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Progress in Natural Science:Materials International 2009年第3期19卷 397-406页

作者： Qiang Chenga,b,c,*, Haibin Zhang d, Bin Wanga, Yonghua Zhao c a LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, PR China b LSEC, Institute of Computing Mathematics, Chinese Academy of Sciences, Beijing 100080, PR China c SC, Institute of Computer Network Information Center, Chinese Academy of Sciences, Beijing 100190, PR China d College of Applied Sciences, Beijing University of Technology, Beijing 100124, PR China LASG Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 PR China LSEC Institute of Computing Mathematics Chinese Academy of Sciences Beijing 100080 PR China SC Institute of Computer Network Information Center Chinese Academy of Sciences Beijing 100190 PR China College of Applied Sciences Beijing University of Technology Beijing 100124 PR China

The differentiation transforming (DFT) system is developed to produce the tangent linear codes, which is used to calculate the Jaco- bian- and the Hessian-vector products with no truncation errors. This paper first gives the introduction of the functionality and features of the DFT system, and then discusses several techniques for the implementation of automatic differentiation tools, including data depen- dence analysis, singular differentiation and code optimization. Finally, the codes generated with DFT used in several applications have been demonstrated.

关键词： Jacobian Hessian tangent linear model Automatic differentiation

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Finite-Time Normal Mode Disturbances and Error Growth During Southern Hemisphere Blocking

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Advances in Atmospheric Sciences 2005年第1期22卷 69-89页

作者： Jorgen S.FREDERIKSEN CSIRO Atmospheric Research

The structural organization of initially random errors evolving in abarotropic tangent linear model, with time-dependent basic states taken from analyses, is examinedfor cases of block development, maturation and decay in the Southern Hemisphere atmosphere duringApril, November, and December 1989. The statistics of 100 evolved errors are studied for six-dayperiods and compared with the growth and structures of fast growing normal modes and finite-timenormal modes (FTNMs). The amplification factors of most initially random errors are slightly lessthan those of the fastest growing FTNM for the same time interval. During their evolution, thestandard deviations of the error fields become concentrated in the regions of rapid dynamicaldevelopment, particularly associated with developing and decaying blocks. We have calculatedprobability distributions and the mean and standard deviations of pattern correlations between eachof the 100 evolved error fields and the five fastest growing FTNMs for the same time interval. Themean of the largest pattern correlation, taken over the five fastest growing FTNMs, increases withincreasing time interval to a value close to 0.6 or larger after six days. FTNM 1 generally, but notalways, gives the largest mean pattern correlation with error fields. Corresponding patterncorrelations with the fast growing normal modes of the instantaneous basic state flow aresignificant' but lower than with FTNMs. Mean pattern correlations with fast growing FTNMs increasefurther when the time interval is increased beyond six days.

关键词： normal modes finite-time normal modes blocking tangent linear model pattern correlations

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