Environ. Sci. Technol. 1991, 25,1627-1637
(33) Eduljee, G. H. Chem. Br. 1988, 24, 1223. (34) Rappe, C.; Nygren, M.; Lindstrom, G.; Buser, H. R.; Blaser, 0.;Wuthrich, C. Enuiron. Sci. Technol. 1987, 21, 964. (35) Travis, C. C.; Hattemer-Frey, H. A. Chemosphere 1987,16, 2331. (36) Jones, K. C.; Bennett, B. G. Sci. Total Environ. 1989, 78, 99. (37) Svensson, B. G.; Nilsson, A.; Hansson, M.; Rappe, C; Akesson, B.; Skerfving, S. N . Engl. J . Med. 1990, 324, 8. (38) Johnston, A. E.; Garner, J. V. Report of the Rothamsted Experimental Station for 1968; Part 2, pp 12-25. (39) Kjeller, L.-0.; Johnson, P.; Rappe, C., in preparation. (40) Nygren, M.; Hansson, M.; Sjostrom, M.; Rappe, C.; Kahn,
P. C.; Gochfeld, M.; Velez, H.; Ghent-Guenther,T.; Wilson, W. P. Chemosphere 1988, 17, 1663. (41) Tondeur, X.; Beckert, W. F.; Billets, S.; Mitchum, R. K. Chemosphere 1989, 18, 119. (42) Wold, S.; Albano, C.; Dunn, W. J.; Edlund, U.; Esbensen,
K.; Geladi, P.; Hellberg, S.; Johansson, E.; Lindberg, W.; Sjostrom, M. Multivariate Data Analysis in Chemistry; B.. Kowalski. Ed.: Proceedings of the NATO Advanced Study on Chemometrics; Maihematics and Statistics in Chemistry. Cosenza, Italy; D. Reidel: Dordrecht, Holland,
1984; pp 1--79. (43) Townsend, D. I.; Lamparski, L. L.; Nestrick, T. J. Chemosphere 11987,16, 1753. (44) Nestrick, T. J.; Lamparski, L. L.; Frawley, N. N.; Hummel, R. A,; Kocher, C. W.; Mahle, N. H.; McCoy, J. W.; Miller,
D. L.; Peters, T. L.; Pillepich, J. L.; Smith, W. E.; Tobey, S. W. Chemosphere 1986, 15, 1453. (45) Creaser, C. S.; Fernandes, A. R.; Al-Haddad, A.; Harrad, S. J.; Homer, R. B.; Skett, P. W.; Cox, E. A. Chemosphere 1989, 18, 161.
(46) Di Domenico, A.; Silano, V.; Viviano, G.; Zapponi, G. Ecotoxicol. Enuiron. Saf. 1980, 4, 327.
(47) Nielsen, P. G.; Lokke, H. Ecotoxicol. Enuiron. Saf. 1987, 14, 147. (48) Arthur, M. F.; Frea, J. I. J . Environ. Qual. 1989, 18, 1. (49) Nakano, T.; Tsuji, M.; Okuno, T. Atmos. Environ. 1990, 24A, 1361. (50) Broman, S.; Naf, C.; Zebuhr, Y.; Lexh, K. Chemosphere 1989, 19, 445. (51) Miller, G. C.; Herbert, V. R.; Miille, M. J.; Mitzel, R.; Zepp, R. G. Chemosphere 1989, 18, 1265. (52) Hagenmaier, H.; Brunner, H. Chemosphere 1987,16,1759. (53) Nestrick,T. J.;Lamparski, L. L. Anal. Chem. 1982,54,2292. (54) Lamparski, L. L.; Stehl, R. H.; Johnson, R. L. Environ. Sci. Technol. 1980, 14, 196. (55) Svensson, A.; Kjeller, L.-0.; Rappe, C. Environ. Sci. Technol. 1989, 23, 900. (56) Oberg, L. G.; Glas, B.; Swanson, S. E.; Rappe, C.; Paul, K. G. Arch. Enuiron. Contam. Toxicol. 1990, 19, 930. (57) Di Domenico, A,; Silano, V.; Viviano, G.; Zapponi, G. Ecotoxicol. Enuiron. Saf. 1980,4, 339. (58) Young, A. L. In Human and Environmental Risks of Chlorinated Dioxin and Related Compounds;Tucker, R. E., Young, A. L., Gray, A. P., Eds.; Plenum: New York, 1983; pp 173-190. (59) Wild, S. R.; Berrow, M. L.; Jones, K. C. Enuiron. Pollut. 1991, 72, 141. (60) Stanley, J. S.; Ayling, R. E.; Cramer, P. H.; Thornburg, K. R.; Remmers, J. C.; Breen, J. J.; Schwemberger, J.; Kang, H. K.; Watanabe, K. Chemosphere 1990, 20, 895. (61) Crummett, W. B.; Townsend, D. I. Chemosphere 1984,13, 778.
Received for review January 8,1991. Revised manuscript received April 9,1991. Accepted May 13,1991. We are grateful to the U.K. Agricultural and Food Research Council for financial support.
“Unmixing” of 137Cs,Pb, Zn, and Cd Records in Lake Sediments Erik R. Christensen* and Richard J. Klein Department of Civil Engineering and Mechanics, University of Wisconsin-Milwaukee,
The inverse Berger-Heath model to unmix sedimentary records of particle-associated tracers, originally used for l80records in deep-sea sediments, is extended to include radioactive materials, environmental pollutants, compaction of sediments, and error analysis. The method is applied to the fallout tracer 137Cs,and to Pb, Zn, and Cd in sediment cores from Lake Michigan. The reconstructed 137Csinput records from northern Lake Michigan are in good agreement with 137Csfallout data. The unmixed influx records of Pb, Zn, and Cd show excellent agreement with input records reconstructed previously by a frequency domain method, thus supporting the validity of the approach. Assuming that tracer concentrations as well as sedimentation and mixing parameters are known with sufficient accuracy, and that the forward model is correct, the ultimate limitation of this or any other reconstruction method lies in the finite depths of the physical sampling intervals. Introduction
Determination of historical fluxes of pollutants to lake or near-shore ocean sediments is of value for environmental 0013-936X/91/0925-1627$02.50/0
Milwaukee, Wisconsin 5320 1
modeling and management. For example, historical records of sulfur have been used to document anthropogenic sources of acid precipitation (1). Other examples include the linking of polycyclic aromatic hydrocarbons in the environment to fossil fuel combustion ( 2 , 3 ) the , demonstration of environmental lead reduction in response to federally mandated curbs on lead in gasoline ( 4 ) )and the correlation of reduced concentrations of polychlorinated biphenyls (PCBs) in lake sediments with the 1977 termination of U.S. domestic PCB production (5). Accurate source functions, as revealed from sedimentary records, can also be used in source apportionment including the assessment of the environmental effects of changes in industrial activity. In the case where no mixing takes place, the historical influx of particle-associated pollutants is directly reflected in the sedimentary record, except for any modification that may occur caused by chemical processes, radioactive decay, or biodegradation. Assuming that the latter processes are either insignificant or take place at a known rate, the influx is directly reflected in the sedimentary record. Mixing, often caused by the activities of bottom-dwelling organisms, can drastically change the input record (6, 7).
0 1991 American Chemical Society
Environ. Sci. Technol., Vol. 25, No. 9, 1991 1627
The top mixing layer acta as a low-pass filter allowing slow variations in the input flux to be reflected in the sedimentary record while attenuating rapid changes. Thus a narrow maximum in the influx may be completely obliterated in the sedimentary record. Models for solving the forward problem, Le., determination of a sedimentary record from a given influx, have been developed successfully by several authors (7-10). However, in practice, the inverse problem of determining the historical influx from a given sediment profile is often more relevant; yet only recently has it attracted significant attention. The f i s t successful attempt to reconstruct input records was made by Berger et al. (II), who developed an unmixing equation to determine l80input records in deep-sea sediments, based on the Berger-Heath model (8). A similar procedure was used by Appleby and Oldfield (12)to correct lead influxes to Lake Michigan for sediment mixing. The latter authors provided few details on the method. More sophisticated inversion methods based on the model of Guinasso and Schink (13) including constant mixing in a mixing layer, or the model of Christensen and Bhunia (7) with half-Gaussian mixing and compaction, have been developed recently (4,14,15). While potentially powerful, these inversion methods are quite complex and require elaborate procedures for error analysis. Also, because of stability problems, the time domain of Christensen and Goetz ( 4 ) is a t present restricted to a time resolution of about 15 years. The objectives of the present work are as follows: (a) to fully develop the inverse Berger-Heath model for reconstructing historical influxes of pollutants or radioactive materials to aquatic sediments, including consideration of compaction and error measures for the reconstructed records, (b) to apply the method to fallout 13'Cs in several sediment cores from Lake Michigan and then compare the reconstructed influxes with atmospheric fallout data, and (c) to apply the method to profiles of lead, zinc, and cadmium in the same cores and then compare the reconstructed influxes with those obtained previously from a frequency domain deconvolution method (15). Method Consider a sediment with rapid mixing in a layer of thickness z, (cm) and influx J (pg/(cm2year) or dpm/(cm2 year) of a tracer from the water column. The mass balance for this system may be written (d/dt)(cz,) = J - uc - XZ,C (1) where t (year) is time, c (pg/cm3 or dpm/cm3) is the concentration of the tracer in the mixing layer, u (cm/year) is the rate of sedimentation, and X (year-l) is the decay constant for a nonconservative substance. Letting c = pms, where p m (g/cm3) is the average concentration of sediment in the mixing layer and s (pg/g or dpm/g) is the concentration of tracer per mass unit of sediment, we can solve eq 1 for the unknown influx J J = z,p, ds/dt + ( r + Xz,p,)s (2) where r (g/ (cm2year) is the mass sedimentation rate, r = UP,.
In order to apply this equation to a sediment core, z,, r, and X must be known. For a conservative substance such as lead, X = 0. The mass sedimentation rate r may be determined as described in ref 7. The mixing depth z, is the depth over which the 210Pbactivity is approximately constant. Values of z, for several Lake Michigan cores are adopted from ref 15. In addition, the concentrations s, corrected for the preindustrial levels, must be known as a function of time
p,,
1628 Environ. Sci. Technol., Vol. 25, No. 9, 1991
t. Each consecutive slice of a core is here labeled with an integer index i increasing with increasing depth z below the sediment-water interface. The corresponding time ti indicates the average time it took to deposit the material above layer i. This time is calculated as ti = (ti + ti-,)/2 where ti = mi/r and mi (g/cm2) is the cumulative mass of sediment above the lower boundary of layer i. A discretized version of eq 2 can now be written as follows:
where t, is the time for deposition of the material in the mixing layer t, = 1 dz = -1I z m ( p , - pleWaz)dz (4) r o r o The expression for the sediment density p is here adopted from ref 7. The average sediment density p m in the mixing layer may be obtained from Pm = tmr/zm (5) The reversal of indexes i and i + 1 in the denominator of the discrete version of ds/dt of eq 3, relative to the sequence in the numerator, reflects the fact that the deeper layer (i + 1) is older than the layer above it (i). The exponentials of eq 3 account for the possible decay of the tracer between layer i + 1and i, and between layer i and the bottom of the mixing layer. Error Analysis. The uncertainty SJi associated with the reconstructed influx Ji (eq 3) can be calculated as follows:
-1'"~
where we have assumed that all entities of eq 3 are known precisely, except the concentrations si+land si, which are assumed to be uncorrelated, and which have the uncertainties and &si,respectively. It can be seen that
Substituting eqs 7 and 8 into eq 6
Note that in case of no mixing (z, = 0) we obtain SJi = eUfz-tm)r &si (10) Thus, from eq 9, the uncertainty of the reconstructed fluxes is, as expected, greater than that obtained in the absence of mixing, when no reconstruction is necessary. Application to Lake Michigan The sediment cores investigated here were taken from Lake Michigan in the summer of 1984. Sampling and experimental procedures have been described elsewhere (4). Figure 1shows a map of Lake Michigan with sampling
2.2 2.0
1.8
46'
NLMW-E1 Pb Influx No Compaction
. -
. i I .
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5
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a>I 450
,
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f
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-
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i
i !
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.
.
.
1 1984 77
2 3 1962 1947
:,"
A
4 5 6 7 8 1933 1918 1903 1889 1874
9 c m 1859 year
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~
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E
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88'
Figure 1. Map 01 Lake Mkhlgan Wim sampling
..........
1.2.
i i
j
....
85'
statbns
0.2 0.0
stations, and core parameters are listed in Table I. In this table the bulk density parameters p., pl, and 01 are applied in eq 4 (3, and the mixing depth z , is between 2.5 and 3.5 times the standard deviation in the half-Gaussian mixing function, as described in ref 15. The parameters p., pl, a,and r were determined as shown in ref 7. Figure 2 illustrates the principles of the unmixing operation for lead in core NLMM-El. The lead influx is here shown vs depth on the upper scales and, for the case of mixing, vs calender year on the lower scales. The dotted lines show the influx aa it appears in the absence of mixing (2, = 0), while the solid lines show the influx after reconstruction according to eq 3 with increasing influence of mixing (z, = 0.5, 1.0, or 2.0 em). The calendar year is the sampling year 1984 plus t , - €j, where t, and ti are the times of deposition of the material in the mixing layer and above a given depth, respectively. In order to not unnecessarily complicate matters we have disregarded compaction in Figure 2, assuming an average porosity @ of 0.925 with a solids density ps = 2.45 g/cm3, which gives an average bulk sediment density p = (1- @)p8 = 0.1838 g/cma. Thus the sedimentation rate u is constant vs depth and given hy u = r/p = 0.01253/0.1838 = 0.0682 cm/year. Also, for the sake of clarity, uncertainty bars have here been omitted from the reconstructed fluxes. We assume linearity between adjacent points of the unprocessed influx record as it appears in the sediment below the mixing layer, meaning that the unmixed record also will exhibit piecewise linear segments that are parallel to those of the unprocessed record (eq 3). As seen in Figure 2, the unmixing operation causes maxima and minima to appear that were not present in the unprocessed record. Also note that the onset of pollution, and the dates of these maxima and minima, are shifted toward more recent times. These effects become more pronounced as the mixing depth z, increases. For example, the onset of pollution and the major maximum
i 1 2 3 1 5 6 1984 1969 1955 1910 1925 1911
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9 c m 1867 year
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i
................. 9.33 y=.
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2 3 4 5 1981 1869 1655 1910
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Figure 2. Unmlxing of the lead Influx recwd in idealized core (NLM84-H) assuming constant bulk sediment density p = 0.1838 g/cm3VI depth. Mixing layers z , and tlmes of deposition of mlxlng layer t. for the three graphs are as follows (top to bottom): (a)z, = 0.5 cm. 1, = 7.33 year, (b) 1. = 1.0 cm, I, = 14.66year, and (c)I, = 2.0 cm. t , = 29.33 year. The mass sedimentawn rate r is 0.01253 gl(cmz year). The solid lines are unmixed influxes cakw lated from eq 3. The dolled lines are these Influxes as thef would appear In the absence of mixing (I, = 0). The time scales of the horizontal axes refer to a core wim mlxlng. The dashed venical llnes indicate the bonwn of Um mixing layer. the sampllng year (1984).and
the time 1, of deposition of the material in the mixing layer (eq 4) on a time scab (not shown) starting at the sediment-water interface.
are shifted from 1867 t o 1951, respectively, for z, = 0.5 cm, to 1889 and 1973, respectively, for 2, = 2 em. Also, the maximum influx is 2.0 pg/(cm2 year) for z, = 0.5 cm, and 3.1 pg/(cm2 year) for z, = 2.0 cm. I3'Cs I n p u t Records. If the method works, we should be able to regenerate ' W s fallout data, such aa the influxes Environ. Sci. Technol..
Vol. 25. NO.9,
IS91 I628
Table I. Lake Michigan Core Parameters core SLM84
NLM84
parameter
DI
HI
CLM84-MO
BO
El
latitude north longitude west water depth, m core depth, cm bulk sediment density parameters P-., g/cm3 Pl? g/cm3 a,cm-l mass sedimentation rate r , g/cm2/yr mixing depth z, cm
42O22’40’’ 87Ol7‘00’‘ 110 59.5
42O19’40’’ 86O 40’35” 72 66.0
43O45’25’’ 86O39’10’’ 81 55.0
44’28’20” 86O 43’25” 250 84.0
44O40’50’’ 86O45’00” 263 73.0
0.360 0.1898 0.1237
0.624 0.3583 0.0445
0.904 0.6822 0.0607
0.437 0.3247 0.0446
0.406 0.2887 0.0707
0.009 70
0.060 88
0.020 86
0.015 86
0.012 53
0.18
1.00
0.35
1.63
1.58
Table 11. Calculation of Reconstructed lS7CsInfluxes in Core NLM 84-El with Uncertainties
index
depth, cm
cumulative mass mi, g/cm2
time of deposition: year
av time of deposition,b year
0-0.5 0.5-1.0 1.0-1.5 1.5-2.0 2.0-2.5 2.5-3.0 3.0-3.5 3.5-4.0 4.0-5.0
0.048 0.111 0.180 0.257 0.346 0.432 0.524 0.630 0.854
3.83 8.86 14.37 20.51 27.61 34.48 41.82 50.28 68.16
1.92 6.35 11.62 17.44 24.06 31.05 38.15 46.05 59.22
activ, dpm/g value si SD asi 137c9
30.79 23.69 18.96 19.38 21.49 19.11 6.11 3.15 0
3.2 2.3 1.9 2.6 1.9 1.7 1.5 1.2 0
calcd 137Csinflux, dpm/(cm2 year) value Ji SD 6J; 0.534 0.396 0.190 0.160 0.407 0.949 0.275 0.206 0
0.171 0.124 0.131 0.148 0.128 0.132 0.125 0.078 0
a t i = mi/r. bfi = (ti t ti-J/2.
Table 111. 13’Cs Focusing Factorsa
30
core
normalized to year of deposition A = F,/F,
normalized to 1984 B=M,,,/M,
AIB
SLM84-D1 SLM84-H1 CLM84-MO NLM84-BO NLM84-E1
0.668 2.860 0.681 1.210 0.675
0.705 2.940 0.961 1.410 0.983
95 97 71 86 69
”t25
10 35
a Defined
‘984
1575
1574
1565
1964
1555
1554
YEAR
Flgure 3. Atmospherlc Input of I3’Cs to Green Bay ( 15).
shown in Figure 3 for Green Bay, from the sedimentary records of this radionuclide. Figure 4 demonstrates the results of applying the unmixing operation to the 137Cs records of the five cores listed in Table I. The 13’Cs influx is here shown vs time of deposition li (upper time scales) and vs calendar year for cores with mixing (lower time scales). It is shown as it appears both in the absence of mixing (z, = 0) and after reconstruction according to eq 3 with measured mixing depths z,. Note that Figures 4-7 contain two time scales. The upper scale indicates the time of deposition ti,and the lower scale indicates the sampling year 1984 plus t , - ti,Le., the actual calendar year. For the case of no mixing (z, = 0), t , = 0, and the calendar year is thus the sampling year 1984 minus the time of deposition ti. Table I1 shows the calculations of the influx Jiand uncertainty SJi from eqs 3 and 9 for core NLM84El. Note that the assumption of linearity between adjacent points of the unprocessed record (z, = 0) implies piecewise 1630
Envlron. Sci. Technol., Vol. 25, No. 9, 1991
(5%)
in text.
linearity of the unmixed record (z, = 1.58 cm), and that the linear segments of the latter are parallel to the corresponding segments of the unprocessed record. For example, from Figure 4 and Table 11, the reconstructed flux between indexes 6 and 7 is determined as a linear segment vs time, parallel to the influx curve for z, = 0, and with the left end passing through J6 = 0.949 dpm/(cm2 year). Similarly, the uncertainty SJ, = 0.132 dpm/(cm2 year) applies between indexes 6 and 7 to create an uncertainty band between lines parallel to the reconstructed linear segment. The left ends of these lines pass through the fluxes J6 = 0.949 f 0.132 dpm/(cm2 year). The reconstructed 137Csinflux records of Figure 4 may be compared to alternative source functions such as the atmospheric fallout data shown in Figure 3 (15,16),and data for 13T!s in the Great Lakes (17). It should be realized that the quality of the reconstructed input is limited by the number of physical sampling intervals. Thus, details will be lost if there are too few of these, as is apparent for cores CLM84-MO containing six points and SLM84-D1 containing only four points. The atmospheric input record of 137Csfor Green Bay (Figure 3) is remarkably well reconstructed in core
NLM84-BO 1.10
1
P
cu
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SLM84-H1
0.35
-2 Ni
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-
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-
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10 20 1984 '74 '64
0 00 30 '54
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60 70 '24 '14
80
YEAR
IO
0
1984
20 '74
30 '64
40 '54
50 '44
60 '34
70 '24
80 '14
YEAR
Flgure 4. Hlstorlcal influxes of I3'Cs to Lake Michigan sediments from cores NLM84-BO, NLMBeEl, CLM8440, SLMBeDl, and SLMB4-Hl. The solid llnes are unmlxed influxes calculated from eq 3. The dashed lines, connecting ends of uncertalnty bars, are these influxes pius or minus the associated errors (eq 9). The dotted lines show the influxes as they would appear in the absence of mixing (2, = 0). The lower time scales of the horizontal axes refer to a core with mixing. The dashed vertical lines indicate the bottom of the mixing layer, the sampling year (1984), and the time t , of deposition of the material in the mixing layer (eq 4) on the upper time scales.
NLM84-El. This result attests to the validity of the method especially since the focusing factor M,/M, for this core is near 1, Le., 0.983 (Table 111),and since the core is from the deep middle portion of the northern basin, indicating that direct atmospheric input should be of major significance. Note also that the reconstructed lead influx
to this core matches the atmospheric loading in the Great Lakes very well (15). The 1963 maximum of the fallout data is accurately reflected in the unmixed records for cores NLM84-BO, CLM84M0, and SLM84-D1. Also, low 13'Cs activities in recent years appear to be present in NLM84-BO, as exEnviron. Sci. Technol., Voi. 25, No. 9, 1991 1631
NLM84-E1 3.0
2.0
n
a
1 .o
0.0 20 1984
0
40 '64
60 '44
80 '24
100 '04
120 1884
140 '64
YEAR
CLM84-MO 3.0
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. 6
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2.
Y
a
a
10
00
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20 64
40 '44
60 '24
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100 1884
120 '64
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SLM84-H1 80
1
4
;
00 0
1984
20 '64
40 'I4
60 24
80, 04
100 1884
120 '64
1
140
YEAR
Flgure 5. Historical influxes of lead to Lake Michigan sediments from cores NLM84-E1, CLM8CM0, SLM8CH1. The solM lines are unmixed Influxes calculated from eq 3. The dashed lines, connecting ends of uncertainty bars, are these Influxes plus or minus the associated errors (eq 9). The dotted lines show the influxes as they would appear in the absence of mlxing ( 2 , = 0). The lower time scales of the horizontal axes refer to a core with mixing. The dashed vertlcai lines indicate the bottom of the mixing layer, the sampling year (1984), and the time t , of depositton of the materlal in the mlxlng layer (eq 4) on the upper time scales. No uncertainty data were available for core SLMBCH1.
pected from Figure 3. The records of cores CLM84-MO and SLM84-D1 from 1963 to 1984 are more difficult to interpret due to the scarcity of physical sampling intervals. It appears likely that high 137Csactivities in this time 1632 Environ. Sci. Technol., Vol. 25, No. 9, 1991
interval for core CLM84-MO could be attributed to stream input of 13Ts, because of the proximity of this core to the Michigan coastline. Some downward migration of 137Cs appears to have taken place in most cores, considering that 1950 is the effective starting date for the presence of this nuclide in the Great Lakes (17). The apparent shift of the maximum of the unmixed 13Ts record in core SLM84-H1 from 1963 to 1960 could be a result of a nonconstant mass sedimentation rate brought about by the deposition of a large amount of material during a 1975 storm (18). The focusing factor M,/Ma for this core of 2.94 may well account for the relatively high 137Cslevels between the time of the maximum and 1984, causing delayed additions of high-activity 137Csto this site. The levels in this time interval are significantly higher than would be expected solely from the concentration of 137Csin Lake Michigan (17). Focusing factors for 137Csnormalized to the year of deposition, A = F,/Fa, and to the sampling year 1984, B = M,/Ma, are listed in Table 111. The latter factor is the one usually quoted ( 4 ) . The quantities F, and Faof the first factor are defined as follows: F , is the area under the reconstructed 13Ts flux vs time curve, and Fa is the sum of the 137Csfluxes of Figure 3. As may be seen from Table 111, the ratio A / B is close to but less than 1, reflecting the failure of the unmixing method to fully restore the 1963 peak when the sampling intervals are spaced too widely to obtain the actual maximal negative slope of the mixed record. Pb, Zn, and Cd Input Records. Unmixed records of Pb, Zn, and Cd for those of the five cores for which data were available are shown in Figures 5-7. The Pb, Zn, and Cd influxes are here shown vs time of deposition (upper time scales) and vs calendar year for cores with mixing (lower time scales). They are shown as they appear in the absence of mixing (2, = 0) and after reconstruction according to eq 3 with measured mixing depths 2,. These records have a remarkable similarity to those generated by a frequency domain method (15). In contrast to the latter records, where uncertainties were calculated only for P b and Cd in core NLM84-E1, we have here estimated uncertainties for all of the records for which error data were available. In the two cases where errors have been calculated by both methods, the error bars are also of equal magnitude. There appears to be only one minor difference between the input records calculated by the two methods. The difference lies in the fact that the records from the frequency domain method have rounded corners and steep, but not vertical, line segments, whereas the present model's influx curves (Figures 5-7) have sharp corners and vertical line segments. This difference may be caused by the fact that the frequency domain method is based on a forward model containing a half-Gaussian mixing function with finite and gradually decreasing mixing intensity vs depth, whereas the simple inverse Berger-Heath model is based on rapid mixing in the top layer of the sediment. The fact that the two entirely independent reconstruction methods give nearly identical results is hardly coincidental, but provides instead significant evidence of the correctness of the reconstructed records. If mixing were ignored, the input records indicated in dashed lines (2, = 0) would be obtained. These records are identical with those defined by the points determined directly from the sedimentary record in ref 15, assuming piecewise linear influx curves. As shown in the latter reference, deconvolution or unmixing can have a dramatic effect on the reconstructed record in creating maxima
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Flgure 6. Historical influxes of zinc to Lake Michigan sediments from cores NLM84B0, NLMBCEl, CLM84-MO, SLM8CD1, and SLM84H1. The solid lines are unmixed influxes calculated from eq 3. The dashed lines, connectlng ends of uncertainty bars, are these influxes plus or minus the associated errors (eq 9). The dotted lines show the influxes as they would appear in the absence of mixing (z, = 0). The lower time scales of the horizontal axes refer to a core with mixing. The dashed vertical lines indicate the bottom of the mixing layer, the sampling year (1984), and the time t , of deposition of the material in the mixing layer (eq 4) on the upper time scales.
where none were present in the unprocessed record as for Pb (Figure 5) and Cd (Figure 7) in core NLM84-El. Also, the onset of pollution will be moved an amount t, toward more recent times, where t, is equal to the time of deposition of the mixing layer. Just as for 13'Cs (Figure 4), the maximum of the P b
input record in core SLM84-H1 (Figure 5) has apparently been shifted several years back, i.e., from 1969 to 1961, due to the violation of the assumption of constant sedimentation rate during the 1975 storm (18) where rapid accumulation of sediment material took place. The successful comparison of the reconstructed Pb input Environ. Sci. Technoi., Vol. 25, No. 9, 1991 1633
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Figure 7. Historical Influxes of cadmium to Lake Michigan sediments from cores NLM84-BO, NLM84-E1, CLM84-MO, and SLM8CH1. The solid lines are unmixed Influxes calculated from eq 3. The dashed lines, connecting ends of uncertainty bars, are these influxes pius or mlnus the assodated errors (eq 9). The dotted lines show the influxes as they would appear in the absence of mixing (zm= 0). The lower time scales of the horizontal axes refer to a core with mixing. The dashed vertical lines indicate the bottom of the mixing layer, the sampling year (1984), and the time t , of deposition of the material in the mixing layer (eq 4) on the upper time scales.
in core NLM84-E1 with the atmospheric loading in the Great Lakes region has been discussed earlier (15). Since the reconstructed ls7Csrecords (Figure 4) provide further indication that direct atmospheric input is of major significance to the middle deep portion of Lake Michigan (cores NLM84-E1 and NLM84-BO), and since error measures now are available for the influx records of Zn and Cd to these sites (Figures 6 and 7), we have extended this evaluation to include the comparison of Zn and Cd records in these cores with alternative source functions for these metals. In Figure 8, the averages of the reconstructed Zn and Cd records for cores NLM84-E1 and NLM84-BO are compared on a normalized scale to the U.S. consumption data for these metals. For Cd, the apparent consumption data for each year, available from 1931 to 1983 (19,20),were used. For Zn,we used the total consumption data for each year as given for the period from 1953 to 1983 (19). Regarding the period from 1897 to 1952, total Zn consumption data were not available, and we used slab Zn consumption data (19-21) and determined a factor (based upon the total and slab information for 1953-1983) to predict total Zn consumption from the slab Zn consumption data. It would have been preferable to use atmospheric loading data also for Zn and Cd, but we were only able to find consumption data. It is apparent from Figure 1634
Envlron. Sci. Technol., Vol. 25, No. 9, 1991
8 that the agreement between the two curves is quite good for Zn, and that the 1969 consumption maximum for Cd is reflected in the reconstructed record. It is also clear that this agreement would not have occurred if the unprocessed records had been used (Figures 6 and 7). This fact supports the validity of the method and gives further indication that the atmospheric pathway is important for the transport of Zn and Cd. The latter statement is based on the expectation of a general correlation between U.S. consumption data and atmospheric loading.
Discussion Both the method described here and the frequency domain method (15)provide more accurate inverse solutions than the time domain method of Christensen and Goetz (4). This is true despite the fact that the latter method, in contrast to the other two methods, allows for mixing a t any depth. The reasons for the limitation of the method of Christensen and Goetz with respect to time resolution, as well as possible ways to circumvent this difficulty, have been discussed previously (15). Validity of Assumptions. In any of these methods it is assumed that mixing is constant in time and is caused by biological activity or bottom currents. Mixing caused by the coring device during sampling, i.e., as a result of
Zinc Flux Average El/BO vs. U.S.Consumption 5
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1944
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poor field techniques, cannot be corrected by the proposed method. However, provided that high-quality corers are used, as is the case here, such mixing is insignificant (4), meaning that there is no need to make any sampling related correlations. The present model is characterized by rapid mixing in a mixing layer and no mixing below. This assumption is, of course, never fully satisfied since the actual mixing intensity is finite and decreases gradually with depth. However, from the similarity of Pb, Zn, and Cd records unmixed by the present method and by a frequency domain method (15),and from other evidence showing that the forward Berger-Heath model is reasonably accurate for small to moderate mixing depths, we conclude that the assumption regarding mixing vs depth in the present inverse model is reasonably well justified. Future improvements in inversion methods based on the advection-diffusion equation for a tracer and the mass conservation equation for sediment solids (4,15) will come from a more realistic formulation of these equations. For example, one should leave out a diffusion term in the sediment solids equation (10, 22), and one could take into account that the tracer may be more associated with fine colloidal particles rather than settling particles. Consideration of conveyor belt transport or tracers and molecular diffusion could also be included. Sedimentation rate has been assumed to be a constant in the three methods discussed here. However, it is known that the sedimentation rate can vary with time, e.g., during
storms or dry periods (23, 18),and it would therefore be desirable to be able to take a variable sedimentation rate into account. This is straightforward in the present method from eq 1 and is also possible in the method of Christensen and Goetz (4), but is not directly feasible in the frequency domain method (15),which in its present formulation is dependent on time-invariant systems characteristics. The assumption of constant sedimentation rate is well justified for cores NLM84-E1 and SLM84-D1, but only approximately so for cores NLM84-BO and CLM84-MO that are affected to some extent by low sedimentation rate during 1920-1947 and 1913-1956, respectively (18). Core SLM84-H1 is clearly influenced by periods of rapid sedimentation during 1888-1905 and 1958, and possibly also 1940 and 1976 (18). From ref 18, there is no evidence to suggest that the most recent sedimentation rates are any different from the overall long-term effects. In the mixing model considered here with rapid mixing within the mixing layer and no mixing below, any change in sedimentation rate would appear instantaneously through a change in slope of zloPb activity vs depth below the mixing layer, and such changes are not found in the records. This is confirmed with a more sophisticated mixing model (7), including finite mixing intensity, by the fact that this model provides good fits to 210pbdistributions vs depth in the upper layers using a constant mass sedimentation rate (4). Correctness of Method. The main criterion to determine that the present or any other inverse method works is that it is based on a valid forward method, and that it is internally consistent, meaning that the original input is regenerated within numerical error when the method is applied to the sediment distribution of a tracer calculated by the forward method. A secondary criterion is that input records reconstructed by different but correct inverse methods should be similar or nearly identical. Finally, while not a criterion in a strict sense, the fact that a reconstructed input record is similar to a known emission record that one would expect to find in a certain area of the lake is certainly an indication that the method works. The present inverse method meets the above criteria as described in the following. From eq 2, the sediment concentration s of a tracer can be found from the influx J and vice versa. In addition, the forward Berger-Heath method has been found to be reasonably accurate, such that the present method clearly meets the above main criterion. Also, as explained previously, the reconstructed input records for Pb, Zn, and Cd are similar to those generated by a frequency domain method, demonstrating that the above secondary criterion is also satisfied. Finally, it is known that inputs of 137Csand 210Pb,as well as several trace metals and organics, to northern Lake Michigan are primarily of atmospheric origin (24,25). Thus, since the reconstructed I3'Cs and P b records in the north in fact are similar to known atmospheric source functions, and since this similarity does not exist if the unprocessed records are used, there is supporting evidence for the correctness of the method. Note that sedimentation parameters including mixing depth z, are determined under the forward method so as to allow the realistic modeling of actual zloPb or 137Cs distributions in the sediments. The values of these parameters are then used without change in the inverse method. Mixing depth or sedimentation rate therefore, cannot be considered an adjustable parameter in the inverse method. Environ. Sci. Technol., Vol. 25, No. 9, 1991 1635
Utility of Unmixed Records. As to the need for deconvolving or unmixing records or pollutants in sediment cores, the argument can be made that this may not really be necessary because one can just make sure to take the core in an area that is unaffected by mixing. While this may be valid in a few cases, we do not find it to be generally true. For example, if we seek a particular input such as the atmospheric influx of 13'Cs, only the two cores from the northern deep basin (NLM84-BO and NLM84-El) contain a good approximation to this record, and then only if the unmixing operation is applied (Figures 3 and 4). The other cores are either affected by stream inputs (CLM84-MO), focusing (SLM84-D1 and SLM84-H1), or irregular features such as increased sedimentation rates during storms (SLM84-Hl). This means that the latter cores, despite being relatively unaffected by mixing, are unsuitable for the determination of the atmospheric input function. For the purpose of determining atmospheric deposition of compounds in the Lake Michigan area, we believe that northern Lake Michigan is a better choice than small remote lakes, isolated from point sources. We base this statement on the following facts: (a) the northern basin has surprisingly uniform sedimentation rates and zloPb fluxes, as well as focusing factors near unity (181, (b) focus-corrected PCB fluxes in the northern basin are also similar, and the tributary inputs of anthropogenic substances such as PCBs are here small (24),and (c) nonfocus-corrected PCB fluxes to four or five small remote lakes in Wisconsin differed within each other by a factor of 4 or 12 (26). The possible influence of near-shore vegetation such as woods in decreasing the lateral transport of substances into the lake from the atmosphere would also be significantly greater for small remote lakes than for Lake Michigan. Thus, especially core NLM84-E1, but also NLM84-BO, are in fact good choices for the determination of the atmospheric input of various compounds. In contrast to northern Lake Michigan, the sedimentation pattern in the southern basin is quite variable, with significant focusing in the middle deep portion and in the southeastern part near Benton Harbor, where core SLM84-H1 is located (18). If we are seeking the variation in sedimentation throughout the lake, rather than the atmospheric input, all cores should be considered. The unmixed records will then reflect the actual input history without the effect of mixing regardless of whether the input is mainly atmospheric (NLM84-BO and NLM84-E1), has a significant stream component (CLM84-MO), or reflects focusing and storm inputs (SLM84-D1 and SLM84-Hl). Conclusions We have further extended the inverse Berger-Heath model for unmixing records of particle-associated tracers in aquatic sediments to include error calculation, radioactive tracers, and compaction of sediments. In addition, the present investigation is the first full-scale demonstration of the effectiveness of this method to unmix sedimentary records of 13'Cs, Pb, Zn, and Cd in lake sediments. The unmixed records of 13'Cs in two northern Lake Michigan cores form a good approximation to atmospheric fallout data of this radionuclide. This is significant since the main contribution of sediment to this area of the lake is of atmospheric origin. The reconstructed records of Pb, Zn, and Cd from cores in Lake Michigan exhibit a striking resemblance to pre1638
Environ. Sci. Technol., Vol. 25, No. 9, 1991
viously published records obtained by a frequency domain method, thus supporting the validity of the method. Average influxes of Zn and Cd from two cores in northern Lake Michigan are in good agreement with US. consumption data for these metals. The inverse Berger-Heath method is reasonably accurate and is easy to use. It is therefore recommended to obtain a good first approximation to the historical input to sediments of particle-associated tracers or pollutants from their sedimentary records affected by mixing.
Glossary concentration of tracer in the mixing layer, rg/cm3 or dpm/cm3 integrated 13'Cs influx from fallout data, dpm/cm2 Fa integrated 137Csinflux from unmixed sediment Fm profile of 137Cs,dpm/cm2 influx of tracer from the water column, pg/(cm2 J year) or dpm/(cm2 year) cumulative mass of sediment above lower boundary mi of layer i, g/cm2 integrated lnCs influx from fallout data normalized Ma to samplin year, 1984, dpm/cm2 integrated l3fCs influx from sediment profile of Mm 137Cs.dDm/cm2 r mass sediLentation rate, g/(cm2 year) concentration of tracer in mass per mass unit of S sediment, pg/g or dpm/g time, year t time of deposition of sediment above lower ti boundary of layer i, year average time of deposition of sediment within layer ti i, year time of deposition of sediment within the mixing tm layer, year sedimentation rate, cm/year u 2 depth below the sediment-water interface, cm thickness of mixing layer, cm Znl parameter characterizing the rate of increase vs ff depth of sediment bulk density, cm-' uncertainty in the tracer influx for layer i, rg/(cm2 SJi year) or dpm/(cm2 year) uncertainty in the tracer concentration for layer i, 6Sl *g/g or dpm/g porosity of sediment dJ tracer decay constant, year-' x sediment bulk density, g/cm3 P difference between the sediment bulk densities at P1 large depths and the sediment-water interface, g/cm3 average sediment bulk density in mixing layer, Pm g/cm3 sediment bulk density at large depths, g/cm3 Pm sediment solids density, g/cm3 PS Registry No. Cs, 10045-97-3;Pb, 7439-92-1;Zn, 7440-66-6; Cd. 7440-43-9. C
Literature Cited Nriagu, J. 0.; Coker, R. D. Nature (London) 1983, 303, 692-694.
Hites, R. A.; Laflamme, R. A.; Farrington, J. W. Science 1977, 198, 829-831.
Gschwend, P. M.; Hites, R. A. Geochim. Cosmochim. Acta 1981,45, 2359-2367.
Christensen,E. R.; Goetz, R. H. Enuiron. Sci. Technol. 1987, 21, 1088-1096.
Christensen,E. R.; Lo, C.-K. Environ. Pollut., Ser. B
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Robbins, J. A. Hydrobiologia 1982, 92, 611-622. Christensen,E. R.; Bhunia, P. K. J. Geophys. Res. C 1986, 91, 8559-8571. Berger, W. H.; Heath, G. R. J. Mar. Res. 1968,26, 134-143. Robbins, J. A.; Edgington, D. N. Geochim. Cosmochim. Acta 1975, 39, 285-304.
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Officer, C. B.; Lynch, D. R. Earth Planet. Sei. Lett. 1982,
U.S. Bureau of Mines. Mineral Resources of the U.S.1 Minerals Yearbook; U.S. Department of Commerce:
61, 55-62.
Berger, W. H.; Johnson, R. F.; Killingley, J. S. Nature
Dependent Loadings of Particle-Associated Contaminants. NOAA Technical Memorandum ERL GLERL-57, Great Lakes Environmental Research Laboratory, Ann Arbor, MI,
Washington, DC, 1924-1933; Part 1 (1924-1931). U.S. Geological Survey. Mineral Resources of the U.S.; U.S. Department of the Interior: Washington, DC, 1897-1923; Part 1 (1907-1923). Fukumori, E.; Christensen, E. R. Earth Planet. Sei. Lett., in preparation. Edgington, D. N.; Robbins, J. A. In Environmental Biogeochemistry; Nriagu, J. O., Ed.; Ann Arbor Science: Ann Arbor, MI, 1976; Vol. 2, pp 705-729. Hermanson, M. H.; Christensen, E. R.; Buser, D. J.; Chen, L.-M. J. Great Lakes Res. 1991, 17(1), 94-108. Strachan, W. M. J.; Eisenreich, S. J. Mass Balancing of Toxic Chemicals in the Great Lakes: The Role of Atmospheric Deposition. International Joint Commission, Windsor, Ontario, 1988. Swackhamer,D. L.; Armstrong, D. E. Enuiron. Sei. Technol.
1985.
1986, 20, 879-833.
(London) 1977,269, 661-663. Appleby, P. G.; Oldfield, F. Enuiron. Sei. Technol. 1979, 13, 478-480. Guinasso, N. L., Jr.; Schink, D. R. J. Geophys. Res. 1975, 80, 3032-3043. Schiffelbein, P. Mar. Geol. 1985, 64, 313-336. Christensen, E. R.; Osuna, J. L. J. Geophys. Res. C 1989, 94, 14585-14597.
Health Saf. Lab. Environ. Q. ( U S .Energy Res. Deu. Adm.) 1977, HASL-329. Robbins, J. A. The Coupled Lakes Model for Estimating the Long-Term Response of the Great Lakes to Time-
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U.S.Bureau of Mines. Minerals Yearbook; US. Department of the Interior: Washington, DC, 1934-1983; Vol. 1 (1952-1983).
Received for review August 6,1990. Revised manuscript received March 15,1991. Accepted May 1,1991. This work is sponsored by U.S. National Science Foundation Grant BCS-8921000.
Polychlorodibenzothiophenes, the Sulfur Analogues of the Polychlorodibenzofurans Identified in Incineration Samples Hans-Rudolf Buser" Swiss Federal Research Station, CH-8820 Wadenswii, Switzerland
Ivan Samuel Dolezal and Max Wolfensberger Swiss Federal Institute for Materials Testing and Research, CH-8600 Dubendorf, Switzerland
Chrlstoffer Rappe Institute of Environmental Chemistry, University of U m e i ,
$90 187 Umei, Sweden
Polychlorodibenzothiophenes (PCDTs), the sulfur analogues of the polychlorodibenzofurans (PCDFs), were identified in fly ash from two municipal solid waste incinerators and from an electric-arc furnace of a carshredding facility. Gas chromatography/mass spectrometry (GC/MS) and MS MS experiments were used to detect the new compoun s in addition to the related polychlorodibenzodioxins (PCDDs) and PCDFs and to differentiate PCDTs from the nominally isobaric PCDDs. Among the PCDTs detected were tetra- and pentachloro isomers including the 2,3,7,8-tetrachlorodibenzothiophene. The concentrat,ions of PCDTs in fly ash were up to 55 ng/g, at or 1magnitude below the concentrations of the PCDDs and PCDFs in these samples. The sources and routes of formation of the new compounds are still unknown. Various pathways seem plausible, and as an example, we report on the formation of PCDTs from the thermal reaction of chloro aromatic compounds [polychlorobiphenyls (PCBs)] with elemental sulfur.
d
Introduction It is more than a decade ago that polychlorodibenzodioxins (PCDDs) and polychlorodibenzofurans (PCDFs) (Figure 1)were detected in incineration samples (fly ash and flue gas) (1, 2). These findings triggered a large number of studies monitoring these compounds in industrial and municipal incinerators (3),and efforts were taken to minimize emissions from such installations. Nevertheless, these emissions are still one of the major 0013-936X/91/0925-1637$02.50/0
sources responsible for the ubiquitous presence of these compounds, especially in the industrialized world (4). Besides the PCDDs and PCDFs, numerous other halogenated organic compounds were detected in emissions from incineration sources. In particular, the presence of polychlorinated biphenyls (PCBs), naphthalenes (PCNs), benzenes, phenols, styrenes, biphenylenes, pyrenes/ fluoranthenes, and other polycyclic aromatic compounds has been reported (5). Other halogenated dibenzodioxins and dibenzofurans were also detected and included the bromo/chloro analogues ( 5 , 6 ) ;polybromodibenzodioxins and polybromodibenzofurans were detected from the burning of brominated flame retardants, present in many plastic consumer products (7). Among all these compounds the PCDDs and the PCDFs are of special importance because of their high toxicity (3, 4, 8). Recently, we reported on the presence of polychlorodibenzothiophenes (PCDTs; Figure 1)in aquatic samples and on analytical methods for the determination of these compounds at trace levels (9). Gas chromatography/mass spectrometry (GC/MS) including MS/MS experiments was investigated for the detection of PCDTs and used to differentiate between PCDTs and the nominally isobaric PCDDs. In that study, individual or mixtures of PCDTs were synthesized by a novel thermal reaction of PCBs with sulfur. Potentially, this or related reactions between chloro aromatic compounds and elemental sulfur (or sulfur compounds) could be of environmental significance and lead to the formation of PCDTs. The analytical methods previously evaluated were now employed to search for
0 1991 American Chemical Society
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