Multifractal Detrended Cross-Correlation Analysis of Sunspot Numbers and River Flow Fluctuations

We use the Detrended Cross-Correlation Analysis (DCCA) to investigate the influence of sun activity represented by sunspot numbers on one of the climate indicators, specifically rivers, represented by river flow fluctuation for Daugava, Holston, Nolichucky and French Broad rivers. The Multifractal Detrended Cross-Correlation Analysis (MF-DXA) shows that there exist some crossovers in the cross-correlation fluctuation function versus time scale of the river flow and sunspot series. One of these crossovers corresponds to the well-known cycle of solar activity demonstrating a universal property of the mentioned rivers. The scaling exponent given by DCCA for original series at intermediate time scale, $(12-24)\leq s\leq 130$ months, is $\lambda = 1.17\pm0.04$ which is almost similar for all underlying rivers at $1\sigma$confidence interval showing the second universal behavior of river runoffs. To remove the sinusoidal trends embedded in data sets, we apply the Singular Value Decomposition (SVD) method. Our results show that there exists a long-range cross-correlation between the sunspot numbers and the underlying streamflow records. The magnitude of the scaling exponent and the corresponding cross-correlation exponent are $\lambda\in (0.76, 0.85)$ and $\gamma_{\times}\in(0.30, 0.48)$, respectively. Different values for scaling and cross-correlation exponents may be related to local and external factors such as topography, drainage network morphology, human activity and so on. Multifractal cross-correlation analysis demonstrates that all underlying fluctuations have almost weak multifractal nature which is also a universal property for data series. In addition the empirical relation between scaling exponent derived by DCCA and Detrended Fluctuation Analysis (DFA), $\lambda\approx(h_{\rm sun} + h_{\rm river})/2$ is confirmed.Comment: 9 pages, 8 figures and 1 table. V2: Added comments, references, figures and major corrections. Accepted for publication in Physica A: Statistical Mechanics and its Application

Multifractal detrended cross-correlation analysis of temporal and spatial seismic data

We use Multi-Fractal Detrended Cross-Correlation Analysis (MF-DXA) method to investigate the cross-correlation of temporal and spatial inter-events seismic data, which expected to be correlated. The mentioned data are the California earthquakes' data which are simultaneously recorded, over an extended period of time. We get the cross-correlation exponent 0.76 ± 0.01. We determine generalized Hurst exponent and singularity spectrum and find that these sequences are joined in various scales and have a multifractality behavior. It means that the correlation in small scales of the sequences (the earthquakes which are close together in space and time) are different from in the large ones. We also find that in spite of the multifractal behavior of temporal and spatial time series, their cross series shows fractal behavior, meaning that the statistical properties of the cross series are invariant under the change of scale