 2022: Evaluation of a Regional Ensemble Data Assimilation System for Typhoon Prediction, ADVANCES IN ATMOSPHERIC SCIENCES, 39, 1816-1832.  doi: 10.1007/s00376-022-1444-4
    [10] Xiaogu ZHENG, 2009: An Adaptive Estimation of Forecast Error Covariance Parameters for Kalman Filtering Data Assimilation, ADVANCES IN ATMOSPHERIC SCIENCES, 26, 154-160.  doi: 10.1007/s00376-009-0154-5
    [11] 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
    [12] Hongqin ZHANG, Xiangjun TIAN, Wei CHENG, Lipeng JIANG, 2020: System of Multigrid Nonlinear Least-squares Four-dimensional Variational Data Assimilation for Numerical Weather Prediction (SNAP): System Formulation and Preliminary Evaluation, ADVANCES IN ATMOSPHERIC SCIENCES, 37, 1267-1284.  doi: 10.1007/s00376-020-9252-1
    [13] Chaoqun MA, Tijian WANG, Zengliang ZANG, Zhijin LI, 2018: Comparisons of Three-Dimensional Variational Data Assimilation and Model Output Statistics in Improving Atmospheric Chemistry Forecasts, ADVANCES IN ATMOSPHERIC SCIENCES, 35, 813-825.  doi: 10.1007/s00376-017-7179-y
    [14] ZHANG Shuwen, LI Haorui, ZHANG Weidong, QIU Chongjian, LI Xin, 2005: Estimating the Soil Moisture Profile by Assimilating Near-Surface Observations with the Ensemble Kalman Filter (EnKF), ADVANCES IN ATMOSPHERIC SCIENCES, 22, 936-945.  doi: 10.1007/BF02918692
    [15] Banglin ZHANG, Vijay TALLAPRAGADA, Fuzhong WENG, Jason SIPPEL, Zaizhong MA, 2016: Estimation and Correction of Model Bias in the NASA/GMAO GEOS5 Data Assimilation System: Sequential Implementation, ADVANCES IN ATMOSPHERIC SCIENCES, 33, 659-672.  doi: 10.1007/ s00376-015-5155-y
    [16] DING Ruiqiang, LI Jianping, 2012: Relationships between the Limit of Predictability and Initial Error in the Uncoupled and Coupled Lorenz Models, ADVANCES IN ATMOSPHERIC SCIENCES, 29, 1078-1088.  doi: 10.1007/s00376-012-1207-8
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    [18] Qizhen SUN, Timo VIHMA, Marius O. JONASSEN, Zhanhai ZHANG, 2020: Impact of Assimilation of Radiosonde and UAV Observations from the Southern Ocean in the Polar WRF Model, ADVANCES IN ATMOSPHERIC SCIENCES, 37, 441-454.  doi: 10.1007/s00376-020-9213-8
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    • Manuscript History

    Manuscript received: 10 May 2009
    Manuscript revised: 10 May 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

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    Ensemble-based Kalman Filters in Strongly Nonlinear Dynamics

    • 1. Department of Atmospheric Sciences, University of Utah, USA;National Center for Atmospheric Research, USA
    • Manuscript received: 2009-05-10
    • Manuscript revised: 2009-05-10

    Abstract: This study examines the effectiveness of ensemble Kalman filters in data assimilation with the strongly nonlinear dynamics of the Lorenz-63 model, and in particular their use in predicting the regime transition that occurs when the model jumps from one basin of attraction to the other. Four configurations of the ensemble-based Kalman filtering data assimilation techniques, including the ensemble Kalman filter, ensemble adjustment Kalman filter, ensemble square root filter and ensemble transform Kalman filter, are evaluated with their ability in predicting the regime transition (also called phase transition) and also are compared in terms of their sensitivity to both observational and sampling errors. The sensitivity of each ensemble-based filter to the size of the ensemble is also examined.

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