A. Montanari, D. Koutsoyiannis, and S.M. Papalexiou, The omnipresence of scaling behaviour in hydrometeorological time series and its implications in climatic change assessments, XXIV General Assembly of the International Union of Geodesy and Geophysics, Perugia, doi:10.13140/RG.2.2.26305.35688, International Union of Geodesy and Geophysics, International Association of Hydrological Sciences, 2007.
It is demonstrated by examples that long hydrometeorological time series exhibit scaling in time, a behaviour equivalent to the Hurst phenomenon. The example time series investigated range from high temporal resolution (10 seconds) rainfall measurements for rainfall events lasting a few hours to proxy time series of temperature for a period over 400 thousand years. The scaling behaviour may reflect a multi-timescale variability of several factors and, thus, can support a more complete physical understanding and uncertainty characterization of hydroclimatic processes. The implications of this behaviour in statistical analyses of hydrometeorological time series is substantial, particularly at large (climatic) time scales, but appear to be not fully understood or recognized as they have been neglected in most climatological studies. To offer insights on these implications, we demonstrate using analytical methods that the characteristics of several temperature proxy series, which appear to exhibit scaling behaviour, imply a dramatic increase of uncertainty in statistical estimation and reduction of significance in statistical testing, in comparison with classical statistics. Therefore, we maintain that statistical analysis in hydroclimatic research should be revisited, in order not to derive misleading results.
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