On the limits of correlation sums when applied to climate variables

Casanovas, Alexandre
February 2000
AIP Conference Proceedings;2000, Vol. 502 Issue 1, p636
Academic Journal
Several quality time series of data of different climate variables, including ozone concentration measured on Mauna Loa and Barrow, the GISP2 and GRIP ice core temperature proxies, Salt Lake volume, down-welling longwave irradiation and atmospheric clearness index show some common characteristics when analyzed with correlation sums: they do not show low-dimensionality if chaotic (a previously well established, and expected, result) and they present an anomalous Grassberger-Procaccia (GP) correlation diagram with three slopes, a result previously reported for coloured noise by Osborne and Provenzale, and by Theiler. The middle, lesser slope is related with the coloured spectrum with a negative power f[sup -n] dependence on frequency and, according to Timashev’s flicker-noise spectroscopy, is related to self-similar time correlations on different scales, which are characteristic of the phenomena studied. The lack of low dimensionality places the study of such systems between deterministic dynamical and stochastic methods. The published estimates of the length of the data series needed to obtain meaningful results on GP diagrams are such that it is not possible to make estimates for climate variables. The shape of the density of points on the GP diagram for ozone concentration shows that some previous estimates of the minimum length of time series overestimate, at least for some climate variables, the density of points in the attractor outer limit, relaxing the requirements on series length. On the basis of the studied time series for ozone (over 200000 hourly data) and with a novel approach to reduce noise and increase the effective number of available points on the sensible parts of the slope, it is shown that at least a comparative value of correlation dimension can be obtained for Barrow ozone concentration measurements. Nevertheless, to obtain meaningful results of such comparative evaluations a thoughtful and appropriate ‘experimental setu...


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