The Contribution of Radioactive and Chemical Dating to the

2 The Contribution of Radioactive and Chemical Dating to the Understanding of the Environmental System

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H. OESCHGER University of Bern, Physics Institute, CH-3012 Bern, Switzerland Radioactive and chemical dating methods are yielding most valuable information on the history of the earth and the planetary system. In this paper mainly methods using cosmic ray produced isotopes are discussed. During the recent past, fluctuations i n radioisotopes produced by cosmic radiation in the earth's atmosphere have been observed, the most convincing example being the fluctuations of the C / C - r a t i o observed in tree-ring samples. Such fluctuations complicate the interpretation of radioactive ages i n terms of absolute ages, and their interpretation asks for the development of models considering not only isotope production variations but also the geochemical behavior of the isotopes of the different elements. For this purpose, i t i s useful to distinguish between noble gas radioisotopes (e.g., Ar, Kr), radioisotopes which get incorporated in molecules of gases and vapors ( C, H), and radioisotopes of solids ( Be, Cl) which get attached to aerosol particles and are deposited with precipitation. In polar ice sheets a i r gets continuously trapped, and ice cores obtained by drilling through the ice caps therefore constitute a continuous set of ancient a i r samples. Ar/Ar and Kr/Kr measurements on these samples primarily reflect the production rates of these radioisotopes averaged over a few h a l f - l i v e s . 14

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I t i s expected t h a t due t o the s h o r t residence time o f Be and CI i n the atmosphere, B e and C 1 mea surements on i c e cores w i l l d i r e c t l y reveal isotope production variations. Due t o d i l u t i o n i n t h e C 0 exchanging system the atmospheric C / C - r a t i o shows a dampened response t o C production r a t e v a r i a t i o n s . In c o n t r a s t t o t h e noble gas r a d i o i s o t o p e s t h e s i z e o f the e f f e c t i v e d i l u t i o n r e s e r v o i r - atmosphere p l u s p a r t s o f the ocean and biosphere - depends on the c h a r a c t e r i s t i c 1 0

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0097-6156/82/0176-0005$09.50/0 © 1982 American Chemical Society Currie; Nuclear and Chemical Dating Techniques ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

6

NUCLEAR AND

CHEMICAL DATING TECHNIQUES

times of the production r a t e v a r i a t i o n s . In a d d i t i o n , C/C v a r i a t i o n s i n atmospheric C0 may be caused by v a r i a t i o n s i n the C0 exchange dynamics, as i n d i c a t e d by the o b s e r v a t i o n of changes i n the atmospheric C0 c o n c e n t r a t i o n i n i c e cores. F i n a l l y a s t r a t e g y f o r the study of the e n v i r o n mental system and i t s h i s t o r y i s proposed. Dating methods provide the time s c a l e f o r a n c i e n t system s t a t e s , and f l u c t u a t i o n s i n the parameters used f o r d a t i n g p o i n t t o important changes i n system processes. Recent d e v e l opments i n f i e l d and a n a l y t i c a l methods as w e l l as model c a l c u l a t i o n s promise a c c e l e r a t e d progress regard ing a q u a n t i t a t i v e understanding of processes determining our environment. This i s badly needed i n view of possible natural and/or anthropogenic changes w i t h e f f e c t s on s o c i e t y . 14

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Radioactive and chemical d a t i n g methods have not only provided unique i n f o r m a t i o n on the h i s t o r y of man and h i s e n v i r o n ment, but a l s o on processes i n the s o l a r system and t h e i r h i s t o r y . I t has been found however t h a t the assumptions on which these d a t i n g methods were based are o n l y p a r t l y f u l f i l l e d . During recent years s t r o n g emphasis has been given t o s t u d i e s of some d e f i c i e n c i e s of these d a t i n g methods and t h e i r causes. They have y i e l d e d most v a l u a b l e r e s u l t s on natural processes; an example i s the C - v a r i a t i o n s which are a t t r i b u t e d t o v a r i a t i o n s i n the isotope production r a t e by cosmic rays on the one hand and t o f l u c t u a t i o n s i n the global C0 exchange on the other. During the l a s t several decades the natural systems have been d i s t u r b e d by human a c t i v i t i e s . Natural and anthropogenic d i s t u r bances of the environmental system are d i s c u s s e d i n terms of models, and answers regarding p o s s i b l e negative consequences of human i n t e r a c t i o n s w i t h natural processes are searched f o r . Again the atmospheric C/C r a t i o i s an e x c e l l e n t example. Man-induced disturbances of the environmental system lead to changes i n the C/C r a t i o which are of the order of magnitude of the natural f l u c t u a t i o n s or even l a r g e r : the emission of C - f r e e C0 from f o s s i l energy consumption leads t o a decrease, and the emission of man-made C from nuclear weapons t e s t i n g , t o an increase of the atmospheric C/C r a t i o . In t h i s a r t i c l e , we f i r s t d i s c u s s b a s i c d a t i n g p r i n c i p l e s and then s t u d i e s based on isotopes produced by cosmic r a d i a t i o n i n extraterrestrial matter and i n the earth's atmosphere. The d i s c u s s i o n s are intended t o i l l u s t r a t e how a n a l y t i c a l p h y s i c a l and chemical s t u d i e s c o n t r i b u t e to the understanding of processes i n the environmental system and t h e i r h i s t o r y . 1 4

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Currie; Nuclear and Chemical Dating Techniques ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

OESCHGER

2.

7

Radioactive and Chemical Dating

P r i n c i p l e s o f Radioactive and Chemical Dating 1U)t

P e r i o d i c (~e ) and a p e r i o d i c (e.g., ~e processes i n nature can be used f o r d a t i n g . For the f o l l o w i n g we mainly con c e n t r a t e on a p e r i o d i c processes, changing the s t a t e o f a system i n nature as well-known f u n c t i o n s o f time. The present ( o r end) s t a t e o f the system i s e x p e r i m e n t a l l y determined and the i n i t i a l s t a t e o f the system i s estimated. The time f u n c t i o n f o r system changes then enables us t o c a l c u l a t e the age, i . e . , the time elapsed between the i n i t i a l and f i n a l s t a t e s . System changes which can be used f o r d a t i n g i n c l u d e : Downloaded by CORNELL UNIV on October 16, 2016 | http://pubs.acs.org Publication Date: January 29, 1982 | doi: 10.1021/bk-1982-0176.ch002

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The decay o f l o n g - l i v e d r a d i o i s o t o p e s s t i l l remaining from the nucleosynthesis. An example i s the c r e a t i o n o f A r by K decay. Based on the measured r a t i o o f the c o n c e n t r a t i o n of daughter A r t o parent K n u c l e i , the time during which Ar was accumulated i n the system (e.g., lunar m a t e r i a l a f t e r a meteorite impact) can be c a l c u l a t e d using the law o f r a d i o a c t i v e decay w i t h the appropriate decay constant. 4 0

4 0

4 0

-

4 0

The decay o f r a d i o a c t i v e isotopes created i n the earth's atmosphere by the i n t e r a c t i o n o f cosmic rays w i t h atomic n u c l e i o f atmospheric c o n s t i t u e n t s . A f t e r such n u c l e i (e.g., H as HH0 o r C as C 0 ) a r e removed from the atmosphere, e.g., f e d i n t o a groundwater system ( H) o r b u i l t i n t o a l i v i n g organism ( C ) , t h e i r number decreases a c c o r d i n g t o the law o f r a d i o a c t i v e decay. The time elapsed since s e p a r a t i o n from the atmosphere i s c a l c u l a t e d from the r a t i o o f the a c t i v i t y a t the time o f sampling t o the estimated a c t i v i t y i n the atmosphere a t the time o f s e p a r a t i o n . 3

3

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S o l a r energy enables the c r e a t i o n o f high order chemical and p h y s i c a l systems i n atmosphere and biosphere. Examples are amino a c i d s i n l i v i n g matter and high order c r y s t a l arrays o f snow f l a k e s . A f t e r these systems are withdrawn from t h e source o f high order they s t a r t continuous t r a n s i t i o n i n t o more probable s t a t e s : amino a c i d s tend t o g e t e q u a l l y d i s t r i b u t e d between l e f t and r i g h t - o r i e n t a t i o n and the s t r u c t u r e of the snow f l a k e gets l e s s and l e s s complex t i l l f i n a l l y f i r n g r a i n s o f approximately s p h e r i c a l shape are formed.

Processes i n nature correspond g e n e r a l l y only i n a f i r s t approximation t o what i s p o s t u l a t e d i n the p r i n c i p l e s o f d a t i n g methods. An e x c e p t i o n i s r a d i o a c t i v e decay which i s almost inde pendent o f v a r i a t i o n s i n the environmental c o n d i t i o n s , s i n c e energy d i f f e r e n c e s are i n v o l v e d which a r e l a r g e compared t o d i f ferences o f thermal e x c i t a t i o n i n the environment. This i s i n c o n t r a s t t o chemical and p h y s i c a l processes which do depend on environmental parameters such as temperature. An example showing


8

NUCLEAR AND CHEMICAL DATING TECHNIQUES 1 4

some o f the c o m p l i c a t i o n s i n v o l v e d i n a d a t i n g method i s C d a t i n g o f groundwater. F i r s t l y the atmospheric C/C r a t i o i s not constant w i t h time, as shown by t r e e - r i n g measurements. For a given atmospheric C/C r a t i o chemical processes which probably a l s o were not constant w i t h time determine the C/C r a t i o o f newly formed groundwater. During groundwater flow the C/C r a t i o decreases due t o r a d i o a c t i v e decay but a l s o due t o exchange w i t h the surface m a t e r i a l o f the a q u i f e r . In a d d i t i o n the water gets dispersed and water masses from d i f f e r e n t o r i g i n may get mixed. Summarizing, we can d i s t i n g u i s h the f o l l o w i n g i d e a l i z e d d a t i n g concepts: 14

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A low entropy system gets c l o s e d , and, according t o a process which can be q u a n t i t a t i v e l y d e s c r i b e d , goes t o s t a t e s of i n c r e a s i n g entropy ( r a d i o a c t i v e decay, r a c e m i z a t i o n , c r y s t a l growth, d i f f u s i o n ) .

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A high entropy system gets exposed t o negative entropy (negentropy) i n f l u x r e s u l t i n g i n an entropy decrease according t o a process which can be described q u a n t i t a t i v e l y . T y p i c a l sources o f negentropy are cosmic r a d i a t i o n ( i s o t o p e produc t i o n ) and s o l a r r a d i a t i o n ( c r e a t i o n o f high order chemical and p h y s i c a l systems).

I n t e r a c t i o n o f Cosmic Rays w i t h M e t e o r i t e s , The Moon and The Earth's Surface G a l a c t i c cosmic rays (mainly protons and α-particles w i t h energies above 1 GeV), and protons emitted from the sun ( w i t h energies i n general below 10 GeV) i n t e r a c t w i t h n u c l e i o f meteor i t e s , o f the surface o f the moon and o f the earth's atmosphere and produce isotopes. The s o l a r proton c o n t r i b u t i o n t o isotope production i s d e t e c t a b l e i n an upper l a y e r o f ~1 mm o f lunar surface m a t e r i a l . For the deeper l a y e r s o f meteorites and the lunar surface and f o r the atmosphere, however, the c o n t r i b u t i o n by the g a l a c t i c cosmic r a d i a t i o n dominates, except f o r extremely large solar f l a r e s . The s o l a r proton f l u x i s r e l a t e d t o s o l a r f l a r e s and i s s t r o n g l y v a r y i n g w i t h time. The g a l a c t i c cosmic rays are modulated due t o s h i e l d i n g e f f e c t s by i n t e r p l a n e t a r y magnetic f i e l d s c a r r i e d outward by the s o l a r wind plasma. The earth's surface i s f u r t h e r s h i e l d e d a g a i n s t charged p a r t i c l e s by the geomagnetic f i e l d .

*For h i g h l y r e l a t i v i s t i c p a r t i c l e s the momentum Ρ expressed i n eV . — ié n u m e r i c a l l y equal t o i t s energy, expressed i n eV.


2.

OESCHGER

than


For a given l a t i t u d e only p a r t i c l e s w i t h a momentum higher a minimum c u t - o f f momentum (P . ) can penetrate the geomin

magnetic

shield.

1

This

according t o ρ = 1 5 Î!Ê¥ mi η c


9

c u t - o f f momentum

C O S

\ .

c :

'

λ:

depends

on

latitude

velocity of l i g h t geomagnetic l a t i t u d e

Figure 1 s c h e m a t i c a l l y shows the modulation e f f e c t s on g a l a c t i c and s o l a r p a r t i c l e s and t h e i r i n t e r a c t i o n s . Whereas isotopes produced i n the s o l i d matter o f meteorites or the lunar surface m a t e r i a l remain a t t h e i r production s i t e s , isotopes produced mainly i n the earth's atmosphere are sepa rated according t o the geochemical p r o p e r t i e s o f the d i f f e r e n t elements. Studies Based on Isotope Production i n Meteorites and on the Lunar Surface Exposure ages The p e n e t r a t i o n depth o f cosmic r a d i a t i o n i s o f the order o f 1 m and t h e r e f o r e isotopes are produced by s p a l l a t i o n only i n the surface l a y e r s o f meteorites and the moon. A f t e r c o l l i s i o n s o f meteorites w i t h each other o r w i t h the moon, newly formed surfaces get exposed t o cosmic r a d i a t i o n and production o f s t a b l e and r a d i o a c t i v e isotopes s t a r t s . I f Ρ i s the production r a t e o f a t

s t a b l e isotope and i f P

r a d

i s the production r a t e of a r a d i o a c t i v e

isotope and i f both r a t e s are constant, then the numbers N ^rad

a r e

9

g t

and

l v e n

βΐ"Λ*βχρ

Μ

N

'-ψ

rad »

(1)

a n d

V - e" exp) Xt

( 2 )

(see a l s o f i g u r e 2) w i t h λ = decay constant and t = exposure time exp w

I f

X t

> > ]

t

h

e

n

1

e

t h e

d

e

c

a

y

r a t e

exp ' ^ r a d ^ r a d ' "' equals the production r a t e P - I f the r a t i o / the exposure age can then be c a l c u l a t e d according t o p

r a d

. e x

=

P

λ

r

-1 u s t _ N

rad

a

c

A

p s

\ t

= X N

l s

rad k n o w n

>

IVad P

st


(3)

10

N U C L E A R A N D C H E M I C A L DATING T E C H N I Q U E S

GALACTIC


COSMIC

SOLAR PROTONS

RAYS

(POSSIBLE VARIATIONS DEPENDING ON SUN'S POSITION WITHIN GALAXY; POSSIBLY CONTRIBUTIONS FROM SUPERNOVAE EXPLOSIONS)

(STRONGLY VARYING WITH SOLAR A C T I V I T Y )

^MODULATION BY SOLAR I PLASMA ( E . G . 1 1 YEAR CYCLE AND I T S AMPLITUDE MODULATION)

ISOTOPE PRODUCTION IN MOON/ METEORITES ( S O L I D MATTER)

_ 1

CUT-OFF OF LOWER ENERGY P A R T I C L E S BY GEOMAGNETIC F I E L D (TIME VARIATIONS)

ISOTOPE PRODUCTION IN ATMOSPHERE; D I F F E R E N T PATHWAYS ACCORDING TO GEOCHEMICAL PROPERTIES

Figure 1.

Cosmic radiation/modulations and interactions.


2. OESCHGER

11


Ο

ω α u CL ο -M υ ο ω

0)

/—> •H C ω no Ο ι—t ω •Η η 4-> ω c υ 4-> •Η D ω '—' "Ο

•Η 4J ω ο ω "Ό Ο «ο ω ^ ·Η

>


ω •Ρ

α χ • ω (Π +-» ο α ω χ &ο ω (ο

(NI CNI

Ο (-ι ·Η

ω Ε D ill

Χ3

ω ΓΗ ο D C


12

N U C L E A R AND

C H E M I C A L DATING T E C H N I Q U E S

P a i r s of isotopes s u i t e d f o r the determination of exposure ages are e.g., K r ( s t a b l e ) and K r ( T = 2.13-10 y ) [ 1 - 2 ] , 8 0

8 1

5

2

1 / £

3

3

4 1

He ( s t a b l e ) and Η ( Τ = 12.4 y ) [ 3 ] , and K ( s t a b l e ) and ° ^ l/2 · ° y) C » ]determination of exposure ages i s an example of a d a t i n g technique which uses the opening of a system to c r e a t i o n of i n f o r m a t i o n . Exposure ages of a great number of meteorites of d i f f e r e n t c l a s s e s have been measured and the question of the grouping of exposure ages, i n d i c a t i n g produc t i o n of a g r e a t e r number of meteorites i n a s i n g l e c o l l i s i o n event has been discussed. In a d d i t i o n i n f o r m a t i o n on l u n a r s u r f a c e dynamics has been obtained. ] / 2


4

K

T

=

Ί

2 7 β 1

9

4

5

T h e

Constancy of cosmic r a d i a t i o n Comparison of

the

activity

\

= λ Ν Γ 3 0

| of

radioisotopes with

d i f f e r e n t decay constants allows one to study the question whether r a d i o i s o t o p e production and t h e r e f o r e a l s o cosmic r a d i a t i o n have been constant w i t h time or have shown s i g n i f i c a n t v a r i a t i o n s . This i s a c r u c i a l question f o r a l l d a t i n g techniques based on cosmic ray produced isotopes. I t w i l l be taken up again w i t h s p e c i a l respect to d a t i n g methods used f o r t e r r e s t r i a l problems. Measurements of isotopes w i t h h a l f - l i v e s up to 4*10 y (e.g., M n ) on meteorite and lunar samples suggest t h a t cosmic r a d i a t i o n d i d not vary more than a f a c t o r of 2 [5-7]. For a v a r y i n g production r a t e Ρ (ΐ) the number of n u c l e i of a 6

53

λ

r a d i o a c t i v e isotope i can be c a l c u l a t e d according t o A (t) Τ — x

X T =

N

rad(« =

X T

Pi(t-T)e- dT =

fyx.t)

( 4 )

(T = age, P . ( X t ) = Laplace transform of the production f

rate P.(t)). Equation

(4)

shows

that

the

activities

A^(t)

essentially

correspond t o the production average over the l a s t one t o two mean lives. Some i n f o r m a t i o n on constancy of cosmic r a d i a t i o n i s gained, e.g., a systematic increase or decrease by a f a c t o r of three or so should be v i s i b l e . We w i l l l a t e r see, however, t h a t on e a r t h geochemical processes make much b e t t e r r e s o l v e d i n f o r m a t i o n available. 2

F i g u r e s i n brackets i n d i c a t e the l i t e r a t u r e references a t the end of t h i s paper.


2.

OESCHGER

13



The Use o f Cosmic Ray Produced Isotopes f o r Studies o f the Environmental System and I t s H i s t o r y Cosmic r a y produced isotopes a r e i d e a l t r a c e r s t o study processes i n the environmental system (see f i g u r e 3). They y i e l d i n f o r m a t i o n on mixing and c i r c u l a t i o n i n the atmosphere and the ocean, on a i r - s e a exchange and on global c y c l e s such as the hydrol o g i c a l and the carbon c y c l e s . They a l s o provide time s c a l e s t o r e c o n s t r u c t the h i s t o r y o f environmental processes stored i n , f o r example, g l a c i e r s and i c e caps, t r e e - r i n g s , peat bogs, and lake and ocean sediments. But, as mentioned b e f o r e , t h e r e are i r r e g u l a r i t i e s i n the r a d i o i s o t o p e records on which much a t t e n t i o n has r e c e n t l y been focussed. These i r r e g u l a r i t i e s r e f l e c t not o n l y v a r i a t i o n s i n the p r o d u c t i o n r a t e s , but a l s o changes i n t h e dynamics o f processes i n t h e environmental system (see a l s o Castagnoli and Lai [ 8 ] ) . I n t e r a c t i o n o f cosmic rays w i t h the atmosphere Radioisotopes a r e c o n t i n u o u s l y produced i n the atmosphere, the s t r a t o s p h e r i c p r o d u c t i o n being roughly t w i c e the t r o p o s p h e r i c one. As shown i n f i g u r e 4 i t i s useful t o d i s t i n g u i s h between isotopes o f noble gases, isotopes i n c o r p o r a t e d i n molecules o f gases o r vapors, and i s o t o p e s which get attached t o a e r o s o l s . R a d i o a c t i v e noble gas i s o t o p e s R a d i o a c t i v e noble gas i s o t o p e s used f o r the study o f proces ses i n atmosphere and ocean a r e given i n Table 1. Over the l a s t 12 years A r has been measured i n atmospheric samples (e.g., Loosli, et a l . , [9]). A r a c t i v i t y has been determined i n samples from the atmosphere, ocean, groundwater, and i c e . The i n i t i a l r e s u l t s suggest t h a t A r might become a very i n t e r e s t i n g d a t i n g t o o l ; see below. U n t i l now K r has o n l y been measured i n present day atmospheric samples. 3 7

3 9

3 9

8 1

Noble gas r a d i o i s o t o p e s w i t h T »atmospheric mixing times 1/p

3 9

8 1

5

A r and K r decay w i t h h a l f - l i v e s (269 y and 2.1 χ 1 0 y ) , which a r e long compared t o t h e atmospheric mixing times. There are only n e g l i g i b l e amounts o f A r i n r e s e r v o i r s other than t h e atmospheric one. Therefore, we e s s e n t i a l l y have cosmic r a y pro duced A r and K r i n one w e l l mixed atmospheric box ( f i g u r e 5 ) . Since t h e atmospheric composition r e g a r d i n g A r and Kr con t e n t s has probably been constant d u r i n g the l a s t 1 0 y we get f o r the a c t i v i t i e s o f A r and K r 3 9

3 9

8 1

6

3 9

M M Λ

8 1

X T

=

N

(

t

) =

r - T ) e " d T = ?

1

m o n t h

-

Ί/2

Specific Activity

35.1 d

M).003 dpm/L Ar

Comments Additional production by underground nuclear r e a c t i o n ( C a ( n , c 0 A r ) up t o 0.2 dpm/L Ar 4 0

39 Ar 81

Kr

269 y

M). 1 dpm/L Ar

2.1 χ 10° y

Kr

Anthropogenic c o n t r i b u t i o n > atmospheric mixing time.



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17


OESCHGER

i . e . , we get the same equation as f o r r a d i o i s o t o p e s produced i n e x t r a t e r r e s t r i a l matter. Only the two noble gas i s o t o p e s mentioned here provide a d i r e c t comparison based on t h i s simple formalism. Regarding t h e study o f constancy o f cosmic r a d i a t i o n based on today's spectrum o f r a d i o i s o t o p e s , we have l e s s informa t i o n on e a r t h than i n e x t r a t e r r e s t r i a l matter. On the other hand, the p h y s i c a l and chemical processes on e a r t h enable us t o get i n f o r m a t i o n on the h i s t o r y o f A ( t ) . An almost i d e a l process o f continuous sampling o f atmospheric a i r takes place i n p o l a r i c e sheets. A t the t r a n s i t i o n o f f i r n t o i c e ( a t a t y p i c a l depth o f 70 m) t h e a i r f i l l i n g the pore space between the f i r n g r a i n s gets pinched o f f . The bubbles thus formed c o n s t i t u t e i d e a l a i r samples. They get b u r i e d deeper and deeper i n t o the i c e , accord ing t o the r h e o l o g i c a l p r i n c i p l e s . Ice cores r e t r i e v e d by d r i l l i n g i n t o the deepest s t r a t a o f p o l a r i c e sheets c o n t a i n a i r t h a t may be 1 0 o r more years o l d . In the f o l l o w i n g t e x t we c a l c u l a t e the A r / A r v a r i a t i o n f o r a given c y c l i c A r p r o d u c t i o n variation. We can express c y c l i c production r a t e v a r i a t i o n s superim posed on a constant term by 5

3 9

3 9

P(t)

= P

+ ?e

iu)t

and

}

Q

expect a corresponding v a r i a t i o n A r n u c l e i i n the atmosphere:

(5)

i n the complex number N ( t ) o f

3 9

N(t) = N

Q

+ N e

iurt

1

(6)

For a one box system we have the d i f f e r e n t i a l equation Ν = Ρ - λΝ, and w i t h the above "Ansatz" iu)t i ω Ν, e

λΝ

ο

λΝ,β

ÎU)t (7)

leading to P

Q

and (λ+ιω) Ν

The r e l a t i v e v a r i a t i o n i n the

3 9

Ρ

A r i n v e n t o r y N^/N i s r e l a t e d Q

to the r e l a t i v e p r o d u c t i o n r a t e v a r i a t i o n P^/P by Q

N

o

λ

+

1 u )

P

o


( 8 )

18

N U C L E A R AND

We can d e f i n e Ρ(ω,λ)

D


λ + im as a damping f a c t o r and λ i arctg

(ω,λ)

obtain

ω/λ (9)

14

From observed v a r i a t i o n s of C/C i n t r e e - r i n g samples we have i n d i c a t i o n s of a 200 y c y c l e i n the r a d i o i s o t o p e production and P / P i s suggested to be of the order of 25 percent [13]. Downloaded by CORNELL UNIV on October 16, 2016 | http://pubs.acs.org Publication Date: January 29, 1982 | doi: 10.1021/bk-1982-0176.ch002

1

q

For the damping f a c t o r f o r obtains: |D|=

12.2

3 9

A r (λ = 1/388 and

y and ω = 2π/200 y )

a r c t g ω/λ

=

one

85°

Therefore, f o r the production r a t e v a r i a t i o n s mentioned above, we o b t a i n a r e l a t i v e amplitude of the a c t i v i t y A^/A = N^/N = 2%. Q

Q

In a d d i t i o n i t i s c a l c u l a t e d t h a t the atmospheric a c t i v i t y v a r i a t i o n s l a g behind the production r a t e v a r i a t i o n s by 47 y. Changes i n the A r l e v e l during the l a s t 100 years t h e r e f o r e cannot be detected w i t h the present p r e c i s i o n of ~5 percent i n A r measurements. 3 9

3 9

The

3 9

A r d a t i n g method 3 9

A r i n atmospheric samples was measured f o r the f i r s t time i n 1968 [10]. I t s modern net a c t i v i t y has been determined t o be 0.112 ± 0.010 dpm/L Ar. A r i s produced mainly by ( n , 2n) reac tions with A r . Because of i t s low s p e c i f i c a c t i v i t y i t i s very d i f f i c u l t t o measure. Compared to C i n "modern" samples, the s p e c i f i c a c t i v i t y of A r i s s m a l l e r by a f a c t o r of 65. Therefore the A r d a t i n g method s t a r t s w i t h s p e c i f i c a c t i v i t i e s correspond ing to t h a t of ca. 35,000 years o l d radiocarbon samples. At present, the minimum sample s i z e r e q u i r e d f o r a measurement i s ^400 mL Ar. For samples of t h a t s i z e a modern net e f f e c t of 0.036 cpm and a background of 0.030 cpm ( i n an underground l a b o r a t o r y ) are measured. The d a t i n g range a t present i s 30 to 1200 y, and 270 y (one h a l f - l i f e ) o l d samples can be measured w i t h a s t a t i s t i c a l e r r o r of ±30 y. Of great importance f o r the method i s the observation t h a t the c o n t r i b u t i o n from nuclear weapon t e s t s i s l e s s than 5 percent. For a p p l i c a t i o n of A r to oceanic c i r c u l a t i o n s t u d i e s we t h e r e f o r e can assume a steady s t a t e d i s t r i b u t i o n and do not need t o d i s t i n g u i s h pre-nuclear and nuclear components as i n the case of C . 3 9

4 0

14

3 9

3 9

3 9

14

3 9

A t e s t of the A r method i s the measurements on Ar e x t r a c t e d from a i r occluded i n p o l a r i c e . On the occasion of several p o l a r p r o j e c t s a t Byrd S t a t i o n , A n t a r c t i c a , under the auspices of


2.

OESCHGER

19


3

4

USARP , and i n Greenland under t h e auspices o f GISP ( c o l l a b o r a t i o n between USA, Denmark, and S w i t z e r l a n d ) samples were obtained by i n s i t u m e l t i n g o f about 3 tons o f i c e i n 400 m deep bore holes. Figure 6 shows the A r ages obtained f o r samples c o l l e c ted i n 1974 a t S t a t i o n Crête i n C e n t r a l Greenland [14]. The ages are p l o t t e d versus depth and compared w i t h those obtained by annual l a y e r counting based on data on the seasonal δ 0 v a r i a t i o n s . As expected the age o f zero years corresponds t o the depth of gas o c c l u s i o n (~70 m). The good agreement between A r and δ 0 ages i s a very v a l u a b l e c o n f i r m a t i o n o f the A r d a t i n g method. I t shows t h a t the d i f f i c u l t experimental steps: sample c o l l e c t i o n i n the f i e l d , s e p a r a t i o n o f A r from the a i r ( e s p e c i a l l y from Kr w i t h a t present r e l a t i v e l y high s p e c i f i c K r a c t i v i t y ) and counting o f the very low a c t i v i t y a r e under good c o n t r o l . A p p l i c a t i o n f i e l d s o f the A r d a t i n g method are g l a c i o l o g y , e.g., d a t i n g o f c o l d g l a c i e r s w i t h complex accumulation and a b l a t i o n c h a r a c t e r i s t i c s , and hydrology, e.g., d a t i n g o f groundwater, e s p e c i a l l y i n comparison w i t h the C d a t i n g technique. For h y d r o l o g i c a l d a t i n g i t i s assumed t h a t newly formed groundwater contains A r w i t h the atmospheric s p e c i f i c A r a c t i v i t y . I f the groundwater i s no longer i n contact w i t h t h e atmosphere i t s A r a c t i v i t y decreases according t o the law o f r a d i o a c t i v e decay. A r measurements on groundwater i n a q u i f e r s w i t h r e l a t i v e l y high U and Th contents, however, show t h a t underground production o f A r may l e a d t o s p e c i f i c A r - a c t i v i t i e s which are even higher than t h a t o f the atmosphere [15]. On the other hand groundwater was found w i t h A r a c t i v i t y below the d e t e c t i o n l i m i t , i n d i c a t i n g the e x i s t e n c e o f a q u i f e r s f o r which the A r d a t i n g technique provides u s e f u l i n f o r m a t i o n . The A r d a t i n g method i s very promising regarding oceanic mixing and c i r c u l a t i o n s t u d i e s , s i n c e i t s h a l f - l i f e compares w e l l w i t h the c h a r a c t e r i s t i c ocean mixing times. A t the ocean s u r f a c e , exchange w i t h the atmosphere brings the A r a c t i v i t y o f t h e d i s s o l v e d Ar c l o s e t o t h a t o f the atmo sphere. I f a water mass moves from the surface t o deeper s t r a t a , i t s A r decays. I t i s expected t h a t the A r a c t i v i t i e s o f the d i s s o l v e d Ar cover a range of 100 percent (ocean s u r f a c e ) t o 10 percent (deep ocean c u r r e n t s ) . Of s p e c i a l i n t e r e s t w i l l be the comparison w i t h C data, s i n c e r a d i o i s o t o p e s w i t h d i f f e r e n t h a l f - l i v e s weigh the age components d i f f e r e n t l y , and t h e r e f o r e the A r - C comparison w i l l g i v e i n f o r m a t i o n on the age d i s t r i b u t i o n of water masses. 3 9

1 8

3 9

1 8

3 9


8 5

3 9

1 4

3 9

3 9

3 9

3 9

3 9

3 9

3 9

3 9

3 9

3 9

3 9

1 4

5

3 9

1 4

3

U n i t e d States A n t a r c t i c Research Program. G r e e n l a n d Ice Sheet Program.


N U C L E A R A N D C H E M I C A L DATING

TECHNIQUES


20

i l Γ

à!

II Is * s

-ta «.s

1?

$ "

2.· en i

5^ r

£?

ι

δ


2.

OESCHGER

21


At ORNL (Oak Ridge National Laboratory) a group o f s c i e n t i s t s i s developing a method t o measure the A r and K r atoms d i r e c t l y w i t h good e f f i c i e n c y , e.g., by mass-spectrometry a f t e r m u l t i p l e electromagnetic enrichment steps. For such measurements a few kilograms o f i c e would provide enough argon and krypton [16]. I f an accuracy o f one percent could be o b t a i n e d , i t would be p o s s i b l e t o measure v a r i a t i o n s o f the a n c i e n t atmospheric a c t i v i t i e s . Because o f the simple geochemical behavior o f Ar and Kr these v a r i a t i o n s could u n e q u i v o c a l l y be a t t r i b u t e d t o p r o d u c t i o n rate v a r i a t i o n s . 3 9


1 4

8 1

C d a t i n g method

In 1947 W. F. Libby and c o l l a b o r a t o r s [17-19] measured f o r the f i r s t time C produced by cosmic r a d i a t i o n i n the atmosphere. He then proposed t h e use o f t h i s r a d i o i s o t o p e f o r d a t i n g o f organic m a t e r i a l . A unique c o n s t e l l a t i o n o f f a c t o r s makes t h e C d a t i n g technique a most f a s c i n a t i n g and powerful instrument f o r s t u d i e s o f the l a s t 50,000 y: 1 4

1 4

-

5

1 4

C i s mainly produced by (n,p) r e a c t i o n s w i t h n i t r o g e n , an element which i s ^5000 times more abundant than carbon i n t h e atmosphere. T h i s leads t o a r e l a t i v e l y high s p e c i f i c a c t i v i t y , thus f a c i l i t a t i n g measurements.

A s an example we assume a w e l l mixed r e s e r v o i r w i t h an average age of water Τ , i . e . , the age d i s t r i b u t i o n i s 9(T) =

For a r a d i o i s o t o p e w i t h decay r e s e r v o i r i s c a l c u l a t e d t o be

constant λ the a c t i v i t y

i n the

XT

A = A e " a p p = A /(λΤ^+l) o

Q

and Τ = Ι 1η(λΤ +1) app λ r For

Τ

= 1000 y e a r s :

(Τ : apparent r a d i o a c t i v e app age)

3 9

Τ

1 4

( A r ) = 496 and Τ ΓΓ

( C ) = 947 rr

years. In the case o f p i s t o n flow t h e r a d i o a c t i v e ages o f t h e two isotopes would be equal.


22

N U C L E A R AND

-


14

1 4

A f t e r i t s c r e a t i o n C gets o x i d i z e d t o C 0 and enters the biosphere; i t i s present i n the environment i n o r g a n i c form ( p l a n t s and animals) and i n o r g a n i c form ( C 0 i n atmosphere, 2

1 4

2

14

14

H C0â i n water, C 0 à i n sediments, e t c . ) 14

-

The C h a l f - l i f e of 5730 y permits d a t i n g o f samples not only from the h i s t o r i c a l l y documented p e r i o d but a l s o from the l a s t g l a c i a l p e r i o d .

-

The atmospheric C/C r a t i o d u r i n g the l a s t 50,000 y was s u f f i c i e n t l y constant t o make radiocarbon a remarkably r e l i able d a t i n g t o o l . Evidence f o r f l u c t u a t i o n s of the C/C r a t i o could be found by high p r e c i s i o n measurements on samples of known age. These f l u c t u a t i o n s can be a t t r i b u t e d to v a r i a t i o n s of processes i n the s o l a r system ( s o l a r a c t i v i t y ) and on e a r t h ( f l u c t u a t i o n s of C0 d i s t r i b u t i o n among the atmospheric, o c e a n i c , and b i o s p h e r i c r e s e r v o i r s ) . Both f l u c t u a t i o n s of s o l a r a c t i v i t y and o f the atmospheric C0 content may have c o n t r i b u t e d t o past c l i m a t i c changes.

14


14

2

2

-

During the i n d u s t r i a l e r a man has i n f l u e n c e d the atmospheric C/C r a t i o . By 1950 input of C0 from combustion of f o s s i l f u e l had l e d t o a decrease i n t h i s r a t i o of about 2 percent. By 1963 due t o n u c l e a r weapon t e s t s , however, the atmo s p h e r i c C l e v e l i n the northern hemisphere had increased by about 100 percent. The present excess i s s t i l l ~30 per cent. There i s a l s o an input of C from n u c l e a r power and reprocessing plants. 14

2

14

14

For i n f o r m a t i o n carbon 1980 [20].

on

the

14

C

dating

method see a l s o Radio-

Carbon Cycle Models and Disturbances As p a r t l y mentioned b e f o r e , n a t u r a l and anthropogenic induced v a r i a t i o n s of the atmospheric C0 c o n c e n t r a t i o n and of the C/ C and C / C r a t i o s have been observed. For a q u a n t i t a t i v e d i s c u s s i o n of these v a r i a t i o n s i n r e l a t i o n t o p o s s i b l e causes, models f o r the carbon c y c l e dynamics have been developed [21-25]. Compared t o the noble gas r a d i o i s o t o p e s A r and K r , f o r which we o n l y have t o c o n s i d e r a w e l l mixed atmospheric r e s e r v o i r , we have a much more complicated system f o r C . The C0 i n the atmosphere exchanges w i t h the carbon i n the biosphere and w i t h the 1 4

2

12

1 3

1 2

3 9

8 1

14

2

HCO3

CO3

C0 , and i n the ocean. Figure 7 shows the d i f f e r e n t r e s e r v o i r s w i t h t h e i r r e l a t i v e amounts of carbon. C i s produced i n the atmosphere, and by exchange and mixing i t gets d i s t r i b u t e d i n the e n t i r e carbon system. The p r e i n d u s t r i a l C/C r a t i o of the carbon i n the mixed ocean s u r f a c e l a y e r i s estimated t o have been 2

14

14


2.

OESCHGER


23

only 95 percent o f the atmospheric r a t i o , and t h a t o f the average carbon i n the deep ocean, only 84 percent o f the atmospheric one. This i n d i c a t e s t h a t i n the mean l i f e C (^8000 y ) the carbon i n the ocean i s not w e l l mixed. To d i s c u s s disturbances o f the system i t i s t h e r e f o r e necessary t o d i v i d e i t i n t o subsystems. The f o l l o w i n g d i s c u s s i o n s a r e based on the b o x - d i f f u s i o n model developed by Oeschger e t a l . , [ 2 6 ] , s i n c e t h i s model seems t o consider the most important c h a r a c t e r i s t i c s o f the carbon c y c l e without being too complicated. The model responses t o a v a r i e t y of system disturbances can be a n a l y t i c a l l y expressed. As i n d i cated i n f i g u r e 7 i n t h i s model the atmosphere, biosphere, and ocean surface mixed l a y e r are assumed t o be w e l l mixed r e s e r v o i r s . The exchange f l u x e s between them are assumed t o obey f i r s t order kinetics. The v e r t i c a l mixing below the ocean surface i s simulated by eddy d i f f u s i o n w i t h constant eddy d i f f u s i v i t y K. From t h e p r e i n d u s t r i a l C d i s t r i b u t i o n i n deeper ocean s t r a t a a value o f 4000 m y r - f o r Κ has been d e r i v e d which w i l l a l s o be used f o r the d i s c u s s i o n o f system disturbances. I t i s f u r t h e r assumed t h a t f o r the type o f disturbances which a r e o f i n t e r e s t here, the exchange w i t h the atmosphere i s n e g l i g i b l e . The average depth o f the ocean H i s 3800 m, t h a t o f the mixed l a y e r


1 4

1 4

2

1

Q C

h , m

75 m.

The e q u i v a l e n t depth o f t h e atmosphere h , d e f i n e d as a

t h i c k n e s s o f an ocean l a y e r c o n t a i n i n g the same amount o f carbon as the p r e i n d u s t r i a l atmosphere, i s taken as 58 m. (Some numbers, e s p e c i a l l y h , do not correspond t o the best p o s s i b l e estimates; a they a r e chosen t o keep c o n s i s t e n c y w i t h r e f e r e n c e s , see a l s o S i e g e n t h a l e r and Oeschger [ 2 7 ] ) . In the f o l l o w i n g s e c t i o n we w i l l now b r i e f l y d e s c r i b e n a t u r a l and anthropogenic disturbances o f the C 0 system which w i l l l a t e r be d i s c u s s e d based on the b o x - d i f f u s i o n model. 2

Observed changes i n the atmospheric composition 1 4

C 0 and i n i t s i s o t o p i c 2

C_fluctuations

During t h e l a s t 15 years i n t e n s i v e s t u d i e s on the h i s t o r y o f the atmospheric C/C r a t i o have been performed on t r e e - r i n g s [20]. The r e s u l t s can be summarized as f o l l o w s : from 7000 BP (before present) t o 2000 BP the average atmospheric C/C r a t i o had decreased by about 10 percent. Superimposed on t h i s general trend a r e s e c u l a r v a r i a t i o n s (Suess-Wiggles) o f the order o f 1 t o 2 percent. In some time i n t e r v a l s a b a s i c p e r i o d o f about 200 years i s v i s i b l e . The s t a t i s t i c a l e r r o r o f the measurements by Suess and c o l l a b o r a t o r s [13,28] i s o f the order o f 0.5 t o 0.7 percent, i . e . , not much s m a l l e r than the observed v a r i a t i o n s themselves. During the l a s t several y e a r s , however, s e v e r a l l a b o r a t o r i e s confirmed 14

14


24

NUCLEAR AND CHEMICAL

BIOSPHERE

ATMOSPHERE NQS 621X10V

N =2.AN K

1/60yr

13

=100·/.

DATING TECHNIQUES

6 C = -7V~

Rb

s R

n

a

1/7.7yr, MIXED LAYER Nm -3N ^=95·/. s 1


a

OCEAN e

ra

R = 8A /. 6 C= •!·/.· KsAOOOmV oc

Figure 7.

Main exchanging C reservoirs: atmosphere, biosphere, and ocean; and exchange fluxes. Carbon content of reservoirs: atmosphere (NJ, biosphere (N ), mixed layer (N ), and ocean (N ). R is the C concentration of C in the reservoir; and atmospheric concentra tion is defined as 100 percent. The C concentrations are corrected for isotopic frac tionation to a common B C = —25 per mil. Κ is the eddy diffusivity, and B C is the C concentration deviation from a standard. b

14

oc

m

14

13

13

13

CARBON DIOXIDE GROWTH TREND I 1 ' I I I 1

58 Figure 8.

60

62

1

64

1

66

68

70

72

74

76

78 1980

The CO concentrations observed at Mauna Loa, Hawaii by C. D. Keel ing and coworkers. t


OESCHGER

2.


25

1 4

these c h a r a c t e r i s t i c C v a r i a t i o n s by high p r e c i s i o n measurements [29-34]. The long-term C f l u c t u a t i o n s can be approximated by a s i n e f u n c t i o n o f time w i t h a p e r i o d o f about 8000 y. 1 4

The atmospheric C 0 increase due t o the f o s s i l f u e l C 0 2

2

input

The atmospheric C 0 c o n c e n t r a t i o n has been r i s i n g during t h e l a s t hundred years mainly due t o the C 0 input from f o s s i l f u e l combustion and p a r t l y due t o C 0 r e l e a s e from d e f o r e s t a t i o n . The increase o f the atmospheric C 0 c o n c e n t r a t i o n has been c o n t i n u ously monitored by K e e l i n g and co-workers [35-37] a t Mauna Loa, Hawaii, and a t the South Pole. The Mauna Loa record covering the p e r i o d 1958 t o 1978 i s given i n f i g u r e 8. During t h a t p e r i o d t h e y e a r l y average C 0 c o n c e n t r a t i o n increased from 315 ppm t o 335 ppm. During the same p e r i o d an amount o f C 0 corresponding t o 36 ppm has been r e l e a s e d i n t o the atmosphere due t o f o s s i l f u e l combustion and cement manufacture [38]. An apparent a i r b o r n e f r a c t i o n f o r the f o s s i l C 0 can be defined as 2

2

2


2

2

2

2

atmospheric C 0 increase ± f o s s i l C0£ input 9

ρ

= a

For the p e r i o d 1958-1978, the apparent a i r b o r n e f r a c t i o n i s F

=

a

20_£E2 36 ppm =

0

5

6

The expression "apparent" i s used, s i n c e the f o s s i l C 0 input does not represent the t o t a l anthropogenic C 0 input i n t o the atmosphere. I t p r o v i d e s , however, the g r e a t e s t p a r t o f i t . 1/F i s the system d i l u t i o n f a c t o r D ; i t expresses the C 0 2

2

a

r n

α

LU

c

2

2

,ο

uptake c a p a c i t y o f the system i n u n i t s o f the atmospheric uptake c a p a c i t y . This q u a n t i t y w i l l l a t e r be estimated using the boxd i f f u s i o n model. The

1 4

C - d i l u t i o n due t o the f o s s i l C 0 input ( S u e s s - e f f e c t ) 2

The f o s s i l C 0 brought i n t o the atmosphere does not c o n t a i n C and leads t o a C d i l u t i o n . Without exchanges between t h e atmosphere and the other r e s e r v o i r s , a f o s s i l C 0 input o f 10 percent u n t i l 1950 would have l e d t o a decrease o f the C/C r a t i o by 10 percent. The a c t u a l l y observed r e d u c t i o n o f the C/C r a t i o , however, i s o f the order o f 2 percent, i . e . , much smaller. This i s t o be explained by the exchange w i t h the b i o s p h e r i c and oceanic r e s e r v o i r s . Again a d i l u t i o n f a c t o r D p ς o f the system can be c a l c u l a t e d . ' 2

1 4

1 4

2

14

14

14



26

C a l c u l a t i o n o f d i l u t i o n f a c t o r s w i t h the b o x - d i f f u s i o n model For the f o l l o w i n g we assume t h a t the atmospheric v a r i a t i o n s i n C 0 and i n i t s carbon i s o t o p i c composition are e n t i r e l y due t o atmospheric system d i s t u r b a n c e s , such as t h e input o f C - f r e e C0 from f o s s i l C 0 p r o d u c t i o n , and d e v i a t i o n s from the average r a t e o f C production by cosmic r a d i a t i o n . The system dynamics, i . e . , the exchange c o e f f i c i e n t s and the eddy d i f f u s i v i t y are kept constant. We approximate the f o s s i l C 0 input p ( t ) by 2

1 4

2

2

1 4

2


p

co

( t )

=

2

p

i,cof

w 1 t h

μ

=

1 / 2 8

y

[ 3 9 ]

'

( 1 0 )

1 4

We a t t r i b u t e the long-term and short-term C v a r i a t i o n s t o c y c l i c v a r i a t i o n s i n the C production r a t e Pi4ç(t) which are iu)t approximated by Pi ç(t) = P i c * ' * frequencies 2π/Ί0,000 y and 2π/200 y. I t thus happens t h a t the C0 exchange system has been and i s subjected t o exponential ( f o s s i l C 0 i n p u t ) and c y c l i c ( s h o r t - t i m e C v a r i a t i o n s ) d i s t u r bances w i t h c h a r a c t e r i s t i c times o f the order o f 30 y. In a d d i t i o n the system has been exposed t o a quasi c y c l i c disturbance of the C production r a t e which i s a t present i n general a t t r i buted t o changes i n the Earth's magnetic d i p o l e moment. Paleomagnetic data i n d i c a t e t h a t 7000 y ago the value o f the d i p o l e moment was only about h a l f o f t h a t o f 2000 y ago, and estimates using a model f o r the geomagnetic modulation o f r a d i o i s o t o p e production and a carbon c y c l e model show t h a t t h i s increase i n the magnetic f i e l d could w e l l have caused most o f the observed decrease i n the atmospheric C/C r a t i o . In the f o l l o w i n g we s h a l l d i s c u s s the short-term system d i s turbances. Figure 9 shows how we can understand the p e n e t r a t i o n of atmospheric disturbances i n t o other r e s e r v o i r s . I f the d i s t u r bances have c h a r a c t e r i s t i c times which are long compared t o the exchange and mixing, the e n t i r e system i s responding and we have a dampening e f f e c t corresponding t o t h a t o f a one box system, as i n the case o f A r . For the kind of disturbances discussed here ( c h a r a c t e r i s t i c times ~30 y ) only f r a c t i o n s o f the biosphere and the ocean are responding. In f i g u r e 9 t h i s i s s c h e m a t i c a l l y explained and d e f i n i t i o n s which are used f o r the f o l l o w i n g are given. As i n the case o f the A r production v a r i a t i o n s a dampening f a c t o r D = ( P J / P ) / ( N J / N ) can be introduced. I t i s the product 1 4

G

+ P

4

, 1 4

w 1

t h

t h e

c h a r a c t e r l < s t l

c

0

2

1 4

2

1 4

14

6

3 9

3 9

0

of the dampening D

G

aflB

( ( i ) we c a l c u l a t e i f only the atmosphere were Mi

( e . g . , Sternberg and Damon, reference [ 4 0 ] ) .



OESCHGER


r 1

27

ι ATMOSPHERE

L

j

_

l

e

ft

mixed l a y e r

/

part o f system responding to perturbation

ι

e q u i l i b r a t i o n o f ocean surface i&l)

/

OCEAN

penetration

disturbances : Fossil

p^e

h C0

2

iu>t 14 C production

Figure 9.

variations

oc

/H

oc

depth i n t o ocean

f r a c t i o n o f ocean i n e q u i l i b r i u m w i t h ocean surface f r a c t i o n of biosphere i n e q u i l i b r i u m w i t h atmosphere

The CO system response to exponential and cyclic disturbances. t


28

N U C L E A R AND

responding response.

and

the

dilution


factor

0 (^ ) $

for

ω

the

system's

The t o t a l dampening becomes 7

D ft ) = D ft ) · D ft ) totHu> atmW Viu> u

The

factor ut input e is C0 increase i n a t i o n s i n the C M

2


14

;

f o r the

u

(11) "

;

u

atmosphere D . ( μ ) f o r the m

considered by ppm of a i r .

fossil

C0

2

expressing the C0 production and ( ) y varia. . production p^ e . This expression corresponds 2

D

1 U )

1 S

f o r

c

c l i c

a t m

t o t h a t obtained f o r the one box model, c o n s i d e r i n g t h a t only 1/58 of the t o t a l C i n the C0 exchange system i s i n the atmo sphere. Using the formalisms e x p l a i n e d i n Oeschger e t a l . , [ 2 6 ] , and Oeschger e t a l . , [ 3 9 ] , the dampening f a c t o r f o r the system 14

2

D

(

s iu,>

1

-

+

e

^W

Η

+

Ν

ε

ΪΓ

oc a (ocean uptake i n atmospheric u n i t s )

(atmosphere)

( 1 2 )

N~

b a (biosphere uptake i n atmospheric u n i t s )

For the f o l l o w i n g we

assume t h a t the p e r t u r b a t i o n s are r e l a H oc and c h a r a c t e r i s t i c times « — i . e . , the d i s t u r 2

tively

small

ance does not e f f e c t i v e l y penetrate to the ocean bottom. The parameters ξ and ε are t o be set equal t o one i f p e r t u r b a t i o n s i n the C/C r a t i o are considered. They d i f f e r from one i f the p e r t u r b a t i o n i s a change i n the C0 content of the atmospheric r e s e r v o i r , s i n c e the f l u x e s to the other r e s e r v o i r s do not change i n p r o p o r t i o n to the r a t i o of the new atmospheric C0 concentration to the steady s t a t e c o n c e n t r a t i o n . An increase i n atmospheric C0 and a d i s s o l v e d C0 gas i n the oceans brings about a s h i f t i n the 14

2

2

2

2

chemical e q u i l i b r i a between d i s s o l v e d C0 , 2

HCO3 and CO3,

resulting

i n an increase of the t o t a l C0 c o n c e n t r a t i o n (C0 +HC0 +C03) which i s s m a l l e r than t h a t of the d i s s o l v e d C0 gas alone. This i s taken i n t o account by i n t r o d u c i n g a b u f f e r f a c t o r ξ: i f the d i s s o l v e d C0 increases by ρ percent, the t o t a l C0 c o n c e n t r a t i o n 2

2

3

2

2

7

In

the expression

2

Di^)

the v a r i a t i o n

i s μ f o r an

exponential

disturbance and iu> f o r a c y c l i c disturbance.


2. OESCHGER


29

of seawater increases quasi s t a t i o n a r i l y only by ρ/ξ percent. For average surface seawater and a C 0 l e v e l o f ^300 ppm, ξ = 10; ξ increases f o r higher C 0 pressure [41]. Since the b i o s p h e r i c growth r a t e depends, among other f a c t o r s , on the C 0 supply, i t i s probable t h a t the C 0 i n c r e a s e induces, a t l e a s t f o r p a r t o f the biosphere, an increased growth r a t e ("C0 f e r t i l i z a t i o n " ) . A simple concept t o take t h i s i n t o account i s the i n t r o d u c t i o n o f a b i o t a growth f a c t o r ε : i f the atmospheric C 0 pressure i n c r e a s e s by ρ percent, t h e C 0 f l u x t o the biosphere increases by ε ρ percent. T y p i c a l l y , values f o r ε between 0 and 0.5 have been used i n carbon c y c l e s models [26,41], 2

2

2

2

2

2

2

In Table 2 the formulas f o r e ( ^ ) , h ft )/H and h.((M/H. iu) oc lu) oc b iu) b f o r the d i f f e r e n t p e r t u r b a t i o n s are given. F i r s t we apply the formalism t o t h e short-term C v a r i a tions. I f we assume t h a t they are caused by quasi c y c l i c C production r a t e v a r i a t i o n s w i t h a p e r i o d o f 200 y [42] we g e t a dilution factor η r* ^ - 1ω (η , . χ oc(iu>) o c . b(iuQ b)nm 1 e(lU rL , tt ontt " λΤδδ * N Ta H ~ · N -a; ( \ oc b


y

1 4

1 4

h

1 4

(

i

}

D

14

Α

Α

N

N

+

D

C,atm

h

° *

14

( 1 3 )

C,S

D,-

(iiu) i s a complex number expressing both the r a t i o o f the C tot r e l a t i v e amplitudes and the phase s h i f t between C production and observed C c o n c e n t r a t i o n s

1 4

1 4

ΙΟ·,/· |~ 20; phase angle φ = 36° corresponding t o a l a g o f C,tot ^20 y. For many y e a r s , t h i s c a l c u l a t e d s t r o n g model a t t e n u a t i o n was the reason why t h e e x i s t e n c e o f the s e c u l a r C f l u c t u a t i o n s was doubted: v a r i a t i o n s i n C o f two percent would correspond t o C production r a t e v a r i a t i o n s o f ~40 percent, compared t o v a r i a t i o n s o f the order of 10 t o 20 percent as p r e d i c t e d from C production models. S t u i v e r and Quay [ 3 1 ] , used the box d i f f u s i o n model t o c a l c u l a t e t h e C production r a t e v a r i a t i o n s observed i n tree-rings. Figure 10 shows these production r a t e v a r i a t i o n s p l o t t e d together w i t h i n v e r s e sun spot numbers. A good c o r r e l a t i o n i s obtained. S t u i v e r and Quay compared t h e magnitude o f these geochemically d e r i v e d production changes w i t h C p r o d u c t i o n changes d e r i v e d from atmospheric neutron f l u x measurements. A , H

1 4

1 4

1 4

1 4

1 4

1 4


30

N U C L E A R A N D C H E M I C A L DATING

Table 2.

C a l c u l a t i o n s Regarding System Response t o Exponential and C y c l i c Disturbances.

e

Perturbation . .. C production ., . variation r


w a

P l

t

e

t

n

i u , t

_ , ξ = 1 *

h

,iUK

(

0C M

H

Parameters

Λa

I4

TECHNIQUES

}

^

oc

h k

h

a am m r— τ—r—— h,k, + h iu> a am oc

m

b

+ VK7TÛ)

π Η

m

oc

k.

ba -τ , . k. + iu> ba

ε = 1

200 y COg input

HV.

t

~

ξη k

h

* a am

i n

" a am

m r

m

oc

+ VK7ÎJ Ύ

r

ba

oc

ba

k

h a

r

ε = 0.2 (assumption) μ = 1/28 y

ι*

14„ .., . . C dilution (Suess E f f e c t ) due t o f o s s i l C 0 input 2

p ^

h k

». _ τ ξ = I h

r—r a am k

a am

h + VK7M m —ρ

+

H

T-—Û— h

" oc

k

m

oc

k

τ ba

ε = 1

ut

μ = 1/28 y


h a

Da

ίγτ,

μ

Currie; Nuclear and Chemical Dating Techniques ACS Symposium Series; American Chemical Society: Washington, DC, 1982. , 1700 Year A.D.

τ • 1800

14

ιπ 1900

τ

Science

14

Figure 10. Carbon-14 production as calculated from tree-ring C concentrations by means of the box-diffusion model (31). The dashed and the dotted curves correspond to two different assumptions for the biosphere. The good correlation with sunspot numbers ( ) suggests that indeed solar modulation of the cosmic radiation causes the C variations.

ι 1640


32

N U C L E A R AND


good agreement i s obtained f o r the 20th and 19th century data, but f o r the Maunder Minimum p e r i o d , A.D. 1654 t o 1741, a g r e a t e r dependence on sun spot numbers i s suggested, which S t u i v e r a t t r i b u t e s t o an a d d i t i o n a l C production i n c r e a s e d u r i n g p e r i o d s when sun spots are absent. A g e n e r a l l y s a t i s f a c t o r y agreement i s obtained, suggesting t h a t f o r c y c l i c p e r t u r b a t i o n s w i t h a charac t e r i s t i c time of 30 years the model seems to g i v e reasonable answers. In the second p l a c e we apply the formalism t o the C0 i n c r e a s e due t o the f o s s i l C0 input. As mentioned b e f o r e , f o r the p e r i o d 1958 to 1978 an apparent a i r b o r n e f r a c t i o n of 0.56 corresponding t o a d i l u t i o n f a c t o r of 1.79 has been observed. For μ = 1/28 y we o b t a i n w i t h ξ = 10, h = 410 m, h / H = 14

2

2


Q C

0 (

0 C

0.108, e = 0.837, h / H = 0.318, f i n a l l y a d i l u t i o n f a c t o r b

b

( ε

D 2 , S (μ = 1/28 y ) = 1 + 0.60

=

0 )

+ (0.15 j° (ε = 0.2)

LU m

U

D

;

The model p r e d i c t e d d i l u t i o n f a c t o r s are w i t h i n the e r r o r l i m i t s of the observed v a l u e , D = 1.79 ± 10 percent, f o r both values of ε. For optimum agreement, the b i o t a growth f a c t o r ε should be 0.25. There would be, however, a c o n s i d e r a b l e discrepancy between the model^calculated d i l u t i o n f a c t o r and the d i l u t i o n f a c t o r r e q u i r e d i f the b i o s p h e r i c C0 i n p u t were of comparable s i z e as the f o s s i l C0 input as s t a t e d by b i o l o g i s t s [43]. For a d i s c u s s i o n of t h i s question see a l s o Oeschger e t a l . , [39]. T h i r d l y , we c a l c u l a t e the C d i l u t i o n corresponding t o the CO? i n c r e a s e . In 1950, before the nuclear weapon t e s t s , the i n t e g r a t e d C0 p r o d u c t i o n amounted t o about 10 percent of the p r e i n d u s t r i a l atmospheric C0 content. I f there had been no exchange w i t h other r e s e r v o i r s , a decrease of the C/C r a t i o by 10 percent would have r e s u l t e d . T r e e - r i n g C measurements i n d i c a t e d , how ever, a decrease by only about 2 percent. Again we c a l c u l a t e the system d i l u t i o n . In a f i r s t approximation ξ and ε are s e t equal to one and we o b t a i n 2

2

14

2

2

14

14

D,(1/28 y) = 1 + 2.4 + 0.8 = 4.2 •*c,s 14

(16)

Thus the C d i l u t i o n i n c l u d i n g system d i l u t i o n i n 1950 i s e s t i mated t o be -10 percent/4.2 = -2.4 percent. Using the a c t u a l C0 production h i s t o r y , Oeschger e t a l . , [26] c a l c u l a t e d f o r the Suess e f f e c t i n 1950 a value of -2.0 percent. T h i s i s e s s e n t i a l l y i n agreement w i t h the measurements [44], though C f l u c t u a t i o n s due t o C production r a t e v a r i a t i o n make a p r e c i s e determination of the Suess e f f e c t d i f f i c u l t . 2

14

14


2.

OESCHGER


Changes i n the CO* system a t the end o f l a s t g l a c i a t i o n 14

Compression £f_the_ „C_ti.me s c a l e around_l0,000 BP D e n d r o c h r o n o l o g i c a l l y dated t r e e - r i n g s f o r t h e o b s e r v a t i o n of C v a r i a t i o n s a r e a v a i l a b l e f o r about t h e l a s t 8000 y. A comparison o f t h e C v a r i a t i o n record w i t h the c l i m a t i c h i s t o r y record suggests the e x i s t e n c e o f r e l a t i o n s between mechanisms producing C v a r i a t i o n s and those r e s p o n s i b l e f o r c l i m a t i c change. I f such a r e l a t i o n indeed e x i s t e d , e s p e c i a l l y pronounced v a r i a t i o n s would be expected t o have occurred d u r i n g the t r a n s i t i o n p e r i o d from G l a c i a l t o P o s t g l a c i a l , i . e . , from about 14,000 t o 9000 BP. When d a t i n g peat bog samples c o v e r i n g the end of t h e Younger Dryas c o l d phase, as determined by p o l l e n analy s i s , we observed i r r e g u l a r i t i e s i n the C time s c a l e . Detailed C analyses c o v e r i n g t h i s p e r i o d were then performed on samples from a peat bog near Wachseldorn ( S w i t z e r land) which from p o l l e n analyses i s known t o have grown c o n t i n u o u s l y d u r i n g the whole Late G l a c i a l and P o s t g l a c i a l . The samples from t h e second h a l f o f t h e Younger Dryas c o l d p e r i o d t o the beginning o f the Preboreal show r a t h e r constant C concentrations over a p e r i o d f o r which, based on t h e assumption o f constant peat growth, one would expect a change by about 7 p e r c e n t , corresponding t o a d i f f e r e n c e o f age o f about h a l f a m i l l e n i u m [45]. These r e s u l t s must be confirmed by a d d i t i o n a l s t u d i e s . A t present we are measuring the C/C r a t i o on lake chalk samples c o v e r i n g the p e r i o d o f i n t e r e s t . A l r e a d y , now we consider i t as very probable t h a t strong C v a r i a t i o n s occurred during t h i s p e r i o d o f major c l i m a t i c change. The q u e s t i o n i s what has caused them. V a r i a t i o n s o f the atmospheric C/C r a t i o can be caused e i t h e r by changes i n the C p r o d u c t i o n r a t e o r by changes i n the t e r r e s t r i a l carbon system o r both. Changes i n the t e r r e s t r i a l carbon system l e a d i n g t o C/C r a t i o changes might have been induced e i t h e r by changes i n the p a r t i t i o n i n g o f the C 0 among the atmospheric, b i o s p h e r i c , and oceanic r e s e r v o i r s o r by changes i n the dynamics o f ocean mixing. Assuming a constant g a l a c t i c cosmic r a d i a t i o n p r o d u c t i o n r a t e , we would expect v a r i a t i o n s t o be caused mainly by changes i n the earth's magnetic f i e l d w i t h i t s s h i e l d i n g p r o p e r t i e s and by modulation o f the g a l a c t i c cosmic r a d i a t i o n by s o l a r plasma magnetic f i e l d s . During the l a t e p l e i s t o c e n e the geomagnetic f i e l d s t r e n g t h seems t o have been g e n e r a l l y lower and the atmospheric C/C r a t i o t h e r e f o r e higher than i n the holocene [ 4 6 ] . B a r b e t t i t h e r e f o r e n o t i c e s t h a t t h e r e should be a compression i n t h e C time s c a l e from 12,000 t o 10,000 BP. But a t the end o f t h e l a s t g l a c i a l p e r i o d there a l s o might have been a change i n s o l a r a c t i v i t y . Periods o f c o l d c l i m a t e c o i n c i d e w i t h p e r i o d s o f high C produc t i o n (Maunder Minimum and L i t t l e Ice Age). The C p l a t e a u i n samples c o v e r i n g the Younger Dryas-Preboreal t r a n s i t i o n t h e r e f o r e might r e f l e c t a s w i t c h i n g from low t o high s o l a r a c t i v i t y . 1 4

1 4


1 4

1 4

1 4

1 4

14

1 4

14

1 4

14

2

14

1 4

1 4

1 4


N U C L E A R AND

34


However, changes i n the carbon c y c l e d u r i n g the p e r i o d o f i n t e r e s t cannot be excluded, as i s d i s c u s s e d i n the next paragraph. The l a s t 30,000 years h i s t o r y of the atmospheric C0

content

g

For an assessment of the C0 problem a knowledge of the h i s t o r y of the atmospheric C0 content would be of great value. What was the p r e - i n d u s t r i a l atmospheric C0 content? Did i t f l u c t u a t e or was i t r a t h e r constant? The answer t o such questions would help on the one hand t o improve our knowledge on the carbon system and i t s response t o d i s t u r b a n c e s , and on the other hand provide i n f o r m a t i o n regarding the s e n s i t i v i t y of the c l i m a t e system t o atmospheric C0 changes. Probably the only p o s s i b i l i t y t o r e c o n s t r u c t d i r e c t l y the h i s t o r y of the atmospheric C0 content (and C / C and C/C r a t i o s ) are measurements on natural a n c i e n t i c e samples. Ice formed by s i n t e r i n g of dry c o l d snow c o n t a i n s a i r w i t h atmo s p h e r i c composition i n i t s bubbles. U n t i l a few years ago attempts t o determine a n c i e n t atmospheric C0 contents by measuring C0 contents of the a i r occluded as a i r bubbles i n n a t u r a l i c e seemed t o provide u n r e l i a b l e r e s u l t s [47-49]. C0 /N r a t i o s much higher than the atmospheric values were found i n d i c a t i n g the presence of a d d i t i o n a l C0 of undefined o r i g i n . In the l a s t few y e a r s , however, the e x t r a c t i o n technique has been f u r t h e r developed and c o n s i d e r a b l y improved by two l a b o r a t o r i e s [50,51]. The group i n Bern obtained C0 c o n c e n t r a t i o n s f o r a i r occluded i n young i c e samples of 270 t o 370 ppm, w i t h an average of 310 ppm [52]. This value i s c l o s e t o the assumed pre i n d u s t r i a l atmospheric C0 l e v e l and supports the theory t h a t on i c e samples from very c o l d accumulation areas, C0 /N r a t i o s can be measured which do i n d i c a t e the atmospheric composition at the time of i c e formation. The e x t r a c t i o n procedure i s as follows: Samples of 300 g of i c e are melted i n vacuum and the gases produced by the e x p l o s i o n of a i r bubbles on the m e l t i n g i c e s u r f a c e are e x t r a c t e d . This so c a l l e d f i r s t e x t r a c t i o n f r a c t i o n i s considered t o be r e p r e s e n t a t i v e f o r the composition of the gases i n the bubbles. E x t r a c t i o n of the gases i s then continued (second e x t r a c t i o n f r a c t i o n ) f o r several hours u n t i l no more C0 i s c o l l e c t e d . Based on the analyses o f the two e x t r a c t i o n f r a c t i o n s an estimate can then be made of how much C0 i s contained i n the a i r bubbles and how much i n the i c e l a t t i c e . A n a l y s i s of the gas composition ( N , 0 , Ar, C0 ) i s made by gas chromatog raphy. Our experience to-date suggests t h a t c u r r e n t measurement and a n a l y s i s techniques a l l o w the r e l i a b l e d e t e c t i o n of v a r i a t i o n s i n the atmospheric C0 content of 30 percent or more. Our f i r s t measurements have been made on samples c o v e r i n g the l a s t 30,000 y e a r s , a p e r i o d of major c l i m a t i c change which might p o s s i b l y have l e d t o a change i n the atmospheric C0 content. Ice cores 2

2

2


2

1 3

1 2

14

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2


OESCHGER

2.


35

s u i t e d f o r such a study were a v a i l a b l e from the s u c c e s s f u l d r i l l i n g by U.S. s c i e n t i s t s i n 1966 t o the bedrock o f t h e Green land i c e cap i n northwest Greenland ( S t a t i o n Camp Century) and i n 1967/1968 t o the bedrock o f the West A n t a r c t i c i c e s h i e l d a t Byrd S t a t i o n . In f i g u r e 11, C 0 contents measured i n t h e f i r s t e x t r a c t i o n f r a c t i o n are p l o t t e d together w i t h the δ 0 record f o r the Camp Century and the Byrd S t a t i o n core [53,54]. The d a t i n g i s based on model c a l c u l a t i o n s given i n references [54,55]. Both records show s i m i l a r trends: low values d u r i n g the l a s t g l a c i a t i o n , and then, p a r a l l e l t o the δ 0 t r a n s i t i o n , an i n c r e a s e t o higher holocene C0 values. For both cores s i m i l a r minimum values (200 t o 230 ppm) are found f o r the l a s t g l a c i a t i o n . F i r s t f r a c t i o n measure ments on young i c e (shown here only f o r the Byrd core) y i e l d values as i n the holocene; f o r the Camp Century core higher values are obtained. The question has t o be answered whether the general C0 t r e n d i n the i c e core i s mainly due t o a change i n atmospheric C0 content o r a c l i m a t i c e f f e c t on C 0 enclosure process. The most probable e x p l a n a t i o n f o r the general t r e n d - low values during G l a c i a l and higher values d u r i n g P o s t g l a c i a l - i s a corresponding change i n the atmospheric C 0 content. The d i f f e r ence between the two p r o f i l e s i n the holocene may p a r t l y be due t o a c o n t r i b u t i o n o f C 0 trapped i n melt l a y e r s d u r i n g the c l i m a t i c optimum o r due t o another c l i m a t i c e f f e c t on C 0 enclosure a t Camp Century. For t h e c l i m a t i c optimum we c o n s i d e r t h e values measured on the Byrd S t a t i o n core as the more r e l i a b l e ones and do not exclude the p o s s i b i l i t y t h a t d u r i n g t h a t p e r i o d t h e atmospheric C 0 content was s i g n i f i c a n t l y higher than a t p r e s e n t . A p o s s i b l e e x p l a n a t i o n f o r a change i n atmospheric C 0 content i s t h a t i t s t r o n g l y depends on the t o t a l C 0 content o f the ocean s u r f a c e . Due t o t h e b u f f e r e f f e c t , a r e l a t i v e change i n t o t a l C 0 i n t h e ocean s u r f a c e l e a d s , f o r assumed constant a l k a l i n i t y , t o a t e n f o l d r e l a t i v e change i n the atmospheric C 0 content. The t o t a l C 0 i s determined p a r t l y by marine b i o s p h e r i c a c t i v i t y which leads to a d e p l e t i o n a t t h e ocean s u r f a c e compared t o t h e ocean average. A r e l a t i v e l y s l i g h t change i n b i o s p h e r i c a c t i v i t y c o u l d , t h e r e f o r e , l e a d t o a s i g n i f i c a n t decrease i n atmospheric C0 . For an i n t e r e s t i n g d i s c u s s i o n o f C 0 v a r i a t i o n s due t o PO4 v a r i a t i o n s i n the ocean, see Broecker [56]. 2

1 8

1 8


2

2 2

2

2

2

2

2

8

2

2

2

2

2

2

2

Recent measurements i n d i c a t e t h a t the r e l a t i v e l y high C 0 concen t r a t i o n s determined f o r p a r t o f the holocene i c e probably are due t o contamination o f the i c e core which f o r t h i s age range shows many small c r a c k s . 2



(ppm)

CO, 1st fraction

400 300 200 30000

10000

Radiocarbon Figure 11. Camp Century, Greenland and Byrd Station, Antarctica ice cores: C0 contents of the first gas extraction fraction and B 0 profiles (50). The B 0 profiles are from Dansgaard and coworkers, and the ages are calculated according to Ref. 54. 2

18


i8

OESCHGER

2.


37

Measurements o f r a d i o i s o t o p e s o f s o l i d s , d i r e c t l y deposited on p o l a r i c e caps One i s compelled t o pose the question i f e x p e r i m e n t a l l y i t w i l l become p o s s i b l e t o decide whether the C v a r i a t i o n s observed on t r e e - r i n g samples, peat bogs, sediments, e t c . , are p r i m a r i l y caused by an e x t e r n a l f o r c i n g o f the system (production r a t e v a r i a t i o n s ) o r by an i n t e r n a l one. Recent progress i n d e t e c t i o n of small numbers o f n u c l e i o f an isotope by mass spectrometry based on the use o f a p a r t i c l e a c c e l e r a t o r [57,58] make i t p o s s i b l e t o measure the cosmic ray produced B e o r C 1 deposited i n only 1 kg o f i c e . These isotopes get attached t o aerosol p a r t i c l e s and deposited w i t h them. T h e i r residence time i n the atmosphere i s r e l a t i v e l y short (months t o a few y e a r s ) . Changes i n t h e i r production r a t e s a r e t h e r e f o r e r e l a t i v e l y unattenuated and r e f l e c t e d i n p r e c i p i t a t i o n w i t h good time r e s o l u t i o n . Several l a b o r a t o r i e s t h e r e f o r e intend t o measure p r o f i l e s of these isotopes on i c e cores d r i l l e d i n p o l a r i c e caps. The new technique a l s o makes p o s s i b l e measurements o f the C i n the C 0 occluded i n about 30 kg o f i c e . From the C measurements again t w o f o l d i n f o r m a t i o n i s expected: 1 4


1 0

3 6

1 4

2

1 4

-

d a t i n g o f i c e o f cores d r i l l e d i n t o the p o l a r i c e caps but a l s o o f surface samples c o l l e c t e d i n t h e i r a b l a t i o n area.

-

s t u d i e s o f C v a r i a t i o n s i n i c e core samples from areas w i t h r e g u l a r s t r a t i g r a p h y enabling independent d a t i n g .

1 4

I t i s p o s s i b l e t o o b t a i n such samples covering the f u l l range o f the C time s c a l e , i . e . , more than 50,000 years back i n time. Comparison o f C and B e v a r i a t i o n s w i l l enable us t o disentangle t h e e x t e r n a l and i n t e r n a l causes o f t h e C v a r i a t i o n s : the B e and C 1 v a r i a t i o n s w i l l serve as a measure f o r the C production r a t e v a r i a t i o n s . To a f i r s t approximation we may assume t h a t they are p r o p o r t i o n a l t o the C production v a r i a t i o n s . Based on the B e and C 1 measurements we t h e r e f o r e w i l l approximately know t h e C production r a t e v a r i a t i o n p ( t ) . Based on t r e e - r i n g measurements t h e atmospheric C v a r i a t i o n s o f the l a s t 8000 years a r e known and from measurement on C 0 e x t r a c t e d from i c e cores i t h o p e f u l l y w i l l be p o s s i b l e t o get i n f o r m a t i o n on atmospheric C/C v a r i a t i o n s over a l a r g e time range. P ( t ) and C ( t ) / C a r e then r e l a t e d t o each other v i a the response o f the C 0 system t o a C 6-input being named R ( t , t ) ; we get the following relation 1 4

1 4

1 0

1 4

1 0

3 6

1 4

1 4

1 0

3 6

1 4

1 4

2

14

1 4

1 4

2

1 4

C(t)/C = A o

1 4

(t-i)R(t,t)dx


(17)


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