非线性优化方法在大气和海洋科学数值研究中的若干应用

段晚锁; 穆穆

非线性优化方法在大气和海洋科学数值研究中的若干应用

段晚锁,
穆穆

中国科学院大气物理研究所大气科学和地球流体力学数值模拟国家重点实验室,北京 100029

基金项目: 国家自然科学基金资助项目(40233029;40221503);中国科学院创新项目资助课题(KZCX2-208)

详细信息

作者简介:
段晚锁(1973- ),男,山西阳城人,博士(Tel:+86-10-62043317;Fax:+86-10-62043526;E-mail:duanws@mail.iap.ac.cn);穆穆(1954- ),男,安微定远人,研究员,博士(联系人.Tel:+86-10-62043317;Fax:+86-10-62043526;E-mail:mumu@lasg.iap.ac.cn).

中图分类号: P456.7
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出版历程
- 收稿日期: 2003-11-21
- 修回日期: 2004-11-04
- 刊出日期: 2005-05-15

Applications of Nonlinear Optimization Method to the Numerical Studies of Atmospheric and Oceanic Sciences

DUAN Wan-suo,
MU Mu

LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, P. R. China

摘要

摘要: 控制大气和海洋运动的模式是复杂的非线性模式，在考虑到线性奇异向量和线性奇异值只能描述切线性模式有效时段内小扰动发展的情况下，介绍了作者们近年来用非线性优化方法数值研究大气和海洋科学的有关工作，其中包括非线性奇异向量和非线性奇异值、条件非线性最优扰动、以及它们在数值天气和气候可预报性研究中的应用．结果表明，上述非线性优化方法在很大程度上揭示了大气和海洋运动的非线性特征；此外，对可预报性问题的新分类也做了详细介绍，即最大可预报时间、最大预报误差和最大允许初始误差A·D2这种分类的应用背景是针对数值天气预报和气候预测产品的评价；最后，讨论了数值模式敏感性分析的非线性优化方法，该方法在一定条件下可以定量识别模式误差和初始误差，量化判断数值模式的模拟能力．
- 非线性优化 /
- 天气 /
- 气候 /
- 可预报性 /
- 敏感性分析
Abstract: Linear singular vect or and linear singular value can only describe the evolution of sufficiently small perturbations during the period in which the tangent linear model is valid. With this in mind, the applications of nonlinear optimization methods to the atmospheric and oceanic sciences are introduced, which include nonlinear singular vector (NSV) and nonlinear singular value (NSVA), conditional nonlinear optimal perturbation (CNOP), and their applications to the studies of predictability in numerical weather and climate prediction. The results suggest that the nonlinear characteristics of the motions of atmosphere and oceans can be explored by NSV and CNOP. Also attentions are paid to the introduction of the classification of predictability problems, which are related to the maximum predictable time, the maximum prediction error, and the maximum allowing error of initial value and the parameters. All the information has the background of application to the evaluation of products of numerical weather and climate prediction. Furthermore the nonlinear optimization methods of the sensitivity analysis with numerical model are also introduced, which can give a quantitative assessment whether a numerical model is able to simulate the observations and find the initial field that yield the optimal simulation. Finally, the difficulties in the lack of ripe algorithms are also discussed, which leave future work to both computational mathematics and scientists in geophysics.
- nonlinear optimization /
- weather /
- climate /
- predictability /
- sensitivity analysis

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参考文献(32)

[1]	Thompson P D.Uncertainty of initial state as a factor in the predictability of large-scale atmospheric flow patterns[J].Tellus,1957,9(3):275—295. doi: 10.1111/j.2153-3490.1957.tb01885.x
[2]	Lorenz E N.Deterministic nonperiodic flow[J].J Atmos Sci,1963,20(2):130—141. doi: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
[3]	丑纪范，郜吉东.长期数值天气预报[M].北京：气象出版社，1995.
[4]	Buizza R, Palmer T N. The singular vector structure of the atmospheric global circulation[J].J Atmos Sci,1995,52(9):1434—1456. doi: 10.1175/1520-0469(1995)052<1434:TSVSOT>2.0.CO;2
[5]	Thompson C J, Initial conditions for optimal growth in couple ocean atmosphere model of ENSO[J].J Atmos Sci,1998:55(4)：537—557.
[6]	Lorenz E N.A study of the predictability of a 28-variable atmospheric model[J].Tellus,1965,17(4):321—333. doi: 10.1111/j.2153-3490.1965.tb01424.x
[7]	Farrell B F.The growth of disturbance in a baroclinic flow[J].J Atmos Sci,1982,39(8):1663—1686. doi: 10.1175/1520-0469(1982)039<1663:TIGODI>2.0.CO;2
[8]	Xue Y, Cane Y M A,Zebiak S E, Predictability of a coupled model of ENSO using singular vector analysis, Part I: Optimal growth in seasonal background and ENSO cycles[J].Mon Wea Rev,1997,125(12):2043—2056.
[9]	Roger M,Samelson E T.Instability of the Chaotic ENSO: The growth-phase predictability barrier[J].J Atmos Sci,2001,58(23): 3613—3625. doi: 10.1175/1520-0469(2001)058<3613:IOTCET>2.0.CO;2
[10]	Lacarra J F, Talagrand O.Short-range evolution of small perturbation in a baratropic model[J].Tellus,1988,40A(1):81—95. doi: 10.1111/j.1600-0870.1988.tb00408.x
[11]	Tanguay M, Bartello P.Four-dimensional data assimilation with a wide range of scales[J].Tellus,1995,47A(6):974—997.
[12]	MU Mu, GUO Huan, WANG Jia-feng,et al.The impact of nonlinear stability and instability on the validity of the tangent linear model[J].Adv Atmos Sci,2000,17(3):375—385. doi: 10.1007/s00376-000-0030-9
[13]	MU Mu.Nonlinear singular vectors and nonlinear singular values[J].Science in China,Ser D,2000,43(4):375—385.
[14]	MU Mu,DUAN Wan-suo.A new approach to studying ENSO predictability: conditional nonlinear optimal perturbation[J].Chinese Science Bulletin,2003,48(10):1045—1047.
[15]	Lorenz E N.Climate predictability: the physical basis of climate modeling[J].WMO, GARP Pub Ser,1975,16(1):132—136.
[16]	MU Mu, DUAN Wan-suo,WANG Jia-cheng.The predictability problems in numerical weather and climate prediction[J].Adv Atmos Sci,2002,19(2):191—204. doi: 10.1007/s00376-002-0016-x
[17]	Talagrand O.Assimilation of observations, an introduction[J].J Meteor Soc Japan,1997,1B(2):191—209.
[18]	Hollingsworth A, Lorenc A C, Tracton M S,et al.The response of numerical weather prediction systems to FGGE level Iib data-Part I:Analyses Quart J Roy Meteor Soc,1985,111(1):1—66.
[19]	Errico R M,Vukicevic T.Sensitivity analysis using an adjoint of the PSU-NCAR mesoscale model[J].Mon Wea Rev,1992,120(8):1644—1660. doi: 10.1175/1520-0493(1992)120<1644:SAUAAO>2.0.CO;2
[20]	Ehrendorfer M,Errico R M.Mesoscale predictability and the spectrum of optimal perturbations[J].J Atmos Sci,1986,52(20):3475—3500.
[21]	Zou X, Navan I M,Dimet Le F X.Incomplete observations and control of gravity waves in varational data assimilation[J].Tellus,1992,44A(2):273—298.
[22]	Rabier F, Klinker E, Courtier P,et al.Sensitivity of forecast errors to initial conditions[J].Quart J Roy Meteor Soc,1996,122(1):121—150. doi: 10.1002/qj.49712252906
[23]	MU Mu, WANG Jia-cheng.Nonlinear fastest growing perturbation and the first kind of predictability[J].Science in China (D),2001,44(12):1128—1139. doi: 10.1007/BF02906869
[24]	Durbiano S.Vecteurs caractéristiques de modéles océaniques pour la ré duction d'ordre er assimilation de données[D].Doctor Dissertation,Université Joseph Fourier-Grenoble Science Et Géographie,2001,1—214.
[25]	Bjerknes J. A possible response of the atmospheric Hadley circulation to equatorial anomalies of ocean temperature[J].Tellus,1966,18(5):820—829. doi: 10.1111/j.2153-3490.1966.tb00303.x
[26]	MU Mu,DUAN Wan-suo,WANG Bin.Conditional nonlinear optimal perturbation and its applications[J].Nonlinear Processes in Geophysics,2003,10(6):493—501. doi: 10.5194/npg-10-493-2003
[27]	Lohmann G,Schneider J.Dynamics and predictability of Stomel's box model. A phase-space perspective with implications for decadal climate variability[J].Tellus,1999,51A(2):326—336.
[28]	MU Mu, SUN Liang,Dijkstra H A.Applications of conditional nonlinear optimal perturbation to the sensitivity of the thermohaline circulation to finite amplitude freshwater perturbations[J].J Physical Oceanography,2004,34(10):2305—2315. doi: 10.1175/1520-0485(2004)034<2305:TSASOT>2.0.CO;2
[29]	MU Mu, DUAN Wan-suo,WANG Jia-feng.Nonlinear optimization problems in atmospheric and oceanic sciences[J].East-West Journal of Mathematics.Thailand, 2002,155—164.
[30]	XU Hui,MU Mu,LUO De-hai.An application of nonlinear optimization method to sensitivity analysis of numerical model[J].Progress in Natural Sciences,2004,14(6):546—549. doi: 10.1080/10020070412331343921
[31]	Liu D C,Nocedal J.On the memory BFGS method for large-scale optimization[J].Mathematical Programming,1989,45(3):503—528. doi: 10.1007/BF01589116
[32]	Powell M J D, VMCWD: A FORTRAN subroutine for constrained optimization[R]. DAMTP Report 1982/NA4, University of Cambridge, England, 1982，1—89.

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非线性优化方法在大气和海洋科学数值研究中的若干应用

作者简介:
段晚锁(1973- ),男,山西阳城人,博士(Tel:+86-10-62043317;Fax:+86-10-62043526;E-mail:duanws@mail.iap.ac.cn);穆穆(1954- ),男,安微定远人,研究员,博士(联系人.Tel:+86-10-62043317;Fax:+86-10-62043526;E-mail:mumu@lasg.iap.ac.cn).

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Applications of Nonlinear Optimization Method to the Numerical Studies of Atmospheric and Oceanic Sciences

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留言板

非线性优化方法在大气和海洋科学数值研究中的若干应用

作者简介: 段晚锁(1973- ),男,山西阳城人,博士(Tel:+86-10-62043317;Fax:+86-10-62043526;E-mail:duanws@mail.iap.ac.cn);穆穆(1954- ),男,安微定远人,研究员,博士(联系人.Tel:+86-10-62043317;Fax:+86-10-62043526;E-mail:mumu@lasg.iap.ac.cn).

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出版历程

Applications of Nonlinear Optimization Method to the Numerical Studies of Atmospheric and Oceanic Sciences

计量

出版历程

目录

作者简介:
段晚锁(1973- ),男,山西阳城人,博士(Tel:+86-10-62043317;Fax:+86-10-62043526;E-mail:duanws@mail.iap.ac.cn);穆穆(1954- ),男,安微定远人,研究员,博士(联系人.Tel:+86-10-62043317;Fax:+86-10-62043526;E-mail:mumu@lasg.iap.ac.cn).