The Long-term structural effect of Coronal index solar activity on the ENSO and QBO Time series data using Fractal Dimension

The study concentrated on the fractal dimension of solar ac-tivity and climatic parameters. We analyzed comparatively for each pa-rameter numerically. All values are estimated by Box Counting tech-nique of fractal dimension. According to the theme of study, we used a monthly dataset of Coronal Mass Ejection (Coronal Index (CI)), El-Nino Southern Oscillation (ENSO) and Quasi-Biennial Oscillation (QBO) from 1954 to 2016. The time seriesof ENSO and QBO are distributed ac-cording to the CORONAL INDEX (CI) cycles (19, 20, 21, 22, 23, and 24) to understand their relationship in the perspective of persistence or anti-persistence.The fractal dimension(D) represents the complexity and Hurst exponent(H) indicates the long memory dependence of the selected time series, with scaling constant (a, c). The results obtained indicate the persistence (1 < D < 1.5) for CORONAL INDEX (CI) with dis-tributed ENSO and QBO cycles. The fractional Brownian motion (fBm) is also found long memory dependence(1¿H¿ 0.5) and locally lowpass signal for all studied cycles observed.A linear relationship implies be-tween Hurst coefficient and fractal dimension for a statistical assumption (H + D = 2).The fractal scaling instrument is established between the global indices (ENSO & QBO) and solar activity (particularly CORO-NAL INDEX (CI)) cycles,the inverse correlation with ENSO and direct with QBO are observed. The results obtained in this research work may help to describe the solar-terrestrial relationship