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The assessment of 21 0 Pb data from sites with varying sediment accumulation rates

P. G. Appleby' & F. Oldfield2I Department of Applied Mathematics & Theoretical Physics, University of Liverpool, Liverpool L69 3BX,U.K.2 Department of Geography, University of Liverpool, Liverpool L69 3BX, U.K.

Keywords: paleolimnology, 210 Pb, sediment accumulation

Abstract

The last few years have seen a dramatic growth in the use of 210 pb sediment dating. Despite this,considerable doubt still surrounds the nature of the processes by which 2 10 Pb is deposited in lake sediments,

and this has lead to a situation where there is a choice of dating models offering different interpretations of2 10 Pb data. In assessing 2 10 Pb data it is therefore essential to first of all determine whether data is consistentwith the assumptions of the dating model, and to then compare the 2 10 b chronology with independentdating evidence. We have tested 2 10b data from a wide variety of sites, and our calculations indicate that thecrs (constant rate of 21 0 Pb supply) model provides a reasonably accurate chronology when the total 2 10 Pbcontents of cores from neighbouring locations are comparable.

Introduction 2 1 0Pb Chronology of lake sediments

In most of the early papers on 2 10 Pb chronology(Krishnaswamy et al. 1971; Koide et al. 1973; Rob-

bins & Edgington 1975), the methods used assumeda constant rate of sediment accumulation, and wereapplicable to sediment cores in which the unsup-ported 2 10 Pb activity declined exponentially downthe core. There is, however, abundant evidence foraccelerating accumulation rates in many lakes inrecent times, and a need therefore to develop areliable model for calculating 2 10 pb dates in siteswith varying rates of sediment accumulation.

Considerable doubt still surrounds the precisenature of the processes by which 2 10 Pb is depositedin lake sediments, and

for this reason2 10

Pb datafrom sites with varying sediment accumulationrates is interpreted by different authors in differentways. Since these processes may well vary from siteto site it is unlikely that on e model will be universal-ly applicable. The purpose of this paper is to outlinethe principal assumptions used in 2 10 pb chronol-ogy, and to present techniques for assessing theconsistency of data with these assumptions.

The processes by which 2 1 0Pb is delivered tocatchment surfaces have been described in detail

elsewhere (e.g. Krishnaswamy & Lal, 1978). Theradium isotope 2 2 6 Ra (half-life 1622 yrs.) decays toyield the inert gas 22 2Rn. This in turn decays (with ahalf-life of 3.83 days) through a series of short-livedisotopes to 21 0 Pb (half-life 22.26 yrs.). A fraction ofthe 22 2 Rn atoms formed by 2 26 Ra decay in soilsescape from the soil particles into the interstices anddiffuse through the soil into the atmosphere wherethey decay to 2 1 0Pb. This is removed from the at-mosphere by rain, snow, or dry fallout, falling eith-er onto the land surface where it is trapped in sur-

face soils (Benninger et al . 1975), or into lakes oroceans. 210 pb falling into lakes is scavenged fromthe lake waters by sediments, and deposited on thebed of the lake. Krishnaswamy & Lal (1978) haveestimated that the mean 2 1 0Pb flux onto the landsurface is about 0.45 pCi cm- z a -1. Local valuesof the mean 21 0 Pb flux are governed by local orregional meteorological factors, and range from0. 15 pC i cm -2 a- in Australia to 0.96 pC i cm- a I

Hydrobiologia 103, 29 35 (1983). Dr W. Junk Publishers, The Hague. Printed in the Netherlands.

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in Hokkaido, Japan.The 2 10 Pb activity of lake sediments has two

components, a supported component Cs derivingfrom 2 22 Rn decay within the sediment column, andan unsupported (or excess) component C derivingfrom the atmospheric fallout of 21 0 Pb. C s can, formost purposes, be approximated by the 22 6Ra con-centration. In the absence of 2 10 Pb fallout, 2 10 Pband 22 6 Ra would be in radioactive equilibrium. C isdetermined by subtracting C s from the total

2 10 Pbconcentration.

The unsupported 2 10 Pb concentration in eachsediment layer declines with its age in accordancewith the usual radioactive decay law. This law canbe used to calculate the age of the sediment pro-vided that the initial unsupported 2 10 Pb concentra-

tion when laid down on the bed of the lake can beestimated in some way.

If the erosive processes in the catchment aresteady, and give rise to a constant rate of sedimentaccumulation, it is reasonable to suppose that everysediment layer will have the same initial unsupport-ed 2 10 Pb concentration. In this case the unsupport-ed 21 0 Pb concentration will decline exponentially

with the cumulative dry mass of sediment. Whenthe unsupported 2 10 Pb concentration C is plottedon a logarithmic scale, the resulting 2 10 Pb profilewill be linear. The sediment accumulation rate canbe determined graphically from the mean slope ofthe profile, or analytically by using a least squaresfit procedure. In this model, sometimes referred toas the constant flux-constant sedimentation rate(cf:cs) model, the exact mechanism by which thesediment accumulated 2 10 Pb is immaterial.

2 1 0 Pb chronology under varying sediment accumu-lation rates

In many cases it is clear that rates of erosion and

sedimentation have varied significantly during thepast 150 years. In this event the 2 10 Pb profile maybe expected to be non-linear. Many authors haveobserved such profiles. Figure I shows 2 10 Pb pro-files from Lough Erne in N. Ireland which are bothnon-linear and non-monotonic over depths of up to30 cm . Since changing accumulation rates may wellresult in variations in the initial 2 10 Pb concentra-

wer L. Erne

re SM 1

lu-

-?

.

a-

0

a

C

10 20 30 40 50 CDepth (cm)

(b)Lower L. Erne

Core FM 1

In

0I

a

a-

c

O1-cS0

.0

W6CL

c

lb 20 30 4b sbDepth (cm)

60 70

(c)

Upper L. Erne

Core FM 2

10 20 30 40Depth (cm)

Fig. i. Non-linear21 0

Pb profiles from Lough Erne, N. Ireland (Oldfield et al. 1978).

an (a)

0(G'

c0

u

i 1-

0c

o

ri

a

Ra

C01-n

n n,

50 60

u- -- i/n lu

uU U

nnl n .i

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tions of sediments, in order to construct a reliable2 1 0 Pb chronology it is necessary to understandmore precisely the processes by which sedimentparticles adsorb 2 10 Pb. The problem is furthercomplicated by the fact that non-linear profiles maybe caused by a number of other factors, includingmigration of 2 10 Pb through interstitial waters nearthe sediment water interface (Koide et al . 1973),mixing of near-surface sediments by physical (Petit,1974) or biological (Robbins et al. 1977) processes,post-depositional redistribution of sediments eitherdiscontinuously through slumping (Edgington &Robbins 1977) or more or less continuously bysediment erosion.

There are essentially two models which are ma-thematically practicable for calculating 21 0Pb dates

under varying sediment accumulation rates, theconstant rate of 2 10 Pb supply (c.r.s.) model and theconstant initial concentration (c.i.c.) model. Thephysical bases for these models are discussed inmore detail in Oldfield & Appleby (in press).

The constant rate of supply (or constant flux)model assumes that there is a constant fallout of21 0Pb from the atmosphere to the lake waters re-sulting in a constant rate of supply of 2 10 Pb to thesediments irrespective of any variations which mayhave occurred in the sediment accumulation rate.

This model was proposed by Krishnaswamy et al.(1971). In support of this model, Benninger et al.(1975) have estimated that, at least in some cases,> 99% of the 2 10 Pb deposited on the land surface istrapped in the soil layers. The dominant source ofthe 2 10 Pb in lake waters is then direct fallout ontothe lake surface. Studies of the residence time ofdissolved 2 1 0 Pb in lake waters (Schell 1977; Dur-ham & Joshi 1980) have shown that this 2 10 pb israpidly transferred from the water to particulates.

If the assumptions of the c.r.s. model are satis-

fied, it may be shown that the cumulative residualunsupported 2 10Pb, A, beneath sediments of age tvaries according to the formula:

A = A(o)e - kt

where A(o) is the total residual unsupported 2 10 Pbin the sediment column and k is the 2 1 0 Pb radioac-tive decay constant. A and A(o) are calculated bydirect numerical integration of the 2 1 0Pb profile.The age of sediments of depth x is then given by:

1 A(o)t = - l n - -

k A

The sedimentation rate can be shown to be givendirectly by the formula (Appleby & Oldfield 1978):

kAr = -

C

The 21 0 Pb supply rate is given by:

P = kA(o)

This procedure for calculating 2 10 Pb dates was firstoutlined by Goldberg (1963), and is se t out in detailin Appleby & Oldfield (1978), and Robbins (1978).

The constant initial concentration (or constantspecific activity) model assumes that an increasedflux of sedimentary particles from the water co-lumn will remove proportionally increased amountsof 210Pb from the water to the sediments. Under theassumptions of this model sediments will have thesame initial unsupported 21 0 Pb concentration ir-respective of any variations in sediment accumula-tion rate.

If the assumptions of the c.i.c. model are satis-fied, the unsupported 2 10 Pb concentration will vary

with depth in accordance with the formula:

C = C(o) e - k t,

where C(o) is the unsupported 2 10 Pb concentrationof sediments at the sediment water interface. Theage of a sediment layer with 2 10 Pb concentration Cis therefore

t=1 In C(o)t = - lnk C

The calculation of 2 10 Pb dates by this procedure isillustrated in Pennington et al. (1976).

Assessment of 2 10 Pb data for consistency with dat-ing models

The 2 1 0Pb supply for a given core is likely todepend in a complex way on both the atmosphericinput and sediment accumulation rate. The deter-mination of a 2 10 pb chronology will be feasible only

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if one or other of these factors is dominant. Inconsidering a given data set it is therefore necessaryto establish whether it conforms to either the c.r.s.model or c.i.c. model.

If the c.r.s. model is applicable, the following

consequences may be noted.I. Non-monotonic profiles may be expected in re-

sponse to major changes in the accumulationrate, since faster ne t sediment accumulation willtend to depress initial unsupported 2 1 0 Pb con-centrations, and vice versa.

2. Different cores from the same lake, or from thesame depositional zone within a very large lake,or from different lakes within the same generalarea will have comparable 2 10 Pb residuals (i.e.total residual unsupported 2 1 0 Pb contents) des-

pite differences in the accumulation rates.

3. The 21 0 Pb residuals of the cores should reflectthe 2 10 Pb fallout from the atmosphere. Since the210 Pb fallout lies in the range 0.2-0.9 pCicm 2 a-l, depending on the locality, the 2IOPb re-siduals should lie in the range 6-30 p Ci cm -2 .

All three points are well illustrated by the data fromLower Lough Erne. The profiles (Fig. 1) are non-monotonic. The 2 10 Pb residuals are virtually iden-tical, 19.2 pCi cm 2 for FMI and 20.7 pCi cm 2 fo rSM I despite a 3-fold difference in the accumulationrates. The corresponding 2 10 Pb supply rates are0.6 pCi cm 2 a-I and 0.64 pCi cm -2 a- respectively.Table I summarises results from a variety of siteswhich satisfy the c.r.s. criteria. Figure 2 illustratesthe convergence of the cumulative 2 10 Pb residualsfor cores from two sites.

Table 1. 2 1 0Pb parameters and sedimentation rates for cores from a variety of sites satisfying the c.r.s. criteria.

Coring site Total residual Unsupported Mean sedimentation rate during2 10Pb flux

unsupported21 0Pb conc. equivalent to

2 1 0Pb content at surface (a) past 30 years (b) past 100 years 2 10Pb residualA(o)(pCicm - 2) C(O)(pCig ) r(o) (g m 2 a ) f(g m 2 a 2 ) pC i cm 2 a I

Ireland (Oldfield et al. 1978)Lower L. Erne Core SM I

Core FM I

Upper L. Erne Core FM2L. Augher (1977)Wales (Elner & Wood 1980)Llyn Peris Core A

Core E

EnglandRostherne Mere Core RMII

Core N7 9Newton Mere

Belgium (Oldfield et al. 1980)L. Mirwart Core I

Core 2Core 3

Finland (Appleby et al. 1979)LaukunlampiLovojarviPaajarvi

L. Michigan U.S.A. (Robbins &Edgington 1975)

S. Margin Core 54

S. Central

N. Central

Core 31Core IICore 17Core 105Core 103

20.719.2

14.912.7

7.131.82

1.261.81

38.842.8

6.55.45.3

1.081.99

2.241.874.43

10.510.010.7

3.292.212.34

20.520.124.5

36.75.55

14.2

3.985.095.376.048.148.31

10.086.727.10

11.4214.515.1

0.080.31

0.350.19

1.070.67

0.0840.0880.032

0.0920.130.14

0.0110.0780.044

0.00750.0180.0200.0130.0140.014

0.0370.12

0.130.11

0.270.28

0.0550.0520.029

0.140.0550.12

0.00720.0590.059

0.00690.0110.0190.0130.0100.011

0.640.60

0.460.40

1.211.33

0.200.170.17

0.330.310.33

0.640.630.76

0.120.160.170.190.250.26

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Lower Lough Erne (a)

FM 1 o

SM 1 +

E

o-

i;

Depth (cm)

Lake Mirwart

Fig. 2. Cumulative total residual unsupported 21OPb contents for cores from (a) Lower Lough Erne and (b) Lake Mirwart, Belgium

(Oldfield et al. 1980).

If the c.i.c. model is applicable, the followingconsequences may be noted.1. The unsupported 210pbconcentration must show

a monotonic decline with depth.2. The total cumulative residual unsupported 20 Pb

in sediment cores from the same lake should varyroughly in proportion to the mean sediment ac-

cumulation rate.In view of the efficiency at which 2 10 Pb is sca-venged from lake waters by particulates, it is unlike-ly that this model will be widely applicable exceptpossibly at sites where sediment focusing is a majorfactor.

In order to assess whether on e or other of themodels is generally valid, we have plotted the 2 10 Pbresiduals A(o) and surface 2 10 Pb activities C(o) forabout 50 cores against the corresponding mean sed-imentation rates r (Fig. 3). If the c.r.s. model weregenerally valid, there should be no significant rela-

tion between A(0) and . On the other hand, sincethe 21 0Pb activity is inversely proportional to thesediment accumulation rate the graph of C(o)against , plotted on log-log paper, should approx-imately follow a line making an angle of 45 witheach axis. If the c.i.c. model were generally valid,A(o) should be proportional to , and there should

be no significant relation between C(o) and . Thegraphs clearly support the c.r.s. model. The greatmajority of the cores have a 2 10 Pb residual in therange 6-30 pCicm- 2 . The average value of 17.7pCi cm -2 corresponds to a mean 2 10 Pb supply rateof 0.55 pCi cm -2 a- 1. This compares well with esti-mates of the mean 21 0 Pb fallout.

Figure 3(a) includes data from Lake Michigan inthe U.S.A. and Lough Neagh in N. Ireland whichappears to be consistent with the c.i.c. model. In thecase of the Lake Michigan data (from Robbins &Edgington 1975), six of the cores (see Table 1) have

(b)

33

E

I

o

C-

0

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E (a)

eA4 0Io

a 30

n 20 .-

. to

0 00

100

-"

t 1

I

r

IfI

a

ra

tL

L MichiganL Neagh 0

. .

1 .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

0 i0 020

(b)

0.0 01F Average sedimentation rate for last 1OOyears g/cr2yr)

Fig. 3. 2 10Pb parameters vs mean sediment accumulation rate rduring the past 100 years for about 50 cores from various locali-ties. Fig. 3(a) plots the total residual unsupported 2 t0Pb contentA(o) vs?. Fig. 3(b) plots the unsupported 210 Pb concentration atthe surface C(o) vs Y.

2 10 Pb residuals which correspond more or less tothe measured atmospheric 2 10 Pb fallout of- 0.2 pCi cm -2 a - I. The tw o remaining cores, how-ever, 29 and 100A, have 21 0 pb residuals well inexcess of these values. Both sets of results can beinterpreted in terms of post-depositional sedimentfocusing (Oldfield & Appleby, in press).

When the 2 1 0 pb profiles satisfy the assumptionsof either model, errors in the chronology may stillarise as a result of vertical mixing processes in thenear surface sediments. Robbins er al. (1977) havemodified the constant flux-constant sedimentationrate model to allow for such processes. A modifiedc.r.s. model which takes account of sediment mix-ing is set out in Oldfield & Appleby (in press).

Summary

Perhaps the most important conclusion that we

would reach is that there is no single model that will

give a reliable 2 10 pb chronology in all cases, andthat each data set must be evaluated independentlyfor consistency with on e or other of the datingmodels. A tentative procedure for evaluating data isas follows:

I Linear ProfilesAll models give the same chronology

II Non-linear Profiles(a) If the 21 0 Pb residuals are comparable with the

known atmospheric flux, or with the 2 10 Pb re-siduals or nearby cores, the c.r.s. model wouldappear to be applicable. In our experience,21 0 pb dates calculated in this way have general-ly been consistent with independent dating evi-dence.

(b) If the 2 1 0 Pb residuals do not satisfy the re-

quirements of the c.r.s. model, but there is in-dependent evidence that the primary sedimentaccumulation rate has been constant, the c.i.c.model will be applicable. This case may occurin situations where sediment focusing takesplace.

(c) If the 2 1 0 pb residuals do not satisfy the re-quirements of either model, a 2 10 Pb chronol-ogy cannot be reliably established. We havefound that 2 10 pb dates calculated in these cir-cumstances have in most cases been in conflict

with independent dating evidence.

Acknowledgements

We wish to thank Dr. R. W. Battarbee for per-mission to use his data from Lough Erne and LochAugher, Mr. R. Nelms for permission to use hisdata from Rostherne mere, and Mr. J. P. Smith forpermission to use his data from Newtonmere.

References

Appleby, P. G. & Oldfield, F., 1978. The calculation of lead-2 10dates assuming a constant rate of supply of unsupported210Pb to the sediment. Catena 5: 1-8.

Appleby, P. G. , Oldfield, F. , Thompson, R., Huttunen, P. &Tolonen, K., 1979. 21OPb dating of annually laminated lakesediments from Finland. Nature 280: 53-55.

Benninger, L. K., Lewis, D. M. & Turekian, K. K., 1975. The useof natural210 Pb as a heavy metal tracer in the river estuarinesystem. In: T. M. Church (ed.). Marine Chemistry in theCoastal Environment. Am . Chem. Soc. Symp. Ser. 18 :

202-210.

w r . r .7

. - I

11 . .

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Edgington, D. N. & Robbins, J. N., 1976. Pattern of depositionof natural and fall-out radionuclides in the sediments of LakeMichigan and their relation to Limnological processes. In:Nriagu, J. O. (Ed.). Environmental Biogeochemistry, 2.Ann. Arbor Science, M.I.: 705 729.

Elner, J. & Wood, C., 1980. Th e history of two linked butcontrasting lakes in N. Wales from a study of pollen, diatomsand chemistry in sediment cores. J. Ecol. 68: 95-121.

Goldberg, E. D., 1963. Geochronology with 210Pb. In: Radioac-tive Dating. Int. Atom. Energy Ag. Vienna: 121 131.

Koide, M., Bruland, K. W. & Goldberg, E. D., 1973. Th-228/Th-232 and Pb-210 geochronologies in marine and lakesediments. Geochim. Cosmochim. Acta 37: 1171-1187.

Krishnaswamy, S., Lal, D. , Martin, J. M. & Meybeck, M., 1971.Geochronology of lake sediments. Earth planet. Sci. Lett. I 1:407 414.

Krishnaswamy, S. & Lal, D. , 1978. Radionuclide Limnochro-nology. In: Lerman, A. (Ed.). Lakes, Chemistry, Geology &Physics. Springer Verlag, N.Y.: 153-177.

Olfield, F. & Appleby, P. G., in press. Empirical testing of 2 1 Pbdating models for lake sediments. In: Haworth, E. Y. &Lund, J.W. G. (Eds.). Lake Sediments and EnvironmentalHistory. Leicester Univ. Press.

Oldfield, F., Appleby, P. G. & Petit, D., 1980. A re-evaluation oflead-210 chronology and the history of total lead influx in asmall South Belgian Pond. Ambio 9: 97-99.

Oldfield, F., Appleby, P. G. & Battarbee, R. W., 1978. Alterna-tive 2 1 0Pb dating: results from the New Guinea Highlandsand Lough Erne. Nature 271: 339-442.

Pennington, W., Cambray, R. S., Eakins, J. D. & Harkness,D. D. , 1975. Radionuclide dating of the recent sediments ofBlelham Tarn. Freshwat. Biol. 6: 317-331.

Petit, D., 1974. Pb-210 et isotopes stables du plomp dans dessediments lacustres. Earth planet. Sci. Lett. 23: 199 205.

Robbins, J. A. , 1978. Geochemical and geophysical applicationsof radioactive lead. In: Nriagu, J. O. (Ed.). Biogeochemistryof Lead in the Environment. Elsevier Scientific, Amsterdam:285 393.

Robbins, J. A. & Edgington, D. N., 1975. Determination ofrecent sedimentation rates in Lake Michigan using 210Pb andCs-137. Geochim. Cosmochim. Acta. 39: 285-304.

Robbins, J. A., Krezoski, J. R., Mozley, S. C., 1977. Radioac-

tivity in sediments of the Great Lakes: Post-depositionalredistribution by deposit-feeding organisms. Earth planet.Sci. Lett. 36: 325-333.

Schell, W. R., 1977. Concentrations, physico-chemical statesand mean residence times of 21OPb and 2 10 po in marine andestuarine waters. Geochem. Cosmochim. Acta. 41: 1019-1031.