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Influence of climate on the atmospheric radiocarbon concentration
Environment International
Vol. 2, pp. 411-416. P e r g a m o n Press Ltd. 1979. Printed in Great Britain
Influence of Climate on the Atmospheric Radiocarbon Concentration K. Kigoshi Department of Chemistry, Gakushuin University, Tokyo, Japan.
In this paper, the climate effect on the atmospheric radiocarbon concentration is estimated using the data, derived by using dendrochronologically dated tree ring samples, on sunspot n u m b e r and global surface temperature during 1650-1800 A.D.; however, in order to use the data as a record of changes in radiocarbon production rate or cosmic ray intensity, the variations due to the geochemical process must be eliminated. The estimated influence o f climate on the atmospheric radiocarbon concentration is 3-5 times greater than the direct contribution of the change of radiocarbon production rate at the end o f M a u n d e r m i n i m u m . The influence o f climate on the atmospheric radiocarbon concentration through a transfer rate of CO 2 between atmosphere and ocean was estimated at a rate o f - 13 °7o per degree. The elimination o f variations caused by climate and sunspot activities from the variations in atmospheric radiocarbon concentration gives a long time scale trend having a m i n i m u m and m a x i m u m which occur in about the seventh century A.D. and the sixth millennium suggesting a good correlation between this trend of variation and paleogeomagnetic data.
Introduction
determine the transfer rate o f C O 2 between the atmosphere and the ocean surface, and also determine the transfer rate between mixed layer of ocean and deep sea. If we can estimate the climatic effect on the atmospheric radiocarbon concentration, and also if we have an exact knowledge about the historical variations of global climatic change, the variations in atmospheric radiocarbon concentration due to climatic change can be eliminated from the variations. The remainder may be correlated directly to the historical variations in radiocarbon production rate. This paper deals with the evaluation o f the possible variations caused by climatic change, and to what extent evaluation depends on the carbon cycle models used for the calculation.
The secular variation in atmospheric radiocarbon concentration provides a key for the conversion of radiocarbon date to calendar year, and also contains information about the historical events concerning geophysics and astrophysics. As the records of atmospheric radiocarbon concentration, the dendrochronologically dated tree ring samples were prepared by the L a b o r a t o r y of Tree-Ring Research o f the University of Arizona, and m a n y data on the radiocarbon concentration in those samples are reported (Damon, 72; Suess, 70a; Ralph, 70; Olsson, 70). The r a d i o c a r b o n concentration in each tree ring sample is corrected for the decay o f 14C to the concentration at the time o f growth of this tree ring using a dendrochronologically determined date. These age corrected concentrations are regarded as the representatives of the atmospheric radiocarbon concentrations in the corresponding dates. In order to use these data as the records of astrophysical or geophysical events, it is necessary to know the causes and mechanisms of the variations in atmospheric radiocarbon concentration. If the terrestrial circulation of the CO2 remained constant during tens of thousands of years, the variations in radiocarbon production rate directly proportional to the variations in atmospheric radiocarbon concentration. However, we have no evidence which supports the constancy of the terrestrial CO2 circulation. The climate m a y be one of the main factors which
3 Box model for terrestrial circulation of 14C Many authors use a well mixed box model of natural radiocarbon reservoirs for the study o f the distribution of radiocarbon in nature. However, there is a significant discrepancy between the transfer rates of radiocarbon a m o n g the reservoirs determined by natural radiocarbon distribution, and those determined by short time scale movement of b o m b produced radiocarbon. Oeschger et al. (75) settled the problem using a diffusion box model for deep sea, and a well mixed, two box model for atmospheric and mixed layer of ocean. Since the translation of the calculation of the well mixed box model to that of the diffusion box model with the use of a computer causes no problem, the well mixed 2 or 3 box model is still valuable, for demonstrating the move411
412
K. Kigoshi
ment o f the radiocarbon a m o n g the reservoirs. In this paper, we adopt the following equations for the variations of radiocarbon concentrations in the three well mixed reservoirs, atmosphere (a), mixed layer of ocean (m), and deep sea (d). dx a
= (kam
-
//2(1
- P-2)
B2 = (kam - /~a(1 - A ) ) / ( p 2 - / 1 , )
v m = N a / N m , v a = N m / N d, R = k m d / k a m .
dx m
-km.(x.
- x m ) + kma(Xa - x m ) - X X m
(2)
In order to simplify the calculation, the following typical volume ratios of the carbon reservoir are assumed in subsequent work. N a :Nm
dx d
dt
-- A ) ) / ( p l
(1)
dt - = kam (Xm - xa) - XXa + q
dt
B1
(3)
- kd m (xm - Xa) - kXa"
Where N i is the carbon content in the reservoir i and N a X a is t h e n u m b e r o f 14C atoms in the present atmosphere, the number of 14C atoms in the reservoir i at time t is given by NiXaXi(t). k is the decay constant o f 14C, kij (yrq) is the transfer rate o f carbon atoms f r o m i to j , and q is the production rate of radiocarbon expressed as a fraction o f present atmospheric radiocarbon. In the derivation of equations (1), (2), and (3) we assumed a steady state distribution of carbon among the three reservoirs, k..N. = K . N . . As the solution of these equations, the atmospheric radiocarbon concentration is given by A B, B2 - Xa(t)= [ L ) + X + D + / a l + D+/a2
where t
q _
D+ a
e--at f qeatdt _oo
and Pl = ~ k + [ ( ~ k ) 2 - 4Y_,kk] ~
P2 = 2;k - [(2~k) 2 - 4Y, k k ] v,
Z k = kam (1 + v m + R ( 1 +Vd) )
Z k k = k:.m R(1 +Va(1 + v m ) )
A = v n va/(1 + Va(1 + v,n ))
] q
(4)
: N a = 1 : 1.3 " 50
These values roughly correspond to the carbon contents in ocean layers with a thickness o f 58 m ( = ha), 76 m (= hm), and 3725 m ( = hd) which are used by Oeschger et al. (75). When the reservoir volumes are fixed, two parameters, kam and R, (or kmd), and the historical variation of production rate q, determine the distribution and variations o f radiocarbon concentrations in the three reservoirs. Although we know the historical variation in the production rate of radiocarbon from present to -t yr ago, one parameter which would be determined by the variation in production rate during - oo to -t yr ago must be introduced as an arbitrary parameter. Solar modulation of radiocarbon production rate
The observed variations in the atmospheric radiocarbon concentration over the last 8000 yr indicate two characteristic fluctuations as pointed out by Houtermans et al. (73). One is the long time scale trend with about a 10,000-yr period, and the other variations are superimposed on this trend with higher frequencies. The former long time scale trend can be explained by geomagnetic modulation o f the cosmic ray flux (Elsasser, 56; Kigoshi, 66; Grey, 69; Lingenfelter, 70). The causality between the latter high frequency radiations and sunspot activity or climate has been discussed also by m a n y authors (Stuiver, 61 ; de Vries, 58; Damon, 70, 78; Suess, 70b). Using the electric model of terrestrial circulation of radiocarbon, Stuiver (61) has obtained the magnitude of the variations in atmospheric radiocarbon concentration due to modulation of incident cosmic ray flux by solar activity. He found that a 2% change of atmospheric radiocarbon concentration yields a 25 % variation in the production rate lasting for 100 yr. Lingenfelter (63) has calculated the variations in radiocarbon production rate due to modulation of the incident cosmic ray flux by the sunspot activity. He obtained the time averaged radiocarbon production rate Q T ( 14C a t o m s / s / c m 2 of earth's surface) as ~ffr = 2.61 - 0.53(ffr - 9.1)/178.4
(5)
where STiS the average sunspot number of that period.
Influence of climate on radiocarbon
413
Eddy (76) revealed a remarkable variation in the sunspot number in the period 1650-1700 A.D., the so-called Maunder minimum. A prominent peak in the atmospheric radiocarbon concentration corresponding to this period has been known as the de Vries peak. Recently, Lerman et aL (70) re-examined the atmospheric radiocarbon concentration during the de Vries peak. As shown in Fig. 1, after the Maunder minimum solar activity was restored to a mean sunspot number of about 50 for more than 70 yr. According to the Lingenfelter's formula (5) the change o f the sunspot number, zero to 50, causes a 5.7% decrease o f the production rate. As has been calculated by Stuiver (61) and by Houtermans et aL (73) this change in the radiocarbon production rate is too small to produce the de Vries peak. Although the peak cannot be directly correlated to the Maunder minimum, the correspondence of the steep decrease of the radiocarbon concentration in the atmosphere to the end o f Maunder minimum strongly supports the hypothesis of the causality o f the de Vries peak by the Maunder minimum. Houtermans et aL (73) calculated the attenuation of the amplitude of sinusoidal variation of the radiocarbon production rate affecting the amplitude of the atmospheric radiocarbon concentration. They obtained an attenuation o f about 0.1 for the input production rate with a period o f 200 yr. Assuming a square pulse as a change o f production rate which lasts 70 yr, the ratio (attenuation Hq) of the
peak height o f atmospheric radiocarbon concentration
(Axa/x a) to the height of input pulse (A q/q) is given by: B.
A
H = [~(1 t2i
q
B.
- e-7°/ai)]/[ -- + Z - L ] . }k
(6)
~i
Figure 2 shows calculated values of Hq for given kam and kind. From these values we can estimate that the change of the production rate after the Maunder minimum (5.7%) may produce at most a 0.7% variation in the atmospheric radiocarbon concentration. This is only one third o f the observed decrease of the atmospheric radiocarbon concentration after the Maunder minimum. The remainder, 1.5% decrease of the atmospheric radiocarbon concentration may be caused by the other change associated with the sunspot number change.
.18
Ko~
.16
/
20 Y 16~ 12
Y
6--
~r .14
4-
/
=.= .10
I
2O -o
15
v
10
10
1800 A,D.
o
161 oo
I ,7oo
I
20
,
I
30
L
I
40 Km~I(Y )
~
I
50
i
I
60
Fig. 2, Attenuation Hq for given ka,n and kma. Hq is ratio of peak height o f atmospheric radiocarbon concentration (Axo/xa) to input square pulse height of production rate (A q/q). Input pulse duration; At = 70yr. Calculated assuming well mixed 3 box model.
-5 150
Climatic effect on atmospheric radiocarbon concentration
cz:
m
~I00
~ so
0
K <
1600
1700
1800 A.D.
1600
1700
1800
288
L~ ~ 287 ~
288
~= ~ 2e5 A.D.
Fig. 1. Atmospheric radiocarbon concentration (after Lerman et al., 70), sunspot number (after Eddy, 76), and global surface temperature (after Schneider et al., 75) during 1600-1800 A.D.
De Vries (58) showed that a 2% variation in the atmospheric radiocarbon concentration can be explained by the variation of factor 2 in the exchange rate between the mixed layer of ocean and deep sea. However, as indicated by Stuiver (61), the factor that induces this big change of transfer rate between mixed layer and deep sea is not known. Damon (70, 78, 68) discussed the climatic effect on the radiocarbon content of the atmospheric reservoir and showed clear evidences of correlation between the estimated climatic history and observed radiocarbon data on the dated tree rings. The correlation between the climate and atmospheric radiocarbon concentration is also supported by Libby and Pandolfi (77) who reported that the short time scale fluctuations in the radiocarbon concentration in a series of tree ring samples can be correlated with oxygen isotope thermometer readings on these samples. Many authors (Suess, 70b; Damon, 68; Lal, 70; Thurber, 70)
414
K. Kigoshi
pointed out the possibility of the influence of climate on the transfer rate of radiocarbon between the atmosphere and the mixed layer of ocean. The global surface temperature during the Little Ice Age, which corresponds to the period of the Maunder minimum, was quantitatively computed by Schneider et al. (75) using the variations in the sunspot number and Lamb's volcanic dust veil index. As shown in Fig. 1 they obtained a temperature drop o f 2.7°C in this period. This big drop of temperature may cause the decrease of transfer rate of radiocarbon between the atmosphere and the mixed layer. In the atmosphere, about 0.7°70 o f atmospheric radiocarbon is being produced and going into the ocean each year. A prohibition o f the transfer to ocean would result in an increase of radiocarbon in the atmosphere, but because the magnitude of this effect is small and of short duration, the change of volumes o f reservoirs and the change of transfer rates between mixed layer and deep sea due to the climatic change are neglected in the subsequent discussion. When we assume a square pulse variation of kam and kma with a height of A kam (kma changes to kma ( l + A k a m / k a m ) ) lasting for A t, the induced peak height o f the atmospheric radiocarbon concentration which appears at the end o f the input square pulse can be calculated analytically by
Ax = Z
d(Bi[# i) d~(1-e
--laiAt )qAkam ,
(7)
am
where we neglect small changes o f relaxation times/z 1 and tt2. The calculated variation o f the atmospheric radiocarbon content is apparently the same as the variation induced by the square pulse o f production rate with the change o f q to q + A q in the same interval A t. The attenuation Hk defined as a ratio of peak height o f the atmospheric radiocarbon concentration to the height o f the input pulse A kam, Hk
=
( A x / x a ) [ ( A kara/kam),
(8)
.10
.O8 :z:
z
.06
~-- .04
8 B 4
.02 10
I
I
I
I
I
20
30
40
50
60
Fig. 3. Attenuation Hk for given kam and k,nd. Hk is ratio of peak height of atmospheric radiocarbon concentration (A xa/xa) to input square pulse height of change" of transfer rate (Akam/kara). kma changes also to kma (1 + A kam/kam). Input pulse duration; At = 70 yr. Calculated assuming well mixed 3 box model.
the radiocarbon content of the atmosphere. Since the biosphere was neglected in the previous discussion, numerical correction is necessary when the biological reservoir is taken into consideration. A diffusion box model proposed by Oeschger et al. (75) has a continuous model for deep sea, coupled with a well mixed atmosphere and a well mixed ocean surface layer. This model is characterized by the addition of a biosphere which exchanges CO2 with the atmosphere. The radiocarbon concentration of the deep sea is governed by eddy diffusion (Ked m2/yr), and its variation along depth z (z = 0 at the boundary of mixed layer and deep sea) is given by the equation
ax d at - Ked
a2Xd az 2
-- ~c d
with the boundary conditions x a = x m for z = 0
can be calculated by equation (7). Assuming A t = 70 years, the numerical values of Hk for different kam and kind a r e shown in Fig. 3. The probable value of Ilk is within 0.03 and 0.055 when we assume that the probable values o f kam "1 and kind -1 are within the range o f 6-9 and 17-30 yr respectively. When we fix the value of H k to 0.045, which corresponds to the values of 7.5 and 22.7 yr for kam d and kmd -l respectively, the required increase of Ram t o produce a 1.5°70 decrease in atmospheric radiocarbon concentration after the Maunder minimum is 33070. This change of kam corresponds to the 2.7°C global surface temperature change, so the estimated change o f kam caused by global surface temperature change is -12070 per degree.
(9)
(10)
ax d
az
= 0 forz =h a ( = 3725m),
(11)
where h d is the average depth o f deep ocean and NdXaXd(Z)/hd is the number o f 14C atoms in a l-m layer of deep ocean of depth z. Assuming a steady state distribution of carbon in the natural carbon cycle, the radiocarbon balances in the atmosphere and mixed layer can be expressed by the following equations.
Climatic effect estimated by diffusion box model
dx
The estimation of the climatic effect on the transfer rates between atmosphere and mixed layer is sensitive to
dt
F - kam (x m - Xa) - Xx a + q - ~ - ( X a ( t ) - x a ( t - r)) tl
(12)
Influence of climate on radiocarbon
415
dx m Ke a dt -kma(Xa-Xm)-LXm+--(h
OXd ~z ) z = O . ( 1 3 )
rrl
In equation (12), F/Na is the amount o f carbon transferred annually between atmosphere and biosphere, and r is the biospheric delay time. In Oeschger's model, the carbon content o f the biosphere is 2.5 times that in the atmospheric carbon reservoir, and z is 60 yr. So the annual transfer is given by
F I N = 2.5/60. In equation (13) the transfer o f carbon from mixed layer to deep sea is given by the last term. The numerical values of the gradient o f Xd at the boundary of two boxes requires numerical computation of equation (9) using the b o u n d a r y conditions (10) and (11). In the steady state, the solution of equations (9)-(13) can be obtained analytically, and radiocarbon concentrations in mixed layer and deep sea are determined by transfer rate kam and eddy diffusion coefficient Ked as shown in Fig. 4. The probable ranges of Xm and Xd are indicated in the broad lines in this figure. The most probable values adopted here are Ked = 3980 m2/yr and 1/kam = 7.3 yr which are given by Oeschger et aL (75).
(Km~) K,,,J (13.10)
7000
(Y)
(m~y)
(]5.24)
6000
(18.22)
5000
(22.65)
4000
and equation (8) depending on the pulse duration A t as shown in Fig. 5. The curve for Hq is similar to that given by H o u t e r m a n s et al. (73), calculated using a two box model with a sinusoidal variation o f input A q. The curves for H k are characterized by short relaxation times which are nearly equal to those given by the 3 box model, and depend also on the pulse height A kam. The exchange rate between biosphere and atmosphere m a y vary with the climatic change as may the transfer rate between atmosphere and ocean. In the p r o g r a m computation, this effect was neglected because the change of F in equation (12) gives the change of x a less than a few percent of the total variation of xa due to the change o f kam and kma. The addition o f biosphere to the diffusion box model increases the content of the atmospheric carbon reservoir. This increase o f carbon content reduces the peak height of the atmospheric radiocarbon concentration produced by the square pulse input of the production rate. By the use of a diffusion box model with biosphere, the estimated direct contribution of the change of sunspot number after the Maunder minimum to the change of the atmospheric radiocarbon concentration is only 0.4%. This means that the direct effect of the variation o f radiocarbon production rate to the de Vries is about one fifth o f the total variation. The remainder 1.8% decrease o f atmospheric radiocarbon concentration after the Maunder minimum m a y be attributed to the increase of kam and kma, which can be estimated using the values of Hg shown in Fig. 5 as 36%. Assuming the temperature change of 2.7°C, the estimated climatic effect on kam is -13o7o per degree which is almost the same as the value estimated using the 3 box model. .30
(29.94)
(44.151
3000
2000
.20
i
.I0 .08
m=60 __
~) .04 J 6
8
I0
12
14
I
16
Hk
__._~.-~/'" "'"
°/o
..........
• Hk
= I0%
-i- .03 .02
Kam'(7) .01
Fig. 4. Calculated radiocarbon concentration in mixed layer of ocean (Xm) and deep sea (xu) (averaged value) assuming diffusion box model (Xa = 1.00). kind indicated in left side column is transfer rate to deep sea from mixed layer in 3 box model corresponding to each eddy diffusion coefficient in deep sea (Kea) written on ordinate. Probable range ofxm and x d are shown by broad lines.
Using this diffusion box model with these most probable values of Ked and kam,the m a x i m u m variation of the atmospheric radiocarbon concentration A xa which is induced by the input square pulse o f change of production rate ( A q ) or change o f transfer rate (A kam) is computed. The values o f attenuation Hq and Hk are defined by =
( xa/xa)l(Z q/q)
(14)
I 2
i 4
i L I 6 8 I0
210
410
l t I 60 I00
I 200
[ 400
J r ] 1000
At(y) Fig. 5. Duration (At) of input square pulse versus peak heights of
variations in atmospheric radiocarbon concentration induced by square pulse input of variation of production rate (Hq)or of transfer rate between atmosphere and mixed layer (H,0. Hq and Hk are defined by equations (14) and (8) respectively. Computed on the base of diffusion box model with karn -I = 7.7 yr, K e d 3980 m2/yr. =
The process o f transfer of C O 2 between atmosphere and ocean has been studied by Dingle (54) and Bolin (60), and recently by Thurber et aL (70). So far the simple physico-chemical rates of processes such as hydration o f carbon dioxide, the temperature dependence of -13% per degree is rather high but acceptable. As suggested by Suess (70b), the transfer process of
416
K. Kigoshi
carbon dioxide between atmosphere and ocean is so complicated that the estimation o f temperature dependence o f kam from the physical aspects o f transfer process is difficult to perform.
Estimation of long time scale trend in atmospheric radiocarbon concentration If most of the short time scale fluctuations in the atmospheric radiocarbon concentration are mainly induced by climatic change, it is necessary to eliminate these fluctuations in order to find long time scale trends o f radiocarbon production. When the fluctuations are the results of solar modulations of incident cosmic ray flux and accompanied climatic change, the highest value in each fluctuation corresponds to the solar minimum, and the lowest value corresponds to solar maximum. Because the sunspot number at solar m a x i m u m may vary widely, the m a x i m u m values of atmospheric A 14C which correspond to solar minima are better representatives for finding long time scale trends. The results of long time scale trend calculations in the atmospheric radiocarbon concentration caused by geomagnetic modulation of incident cosmic ray indicate that m a x i m u m and minimum must appear several hundred years after the occurrence of minimum and m a x i m u m geomagnetism ( H o u t e r m a n , 73; Damon, 70; Lingenfelter, 70). The variation in the intensity of the geomagnetism during the past nine millennia has been measured by thermoremanent magnetization which shows that m a x i m u m intensity occurred near the beginning of the Christian Era, and minimum intensity occurred in the previous sixth millennium (Cox, 68; Bucha, 70). The minimum and the m a x i m u m of curve A in Fig. 6, which is obtained as a smoothed curve of observed points, occurs too early to correlate the variation to geomagnetism. The curve B, which is
B
,"
-
"
90 / /
7O /
/
t~
/ t
~
ill
50
v
t,)
/
<13o
-I0
I
0
I
2000
I
t
4000
I
I
6000
BP
Fig. 6. Variations in atmospheric radiocarbon concentration during last 8000 yr. Data from three laboratories (Suess, 70a; Damon, 72; Ralph, 70; Olsson, 70) are averaged and smoothed. Curve A is smoothed curve of observed values. Curve B is long time scale trend estimated from the maximum points of short time scale fluctuations.
obtained by the use of m a x i m u m points in short time scale fluctuations as the representatives of long time scale variation, gives minimum and m a x i m u m points occurring in about the seventh century A.D. and the sixth millennium before present respectively. These points agree with the expected variation from the paleogeomagnetic data.
References B. Bolin. (1960) On the exchange of carbon dioxide between the atmosphere and the sea, Tellus 12,274-281. V. Bucha. (1970) Influence of the Earth's magnetic field on radiocarbon dating, Proc. XII Nobel Syrnp., pp. 501-511, Wiley, New ~brk. A. Cox. (1968) Length of geomagnetic polarity intervals, J. Geophys. Res. 73, 3247-3260. P.E. Damon. (1968) The relationship between terrestrial factors and climate, Meteorol. Monograpl~s 8, 106-111. P.E. Damon. (1970) Climate versus magnetic perturbation of the atmospheric C14 reservoir, Proc. X I I Nobel Syrup., pp. 571-593, Wiley, New York. P.E. Damon, A. Long and E.I. Wallick. (1972) Dendrochronologic calibration of the Carbon-14 time scale, Proc. 8th Int. Radiocarbon Dating Conf., pp. A28-A43, R. Soc. N.Z., Wellington, New Zealand. P.E. Damon, J.C. Lerman and A. Long. (1978) Temporal fluctuations of atmospheric 14C: Causal factors and implications, Ann. Rev. Earth Planet. Sci. 6,457-494. A.N. Dingle. (1954) The carbon dioxide exchange between the North Atlantic Ocean and the atmosphere, Tellus 6,342-350. J.A. Eddy. (1976) The Maunder minimum, Science 192, 1189-1202. W. Elsasser, E.P. Ney and J.R. Winkler. (1956) Cosmic-ray intensity and geomagnetism, Nature 178, 1226-1227. D.C. Gray. (1969) Geophysical mechanisms for 14C variations, J. Geophys. Res. 74, 6333-6340. J.C. Houtermans and H.E. Suess. (1973) Reservoir models and production rate variations of natural radiocarbon, J. Geophys. Res. 78, 1897-1908. K. Kigoshi and H. Hasegawa. (1966) Secular variations of atmospheric radiocarbon concentration and its dependence on geomagnetism, J. Geophys. Res. 71, 1065-1071. D. Lal and V.S. Venkatavaradan. (1970) Analysis of the causes of CI4 variations in the atmosphere, Proc. X I I Nobel Symp., pp. 549-569, Wiley, New York. J.C. Lerman, E.G. Mook and J.C. Vogel. (1970) C14 in tree rings from different localities, ibid., pp. 275-301. L.M. Libby and L.J. Pandolfi. (1977) Climate periods in tree, ice and tides, Nature 266, 415-417. R.E. Lingenfelter. (1963) Production of carbon 14 by cosmic-ray neutrons, Rev. Geophys. 1, 35-55. R.E. Lingenfelter and R. Ramaty. (1970) Astrophysical and geophysical variations in C14 production, Proc. X I I Nobel Syrup., pp. 513537, Wiley, New York. H. Oeschger, U. Siegenthalter, U. Schonerer and A. Gugelmann. (1975) A box diffusion model to study the carbon dioxide exchange in nature, Tellus 27, 168-192. I.U. Olsson. (1970) Explanation of Plate IV, Proc. XII Nobel Symp., pp. 625-626, Wiley, New York. E.K. Ralph and H.N. Michael. (1970) MASCA radiocarbon dates for sequoia and bristlecone-pine samples, ibid., pp. 619-623. H. Schneider and C. Mass. (1975) Volcanic dust, sunspots, and temperature trends, Science 190, 741-746. M. Stuiver. (1961) Variations in radiocarbon concentration and sunspot activity, J. Geophys. Res. 66,273-276. H.E. Suess. (1970a) Bristlecone-pine calibration of the radiocarbon time-scale 5200 B.C. to present, Proc. X H Nobel Symp., pp. 303-311, Wiley, New York. H.E. Suess. (1970b) The three causes of the secular C14 fluctuations, their amplitudes and constants, ibid., pp. 595-605. D.L. Thurber and W.S. Broecker. (1970) The behavior of radiocarbon in the surface waters of the Great Basin, ibid., pp. 379400. H.L. de Vries. (1958) Variation in concentration of radiocarbon with time and location on earth, K. Ned. Akad. Wet. Proc. Ser. B61, 94102.
Vol. 2, pp. 411-416. P e r g a m o n Press Ltd. 1979. Printed in Great Britain
Influence of Climate on the Atmospheric Radiocarbon Concentration K. Kigoshi Department of Chemistry, Gakushuin University, Tokyo, Japan.
In this paper, the climate effect on the atmospheric radiocarbon concentration is estimated using the data, derived by using dendrochronologically dated tree ring samples, on sunspot n u m b e r and global surface temperature during 1650-1800 A.D.; however, in order to use the data as a record of changes in radiocarbon production rate or cosmic ray intensity, the variations due to the geochemical process must be eliminated. The estimated influence o f climate on the atmospheric radiocarbon concentration is 3-5 times greater than the direct contribution of the change of radiocarbon production rate at the end o f M a u n d e r m i n i m u m . The influence o f climate on the atmospheric radiocarbon concentration through a transfer rate of CO 2 between atmosphere and ocean was estimated at a rate o f - 13 °7o per degree. The elimination o f variations caused by climate and sunspot activities from the variations in atmospheric radiocarbon concentration gives a long time scale trend having a m i n i m u m and m a x i m u m which occur in about the seventh century A.D. and the sixth millennium suggesting a good correlation between this trend of variation and paleogeomagnetic data.
Introduction
determine the transfer rate o f C O 2 between the atmosphere and the ocean surface, and also determine the transfer rate between mixed layer of ocean and deep sea. If we can estimate the climatic effect on the atmospheric radiocarbon concentration, and also if we have an exact knowledge about the historical variations of global climatic change, the variations in atmospheric radiocarbon concentration due to climatic change can be eliminated from the variations. The remainder may be correlated directly to the historical variations in radiocarbon production rate. This paper deals with the evaluation o f the possible variations caused by climatic change, and to what extent evaluation depends on the carbon cycle models used for the calculation.
The secular variation in atmospheric radiocarbon concentration provides a key for the conversion of radiocarbon date to calendar year, and also contains information about the historical events concerning geophysics and astrophysics. As the records of atmospheric radiocarbon concentration, the dendrochronologically dated tree ring samples were prepared by the L a b o r a t o r y of Tree-Ring Research o f the University of Arizona, and m a n y data on the radiocarbon concentration in those samples are reported (Damon, 72; Suess, 70a; Ralph, 70; Olsson, 70). The r a d i o c a r b o n concentration in each tree ring sample is corrected for the decay o f 14C to the concentration at the time o f growth of this tree ring using a dendrochronologically determined date. These age corrected concentrations are regarded as the representatives of the atmospheric radiocarbon concentrations in the corresponding dates. In order to use these data as the records of astrophysical or geophysical events, it is necessary to know the causes and mechanisms of the variations in atmospheric radiocarbon concentration. If the terrestrial circulation of the CO2 remained constant during tens of thousands of years, the variations in radiocarbon production rate directly proportional to the variations in atmospheric radiocarbon concentration. However, we have no evidence which supports the constancy of the terrestrial CO2 circulation. The climate m a y be one of the main factors which
3 Box model for terrestrial circulation of 14C Many authors use a well mixed box model of natural radiocarbon reservoirs for the study o f the distribution of radiocarbon in nature. However, there is a significant discrepancy between the transfer rates of radiocarbon a m o n g the reservoirs determined by natural radiocarbon distribution, and those determined by short time scale movement of b o m b produced radiocarbon. Oeschger et al. (75) settled the problem using a diffusion box model for deep sea, and a well mixed, two box model for atmospheric and mixed layer of ocean. Since the translation of the calculation of the well mixed box model to that of the diffusion box model with the use of a computer causes no problem, the well mixed 2 or 3 box model is still valuable, for demonstrating the move411
412
K. Kigoshi
ment o f the radiocarbon a m o n g the reservoirs. In this paper, we adopt the following equations for the variations of radiocarbon concentrations in the three well mixed reservoirs, atmosphere (a), mixed layer of ocean (m), and deep sea (d). dx a
= (kam
-
//2(1
- P-2)
B2 = (kam - /~a(1 - A ) ) / ( p 2 - / 1 , )
v m = N a / N m , v a = N m / N d, R = k m d / k a m .
dx m
-km.(x.
- x m ) + kma(Xa - x m ) - X X m
(2)
In order to simplify the calculation, the following typical volume ratios of the carbon reservoir are assumed in subsequent work. N a :Nm
dx d
dt
-- A ) ) / ( p l
(1)
dt - = kam (Xm - xa) - XXa + q
dt
B1
(3)
- kd m (xm - Xa) - kXa"
Where N i is the carbon content in the reservoir i and N a X a is t h e n u m b e r o f 14C atoms in the present atmosphere, the number of 14C atoms in the reservoir i at time t is given by NiXaXi(t). k is the decay constant o f 14C, kij (yrq) is the transfer rate o f carbon atoms f r o m i to j , and q is the production rate of radiocarbon expressed as a fraction o f present atmospheric radiocarbon. In the derivation of equations (1), (2), and (3) we assumed a steady state distribution of carbon among the three reservoirs, k..N. = K . N . . As the solution of these equations, the atmospheric radiocarbon concentration is given by A B, B2 - Xa(t)= [ L ) + X + D + / a l + D+/a2
where t
q _
D+ a
e--at f qeatdt _oo
and Pl = ~ k + [ ( ~ k ) 2 - 4Y_,kk] ~
P2 = 2;k - [(2~k) 2 - 4Y, k k ] v,
Z k = kam (1 + v m + R ( 1 +Vd) )
Z k k = k:.m R(1 +Va(1 + v m ) )
A = v n va/(1 + Va(1 + v,n ))
] q
(4)
: N a = 1 : 1.3 " 50
These values roughly correspond to the carbon contents in ocean layers with a thickness o f 58 m ( = ha), 76 m (= hm), and 3725 m ( = hd) which are used by Oeschger et al. (75). When the reservoir volumes are fixed, two parameters, kam and R, (or kmd), and the historical variation of production rate q, determine the distribution and variations o f radiocarbon concentrations in the three reservoirs. Although we know the historical variation in the production rate of radiocarbon from present to -t yr ago, one parameter which would be determined by the variation in production rate during - oo to -t yr ago must be introduced as an arbitrary parameter. Solar modulation of radiocarbon production rate
The observed variations in the atmospheric radiocarbon concentration over the last 8000 yr indicate two characteristic fluctuations as pointed out by Houtermans et al. (73). One is the long time scale trend with about a 10,000-yr period, and the other variations are superimposed on this trend with higher frequencies. The former long time scale trend can be explained by geomagnetic modulation o f the cosmic ray flux (Elsasser, 56; Kigoshi, 66; Grey, 69; Lingenfelter, 70). The causality between the latter high frequency radiations and sunspot activity or climate has been discussed also by m a n y authors (Stuiver, 61 ; de Vries, 58; Damon, 70, 78; Suess, 70b). Using the electric model of terrestrial circulation of radiocarbon, Stuiver (61) has obtained the magnitude of the variations in atmospheric radiocarbon concentration due to modulation of incident cosmic ray flux by solar activity. He found that a 2% change of atmospheric radiocarbon concentration yields a 25 % variation in the production rate lasting for 100 yr. Lingenfelter (63) has calculated the variations in radiocarbon production rate due to modulation of the incident cosmic ray flux by the sunspot activity. He obtained the time averaged radiocarbon production rate Q T ( 14C a t o m s / s / c m 2 of earth's surface) as ~ffr = 2.61 - 0.53(ffr - 9.1)/178.4
(5)
where STiS the average sunspot number of that period.
Influence of climate on radiocarbon
413
Eddy (76) revealed a remarkable variation in the sunspot number in the period 1650-1700 A.D., the so-called Maunder minimum. A prominent peak in the atmospheric radiocarbon concentration corresponding to this period has been known as the de Vries peak. Recently, Lerman et aL (70) re-examined the atmospheric radiocarbon concentration during the de Vries peak. As shown in Fig. 1, after the Maunder minimum solar activity was restored to a mean sunspot number of about 50 for more than 70 yr. According to the Lingenfelter's formula (5) the change o f the sunspot number, zero to 50, causes a 5.7% decrease o f the production rate. As has been calculated by Stuiver (61) and by Houtermans et aL (73) this change in the radiocarbon production rate is too small to produce the de Vries peak. Although the peak cannot be directly correlated to the Maunder minimum, the correspondence of the steep decrease of the radiocarbon concentration in the atmosphere to the end o f Maunder minimum strongly supports the hypothesis of the causality o f the de Vries peak by the Maunder minimum. Houtermans et aL (73) calculated the attenuation of the amplitude of sinusoidal variation of the radiocarbon production rate affecting the amplitude of the atmospheric radiocarbon concentration. They obtained an attenuation o f about 0.1 for the input production rate with a period o f 200 yr. Assuming a square pulse as a change o f production rate which lasts 70 yr, the ratio (attenuation Hq) of the
peak height o f atmospheric radiocarbon concentration
(Axa/x a) to the height of input pulse (A q/q) is given by: B.
A
H = [~(1 t2i
q
B.
- e-7°/ai)]/[ -- + Z - L ] . }k
(6)
~i
Figure 2 shows calculated values of Hq for given kam and kind. From these values we can estimate that the change of the production rate after the Maunder minimum (5.7%) may produce at most a 0.7% variation in the atmospheric radiocarbon concentration. This is only one third o f the observed decrease of the atmospheric radiocarbon concentration after the Maunder minimum. The remainder, 1.5% decrease of the atmospheric radiocarbon concentration may be caused by the other change associated with the sunspot number change.
.18
Ko~
.16
/
20 Y 16~ 12
Y
6--
~r .14
4-
/
=.= .10
I
2O -o
15
v
10
10
1800 A,D.
o
161 oo
I ,7oo
I
20
,
I
30
L
I
40 Km~I(Y )
~
I
50
i
I
60
Fig. 2, Attenuation Hq for given ka,n and kma. Hq is ratio of peak height o f atmospheric radiocarbon concentration (Axo/xa) to input square pulse height of production rate (A q/q). Input pulse duration; At = 70yr. Calculated assuming well mixed 3 box model.
-5 150
Climatic effect on atmospheric radiocarbon concentration
cz:
m
~I00
~ so
0
K <
1600
1700
1800 A.D.
1600
1700
1800
288
L~ ~ 287 ~
288
~= ~ 2e5 A.D.
Fig. 1. Atmospheric radiocarbon concentration (after Lerman et al., 70), sunspot number (after Eddy, 76), and global surface temperature (after Schneider et al., 75) during 1600-1800 A.D.
De Vries (58) showed that a 2% variation in the atmospheric radiocarbon concentration can be explained by the variation of factor 2 in the exchange rate between the mixed layer of ocean and deep sea. However, as indicated by Stuiver (61), the factor that induces this big change of transfer rate between mixed layer and deep sea is not known. Damon (70, 78, 68) discussed the climatic effect on the radiocarbon content of the atmospheric reservoir and showed clear evidences of correlation between the estimated climatic history and observed radiocarbon data on the dated tree rings. The correlation between the climate and atmospheric radiocarbon concentration is also supported by Libby and Pandolfi (77) who reported that the short time scale fluctuations in the radiocarbon concentration in a series of tree ring samples can be correlated with oxygen isotope thermometer readings on these samples. Many authors (Suess, 70b; Damon, 68; Lal, 70; Thurber, 70)
414
K. Kigoshi
pointed out the possibility of the influence of climate on the transfer rate of radiocarbon between the atmosphere and the mixed layer of ocean. The global surface temperature during the Little Ice Age, which corresponds to the period of the Maunder minimum, was quantitatively computed by Schneider et al. (75) using the variations in the sunspot number and Lamb's volcanic dust veil index. As shown in Fig. 1 they obtained a temperature drop o f 2.7°C in this period. This big drop of temperature may cause the decrease of transfer rate of radiocarbon between the atmosphere and the mixed layer. In the atmosphere, about 0.7°70 o f atmospheric radiocarbon is being produced and going into the ocean each year. A prohibition o f the transfer to ocean would result in an increase of radiocarbon in the atmosphere, but because the magnitude of this effect is small and of short duration, the change of volumes o f reservoirs and the change of transfer rates between mixed layer and deep sea due to the climatic change are neglected in the subsequent discussion. When we assume a square pulse variation of kam and kma with a height of A kam (kma changes to kma ( l + A k a m / k a m ) ) lasting for A t, the induced peak height o f the atmospheric radiocarbon concentration which appears at the end o f the input square pulse can be calculated analytically by
Ax = Z
d(Bi[# i) d~(1-e
--laiAt )qAkam ,
(7)
am
where we neglect small changes o f relaxation times/z 1 and tt2. The calculated variation o f the atmospheric radiocarbon content is apparently the same as the variation induced by the square pulse o f production rate with the change o f q to q + A q in the same interval A t. The attenuation Hk defined as a ratio of peak height o f the atmospheric radiocarbon concentration to the height o f the input pulse A kam, Hk
=
( A x / x a ) [ ( A kara/kam),
(8)
.10
.O8 :z:
z
.06
~-- .04
8 B 4
.02 10
I
I
I
I
I
20
30
40
50
60
Fig. 3. Attenuation Hk for given kam and k,nd. Hk is ratio of peak height of atmospheric radiocarbon concentration (A xa/xa) to input square pulse height of change" of transfer rate (Akam/kara). kma changes also to kma (1 + A kam/kam). Input pulse duration; At = 70 yr. Calculated assuming well mixed 3 box model.
the radiocarbon content of the atmosphere. Since the biosphere was neglected in the previous discussion, numerical correction is necessary when the biological reservoir is taken into consideration. A diffusion box model proposed by Oeschger et al. (75) has a continuous model for deep sea, coupled with a well mixed atmosphere and a well mixed ocean surface layer. This model is characterized by the addition of a biosphere which exchanges CO2 with the atmosphere. The radiocarbon concentration of the deep sea is governed by eddy diffusion (Ked m2/yr), and its variation along depth z (z = 0 at the boundary of mixed layer and deep sea) is given by the equation
ax d at - Ked
a2Xd az 2
-- ~c d
with the boundary conditions x a = x m for z = 0
can be calculated by equation (7). Assuming A t = 70 years, the numerical values of Hk for different kam and kind a r e shown in Fig. 3. The probable value of Ilk is within 0.03 and 0.055 when we assume that the probable values o f kam "1 and kind -1 are within the range o f 6-9 and 17-30 yr respectively. When we fix the value of H k to 0.045, which corresponds to the values of 7.5 and 22.7 yr for kam d and kmd -l respectively, the required increase of Ram t o produce a 1.5°70 decrease in atmospheric radiocarbon concentration after the Maunder minimum is 33070. This change of kam corresponds to the 2.7°C global surface temperature change, so the estimated change o f kam caused by global surface temperature change is -12070 per degree.
(9)
(10)
ax d
az
= 0 forz =h a ( = 3725m),
(11)
where h d is the average depth o f deep ocean and NdXaXd(Z)/hd is the number o f 14C atoms in a l-m layer of deep ocean of depth z. Assuming a steady state distribution of carbon in the natural carbon cycle, the radiocarbon balances in the atmosphere and mixed layer can be expressed by the following equations.
Climatic effect estimated by diffusion box model
dx
The estimation of the climatic effect on the transfer rates between atmosphere and mixed layer is sensitive to
dt
F - kam (x m - Xa) - Xx a + q - ~ - ( X a ( t ) - x a ( t - r)) tl
(12)
Influence of climate on radiocarbon
415
dx m Ke a dt -kma(Xa-Xm)-LXm+--(h
OXd ~z ) z = O . ( 1 3 )
rrl
In equation (12), F/Na is the amount o f carbon transferred annually between atmosphere and biosphere, and r is the biospheric delay time. In Oeschger's model, the carbon content o f the biosphere is 2.5 times that in the atmospheric carbon reservoir, and z is 60 yr. So the annual transfer is given by
F I N = 2.5/60. In equation (13) the transfer o f carbon from mixed layer to deep sea is given by the last term. The numerical values of the gradient o f Xd at the boundary of two boxes requires numerical computation of equation (9) using the b o u n d a r y conditions (10) and (11). In the steady state, the solution of equations (9)-(13) can be obtained analytically, and radiocarbon concentrations in mixed layer and deep sea are determined by transfer rate kam and eddy diffusion coefficient Ked as shown in Fig. 4. The probable ranges of Xm and Xd are indicated in the broad lines in this figure. The most probable values adopted here are Ked = 3980 m2/yr and 1/kam = 7.3 yr which are given by Oeschger et aL (75).
(Km~) K,,,J (13.10)
7000
(Y)
(m~y)
(]5.24)
6000
(18.22)
5000
(22.65)
4000
and equation (8) depending on the pulse duration A t as shown in Fig. 5. The curve for Hq is similar to that given by H o u t e r m a n s et al. (73), calculated using a two box model with a sinusoidal variation o f input A q. The curves for H k are characterized by short relaxation times which are nearly equal to those given by the 3 box model, and depend also on the pulse height A kam. The exchange rate between biosphere and atmosphere m a y vary with the climatic change as may the transfer rate between atmosphere and ocean. In the p r o g r a m computation, this effect was neglected because the change of F in equation (12) gives the change of x a less than a few percent of the total variation of xa due to the change o f kam and kma. The addition o f biosphere to the diffusion box model increases the content of the atmospheric carbon reservoir. This increase o f carbon content reduces the peak height of the atmospheric radiocarbon concentration produced by the square pulse input of the production rate. By the use of a diffusion box model with biosphere, the estimated direct contribution of the change of sunspot number after the Maunder minimum to the change of the atmospheric radiocarbon concentration is only 0.4%. This means that the direct effect of the variation o f radiocarbon production rate to the de Vries is about one fifth o f the total variation. The remainder 1.8% decrease o f atmospheric radiocarbon concentration after the Maunder minimum m a y be attributed to the increase of kam and kma, which can be estimated using the values of Hg shown in Fig. 5 as 36%. Assuming the temperature change of 2.7°C, the estimated climatic effect on kam is -13o7o per degree which is almost the same as the value estimated using the 3 box model. .30
(29.94)
(44.151
3000
2000
.20
i
.I0 .08
m=60 __
~) .04 J 6
8
I0
12
14
I
16
Hk
__._~.-~/'" "'"
°/o
..........
• Hk
= I0%
-i- .03 .02
Kam'(7) .01
Fig. 4. Calculated radiocarbon concentration in mixed layer of ocean (Xm) and deep sea (xu) (averaged value) assuming diffusion box model (Xa = 1.00). kind indicated in left side column is transfer rate to deep sea from mixed layer in 3 box model corresponding to each eddy diffusion coefficient in deep sea (Kea) written on ordinate. Probable range ofxm and x d are shown by broad lines.
Using this diffusion box model with these most probable values of Ked and kam,the m a x i m u m variation of the atmospheric radiocarbon concentration A xa which is induced by the input square pulse o f change of production rate ( A q ) or change o f transfer rate (A kam) is computed. The values o f attenuation Hq and Hk are defined by =
( xa/xa)l(Z q/q)
(14)
I 2
i 4
i L I 6 8 I0
210
410
l t I 60 I00
I 200
[ 400
J r ] 1000
At(y) Fig. 5. Duration (At) of input square pulse versus peak heights of
variations in atmospheric radiocarbon concentration induced by square pulse input of variation of production rate (Hq)or of transfer rate between atmosphere and mixed layer (H,0. Hq and Hk are defined by equations (14) and (8) respectively. Computed on the base of diffusion box model with karn -I = 7.7 yr, K e d 3980 m2/yr. =
The process o f transfer of C O 2 between atmosphere and ocean has been studied by Dingle (54) and Bolin (60), and recently by Thurber et aL (70). So far the simple physico-chemical rates of processes such as hydration o f carbon dioxide, the temperature dependence of -13% per degree is rather high but acceptable. As suggested by Suess (70b), the transfer process of
416
K. Kigoshi
carbon dioxide between atmosphere and ocean is so complicated that the estimation o f temperature dependence o f kam from the physical aspects o f transfer process is difficult to perform.
Estimation of long time scale trend in atmospheric radiocarbon concentration If most of the short time scale fluctuations in the atmospheric radiocarbon concentration are mainly induced by climatic change, it is necessary to eliminate these fluctuations in order to find long time scale trends o f radiocarbon production. When the fluctuations are the results of solar modulations of incident cosmic ray flux and accompanied climatic change, the highest value in each fluctuation corresponds to the solar minimum, and the lowest value corresponds to solar maximum. Because the sunspot number at solar m a x i m u m may vary widely, the m a x i m u m values of atmospheric A 14C which correspond to solar minima are better representatives for finding long time scale trends. The results of long time scale trend calculations in the atmospheric radiocarbon concentration caused by geomagnetic modulation of incident cosmic ray indicate that m a x i m u m and minimum must appear several hundred years after the occurrence of minimum and m a x i m u m geomagnetism ( H o u t e r m a n , 73; Damon, 70; Lingenfelter, 70). The variation in the intensity of the geomagnetism during the past nine millennia has been measured by thermoremanent magnetization which shows that m a x i m u m intensity occurred near the beginning of the Christian Era, and minimum intensity occurred in the previous sixth millennium (Cox, 68; Bucha, 70). The minimum and the m a x i m u m of curve A in Fig. 6, which is obtained as a smoothed curve of observed points, occurs too early to correlate the variation to geomagnetism. The curve B, which is
B
,"
-
"
90 / /
7O /
/
t~
/ t
~
ill
50
v
t,)
/
<13o
-I0
I
0
I
2000
I
t
4000
I
I
6000
BP
Fig. 6. Variations in atmospheric radiocarbon concentration during last 8000 yr. Data from three laboratories (Suess, 70a; Damon, 72; Ralph, 70; Olsson, 70) are averaged and smoothed. Curve A is smoothed curve of observed values. Curve B is long time scale trend estimated from the maximum points of short time scale fluctuations.
obtained by the use of m a x i m u m points in short time scale fluctuations as the representatives of long time scale variation, gives minimum and m a x i m u m points occurring in about the seventh century A.D. and the sixth millennium before present respectively. These points agree with the expected variation from the paleogeomagnetic data.
References B. Bolin. (1960) On the exchange of carbon dioxide between the atmosphere and the sea, Tellus 12,274-281. V. Bucha. (1970) Influence of the Earth's magnetic field on radiocarbon dating, Proc. XII Nobel Syrnp., pp. 501-511, Wiley, New ~brk. A. Cox. (1968) Length of geomagnetic polarity intervals, J. Geophys. Res. 73, 3247-3260. P.E. Damon. (1968) The relationship between terrestrial factors and climate, Meteorol. Monograpl~s 8, 106-111. P.E. Damon. (1970) Climate versus magnetic perturbation of the atmospheric C14 reservoir, Proc. X I I Nobel Syrup., pp. 571-593, Wiley, New York. P.E. Damon, A. Long and E.I. Wallick. (1972) Dendrochronologic calibration of the Carbon-14 time scale, Proc. 8th Int. Radiocarbon Dating Conf., pp. A28-A43, R. Soc. N.Z., Wellington, New Zealand. P.E. Damon, J.C. Lerman and A. Long. (1978) Temporal fluctuations of atmospheric 14C: Causal factors and implications, Ann. Rev. Earth Planet. Sci. 6,457-494. A.N. Dingle. (1954) The carbon dioxide exchange between the North Atlantic Ocean and the atmosphere, Tellus 6,342-350. J.A. Eddy. (1976) The Maunder minimum, Science 192, 1189-1202. W. Elsasser, E.P. Ney and J.R. Winkler. (1956) Cosmic-ray intensity and geomagnetism, Nature 178, 1226-1227. D.C. Gray. (1969) Geophysical mechanisms for 14C variations, J. Geophys. Res. 74, 6333-6340. J.C. Houtermans and H.E. Suess. (1973) Reservoir models and production rate variations of natural radiocarbon, J. Geophys. Res. 78, 1897-1908. K. Kigoshi and H. Hasegawa. (1966) Secular variations of atmospheric radiocarbon concentration and its dependence on geomagnetism, J. Geophys. Res. 71, 1065-1071. D. Lal and V.S. Venkatavaradan. (1970) Analysis of the causes of CI4 variations in the atmosphere, Proc. X I I Nobel Symp., pp. 549-569, Wiley, New York. J.C. Lerman, E.G. Mook and J.C. Vogel. (1970) C14 in tree rings from different localities, ibid., pp. 275-301. L.M. Libby and L.J. Pandolfi. (1977) Climate periods in tree, ice and tides, Nature 266, 415-417. R.E. Lingenfelter. (1963) Production of carbon 14 by cosmic-ray neutrons, Rev. Geophys. 1, 35-55. R.E. Lingenfelter and R. Ramaty. (1970) Astrophysical and geophysical variations in C14 production, Proc. X I I Nobel Syrup., pp. 513537, Wiley, New York. H. Oeschger, U. Siegenthalter, U. Schonerer and A. Gugelmann. (1975) A box diffusion model to study the carbon dioxide exchange in nature, Tellus 27, 168-192. I.U. Olsson. (1970) Explanation of Plate IV, Proc. XII Nobel Symp., pp. 625-626, Wiley, New York. E.K. Ralph and H.N. Michael. (1970) MASCA radiocarbon dates for sequoia and bristlecone-pine samples, ibid., pp. 619-623. H. Schneider and C. Mass. (1975) Volcanic dust, sunspots, and temperature trends, Science 190, 741-746. M. Stuiver. (1961) Variations in radiocarbon concentration and sunspot activity, J. Geophys. Res. 66,273-276. H.E. Suess. (1970a) Bristlecone-pine calibration of the radiocarbon time-scale 5200 B.C. to present, Proc. X H Nobel Symp., pp. 303-311, Wiley, New York. H.E. Suess. (1970b) The three causes of the secular C14 fluctuations, their amplitudes and constants, ibid., pp. 595-605. D.L. Thurber and W.S. Broecker. (1970) The behavior of radiocarbon in the surface waters of the Great Basin, ibid., pp. 379400. H.L. de Vries. (1958) Variation in concentration of radiocarbon with time and location on earth, K. Ned. Akad. Wet. Proc. Ser. B61, 94102.