初始扰动振幅和集合样本数对CNOPs集合预报的影响
|
摘要
初始扰动振幅的大小和集合样本数对于集合预报取得更高预报技巧具有重要意义。本文将正交条件非线性最优扰动方法(orthogonal conditional nonlinear optimal perturbations,简称CNOPs)应用于概念模型Lorenz-96模式探讨了初始扰动振幅和集合样本数对集合预报技巧的影响,从而为使用更复杂模式进行集合预报提供指导。结果表明,由于CNOPs扮演了非线性系统中的最优初始扰动,从而使得当初始扰动振幅小于初始分析误差的大小时,CNOPs集合预报获得更高的预报技巧,并且CNOPs集合预报的最高预报技巧总是高于奇异向量法(singular vectors,简称SVs)集合预报的最高预报技巧。结果还表明,CNOPs集合预报倾向于具有一个合适的样本数时,达到最高技巧。更好的集合离散度——预报误差关系和更为平坦的Talagrand图(Talagrand diagram)进一步证明了CNOPs集合预报系统的可靠性,从而夯实了上述结果的合理性。因此,针对CNOPs集合预报,本文认为采用一个适当小于初始分析误差的初始扰动振幅和一个合适的集合样本数,有利于CNOPs集合预报达到最高预报技巧。
The initial perturbation amplitude and ensemble size are important for ensemble forecast. The present study explores the impacts of initial perturbation amplitude and ensemble size on the ensemble forecast skill using a new strategy that applies orthogonal conditional nonlinear optimal perturbations(CNOPs) to the Lorenz-96 model. It is found that due to the effect of nonlinearity, the CNOPs-based ensemble forecast can achieve higher skills when the initial perturbation amplitude is appropriately smaller than the amplitude of initial analysis errors, and the highest skill of the CNOPs-based ensemble forecasts is always higher than that of its linear counterpart [i.e., singular vectors(SVs)-based ensemble forecast]. The results also show that an appropriate ensemble size is helpful for achieving higher skills in ensemble forecast. A better spread-skill relationship and a much flatter Talagrand diagram are found in CNOPs-based ensemble forecast, which indicates the reliability of the corresponding ensemble forecast system and makes the above results much solid. It is therefore inferred that the highest skill of CNOPs-based ensemble forecast is mostly likely achieved when initial perturbation amplitudes are properly smaller than those of initial analysis errors and the ensemble size is appropriate.
The initial perturbation amplitude and ensemble size are important for ensemble forecast. The present study explores the impacts of initial perturbation amplitude and ensemble size on the ensemble forecast skill using a new strategy that applies orthogonal conditional nonlinear optimal perturbations(CNOPs) to the Lorenz-96 model. It is found that due to the effect of nonlinearity, the CNOPs-based ensemble forecast can achieve higher skills when the initial perturbation amplitude is appropriately smaller than the amplitude of initial analysis errors, and the highest skill of the CNOPs-based ensemble forecasts is always higher than that of its linear counterpart [i.e., singular vectors(SVs)-based ensemble forecast]. The results also show that an appropriate ensemble size is helpful for achieving higher skills in ensemble forecast. A better spread-skill relationship and a much flatter Talagrand diagram are found in CNOPs-based ensemble forecast, which indicates the reliability of the corresponding ensemble forecast system and makes the above results much solid. It is therefore inferred that the highest skill of CNOPs-based ensemble forecast is mostly likely achieved when initial perturbation amplitudes are properly smaller than those of initial analysis errors and the ensemble size is appropriate.
引文
Anderson J L.1997.The impact of dynamical constraints on the selection of initial conditions for ensemble predictions:Low-order perfect model results[J].Mon.Wea.Rev.,125(11):2969-2983.doi:10.1175/1520-0493(1997)125<2969:TIODCO>2.0.CO;2
Basnarkov L,Kocarev L.2012.Forecast improvement in Lorenz 96system[J].Nonlinear Processes in Geophysics,19(5):569-575.doi:10.5194/npg-19-569-2012
Birgin E G,Martínez J M,Raydan M.2000.Nonmonotone spectral projected gradient methods on convex sets[J].SIAM Journal on Optimization,10(4):1196-1211.doi:10.1137/S1052623497330963
Bowler N E.2006.Comparison of error breeding,singular vectors,random perturbations and ensemble Kalman filter perturbation strategies on a simple model[J].Tellus A,58(5):538-548.doi:10.1111/j.1600-0870.2006.00197.x
Brankovi??,Palmer T N,Molteni F,et al.1990.Extended-range predictions with ECMWF models:Time-lagged ensemble forecasting[J].Quart.J.Roy.Meteor.Soc.,116(494):867-912.doi:10.1002/qj.49711649405
Brier G W.1950.Verification of forecasts expressed in terms of probability[J].Mon.Wea.Rev.,78(1):1-3.doi:10.1175/1520-0493(1950)078<0001:VOFEIT>2.0.CO;2
Buckingham C,Marchok T,Ginis I,et al.2010.Short-and mediumrange prediction of tropical and transitioning cyclone tracks within the NCEP global ensemble forecasting system[J].Wea.Forecasting,25(6):1736-1754.doi:10.1175/2010WAF2222398.1
Buizza R,Palmer T N.1995.The singular-vector structure of the atmospheric global circulation[J].J.Atmos.Sci.,52(9):1434-1456.doi:10.1175/1520-0469(1995)052<1434:TSVSOT>2.0.CO;2
Buizza R,Palmer T N.1998.Impact of ensemble size on ensemble prediction[J].Mon.Wea.Rev.,126(9):2503-2518.doi:10.1175/1520-0493(1998)126<2503:IOESOE>2.0.CO;2
Buizza R,Tribbia J,Molteni F,et al.1993.Computation of optimal unstable structures for a numerical weather prediction model[J].Tellus A,45(5):388-407.doi:10.3402/tellusa.v45i5.14901
Buizza R,Houtekamer P L,Pellerin G,et al.2005.A comparison of the ECMWF,MSC,and NCEP global ensemble prediction systems[J].Mon.Wea.Rev.,133(5):1076-1097.doi:10.1175/MWR2905.1
Candille G,Talagrand O.2005.Evaluation of probabilistic prediction systems for a scalar variable[J].Quart.J.Roy.Meteor.Soc.,131(609):2131-2150.doi:10.1256/qj.04.71
Daron J D,Stainforth D A.2013.On predicting climate under climate change[J].Environ.Res.Lett.,8(3):034021.doi:10.1088/1748-9326/8/3/034021
Descamps L,Talagrand O.2007.On some aspects of the definition of initial conditions for ensemble prediction[J].Mon.Wea.Rev.,135(9):3260-3272.doi:10.1175/MWR3452.1
Ding R Q,Li J P,Li B S.2017.Determining the spectrum of the nonlinear local Lyapunov exponents in a multidimensional chaotic system[J].Adv.Atmos.Sci.,34(9):1027-1034.doi:10.1007/s00376-017-7011-8
Duan W S,Huo Z H.2016.An approach to generating mutually independent initial perturbations for ensemble forecasts:Orthogonal conditional nonlinear optimal perturbations[J].J.Atmos.Sci.,73(3):997-1014.doi:10.1175/JAS-D-15-0138.1
Eckel F A,Mass C F.2005.Aspects of effective mesoscale,short-range ensemble forecasting[J].Wea.Forecasting,20(3):328-350,doi:10.1175/WAF843.1.
Epstein E S.1969.Stochastic dynamic prediction[J].Tellus,21(6):739-759.doi:10.3402/tellusa.v21i6.10143
Feng J,Ding R Q,Liu D Q,et al.2014.The application of nonlinear local Lyapunov vectors to ensemble predictions in Lorenz systems[J].J.Atmos.Sci.,71(9):3554-3567.doi:10.1175/JAS-D-13-0270.1
Gilmour I,Smith L A.1997.Enlightenment in shadows[C]//AIPConference Proceedings.AIP,411:335-340.doi:10.1063/1.54200
Hamill T M,Snyder C,Morss R E.2000.A comparison of probabilistic forecasts from bred,singular-vector,and perturbed observation ensembles[J].Mon.Wea.Rev.,128(6):1835-1851.doi:10.1175/1520-0493(2000)128<1835:ACOPFF>2.0.CO;2
Hoffman R N,Kalnay E.1983.Lagged average forecasting,an alternative to Monte Carlo forecasting[J].Tellus A,35(2):100-118.doi:10.3402/tellusa.v35i2.11425
Hollingsworth A.1979.An experiment in Monte Carlo forecasting[C]//Proceedings Workshop on Stochastic Dynamic Forecasting.Reading,UK,65-85.
Hou Z L,Li J P,Ding R Q,et al.2018.The application of nonlinear local Lyapunov vectors to the Zebiak-Cane model and their performance in ensemble prediction[J].Climate Dyn.,51(1-2):283-304.doi:10.1007/s00382-017-3920-6
Huo Z H,Duan W S.2018.The application of the orthogonal conditional nonlinear optimal perturbations method to typhoon track ensemble forecasts[J].Sci.China Earth Sci.,62(2):376-388.doi:10.1007/s11430-018-9248-9
Jiang Z N,Mu M.2009.A comparison study of the methods of conditional nonlinear optimal perturbations and singular vectors in ensemble prediction[J].Adv.Atmos.Sci.,26(3):465-470.doi:10.1007/s00376-009-0465-6
Kalnay E.2003.Atmospheric Modeling,Data Assimilation and Predictability[M].Cambridge:Cambridge University Press,341pp.
Kalnay E,Toth Z.1995.The breeding method[C]//Proceedings of the ECMWF Seminar on Predictability.Reading,UK,69-82.
Koyama H,Watanabe M.2010.Reducing forecast errors due to model imperfections using ensemble Kalman filtering[J].Mon.Wea.Rev.,138(8):3316-3332.doi:10.1175/2010MWR3067.1
Kumar A,Hoerling M P.2000.Analysis of a conceptual model of seasonal climate variability and implications for seasonal prediction[J].Bull.Amer.Meteor.Soc.,81(2):255-264.doi:10.1175/1520-0477(2000)081<0255:AOACMO>2.3.CO;2
Kumar A,Barnston A G,Hoerling M P.2001.Seasonal predictions,probabilistic verifications,and ensemble size[J].J.Climate,14(7):1671-1676.doi:10.1175/1520-0442(2001)014<1671:SPPVAE>2.0.CO;2
Leith C E.1974.Theoretical skill of Monte Carlo forecasts[J].Mon.Wea.Rev.,102(6):409-418.doi:10.1175/1520-0493(1974)102<0409:TSOMCF>2.0.CO;2
Leutbecher M,Palmer T N.2008.Ensemble forecasting[J].J.Comput.Phys.,227(7):3515-3539.doi:10.1016/j.jcp.2007.02.014
Lorenz E N.1963.Deterministic nonperiodic flow[J].J.Atmos.Sci.,20(2):130-141.doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
Lorenz E N.1995.Predictability:A problem partly solved[C]//Proceedings of Seminar on Predictability.Shinfield Park,Reading:ECMWF,40-58.
Lorenz E N,Emanuel K A.1998.Optimal sites for supplementary weather observations:Simulation with a small model[J].J.Atmos.Sci.,55(3):399-414.doi:10.1175/1520-0469(1998)055<0399:OSFSWO>2.0.CO;2
Mason I.1982.A model for assessment of weather forecasts[J].Aust.Meteor.Mag.,30(4):291-303.
Mason S J.2004.On using“climatology”as a reference strategy in the Brier and ranked probability skill scores[J].Mon.Wea.Rev.,132(7):1891-1895.doi:10.1175/1520-0493(2004)132<1891:OUCAAR>2.0.CO;2
Mason S J,Graham N E.1999.Conditional probabilities,relative operating characteristics,and relative operating levels[J].Wea.Forecasting,14(5):713-725.doi:10.1175/1520-0434(1999)014<0713:CPROCA>2.0.CO;2
Molteni F,Buizza R,Palmer T N,et al.1996.The ECMWF ensemble prediction system:Methodology and validation[J].Quart.J.Roy.Meteor.Soc.,122(529):73-119.doi:10.1002/qj.49712252905
Mu M,Jiang Z N.2008.A new approach to the generation of initial perturbations for ensemble prediction:Conditional nonlinear optimal perturbation[J].Chinese Science Bulletin,53(13):2062-2068.doi:10.1007/s11434-008-0272-y
Mu M,Duan W S,Wang B.2003.Conditional nonlinear optimal perturbation and its applications[J].Nonlinear Processes in Geophysics,10(6):493-501.doi:10.5194/npg-10-493-2003
Murphy A H,Epstein E S.1989.Skill scores and correlation coefficients in model verification[J].Mon.Wea.Rev.,117(3):572-582.doi:10.1175/1520-0493(1989)117<0572:SSACCI>2.0.CO;2
Otsuka S,Miyoshi T.2015.A Bayesian optimization approach to multimodel ensemble Kalman filter with a low-order model[J].Mon.Wea.Rev.,143(6):2001-2012.doi:10.1175/MWR-D-14-00148.1
Revelli J A,Rodríguez M A,Wio H S.2010.The use of rank histograms and MVL diagrams to characterize ensemble evolution in weather forecasting[J].Adv.Atmos.Sci.,27(6):1425-1437.doi:10.1007/s00376-009-9153-6
Scaife A A,Arribas A,Blockley E,et al.2014.Skillful long-range prediction of European and North American winters[J].Geophys.Res.Lett.,41(7):2514-2519.doi:10.1002/2014GL059637
Talagrand O,Vautard R,Strauss B.1997.Evaluation of probabilistic prediction systems[C]//Workshop on Predictability,European Center for Medium Range Weather Forecasts.Reading,UK.
Toth Z,Kalnay E.1993.Ensemble forecasting at NMC:The generation of perturbations[J].Bull.Amer.Meteor.Soc.,74(12):2317-2330.doi:10.1175/1520-0477(1993)074<2317:EFANTG>2.0.CO;2
Toth Z,Kalnay E.1997.Ensemble forecasting at NCEP and the breeding method[J].Mon.Wea.Rev.,125(12):3297-3319.doi:10.1175/1520-0493(1997)125<3297:EFANAT>2.0.CO;2
Wang X G,Bishop C H.2003.A comparison of breeding and ensemble transform Kalman filter ensemble forecast schemes[J].J.Atmos.Sci.,60(9):1140-1158.doi:10.1175/1520-0469(2003)060<1140:ACOBAE>2.0.CO;2
Wilks D S.2011.Statistical Methods in the Atmospheric Sciences[M].3rd ed.Oxford:Academic Press,467pp.
Yoden S.2007.Atmospheric predictability[J].J.Meteor.Soc.Japan,85:77-102.doi:10.2151/jmsj.85B.77
Basnarkov L,Kocarev L.2012.Forecast improvement in Lorenz 96system[J].Nonlinear Processes in Geophysics,19(5):569-575.doi:10.5194/npg-19-569-2012
Birgin E G,Martínez J M,Raydan M.2000.Nonmonotone spectral projected gradient methods on convex sets[J].SIAM Journal on Optimization,10(4):1196-1211.doi:10.1137/S1052623497330963
Bowler N E.2006.Comparison of error breeding,singular vectors,random perturbations and ensemble Kalman filter perturbation strategies on a simple model[J].Tellus A,58(5):538-548.doi:10.1111/j.1600-0870.2006.00197.x
Brankovi??,Palmer T N,Molteni F,et al.1990.Extended-range predictions with ECMWF models:Time-lagged ensemble forecasting[J].Quart.J.Roy.Meteor.Soc.,116(494):867-912.doi:10.1002/qj.49711649405
Brier G W.1950.Verification of forecasts expressed in terms of probability[J].Mon.Wea.Rev.,78(1):1-3.doi:10.1175/1520-0493(1950)078<0001:VOFEIT>2.0.CO;2
Buckingham C,Marchok T,Ginis I,et al.2010.Short-and mediumrange prediction of tropical and transitioning cyclone tracks within the NCEP global ensemble forecasting system[J].Wea.Forecasting,25(6):1736-1754.doi:10.1175/2010WAF2222398.1
Buizza R,Palmer T N.1995.The singular-vector structure of the atmospheric global circulation[J].J.Atmos.Sci.,52(9):1434-1456.doi:10.1175/1520-0469(1995)052<1434:TSVSOT>2.0.CO;2
Buizza R,Palmer T N.1998.Impact of ensemble size on ensemble prediction[J].Mon.Wea.Rev.,126(9):2503-2518.doi:10.1175/1520-0493(1998)126<2503:IOESOE>2.0.CO;2
Buizza R,Tribbia J,Molteni F,et al.1993.Computation of optimal unstable structures for a numerical weather prediction model[J].Tellus A,45(5):388-407.doi:10.3402/tellusa.v45i5.14901
Buizza R,Houtekamer P L,Pellerin G,et al.2005.A comparison of the ECMWF,MSC,and NCEP global ensemble prediction systems[J].Mon.Wea.Rev.,133(5):1076-1097.doi:10.1175/MWR2905.1
Candille G,Talagrand O.2005.Evaluation of probabilistic prediction systems for a scalar variable[J].Quart.J.Roy.Meteor.Soc.,131(609):2131-2150.doi:10.1256/qj.04.71
Daron J D,Stainforth D A.2013.On predicting climate under climate change[J].Environ.Res.Lett.,8(3):034021.doi:10.1088/1748-9326/8/3/034021
Descamps L,Talagrand O.2007.On some aspects of the definition of initial conditions for ensemble prediction[J].Mon.Wea.Rev.,135(9):3260-3272.doi:10.1175/MWR3452.1
Ding R Q,Li J P,Li B S.2017.Determining the spectrum of the nonlinear local Lyapunov exponents in a multidimensional chaotic system[J].Adv.Atmos.Sci.,34(9):1027-1034.doi:10.1007/s00376-017-7011-8
Duan W S,Huo Z H.2016.An approach to generating mutually independent initial perturbations for ensemble forecasts:Orthogonal conditional nonlinear optimal perturbations[J].J.Atmos.Sci.,73(3):997-1014.doi:10.1175/JAS-D-15-0138.1
Eckel F A,Mass C F.2005.Aspects of effective mesoscale,short-range ensemble forecasting[J].Wea.Forecasting,20(3):328-350,doi:10.1175/WAF843.1.
Epstein E S.1969.Stochastic dynamic prediction[J].Tellus,21(6):739-759.doi:10.3402/tellusa.v21i6.10143
Feng J,Ding R Q,Liu D Q,et al.2014.The application of nonlinear local Lyapunov vectors to ensemble predictions in Lorenz systems[J].J.Atmos.Sci.,71(9):3554-3567.doi:10.1175/JAS-D-13-0270.1
Gilmour I,Smith L A.1997.Enlightenment in shadows[C]//AIPConference Proceedings.AIP,411:335-340.doi:10.1063/1.54200
Hamill T M,Snyder C,Morss R E.2000.A comparison of probabilistic forecasts from bred,singular-vector,and perturbed observation ensembles[J].Mon.Wea.Rev.,128(6):1835-1851.doi:10.1175/1520-0493(2000)128<1835:ACOPFF>2.0.CO;2
Hoffman R N,Kalnay E.1983.Lagged average forecasting,an alternative to Monte Carlo forecasting[J].Tellus A,35(2):100-118.doi:10.3402/tellusa.v35i2.11425
Hollingsworth A.1979.An experiment in Monte Carlo forecasting[C]//Proceedings Workshop on Stochastic Dynamic Forecasting.Reading,UK,65-85.
Hou Z L,Li J P,Ding R Q,et al.2018.The application of nonlinear local Lyapunov vectors to the Zebiak-Cane model and their performance in ensemble prediction[J].Climate Dyn.,51(1-2):283-304.doi:10.1007/s00382-017-3920-6
Huo Z H,Duan W S.2018.The application of the orthogonal conditional nonlinear optimal perturbations method to typhoon track ensemble forecasts[J].Sci.China Earth Sci.,62(2):376-388.doi:10.1007/s11430-018-9248-9
Jiang Z N,Mu M.2009.A comparison study of the methods of conditional nonlinear optimal perturbations and singular vectors in ensemble prediction[J].Adv.Atmos.Sci.,26(3):465-470.doi:10.1007/s00376-009-0465-6
Kalnay E.2003.Atmospheric Modeling,Data Assimilation and Predictability[M].Cambridge:Cambridge University Press,341pp.
Kalnay E,Toth Z.1995.The breeding method[C]//Proceedings of the ECMWF Seminar on Predictability.Reading,UK,69-82.
Koyama H,Watanabe M.2010.Reducing forecast errors due to model imperfections using ensemble Kalman filtering[J].Mon.Wea.Rev.,138(8):3316-3332.doi:10.1175/2010MWR3067.1
Kumar A,Hoerling M P.2000.Analysis of a conceptual model of seasonal climate variability and implications for seasonal prediction[J].Bull.Amer.Meteor.Soc.,81(2):255-264.doi:10.1175/1520-0477(2000)081<0255:AOACMO>2.3.CO;2
Kumar A,Barnston A G,Hoerling M P.2001.Seasonal predictions,probabilistic verifications,and ensemble size[J].J.Climate,14(7):1671-1676.doi:10.1175/1520-0442(2001)014<1671:SPPVAE>2.0.CO;2
Leith C E.1974.Theoretical skill of Monte Carlo forecasts[J].Mon.Wea.Rev.,102(6):409-418.doi:10.1175/1520-0493(1974)102<0409:TSOMCF>2.0.CO;2
Leutbecher M,Palmer T N.2008.Ensemble forecasting[J].J.Comput.Phys.,227(7):3515-3539.doi:10.1016/j.jcp.2007.02.014
Lorenz E N.1963.Deterministic nonperiodic flow[J].J.Atmos.Sci.,20(2):130-141.doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
Lorenz E N.1995.Predictability:A problem partly solved[C]//Proceedings of Seminar on Predictability.Shinfield Park,Reading:ECMWF,40-58.
Lorenz E N,Emanuel K A.1998.Optimal sites for supplementary weather observations:Simulation with a small model[J].J.Atmos.Sci.,55(3):399-414.doi:10.1175/1520-0469(1998)055<0399:OSFSWO>2.0.CO;2
Mason I.1982.A model for assessment of weather forecasts[J].Aust.Meteor.Mag.,30(4):291-303.
Mason S J.2004.On using“climatology”as a reference strategy in the Brier and ranked probability skill scores[J].Mon.Wea.Rev.,132(7):1891-1895.doi:10.1175/1520-0493(2004)132<1891:OUCAAR>2.0.CO;2
Mason S J,Graham N E.1999.Conditional probabilities,relative operating characteristics,and relative operating levels[J].Wea.Forecasting,14(5):713-725.doi:10.1175/1520-0434(1999)014<0713:CPROCA>2.0.CO;2
Molteni F,Buizza R,Palmer T N,et al.1996.The ECMWF ensemble prediction system:Methodology and validation[J].Quart.J.Roy.Meteor.Soc.,122(529):73-119.doi:10.1002/qj.49712252905
Mu M,Jiang Z N.2008.A new approach to the generation of initial perturbations for ensemble prediction:Conditional nonlinear optimal perturbation[J].Chinese Science Bulletin,53(13):2062-2068.doi:10.1007/s11434-008-0272-y
Mu M,Duan W S,Wang B.2003.Conditional nonlinear optimal perturbation and its applications[J].Nonlinear Processes in Geophysics,10(6):493-501.doi:10.5194/npg-10-493-2003
Murphy A H,Epstein E S.1989.Skill scores and correlation coefficients in model verification[J].Mon.Wea.Rev.,117(3):572-582.doi:10.1175/1520-0493(1989)117<0572:SSACCI>2.0.CO;2
Otsuka S,Miyoshi T.2015.A Bayesian optimization approach to multimodel ensemble Kalman filter with a low-order model[J].Mon.Wea.Rev.,143(6):2001-2012.doi:10.1175/MWR-D-14-00148.1
Revelli J A,Rodríguez M A,Wio H S.2010.The use of rank histograms and MVL diagrams to characterize ensemble evolution in weather forecasting[J].Adv.Atmos.Sci.,27(6):1425-1437.doi:10.1007/s00376-009-9153-6
Scaife A A,Arribas A,Blockley E,et al.2014.Skillful long-range prediction of European and North American winters[J].Geophys.Res.Lett.,41(7):2514-2519.doi:10.1002/2014GL059637
Talagrand O,Vautard R,Strauss B.1997.Evaluation of probabilistic prediction systems[C]//Workshop on Predictability,European Center for Medium Range Weather Forecasts.Reading,UK.
Toth Z,Kalnay E.1993.Ensemble forecasting at NMC:The generation of perturbations[J].Bull.Amer.Meteor.Soc.,74(12):2317-2330.doi:10.1175/1520-0477(1993)074<2317:EFANTG>2.0.CO;2
Toth Z,Kalnay E.1997.Ensemble forecasting at NCEP and the breeding method[J].Mon.Wea.Rev.,125(12):3297-3319.doi:10.1175/1520-0493(1997)125<3297:EFANAT>2.0.CO;2
Wang X G,Bishop C H.2003.A comparison of breeding and ensemble transform Kalman filter ensemble forecast schemes[J].J.Atmos.Sci.,60(9):1140-1158.doi:10.1175/1520-0469(2003)060<1140:ACOBAE>2.0.CO;2
Wilks D S.2011.Statistical Methods in the Atmospheric Sciences[M].3rd ed.Oxford:Academic Press,467pp.
Yoden S.2007.Atmospheric predictability[J].J.Meteor.Soc.Japan,85:77-102.doi:10.2151/jmsj.85B.77