Physics and Chemistry of the Earth 31 (2006) 99–108 www.elsevier.com/locate/pce Solar activity, Earth’s rotation rate and climate variations in the secular and semi-secular time scales S. Duhau * Facultad de Ciencias Exactas, Departamento de Fı´sica, Universidad de Buenos Aires, Argentina Received 17 January 2005; accepted 18 March 2005 Available online 29 March 2006 Abstract By applying the wavelet formalism to sudden storm commencements and aa geomagnetic indices and solar total irradiation, as a proxy data for solar sources of climate-forcing, we have searched the signatures of those variables on the Northern Hemisphere surface temperature. We have found that cyclical behaviour in surface temperature is not clearly related to none of these variables, so we have suggested that besides them surface temperature might be related to Earth’s rotation rate variations. Also it has been suggested that in the long-term Earth’s rotation rate variations might be excited by geomagnetic storm time variations which, in turn, depends on solar activity. The study of these phenomena and its relationships is addressed in the present paper. With this purpose we perform an analysis of the evolution during the last 350 years of the signals that conform the 11-year sunspot cycle maxima envelope for different time scales. The result is applied to analyze the relationship between long-term variations in sunspot number and excess of length of day; and to unearth the signature in surface temperature of this last from that of sudden storm commencement and aa geomagnetic indices and total solar irradiation. As solar dynamo experiments transient processes in all the time scales from seconds to centuries, Fourier analysis and its requirement for the process to be stationary is likely to produce spurious periodicities. We resort instead to wavelet formalism. By this representation we found that sunspot maxima envelope for the last 350 years may be described by means of the superposition of two cycles – a decadal and a semi-secular one – and a secular trend. And that the changing amplitude and phase of the cycles are well reconstructed using the superposition of two wavelets with nearby periods. The strong temporal changes in amplitude of the cycles facilitate to detect its phase in a given time series. It is found that a strong semi-secular cycle in the sunspot maxima envelope that started during the 1705 chaotic tran- sition having its maximum amplitude at the Dalton minimum, was mapped 94 years later in Earth’s rotation rate and simultaneously in surface temperature. Also, there was a decrease (increase) of 0.022 °C for each millisecond of decrease (increase) in the Earth’s rotation period for the semi-secular cycle as well as the secular trend. Ó 2006 Published by Elsevier Ltd. Keywords: Earth rotational variations; Origin and modelling, of the magnetic field, dynamo theory; Geomagnetic secular variation; Climatology 1. Introduction climate changes. They based this suggestion in the fact that trends towards colder climates with weakened general Besides anthropogenic and solar source of climate-forc- atmospheric circulation goes with slower Earth’s rotation ing, Lambeck and Cazenave (1976) proposed the angular rate. In agreement with this Courtillot et al. (1982) found momentum transferred to the atmosphere by the solid that variations in Earth rotation rate and global surface Earth as another possible source, in the long-term, of temperature time series from 1880 to 1975 are connected (cross-correlation coefficient = 0.85) with surface tempera- tures lagging Earth’s rotation rate by 5 year). Periods of * Fax: +54 51 011 4576 3357. increasing zonal troposphere circulation and increasing E-mail address: [email protected] surface temperatures are found that they correspond 1474-7065/$ - see front matter Ó 2006 Published by Elsevier Ltd. doi:10.1016/j.pce.2005.03.006 100 S. Duhau / Physics and Chemistry of the Earth 31 (2006) 99–108 to Earth’s mantle acceleration, while deceleration of this and Cazenave (1976) indicates that these changes in angu- last corresponds to decrease in zonal circulation and lar momentum of the crust are transferred in a few years to surface temperature. More recently, Mo¨rner (1999) sug- the atmosphere–hydrosphere system. Therefore, if long- gested that the angular momentum of the hydrosphere term variations in Earth’s rotation rate are the source of might play a role in climate warming (cooling) by the climate changes, long-term variations in sunspot maxima deceleration (acceleration) in Earth’s rotation and Duhau envelope will appear by about 94 years later in surface (2003c) found that a 70% of the long-term northern hemi- temperature. sphere surface temperature anomalies (NHT) increase Further evidences on the relationship between solar during the period 1868–1960 might be attributed to sudden activity, Earth’s rotation rate and surface temperature are commencement storm increases in intensity and frequency explored in the present work. Since other sources of cli- (as measured by SSC geomagnetic index (Duhau, 2003b)) mate-forcing have strong signatures in surface temperature and the remainder 30% to total solar irradiance (TSI), a careful study of the long-term evolution of the related but cyclical behaviour in NHT is not clearly related neither time series is necessary to unambiguously unearth these to SSC index nor to TSI, so she suggested that besides these long-term relationships between solar activity, Earth’s variables surface temperature is influenced by Earth’s rotation rate and surface temperature. rotation rate variations as suggested by Lambeck and There are evidences of the occurrence of transient phe- Cazenave. nomena in solar dynamo; even in time scales larger than It is well established that the origin of the short-period a decade (see e.g. Duhau and Chen, 2000a, 2002). Fourier variations (below the decadal scale) in the Earth’s rotation analysis assumes that the time series is the result of a rate is the transfer of angular momentum from the atmo- stationary process. Therefore, as there are transient phe- sphere to the solid Earth (see e.g. Eubanks, 1993; Dickey nomena in solar activity, Fourier analysis of solar and et al., 1994). For example, the 1982–1983 El Nin˜o/South- solar–terrestrial time series is likely to produce spurious ern Oscillation (ENSO) event was accompanied by the periodicities and inconsistency in the results. This problem largest interannual variation in the Earth’s rotation period has lead to a ‘‘cycle-mania’’ that obscures the searching for (Dickey et al., 1994; Chao, 1999), lagging Earth rotation solar–climate relationship (see e.g. Hoyt and Schatten, period to ENSO axial momentum by 2 months. To pre- 1997). A suitable tool to solve this problem, is the wavelet serve the total angular momentum of the atmosphere–solid transform formalism (see e.g. Rioul and Vetterli, 1991; Earth system during this event, the changes on atmosphere Torrence and Compo, 1998; Antoine, 1999). angular momentum were compensated by changes in Moreover, our main task is to accurately decompose the Earth’s angular momentum. However, a residual of 46 ± studied signals in the cycles that conform a quasi-periodic 6 ls (over a total of 0.5 ms) still remained. This residual state in the different time scales. The wavelet formalism is was suggested to be due to a contribution of oceanic specially suited for this task since a given cycle in the strong angular momentum. turbulence regimen on which solar dynamo system oper- For larger time scales Earth’s rotation rate variations ates, has strong variations in intensity that go with appre- are due to an interchange of momentum between the ciable changes in periodicity. Therefore as a cycle evolves in Earth’s core with the mantle (Vestine, 1953; Jackson time never repeat itself with the same shape. We may rep- et al., 1993). A mechanism by which geomagnetic storm resent this behaviour by the wavelet formalism by super- long-term variations might excite geomagnetic field and posing a few wavelet component with different Fourier motions in the liquid core and so Earth’s rotation rate vari- periods (Duhau, 2003a and references therein). We need ations by the topographic torque (Hide, 1969) excerpted by more than a Fourier period to be able to reproduce the the outer boundary of the liquid core on the mantle was change of its periodicity as the cycle evolves. So this for- proposed by Duhau and Martinez (1995). As geomagnetic malism provides a simple and precise tool to individualise storm intensity depends on solar activity level this mecha- the time scales on which operates a given cycle and com- nism implies that long-term variations in Earth’s rotation pare its signature in different time series. rate depends also on solar activity variations. In a strong turbulent regimen of a fluid the amplitude of Total angular momentum must be preserved in the cou- the cycles change so fast that their modulation is well rep- pled atmosphere–hydrosphere–mantle–core system. For resented by a resonant function, that just for simplicity we short period the atmosphere drives the Earth and for large have selected to be a gaussian (Sudan and Kiskenin, 1977; period the core–mantle system drives the atmosphere– Duhau and Hurtado de Mendoza, 1996). Therefore the hydrosphere system. The precise limit between the time Morlet wavelet functions that are gaussian wave packets scales that correspond to each case has not been deter- will be used in our analyses. mined yet. We start with the application of the wavelet formalism Duhau and Martinez (1995) found that the 5-year run- to a full description of the evolution during the last ning mean of Earth’s rotation rate followed variations in 350 years of the cycles that constitute the envelope of the the 11-year running mean Wolf sunspot number during 11-year sunspot cycle maxima.