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根据非线性局部Lyapunov向量方法和增长模繁殖方法，选取Lorenz63模型和Lorenz96模型的不同状态为例，对集合预报与单一预报的预报技巧开展了对比研究.结果表明：与单一预报比较，集合预报的均方根误差和型异常相关有明显改善，随预报时间推移，改善效果越显著，且集合平均优于单一预报的实验个例数逐渐增多.就概率分布（f）而言，单一预报状态的f与真实状态基本一致，不随时间变化；而集合平均预报状态的f则随时间呈现出值域变窄、峰值变大的特点.表明随预报时间的延长，单一预报状态为混沌吸引子上的随机状态，而集合平均预报状态为吸引子子集上的随机状态，这可能是集合平均误差小于单一预报的原因.
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关键词:
- 非线性局部Lyapunov向量 /
- 集合预报 /
- 单一预报 /
- Lorenz模型
In the past two decades,the ensemble forecasting has gained considerable attention.The atmosphere is a chaotic system,and a small error in the initial conditions will result in an enormous forecast uncertainty with time.It is impossible to precisely predict the future state of the atmosphere by a single (or control) forecasting.The ensemble forecasting is a feasible method to reduce the forecast uncertainty and to provide the reliability information about forecast.Many studies showed that because of the nonlinear filtering effect,the ensemble forecasting is more skillful than the single forecasting according to the statistical average over a large number of numerical experimental cases. However,the forecast skill can vary widely from day to day according to the specific synoptic events.The dependence of the ensemble forecasting on specific event has not been fully addressed in previous studies.Therefore,the performances of the ensemble forecasting in specific experimental cases should be further studied,which is important for improving the forecast skill in weather and climate events.In this paper,the nonlinear local Lyapunov vectors (NLLVs),which indicate orthogonal directions in phase space with different perturbation growth rates,are introduced to generate the initial perturbations for the ensemble forecasting.The NLLVs span the fast-growing perturbation subspace efficiently, and thus may grasp more components in analysis errors than other ensemble methods.Meanwhile,the bred growing mode (BGM) method,which indicates the fastest growing perturbation mode,is also used for the ensemble forecasting. Based on the NLLV and BGM methods,the forecast performances of the ensemble forecasting and single forecasting are compared in the Lorenz63 and Lorenz96 models for specific experimental cases.Additionally,two practical measures, namely the root mean square error (RMSE) and pattern anomaly correlation (PAC),are used to assess the performances of the ensemble forecasting.The results indicate that each ensemble mean forecasting is more skillful than its single forecasting in terms of RMSE and PAC.For each experimental case,the proportion of the ensemble forecasting better than single forecasting gradually increases with time in Lorenz63(Lorenz96) model by both NLLV and BGM methods, respectively.In addition,the variation of probability distribution of the ensemble mean states might be the reason why the forecast error of ensemble forecasting is less than that of the single forecast.The results based on simple model could provide a new perspective to understand ensemble forecasting and may be conducive to the weather and climate prediction.-
Keywords:
- nonlinear local Lyapunov vector /
- ensemble forecasting /
- single forecasting /
- Lorenz model
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[32] Ding R Q, Li J P 2009 Acta Meteor. Sin. 67 241 (in Chinese) [丁瑞强, 李建平 2009 气象学报 67 241]
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[34] Ding R Q, Li J P, Ha K J 2008 J. Geophys. Res. 113 D24112
[35] Li J P, Ding R Q 2011 Mon. Wea. Rev. 139 3265
[36] Lorenz E N, Emanuel K A 1998 J. Atmos. Sci. 55 399
[37] Lorenz E N 1995 Seminar on Predictability Shinfield Park, Reading, United Kingdom, September 4-8, 1995 p1
[38] Buizza R, Houtekamer P L, Toth Z, Pellerin G, Wei M, Zhu Y 2005 Mon. Wea. Rev. 133 1076
[39] Houtekamer P L, Derome J 1994 Mon. Wea. Rev. 122 2179
[40] Zhuang Z R, Xue J S, Li X L 2011 Acta Meteor. Sin. 69 620 (in Chinese) [庄照荣, 薛纪善, 李兴良 2011 气象学报 69 620]
[41] Eckmann J P, Ruelle D 1985 Rev. Mod. Phys. 57 617
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[1] Lorenz E N 1963 J. Atmos. Sci. 20 130
[2] Chou J F 1990 New Advances of Atmospheric Dynamic (Lanzhou: Lanzhou University Press) p214 (in Chinese) [丑纪范 1990 大气动力学的新进展(兰州: 兰州大学出版社) 第214页]
[3] Li J P, Chou J 1996 Chin. Sci. Bull. 41 587
[4] Epstein E S 1969 Tellus 21 739
[5] Leith C E 1974 Mon. Wea. Rev. 102 409
[6] Fritsch J M, Hilliker J, Ross J 2000 Wea. Forecasting 15 571
[7] Visloscky R L, Fritsch J M 1995 Bull. Amer. Meteor. Soc. 76 1157
[8] Hoffman R N, Kalnay E 1983 Tellus 35A 100
[9] Toth Z, Kalnay E 1993 Bull. Amer. Meteor. Soc. 74 2317
[10] Toth Z, Kalnay E 1997 Mon. Wea. Rev. 125 3297
[11] Molteni F, Palmer T N 1993 Q. J. R. Meteorol. Soc. 119 269
[12] Molteni F, Buizza R, Palmer T N, Petroliagis T 1996 Q. J. R. Meteorol. Soc. 122 73
[13] Buizza R 1996 Mon. Wea. Rev. 125 99
[14] Houtekamer P L, Lefaivre L, Derome J, Ritchie H, Mitchell H L 1996 Mon. Wea. Rev. 124 1225
[15] Houtekamer P L, Mitchell H L 1998 Mon. Wea. Rev. 126 796
[16] Mu M, Jiang Z N 2008 Chin. Sci. Bull. 53 2062
[17] Duan W S, Mu M 2009 Sci. China Ser. D: Earth Sci. 52 883
[18] Evensen G 2003 Ocean Dyn. 53 343
[19] Wang X, and Bishop C 2003 J. Atmos. Sci. 60 1140
[20] Feng J, Ding R Q, Liu D Q, Li J P 2014 J. Atmos. Sci. 71 3554
[21] Feng J, Ding R Q, Li J P, Liu D Q 2016 Adv. Atmos. Sci. 33 1036
[22] Ding R Q, Li J P, Li B S 2017 Adv. Atmos. Sci. 34 1027
[23] Anderson J L 1997 Mon. Wea. Rev. 125 2969
[24] Feng G L, Dong W J 2003 Acta Phys. Sin. 52 2347 (in Chinese) [封国林, 董文杰 2003 物理学报 52 2347]
[25] Bowler N E 2006 Tellus 58A 538
[26] Li Z C, Chen D H 2002 J. Appl. Meteor. Sci. 13 1 (in Chinese) [李泽椿, 陈德辉 2002 应用气象学报 13 1]
[27] He W P, Feng G L, Dong W J, Li J P 2006 Acta Phys. Sin. 55 969 (in Chinese) [何文平, 封国林, 董文杰, 李建平 2006 物理学报 55 969]
[28] Ma J H, Zhu Y J, Wang P X, Duan M J 2011 Trans. Atmos. Sci. 34 370 (in Chinese) [麻巨慧, 朱跃建, 王盘兴, 段明铿 2011 大气科学学报 34 370]
[29] Tan N, Chen J, Tian H 2013 Meteor. Mon. 39 543 (in Chinese) [谭宁, 陈静, 田华 2013 气象 39 543]
[30] Zheng Z H, Feng G L, Huang J P, Chou J F 2012 Acta Phys. Sin. 61 199203 (in Chinese) [郑志海, 封国林, 黄建平, 丑纪范 2012 物理学报 61 199203]
[31] Zhang H B, Chen J, Zhi X F, Long K J, Wang Y N 2014 Trans. Atmos. Sci. 37 276 (in Chinese) [张涵斌, 陈静, 智协飞, 龙柯吉, 王亚男 2014 大气科学学报 37 276]
[32] Ding R Q, Li J P 2009 Acta Meteor. Sin. 67 241 (in Chinese) [丁瑞强, 李建平 2009 气象学报 67 241]
[33] Ding R Q, Li J P 2009 Acta Meteor. Sin. 67 343 (in Chinese) [丁瑞强, 李建平 2009 气象学报 67 343]
[34] Ding R Q, Li J P, Ha K J 2008 J. Geophys. Res. 113 D24112
[35] Li J P, Ding R Q 2011 Mon. Wea. Rev. 139 3265
[36] Lorenz E N, Emanuel K A 1998 J. Atmos. Sci. 55 399
[37] Lorenz E N 1995 Seminar on Predictability Shinfield Park, Reading, United Kingdom, September 4-8, 1995 p1
[38] Buizza R, Houtekamer P L, Toth Z, Pellerin G, Wei M, Zhu Y 2005 Mon. Wea. Rev. 133 1076
[39] Houtekamer P L, Derome J 1994 Mon. Wea. Rev. 122 2179
[40] Zhuang Z R, Xue J S, Li X L 2011 Acta Meteor. Sin. 69 620 (in Chinese) [庄照荣, 薛纪善, 李兴良 2011 气象学报 69 620]
[41] Eckmann J P, Ruelle D 1985 Rev. Mod. Phys. 57 617
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