Exploring the physical interpretation of long-term memory in hydrology
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ORIGINAL PAPER
Exploring the physical interpretation of long-term memory in hydrology Abrar Habib1 Accepted: 23 September 2020 Ó Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Long-term memory has been studied for decades and it has long been acknowledged that hydrological and hydrometeorological time series exhibit this property. Physically, long-term memory is explained by saying that the stronger the long-term memory the more likely a series will ‘remember’ its previous value, in other words, the longer a time series is likely to persist in the proximity of a certain value. To increase the benefit of the study of long-term memory, we investigate the extent to which this explanation is accurate and descriptive of long-term memory by developing a ‘persistence measure’ that quantifies the intuitive description of long-term memory. The ‘persistence measure’ is compared to the scaling exponent (a) which quantifies long-term memory using detrended fluctuation analysis. A total of 17,359 series, including hydrological and hydro-meteorological series, downloaded from online sources and 130 synthetic series are analyzed. The main outcome is that two regimes are found. The first is for series with a [ 1.05 where the persistence measure is not sensitive to the scaling exponent. Hence, changes in a does not lead to an increase in the memory strength (i.e. the persistence measure). The second regime is for series with a Z 1.05 where a statistically significant positive correlation was found. Hence, for a certain range of values of a the physical explanation of long-term memory holds. Nevertheless, it is proposed that adding additional factors may create a more robust ‘persistence measure’ that can be easily understood and incorporated in hydrologists’ work. Keywords Long-term memory Detrended fluctuation analysis Time series analysis
1 Introduction Long-term memory (or fractal behavior) is a property exhibited by hydrological and geophysical time series (Gelhar 1974; Little and Bloomfield 2010; Ozger 2011; Zhu et al. 2012), among variables in different fields such as medical (Peng et al. 1995) and economy fields (Caraiani 2012; Reboredo et al. 2013; Zunino et al. 2008). The study of long-term behavior in Hydrology was initiated in the 1950’s when the hydrologist, Harold E. Hurst, who took part in the design of the Aswan High Dam (in Egypt) Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00477-020-01883-0) contains supplementary material, which is available to authorized users. & Abrar Habib [email protected]; [email protected] 1
Civil Engineering Department, College of Engineering, University of Bahrain, Isa Town, Kingdom of Bahrain
noticed that the annual streamflow data of the River Nile tended to cluster at high and low flows (Hurst 1951, 1956). Over the years, the Hurst phenomena was further investigated and developed. One of the milestones in the study of long-term memory is its association with fractals and describing it mathematically in t
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