(untitled) (Contemporary Mathematics, 2025)
The ozone layer has acted as the planet’s natural sunscreen, protecting people, plants, and animals from harmful ultraviolet rays. The Antarctic ozone hole was first announced in a paper by the British Antarctic Survey’s Joe Farman, Brian Gardiner, and Jonathan Shanklin in 1985. Many investigations are still conducting to determine the connection between ozone depletion and climate change. This research study investigates the impact of the ozone layer’s depletion at the Antarctic pole on global climate change data such as temperature and precipitation, after the year 1985 through a fractal dimension, Multifractal Detrended Fluctuation Analysis (MFDFA), and standard correlation coefficient. For this, the research work has analyzed 45 years of climate change variables such as global monthly temperature anomaly, global monthly precipitation anomaly, and Southern Hemisphere minimum ozone time series data from 1979 to 2023. The fractal dimension of the time series is obtained by rescaled range analysis, which is used to identify the fractality of the time series and long-range correlations and persistence. To study the multifractality of these fractal time series, MFDFA procedure has been applied. By applying MFDFA to these time series data, this research has identified significant multifractal characteristics, indicating complex dynamics and long-range correlations, and identified potential nonlinear patterns. This research provides valuable insights into the complex dynamics of time series data, as revealed by the calculated exponent values and MFDFA spectrum. The strong correlation observed between the exponent values of temperature anomalies, and precipitation anomalies, with ozone depletion time series provides compelling evidence for the significant impact of ozone depletion on climate change. These results highlight the potential of multifractality for understanding the intricate mechanisms underlying climate change.