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背景误差方差的集合估计值中带有大量采样噪声,在应用之前需进行降噪处理.区别于一般的高斯白噪声,采样噪声具有空间和尺度相关性,部分尺度上的噪声能级远大于平均能级.本文针对背景误差方差中采样噪声的特征,引入小波阈值去噪方法,并根据截断余项的小波系数分布特征发展了一种计算代价很小,能自动修正阈值的算法.一维理想试验结果表明,该方法能滤除大量采样噪声,提高背景误差方差估计值的精度.相对于原来的小波阈值方法,修正阈值后减少了因部分尺度上噪声能级过大导致的残差,去噪后的RMSE减少了13.28%.将该方法应用在实际的集合资料同化系统中,结果表明,小波阈值方法优于谱方法,阈值修正后能在不影响信号的前提下增大小波去噪强度.
[1] Zhang W M, Cao X Q, Song J Q 2012 Acta Phys. Sin. 61 249202(in Chinese)[张卫民, 曹小群, 宋君强2012物理学报61 249202]
[2] Wang S C, LI Y, Zhang W M, Zhao J, Cao X Q 2011 Acta Phys. Sin. 60 099203(in Chinese)[王舒畅, 李毅, 张卫民, 赵军, 曹小群2011物理学报60 099203]
[3] Laroche S, Gauthier G 1998 Tellus Ser. A 50 557
[4] Derber J, Bouttier F 1999 Tellus Ser. A 51 195
[5] Buizza R, Houtekamer P L, Pellerin G, Toth Z, Zhu Y J, Wei M Z 2005 Mon. Weather Rev. 133 1076
[6] Houtekamer P L, Mitchell H L 1998 Mon. Weather Rev. 126 3
[7] Evensen G 1994 J. Geophys. Res. 99 10143
[8] Bonavita M, Raynaud L, Isaksen L 2011 Q. J. R. Meteorol. Soc. 137 423
[9] Berre L, Varella H, Desroziers G 2015 Q. J. R. Meteorol. Soc. 141 2803
[10] Raynaud L, Berre L, Desroziers G 2009 Q. J. R. Meteorol. Soc. 135 1177
[11] Pereira M B, Berre L 2006 Mon. Weather Rev.134 2466
[12] Raynaud L, Berre L, Desroziers G 2008 Q. J. R. Meteorol. Soc. 134 1003
[13] Wiener N 1949 Extrapolation, Interpolation, and Smoothing of Stationary Time Series (Cambridge:Massachusetts Institute of Technology) pp86-90
[14] Bonavita M, Isaksen L, Hólm E 2012 Q. J. R. Meteorol. Soc. 138 1540
[15] Liu B N, Zhang W M, Cao X Q, Zhao Y L, Huang Q B 2015 China J. Geophys. 58 1526(in Chinese)[刘柏年, 张卫民, 曹小群, 赵延来, 皇群博, 罗雨2015地球物理学报58 1526]
[16] Donoho D L, Johnstone J M 1994 Biometrical81 425
[17] Parrish D F, Derber J C 1992 Mon. Weather Rev.120 1747
[18] Fisher M 2003 Proceedings ECMWF Seminar on "Recent Developments in Data Assimilation for Atmosphere and Ocean" Reading, September 8-12, 2003 p45
[19] Isaksen L, Fisher M, Berner J 2006 ECMWF Tech. Memo. 492
[20] Moore S, Wood S, Davies P 1998 Annals of Statistics 26 1
[21] Daley R 1993 Atmospheric Data Analysis1993(Cambridge:Cambridge University Press) pp46-50
[22] Azzalini A, Farge M, Schneider K 2005 Appl. Comput. Harmon. Anal. 18 177
[23] Yen R N V, Farge M, Schneider K 2012 Physica D Nonlinear Phenomena 241 186
[24] Pannekoucke O, Raynaud L, Farge M 2014 Q. J. R. Meteorol. Soc. 140 316
[25] Zhang W M, Liu B N, Cao X Q, Zhao Y L, Zhu M B, Zhao W J 2016 Acta Meteorol Sin. 74 410(in Chinese)[张卫民, 刘柏年, 曹小群, 赵延来, 朱孟斌, 赵文静2016气象学报74 410]
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[1] Zhang W M, Cao X Q, Song J Q 2012 Acta Phys. Sin. 61 249202(in Chinese)[张卫民, 曹小群, 宋君强2012物理学报61 249202]
[2] Wang S C, LI Y, Zhang W M, Zhao J, Cao X Q 2011 Acta Phys. Sin. 60 099203(in Chinese)[王舒畅, 李毅, 张卫民, 赵军, 曹小群2011物理学报60 099203]
[3] Laroche S, Gauthier G 1998 Tellus Ser. A 50 557
[4] Derber J, Bouttier F 1999 Tellus Ser. A 51 195
[5] Buizza R, Houtekamer P L, Pellerin G, Toth Z, Zhu Y J, Wei M Z 2005 Mon. Weather Rev. 133 1076
[6] Houtekamer P L, Mitchell H L 1998 Mon. Weather Rev. 126 3
[7] Evensen G 1994 J. Geophys. Res. 99 10143
[8] Bonavita M, Raynaud L, Isaksen L 2011 Q. J. R. Meteorol. Soc. 137 423
[9] Berre L, Varella H, Desroziers G 2015 Q. J. R. Meteorol. Soc. 141 2803
[10] Raynaud L, Berre L, Desroziers G 2009 Q. J. R. Meteorol. Soc. 135 1177
[11] Pereira M B, Berre L 2006 Mon. Weather Rev.134 2466
[12] Raynaud L, Berre L, Desroziers G 2008 Q. J. R. Meteorol. Soc. 134 1003
[13] Wiener N 1949 Extrapolation, Interpolation, and Smoothing of Stationary Time Series (Cambridge:Massachusetts Institute of Technology) pp86-90
[14] Bonavita M, Isaksen L, Hólm E 2012 Q. J. R. Meteorol. Soc. 138 1540
[15] Liu B N, Zhang W M, Cao X Q, Zhao Y L, Huang Q B 2015 China J. Geophys. 58 1526(in Chinese)[刘柏年, 张卫民, 曹小群, 赵延来, 皇群博, 罗雨2015地球物理学报58 1526]
[16] Donoho D L, Johnstone J M 1994 Biometrical81 425
[17] Parrish D F, Derber J C 1992 Mon. Weather Rev.120 1747
[18] Fisher M 2003 Proceedings ECMWF Seminar on "Recent Developments in Data Assimilation for Atmosphere and Ocean" Reading, September 8-12, 2003 p45
[19] Isaksen L, Fisher M, Berner J 2006 ECMWF Tech. Memo. 492
[20] Moore S, Wood S, Davies P 1998 Annals of Statistics 26 1
[21] Daley R 1993 Atmospheric Data Analysis1993(Cambridge:Cambridge University Press) pp46-50
[22] Azzalini A, Farge M, Schneider K 2005 Appl. Comput. Harmon. Anal. 18 177
[23] Yen R N V, Farge M, Schneider K 2012 Physica D Nonlinear Phenomena 241 186
[24] Pannekoucke O, Raynaud L, Farge M 2014 Q. J. R. Meteorol. Soc. 140 316
[25] Zhang W M, Liu B N, Cao X Q, Zhao Y L, Zhu M B, Zhao W J 2016 Acta Meteorol Sin. 74 410(in Chinese)[张卫民, 刘柏年, 曹小群, 赵延来, 朱孟斌, 赵文静2016气象学报74 410]
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