NPG Nonlinear Processes in Geophysics NPG Nonlin. Processes Geophys. 1607-7946 Copernicus Publications Göttingen, Germany 10.5194/npg-13-449-2006 Statistical characteristics of surrogate data based on geophysical measurements Venema V. 1 Bachner S. 1 Rust H. W. 2 Simmer C. 1 Meteorologisches Institut, Universität Bonn, Germany Potsdam Institute for Climate Impact Research, Germany 12 09 2006 13 4 449 466 Copyright: © 2006 V. Venema et al. 2006 This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Generic License. To view a copy of this licence, visit https://creativecommons.org/licenses/by-nc-sa/2.5/ This article is available from https://npg.copernicus.org/articles/13/449/2006/npg-13-449-2006.html The full text article is available as a PDF file from https://npg.copernicus.org/articles/13/449/2006/npg-13-449-2006.pdf

In this study, the statistical properties of a range of measurements are compared with those of their surrogate time series. Seven different records are studied, amongst others, historical time series of mean daily temperature, daily rain sums and runoff from two rivers, and cloud measurements. Seven different algorithms are used to generate the surrogate time series. The best-known method is the iterative amplitude adjusted Fourier transform (IAAFT) algorithm, which is able to reproduce the measured distribution as well as the power spectrum. Using this setup, the measurements and their surrogates are compared with respect to their power spectrum, increment distribution, structure functions, annual percentiles and return values. It is found that the surrogates that reproduce the power spectrum and the distribution of the measurements are able to closely match the increment distributions and the structure functions of the measurements, but this often does not hold for surrogates that only mimic the power spectrum of the measurement. However, even the best performing surrogates do not have asymmetric increment distributions, i.e., they cannot reproduce nonlinear dynamical processes that are asymmetric in time. Furthermore, we have found deviations of the structure functions on small scales.

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