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<p>Classical fractional climate models struggle with low-frequency spectral flattening. To resolve this, we propose the tempered fractional integral statistical model (TFISM), utilizing exponential tempering to naturally bound low-frequency spectra while preserving intermediate-frequency scaling. To overcome parameter coupling challenges, we developed the adaptive weighted segmented logarithmic fitting (AWSLF) algorithm for robust inversion. Crucially, TFISM enables a novel physical decomposition of climate variability into three components: slow external forcing, memory-mediated response, and fast stochastic excitation. Applying this to 269 years of Stockholm temperatures, we identified an 1882 regime shift driven by persistent external forcing. Furthermore, global daily temperature analysis (1985–2024) reveals pronounced spatial memory heterogeneities: memory scaling (<i>q</i>) exhibits a strong latitudinal gradient, while memory truncation (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\lambda \)</EquationSource> </InlineEquation>) significantly accelerates in mid-latitude regions experiencing intensive vegetation degradation. These findings provide a rigorous mathematical framework for detecting multi-scale climate changes and anthropogenic footprints.</p>

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Disentangling climate memory: a tempered fractional framework reveals century-scale persistence and anthropogenic fingerprints

  • 期刊论文

  • 发表日期：

    2026年5月28日

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  • Yejuan Wang,
  • Zichen Zhao,
  • Zuntao Fu,
  • Naiming Yuan

摘要

Classical fractional climate models struggle with low-frequency spectral flattening. To resolve this, we propose the tempered fractional integral statistical model (TFISM), utilizing exponential tempering to naturally bound low-frequency spectra while preserving intermediate-frequency scaling. To overcome parameter coupling challenges, we developed the adaptive weighted segmented logarithmic fitting (AWSLF) algorithm for robust inversion. Crucially, TFISM enables a novel physical decomposition of climate variability into three components: slow external forcing, memory-mediated response, and fast stochastic excitation. Applying this to 269 years of Stockholm temperatures, we identified an 1882 regime shift driven by persistent external forcing. Furthermore, global daily temperature analysis (1985–2024) reveals pronounced spatial memory heterogeneities: memory scaling (q) exhibits a strong latitudinal gradient, while memory truncation ( \(\lambda \) ) significantly accelerates in mid-latitude regions experiencing intensive vegetation degradation. These findings provide a rigorous mathematical framework for detecting multi-scale climate changes and anthropogenic footprints.