Lak Maedeh, Hosseinabadi Sakineh, Masoudi Amir Ali
Department of Condensed Matter Physics, Faculty of Physics, Alzahra University, Tehran, Iran.
Department of Physics, ET.C., Islamic Azad University, Tehran, Iran.
Sci Rep. 2025 Aug 11;15(1):29403. doi: 10.1038/s41598-025-15149-8.
Markov equations are used to solve complex nonlinear differential equations that are not easily solvable. In the context of climate data, these equations can provide insights into patterns and trends in temperature changes over time. Temperature fluctuations are the backbone of climate change, and due to their nonlinear nature, applying novel approaches is vital. This paper investigates the nonlinear dynamics of Earth's surface temperature data from NASA's Goddard Institute for Space Studies (GISS). Through the application of Markov analysis to the GISS temperature data and a thorough investigation of key transition states, we can explore the potential for formulating a robust equation that effectively captures the dynamics of Earth's temperature fluctuations. Here, we investigate the Markovian nature of the temperature data via Chapman-Kolmogorov (CK) verification. The Markov time interval is determined by the CK equation as [Formula: see text]. This indicates that for time intervals larger than 2 months, temperature fluctuations can be considered a Markov process. By recognizing the Markov characteristic time, we derive the Fokker-Planck equation for the temperature fluctuations. The drift and diffusion coefficients in this equation demonstrate linear and quadratic trends with respect to the fluctuations, respectively. The drift coefficient is given by [Formula: see text], which shows a degree of correlation among the temperature data. The quadratic nature of the diffusion coefficient, represented as [Formula: see text], implies that at higher temperatures, the influence of random fluctuations increases significantly, leading to multiaffinity and nonlinearity in the scaling exponents of the temperature data. Finally, the governed Langevin equation related to the dynamics of the GISS temperature fluctuations is derived, providing a complex theoretical framework with practical applications and significance in advancing climate research.
马尔可夫方程用于求解不易求解的复杂非线性微分方程。在气候数据的背景下，这些方程可以洞察温度随时间变化的模式和趋势。温度波动是气候变化的核心，由于其非线性性质，应用新颖的方法至关重要。本文研究了美国国家航空航天局戈达德空间研究所（GISS）提供的地球表面温度数据的非线性动力学。通过将马尔可夫分析应用于GISS温度数据并深入研究关键转变状态，我们可以探索制定一个能有效捕捉地球温度波动动态的稳健方程的潜力。在这里，我们通过查普曼 - 柯尔莫哥洛夫（CK）验证来研究温度数据的马尔可夫性质。由CK方程确定的马尔可夫时间间隔为[公式：见原文]。这表明对于大于2个月的时间间隔，温度波动可被视为一个马尔可夫过程。通过识别马尔可夫特征时间，我们推导出了温度波动的福克 - 普朗克方程。该方程中的漂移系数和扩散系数分别呈现出关于波动的线性和二次趋势。漂移系数由[公式：见原文]给出，这显示了温度数据之间的一定相关性。扩散系数的二次性质表示为[公式：见原文]，这意味着在较高温度下，随机波动的影响显著增加，导致温度数据的标度指数出现多亲和性和非线性。最后，推导了与GISS温度波动动力学相关的朗之万方程，为推进气候研究提供了一个具有实际应用和意义的复杂理论框架。
