V. A. Dergachev and S. S. Vasiliev
Ioffe Physico-Technical Institute, St. Petersburg, Russia
O. M. Raspopov
St. Petersburg Branch of the Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation, St. Petersburg, Russia
The cosmogenic isotope 14C is produced in the Earth's upper atmosphere by the nuclear interaction of cosmic rays of both galactic and solar origin with the atmospheric components 14N (n,p)14C. Radiocarbon enters the global carbon cycle by the way of CO2. The atmosphere, biosphere, mixed surface and deep oceanic layers - all play a role in storage and exchange of radiocarbon. Radiocarbon activity measurements in tree rings of known calendar age make it possible to calculate the 14C/C ratio for the atmosphere and also for surface and deep oceanic water. The atmospheric 14C concentration is typically expressed as D14C, namely, a relative deviation of the measured 14C activity from the standard activity corrected for isotope fractionation and radioactive decay related to age [Stuiver and Polach, 1977]. The deviations from the mid-19th century value are the per cent (or per mil) values that represent the fluctuation of either the 14C/C ratio or the 14C activity in the atmosphere.
High-precision measurements of the 14C concentration in the atmosphere based on counting of dendrochronologically dated wood samples are now available for the Holocene period. These data indicate that the 14C concentration experienced considerable variations - from a few per mil on a short time scale (from a few years to several decades) to more than 10% on the millennial time scales. Much of this variability is quasi-periodic. The radiocarbon concentration and tree rings respond very rapidly to external forcing. Owing to this it is possible to obtain valuable and reliable information about the physical processes affecting the radiocarbon concentration. The causal mechanisms responsible for the atmospheric D14C variability include solar and geomagnetic factors affecting the 14C production rate in the Earth's atmosphere and also the climatic factor inducing variations in the carbon reservoir parameters. Most of the atmospheric D14C variability during the Holocene can be explained by changes in the geomagnetic field intensity and solar activity which result in the 14C production rate variations. Determination of various forcings responsible for the atmospheric D14C variability is a major problem of astrophysics, geophysics, and climatology.
De Vries [1958] was the first to reveal secular variations of the natural 14C concentration in the Earth's atmosphere and to correlate these variations with climatic changes. Stuiver [1961] was the first to give a convincing relationship between variations in the 14C concentration and solar activity during an 11-year cycle. Willis et al. [1960] showed that atmospheric 14C activity is cyclic, with a period of about 200 authors [e.g., Damon and Jiricowic, 1992; Damon and Sonett, 1992; Stuiver et al., 1991]. It turned out that the power spectra are distinguished by both the height of lines and their positions. This difference in the spectral estimations can be attributed to non-stationarity of the time sequences. Damon and Jiricowic [1992] and Damon and Sonett [1992] assumed that spectral lines corresponding to the periods of ~2400, ~210, and ~88 years are fundamental, and other spectral lines in the D14C time series can be regarded as harmonics of the fundamental ~2400-year wave. An important property of the 2400-year cycle is that amplitudes of the ~210-year cycles are modulated by this superlong period [Damon et al. 1990; Sonett, 1984]. Therefore, in order to gain a more penetrating insight into the physical nature of many processes taking place in the vicinity of the Earth, it is highly important to study sources of the ~2400-year wave in the radiocarbon concentration.
As a rule, changes in the atmospheric radiocarbon concentration with a period of ~2400 years are attributed to variations in the geomagnetic field intensity and climatic changes [e.g., Damon and Sonett, 1992]. There are a few arguments indicating that a source of changes in the D14C time series with the 2400-year period during the last 10 millennia is the geomagnetic field. At the same time, some authors [e.g., Arabadji, 1986; Dansgaard et al., 1984; Pestiaux et al., 1988; Rotlisberger, 1986; Schmidt and Gruhle, 1988] demonstrated the presence of this super-long-term period in climatic data.
In this work the major attention will be given to the super-long cyclic period of ~2400 years in radiocarbon concentration variations and to possible factors forcing this long-term cyclic variability of the D14C time series.
![]() |
Figure 1 |
![]() |
Figure 2 |
![]() |
Figure 3 |
![]() |
Figure 4 |
Some conclusions can be inferred from this analysis. The D14CD sequence is found to be amplitude modulated in a wide interval of frequencies. The modulation period coincides with the ~2400-year period of the most intensive line in the power spectrum. As it should be for the modulation process, the phases of the maximum modulating signal (period of ~2400 years) and the phases of the largest amplitude fall within the same time interval (Figure 3). To study the amplitude modulation in more detail, we applied the bispectral analysis proposed by King [1996].
A slow temporal variation of the radiocarbon concentration fluctuation amplitudes is meant by modulation. Modulation is a particular case of nonlinear wave coupling. In the simplest case the modulation can be described as
![]() | (1) |
where c is the average radiocarbon concentration, dc(t) is the concentration fluctuation, w is the modulation frequency, A is the modulation amplitude, and C(t) is the concentration including the modulation effect. Taking into account the cyclic changes in the concentration c(t), the expression dc(t) can be represented as a sum of harmonics
![]() | (2) |
where Bi, wi and fi are the amplitude, frequency, and phase of the i th harmonic, respectively. Taking into account (2), expression (1) can be written as
![]() | (3) |
Expression (3) for the concentration contains, in addition to a regular c component, harmonic components with the frequencies: wi- = wi - w, wi, wi+ =wi + w. Thus, as a consequence of modulation, two side frequencies appear for each basic harmonic component. They are separated from the basic frequency by w. Because of modulation, the analysis of the signal power spectrum becomes complicated if the estimation of the frequency of spectral lines is insufficiently accurate.
Many problems arising in the analysis of the data containing information on interaction between modes can be solved by using the bispectral analysis [King, 1996]. The tools of this method are in many respects similar to the routine spectral analysis. It follows from the properties of a bispectrum that if the data involve harmonics with the frequency w modulated by frequency w, the analysis can reveal maxima of a two-dimensional spectral density P(wx, wy) for frequencies of the upper half-plane, wy > 0, listed in Table 1.
![]() |
Figure 5 |
![]() |
Figure 6 |
The modulation of the 210-year cycle traced in the radiocarbon concentration was discussed by Sonett [1984]. It is widely believed that there are three sources of the ~2400-year modulation of the radiocarbon concentration: solar activity, changes in the carbon dioxide exchange between the atmosphere and ocean (climatic influence), and variations in the dipole magnetic moment with the period of ~2400 years. The Sun as a source of excitation of the ~2400-year cycle was considered by Hood and Jiricowic [1990]. Elsasser et al. [1956] and O'Brien [1979] described and substantiated the mechanism of the geomagnetic field effect on the radiocarbon production rate. The amount of 14C atoms produced is proportional to m(t)0.52, where m (t) is the magnetic dipole moment of the Earth. The attempt to explain the change in the 210-year cycle amplitude by the time-varying Earth's magnetic moment failed because, as evidenced by archaeomagnetic and palaeomagnetic data, the Earth's dipole magnetic moment had no sufficiently large fluctuations with this period [Damon and Sonett, 1992]. Earlier Sonett [1984] emphasized that the dipole moment variation amplitude should be sufficiently large to induce the observed 210-year variations in the radiocarbon concentration.
The most probable source of a long-term modulation of the
radiocarbon concentration is global climatic changes in the past.
Let us briefly consider the basic reasons for the climatic effect.
An average temperature and wind velocity define the intensity of the
CO2 exchange between the atmosphere and ocean. The carbon masses
concentrated in the atmosphere and ocean markedly differ. The
atmosphere contains approximately
7 1011 tons of carbon,
and the ocean contains about
4
1013 tons of carbon
[Damon et al. 1978].
Under equality of flows from the atmosphere
to the ocean and back, the carbon circulation time in the ocean
considerably exceeds its residence time in the atmosphere, and the
relative radiocarbon concentration in the ocean is lower than in the
atmosphere. Because of such proportion in the radiocarbon
distribution in the reservoirs, an increase in the radiocarbon
exchange rate leads to a decrease in its concentration in the
atmosphere. A cyclic change in the parameters determining the
exchange rate should cause a corresponding change in the
14C
concentration in the Earth's atmosphere.
Using a three-reservoir model of exchangeable carbon with the parameters given by Damon et al. [1978] and the relationship between changes in the temperature and d18O concentration [Salamatin et al. 1998], we estimated the amplitude of the 2400-year cyclic wave in D14C D resulting from the climatic effect on the exchange processes in the carbon system. A relative amplitude of the radiocarbon concentration variation is in a satisfactory agreement with temperature changes, which suggests that the climatic influence on the exchange processes in the ocean and atmosphere can be a source of the 2400-year cyclic wave in the long-time series of the radiocarbon concentration.
Let us briefly consider some details of the bispectrum which are not obtained from the climatic model. The presence of the first harmonic with frequency 2wa of the basic line at wa follows from the fact of the existence of the vertex with coordinates wa and wa. The harmonics with frequency 2wa also manifest themselves in the bispectrum by the vertex with coordinates 2wa and -wa. As expected, this harmonic is splitted by the fundamental modulating frequency w (for instance, see the vertex with coordinates 2wa + w and -w in Figure 5). Another interesting detail of the bispectrum is the point with coordinates wb + w and wb- w arising due to splitting of the basic line at wb and coherence of the lines with frequencies wb and 2wb. As follows from the analysis of the left-hand part of the spectrogram (Figure 5), fluctuations with frequencies wb and wg are coherent, and hence frequencies wb and wg are multiples. The ratio between the amplitudes of these lines (Figure 4 and 6) does not permit one to regard the line wg as the first harmonic of the line wb. More likely, this points to a weak modulation of the ~210-year variations resulting in asymmetry of even and odd cycles. Note that the question of multiplicity of frequencies of the lines corresponding to the ~420-year and ~210-year periods was earlier discussed by Stuiver and Braziunas [1989].
There are numerous palaeoclimatic data which confirm the cyclic character of climate change with the period of about 2400 year. Dansgaard et al. [1984] demonstrated the existence of the ~2500-year period of the climatic origin inferred from the studies of the d18O content in Greenland ice cores. The ~2400-year quasiperiod was found by Pestiaux [1988] in the d18O concentration in ice cores and foraminifera in oceanic sediments. The dendroclimatic investigations of Schmidt and Gruhle [1988] showed that the Little Ice Age (1500-1800 AD) was preceded by the cold Hallstattzeit epoch, 750-400 BC, which in turn was preceded by the earlier cold epoch, 3200-2800 BC. All these epochs are separated by 2200-2500 years and coincide with the epochs of large D14C D amplitudes (Figure 3). Investigations of average temperature extrema of the Atlantic water [Arabadji, 1986] led to the conclusion about the existence of temperature minima 400, 2800 and 5100 years BP. Recently, Finkel and Nishizumi [1997] have found a good correlation between the observed millennial-scale variations in the concentrations of radiocarbon and 10 Be during the Holocene. The authors interpreted changes in the 10 Be concentration as resulting from the climatic effect. Note that two rather high amplitude peaks of the 10Be concentration in an ice core 5200-5600 and 7100-7600 cal BP coincided in time with large amplitudes of the radiocarbon concentration in the Earth's atmosphere. Thus it is highly probable that the long-term cyclic variations in the radiocarbon concentration in the Earth's atmosphere have the climatic origin.
Radiocarbon series of dated samples can give valuable information on the intensity of the sources of 14C formation and modulation of the 14C production rate by both solar activity and geomagnetic field and also show the extent to which the climate affects the parameters of the carbon exchange system at the Earth. To elucidate find answers to the questions about the nature of variations in the 14C concentration, complex analysis of the data available should be carried out. We have performed spectral, temporal-spectral, and bispectral analysis of the high-precision data on radiocarbon concentration in the Earth's atmosphere for the past 8000 years. The spectral-time analysis has revealed that after removal of the long-term trend in the 14C series, a cyclic change in the 14C concentration variation amplitudes is observed. The fundamental period of the large-scale cycle is about 2300-2500 years, and the periods of the modulated components are hundreds of years. The bispectral analysis of the data has demonstrated the existence of amplitude modulation and allowed the lines in the power spectrum of the radiocarbon series to be classified. It has also given information about the interrelation between spectral lines and some of their properties. The period of the fundamental modulating component has been found to be ~2400 years. In addition to the modulating component, three basic lines, a, b, and g, with periods 710, 420, and 210 years, respectively, have been identified. It has been shown that each basic line has a left-hand and right-hand satellite which result from modulation. As follows from the analysis of the bispectrum, the line a has the first harmonic. In addition, the properties of the obtained bispectrum unambiguously indicate that the b and g lines are coherent and multiple to the ~420 and ~210-year periods at the observed ratio between frequencies. The ratio between amplitudes of lines b and g is such that fluctuations with the frequency wb can be regarded as the modulating factor with respect to the line g. Then because of multiplicity of frequencies of lines b and g, even and odd cycles of ~210-year variations must be asymmetric.
It is widely believed that there are three sources of the ~2400-year modulation of the radiocarbon concentration: solar activity, changes in the carbon dioxide transfer between the atmosphere and ocean (climatic influence), and variations in the dipole magnetic moment with the period of ~2400 years. In our opinion, the most probable source of this period is global climatic change in the past. In this case the cyclic variation in the parameters of the carbon exchange system induced by climatic forcing should give rise to corresponding changes in the 14C concentration in the Earth's atmosphere.
Using a three-reservoir model of exchangeable carbon and the relationship between changes in temperature and d18O concentration, we have estimated the amplitude of the 2400-year cyclic wave in D14C D resulting from the climatic forcing of the exchange processes in the carbon system. A relative amplitude of the radiocarbon concentration variation has been found to be in a satisfactory agreement with temperature changes, which suggests that the climatic influence on the exchange processes in the ocean and atmosphere can be a source of the 2400-year cyclic wave in the long-time series of the radiocarbon concentration.
In addition, analysis of the bispectrum has revealed the first and second harmonics of the fundamental modulating component. Along with the absence of splitting of basic lines by these harmonics, this is an additional argument speaking in favor of the climatic origin of the ~2400-year modulation derived by analyzing fluctuations in the radiocarbon concentration in the 8000-year sequence.
Arabadji, M. S., In Interior of Light-Blue Continent, 142 pp., Nedra, Moscow, 1986.
Damon, P. E., and J. L. Jiricowic, Radiocarbon evidence for low frequency solar oscillation, in Rare Nuclear Processes, Proc. 14th Europhys. Conf. on Nuclear Physics, edited by P. Povinec, pp. 177-202, Singapore, 1992.
Damon, P. E., and C. P. Sonett, Solar and terrestrial components of the atmospheric 14C variation spectrum, in The Sun in Time, edited by C. P. Sonett, M. S. Giampapa, and M. S. Mathews, pp. 360-388, Univ. of Arizona Press, Tucson, 1992.
Damon, P. E., S. Cheng, and T. W. Linick, Fine and hyperfine structure in the spectrum of secular variations of atmospheric 14C, Radiocarbon, 31 (3), 704, 1990.
Damon, P. E., J. C. Lerman, and A. Long, Temporal fluctuations of atmospheric 14C causal factors and implications, Ann. Rev. Earth Planet. Sci., 6, 457, 1978.
Damon, P. E., A. Long, and D. C. Grey, Fluctuation of atmospheric 14C during the last six millennia, J. Geophys. Res., 7, 1055, 1966.
Dansgaard, W., S. J. Johnsen, H. B. Clausen, D. Dahl-Jensen, N. Gunderstrup, C. Hammer, and H. Oeschger, North Atlantic climate oscillations revealed by deep Greenland ice core, in Climate Processes and Climate Sensitivity, edited by J. E. Hansen and T. Takahashi, pp. 288-298, Amer. Geophys. Union, Washington, D.C., 1984.
de Vries, H., Variations in concentration of radiocarbon with time and location on Earth, Koninkl. Nederland. Acad. Wetensch., B61, 94, 1958.
Dziewonski, K., S. Bloch, and M. A. Landisman, A technique for the analysis of the transient seismic signals, Bull. Seismol. Soc. Amer., 59, 427, 1969.
Eddy, J. A., The Maunder minimum, Science, 192, 1189, 1976.
Elsasser, W., E. P. Ney, and J. R. Winckler, Cosmic-ray intensity and geomagnetism, Nature, 178, 1226, 1956.
Finkel, R. C., and K. Nishisumi, Beryllium 10 concentrations in the Greenland Ice Sheet Project 2 ice core from 3-40 ka, J. Geophys. Res., 102 (C12), 26,699, 1997.
Hood, L. L., and J. L. Jiricowic, Recurring variations of probable solar origin in the atmospheric D14C time record, Geophys. Res. Lett., 17, 85, 1990.
Houtermans, J. C., Geophysical interpretation of Bristlecone pine radiocarbon measurements using a method of Fourier analysis of unequally spaced data, Ph. D. Thesis, Univ. of Bern, 1971.
King, T., Quantifying non-linearity and geometry in time series of climate, Quatern. Sci. Rev., 15, 247, 1996.
O'Brien, K., Secular variations in the production rate of cosmogenic isotopes in the Earth's atmosphere, J. Geophys. Res., 84, 423, 1979.
Pestiaux, P., A. Berger, and J. C. Duplessy, Paleoclimatic variability at frequencies ranging from 1 cycle per 10,000 years to 1 cycle per 1,000 years: Evidence foronlinear behavior of the climate system, Clim. Change, 12 (1), 9, 1988.
Rothlisberger, P., 1000 Jahre Gletschergeschichte der Erde, Verlag Sauerlander, Aarau, 1986.
Salamatin, A. N., et al., Ice age dating and paleothermometer calibration based on isotope and temperature profiles from deep boreholes at Vostok Station (East Antarctica), J. Geophys. Res., 103, 8963, 1998.
Schmidt, B., and W. Gruhle, Radiokohlenstoffgehalt und dendrochronologie, Naturwissen-Schaftliche Rundschau, 5, 177, 1988.
Sonett, C. P., Very long solar periods and radiocarbon record, Rev. Geophys. Space Phys., 22 (3), 239, 1984.
Stuiver, M., Variations in radiocarbon concentration and sunspot activity, J. Geophys. Res., 66, 273, 1961.
Stuiver, M., and B. Becker, High precision decadal calibration of the radiocarbon time scale AD 1950-6000 BC, Radiocarbon, 35 (1), 35, 1993
Stuiver, M., and T. F. Braziunas, Atmospheric 14C and century-scale solar oscillations, Nature, 338, 405, 1989.
Stuiver, M., and H. S. Polach, Discussion - Reporting of 14C data, Radiocarbon, 19, 355, 1977.
Stuiver, M., and P. D. Quay, Changes in atmospheric 14C attributed to a variable Sun, Science, 9, 1, 1980.
Stuiver, M., T. F. Braziunas, B. Becker, and B. Kromer, Climatic, solar, oceanic, and geomagnetic influences on Late-glacial and Holocene atmospheric 14C/12C change, Quatern. Res., 35, 1, 1991.
Vasiliev, S. S., and V. A. Dergachev, A change of natural radiocarbon level in the Earth's atmosphere over the past 8000 years as a consequence of solar activity, geomagnetic field and climatic factors: 2400-year cycle, Biophysics, 43 (4), 681, 1998.
Willis, E. H., H. Tauber, and K. O. Munnich, Variations in the atmospheric radiocarbon concentration over the past 1300 years, Amer. J. Sci. Radiocarbon Suppl., 2, 1, 1960.