Fractal dimension approach on climate analysis of India

M. Meenakshi; A. Gowrisankar; Jinde Cao; Pankajam Natarajan; M. Meenakshi; A. Gowrisankar; Jinde Cao; Pankajam Natarajan

doi:10.3934/mmc.2025002

Mathematical Modelling and Control

2025, Volume 5, Issue 1: 15-30. doi: 10.3934/mmc.2025002

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Research article

Fractal dimension approach on climate analysis of India

1.
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, Tamil Nadu, India
2.
School of Mathematics, Southeast University, Nanjing 210096, China
3.
Department of Mathematics, School of Engineering and Technology, CMR University, Chagalahatti, Bangalore 562149, Karnataka, India

Received: 20 August 2023 Revised: 27 November 2023 Accepted: 17 May 2024 Published: 07 March 2025

Climate change is an inevitable and important problem faced worldwide. Around the world, many researchers are doing research work on climate change with different factors. The authors of this study have used the fractal dimension to analyze the $ 41 $ years of climate change in India, from $ 1981 $ to $ 2021 $. The meteorological parameters, surface pressure, temperature, wind speed, and precipitation of $ 45 $ places in India were investigated for this research study. Each parameter was individually examined. As a result of this research, the mean average fractal dimension value of all parameters was acquired from $ 1.184 $ to $ 1.198 $. It was found that all the parameters within the data set, had a long-term persistence behavior. With these values, a suggestion for the prediction of the parameters was proposed. The results of the integrated analysis of these parameters showed that, with the exception of a location, all landscapes had a feature that precipitation increased with the temperature. Moreover, with the exception of two landscapes (the island and the frosty mountains), all areas received heavy rainfall during periods of low wind. Thus, this study contributes to a better understanding of the fractal aspects of climate change and the complexity of irregularity and the classification of weather characteristics.
- rescaled range analysis,
- Hurst exponent,
- fractal dimension
Citation: M. Meenakshi, A. Gowrisankar, Jinde Cao, Pankajam Natarajan. Fractal dimension approach on climate analysis of India[J]. Mathematical Modelling and Control, 2025, 5(1): 15-30. doi: 10.3934/mmc.2025002

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Abstract

Climate change is an inevitable and important problem faced worldwide. Around the world, many researchers are doing research work on climate change with different factors. The authors of this study have used the fractal dimension to analyze the $ 41 $ years of climate change in India, from $ 1981 $ to $ 2021 $. The meteorological parameters, surface pressure, temperature, wind speed, and precipitation of $ 45 $ places in India were investigated for this research study. Each parameter was individually examined. As a result of this research, the mean average fractal dimension value of all parameters was acquired from $ 1.184 $ to $ 1.198 $. It was found that all the parameters within the data set, had a long-term persistence behavior. With these values, a suggestion for the prediction of the parameters was proposed. The results of the integrated analysis of these parameters showed that, with the exception of a location, all landscapes had a feature that precipitation increased with the temperature. Moreover, with the exception of two landscapes (the island and the frosty mountains), all areas received heavy rainfall during periods of low wind. Thus, this study contributes to a better understanding of the fractal aspects of climate change and the complexity of irregularity and the classification of weather characteristics.

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