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Volume 27 Issue 6

Nov.  2010

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Article >  ADVANCES IN ATMOSPHERIC SCIENCES  > 2010 >  27(6): 1303-1310

The Structure of Background-error Covariance in a Four-dimensional Variational Data Assimilation System: Single-point Experiment

  • 1.

    State Key Laboratory of Numerical Modeling for Atmospheric Sciences & Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,State Key Laboratory of Numerical Modeling for Atmospheric Sciences &Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,State Key Laboratory of Numerical Modeling for Atmospheric Sciences & Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, Graduate University of the Chinese Academy of Sciences, Beijing 100049


doi: 10.1007/s00376-010-9067-6

  • A four dimensional variational data assimilation (4DVar) based on a dimension-reduced projection (DRP-4DVar) has been developed as a hybrid of the 4DVar and Ensemble Kalman filter (EnKF) concepts. Its good flow-dependent features are demonstrated in single-point experiments through comparisons with adjoint-based 4DVar and three-dimensional variational data (3DVar) assimilations using the fifth-generation Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model (MM5). The results reveal that DRP-4DVar can reasonably generate a background error covariance matrix (simply B-matrix) during the assimilation window from an initial estimation using a number of initial condition dependent historical forecast samples. In contrast, flow-dependence in the B-matrix of MM5 4DVar is barely detectable. It is argued that use of diagonal estimation in the B-matrix of the MM5 4DVar method at the initial time leads to this failure. The experiments also show that the increments produced by DRP-4DVar are anisotropic and no longer symmetric with respect to observation location due to the effects of the weather trends captured in its B-matrix. This differs from the MM5 3DVar which does not consider the influence of heterogeneous forcing on the correlation structure of the B-matrix, a condition that is realistic for many situations. Thus, the MM5 3DVar assimilation could only present an isotropic and homogeneous structure in its increments.
  • [1] ZHAO Juan, WANG Bin, LIU Juanjuan, 2011: Impact of Analysis-time Tuning on the Performance of the DRP-4DVar Approach, ADVANCES IN ATMOSPHERIC SCIENCES, 28, 207-216.  doi: 10.1007/s00376-010-9191-3
    [2] LIU Juanjuan, WANG Bin, 2011: Rainfall Assimilation Using a New Four-Dimensional Variational Method: A Single-Point Observation Experiment, ADVANCES IN ATMOSPHERIC SCIENCES, 28, 735-742.  doi: 10.1007/s00376-010-0061-9
    [3] 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
    [4] Banglin ZHANG, Vijay TALLAPRAGADA, Fuzhong WENG, Jason SIPPEL, Zaizhong MA, 2015: Use of Incremental Analysis Updates in 4D-Var Data Assimilation, ADVANCES IN ATMOSPHERIC SCIENCES, 32, 1575-1582.  doi: 10.1007/s00376-015-5041-7
    [5] Yaodeng CHEN, Jie SHEN, Shuiyong FAN, Deming MENG, Cheng WANG, 2020: Characteristics of Fengyun-4A Satellite Atmospheric Motion Vectors and Their Impacts on Data Assimilation, ADVANCES IN ATMOSPHERIC SCIENCES, 37, 1222-1238.  doi: 10.1007/s00376-020-0080-0
    [6] Rong KONG, Ming XUE, Edward R. MANSELL, Chengsi LIU, Alexandre O. FIERRO, 2024: Assimilation of GOES-R Geostationary Lightning Mapper Flash Extent Density Data in GSI 3DVar, EnKF, and Hybrid En3DVar for the Analysis and Short-Term Forecast of a Supercell Storm Case, ADVANCES IN ATMOSPHERIC SCIENCES, 41, 263-277.  doi: 10.1007/s00376-023-2340-2
    [7] Dongmei XU, Feifei SHEN, Jinzhong MIN, Aiqing SHU, 2021: Assimilation of GPM Microwave Imager Radiance for Track Prediction of Typhoon Cases with the WRF Hybrid En3DVAR System, ADVANCES IN ATMOSPHERIC SCIENCES, 38, 983-993.  doi: 10.1007/s00376-021-0252-6
    [8] Jie HE, Xulin MA, Xuyang GE, Juanjuan LIU, Wei CHENG, Man-Yau CHAN, Ziniu XIAO, 2021: Variational Quality Control of Non-Gaussian Innovations in the GRAPES m3DVAR System: Mass Field Evaluation of Assimilation Experiments, ADVANCES IN ATMOSPHERIC SCIENCES, 38, 1510-1524.  doi: 10.1007/s00376-021-0336-3
    [9] GAO Feng*, Peter P. CHILDS, Xiang-Yu HUANG, Neil A. JACOBS, and Jinzhong MIN, 2014: A Relocation-based Initialization Scheme to Improve Track-forecasting of Tropical Cyclones, ADVANCES IN ATMOSPHERIC SCIENCES, 31, 27-36.  doi: 10.1007/s00376-013-2254-5
    [10] SHEN Feifei, MIN Jinzhong, 2015: Assimilating AMSU-A Radiance Data with the WRF Hybrid En3DVAR System for Track Predictions of Typhoon Megi (2010), ADVANCES IN ATMOSPHERIC SCIENCES, 32, 1231-1243.  doi: 10.1007/s00376-014-4239-4
    [11] Zhiyong MENG, Eugene E. CLOTHIAUX, 2022: Contributions of Fuqing ZHANG to Predictability, Data Assimilation, and Dynamics of High Impact Weather: A Tribute, ADVANCES IN ATMOSPHERIC SCIENCES, 39, 676-683.  doi: 10.1007/s00376-021-1362-x
    [12] Zhu Jiang, Wang Hui, Masafumi Kamachi, 2002: The Improvement Made by a Modified TLM in 4DVAR with a Geophysical Boundary Layer Model, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 563-582.  doi: 10.1007/s00376-002-0001-4
    [13] 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
    [14] 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
    [15] FU Weiwei, ZHOU Guangqing, WANG Huijun, 2004: Ocean Data Assimilation with Background Error Covariance Derived from OGCM Outputs, ADVANCES IN ATMOSPHERIC SCIENCES, 21, 181-192.  doi: 10.1007/BF02915704
    [16] Jidong GAO, Keith BREWSTER, Ming XUE, 2006: A Comparison of the Radar Ray Path Equations and Approximations for Use in Radar Data Assimilation, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 190-198.  doi: 10.1007/s00376-006-0190-3
    [17] 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
    [18] 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
    [19] Dongmei XU, Zhiquan LIU, Shuiyong FAN, Min CHEN, Feifei SHEN, 2021: Assimilating All-sky Infrared Radiances from Himawari-8 Using the 3DVar Method for the Prediction of a Severe Storm over North China, ADVANCES IN ATMOSPHERIC SCIENCES, 38, 661-676.  doi: 10.1007/s00376-020-0219-z
    [20] Sen YANG, Deqin LI, Liqiang CHEN, Zhiquan LIU, Xiang-Yu HUANG, Xiao PAN, 2023: The Regularized WSM6 Microphysical Scheme and Its Validation in WRF 4D-Var, ADVANCES IN ATMOSPHERIC SCIENCES, 40, 483-500.  doi: 10.1007/s00376-022-2058-6
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    • Manuscript History

    Manuscript received: 10 November 2010
    Manuscript revised: 10 November 2010
    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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    The Structure of Background-error Covariance in a Four-dimensional Variational Data Assimilation System: Single-point Experiment

    • 1. State Key Laboratory of Numerical Modeling for Atmospheric Sciences & Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,State Key Laboratory of Numerical Modeling for Atmospheric Sciences &Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029,State Key Laboratory of Numerical Modeling for Atmospheric Sciences & Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, Graduate University of the Chinese Academy of Sciences, Beijing 100049
    • Manuscript received: 2010-11-10
    • Manuscript revised: 2010-11-10

    Abstract: A four dimensional variational data assimilation (4DVar) based on a dimension-reduced projection (DRP-4DVar) has been developed as a hybrid of the 4DVar and Ensemble Kalman filter (EnKF) concepts. Its good flow-dependent features are demonstrated in single-point experiments through comparisons with adjoint-based 4DVar and three-dimensional variational data (3DVar) assimilations using the fifth-generation Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model (MM5). The results reveal that DRP-4DVar can reasonably generate a background error covariance matrix (simply B-matrix) during the assimilation window from an initial estimation using a number of initial condition dependent historical forecast samples. In contrast, flow-dependence in the B-matrix of MM5 4DVar is barely detectable. It is argued that use of diagonal estimation in the B-matrix of the MM5 4DVar method at the initial time leads to this failure. The experiments also show that the increments produced by DRP-4DVar are anisotropic and no longer symmetric with respect to observation location due to the effects of the weather trends captured in its B-matrix. This differs from the MM5 3DVar which does not consider the influence of heterogeneous forcing on the correlation structure of the B-matrix, a condition that is realistic for many situations. Thus, the MM5 3DVar assimilation could only present an isotropic and homogeneous structure in its increments.

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