Correlation analysis between sunspot activity and ENSO

The El Niño-Southern Oscillation (ENSO) is the most prominent mode of interannual climate variability in the tropical Pacific, exerting significant influences on global climate patterns and ecosystems. However, the mechanisms driving ENSO—particularly the potential role of external forcings such as solar activity—remain incompletely understood and continue to be debated. To systematically assess the relationship between solar activity and ENSO, we analyze the correlation between monthly sunspot numbers and two widely used ENSO indices—the Niño 3.4 index and the Southern Oscillation Index (SOI)—over the period from 1950 to 2023. A multi-method statistical approach is employed, incorporating linear cross-correlation analysis following the G24 method, Chatterjee's coefficient for nonlinear association, and wavelet coherence analysis, enabling evaluation across time and time-frequency domains. The results show no statistically significant linear or nonlinear correlations: both the cross-correlation and Chatterjee's coefficients are insignificant at conventional significance levels. In the time-frequency domain, cross-wavelet transforms and wavelet coherence reveal only isolated pockets of coherence. Furthermore, the phase relationships within these regions lack consistency and do not exhibit a stable phase-locked pattern aligned with the solar cycle. By integrating complementary statistical techniques, this study provides robust empirical evidence that does not support solar activity as a dominant driver of ENSO variability, thereby refining our understanding of the complex processes underlying ENSO dynamics.