Physics
Scientific paper
Dec 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008agufmsh43a1628k&link_type=abstract
American Geophysical Union, Fall Meeting 2008, abstract #SH43A-1628
Physics
2159 Plasma Waves And Turbulence, 2162 Solar Cycle Variations (7536), 3265 Stochastic Processes (3235, 4468, 4475, 7857), 4475 Scaling: Spatial And Temporal (1872, 3270, 4277), 7857 Stochastic Phenomena (3235, 3265, 4475)
Scientific paper
The accurate estimation of scaling exponents is central to the quantitative observational study of scale- invariant phenomena such as turbulence- they allow direct comparison between the data and the predictions of turbulence theories. Stable, time stationary intervals of naturally occurring turbulence, such as that seen in the solar wind, magnetosheath and magnetotail, are unavoidably restricted in space and time. However, methods to quantify the scaling exponents of a stationary stochastic process (time series) can, when applied to finite length intervals of data, also yield apparent time variation in the scaling exponents, suggestive of non-stationarity. This needs to be distinguished from physical non- stationarity that may also be intrinsic to the phenomena under study. We present the results of a study to determine the optimal number of datapoints (length of timeseries) N required to obtain estimates of scaling exponents to a given precision. We focus on structure function estimates but our results are also applicable to power law power spectral estimates. For power law power spectra, the variance in the computed scaling exponents is known for finite variance processes to vary as ~1/N as N goes to infinity, however, the convergence to this behaviour will depend on the details of the process, and may be slow. We study the variation in the scaling of second order moments of the time series increments with N, for a variety of synthetic timeseries and solar wind in- situ observations. We find that in particular for heavy tailed processes, for typical realizable N, one is far from this ~1/N limiting behaviour, and propose a semi-empirical estimate for the minimum N needed to make a meaningful estimate of the scaling exponents. For a given process, once the variance in the computed scaling exponents is known as a function of N, it may be possible for a given dataset to discern 'pseudo' time variation in the exponents due to finite N effects from intrinsic time variation, the prospects for this will also be discussed.
Chapman Sandra C.
Kiyani Khurom
Watkins Nicholas Wynn
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