Variations in solar magnetic activity during the last 200 000 years: is there a Sun–climate...

Variations in solar magnetic activity during the last200 000 years: is there a Sun^climate connection?

Mukul Sharma �

Department of Earth Sciences, Dartmouth College, Hanover, NH 03755, USA

Received 25 September 2001; received in revised form 18 January 2002; accepted 29 January 2002

Abstract

The production of 10Be in the Earth’s atmosphere depends on the galactic cosmic ray influx that, in turn, is affectedby the solar surface magnetic activity and the geomagnetic dipole strength. Using the estimated changes in 10Beproduction rate and the geomagnetic field intensity, variations in solar activity are calculated for the last 200 ka.Large variations in the solar activity are evident with the Sun experiencing periods of normal, enhanced andsuppressed activity. The marine N

18O record and solar modulation are strongly correlated at the 100 ka timescale. It isproposed that variations in solar activity control the 100 ka glacialînterglacial cycles. However, the 10Be productionrate variations may have been under-estimated during the interval between 115 ka and 125 ka and may have biasedthe results. Future tests of the hypothesis are discussed. 4 2002 Elsevier Science B.V. All rights reserved.

Keywords: solar activity; climate change; Be-10; cosmogenic elements; magnetic ¢eld; Milankovitch theory; solar cycles

1. Introduction

The way the solar surface magnetic activity af-fects the Earth’s climate on short timescales (daysthrough centuries) constitutes an area of activeresearch [1] with postulated mechanisms that in-clude: (1) changes in solar luminosity as the Sunbecomes magnetically more active [2^5], and (2)variations in solar activity leading to largechanges in solar ultraviolet radiation [6] that, inturn, a¡ects the stratospheric ozone content [7],and (3) modulated galactic cosmic rays in£uenc-ing the cloud formation via inducing changes in

the tropospheric ion production [8^10]. Evidencelinking solar activity to climate change during thelast millennium has also accumulated on a 100-yrtimescale. Friis-Christensen and Lassen [11] re-port a close correspondence in the last 100 yrbetween average Northern Hemisphere tempera-tures and changes in the length of the solar mag-netic cycle. An often-cited example is that of theMaunder Minimum (1645^1715 AD) correspond-ing to the Little Ice Age during which no sunspotactivity was observed [12]. Using the combined14C and 10Be records, a solar activity minimumhas been inferred for this period centered at1690 AD [13,14]. Other solar activity minima cen-tered at 1060, 1320 (Wolf), 1500 (Spo«rer), and1820 AD [14]. Also, the solar activity is inferredto be high during the Medieval Warm Period(12th and 13th centuries) [15,16]. On the basis of

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Earth and Planetary Science Letters 199 (2002) 459^472

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variations observed in the 14C contents of treerings and their growth, Suess and co-workers in-ferred that the solar activity varies with a 200-yrcycle [17,18], which also controls the climate [19].Stuiver and Braziunas [20] investigated a 9600-yr-long high precision 14C record and found that theSun is oscillating with a fundamental frequency of1/420 yr31 with the second and third harmonicscorresponding to 218- and 143-yr periods, respec-tively. These workers suggest that there may be aSun^climate relationship for the third harmonic.A recent paper concludes that surface winds andsurface ocean hydrography in the sub-polarNorth Atlantic have been in£uenced by 1500-yroscillations in solar activity through the entireHolocene [21]. Does the solar activity also varyon a longer timescale? If so, what is its relation-ship to long-term climate change? In this paper Iexplore these two questions by estimating the rel-ative variations in solar modulation of galacticcosmic rays (GCR), assuming that the modulationdepends directly on the mean interplanetary mag-netic ¢eld generated by solar surface magnetic ac-tivity (see a recent review [22]).

2. Theory

Variations in the solar surface magnetic ¢eld,which are carried out by the solar wind andstretch across the heliosphere, inversely modulatethe intensity of the GCR incident on the helio-spheric boundary (e.g., [22]). The cosmic ray par-ticles reaching the Earth are further a¡ected bythe geomagnetic ¢eld, which de£ects them de-pending on their energy and angle of incidence.For each angle of incidence there is a cut-o¡ en-ergy (‘rigidity’) below which the incoming particlecannot interact with the Earth’s atmosphere.Modulation of GCR particles with energies aboveV1 GeV/nucleon leads to variations in the terres-trial production rates of cosmogenic radionuclidessuch as 14C and 10Be, formed due to the interac-tion of cosmic ray particles with atmospheric ni-trogen and oxygen [23]. It follows that by deter-mining the long-term variations in the productionrates of cosmogenic radionuclides one can assesstemporal changes in the solar surface magnetic

activity, provided that the variations in geomag-netic-dipole strength for the same time period areknown, a functional relationship between solarmodulation of cosmic rays, geomagnetic-dipolestrength and cosmogenic radionuclide productionrate is available, and the GCR £ux incident onthe heliospheric boundary has remained constantover the time period of interest.

Due to its long half-life (t1=2 = 1.5U106 yr) andrelatively simple geochemical cycle [24,25], 10Be isa cosmogenic radionuclide suitable for investigat-ing the long-term variations in solar magnetic ac-tivity. Masarik and Beer [26] have theoreticallycalculated the global average production rate of10Be for discrete values of geomagnetic ¢eldstrength and solar modulation. Fig. 1 shows therelationships between the global average produc-tion rate of 10Be (Q), the geomagnetic ¢eldstrength (M), and the solar modulation factor(P) (data from J. Masarik). All parameters havebeen normalized to their present-day values(shown by subscript ‘0’). The data plot along asurface and show that the 10Be production rate isinversely related to the geomagnetic ¢eld strengthand the solar modulation factor, the latter beingthe energy lost by cosmic ray particles while tra-versing the heliosphere and reaching the Earth’sorbit. There is a direct but not one-to-one rela-tionship between the solar modulation factor andsolar surface magnetic activity [23]. I approximatethe global average production rate of 10Be at atime ‘t’ normalized to present-day by a productof two functions F and G that are independent ofM and P, respectively:

QMtP t

QM0P 0

� �¼ f

P t

P 0;Mt

M0

� �WF

P t

P 0

� �MWG

Mt

M0

� �P

ð1Þ

The data obtained through the empirical func-tion thus ¢tted are plotted in Fig. 1 and show ageneral coherence with the data from Masarik,except when M/M0 and P/P0 are close to zero(R2 = 0.84). This function permits us to assessthe relative variations in solar modulation factorfor any time in the past for which the averageproduction rate of 10Be and the geomagnetic di-pole strength are available. In this paper I will


M. Sharma / Earth and Planetary Science Letters 199 (2002) 459^472460

estimate relative solar modulation for the last 200ka, assuming that the above relationship holds forthis time period by utilizing the existing compila-tions of past variations in 10Be production rateand geomagnetic-dipole strength. In order touniquely determine the variations in the solarmagnetic activity, it is necessary that the estab-lished long-term production rates of 10Be and cor-

responding variations in the geomagnetic-dipolestrength are ‘time-tuned’ to each other and thatneither of the records depends on parameters oth-er than the ones described above. As discussedbelow, while the best existing dataset will beused for the calculation of solar modulation fac-tor, high ¢delity data strictly satisfying the abovecriteria are not yet available.

3. Data

3.1. Geomagnetic ¢eld intensity variations

Most reliable information on the prevailinggeomagnetic ¢eld intensity comes from volcanicrocks. However, the volcanic rocks do not pro-vide a continuous record. Continuous recordshave been obtained from the natural remanentmagnetizations (NRM) of marine sediments [27^30]. The NRM signal of marine sediments can,however, be disturbed by variations in lithologicalparameters that are mostly climatically controlled.I will use an 800-ka synthetic record of relativevariations in geomagnetic ¢eld intensity (Sint-800)that has been reconstructed from stacking the re-sults of 33 marine sediment cores [30]. This recordincorporates the results of an earlier shorter ver-sion extended to the last 200 ka (Sint-200 [29]).Using volcanic records of absolute ¢eld intensitydata for the last 40 ka, this record has been con-verted to virtual axis dipole moments (VADMs).The Sint-800 shows an overall internal coherenceand no stable periodicity, indicating that distur-bances of the NRM signals in individual sedimentcores were minimized [30]. This record does notprovide data for the last 2 ka because the upper-most part of sedimentary records is not alwaysreliable as it may be a¡ected by coring (J. Guyo-do, written communication, 2000). For this timeperiod I will use the VADMs obtained from Ha-waiian lavas [31]. Fig. 2a shows the relative geo-magnetic ¢eld intensity normalized to present-day(M/M0). The geomagnetic ¢eld intensity appearsto have varied by a factor of three over the last200 ka with three excursions when the intensitybecame less than half of the present value(Fig. 2a).

Fig. 1. A three-dimensional plot giving theoretically expectedvariations in the atmospheric 10Be production rate as a func-tion of solar modulation factor and geomagnetic ¢eld inten-sity (black surface) [26]. A nearly identical relationship canalso be obtained using the data from Lal [23], but is notused here for calculations. As expected, the solar modulationand geomagnetic ¢eld intensity inversely a¡ect the produc-tion rate. The data can be ¢tted to a function with explicitdependence of the production rate over solar modulationand geomagnetic ¢eld intensity (white mesh), with all param-eters normalized to their respective present-day values. Thefunction has the following form (see text):

QMtP t

QM0P 0

� �W

1aþ bðP t=P 0Þ

� �cþ ðMt=M0Þd þ eðMt=M0Þ

� �

where the constants aê were determined using the dataprovided by J. Masarik: a= 0.7476, b= 0.2458, c= 2.347,d= 1.077, and e= 2.274. This treatment permits calculation ofnormalized solar modulation at any time in the past forwhich the normalized 10Be production rate and relative geo-magnetic ¢eld intensity are speci¢ed.


M. Sharma / Earth and Planetary Science Letters 199 (2002) 459^472 461

3.2. 10Be production rates

In this study I will use previously estimatedvariations in 10Be production rate obtained fromdeep marine sediments. 10Be produced in the at-mosphere is quickly attached to aerosols, andthen removed via dry and wet precipitation. Theatmospheric residence time of 10Be is of the orderof a year. The maximum atmospheric depositionof 10Be takes place between 40‡ and 50‡ latitude[32]. The residence time of 10Be in the deep oceansappears to be long enough to homogenize thelatitudinal fallout pattern. The oceanic processescontrolling the transport of particle reactive spe-cies to the ocean £oor should then determine the10Be distribution in marine sediments. The record

of 10Be £ux into deep marine sediment may po-tentially be compromised from the following cli-mate-related e¡ects: (1) sedimentary focusing andwinnowing and (2) recycled 10Be contributionfrom continental mineral dust. The sedimentaryredistribution e¡ects can be eliminated using230Thex normalization [33,34]. Additional 10Beintroduced into ocean basins with detrital materi-al from the continents may bias a purely ¢eldintensity-controlled stacked global 10Be £ux intomarine sediments if its £ux is related to climate.Typical 10Be concentration in the continentaldust = 5U108 atoms/g and marine cores = 3.5U109 atoms/g, indicating that large contributionsfrom continental dust would be needed to havea signi¢cant impact on the 10Be inventory of themarine core. However, it could be imagined thatglobal hydrography and ocean circulation be-tween glacial and interglacial periods may havebeen signi¢cantly di¡erent, impacting not onlythe latitudinal fallout pattern but also the resi-dence time of 10Be in the deep oceans. Thiswould, of course, introduce systematic errors inthe estimated 10Be production rates for glacialand interglacial times. The above e¡ects couldbe removed by using a stack of several sedimentcores from di¡erent parts of the world.

I will utilize the recently established globallystacked record of 230Thex-normalized 10Be deposi-tion in deep marine sediments that yields relativevariations in 10Be production rate over the past200 ka [34]. Fig. 2b shows the globally stackedproduction rate of 10Be normalized to present-day (Q/Q0). It is evident that the 10Be productionrate varied by more than a factor of two over thepast 200 ka. This record was used by Frank et al.[34] to estimate past variations in geomagnetic¢eld strength assuming a constant solar magneticactivity. Kok [35] has noted that whilst the spec-trum of past variations in geomagnetic ¢eldstrength thus obtained is similar to the indepen-dently determined stack of relative paleointensi-ties ( = Sint-200 [29] ; see below), the record alsostrongly resembles the N

18O curve for the sametime period. This observation has led him to sug-gest that climatic in£uences have not been aver-aged out in the 10Be compilation. Frank [36],however, has argued that the paleointensity re-

Fig. 2. (a) Globally stacked record of relative geomagnetic¢eld intensity obtained from NRM of marine sediments(Sint-800) [30]. The record has been calibrated for the abso-lute paleomagnetic intensity by calibrating it against theVADM data for the Hawaiian lavas. For the last 2 ka I usethe Hawaiian lava data [31]. All data have been normalizedto the present-day VADM = 8U1022 A m2. (b) Globallystacked record of 230Thex-normalized 10Be deposition in deepmarine sediments yielding relative variations in 10Be produc-tion rate for the last 200 ka [34].



cords are not signi¢cantly a¡ected by climatic fac-tors, although there may still be a ‘residual cli-matic’ signal in the record of the productionrate of 10Be (M. Frank, personal communication,2000). This issue is investigated in Fig. 3, wherethe inverse of the normalized 10Be production rateis plotted against time and compared with thestacked oxygen-isotope record of the oceans [37].It is interesting that the gross features of the N

18Orecord can be reproduced by (Q/Q0)31 suggestingthat the estimated 10Be production rate was sys-tematically higher during the glacials and lowerduring the interglacials. This e¡ect could eitherbe real or due to problems with core selection.Lao et al. [33] have argued that there was a real30% increase in the 10Be production during thelast glacial maximum. In contrast, the observeddecrease in the 10Be production rate between115 and 125 ka may have been due to samplingof cores with uniformly reduced local 10Be rainrates [34]. The latter explanation was o¡ered,however, because Frank et al. [34] observed a sig-ni¢cant discrepancy between Sint-200 [29] andtheir reconstruction of relative paleointensities us-ing 10Be data. An alternative explanation could bethat the discrepancy has resulted from variationsin solar activity, which was assumed to be con-stant. However, to the extent that the relative res-idence times of 10Be and 230Th may have varied

between glacial and interglacial times [38], there isstill the issue of the extent to which 230Thex nor-malization is e¡ective in determining precise rela-tive variations in the 10Be production rate. Therainout rate of 10Be at a given site is ([34] andreferences therein) :

Rate ¼ ½10Be�U½MassAccumRate� ¼

½10Be�U L z230Th

� �ð2Þ

Here, L is the production rate of 230Th in thewater column, z is the water depth, and [10Be] isthe initial concentration of 10Be. A number ofcores in the 115^125-ka interval display anoma-lously high 230Thex that may have led to lowercalculated production rates of 10Be [36]. If true,this observation would constitute the main weak-ness of the stacked dataset and the results of thisstudy would be biased. Future data would beneeded to clarify this issue. An additional sourceof error in the global stack of 10Be productioncomes from the assumption that the water depthat the cores sites has remained constant and isequal to the present-day. However, this wouldlead to an overestimation of 10Be by only V6%or less during the glacial times when the depthwas lower.

Prior to proceeding further, I also need to en-sure that the observed variations in the 10Be pro-duction rate are not the result of the variations inthe sources of energetic particles. Studies of mete-orites and lunar samples have indicated that thelong-term averaged GCR £ux has remained essen-tially constant within 30% over time periods of104^107 yr [39,40]. Solar energetic protons (alsocalled solar cosmic rays, SCR) with energies v 35MeV can also produce 10Be. Because of the shield-ing by the geomagnetic ¢eld only a small percent-age of these particles induce nuclear reactions andthat too at the very top of the atmosphere. Atpresent, the SCR contribution to the atmospheric10Be production is 6 1% [41]. This situation may,however, change during times of extremely lowgeomagnetic intensities (see below). The 10Be pro-duction in the latter scenario may be assessed us-ing the Moon, which has no global magnetic ¢eld,

Fig. 3. Plot displaying the inverse of the relative 10Be pro-duction rate ( = (Q/Q0)31) plotted against time (solid curve)and compared with N

18O (dotted line) record. In this repre-sentation, time-periods with reduced 10Be production rate areshown as peaks. Remarkably, the function (Q/Q0)31 reprodu-ces gross features of N

18O record.



as an end-member. Recent studies of lunar silicatesamples have demonstrated that SCR £ux hasprovided about 10% of the 10Be production andmay have remained constant for the last severalhundred thousand years [42]. As the geomagnetic¢eld intensity has not been equal to zero over thepast 200 ka and the reaction cross-sections for16O(p,5pxn)10Be are similar to or somewhat high-er than those for 14N(p,4pxn)10Be at given ener-gies [43], the SCR contribution to 10Be productionmay be considered an upper limit for terrestrialatmosphere that predominantly contains nitrogen.

A third source of energetic particles is a super-nova explosion: propagating shock waves fromthe explosion may increase the GCR £ux at theheliospheric boundary [44]. Due to the short na-ture of this event, it would be noted as a sharppeak in a time series of 10Be production rate. In-deed, the presence of a 10Be peak in ice cores atV40 ka has been interpreted to be the result of asupernova [44]. Fig. 2b shows that the relativeproduction rate of 10Be gradually increased from50 ka, peaked at 36 ka, and then decreased tonear present-day values over the next V25 ka.However, these variations appear to follow con-comitant changes in geomagnetic ¢eld intensity(Fig. 2a), which is reduced to nearly half itspresent-day value at V40 ka. The variations in10Be production rate therefore appear not to bedue to changes in GCR £ux.

3.3. Time-tuning of the records

The cores used in both composite records havebeen dated using globally stacked oxygen-isotopestratigraphy [37] and thus both records are time-tuned to each other. However, in detail there canbe some age discrepancy between the two recordswith uncertainties introduced from various sour-ces, including the sampling rate and sedimenta-tion rate model used and the correlation to thereference value. For example, the ages in betweenthe two tie-points determined by oxygen-isotopestratigraphy were calculated using a linear sedi-mentation rate for Sint-800 and a 230Th constant£ux model for 10Be production. The estimated ageuncertainties in the records are, however, of theorder of 2^3 ka, and will not introduce large un-

certainties in the calculated solar modulation fac-tors.

4. Results

The estimated relative variations in the solarmodulation factor over the last 200 ka are plottedin Fig. 4. The uncertainties in the modulationfactor depend on the estimated uncertainties in10Be production and in geomagnetic ¢eld intensityand were calculated using the Monte Carlo tech-nique. The gross features of the solar modulationover the past 200 ka are: (1) the solar modulationover the last 200 ka has ranged from V0 to s 2,(2) for only one period during the last 200 ka doesthe P/P0 signi¢cantly exceed 1 (between 111 and125 ka), and (3) between 25 and 35 ka, and 175and 190 ka the P/P0 ratio was close to zero. It isevident that the Sun has experienced at least threeperiods, each of thousands of years duration, ofgreatly enhanced and suppressed activity (Fig. 4).In addition, it has also been close to its presentlevel of activity several times during the last 200ka. The estimated high solar modulation for thetime period between 111 and 125 ka is potentiallythe result of underestimated 10Be production ratesduring this interval due to anomalously high

Fig. 4. The normalized solar modulation factor calculatedfrom the records in Fig. 2 using the function in Fig. 1. Theplotted formal uncertainties are 1c standard deviations foreach data point. The uncertainties in the y-direction were cal-culated by propagating errors in the normalized productionrate and relative geomagnetic ¢eld intensity. The uncertain-ties in the x-direction were calculated assuming that the ageuncertainty in the records is of the order of 2 ka. The result-ing uncertainties in the x-direction are smaller than the sizeof the symbols.



230Thex in the cores (Fig. 2b; see above). In orderto estimate the sensitivity of P/P0 calculations forthis time interval, I calculated the 10Be productionrates for this interval by interpolating those at 110and 129 ka (see Fig. 2b). This led to on average a20% increase in the production rates. Using theinterpolated values I ¢nd that the resulting P/P0

ratios are not signi¢cantly di¡erent from 1.0.Fig. 4 also compares the normalized solar mod-

ulation factor with the N18O record [37]. Note that

the two spectra are much better correlated thanthe function based solely on 10Be production (Fig.3). Also, the above correlation results when thecorrect relationship between P/P0, M/M0 and Q/Q0 (Eq. 1) is utilized and is the reason behind theapparent correlation observed by Kok [35] be-tween N

18O and M, where the latter was obtainedfrom Q by assuming a constant P. As the 18Orecord is a proxy of the global ice volume and,in turn, of the Earth’s mean surface temperature,the correlation between P/P0 and N

18O in Fig. 4suggests that during the past 200 ka the Earth hasexperienced a warmer climate whenever the Sunhas been magnetically more active. Also, at theheight of the last glacial maximum the solar ac-tivity was suppressed. These observations are stillvalid when Q/Q0 ratios interpolated from those at110 and 129 ka are used, although the correlationin 4 becomes worse. For the following discussionI will assume that the correlation in Fig. 4 is valid.

5. Discussion

I now address the question of the relationshipbetween proxies for solar surface magnetic activ-ity (P/P0) and global surface temperature (N18O). Itis clear that a spurious correlation between P/P0

and N18O would result if the estimated M/M0 and/

or Q/Q0 depended on N18O and this issue is cen-

tral to the arguments for and against the observedrelationship. Also, there is the observation of theapparent long-term variability of the solar surfaceactivity, which appears to be cyclical. These issueswill be investigated using cross-spectral analysis,although it should be noted that this type of sta-tistical analysis assumes data with Gaussian noiseand does not account for systematic shifts from

another e¡ect (e.g., anomalously high 230Thex insome cores at a speci¢c time). Finally, the weak-nesses of the calculations and future tests to fur-ther investigate P/P0 and N

18O relationship are dis-cussed.

5.1. Spectral analysis

Spectral analysis of the N18O record over the last

one million years has indicated the existence ofcycles with periods of 23 ka, 41 ka and 100 ka[45]. The questions that we need to address are:(1) whether the P/P0, M/M0 and Q/Q0 display spec-tra with power at frequencies resembling thoseobtained from N

18O record, and (2) to what extentdo the P/P0, M/M0 and Q/Q0 spectra cross-corre-late with the N

18O spectrum. Fig. 5a plots thetime-integral power spectral densities (PSD) ob-tained for the data against frequency and showsthat P/P0 and M/M0 have PSD concentrations at awavenumber of 0.01 ( = 100-ka cycle), identical tothat for the N

18O record, which for the purpose ofthis analysis was truncated at 200 ka. On the oth-er hand, the Q/Q0 does not appear to have PSDconcentrations at any wavenumber.

Does the above analysis indicate that the esti-mated geomagnetic ¢eld intensity depends uponN

18O? I investigate this issue using cross-analysisof spectral power that provides a more quantita-tive assessment to determine the degree of resem-blance of two data sets. The source code for thiscalculation called CROSS uses a Fourier multi-taper estimation based on sine weight functions[46,47]. The calculation gives squared coherenceand phasing between two spectra of interest.The squared coherence Q

2 of two uncorrelatedGauss^Laplace distributed time series are ex-pected to fall below a calculated zero coherencelevel 95% of the time. Phasing of the spectra canbe used in conjunction with Q

2 as an additionalmeasure to evaluate the degree of resemblance[47]. Fig. 5b,c shows the squared coherence andphase, respectively, as a function of frequency forP/P0 and N

18O, M/M0 and N18O, and Q/Q0 and

N18O. Signi¢cant cross-spectral coherence betweenP/P0 and N

18O at wavenumbers 9 0.05 is evidentin Fig. 5b (see also Fig. 4). At wavenumbers9 0.02 the data are also in phase. In contrast,



the M/M0 and N18O cross-spectrum does not dis-

play any coherence. The Q/Q0 and N18O cross-

spectrum, while coherent between wavenumbers0.024 and 0.05, is not in phase. Taken together,the above results suggest that the long-term solar

activity and Earth’s surface temperature are di-rectly related. Furthermore, the spectral analysissuggests that the 100-ka cyclicity observed in theN

18O record may be related to solar modulation.The latter observation is intriguing as it couldprovide yet another astronomical driver of thenotorious 100-ka cycle of the ice ages.

5.2. Sun and the 100-ka cycle

The ice ages, according to the Milankovitchtheory, are the consequence of secular variationsin solar insolation caused by changes in theEarth’s orbital parameters [45,48,49]. The marineN

18O record has shown that, while the Earth hasbeen cooling for the last 40 Ma, the ice agesmarked by relatively cold (glacial) and warm (in-terglacial) periods began V2.5 Ma ago. With theexception of the last one million years, the gla-cialînterglacial cycles are dominated by perio-dicities corresponding to the predicted cycles oforbital obliquity (41-ka cycle) and precession ofthe Earth’s orbit (23-ka cycle). A 100-ka oscilla-tion is the most dominant during the last onemillion years [50] and corresponds rather closelyto the predicted cycles of orbital eccentricity (95ka and 125 ka). However, the eccentricity varia-tions are rather insigni¢cant and the predictedsolar insolation changes too small (6 0.2%) toinduce climate changes by direct forcing [51]. Asthe Milankovitch theory implicitly assumes theSun to be a source of constant radiation on amillion-year timescale, non-linear models invok-ing ice-sheet dynamics have been propounded toexplain the existence of the 100-ka cycles [51,52].This has led to another problem: a 400-ka cyclepredicted by the eccentricity variations is absentfrom the N

18O record [51,53,54] but strengthenedby the non-linear ice models [55].

The 100-ka problem is discussed in detail byMuller and MacDonald [55^58], who arguedthat by looking at the narrowness of the 100-kaspectral peak it could only be generated throughastronomical forces and not through internal os-cillations, which would tend to broaden it. Theyalso discovered that changes in the inclination ofthe Earth’s orbit follow a 100-ka cycle and arguedthat such variations would engender periodic cos-

Fig. 5. (a) Time-integral PSD plotted against frequency.Note that P/P0, M/M0 and as expected N

18O have PSD con-centrations at a wave number of 0.01 ( = 100-ka cycle). TheQ/Q0 does not have PSD concentrations at any wavenumber.The PSD concentrations were estimated using AutoSignalfrom SPSS Science as well as CROSS. (b) Squared coher-ences are signi¢cant for P/P0 and N

18O and Q/Q0 and N18O at

some frequencies but not for M/M0 and N18O. (c) Phase of

squared coherences of panel b. Only P/P0 and N18O at wave-

numbers s 0.02 are in phase. These observations indicatethat the 100-ka ice age cycle and solar activity are stronglyrelated.



mic dust accretion on Earth, which may lead toclimatic changes on 100-ka timescales [55^58].This astronomical hypothesis, however, su¡ersfrom the absence of any concrete physical mech-anism through which signi¢cant changes in cli-mate result from accretion of cosmic dust. So, incontrast to the observed 23-ka and 41-ka cycles inmarine records, which can be explained by solarinsolation cycles, an understanding of the 100-kacycle remains elusive. A recent study suggests thatthe 100-ka cycle does not arise from ice sheetdynamics but is generated in response to changesin atmospheric carbon dioxide concentration [59].Yet the general argument that the 100-ka cyclemust be astronomically driven [55,57] should bevalid. Figs. 4 and 5 show that the N

18O record andsolar modulation are coherent and in phase on a100-ka timescale. The simplest explanation of thisobservation is that variations in solar surfacemagnetic activity cause changes in the Earth’s cli-mate on a 100-ka timescale.

As mentioned above, there are strong correla-tions between solar surface magnetic activity andclimate at di¡erent timescales, which range fromdays through centuries. Whereas these observa-tions have pointed to a causal relationship be-tween solar activity and climate change, the de-tails of physical mechanism(s) still need to beworked out (see e.g., [60]). It has been generallybelieved that the variations in solar magnetic ac-tivity lead to changes in total or ultraviolet irra-diance of the Sun through the disc passage andevolution of sunspots and faculae [3^5,61], which,in turn, a¡ects climate. Another posited mecha-nism through which solar activity could directlya¡ect climate is via modulation of GCRs, whichin£uences cloud formation by inducing changes inthe tropospheric ion production [8^10,62,63]. Ifthe changes in cosmic ray £ux cause cloud covervariations, one would expect an inverse relation-ship between solar modulation and surface tem-perature, assuming that the proportion of low andhigh clouds remains constant. This is consistentwith the observation in Fig. 4, although variationsin irradiance could also a¡ect climate by e.g., af-fecting the ozone cover [7]. However, it is notapparent why the solar activity should vary on a100-ka timescale.

Observations over the last few centuries haveshown the solar activity to vary with an 11-yrperiodicity of sunspots (Schwabe cycle), a 22-yroscillation in solar magnetic polarity (Hale cycle)and an about 90-yr period of a sequence of lowsunspot numbers (Gleissberg cycle). Additionally,the cosmogenic nuclei proxies indicate solar oscil-lations of 1/420 yr31 [20] and 1/1500 yr31 [21]. Ifthe presence of a 100-ka solar activity cycle couldbe further substantiated, it would help elucidateprocesses occurring deep within the Sun’s interior.Observations of Sun-like stars have shown themto be a much more magnetically variable [6,64]and thus it is conceivable that in comparison toits present state, the Sun could have been more orless magnetically active in the past. However, thecurrent models of solar magnetohydrodynamicsare not su⁄ciently developed to predict long-term solar activity variations (e.g., [65^67]).

In summary, it is evident that while there arestrong correlations between solar activity and cli-mate at di¡erent timescales more work is neededtowards ¢nding mechanisms that change the solaractivity in the ¢rst place and that explain thephysical link between the solar magnetism andclimate. Nevertheless, if the results of this studycan be further substantiated, a causal connectionbetween solar surface magnetic activity and 100-ka cycle would be consistent with other short-term observations mentioned above.

5.3. Caveats and further tests

5.3.1. Data length and uncertaintyFirst of all, it is important to recognize that the

calculations presented in this study encompassonly two cycles of the postulated 100-ka solaractivity variations. While it is possible to extractthe 100-ka cycle from a 200-ka-long record (asshown above using the N

18O record truncated at200 ka), one needs to extend this calculationto s 1 Ma in order to ratify the claims of thisstudy. It is, however, easier said than done: areliable 10Be production record requiring 230Thnormalization is not possible beyond 250 ka.This issue is discussed in Section 5.3.2. Also, thegeomagnetic ¢eld intensity is not well constrainedprior to 800 ka. While it may be di⁄cult to obtain



a continuous record of geomagnetic ¢eld varia-tions, well-dated submarine basalt glasses couldprovide discrete VADMs [68,69].

The calculations presented here make use ofdata obtained by stacking a series of data points.In doing so the authors developed certain subjec-tive criteria to combine selected data sets and toreject others. Guyodo and Valet [30] used 33 dif-ferent cores to estimate the M/M0 for the last 800ka. They describe in detail the manner in whichthey combine data in an initial study where theyused 17 di¡erent cores to estimate the M/M0 forthe last 200 ka [29]. In addition to utilizing estab-lished selection criteria, these authors used a boot-strap method to remove one of the cores from thedata. This led to a considerable reduction in theestimated uncertainties.

The 10Be production rate at each time step wascalculated in the following manner [34,70] : the230Thex-normalized deposition rate was calculatedfor each sample and interpolated to a 1-ka inter-val knowing the N

18O or 14C chronology and incase of continuous core samples high resolutiondating using a 230Thex constant £ux model. Inorder to reduce enrichments/depletions due to lo-cal e¡ects (e.g., boundary scavenging), the esti-mated 10Be deposition rates in each core werenormalized to their average values. Finally, thedata for each time step were globally averaged.The number of records used at each time step isvariable with 10^31 records between 0 ka and 144ka and with four to nine records between 145 kaand 200 ka. A large number of cores used byFrank et al. [34] are clustered in the South Atlan-tic. Additional data from other oceans and fromdi¡erent latitudes need be combined to obtain amore global coverage.

While both 10Be production rate and geomag-netic ¢eld intensity records were carefully pre-pared to minimize introducing a bias to thedata, it is possible that selection criteria mayhave led to a reduction in data scatter and, con-sequently, a smaller apparent uncertainty in thecalculated solar modulation factor. A major prob-lem, as discussed above, is that certain cores usedto determine 10Be production rate may haveanomalously high 230Thex. If true, the observedvariations in the solar modulation factor would

be swamped by noise. Future tests with betterdatasets are therefore essential to investigate theclaims made in this study.

5.3.2. TestsThe most important test of the hypothesis pre-

sented in this study would be to re-determine P

using other datasets and to search for periodici-ties. It would be discarded if the predicted corre-lation between P and climate is not seen. In viewof the potential problems with the 10Be produc-tion record used in this study, a simpler and ro-bust test is to use well-characterized Fe^Mncrusts, which display constant 10Be/9Be ratios[71] and whose growth rate have been estimatedusing 230Thex dating. High resolution sampling ofsuch crusts (resolution = 10^20 ka) and determina-tion of 10Be and 9Be in resulting aliquots wouldprovide data that could be used in conjunctionwith Guyodo and Valet’s Sint-800 [30] to estimateP/P0. This is a technically challenging problemgiven that the number of atoms to be measuredwould be rather small.

In order to minimize errors introduced in thecalculations due to the stacked nature of Q and Mrecords, it may be useful if normalized P wereobtained on individual cores and then globallyaveraged. This is a challenging task and wouldentail selecting those cores where Q and M aswell as high resolution N

18O data could be reliablyobtained. Useful sites around the globe would bethose at low latitudes, away from the continentsin relatively deep water, and displaying a rela-tively constant sedimentation rate. Southon etal. [72] found that 10Be is 10 times more enrichedin clays than in carbonates. As dissolution of car-bonates could be problematic, it would be impor-tant to concentrate on cores with a high clay tocarbonate ratio. In order to minimize the e¡ectsdue to sediment focusing and winnowing, normal-ization with 230Thex could be used for samples lessthan 250 ka old [33,34,70] on cores that do notdisplay anomalously high 230Thex [36,38]. Forsamples older that 250 ka one could use anothernormalizing element such as 3He in interplanetarydust particles [73^75], although this method doeshave its own set of problems [76].

Another test would be to compare activities of



cosmogenic nuclides in well-dated surfaces. Thebest surfaces for such purpose are coral terraces,which have been dated quite precisely using U^Thsystematics (e.g., [77,78]). The spallation target incorals is 40Ca and its interaction with neutronsand negative muons produces 36Cl (t1=2 = 300 ka)(e.g., [79]). The relative production rates of 36Cl incorals from a given study area would re£ect pastchanges in solar modulation of GCR. As with anyexposed surface, two variables that would poten-tially control the measured 36Cl concentrationand, therefore, impact the estimated productionrate in coral terraces are their erosion and burialunder debris. Independent estimates of the extentto which these processes may have operated onthese surfaces would be needed a priori to assessthe variations in 36Cl production rate.

6. Conclusions

Using the established variations in geomagnetic¢eld intensity and 10Be production rates, I havedetermined the variations in solar modulation ofgalactic cosmic rays over the past 200 ka. Thevariations in solar modulation indicate that theSun displays periods of enhanced and suppressedmagnetic activity that are of several thousandyears in duration. Spectral and cross-spectralanalyses indicate that the solar activity has a100-ka cycle in phase with the N

18O record ofglacialînterglacial cycles. The long-term solar ac-tivity and Earth’s surface temperature appear tobe directly related. The variations in solar activitymay control the 100-ka glacialînterglacial cyclesproviding a more tangible astronomical forcingthan the estimated changes in solar insolation orcosmic dust accretion rates. Further tests usinghigh ¢delity datasets, which give time-tuned geo-magnetic ¢eld intensity and cosmogenic radionu-clide production rates, would be needed to sub-stantiate this hypothesis.

Acknowledgements

I began working on this project while at theMax Planck Institute for Chemistry, Mainz, Ger-

many and am grateful to Al Hofmann for hiscontinuous interest and support. I dedicate thispaper to G.J. Wasserburg on his 75th birthdayand for inspiring me to examine this issue. I thankJ. Masarik and Y. Guyodo for providing dataand W. Abouchami, S. Galer, J.N. Goswami,A.W. Hofmann, W. Soon, J. Tarduno and G.J.Wasserburg for discussions and encouragement.R. Parker provided the source code of CROSSand support to ensure successful installation ofthe program. E. Bard, M. Frank, J.N. Goswami,W. Soon, S. Solanki and J. Tarduno read an ear-lier version of this paper and gave useful com-ments. Discussions with R.F. Anderson, A. Heim-sath, G. Henderson and D. Lal were helpful.O⁄cial reviews were given by M. Frank, R. Mul-ler and two anonymous reviewers. I am especiallygrateful to R. Muller for going through the paperwith a ¢ne-tooth comb, for Fig. 3 and for his noteto the editor: ‘‘This could even be right T’’. I alsothank A.N. Halliday (Editor) for his commentsand support. This work was supported by Dart-mouth College, the Max Planck Society and by agrant (OCE-0099231) from the National ScienceFoundation.[AH]

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