Abstract
Complex network approaches have been recently developed as an alternative framework to study the statistical features of time-series data. We perform a visibility-graph analysis on both the daily and monthly sunspot series. Based on the data, we propose two ways to construct the network: one is from the original observable measurements and the other is from a negative-inverse-transformed series. The degree distribution of the derived networks for the strong maxima has clear non-Gaussian properties, while the degree distribution for minima is bimodal. The long-term variation of the cycles is reflected by hubs in the network that span relatively large time intervals. Based on standard network structural measures, we propose to characterize the long-term correlations by waiting times between two subsequent events. The persistence range of the solar cycles has been identified over 15–1000 days by a power-law regime with scaling exponent γ = 2.04 of the occurrence time of two subsequent strong minima. In contrast, a persistent trend is not present in the maximal numbers, although maxima do have significant deviations from an exponential form. Our results suggest some new insights for evaluating existing models.
Highlights
Solar-cycle prediction, i.e. forecasting the amplitude and/or the epoch of an upcoming maximum, is of great importance as solar activity has a fundamental impact on the weather conditions of the Earth, especially with increasing concern over the various climate change scenarios
Figures 2(A) and (B) show the degree distributions p(k) of the visibility graph (VG) derived from the international sunspot number (ISN) x(ti ) with heavy-tails corresponding to hubs of the graph, which clearly deviates from Gaussian properties
Since well-defined scaling regimes are absent in either p(k) or p(k−x ), we may reject the hypothetical power laws—in contrast to what has been reported in other contexts [23, 24]
Summary
Solar-cycle prediction, i.e. forecasting the amplitude and/or the epoch of an upcoming maximum, is of great importance as solar activity has a fundamental impact on the weather conditions of the Earth, especially with increasing concern over the various climate change scenarios. Most successful methods in this regard can give reasonably accurate predictions only when a cycle is well advanced (e.g. 3 years after the minimum) or with guidance from its past [3, 4] These methods show very limited power in forecasting a cycle which has not yet started. The theoretical reproduction of a sunspot series by most current models shows convincingly the ‘illustrative nature’ of the existing record [5] They generally failed to predict the slow start of the present cycle 24 [6]. One reason cited for this is the emergence of prolonged periods of extremely low activity The existence of these periods of low activity brings a big challenge for solar-cycle prediction and reconstruction by the two classes of methods described above, and prompted the development of special ways to evaluate the appearance of these minima [7]. There is increasing interest in the minima since they are known to provide insight for predicting the maximum [8]
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