Climatic forcing of the ~2400-year variations in the radiocarbon concentration in the Earth's atmosphere

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

Contents

Abstract

Introduction

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.

Spectral Properties of Radiocarbon Time Series

Figure 1

High-precision ¹⁴C measurements of dendrochronologically dated wood samples from 6000 BC to AD 1950 [Stuiver and Becker, 1993], each covering 10 years, were used (Figure 1). The average standard deviation was about 2-3 per mil. Figure 1 shows that there is a monotonous long-term change in D¹⁴C by more than 10%. One can also see more or less continuous short-term ~1% fluctuations with a duration of up to several decades. The cyclic variations in D¹⁴C with the amplitude < 1% and duration from decades to hundreds of years may be attributed to changes in solar activity.

Figure 2

The generally accepted physical mechanism explaining the long-term ~10% change in D¹⁴C which is qualitatively supported by experimental data is a corresponding change in the dipole moment of the Earth's magnetic field [Elsasser et al., 1956; O'Brien, 1979]. In order to study shorter cyclic fluctuations in the D¹⁴C time series, the long-term trend was removed. Figure 2 shows the residual D¹⁴ C _D time series after subtraction of the long-term trend from the initial radiocarbon time series [Stuiver and Becker, 1993]. The dashed lines in Figure 2 indicate the levels corresponding to the triple average error of measurement ( 3 s ). One can observe short outliers above the level of 3 s approximately 500, 2700, 5400, and 7200 years ago. Note that extrema of some climatic anomalies, such as cold epochs estimated from the dendroclimatic anomalies [Schmidt and Gruhle, 1988] and epochs of an advance of mountain glaciers [Rotlisberger, 1986], coincide with the time intervals of high amplitudes of D¹⁴C _D.

Figure 3

The examination of the nonstationary series of D¹⁴C _D can be performed in various ways [Vasiliev and Dergachev, 1998]. We used the multiple filtration method [Dziewonski et al. 1969]. It makes it possible to derive a dependence of the fluctuation amplitude on two parameters: frequency and time. As it follows from our analysis (Figure 3), the fluctuation amplitude of D¹⁴C _D varies in time. Dark spots in Figure 3 mark the well-defined intervals of large amplitudes in the D¹⁴C_D sequence. These large-amplitude peaks of D¹⁴C_D occur every 2300-2500 years. It is also evident that amplitude changes for the periods on the order of several hundreds of years are synchronous, and epochs of large fluctuations in the D¹⁴C _D amplitudes are seen to take place 400, 2500, 5200, and 7200 years ago. The cyclic curve in Figure 3 was obtained by using a low-pass filter removing harmonic components with the periods < 1500 years. Thus the features of the radiocarbon time series point to the amplitude modulation by the long-term period of about 2400 year. As stated above, the 2400-year modulation was at first established only for the 210-year period [Sonett, 1984]. According to our results, the ~2400-year amplitude changes also take place for other harmonics derived from the D¹⁴C_D

Figure 4

sequence (Figure 4). Note that the amplitudes of the lines in the radiocarbon power spectra increase with increasing period. This effect can be explained by the properties of the atmosphere-ocean carbon exchange system. The spectral analysis of the series makes it possible the average modulation period to be estimated. The power spectrum in Figure 4 exhibits a very strong line with a period of ~2400 years. Its amplitude considerably exceeds the amplitudes of other lines in the spectrum, which means that the ~2400-year component is fundamental in the super-long changes in the temporal D¹⁴C _D sequence. The low-frequency filtration in the vicinity of this period reveals extrema in the long-term radiocarbon concentration variations. In Figure 3 the curve obtained by filtering is compared with the results of the frequency-time analysis. It is evident from Figure 3 that the long-term variation maxima coincide with the epochs of large D¹⁴C_D amplitudes.

Some conclusions can be inferred from this analysis. The D¹⁴C_D 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].

Modulation of Atmospheric ¹⁴C Concentration

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 B_i, w_i and f_i 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: w_i^- = w_i - w, w_i, w_i⁺ =w_i + 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(w_x, w_y) for frequencies of the upper half-plane, w_y > 0, listed in Table 1.

Figure 5

We have carried out the bispectral analysis of the temporal D¹⁴C _D sequence. Figure 5 shows the projection of the two- dimensional spectral density P(w_x, w_y) on the (w_x,w_y) plane. The dark areas in the plot correspond to local maxima of the spectral density. The symmetry of the left-hand and right-hand parts of the spectrogram is well seen. Because of the symmetry, it is enough to analyze the part of the spectrogram bounded by the triangle with the vertex at w_x = 0 and w_y = 0. Figure 5 shows two vertical lines, marked as 1A and 2A, with projections of the vertexes. The positions of these vertical lines correspond to the period of ~2400 years. Moreover, of interest is the inclined line 1B above the left axis of symmetry with the shift corresponding to the period of ~2400 years. In addition, Figure 5 presents curves 3A, 4A, and 4B, which are the mirror lines with respect to 1A, 2A, and 1B. The fact that the projections of the triangle vertexes are located on these lines is the evidence of monotonous amplitude variation of the basic harmonics forming the spectrum of temporal D¹⁴C_D variations. The period of the monotonous changes is equal to ~2400 years. By analyzing the bispectrum, basic harmonics w_a, w_b, and w_g in the power spectrum were derived (Table 2).

Figure 6

In order to form the vertex with coordinates w_x and w_y in the bispectrum, the signal must include these frequencies and also their sum, w⁺ = w_x + w_y. The frequencies can take both positive and negative values. Another necessary condition is the coherence of three harmonic components. Owing to these properties the bispectral analysis has a high sensitivity and selectivity. The bispectrum of the D¹⁴C_D series is shown in Figure 5. Due to the modulation effect there are several kinds of harmonics with the frequency w_a. They are vertexes (-w and w_a ) and (-w and w_a + w ) in line 1A, (w and w_a ) and (w and w_a -w ) in line 2A, and (-w_a + w and w_a) and (-w_a and w_a +w) in line 1B. The same pattern is observed for harmonics with frequencies w_b and w_g. Some vertexes are not seen because the spectral line with frequency w_y +w is weak (Figure 6). The presence and positions of the indicated vertexes in the bispectrogram speak in favor of the existence of the mechanism of the ~2400-year modulation of the atmospheric radiocarbon concentration.

Nature of the ~2400-Year Modulation

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.

Thin Details of Bispectrum

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 2w_a of the basic line at w_a follows from the fact of the existence of the vertex with coordinates w_a and w_a. The harmonics with frequency 2w_a also manifest themselves in the bispectrum by the vertex with coordinates 2w_a and -w_a. As expected, this harmonic is splitted by the fundamental modulating frequency w (for instance, see the vertex with coordinates 2w_a + w and -w in Figure 5). Another interesting detail of the bispectrum is the point with coordinates w_b + w and w_b- w arising due to splitting of the basic line at w_b and coherence of the lines with frequencies w_b and 2w_b. As follows from the analysis of the left-hand part of the spectrogram (Figure 5), fluctuations with frequencies w_b and w_g are coherent, and hence frequencies w_b and w_g are multiples. The ratio between the amplitudes of these lines (Figure 4 and 6) does not permit one to regard the line w_g as the first harmonic of the line w_b. 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].

Palaeoclimatological Data and the 2400-Year Cycle

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.

Conclusions

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 w_b 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.

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