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Volume 23 Issue 1

Jan.  2006

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Article >  ADVANCES IN ATMOSPHERIC SCIENCES  > 2006 >  23(1): 33-44

Application of an Error Statistics Estimation Method to the PSAS Forecast Error Covariance Model

  • 1.

    Science Systems and Applications Inc., Lanham, USA, Global Modeling and Assimilation Office, NASA Goddard Space Flight Center, Greenbelt, USA,Science Applications International Corporation, Beltsville, USA, Global Modeling and Assimilation Office, NASA Goddard Space Flight Center, Greenbelt, USA,Joint Center for Earth Systems Technology/UMBC, Baltimore, USA, Global Modeling and Assimilation Office, NASA Goddard Space Flight Center, Greenbelt, USA


doi: 10.1007/s00376-006-0004-7

  • In atmospheric data assimilation systems, the forecast error covariance model is an important component. However, the parameters required by a forecast error covariance model are difficult to obtain due to the absence of the truth. This study applies an error statistics estimation method to the Physical-space Statistical Analysis System (PSAS) height-wind forecast error covariance model. This method consists of two components: the first component computes the error statistics by using the National Meteorological Center (NMC) method, which is a lagged-forecast difference approach, within the framework of the PSAS height-wind forecast error covariance model; the second obtains a calibration formula to rescale the error standard deviations provided by the NMC method. The calibration is against the error statistics estimated by using a maximum-likelihood estimation (MLE) with rawindsonde height observed-minus-forecast residuals. A complete set of formulas for estimating the error statistics and for the calibration is applied to a one-month-long dataset generated by a general circulation model of the Global Model and Assimilation Office (GMAO), NASA. There is a clear constant relationship between the error statistics estimates of the NMC-method and MLE. The final product provides a full set of 6-hour error statistics required by the PSAS height-wind forecast error covariance model over the globe. The features of these error statistics are examined and discussed.
  • [1] 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
    [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] 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
    [4] Tao SUN, Yaodeng CHEN, Deming MENG, Haiqin CHEN, 2021: Background Error Covariance Statistics of Hydrometeor Control Variables Based on Gaussian Transform, ADVANCES IN ATMOSPHERIC SCIENCES, 38, 831-844.  doi: 10.1007/s00376-021-0271-3
    [5] 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
    [6] Isidora JANKOV, Scott GREGORY, Sai RAVELA, Zoltan TOTH, Malaquías PEÑA, 2021: Partition of Forecast Error into Positional and Structural Components, ADVANCES IN ATMOSPHERIC SCIENCES, 38, 1012-1019.  doi: 10.1007/s00376-021-0251-7
    [7] LIU Juanjuan, WANG Bin, WANG Shudong, 2010: The Structure of Background-error Covariance in a Four-dimensional Variational Data Assimilation System: Single-point Experiment, ADVANCES IN ATMOSPHERIC SCIENCES, 27, 1303-1310.  doi: 10.1007/s00376-010-9067-6
    [8] 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
    [9] Xingchao CHEN, Kun ZHAO, Juanzhen SUN, Bowen ZHOU, Wen-Chau LEE, 2016: Assimilating Surface Observations in a Four-Dimensional Variational Doppler Radar Data Assimilation System to Improve the Analysis and Forecast of a Squall Line Case, ADVANCES IN ATMOSPHERIC SCIENCES, 33, 1106-1119.  doi: 10.1007/s00376-016-5290-0
    [10] 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
    [11] HUA Wei, Samuel S. P. SHEN, WANG Huijun, 2014: Analysis of Sampling Error Uncertainties and Trends in Maximum and Minimum Temperatures in China, ADVANCES IN ATMOSPHERIC SCIENCES, 31, 263-272.  doi: 10.1007/s00376-013-2316-8
    [12] BAI Yulong, LI Xin, and HUANG Chunlin, 2013: Handling error propagation in sequential data assimilation using an evolutionary strategy, ADVANCES IN ATMOSPHERIC SCIENCES, 30, 1096-1105.  doi: 10.1007/s00376-012-2115-7
    [13] 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
    [14] Lan XU, Wei CHENG, Zhongren DENG, Juanjuan LIU, Bin WANG, Bin LU, Shudong WANG, Li DONG, 2023: Assimilation of the FY-4A AGRI Clear-Sky Radiance Data in a Regional Numerical Model and Its Impact on the Forecast of the “21·7” Henan Extremely Persistent Heavy Rainfall, ADVANCES IN ATMOSPHERIC SCIENCES, 40, 920-936.  doi: 10.1007/s00376-022-1380-3
    [15] WANG Pengfei, HUANG Gang, WANG Zaizhi, 2006: Analysis and Application of Multiple-Precision Computation and Round-off Error for Nonlinear Dynamical Systems, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 758-766.  doi: 10.1007/s00376-006-0758-y
    [16] Chen Jiabin, Ji Liren, Wu Wanli, 1987: DESIGN AND TEST OF AN IMPROVED SCHEME FOR GLOBAL SPECTRAL MODEL WITH REDUCED TRUNCATION ERROR, ADVANCES IN ATMOSPHERIC SCIENCES, 4, 156-168.  doi: 10.1007/BF02677062
    [17] Seung-Woo LEE, Dong-Kyou LEE, 2011: Improvement in Background Error Covariances Using Ensemble Forecasts for Assimilation of High-Resolution Satellite Data, ADVANCES IN ATMOSPHERIC SCIENCES, 28, 758-774.  doi: 10.1007/s00376-010-0145-6
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    • Manuscript History

    Manuscript received: 10 January 2006
    Manuscript revised: 10 January 2006
    通讯作者: 陈斌, bchen63@163.com
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    Application of an Error Statistics Estimation Method to the PSAS Forecast Error Covariance Model

    • 1. Science Systems and Applications Inc., Lanham, USA, Global Modeling and Assimilation Office, NASA Goddard Space Flight Center, Greenbelt, USA,Science Applications International Corporation, Beltsville, USA, Global Modeling and Assimilation Office, NASA Goddard Space Flight Center, Greenbelt, USA,Joint Center for Earth Systems Technology/UMBC, Baltimore, USA, Global Modeling and Assimilation Office, NASA Goddard Space Flight Center, Greenbelt, USA
    • Manuscript received: 2006-01-10
    • Manuscript revised: 2006-01-10

    Abstract: In atmospheric data assimilation systems, the forecast error covariance model is an important component. However, the parameters required by a forecast error covariance model are difficult to obtain due to the absence of the truth. This study applies an error statistics estimation method to the Physical-space Statistical Analysis System (PSAS) height-wind forecast error covariance model. This method consists of two components: the first component computes the error statistics by using the National Meteorological Center (NMC) method, which is a lagged-forecast difference approach, within the framework of the PSAS height-wind forecast error covariance model; the second obtains a calibration formula to rescale the error standard deviations provided by the NMC method. The calibration is against the error statistics estimated by using a maximum-likelihood estimation (MLE) with rawindsonde height observed-minus-forecast residuals. A complete set of formulas for estimating the error statistics and for the calibration is applied to a one-month-long dataset generated by a general circulation model of the Global Model and Assimilation Office (GMAO), NASA. There is a clear constant relationship between the error statistics estimates of the NMC-method and MLE. The final product provides a full set of 6-hour error statistics required by the PSAS height-wind forecast error covariance model over the globe. The features of these error statistics are examined and discussed.

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