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      Decoding the Morphological Differences between Himalayan Glacial and Fluvial Landscapes Using Multifractal Analysis

      research-article
      Scientific Reports
      Nature Publishing Group UK

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          Abstract

          Himalayas is the home to nearly 10,000 glaciers which are mostly located at high and inaccessible region. Digital Elevation Model (DEM) can be effective in the study of these glaciers. This paper aims at providing an automated distinction of glacial and fluvial morphologies using multifractal technique. We have studied the variation of elevation profile of Glacial and Fluvial landscapes using Multifractal Detrended Fluctuation Analysis (MFDFA). Glacial landscapes reveal more complex structure compared to the fluvial landscapes as indicated by fractal parameters degree of multifractality, asymmetry index.

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          Most cited references41

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          Multifractal detrended fluctuation analysis of nonstationary time series

          , , (2002)
          We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition function-based multifractal formalism, and prove that both approaches are equivalent for stationary signals with compact support. By analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series. By comparing the multifractal DFA results for original series to those for shuffled series we can distinguish multifractality due to long-range correlations from multifractality due to a broad probability density function. We also compare our results with the wavelet transform modulus maxima (WTMM) method, and show that the results are equivalent.
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            Detecting Long-range Correlations with Detrended Fluctuation Analysis

            We examine the Detrended Fluctuation Analysis (DFA), which is a well-established method for the detection of long-range correlations in time series. We show that deviations from scaling that appear at small time scales become stronger in higher orders of DFA, and suggest a modified DFA method to remove them. The improvement is necessary especially for short records that are affected by non-stationarities. Furthermore, we describe how crossovers in the correlation behavior can be detected reliably and determined quantitatively and show how several types of trends in the data affect the different orders of DFA.
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              Effect of Trends on Detrended Fluctuation Analysis

              , , (2001)
              Detrended fluctuation analysis (DFA) is a scaling analysis method used to estimate long-range power-law correlation exponents in noisy signals. Many noisy signals in real systems display trends, so that the scaling results obtained from the DFA method become difficult to analyze. We systematically study the effects of three types of trends -- linear, periodic, and power-law trends, and offer examples where these trends are likely to occur in real data. We compare the difference between the scaling results for artificially generated correlated noise and correlated noise with a trend, and study how trends lead to the appearance of crossovers in the scaling behavior. We find that crossovers result from the competition between the scaling of the noise and the ``apparent'' scaling of the trend. We study how the characteristics of these crossovers depend on (i) the slope of the linear trend; (ii) the amplitude and period of the periodic trend; (iii) the amplitude and power of the power-law trend and (iv) the length as well as the correlation properties of the noise. Surprisingly, we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws -- i.e. long-range power-law dependence of the position of the crossover on the parameters of the trends. We show that the DFA result of noise with a trend can be exactly determined by the superposition of the separate results of the DFA on the noise and on the trend, assuming that the noise and the trend are not correlated. If this superposition rule is not followed, this is an indication that the noise and the superimposed trend are not independent, so that removing the trend could lead to changes in the correlation properties of the noise.
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                Author and article information

                Contributors
                srimantid@yahoo.co.in
                Journal
                Sci Rep
                Sci Rep
                Scientific Reports
                Nature Publishing Group UK (London )
                2045-2322
                8 September 2017
                8 September 2017
                2017
                : 7
                : 11032
                Affiliations
                Department of Physics, Behala College, Parnasree Pally, Kolkata, 700060 India
                Article
                11669
                10.1038/s41598-017-11669-0
                5591223
                28887519
                08b56790-200c-4e29-8258-87783e7ea48d
                © The Author(s) 2017

                Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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                : 8 May 2017
                : 29 August 2017
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