Symbolic Dynamics of Reanalysis Data
Abstract
Symbolic dynamics1 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 partition function--a process called symbolization. Symbolic dynamics has been used widely in the physical sciences; a geophysical example being the application of C1 and C2 complexity2 to hourly precipitation station data3. The C1 and C2 complexities are computed by examining subsequences--or 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--levels of entropy convergence4. 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 reanalysis5. Topics to be discussed include: a brief introduction to symbolic dynamics; a description of the partition function/symbolization strategy; a discussion of C1 and C2 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 C1 and C2 complexities and entropy convergence rates. Finally, we will discuss how these results may be used to validate climate models.
1{Hao, Bai-Lin, Elementary Symbolic Dynamics and Chaos in Dissipative Systems, Wold Scientific, Singapore (1989)} 2{d'Alessandro, G. and Politi, A., Phys. Rev. Lett., 64, 1609-1612 (1990).} 3{Elsner, J. and Tsonis, A., J. Atmos. Sci., 50, 400-405 (1993).} 4{Crutchfield, J. and Feldman, D., 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.~, Bull. Amer. Met. Soc., 77, 437-471 (1996).}- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2003
- Bibcode:
- 2003AGUFMNG51A0838L
- Keywords:
-
- 3220 Nonlinear dynamics;
- 3240 Chaos;
- 3399 General or miscellaneous