Multifractal Analysis of Hydrologic Data Using Wavelet Methods and Fluctuation Analysis

Zhao, Tongzhou; Wu, Liang; Li, Dehua; Ding, Yong

doi:10.1155/2017/3148257

Cited by 8 publications

(10 citation statements)

References 44 publications

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“…Wavelet transformation is a relatively new tool, which is widely used to detect the climatic trends [64,68]. Not only in rainfall trends but also wavelet analysis is popular in many other trend detections, including freak waves in the ocean [69], water levels in rivers and reservoirs [79], and droughts [70]. A time series can be easily decomposed into several smaller time series based on time and frequency.…”

Section: Wavelet Transformationmentioning

confidence: 99%

Comparison of Statistical, Graphical, and Wavelet Transform Analyses for Rainfall Trends and Patterns in Badulu Oya Catchment, Sri Lanka

2020

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Climate change has adversely influenced many activities. It has increased the intensified precipitation events in some places and decreased the precipitation in some other places. In addition, some research studies revealed that the climate change has moved seasons in the temporal scale. Therefore, the changes can be seen in both spatial and temporal scales. Thus, analyzing climate change in the localized environments is highly essential. Rainfall trend analysis in a localized catchment can improve many aspects of water resource management not only to the catchment itself but also to some of the related other catchments. This research is carried to identify the rainfall trends in Badulu Oya catchment, Sri Lanka. The catchment is important as it is in the intermediate climate zone and rich in agricultural productions. Four rain gauges (namely, Badulla, Kandekatiya, Lower Spring Valley, and Ledgerwatte Estate) were used to analyze the rainfalls in the resolutions of monthly, seasonally, and annually. 30-year monthly cumulative rainfall data for the above four gauging stations are analyzed using various standard tests. Nonparametric tests including Mann–Kendall test and sequential Mann–Kendall test and innovative trend analysis methods are used to identify the potential rainfall trends in Badulu Oya catchment. In addition, continuous wavelet transforms and discrete wavelet transforms tests are carried out to check the patterns on rainfall to the catchment. The trend analysis methods are compared against each other to identify the better technique. The results reveal that the nonparametric Mann–Kendall test is powerful to produce the statistically significant rainfall trends in qualitative and quantitative manner. Mann–Kendall analysis shows a positive trend to Ledgerwatte Estate in monthly (3.7 mm in February and 7.4 mm in October), seasonal (6.9 mm in the 2ndintermonsoon), and annual (3 mm annually) scales. However, the analysis records one decreasing rainfall trend to Kandekatiya (8.1 mm in December) only in monthly scale. Nevertheless, it was found that the graphical method can be easily used in qualitative analysis, while discrete wavelet transformations are efficient in identifying the rainfall patterns effectively.

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Section: Wavelet Transformationmentioning

confidence: 99%

Comparison of Statistical, Graphical, and Wavelet Transform Analyses for Rainfall Trends and Patterns in Badulu Oya Catchment, Sri Lanka

2020

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“…e processing of economic and social experimental data requires accurate parameter estimation [1][2][3][4], which can analyze the experimental results more precisely [5][6][7]. Parameter estimation in physical model is an important part of physical analysis [8,9].…”

Section: Introductionmentioning

confidence: 99%

Parameter Resolution of the Estimation Methods for Power Law Indices

Zhou

Ding

2021

Discrete Dynamics in Nature and Society

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The accuracy of parameter estimation plays an important role in economic and social models and experiments. Parameter resolution is the capability of an estimation algorithm to distinguish different parameters effectively under given noise level, which can be used to select appropriate algorithm for experimental or empirical data. We use a flexible distinguishing criterion and present a framework to compute the parameter resolution by bootstrap and simulation, which can be used in different models and algorithms, even for non-Gaussian noises. The parameter resolutions are computed for power law models and corresponding algorithms. For power law signal, with the increase of SNR, parameter resolution is finer; with the decrease of parameter, the resolution is finer. The standard deviation of noise and parameter resolution satisfies the linear relation; it relates to interval estimation naturally if the estimation algorithm is asymptotically normal. For power law distribution, parameter and resolution satisfy the linear relation, and experimental slope and theoretical slope tend to be consistent when significance level approaches zero. Last, we select an algorithm with finer resolution to estimate the Pareto index for the Forbes list of global rich data in recent 10 years and analyze the changes in the gap between the rich and the poor.

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“…[38] combines empirical modal decomposition and multi-fractal detrended fluctuation analysis to study the fractal characteristics of harmonic signals. To address the multi-fractal characteristics of hydrographic data, Zhao established a wavelet method and a multi-fractal detrended fluctuation analysis model to study the multi-fractal characterization and simulation of river levels [39]. Additionally, the fractal dimension has been introduced in the studies of biological molecules.…”

Section: Introductionmentioning

confidence: 99%

Detrended Fluctuation Analysis and Discrete Wavelet Transform for Similarity Comparison of RNA secondary structure

Yang

Liu

Wang

et al. 2020

Preprint

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Background Ribonucleic acid (RNA) is an important biological macromolecule. Through in-depth studies of RNA, its function has been increasingly discovered. The function of RNA is mostly dependent on its secondary structure because of its conserved nature. The discovery of an approximate relationship between two RNA secondary structures can help to understand their functional relationship better. This discovery can also help in exploring many unknown functions. Currently, RNA secondary structural similarity analysis methods are mainly divided into alignment-based methods and alignment-free methods. Alignment-free methods can obtain similarities and differences among RNA secondary structures more quickly and more accurately than alignment-based methods. Results In this paper, a novel alignment-free method based on the triple vector curve representation of RNA is proposed. A combinational method involving a discrete wavelet transform and detrended fluctuation analysis (DFA) with a sliding window is used to generate the distance matrix. Finally, a phylogenetic tree is constructed using the distance matrix. Experiments are performed on RNA viruses and non-coding RNA datasets, and the phylogenetic trees generated by different methods are compared. The results show that our method yields more accurate results in the comparison of RNA secondary structures. Conclusion The method in this paper enables a more accurate analysis of the similarities between RNA secondary structures. This method has certain application value in the comparison of RNA secondary structures, especially in the analysis of longer RNA sequences.

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Multifractal Analysis of Hydrologic Data Using Wavelet Methods and Fluctuation Analysis

Cited by 8 publications

References 44 publications

Comparison of Statistical, Graphical, and Wavelet Transform Analyses for Rainfall Trends and Patterns in Badulu Oya Catchment, Sri Lanka

Comparison of Statistical, Graphical, and Wavelet Transform Analyses for Rainfall Trends and Patterns in Badulu Oya Catchment, Sri Lanka

Parameter Resolution of the Estimation Methods for Power Law Indices

Detrended Fluctuation Analysis and Discrete Wavelet Transform for Similarity Comparison of RNA secondary structure

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