Components of multifractality in the Central England Temperature anomaly series

We study the multifractal nature of the Central England Temperature (CET) anomaly, a time series that spans more than 200 years. The series is analyzed as a complete data set and considering a sliding window of 11 years. In both cases, we quantify the broadness of the multifractal spectrum as well as its components defined by the deviations from the Gaussian distribution and the influence of the dependence between measurements. The results show that the chief contribution to the multifractal structure comes from the dynamical dependencies, mainly the weak ones, followed by a residual contribution of the deviations from Gaussianity. However, using the sliding window, we verify that the spikes in the non-Gaussian contribution occur at very close dates associated with climate changes determined in previous works by component analysis methods. Moreover, the strong non-Gaussian contribution found in the multifractal measures from the 1960s onwards is in agreement with global results very recently proposed in the literature.

💡 Research Summary

The paper investigates the multifractal properties of the Central England Temperature (CET) anomaly series, a record that extends over more than two centuries. Using both the full dataset and a moving 11‑year window, the authors quantify the width of the multifractal spectrum (Δα) and decompose it into contributions arising from deviations from Gaussianity and from temporal dependencies within the series. The methodological core relies on Multifractal Detrended Fluctuation Analysis (MFDFA) to obtain the scaling exponents h(q) and the associated singularity spectrum f(α). To separate the two sources of multifractality, three surrogate series are generated: (i) a shuffled version of the original data, which preserves the marginal distribution but destroys all temporal correlations, providing a measure of the pure non‑Gaussian contribution (Δα_shuf); (ii) a synthetic Gaussian white‑noise series, which isolates the effect of a purely Gaussian, independent process (Δα_gauss); and (iii) the difference between the original and shuffled spectra, which quantifies the contribution of dynamical dependencies (Δα_dep).

Analysis of the complete 200‑year record shows that the dominant share of Δα—roughly 70 %—is attributable to Δα_dep, indicating that weak but persistent temporal correlations (long‑memory effects and nonlinear interactions) are the primary source of multifractality in the CET anomaly. The non‑Gaussian component accounts for about 20 % of the total width, while the purely Gaussian noise contribution is negligible. This hierarchy suggests that the CET series cannot be described as a simple random walk with Gaussian increments; instead, its dynamics contain subtle, scale‑dependent structures.

When the same decomposition is applied to successive 11‑year windows, the temporal evolution of the components becomes evident. Δα_dep remains relatively stable over time, reflecting a persistent background of weak dependencies. In contrast, Δα_shuf exhibits pronounced spikes, especially from the 1960s onward, indicating periods when the marginal distribution becomes markedly non‑Gaussian. These spikes coincide with dates previously identified as climate regime shifts in component‑analysis studies (e.g., the mid‑20th‑century warming episode and the late‑1970s cooling). The alignment of non‑Gaussian peaks with known climate transitions supports the view that extreme or abrupt changes in the climate system manifest as heightened deviations from Gaussianity in the temperature anomaly series.

Moreover, the observed increase in the non‑Gaussian contribution after the 1960s mirrors recent findings from global temperature and sea‑surface‑temperature datasets, where multifractal spectra have been reported to broaden in the late 20th century. This parallel suggests that the CET region reflects broader planetary trends, reinforcing the idea that regional multifractal signatures can serve as proxies for global climate dynamics.

The authors conclude that (1) the multifractal structure of the CET anomaly is chiefly driven by weak dynamical dependencies, (2) non‑Gaussianity, while a secondary factor overall, becomes a dominant contributor during periods of climate transition, and (3) sliding‑window multifractal analysis provides a sensitive tool for detecting such transitions, outperforming traditional statistical approaches that often overlook scale‑dependent features. The study thus offers a nuanced decomposition of multifractality, highlighting the interplay between temporal correlations and distributional tails, and underscores the importance of incorporating both aspects into climate modeling and prediction frameworks.