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Cumulative distributions of the meteorological time series of original data of meteorological variables from 6 stations in Germany (DE), Finland (FI), Poland (PL) and Spain (ES). α: singularity strength; x: values of time series
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Agro-meteorological quantities are often in the form of time series, and knowledge about their temporal scaling properties is fundamental for transferring locally measured fluctuations to larger scales and vice versa. However, the scaling analysis of these quantities is complicated due to the presence of localized trends and nonstationarities. The...
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... To determine the origin of multifractality, the original data was shuffled and surrogate data generated. Shuffling removes temporal correlation; hence, it showed the role of long-range correlation in multifractality (Baranowski et al., 2015). However, broad distributions are destroyed by surrogate data. ...
... However, later rainfall series were shown to be better characterized by different dimensions or fractal exponents, revealing their multifractal nature Lovejoy and Schertzer, 1990;Duncan, 2013). In the last decades, different studies have been successful in characterizing these fractal exponents in relatively large records of rainfall series from distinct regions with the multifractal detrended fluctuation analysis (MF-DFA) Yu et al., 2014;Baranowski et al., 2015;Krzyszczak et al., 2017;Tan and Gan, 2017;Júnior et al., 2018;Adarsh et al., 2019;Krzyszczak et al., 2019;Zhang et al., 2019;Adarsh et al., 2020;Martínez et al., 2021;Sarker and Mali, 2021;Gómez-Gómez et al., 2022;Rahmani and Fattahi, 2022). This method is suitable for multifractal analysis of time series because it computes the fluctuations for different statistical moment orders by previously removing trends in the series. ...
... The fluctuation function follows a power law ( ) ∼ ℎ( ) if the analyzed time series is long-range power law correlated. Many climatic variables show long-range correlated fluctuations following a power law (Baranowski et al., 2015Krzyszczak et al., 2019). In particular, previous studies show that rainfall can exhibit different scaling regions which follow power laws with different exponents (Yang and Fu, 2019;Gómez-Gómez et al., 2022). ...
Due to the vulnerability of the Caribbean islands to the climate change issue, it is important to investigate the behavior of rainfall. In addition, the soil of the French West Indies Islands has been contaminated by an organochlorine insecticide (Chlordecone) whose decontamination is mainly done by drainage water. Thus, it is crucial to investigate the fluctuations of rainfall in these complex environments. In this study, 19 daily rainfall series recorded in different stations of Guadeloupe archipelago from 2005 to 2014 were analyzed with the multifractal detrended fluctuation analysis (MF-DFA) method. The aim of this work is to characterize the long-range correlations and multifractal properties of the time series and to find geographical patterns over the three most important islands: Basse-Terre, Grande-Terre and Marie-Galante. This is the first study that addresses the analysis of multifractal properties of rainfall series in the Caribbean islands. This region is typically characterized by the almost constant influence of the trade winds and a high exposure to changes in the general atmospheric circulation. 12 stations exhibit two different power-law scaling regions in rainfall series, with distinct long-range correlations and multifractal properties for large and small scales. On the contrary, the rest of stations only show a single region of scales for relatively small scales. Hurst exponents reveal persistent long-range correlations which agree with other studies in nearby tropical locations. In the most eastern analyzed areas, larger scales exhibit higher persistence than smaller scales, which suggests a relationship between persistence and the highest exposure to the trade winds. Stronger conclusions can be drawn from multifractal spectra, which indicate that most rainfall series have a multifractal nature with higher complexity and degree of multifractality at the smallest scales. Furthermore, a clear dependence of multifractal nature on the latitude is revealed. All these results showed that MF-DFA is a robust tool to assess the nonlinear properties of environmental time series in a complex area.
... This method combines MFA and chaos methods and can be successfully applied to series that presented long-range correlations. Several examples are found in rainfall [20], surface temperature [21], air temperature [22], landscape [23] and environmental variables [24], among others. ...
... Most meteorological variables show multifractal characteristics due to long-range correlations, except rainfall. This variable presents multifractality mainly from the PDF shape [22]. Besides rainfall, temperature and evapotranspiration are two driving forces influencing soil pore structure. ...
The combined action of physical, chemical and biological processes at different scales creates a highly complex soil architecture. At the same time, this soil pores' complexity is crucial in maintaining soil biogeochemical and biophysical processes. The development of digital image processing and a multiscaling analysis allow a better study to quantify pore complexity and evaluate pore spatial variability. This study took saline soils from coastal reclamation areas as an example and aimed to compare the multifractality of porosity series using different methods on sample cubes of 512 pixels in length extracted at different soil depths. Two measures were selected to represent the porosity series: the average grey values (AVG) of each slice and the CT-porosity (CTP) of binarized slices. The mass distribution (MD), detrended fluctuation analysis (DFA), and the moments function (K) were the methods applied in the multiscaling study. Shuffled and surrogated series were used to analyze the two possible multifractality sources, the probability distribution density function (PDF) and long-range correlations, respectively. The results showed that MD gave the minimum multifractal spectrum, which appeared as a point in AGV and a narrow concave parabola in CTP. On the other hand, both AGV and CTP showed a higher complexity, a clear and significant multifractal behaviour when DFA and K were used. The shuffled and surrogated series pointed out that the long-range correlations were the main factor of the multifractal sources of the porosity series. Both long-range correlations and PDF influenced more heavily on the multifractality of porosity in topsoil (0-20 cm) than in the deeper soil (20-60 cm), implying that the porosity series in topsoil had stronger multifractality. In addition, the DFA and K, combined with shuffled and surrogated series analysis, can distinguish between different factors in the multiscaling behaviour of different soil textures and time reclamation.
... Kantelhardt et al. (2002a) developed the Multifractal Detrended Fluctuation Analysis (MF-DFA) to examine the scaling behavior of time series with temporally variable statistical properties. It has been used in many environmental studies and is generally recognized as a key tool for time series analysis (Du et al. 2013, Zhou et al. 2014, Baranowski et al. 2015. Philippopoulos et al. (2019) used the ERA-Interim reanalysis dataset further to explore the multifractal characteristics of daily temperature time series. ...
... Monofractal and multifractal scaling behavior has been investigated in the context of many natural time series generated by complex systems, e.g., geophysics time series, medical and physiological time series, DNA sequences, astrophysical time series, technical time series, as well as social time series (see [3][4][5] and references therein). Recently, improved techniques have been used in various areas to determine the multifractal nature of a non-stationary time series [6,7]. We can cite the MF-DFA (multifractal detrended fluctuation analysis) method, proposed by Kantelhardt [8], which describes different statistical characteristics of time series on different time scales, besides being an efficient way to test if the non-stationary series is multifractal. ...
We investigate the RNA fractal properties of some textual viruses of the Coronaviridae family. These organisms can seriously infect people and endanger the world’s health systems. The whole data follows from the NCBI databases. After investigating fractality at various scales, we created two dummy time series to compare with the walks of the coronavirus sequences. We also employ a technique to look for crossover in DNA temporal sequences. Our findings demonstrate that the sequences do not act randomly and contain more significant concentrations of adenine and guanine bases. It proves the existence of power law correlations for RNA sequences at various sizes and the persistence tendency that all species exhibit in their RNA sequences. We also observe that there are no crossover timeframes and that all sequences are monoscale.
... These techniques are being used effectively for studies of various real world systems using their observational data or average responses like data from stars 11 , EEG 12 , ECG 13 , combustion data 14 , atmospheric data 15 and financial data 16 , etc. In the context of climate, the MFDFA method was applied to study climate impacts and breakpoints in climate data and to understand how non-linearity and multifractality occur in temperature data [17][18][19][20][21][22][23][24][25] and wind data 26 . In the context of the Indian climate, studies are reported along similar directions using rainfall and temperature data series 27,28 . ...
We present a study on the pattern underlying the climate dynamics in various locations spread over India, including the Himalayan region, coastal region, central and north eastern parts of India. We try to capture the variations in the complexity of their dynamics derived from temperature and relative humidity data, which can lead to the characterization of the differences in climate dynamics over the last seventy years. Based on the computed measures of their multifractal spectra, we could group the locations into six clusters, each having similar underlying dynamics in their temperature and relative humidity variations. We also report the variations in climate dynamics over time in these locations by estimating the recurrence-based measures using a sliding window analysis on the data sets. They provide evidences of changes in climate dynamics related to global warming and how their variations differ among the different locations of the country. The major changes in dynamics can be related to the consequences of the global climate regime shifts reported in the mid-1970s, late 1980s, and late 1990s. The study can thus contribute to our understanding of the complexity of the dynamics of the climate system over the Indian subcontinent and its variations and shifts over time.
... However, none of these studies investigated how climate change affects temperature and precipitation nonlinear dynamic patterns (as elements generating droughts and floods), which was explored in the present study. Studies on the multifractality source of precipitation, temperature, and droughts were conducted in study areas other than CE (Zhan et al. 2023;Agbazo et al. 2019;Zhang et al. 2019b;Baranowski et al. 2015). Those studies assessed the source of multifractal time series of temperature, precipitation, and drought. ...
The study of shifts in patterns of precipitation and temperatures is central to managing water resources and controlling damages yielded by natural hazards. Thus, this study investigated modifications in precipitation and temperature patterns using multifractal detrended fluctuation analysis and shuffling technique. The novelty of this study lies in exploring the influence of climate change on precipitation and temperatures from a novel nonlinear dynamic perspective. The temperatures and precipitation data regarding central England (1931-2019) were analyzed by multifractal theory. The results demonstrated that the sources of precipitation and temperature multifractal patterns altered owing to climate change on the daily and monthly scales. Concerning maximum temperature (T max), on a daily scale, multifractal patterns with probability density function (PDF) origin were intensified, whereas, on a monthly scale, multifractal patterns with long-range correlations (LRC) source were amplified. Regarding precipitation and minimum temperature (T min), on a daily scale, multifractal patterns with LRC origin were strengthened, whereas, on a monthly scale, multifractal patterns with PDF source were augmented. On a daily scale, multifractality of precipitation and T max increased by 85.66% and 87.37%, respectively, and regarding T min , decreased by 7.28%. The multifractal patterns of precipitation were dependent on the T min multifractal patterns. It was concluded that alterations in drought and flood patterns were consequences of variations in the multifractal source of T min patterns. The present study contributes to understanding the mechanism of climate change impacts on multifractal patterns of precipitation and temperatures and furnished references for multifractal studies of precipitation and temperatures.
... From ℎ( ), other interesting exponents can be derived [19]. The singularity exponent, , and its spectrum, ( ), were considered relevant for this study since their results are widely used to assess the complexity of the studied signals [16,[41][42][43][44][45]. The singularity exponent or Lipschitz-Hölder exponent, ( ), can be obtained as: ...
... The first property correspond to the most dominant scaling behavior, while the width indicates the strength of the multifractality of the signal [43]. Asymmetry is measured in different ways in the literature [41,43,46]. Here, the asymmetry index (AI) was used, in a similar manner as previous in studies of reference evapotranspiration [17,19]: ...
The multifractal relationship between reference evapotranspiration (ET0), computed by the Penmann-Monteith equation (PM), relative humidity (RH) and mean surface temperature (Tmean) was studied in the middle zone of the Guadalquivir River Valley (south Spain) in a previous study. This work extends that study to the average wind speed (U2) and solar radiation (SR), focusing on more recent years. All agro-meteorological variables were analyzed by multifractal detrended cross-correlation analysis (MFCCA) and multifractal detrended fluctuation analysis (MFDFA). The outcomes revealed persistent long-term autocorrelations, with Tmean and RH having the highest persistence (H>0.75). More precise results of multifractal properties than in the previous study were obtained for ET0, Tmean, and RH due to the elimination of trends in the signals. Only medium and large fluctuations in ET0 showed multifractal cross-correlations with its controlling factors, except for U2. Moreover, joint scaling exponents differed from individual exponents. These phenomena contrast with what has been observed in previous cross-correlation studies, revealing that some differences exist in the dynamics of multifractality among the analyzed variables. On the other hand, the Tmean–ET0 relation showed that extreme events in ET0 are mainly ruled by high temperature fluctuations, which match conclusions drawn in the previous study.
... In contrast, we have the full singularity spectrum for large time scales, and less width denotes a more stable market suitable for investment for more extended time scales. Table 2 shows the most important parameters of the multifractal spectrum: ∆α, H 2 , dH, and B [30,32,41,59]. α max and α min denote the most extreme and smoothest event in the considered data-set and α 0 (=value of α at f (α) max ) provides the information about the structure of the process, e.g. lower value will signify more correlated process which loose its fine structure and appears to be more regular [41]. ...
... lower value will signify more correlated process which loose its fine structure and appears to be more regular [41]. In addition, left skewed multifractal spectrum indicates the dominance of large fluctuations which can lead to extreme events [32,59]. A right skewed spectrum, in contrast, signifies presence of more small fluctuations and thus is a sign of stable sector. ...
... We can conclude that RE, IT, and CDGS show the lowest level of dependency among all. Value of B parameter included in Table 2 thus helps one to study the dynamics of the market quantitatively, as well as qualitatively [32,59]. ...
This paper, for the first time, focuses on the sector-wise analysis of a stock market through multifractal analysis. We have considered Bombay Stock Exchange, India, and identified two time scales, short ($<200$ days) and long time-scale ($>200$ days) for investment. We infer that long-term investment will be more profitable. For long time scale, sectors can be separated into two categories based on the Hurst exponent values; one corresponds to stable sectors with small fluctuations, and the other with dominance of large fluctuations leading to possible downturns in those sectors.
... Previous research used multifractal methods for characterising temperature and precipitation time-series variability (Svensson et al. 1996;Ghanmi et al. 2013;Domino et al. 2014; Santos da Silva et al. 2020;Morales Martínez et al. 2021). Baranowski et al. (2015) showed that precipitation was the meteorological variable most vulnerable to climate change effects in Europe and these authors, in 2019, also demonstrated how topography and atmosphere patterns influenced the variability of multifractal spectra in Poland (Baranowski et al. 2019). Recently, Santos da Silva et al. (2020) found significant differences between the north and south of Brazil, in terms of stochastic processes that generate fluctuations in air temperature. ...
... Furthermore, this methodology allows the analysis of signals, even if the time series are affected by non-stationary processes (Gómez and Poveda 2008;Zhou and Leung 2010;Morales Martínez et al. 2021). Another advantage of this technique is that it is less sensitive to the length of the studied time series (Baranowski et al. 2015(Baranowski et al. , 2019 in contrast to traditional methods such as wavelets and the fast Fourier transform. For these reasons, MFDFA is useful for the fractal characterisation of daily, monthly and annual precipitation and temperature time-series (Ghanmi et al. 2013;Domino et al. 2014;Yu et al. 2014;Baranowski et al. 2015; Santos da Silva et al. 2020;Morales Martínez et al. 2021). ...
... Another advantage of this technique is that it is less sensitive to the length of the studied time series (Baranowski et al. 2015(Baranowski et al. , 2019 in contrast to traditional methods such as wavelets and the fast Fourier transform. For these reasons, MFDFA is useful for the fractal characterisation of daily, monthly and annual precipitation and temperature time-series (Ghanmi et al. 2013;Domino et al. 2014;Yu et al. 2014;Baranowski et al. 2015; Santos da Silva et al. 2020;Morales Martínez et al. 2021). MFDFA was implemented for the calculation of the multifractal spectrum and its dimensions from the temperature and precipitation records of Northern Patagonia. ...
The fundamentals of Chaos theory allow the study of climatic conditions and long-term modifications produced by changes in their spatial and temporal scales. The aim of this work is to analyse the variability and changes produced in the annual cycles of temperature and precipitation in Northern Patagonia, Argentina, applying multifractal analysis as a practical mathematical tool of Chaos theory. Data from the NASA POWER Project (2021) was implemented as an alternative dataset for carrying out climatological studies in the area. Annual mean temperature and precipitation time-series data (1981–2019) were analysed at 72 grid points with 1° of spatial resolution. The Mann–Kendall test was used to calculate the trends through the annual cycles of the meteorological variables. Fractal dimension values were calculated using Multifractal Detrended Fluctuation Analysis. The Hurst exponent, complexity and asymmetry were the multifractal dimensions describing the persistence of time-series trends and climatic variability. The results showed changes in the annual cycles of both variables during the study period. The most significant finding was a large area in the centre and north of the study area, where the decrease in the rainfall regime was persistent. The Hurst exponent detected a sector in the Patagonian Andes mountain range where the temperature increase was constant. This work demonstrates that fractal geometry is useful to describe meteorological variability and obtain better short-, medium- and long-term forecasts.
