HR: 0830h
AN: NG51A-0838    [PDF]
TI: Symbolic Dynamics of Reanalysis Data
AU: * Larson, J W
EM: larson@mcs.anl.gov
AF: Mathematics and Computer Science Division Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439 United States
AU: Dickens, P M
EM: pmd@cs.iit.edu
AF: Department of Computer Science Illinois Institute of Technology, 10 W. 31st St., Chicago, IL 60616 United States
AB: Symbolic dynamics$^1$ is the study of sequences of symbols belonging to a discrete set of elements, the most commmon example being a sequence of ones and zeroes. Often the set of symbols is derived from a timeseries of a continuous variable through the introduction of a {\em partition function}--a process called {\em symbolization}. Symbolic dynamics has been used widely in the physical sciences; a geophysical example being the application of $C^1$ and $C^2$ complexity$^2$ to hourly precipitation station data$^3$. The $C^1$ and $C^2$ complexities are computed by examining subsequences--or {\em words}--of fixed length $L$ in the limit of large values of $L$. Recent advances in information theory have led to techniques focused on the growth rate of the Shannon entropy and its asymptotic behavior in the limit of long words--{\em levels of entropy convergence}$^4$. The result is a set of measures one can use to quantify the amount of memory stored in the sequence, whether or not an observer is able to synchronize to the sequence, and with what confidence it may be predicted. These techniques may also be used to uncover periodic behavior in the sequence. We are currently applying complexity theory and levels of entropy convergence to gridpoint timeseries from the NCAR/NCEP 50-year reanalysis$^5$. Topics to be discussed include: a brief introduction to symbolic dynamics; a description of the partition function/symbolization strategy; a discussion of $C^1$ and $C^2$ complexity and entropy convergence rates and their utility; and example applications of these techniques to NCAR/NCEP 50-reanalyses gridpoint timeseries, resulting in maps of $C^1$ and $C^2$ complexities and entropy convergence rates. Finally, we will discuss how these results may be used to validate climate models.\\ \noindent $^1${Hao, Bai-Lin, {\em Elementary Symbolic Dynamics and Chaos in Dissipative Systems}, Wold Scientific, Singapore (1989)}\\ $^2${d'Alessandro, G. and Politi, A., {\em Phys. Rev. Lett.}, {\bf 64}, 1609-1612 (1990).}\\ $^3${Elsner, J. and Tsonis, A., {\em J. Atmos. Sci.}, {\bf 50}, 400-405 (1993).}\\ $^4${Crutchfield, J. and Feldman, D., {\em Chaos}, {bf 13}, 25-54 (2003).}\\ $^5${Kalnay, E.~, Kanamitsu, M.~, Kistler, R.~, Collins, W.~, Deaven, D.~, Gandin, L.~, Iredell, M.~, Saha, S.~, White, G.~, Woolen, J.~, Zhu, Y.~, Chelliah, M.~, Ebisuzaki, W.~, Higgins, W.~, Janowiak, J.~, Mo, K.~C.~, Ropelewski, C.~, Wang, J.~, Leetmaa, A.~, Reynolds, R.~, Jenne, R.~, and Joseph, D.~, {\em Bull. Amer. Met. Soc.}, {\bf 77}, 437-471 (1996).}
UR: http://www.mcs.anl.gov/~larson
DE: 3220 Nonlinear dynamics
DE: 3240 Chaos
DE: 3399 General or miscellaneous
SC: Nonlinear Geophysics [NG]
MN: 2003 Fall Meeting