The probability distributions and fractal dimension of sunspot cycles associated with ENSO phenomena
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Various methods have been used to secure the certainty of significant relations among the sunspot cycles and some of the terrestrial climate parameters such as temperature, rainfall, and ENSO. This study investigates the behavior of ENSO cycles and mean monthly sunspot cycles. Sunspot cycles range from 1755 to 2016 whereas, ENSO cycles range from 1866 to 2012. In this regard, the appropriateness of distributions is investigated with the help of Kolmogorov-Smirnov D, Anderson-Darling, and chi-square tests. It is found that most of the sunspot cycle follows generalized Pareto distribution whereas, generalized extreme value distribution was found appropriate for ENSO cycles. Probability distribution is used to analyze the behavior of each sunspot cycle and ENSO cycle separately. Probability distribution indicates the tail behavior of each cycle; tail explored correlation cycles. Furthermore, self-similar and self-affine fractal dimension methods are used to compute Hurst exponents to determine the persistency of the available data. Fractal dimension has an ability to study the complexity involved in sunspot and ENSO cycles. The fractal dimension and Hurst exponent describe persistency (smoothness) and complexity of data. Hurst exponent measures long-term behavior of time series, making it more helpful for forecasting. This is the measure of regularity or irregularity (chaos) of the time function in the form of their persistency or anti-persistency, respectively. Hurst exponents are computed using rescaled range analysis method and box counting methods. Both these methods are suitable for long-term forecasting. The results of this study confirm that during the period 1980–2000, ENSO cycles were very active. Simultaneously, ENSO was active for the periods 1982–1983, 1986–1987, 1991–1993, 1994–1995, and 1997–1998; these periods include two strongest periods of the century viz., 1982–1983 and 1997–1998. Sunspot cycles and ENSO cycles both were found to be persistent. Self-similar fractal dimensions exhibited a better persistency and a better correlation as compared to self-affine fractal dimension. This research is a part of a larger research project investigating the correlation of sunspot cycles and ENSO cycles, and the influence of ENSO cycles on variations of the local climatic parameters which in turn depends on solar activity changes.
KeywordsEl Niño-southern oscillation (ENSO) Hurst exponent (HE) Fractal dimension (FD) Kolmogorov-Smirnov D test (KST) Anderson-Darling test (ADT) Chi-square test (CST)
The contents of the paper are a form of the first author’s doctoral thesis. The authors are also thankful to the World Data Centre (WDC) and National Oceanic and Atmospheric Administration (NOAA) for providing the sunspot and ENSO data.
- Anderson RY (1990) Solar cycle of modulation of ENSO: a mechanism for specific and globel climate change. In betan court, J.L and Mackey, A.M.(eds), proceeding Six annual pacific climate (PACLIM) workshop march 5–8, 1989, California Department of water resources, interagency Ecological studies program technical report 23, 27–81Google Scholar
- Anderson RY (1992). Possible connection between surface winds, solar activity and the earth’s magnetic field. Nature 358, 51–53Google Scholar
- Demon PE (1988), Production and decay of radio carbon and its modulation by geomagnetic field-solar activity changes with possible implication for global environment. In Stephenson FR and wolfendala AW (eds) secular, solar an geomagnetic variation in the last 10000 years. Dordrecht, Kluwer, 267–285Google Scholar
- Hussain MA (2006) Mathematical Aspects of The Impact of Urban Greenhouse Gas Emissions on Global Warming (Doctoral dissertation, Federal Urdu University of Arts, Science and TechnologyGoogle Scholar
- Hurst HE (1951) Long term storage capacity of reservoirs. Trans Am Soc Eng 116:770–799Google Scholar
- Kevin RM, Jimmy JL, Véronique D, Fraser W and Alfred OH III (2014) Image patch analysis and clustering of sunspots: a dimensionality reduction approach, arXiv: 1406.6390v1 [cs.CV]Google Scholar
- Tinsley B, Deen G (1991), Apparent tropospheric response to MeV-GeV particle flux variations: A connection via electrofreezing of supercooled water in high-level clouds? J. Geophys. Res.,96 (D12), 22283–22296. https://doi.org/10.1029/91JD02473
- TJO News (2006). The Theodor Jacobsen Observatory. NewsletterGoogle Scholar