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Abstract：
Serial correlations within temperature time series serve as indicators of the temporal consistency of climate events. This study delves into the serial correlations embedded in global surface air temperature (SAT) data. Initially, we preprocess the SAT time series to eradicate seasonal patterns and linear trends, resulting in the SAT anomaly time series, which encapsulates the inherent variability of Earth\'s climate system. Employing diverse statistical techniques, we identify three distinct types of serial correlations: short-term, long-term, and nonlinear. To identify short-term correlations, we utilize the first-order autoregressive model, AR(1), revealing a global pattern that can be partially attributed to atmospheric Rossby waves in extratropical regions and the Eastern Pacific warm pool. For long-term correlations, we adopt the standard detrended fluctuation analysis, finding that the global pattern aligns with long-term climate variability, such as the El Niño-Southern Oscillation (ENSO) over the Eastern Pacific. Furthermore, we apply the horizontal visibility graph (HVG) algorithm to transform the SAT anomaly time series into complex networks. The topological parameters of these networks aptly capture the long-term correlations present in the data. Additionally, we introduce a novel topological parameter, Δσ, to detect nonlinear correlations. The statistical significance of this parameter is rigorously tested using the Monte Carlo method, simulating fractional Brownian motion and fractional Gaussian noise processes with a predefined DFA exponent to estimate confidence intervals. In conclusion, serial correlations are universal in global SAT time series and the presence of these serial correlations should be considered carefully in climate sciences.
摘要：
温度时间序列中的序列相关性可作为气候事件时间一致性的指标。这项研究深入研究了嵌入在全球地表气温（SAT）数据中的序列相关性。最初，我们对SAT时间序列进行预处理，以消除季节性模式和线性趋势，导致SAT异常时间序列，它包含了地球气候系统的内在变异性。采用不同的统计技术，我们确定了三种不同类型的序列相关性：短期，长期的,和非线性。为了识别短期相关性，我们利用一阶自回归模型，AR(1),揭示了一种全球模式，该模式可部分归因于温带地区和东太平洋暖池的大气Rossby波。对于长期相关性，我们采用标准的去趋势波动分析，发现全球格局与长期气候变化相一致，例如东太平洋上的厄尔尼诺-南方涛动（ENSO）。此外，我们应用水平可见性图（HVG）算法将SAT异常时间序列转换为复杂网络。这些网络的拓扑参数恰当地捕获了数据中存在的长期相关性。此外,我们引入了一个新的拓扑参数，Δσ，检测非线性相关性。用蒙特卡罗方法严格检验了该参数的统计显著性,用预定义的DFA指数模拟分数布朗运动和分数高斯噪声过程，以估计置信区间。总之,序列相关性在全球SAT时间序列中是普遍的，在气候科学中应该仔细考虑这些序列相关性的存在。
