Figure 1
(a) The scaling exponents of solar flare waiting time intervals, long solar records, and temperature are the same. Thus, the same dynamics that generates the LW solar flare statistics at least up to four months [
2,
7] drives the solar activity also at longer scales that drives climate [
4]. (b) A LW noise (bottom) [
2,
7] with waiting time exponent
that symbolizes the solar flare data. (Top) A Gaussian random noise modulated with the LW smooth black curve; it symbolizes a long scale solar record or the temperature record (note that its increments are Gaussian distributed). The upper smooth curve is a fourth-order polynomial fit revealing that LW signals can present large trends generated by their LW memory, which would be lost through detrending. The synthetic sequence simulates the fact that solar activity was lower 100 year ago [
5], which likely implies that large flares were rarer. (c) The same model as in [
2] with
that yields
and
. Panels (d) and (e) analyze the signals in (c) and show that both the original and synthetic records present LW scaling within the scale interval 0–100 time units. Panel (f) shows that if the LW noise is detrended of its smooth component, its intrinsic LW scaling properties disappear also within the scale interval 0–100 despite the fact that the detrending has smoothed the scale
, which is what is observed in Figs. 2b and 2d in
1.
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