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

## TL;DR

This study applies multifractal detrended cross-correlation analysis to sunspot numbers and river flow data, revealing universal properties, long-range correlations, and the influence of solar activity on river fluctuations.

## Contribution

It introduces the use of MF-DXA to analyze the cross-correlation between solar activity and river flows, identifying universal behaviors and validating empirical relations.

## Key findings

- Existence of crossovers in cross-correlation functions at solar cycle scales.
- Universal scaling exponents for river flows and sunspot numbers.
- Long-range cross-correlation between solar activity and river fluctuations.

## Abstract

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.