Testing Hypotheses about Sun-Climate Complexity Linking

Abstract

We reexamine observational evidence presented in support of the hypothesis of a sun-climate complexity linking by N. Scafetta and B. West, Phys. Rev. Lett. 90, 24 (2003). The original analysis concluded that the integrated solar flare index and the global temperature anomaly both follow Lévy-walk statistics with the same waiting-time exponent µ. However, this analysis did not account for trends in the signal, cannot deal correctly with infinite variance processes (Lévy flights), and crucial information about the stochastic properties of the signals is lost by considering only the second moment. The Lévy-walk signatures and common waiting-time exponent µ ≈ 2.1 found for the two signals are essentially a result of failure to eliminate the effects of trends. Our analysis shows that properly detrended, integrated solar flare index is well described as an uncorrelated Lévy flight, while the detrended, integrated temperature anomaly record is consistent with a persistent fractional Brownian motion. These very different stochastic properties of the solar and climate records do not support the hypothesis of a sun-climate complexity linking.

Long‐range memory in Earth's surface temperature on time scales from months to centuries

“…For a stronger trend, FA on the signal with trend will return β ≈1, i.e., the FA is totally overwhelmed by the trend. How such analyses have lead to misinterpretations were discussed by Rypdal and Rypdal []. In Figure b, we show the corresponding results from the WVA.…”

“…The Gaussian approximation is valid for deseasonalized surface temperature records, which are averaged over synoptic spatiotemporal scales (e.g., monthly means averaged over spatial scales km). Such records are also devoid of signatures of multifractality Rypdal and Rypdal []. For all data records analyzed in the present paper, Gaussianity of the deseasonalized and detrended records has been tested by the standard Q‐Q‐plot technique [ Wilk and Gnanadesikan , ], suggesting that fractional Gaussian noise (fGn) is a proper model for the LRM in these data [ Beran , ].…”

Is there long‐range memory in solar activity on timescales shorter than the sunspot period?

“…Since the correlation between the solar cycle variation of TSI and climate signals like global temperature anomaly (GTA) appears to be quite weak, some papers have drawn the attention to a possible “complexity linking” between solar activity and Earth climate which is proposed to be discernible by identification of a common long‐range memory process in the solar and climate signals, represented by a common Hurst exponent H [ Grigolini et al , 2002; Scafetta and West , 2003, 2005, 2008; Scafetta et al , 2004]. This view was criticized by us in a recent paper [ Rypdal and Rypdal , 2010a], which triggered a comment by Scafetta and West [2010] and a reply [ Rypdal and Rypdal , 2010b]. Our view is that trends, like the sunspot cycle in solar signals and multidecadal oscillations superposed on a rising trend in global temperature signals, will create spuriously high Hurst exponents.…”

TheEregion at 69°N, 19°E: Trends, significances, and detectability

“…For 0.5 < H < 1 the data is a colored noise with positive and algebraically decaying autocorrelations. Following the structure function analysis described by Rypdal and Rypdal [2010] we make the estimate H = 0.84. The analysis fails to reveal any clear periodicities, which would indicate inadequate exclusion of the deterministic component of f o E , giving support for our high‐pass filter followed by seasonal climatology subtraction strategy for identification of the stochastic component.…”