Multifractality and cross-correlation analysis of streamflow and sediment fluctuation at the apex of the Pearl River Delta

Multifractal characterization of meteorological to agricultural drought propagation over India

Agricultural drought affects the regional food security and thus understanding how meteorological drought propagates to agricultural drought is crucial. This study examines the temporal scaling trends of meteorological and agricultural drought data over 34 Indian meteorological sub-divisions from 1981 to 2020. A maximum Pearson's correlation coefficient (MPCC) derived between multiscale Standardised Precipitation Index (SPI) and monthly Standardised Soil Moisture Index (SSMI) time series was used to assess the seasonal as well as annual drought propagation time (DPT). The multifractal characteristics of the SPI time series at a time scale chosen from propagation analysis as well as the SSMI-1 time series were further examined using Multifractal Detrended Fluctuation Analysis (MF-DFA). Results reveal longer average annual DPT in arid and semi-arid regions like Saurashtra and Kutch (~ 6 months), Madhya Maharashtra (~ 5 months), and Western Rajasthan (~ 6 months), whereas, humid regions like Arunachal Pradesh, Assam and Meghalaya, and Kerala exhibit shorter DPT (~ 2 months). The Hurst Index values greater/less than 0.5 indicates the existence of long/short-term persistence (LTP/STP) in the SPI and SSMI time series. The results of our study highlights the inherent connection among drought propagation time, multifractality, and regional climate variations, and offers insights to enhance drought prediction systems in India.

Multiple-Resampling Cross-Spectral Analysis: An Unbiased Tool for Estimating Fractal Connectivity With an Application to Neurophysiological Signals

Investigating scale-free (i.e., fractal) functional connectivity in the brain has recently attracted increasing attention. Although numerous methods have been developed to assess the fractal nature of functional coupling, these typically ignore that neurophysiological signals are assemblies of broadband, arrhythmic activities as well as oscillatory activities at characteristic frequencies such as the alpha waves. While contribution of such rhythmic components may bias estimates of fractal connectivity, they are also likely to represent neural activity and coupling emerging from distinct mechanisms. Irregular-resampling auto-spectral analysis (IRASA) was recently introduced as a tool to separate fractal and oscillatory components in the power spectrum of neurophysiological signals by statistically summarizing the power spectra obtained when resampling the original signal by several non-integer factors. Here we introduce multiple-resampling cross-spectral analysis (MRCSA) as an extension of IRASA from the univariate to the bivariate case, namely, to separate the fractal component of the cross-spectrum between two simultaneously recorded neural signals by applying the same principle. MRCSA does not only provide a theoretically unbiased estimate of the fractal cross-spectrum (and thus its spectral exponent) but also allows for computing the proportion of scale-free coupling between brain regions. As a demonstration, we apply MRCSA to human electroencephalographic recordings obtained in a word generation paradigm. We show that the cross-spectral exponent as well as the proportion of fractal coupling increases almost uniformly over the cortex during the rest-task transition, likely reflecting neural desynchronization. Our results indicate that MRCSA can be a valuable tool for scale-free connectivity studies in characterizing various cognitive states, while it also can be generalized to other applications outside the field of neuroscience.

Possible Linkages of Hydrological Variables to Ocean–Atmosphere Signals and Sunspot Activity in the Upstream Yangtze River Basin

Profiling the hydrological response of watershed precipitation and streamflow to large-scale circulation patterns and astronomical factors provides novel information into the scientific management and prediction of regional water resources. Possible contacts of El Niño–Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO), sunspot activity to precipitation and streamflow in the upper Yangtze River basin (UYRB) were investigated in this work. Monthly precipitation and streamflow were utilized as well as contemporaneous same-scale teleconnections time series spanning a total of 70 years from 1951 to 2020 in precipitation and 121 years from 1900 to 2020 in streamflow. The principal component analysis (PCA) method was applied so as to characterize the dominant variability patterns over UYRB precipitation time series, with the temporal variability of first two modes explaining more than 80% of total variance. Long-term evolutionary pattern and periodic variation characteristics of precipitation and streamflow are explored by applying continuous wavelet transform (CWT), cross-wavelet transform (XWT) and wavelet coherence (WTC), analyzing multi-scale correlation between hydrological variables and teleconnections in the time-frequency domain. The results manifest that ENSO exhibits multiple interannual period resonance with precipitation and streamflow, while correlations are unstable in time and phase. PDO and sunspot effects on precipitation and streamflow at interannual scales vary with time-frequency domains, yet significant differences are exhibited in their effects at interdecadal scales. PDO exhibits a steady negative correlation with streamflow on interdecadal scales of approximately 10 years, while the effect of sunspot on streamflow exhibits extremely steady positive correlation on longer interdecadal scales of approximately 36 years. Analysis reveals that both PDO and sunspot have significantly stronger effects on streamflow variability than precipitation, which might be associated with the high spatiotemporal variability of precipitation.

Multifractal Cross Correlation Analysis of Agro-Meteorological Datasets (Including Reference Evapotranspiration) of California, United States

The multifractal properties of six acknowledged agro-meteorological parameters, such as reference evapotranspiration (ET0), wind speed (U), incoming solar radiation (SR), air temperature (T), air pressure (P), and relative air humidity (RH) of five stations in California, USA were examined. The investigation of multifractality of datasets from stations with differing terrain conditions using the Multifractal Detrended Fluctuation Analysis (MFDFA) showed the existence of a long-term persistence and multifractality irrespective of the location. The scaling exponents of SR and T time series are found to be higher for stations with higher altitudes. Subsequently, this study proposed using the novel multifractal cross correlation (MFCCA) method to examine the multiscale-multifractal correlations properties between ET0 and other investigated variables. The MFCCA could successfully capture the scale dependent association of different variables and the dynamics in the nature of their associations from weekly to inter-annual time scales. The multifractal exponents of P and U are consistently lower than the exponents of ET0, irrespective of station location. This study found that joint scaling exponent was nearly the average of scaling exponents of individual series in different pairs of variables. Additionally, the α-values of joint multifractal spectrum were lower than the α values of both of the individual spectra, validating two universal properties in the MFCCA studies for agro-meteorological time series. The temporal evolution of cross-correlation determined by the MFCCA successfully captured the dynamics in the nature of associations in the P-ET0 link.

Multifractal characterization of the Coniacian-Santonian OAE3 in lacustrine and marine deposits based on spectral gamma ray logs

Limited to the Atlantic and its surrounding basins, the expression of the Coniacian-Santonian oceanic anoxic event (OAE3) was discovered in the non-marine Cretaceous Songliao Basin, Eastern Asia not long ago. In this study, based on spectral gamma ray logs data recorded in three basins, the self-similarity of the OAE3 was studied through the analysis of the scaling properties of thorium-potassium and thorium-uranium distributions both in marine and terrestrial environments using the multifractal detrending fluctuation analysis. The results indicate that, in both marine and terrestrial systems, the OAE3 intervals are characterized by their multifractal nature due to long-range correlation. However, the multifractal features of the studied OAE3 intervals are different in the three basins, although some common trends were observed. By comparing the degree of multifractality of the OAE3 deposits with the clay minerals and the redox conditions, it appears that the changes of the multifractal features are controlled by local changes such as clay mineralogy and redox conditions in both milieus under different sedimentation patterns. At all sites, the left side shortened spectrum of the thorium-potassium distribution suggests the presence of local fluctuations with minor amplitudes during the OAE3. Furthermore, the shortened singularity spectrum of the thorium-uranium distribution reflects the existence of small-scale fluctuations with large amplitudes at marine sites while in the non-marine Songliao Basin, the thorium-uranium distribution suggests the presence of local fluctuations with small amplitudes during the OAE3. Therefore, a more local behavior of the event is considered although the regional character is not neglected.

Identification of Active Gully Erosion Sites in the Loess Plateau of China Using MF-DFA

Gullies of different scales and types have developed in the Loess Plateau, China. Differences in the amount of gully erosion influence the development, evolution, morphology, and spatial distribution of these gullies. The strengths of headward erosion on the gully shoulder line are used to dictate soil and water conservation measures. In this study, six typical loess landforms in the Loess Plateau were selected as sampling sites: Shenmu, Suide, Ganquan, Yanchuan, Yijun, and Chunhua, which respectively represent loess–aeolian and dune transition zones, loess hills, loess ridge hills, loess ridges, loess long-ridge fragmented tablelands, and loess tablelands. Using 5 m resolution digital elevation model data from the National Basic Geographic Information Database, a small representative watershed was selected from each sampling site to obtain elevation data on the terrain profiles of gully shoulder lines. Multifractal detrended fluctuation analysis (MF-DFA) was used to conduct statistical and comparative analysis of the elevation fluctuation characteristics of these profiles. The results show that MF-DFA is capable of detecting active gully erosion sites. Sites of active gully erosion are concentrated in Shenmu and Suide but more widely distributed in the other five sites. The results provide a scientific basis for small watershed management planning and the design of soil and water conservation measures.