AmbadanTangComment.doc - Comment on Sigma-Point Kalman...

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Comment on “Sigma-Point Kalman Filter Data Assimilation Methods for Strongly Nonlinear Systems” THOMAS M. HAMILL and JEFFREY S. WHITAKER NOAA Earth System Research Laboratory, Boulder, Colorado JEFFREY L. ANDERSON and CHRIS SNYDER National Center for Atmospheric Research, Boulder, Colorado Submitted to Journal of the Atmospheric Sciences 25 June 2009 Corresponding author address : Dr. Thomas M. Hamill NOAA Earth System Research Laboratory Physical Sciences Division R/PSD1 325 Broadway Boulder, Colorado 80305 Phone: (303) 497-3060 Fax: (303) 497-6449 e-mail: [email protected] 1
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Ambadan and Tang (2009; hereafter “AT09”) recently performed a study of several varieties of a “sigma-point” Kalman filter (SPKF) using two strongly nonlinear models, Lorenz (1963; hereafter L63) and Lorenz (1996; hereafter L96). In this comparison, a reference benchmark was the performance of a standard ensemble Kalman filter (EnKF) of Evensen (1994, 2003), presumably with perturbed observations following Houtekamer and Mitchell (1998) and Burgers et al. (1998). We have identified problems in the description of the EnKF as well as its application with the L63 and L96 models. a. Problem in the description of the EnKF . AT09 stated (page 262, column 1) as a drawback of the EnKF that it “ … assumes a linear measurement operator; if the measurement function is nonlinear, it has to be linearized in the EnKF.” This statement is incorrect; the EnKF is routinely applied with nonlinear measurement operators; the standard formulation for this is shown in Hamill (2006), eqs. 6.11, 6.14, and 6.15. b. L63 experiments. AT09’s examination of the EnKF with small ensembles was potentially misleading. They chose to include a white-noise model of unknown model errors in their assimilating model. This representation of model error was particularly poorly suited for use with EnKFs; in fact, AT09 showed that a 19-member ensemble had a root-mean square error (RMSE) more than three times larger than a 1000-member ensemble. However, a 19-member ensemble in fact has an RMSE that is only 1.05 times that of the 2
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1000-member ensemble when white noise is removed from the assimilating model. This is consistent with the successful application of EnKFs with 10 to 100 members, even in large numerical weather prediction models (e.g., Houtekamer et al. 2005, 2009, and Whitaker et al. 2008). c. L96 experiments. AT09’s EnKF reference was badly degraded by not using covariance localization and/or other methods to stabilize the filter. Much has been learned about the performance of the ensemble-based data assimilation methods since the preliminary studies of the 1990s, lessons that AT09 apparently did not incorporate into their L96 EnKF reference. Since the early implementations of the EnKF, several now standard modifications are commonly considered to be essential in spatially distributed systems; the first is some form of “localization” of covariances (Houtekamer and Mitchell 2001; Hamill et al. 2001).
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