Cosmogenic radionuclides are more and more used in solar activity reconstructions. However, the cosmogenic radionuclide signal also contains a climate component. It is therefore crucial to eliminate the climate information to allow a better interpretation of the reconstructed solar activity indices. In this paper the method of principal components is applied to 10Be data from two ice cores from opposite hemispheres as well as to 14C data from tree rings. The analysis shows that these records are dominated by a common signal which explains about 80% of the variance on multi decadal to multi millennial time scales, reflecting their common production rate. The second and third components are significantly different for 14C and 10Be. They are interpreted as system effects introduced by the transport of 10Be and 14C from the atmosphere where they are produced to the respective natural archives where they are stored. Principal component analysis improves significantly extraction of the production signal from the cosmogenic isotope data series, which is more appropriate for astrophysical and terrestrial studie

Abreu, J.

Beer, J.

Christl, M.

Kubik, P.

Steinhilber, F.

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Space Sci Rev (2013) 176:343–349DOI 10.1007/s11214-011-9864-y10Be in Ice Cores and 14C in Tree Rings: Separationof Production and Climate EffectsJ.A. Abreu · J. Beer · F. Steinhilber · M. Christl ·P.W. KubikReceived: 4 October 2010 / Accepted: 2 December 2011 / Published online: 3 January 2012© Springer Science+Business Media B.V. 2011Abstract Cosmogenic radionuclides are more and more used in solar activity reconstruc-tions. However, the cosmogenic radionuclide signal also contains a climate component. Itis therefore crucial to eliminate the climate information to allow a better interpretation ofthe reconstructed solar activity indices. In this paper the method of principal componentsis applied to 10Be data from two ice cores from opposite hemispheres as well as to 14Cdata from tree rings. The analysis shows that these records are dominated by a commonsignal which explains about 80% of the variance on multi decadal to multi millennial timescales, reflecting their common production rate. The second and third components are sig-nificantly different for 14C and 10Be. They are interpreted as system effects introduced bythe transport of 10Be and 14C from the atmosphere where they are produced to the respectivenatural archives where they are stored. Principal component analysis improves significantlyextraction of the production signal from the cosmogenic isotope data series, which is moreappropriate for astrophysical and terrestrial studies.Keywords Cosmic rays · Cosmogenic isotopes · Principal component analysis1 IntroductionCosmogenic radionuclides stored in natural archives such as 10Be in ice cores and 14C intree rings have proven to be very useful in reconstructing past solar activity (Vonmoos et al.Electronic supplementary material The online version of this article(doi:10.1007/s11214-011-9864-y) contains supplementary material, which is available to authorizedusers.J.A. Abreu ()ETH Zürich, Institut für Geophysik, Zurich, Switzerlande-mail: jose.abreu@erdw.ethz.chJ.A. Abreu · J. Beer · F. SteinhilberEAWAG, Dübendorf, SwitzerlandM. Christl · P.W. KubikLaboratory of Ion Beam Physics, ETH Zürich, Zurich, Switzerland344 J.A. Abreu et al.2006) and changes in the geomagnetic field intensity over many millennia (Muscheler et al.2005). At present, cosmogenic radionuclides are the only proxy to significantly extend therecord of solar activity which is restricted to the past 400 years of sunspot observations. Theyoffer the unique opportunity not only to study the long-term history of solar activity (Solankiet al. 2004; Vonmoos et al. 2006; Steinhilber et al. 2008) and solar forcing (Steinhilber etal. 2009), but also to make predictions about future trends in solar variability (Abreu et al.2008). However, the cosmogenic radionuclide signal contains also a climate component in-troduced by the transport of the radionuclides from the atmosphere where they are producedto the archive where they are stored. In order to make full use of the large potential of cosmo-genic radionuclides the climate signal must be removed. Fortunately, while both nuclides areproduced in a similar way, the response of the 10Be and the 14C systems to climate variationsis very different by virtue of their different geochemical properties. 14C enters the global car-bon cycle, whereas 10Be is removed within 1–2 years from the atmosphere by precipitation.Thus, comparing both radionuclides makes it possible to distinguish between climate in-duced and production (solar/geomagnetic) variations. Since this idea was first put forwardby Siegenthaler and Beer (1988), many authors have compared 14C and 10Be records andconfirmed the presence of a dominant common signal of solar/geomagnetic origin as wellas a less dominant climate component in cosmogenic radionuclides (e.g. Beer et al. 1988;Bard et al. 1997; Muscheler et al. 2004; Usoskin et al. 2009). In this article, we go an stepfurther and propose to apply principal component analysis (PCA) to 10Be from ice coresand 14C from tree rings in order to decompose them into a production and a climate sig-nal.2 10Be and 14C Systems2.1 The Production of Cosmogenic RadionuclidesCosmic rays are composed roughly of 90% protons, 9% helium nuclei, and 1% of heaviernuclei. When these highly energetic primary particles of galactic cosmic rays interact withatmospheric N and O, a chain of secondary particles is generated which is responsible forthe production of cosmogenic radionuclides. There are two main processes which modu-late the production rate of cosmogenic radionuclides in the atmosphere: changes in solaractivity and changes in the geomagnetic field intensity. Since 10Be and 14C are produced bythe same nucleonic secondaries of the cosmic ray induced atmospheric cascade, thereforetheir production signals are very similar. However, this production signal is modified by cli-mate induced effects on the transport from the atmosphere into the respective archives asdiscussed in the next section.2.2 10Be and 14C in the Climate SystemFigure 1 illustrates the similarities and differences between 10Be and 14C radionuclides inthe Earth’s system. After production, 14C oxidizes to CO2 and enters in the carbon cycle.Within the carbon cycle, 14C gets involved in exchange processes among the atmosphere, thebiosphere and the ocean. Its atmospheric residence time of about 8 years regarding exchangewith the ocean is long enough that it can be considered as globally well mixed (Siegenthaleret al. 1980). In contrast, 10Be has an atmospheric residence time of 1 to 2 years. The factthat 14C enters the carbon cycle constitutes a fundamental difference between the measuredsignal in tree rings and the 10Be signal measured in ice cores. The carbon cycle acts like10Be in Ice Cores and 14C in Tree Rings: Separation of Production 345Fig. 1 10Be and 14C in theEarth’s system. Similarities: Bothradionuclides are produced in thesame way, modulated by changesin solar activity and geomagneticfield intensity. Differences: Afterproduction, 10Be becomesattached to aerosols and isremoved from the atmosphereafter a mean residence time of 1to 2 years, while 14C enters thecarbon cycle. Therefore, climatechanges influence the tworadionuclides differentlyFig. 2 a: 14C (per mil) as measured in tree rings. b: Standardized (i.e., subtracting the mean, then dividingby the standard deviation) of 14C production rate calculated from 14C (per mil) by using a carbon cyclemodel. c: Standardized 10Be concentrations (GRIP ice core) after being linearly interpolated to 1 year andlow-pass filtered with a cutoff 40 years. d: Standardized 10Be fluxes (GRIP ice core) after being linearlyinterpolated to 1 year and low-pass filtered with cutoff 40 yearsa filter changing the original amplitude and phase of the 14C production signal (Peristykhand Damon 2003). As a consequence, direct comparison between 14C measured in treerings with 10Be measured in ice cores is not informative. We must first remove the effectof the carbon cycle on 14C. Figure 2a shows 14C as measured in tree rings (Reimer etal. 2004). Figure 2b shows the corresponding 14C production rate calculated after applyingthe carbon cycle model by Oeschger et al. (1975). Figure 2c shows the 10Be concentrationsas measured in ice cores whereas Fig. 2d shows the corresponding 10Be flux. Comparisonof the four panels shows clearly that 10Be reflects changes in production rate much more346 J.A. Abreu et al.directly than 14C. Furthermore, modelling shows that even a climate change from the presentwarm period with high solar activity to the Maunder minimum period with very low solaractivity has only a small effect on the atmospheric transport and deposition processes of10Be, confirming that production is the dominant factor (Heikkilä et al. 2008). Our two mainworking hypotheses are: (I) the 10Be and 14C records can be interpreted as being composedof a production signal, which is common to both radionuclides, and (II) a system signal,which is, most likely, not a common signal. Due to the different geochemical properties thecombination of these two cosmogenic radionuclides in a PCA study provides a powerfultool to disentangle production and system effects.2.3 The DataIn the present work we use 10Be measured in EDML (Ice core drilled in the frameworkof the European Project for Ice Coring in Antartica (EPICA); Steinhilber et al. 2011 (sub-mitted)) and GRIP (Greenland Ice Core Project; Yiou et al. 1997) ice cores and 14C pro-duction derived from tree rings (INTCAL04; Reimer et al. 2004). The records employedin the analysis cover a common period of 8180 years from 1210 BP to 9390 BP (740AD to 7440 BC). The averaged temporal resolution of the EDML time series is 4–5years. The GRIP data have an average temporal resolution of 2–7 years. The 10Be recordswere linearly interpolated to 1 y, resampled to 10 y, and 40 y low-pass filtered. The 10Befluxes were calculated from 10Be concentrations and the corresponding accumulation rates(Flux = density of ice ∗ accumulation rate ∗ concentration). The 14C record has a constanttime resolution of 10 years and was 40 y low-pass filtered.Based on the previous discussion, we assume that the three data sets are composed of aproduction signal P (t), as well as a system effect signal S(t). P (t) takes into account themodulation effect of the Sun and the geomagnetic field whereas S(t) represents the effectthat the climate exerts on the radionuclides including noise10Begrip(t) = P (t) + S1(t),10Beedml(t) = P (t) + S2(t),14C(t) = P (t) + S3(t),where the subscripts indicate that the radionuclides are influenced differently by the climate.Additionally, the Si(t) terms may be written asSi(t) = Si[K(t)],where K(t) stands for climate, an idealized variable which takes into account the temporalevolution of the climate. If the climate remains unchanged, then 14C changes must be equalto 10Be changes. As can be seen in Fig. 3 (only the interval 4400 to 5800 BP is shown) thethree curves are over all very similar, but there are some differences, which must be due tochanges in the climate system. To separate the data into two components, we assume thatP (t) and Si(t) are uncorrelated. This assumption is supported by the following arguments:(1) the production does not depend on the climate and (2) although the climate componentsmay correlate through solar modulation slightly with the production, climate change affectsthe 14C and 10Be systems very differently due to their different geochemical behaviors.10Be in Ice Cores and 14C in Tree Rings: Separation of Production 347Fig. 3 Standardized timeseriesof 10Be and 14C data after beinglinearly interpolated to 1 year,resampled with 10 years, andlow-pass filtered with a cutoff 40years. Here we only depict theinterval 4400 to 5800 BP to showthe structure of the data3 Separation of Production and System Effects Using PCAGiven the set of p correlated time series (X1(t),X2(t),X3(t), . . . ,Xi(t), . . . ,Xp(t)) (in thepresent case p = 3, two 10Be records and one 14C record), we can use PCA to find a newset of uncorrelated time series Cj(t), j ≤ p such as the original p time series Xi (t) can bedecomposed as a linear combination of them, i.e.Xi(t) =∑jαi,jCj (t) (1)where1. αi,j = σ(Xi)R(Cj ,Xi)/λ0.5j with R(Cj ,Xi) the correlation coefficient between the timeseries Ci and Xj and σ is the standard deviation.2. λj are the eigenvalues of the covariance corresponding to the data matrix whose elementsare Cov(Xi,Xj ). They give the fraction of the total variance explained by the time seriesCj .The new time series Cj are known as the principal components (Jolliffe 2002, see also theelectronic supplementary material).4 ResultsTable 1 shows the calculated coefficients αi,j , i.e. the contribution of component j to nuclidei as expressed by (1). Additionally, the squared correlation coefficients along with the eigen-values are shown. The eigenvalue corresponding to the first component explains 65% of thetotal variance whereas the second and third components are responsible for 22% and 14% ofthe total variance, respectively. Clearly, all the original data sets are well correlated with thefirst principal component supporting our hypothesis (I) that production dominates both ra-dionuclides. Production changes are indeed responsible for most of the variance in the data.We attribute it to solar activity as well as to geomagnetic field variations.1 It is remarkablethat the α2 coefficient corresponding to 14C is significantly smaller than the correspondingα2 of the two 10Be records. We note that1The effect of the Earth’s magnetic field, can be removed by taking into account paleorecords of the geomag-netic field and production calculations (Masarik and Beer 2009).348 J.A. Abreu et al.Table 1 αi,j , R(Cj ,Xi)2 andλi before synchronizationα1 α2 α310Begrip 0.54 0.79 0.2910Beedml 0.57 −0.60 0.5614C 0.62 −0.13 −0.77R2 R2 R210Begrip 0.55 0.41 0.0410Beedml 0.64 0.23 0.1314C 0.74 0.01 0.24λ1 λ2 λ365% 22% 14%Table 2 αi,j , R(Cj ,Xi)2 andλi after synchronizationα1 α2 α310Begrip 0.58 0.72 0.3810Beedml 0.58 −0.70 0.4214C 0.57 −0.02 −0.82R2 R2 R210Begrip 0.77 0.18 0.0610Beedml 0.77 0.16 0.0714C 0.72 0.00 0.27λ1 λ2 λ376% 11% 13%1. the variance not explained by the first principal component for 14C is explained only bythe third component and2. the variance not explained by the first principal component for both 10Be records ismainly explained by the second component.This confirms our initial hypothesis (II) that climate affects the 14C and 10Be systems differ-ently. Hence, we attribute the second and third components to the climate effect on the 14Cand 10Be systems, respectively.The outcome of the PCA analysis depends critically on the accuracy of the time scalesof the involved cosmogenic radionuclide records. While the time scale of 14C is based ondendrochronology and therefore accurate to one year, the uncertainty of the time scales ofthe ice cores increases with age to a few decades. This is due to the fact that a perfect annualmarker as in the case of trees is missing. In addition ice is flowing which leads to a decreasein the annual layer thickness with increasing depth. As a result of small time shifts, PCAinterprets part of the common production changes as a different signal and assigns it to thesecond component. To test this effect, we slightly adjusted the two 10Be time scales withinthe stated uncertainties to the 14C time scale using wiggle matching (Ruth et al. 2007).The adjustments relative to the original time scales are smaller than 30 y for EDML and10Be in Ice Cores and 14C in Tree Rings: Separation of Production 349smaller than 50 y for GRIP. Now the first principal component explains 76% and the secondcomponent 11% of the total variance respectively (Table 2). However, the structure of thedata remains relatively unchanged. The α2 coefficient for 14C is one order of magnitudesmaller than the corresponding values for 10Be. The third component is still the main non-production source of variability in 14C, whereas the second component is the main non-production source of variability for both 10Be data sets. We notice that in both calculationsthe sign of α2 for GRIP and EDML are different. This is a mathematical consequence of thePCA method because of the limited number of 10Be proxies used.5 ConclusionsThe method of PCA confirms that 10Be and 14C records which were all low-pass filteredwith 40 years are dominated by a common signal which reflects the production rate andexplains 76% of the variance on multi decadal to multi millennial time scales. The secondand third components account for about 24% of the variance, which is significantly differentfor 14C and 10Be. This can be explained as system effects introduced by the transport ofthe respective radionuclides from the atmosphere where they are produced to the archivewhere they are stored (tree rings in the case of 14C and ice cores in the case of 10Be).The presence of such a high common variability is remarkable if we take into account thatthe 10Be records are from different hemispheres, and that 10Be and 14C are characterizedby completely different geochemical systems (compare panels (a) and (c) in Fig. 2). Wehave focused on the decomposition of cosmogenic radionuclides into production and systemeffects. Since cosmogenic radionuclides are the only tool to reconstruct past solar activityindices such as sunspots and total solar irradiance, it is crucial to eliminate the climatecomponent. PCA is an adequate tool to achieve this aim.Acknowledgements This work was financially supported by the Swiss National Science Foundation, andNCCR Climate–Swiss climate research.ReferencesJ.A. Abreu, J. Beer, F. Steinhilber, S.M. Tobias, N.O. Weiss, Geophys. Res. Lett. 35, L20109 (2008)E. Bard, G.M. Raisbeck, F. Yiou, J. Jouzel, Earth Planet. Sci. Lett. 150(3–4), 453–462 (1997)J. Beer, U. Siegenthaler, H. Oeschger, G. Bonani, R.C. Finkel, Nature 331, 675–679 (1988)U. Heikkilä, J. Beer, J. Feichter, Atmos. Chem. Phys. 8, 2797–2809 (2008)I.T. Jolliffe, Principal Component Analysis, 2nd edn. Springer Series in Statistics (Springer, New York, 2002)J. Masarik, J. Beer, J. Geophys. Res. 114, D11103 (2009)R. Muscheler, J. Beer, G. Wagner, C. Laj, C. Kissel, G.M. Raisbeck, F. Yiou, P.W. Kubik, Earth Planet. Sci.Lett. 219(3–4), 325–340 (2004)R. Muscheler, J. Beer, P. Kubik, H.-A. Synal, Quat. Sci. Rev. 24(16–17), 1849–1860 (2005)H. Oeschger, U. Siegenthaler, U. Schotterer, A. Gugelmann, Tellus 27(2), 168–192 (1975)A.N. Peristykh, P.E. Damon, J. Geophys. Res. 108, 1003 (2003)P.J. Reimer et al., Radiocarbon 46(3), 1029–1058 (2004)U. Ruth et al., Clim. Past 3(3), 475–484 (2007)U. Siegenthaler, M. Heimann, H. Oeschger, Radiocarbon 22(2), 177 (1980)U. Siegenthaler, J. Beer, in Secular Solar and Geomagnetic Variations in the Last 10,000 Years, ed. by F.R.Stephenson, A.W. Wolfendale (Kluwer Academic, Dordrecht, 1988), p. 315S.K. Solanki, I.G. Usoskin, B. Kromer, M. Schüssler, J. Beer, Nature 431, 1084–1087 (2004)F. Steinhilber, J.A. Abreu, J. Beer, Astrophys. Space Sci. Trans. 4, 1–6 (2008)F. Steinhilber, J. Beer, C. Fröhlich, Geophys. Res. Lett. 36, L19704 (2009)F. Steinhilber, et al., 9400 years of cosmic radiation and solar activity from ice cores and tree rings. Proc.Natl. Acad. Sci. USA (2011, submitted)I.G. Usoskin, K. Horiuchi, S. Solanki, G.A. Kovaltsov, E. Bard, J. Geophys. Res. 114, A03112 (2009)M. Vonmoos, J. Beer, R. Muscheler, J. Geophys. Res. 111, A10105 (2006)F. Yiou et al., J. Geophys. Res. 102(C12), 26783–26794 (1997)

10Be in Ice Cores and 14C in Tree Rings: Separation of Production and Climate Effects

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10Be in Ice Cores and 14C in Tree Rings: Separation of Production and Climate Effects

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