Journal of Environmental Radioactivity 46 (1999) 153}169
Radiocaesium accumulation from Chernobyl fallout in nestlings of two pied #ycatcher populations (aves) in central Norway; estimating ecological timelag responses and transfer mechanisms Knut L+nvik , Per Gustav Thingstad* Faculty of Physics, Informatics and Mathematics, Norwegian University of Science and Technology, N-7034 Trondheim, Norway Museum of Natural History and Archaeology, Norwegian University of Science and Technology, N-7034 Trondheim, Norway Received 5 June 1998; accepted 6 November 1998
Abstract The accumulation of caesium isotopes (Cs and Cs) from the Chernobyl fallout in nestlings of two breeding populations of Pied Flycatcher (Ficedula hypoleuca) in central Norway was determined from 1986 to 1992. The birds at the Luru site showed a mean accumulation of 844, 535, 383, 607, 515, 348 and 327 Bq kg\ during these years. At Lauvsj+en, the corresponding accumulation was 102, 111, 74, 89, 293, 175 and 193 Bq kg\. In 1996, the levels had decreased to 118 Bq kg\ at Luru and 32 Bq kg\ at Lauvsj+en. The mean values of radiocaesium activity in the nestlings rose a few years (1989 and 1990) after the accident in 1986. The data show large variations within and between years in the initial period of this study, suggesting that these ecosystems were not at equilibrium during this period. However, equilibrium may have been approached during the last years. The measurements from 1992 and 1996 correspond to an ecological exchange rate of 0.22 year\ at Luru and 0.34 year\ at Lauvsj+en (on average 0.28), implying an approximate ecological half-life equivalent for caesium transfer in the monitor organisms, the young #ycatchers, of 3.2 years at Luru and 2.0 years at Lauvsj+en (on average 2.6 years). 1999 Elsevier Science Ltd. All rights reserved. Keywords: Radiocaesium; Birds; Flycatchers; Nestlings
* Corresponding author. Current address: Nord-Tr+ndelag College, Department of Resource Sciences, Box 169, N-7701 Steinkjer, Norway. Tel.: 0047 73 59 2280; fax: 0047 73 59 2295, e-mail:
[email protected]. 0265-931X/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 02 6 5-9 3 1X (9 8) 0 0 12 2 - 2
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1. Introduction Radioactive fallout arising from the Chernobyl accident on 26 April 1986 (Mould, 1988) was deposited in rain and snow over central Norway a few days later (Smethurst, 1995a, b). The amount of fallout varied considerably from one part of the region to another, depending on the local weather conditions at the time. There were also ecological variations in the content of the contamination from site to site over the years because of transport, di!usive processes and local circulation of radioactive material in the food chain. One way to investigate the e!ect of these phenomena and to trace the actual environmental contamination was to measure the radioactivity accumulated in the o!spring of birds, since birds are known to be particularly suitable indicators of substances that accumulate through the food chain (Furness & Greenwood, 1993). The radiocaesium in question is a mixture of two isotopes: Cs (long-lived "ssion product) and Cs (short-lived neutron induced product), whose physical half-lives are 30 and 2.1 years, respectively. Likewise, a biological half-life is speci"cally de"ned for an element or chemical substance by its retention time within a living organism. A single biological turnover rate for a complex individual is not uniquely expressed, but can be stated as an overall averaged factor with substantial interspeci"c variation. However, it tends to be shorter for homeotherms than for poikilotherms (Brisbin, 1991). For many bird species, these rates may be only a few days (Anderson, Dodson & van Hook, 1976; Halford, Markham & White, 1983; Moss & Horrill, 1996) and are particularly short for small species such as most passerines (Brisbin, 1991). Furthermore, the biological materials and fauna into which these radioisotopes become incorporated are usually not chemically stable, but are in a state of dynamic #ux. These biochemical pathway or food chain processes therefore tend to vary the content of radioactivity in the food being consumed, leading to the concept of an ecological half-life. However, this is in practice complicated and not a fully adequate unit. According to Brisbin (1991), it represents the length of time required for a given level of a nuclide to decrease by 50%, once it has become established and is at equilibrium within a given ecosystem. The e!ective ecological half-lives tend to be much longer than the biological half-lives and may di!er greatly between di!erent habitats due to the more stable biogeochemical reservoir of some habitats (Bergeijk, Noordijk, Lembrechts & Frissel, 1992; Rowen & Rasmussen, 1994; Avery, 1996). The Pied Flycatcher (Ficedula hypoleuca) was chosen as the target species in this study. It breeds quite commonly in many types of habitat in Fennoscandia and is very easily manipulated to breed in arti"cial nest boxes, thus enabling the necessary data from the breeding season to be easily collected. Furthermore, this migrating, insectivorous passerine species is sensitive to the amount of available food resources and the weather conditions during the breeding season (JaK rvinen, 1983, 1986; Lundberg & Alatalo, 1992; Thingstad, 1997a), and is more susceptible to pollutants than some other passerines (Nyholm & Myhrberg, 1977; Eeva & Lehikoinen, 1995). It should therefore be a suitable indicator for monitoring the e!ects of varying environmental conditions as well as more acute contaminating events (Thingstad, 1997b).
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155
In this study, the radioactivity in the birds is assumed to be in equilibrium with the level of contaminated food in the surroundings of the nest. The main aim of this investigation was to determine the accumulation of caesium in the o!spring of Pied Flycatchers. A secondary objective was to trace the relative change in the turnover rate of radioactive caesium in the two breeding populations studied.
2. The study areas The data were obtained in subalpine birch-spruce forest close to a lake, Lauvsj+en (approximately 600 m a.s.l.), near the Swedish border at Lierne in central Norway (64320n N, 13345n E), and in spruce-dominated forest close to the River Luru in Sna sa (300 m a.s.l.), approximately 40 km southwest of Lauvsj+en (Fig. 1). Apart from the special fallout of condensed radiocaesium and other short-lived "ssion products from the Chernobyl accident, levels of airborne pollutants should be low in these areas (Bernes, 1993). There are no local contamination sources. The water in Lauvsj+en is almost neutral (pH"6.4}6.7) and the conductivity is normal (20 lS cm\), while the water in the River Luru has a pH close to 5.0 and the conductivity is very low
Fig. 1. Location of the two study areas.
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(9} 11 lS cm\) (Reinertsen, Olsen, N+st, Rueslas tten & Skotvold, 1982). According to Sigmond, Gustavson and Roberts (1984), the main types of bedrock in the Lauvsj+en area are mica schist and mica gneiss, which should be good acidi"cation bu!ers, while the rocks at Luru consist of foliated granite and granodiorite, which have low bu!ering capacity. The amount of radioactive fallout di!ered substantially in the two study areas. Airborne surveys of ground-level contamination calculated back to 1986 give about 1300}1500 counts s\ for the Luru area and 700}900 counts s\ for the Lauvsj+en area (Walker & Smethurst, 1993). According to our measurements in 1996, the contamination levels in the humi"cation layers of the mineral soil were approximately 1000 Bq kg\ in dry soil from Luru and 150 Bq kg\ in the surface layer (0}2 cm) at Lauvsj+en, but only 60 Bq kg\ was measured at a depth of 4}5 cm at Lauvsj+en.
3. Materials and methods Almost #edged Pied Flycatchers were collected during early to mid July from nest-box transects in both areas (cf. Thingstad, 1992). Some nestlings were collected each year from 1986 to 1992. A supplementary collection was made in 1996 to verify the longer-term trend. Tables 1 and 2 show the numbers collected and the annual mean radiocaesium contamination in these birds. Only one nestling was taken from each brood. The birds were stored in standardised plastic boxes in a frozen state. This was done to maintain a well-de"ned geometry, appropriate for the reference radioactive dummy source used for calibration. The boxes were placed on the detection unit, which consisted of a 2;3 in sodium-iodide scintillation crystal attached to a photomultiplier inside a lead screening tower. The radioactivity was traced by registering the gamma rays issuing from the radiocaesium isotopes, Cs and Cs. The counting system otherwise consisted of an ordinary pulse-high analyser (PHA) for gamma-ray spectroscopy. Two count readings were taken from the spectrum, the one window region (marked 2 in Fig. 2) covering the photopeak of Cs at 794 keV, Table 1 The mean values ($1 S.E.) of the radiocaesium measurements (Bq kg\) in the Luru area, the proportion of the activity measured for Cs to that of Cs (R $1 S.E.), and the theoretical physical "gures each year (R ). N"number of samples, bld"below level of detection Date
Radiocaesium
R
R
N
01/7}86 01/7}87 01/7}88 01/7}89 01/7}90 01/7}91 01/7}92 01/7}96
844$86 535$37 383$48 607$83 515$119 348$28 327$31 118$23
0.41$0.08 0.30$0.03 0.27$0.07 0.27$0.08 0.17$0.05 0.10$0.02 0.08$0.01 bld
0.520 0.383 0.281 0.207 0.152 0.112 0.082 0.044
6 6 6 6 6 6 6 6
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Table 2 The mean values ($1 S.E.) of the radiocaesium measurements (Bq kg\) in the Lauvsj+en area. See legend for Table 1 for further explanations Date
Radiocaesium
R
R
N
01/7}86 01/7}87 01/7}88 01/7}89 01/7}90 01/7}91 01/7}92 01/7}96
102$13 111$16 74$16 89$18 293$65 175$88 193$29 32$5
0.25$0.06 0.25$0.11 0.24$0.11 0.23$0.07 0.30$0.08 0.11$0.09 0.09$0.03 bld
0.520 0.383 0.281 0.207 0.152 0.112 0.082 0.044
5 5 9 5 4 6 6 6
Fig. 2. A characteristic scintillation spectrum of gamma rays from a dust sample of primary fallout radioactivity (from L+nvik & Koksvik, 1990). The energy windows of interest in this study are marked 1 and 2 (see the text).
called N net cps, and the other window (marked 1 in Fig. 2) covering the overlapping photopeaks of Cs at 662 keV and the second peak of Cs at 607 keV, called N net cps. When the main fallout occurred (27}28 April 1986), the ratio of radioactivity between the two radioisotopes of interest was assumed to be R "0.537"(Bq Cs)/(Bq Cs) in this particular district (cf. L+nvik & Koksvik, 1990). Assuming
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that these two combined radioisotopes do not become separated either chemically or biologically, the value for this "gure over the ensuing years can be theoretically estimated by the formula R "R (0.735)2, where ¹ is the number of years elapsed. Because these two radioisotopes overlap in the resulting spectrum, an equation had to be designed to calculate the quantity of each in the samples: Q "A(N !aN )
(Bq),
Q
"B(N !bN ) (Bq).
The total caesium radioactivity is then read as: Q"Q #Q "(A!bB)N #(B!aA)N (Bq). The coe$cients a ("1.810) and b ("0.040) are stripping parameters determined separately by calibration. The proportionality factors A ("42.8 Bq cps\) and B ("45.8 Bq cps\) convert the net count rate to an existing radioactivity in the bird samples in relation to the reference sources. The natural background impulses in every window area were determined by measuring over a very long period of time, partly to incorporate instrument #uctuation. The e!ective background "gure for the upper window (window 2 in Fig. 2) channels of Cs was around 0.3870$0.0010 cps, based on several repeated readings of 100 h each year. Using the same counting procedure, the corresponding "gure for window 1 (Cs and Cs) was 0.6225$0.0011 cps. Instrument instability is mostly responsible for the observed standard error given in the background counts. In addition to the nominal background subtraction in the total count readings, interference from the natural radiation of K also has to be taken into account. A third window at 1.461 MeV served as a pilot for this registration. The level of con"dence is related to one standard deviation of background. A single measuring time of at least 24 h was used for samples with very low radioactivity. With a proportionality factor of about 45 Bq cps\ and a normal bird weight of 15 g the lower detection level for the measurement should be around 20 Bq kg\. Six individual samples were usually considered to represent the situation at each site. Biological variations and di!erences in nutrition and accumulation before food intake have a greater in#uence on the spread in the "nal results than the counting statistics chosen. However, measurements on eggs showed very little radioactivity. Food intake is therefore believed to be responsible for most of the radioactivity in the nestling samples. The relative slope (rate) of the physical decay alone on the fallout day (prompt fallout or "ctitious zero point) is: (dQ/dt/Q) "!(1/¹ #R /¹ ) ln 2/(1#R )"!0.1320 (year\)
(1)
A theoretical equation for calculating an estimated relative change in radioactivity during one year, based on physical reasons only, is (ðQ/dt/Q) "+(0.023#0.332R )/(1#1.014R ), (year\) (see the D values in Table 3).
(2)
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K. L~nvik, P.G. Thingstad/J. Environ. Radioactivity 46 (1999) 153}169 Table 3 Calculated annual mean values derived by averaging the primary data from the two study areas Year (1/7-1/7)
A (Bq kg\)
B (Bq kg\ year\)
C (year\)
D (year\)
E (year\)
Luru 1986}87 1987}88 1988}89 1989}90 1990}91 1991}92 1992}96
689.5 459.0 495.0 581.0 431.5 337.5 55.5
!309 !152 #224 !92 !167 !21 !52
!0.45 !0.33 #0.45 !0.16 !0.39 !0.06 !0.24
!0.117 !0.098 !0.082 !0.069 !0.058 !0.049 !0.022
!0.33 !0.23 #0.53 !0.09 !0.33 !0.01 !0.22
Lauvsj+en 1986}87 1987}88 1988}89 1089}90 1990}91 1991}92 1992}96
106.5 92.9 81.5 191.0 234.0 184.0 28.2
#9 !37 #15 #204 !118 #18 !40
#0.08 !0.40 #0.18 #1.07 !0.50 #0.10 !0.36
!0.117 !0.098 !0.082 !0.069 !0.058 !0.050 !0.022
#0.20 !0.30 #0.26 #1.14 !0.44 #0.15 !0.34
A:"average value between two successive years. B:"di!erence in value observed between two successive years. C:"relative average change of activity during that year (B/A). D:"relative physical change during the same year. E:"remainder of the relative change (C!D"E). The values given in column E re#ect the apparent supply rate (#) or reduction rate (!) of radioactivity during a single year and are only in#uenced by the environmental conditions and ecological food chain e!ects. average value for the actual period, given a linear trend.
The di!erence between the theoretical and the observed mean slopes per year gives an idea of changes caused by processes (ecological) other than exact, real physical decay alone: (ðQ/dt/Q) "+(ðQ/dt/Q) !(ðQ/dt/Q) , (year\) (3) (see the E values in Table 3 and the appendix for further explanation). This quantity is only exponential if it is assumed that the ecological state is in equilibrium. Our measurements show that the calculated values #uctuate irregularly from one year to the next. Hence, the equation for the changes caused by ecological processes is only an apparent "gure for a temporary variation in the ecological turnover rate (exponentially de"ned). The physical rates of decay of the separate radionuclides are 0.330 yr\ for Cs (2.1 year\ half-life) and 0.023 year\ for Cs (30 year half-life). The relative reduction rate for the combined radiocaesium isotopes is 0.131 year\ for the original fallout at the "ctitious zero point (Chernobyl). The mean annual change in the
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observed values is also used as a gauge in this investigation, and 1 July each year is taken as the nominal date. The counting statistics for each measurement are normalised to 3% or better. The proportion of the activity of Cs to that of Cs as a function of time is calculated from the data observed given as R "Q /Q , where the radioactivity Q values used are taken from the mean of several independent samples (usually six).
4. Results The mean concentrations and standard errors of the accumulation activity from Luru and Lauvsj+en are summarised in Tables 1 and 2, respectively. The results reveal great variations among the individual samples within years (as seen from the S.E. of the mean). Fig. 3 shows the mean values of the accumulated radioactivity in the nestlings measured at the two sites as a function of time. The trend in radioactivity at the two sites di!ers considerably in character over the years. The radioactivity initially drops at Luru from a high value, while Lauvsj+en has a continuing low radioactivity in the same period. Both sites show a similar sudden increase in accumulation after a few years, but this is delayed at Lauvsj+en. The radioactivity curves after 5 years then look similar in following a more stable rate of decay. To trace the transfer of radiocaesium, calculations were made to "nd the relative change by loss or gain in the accumulation values between years, as shown in Table 3. For 1986}1987, the physically dependent slope is calculated to be 0.117 year\. The e!ective relative mean change in radioactivity at Luru in the "rst year is approximately 0.45 (Table 3). Hence, the di!erence of about 0.33 year\ shows a probable additional transfer of radioactivity from the current source of food originating primarily from insects. The situation at Lauvsj+en is quite di!erent. The trend there shows an increased accumulation of radioactivity during the "rst years. This implies a supply of caesium from the food, which exceeds the reduction rate by a relative amount of 0.20 year\. Assuming a linear trend during the last period of years (1992}1996), the corresponding ecological turnover rates become 0.22 year\ at Luru nd 0.34 year\ at Lauvsj+en (cf. Table 3). The huge #uctuations in accumulation values between years strongly suggested that the ecosystem was not in equilibrium, a necessity for determining the caesium turnover rate and the ecological half-life in the system. Consequently, these results should not permit direct derivation and our compartment model, based on calculated turnover rates at both sites, was used to estimate that the ecological half-life equivalent was 3.2 years at Luru and 2.0 years at Lauvsj+en. The mean value of the ecological turnover rate at these two sites would be 0.28 year\, which corresponds to an approximate ecological half-life equivalent of 2.6 years. The complex ecological transfer mechanisms are described in our compartment model proposed in Fig. 4. Visual comparison of the pattern of the curves drawn from our measurements (Figs. 3a and b) shows a similar performance to that of the relative curves given by our model (Fig. 5 in the appendix). The actual correlation coe$cients between the measurements corrected for physical decay, i.e. &&the ecologically transferred contents'',
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161
Fig. 3. The annual mean accumulation of radiocaesium ($1 S.E.) in young pied #ycatchers from (a) the Luru area and (b) the Lauvsj+en area during the study period. Each point of measurement given is referred to 1 July of each year.
and those obtained from our compartment model become 0.99 for Luru and 0.87 for Lauvsj+en. The corresponding shapes of the corrected curves and the theoretical performance are the basis of the evaluated transfer coe$cients given in the appendix. 5. Discussion The Pied Flycatchers, being migratory birds, received their radioactive burden from the Chernobyl accident when they returned in spring to their breeding sites in central
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Fig. 4. Diagram illustrating the principle of the compartment model for an ecosystem, as proposed in the text. To simplify the model, only one parallel bu!ering branch for delayed radioactivity transfer is shown, but in a natural situation more than one will certainly be involved. Q "initial unknown reference value (equal to 1), a"e!ective decay coe$cient, j"physical decay constant, k"mass turnover rate (transfer coe$cient), e"distribution coe$cient in each compartment (& e "1), f"distribution coe$cient of k (& f "1). See the appendix for further explanation.
Norway. Some complications arise when the nestling is used to monitor the transport and deposition of environmental radionuclide contamination. These are mainly due to variability in the samples available. To obtain more representative mean values, the sample size should have been somewhat larger. However, the lack of "tness between R and R may also be caused by the non-systematic and shifting contribution of contamination from the food. A closer look at the curves giving the annual mean values of the total radioactivity measured at the two sites (Fig. 3) shows that their shape is similar as time passes. It seems likely that they will become parallel in the long run, probably evolving to the same rate of decrease due to the decay of Cs. This probably indicates some kind of spreading and smoothing e!ect of the contamination with time. The rise in the mean value of radioactivity appearing at Luru in the fourth year after the accident can also be observed in the curve from Lauvsj+en, but it is displaced to the year after. At "rst sight, an after-e!ect like this seems inexplicable, and Ka la s, Bretten, Byrkjedal and Njas stad (1994) found a decreasing trend in radiocaesium in the woodcock (Scolopax rusticula) during 1986}1990 in the Dovre area in central Norway. However, an extra supply of contaminated material could easily arise depending on the topographical situation and weather conditions, or as a result of eruptive and transfer processes (cf. Oughton & Salbu, 1994). For instance, Gaare (1991) found that in the same general area of Dovre as Ka la s et al. (1994) used for their study, such e!ects raised the levels of Cs in some lichens three to four years after the fallout. Earthworms (¸umbricidae) in the same area also showed higher radiocaesium levels in 1988 than in the "rst two years after the accident. Elements from the fallout that
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163
migrate to lower soil layers can also be bound to soil colloids and mix with nutrients, thus contributing to local recycling of foodstu!s some time later (Pennock, 1990; Oughton & Salbu, 1994). The apparent increase of the isotope in the environment may therefore have a time lag caused by the low availability of root uptake in vascular plants, whereas the levels of Cs in the organic soil increased during the 50 months after the Chernobyl accident in the Dovre area (Bretten, 1991). Moreover, lichens and mosses absorb radioactive fallout directly from the rain, and when they decompose and are transformed into humus, the radioactive isotopes become available for absorption via the root system (Gaare, Jonsson, Skogland & Steinnes, 1991). This root uptake is in#uenced by the type of soil (Askbrant & Sandalls, 1998). Furthermore, the organic matter in the soil has a large impact on the transfer, the rate increasing with the increasing content of organic matter; but this would probably not be a!ected by soil pH in the range 3.9}8.4 (Bergeijk et al., 1992). However, the bioaccumulation of radiocaesium by freshwater "sh is known to be in#uenced by physicochemical factors; "sh in soft water environments are more vulnerable to radiocaesium contamination than those in hard water (Rowen & Rasmussen, 1994). Solem and Gaare (1992) found that aquatic invertebrates in some alpine streams showed a rapid decrease in the activity of Cs in the years after 1986, whereas detritivorous species had the same load the following two years. The levels of radioactivity in herbivorous invertebrates are approximately proportional to the levels in their diets (Rudge, Johnson, Leah, Jones, 1993). Seasonal shifts in diet may also give clear e!ects in, for instance, "sh (L+nvik & Koksvik, 1990), reindeer (Skogland, Strand & Espelien, 1991) and birds (Pedersen & Nyb+, 1991). However, since measurements in this particular study were only made on almost #edged young of a migrating bird species, this seasonal complication would not arise. The partitioning of the radioactive isotopes between biotic and abiotic components in di!erent ecosystems is very complex and depends on a number of factors. The most interesting feature observed is the trend in the decrease of radioactivity in the Luru area while the Lauvsj+en area shows a nearly constant level of local radioactivity during the "rst three years (Figs. 3a and b). The increase in radioactivity appearing in the birds after some years indicates a build-up of radioactivity in their food caused by local accumulation in a reservoir (e.g. the soil) or some form of transfer from other sources in the surroundings. In our model (Fig. 4), this simply implies that most of the radioactive material transferred from the source goes through a bu!er in the Lauvsj+en area, which has the most calcareous bedrock. However, a signi"cant part of the contamination was more directly concentrated in the food chain at Luru, which had the highest initial fallout level and whose soil and bedrock have a lower bu!ering capacity (cf. the Appendix for further interpretation of the model). During the last part of the study period, more normal decay seems to have taken place approaching a common, lower level of radioactivity with an apparent overall ecological half-life of 2.6 years, corresponding to a turnover rate of 0.28 year\. This is somewhat shorter than in grazing reindeer, in which Cs is estimated to have an ecological half-life of about 3}4 years (Gaare & Staaland, 1994). However, our survey indicates that the presence of radioactive elements within a speci"c area shows annual #uctuations caused by ecological exchange processes and an unequal distribution of
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the initial fallout. An exponential activity reduction can probably only be expected in special cases, or it will at least take a long time before equilibrium is reached between the original amount of radioactive fallout and that in the biologically useful food (in this case, primarily insects) for birds in the food chain. The delayed transfer of di!erent ecological bu!ering mechanisms in the environment gives these dynamic oscillating patterns, and these observations might even raise the question of whether we have reached a state of equilibrium, the condition necessary for calculating the ecological half-life values in the current situation more than a decade after the Chernobyl accident.
Acknowledgements We are indebted to Folke Andersson, Sna sa Fjellstyeare and Bernt Aasen for assistance in putting up the nest boxes, two anonymous referees for instructive comments and Richard Binns for improving the English.
Appendix: Some analytical considerations The original fallout of radioactivity in any particular area is an unknown quantity. However, according to previous investigations, the ratio of the two radioisotopes is R "0.537. For the sake of simplicity, in this analysis, the total acute radioactivity is assigned a speci"c input unknown reference value, Q (Bq), administered to a single, "ctitious compartment on the "rst fallout day. The quantity of speci"c radioactivity in the birds, Q(t) (Bq kg\) (functionally referred to a speci"ed date, t"1 July each year), is calculated by the conversion formula given in the text from the number of counts recorded N(t) (cps) divided by the weight of the sample = (t) (kg). A new speci"c and relative "gure is then de"ned by introducing a working function (fraction), F(t)"Q(t)/Q (per unit fallout), in an attempt to describe this situation. The supply of radioactivity from food is governed by a proposed (unknown) relative transfer function ¹ (t) that is believed to be only dependent on ecological factors. In addition to the mechanism which transports contaminated substances within the area, the observed, speci"c radioactivity also depends upon the known physical decay processes expressed by a relative time function Ph(t) for the two isotopes involved. This working relationship can be written as F (t)"¹ (t) ' Ph(t) N ln ¹ (t)"ln F (t)!ln Ph(t) and by time derivation equating a relative transfer value: (d¹/dt)/¹"(dF/dt)/F!(dPh/dt) Ph (year\) (cf. Eq. (3) in the text) (A1) which only concerns the relative rate of change in the content of contaminated nutrition from mass transfer. A descriptive interpretation of the functionality is related to the proposed, simpli"ed compartment model shown in Fig. 4. Each term in the suggested expression could (at least for a short period) be replaced by the average amount of loss or gain of radioactivity from one year to the next,
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165
relative to the mean value that year. This approximation is the basis for the calculations in Table 3. The results of averaging the point measurements are shown in Table 3. The radioactive mass transfer function is presumed to be the same for both radioisotopes, since they are chemically similar. On the other hand, the physical decay function is also determined mathematically. The respective relative amounts of decay of the fallout of Cs and Cs that need to be incorporated in the physical function are, in any case, the same. Ultimately, this will lead to the following numeric equation for the course of the physical function (cf. D in Table 3): Ph(t)"+0.65 exp (!0.023t)#0.35 exp (!0.33t), (year\)
(A2)
The mean point rate values of the transferring function ¹ (t ) (cf. B in Table 3), as V well as the measurements, show an oscillating pattern which re#ects the very complex ecological conditions. Under such circumstances, it is pointless to exactly de"ne a speci"c, single turnover rate (or ecological half-life) for the system as a whole. The amount of radioactivity in nutrition is continuously changing and our data suggest that equilibrium is not approached during our investigation period (1986}1992). The e!ect of bu!ering is shown by an increase in radioactivity at Luru about 3}4 years after the fallout. The same took place in Lauvsj+en about one year later. This e!ect is veri"ed by the change in the sign in the e!ective relative value of the yearly loss or gain of radioactivity brought about by ecological causes (Table 3). In the long run, the calculated course of variations in contamination induced by the transfer e!ect seems to approach that given by the physical data (the state of equilibrium) in both areas by the end of the period investigated (1996). According to our idea for the compartment model (Fig. 4), the transfer function, in principle, consists of several parallel branches. The "rst gives a more direct (prompt) supply from the source to the nutrition compartment, and the other branches consist of a coupling bu!er with an incorporated time factor (temporary residency): ¹ (t) # ¹ (t )"¹ (t); t "t!t ; t "delay time. R V V V V (promt#delay"transfer)
(A3)
By taking the contributions of contaminated mass transfer into the nutrition compartment from two branches only, to show the principle of the mathematics applied, the continuous solution is summarised in the following theoretical equations for one unit of speci"c radioactive fallout: (A.3) (Prompt term): ¹ (t)"R [exp(!k t)!exp (!k t)], , (A.3) (Delay terms): ¹ (t)" R +F [exp(!k t )!exp (!k t )] G G , G G G !D [exp (!k t )!exp (!k t )],, G G G G
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t "t!q , q ""xation time of delay, G V V R "e k /(k !k ), ; R "+e k /(k !k ), ; , G , G F "+k /(k !k ), ; D "+k /(k !k ), . G G G , G G G G Further delay terms of the same character as Eq. (A4) must, in principle, be added. The turnover rate factors for nutrition k and the radioactive source k are the same for all , parallel branches. The delay (residency time t), the bu!er turnover rate k and the distribution coe$cient e, are given di!erent values in each case. The e coe$cients express the relative distribution of the fallout radioactivity into the di!erent branches for each spot area chosen (see the compartment model in Fig. 4). According to our compartment model, the local turnover mass rate (year\) &a priori' has to satisfy the condition k k 'k . By introducing the e!ective decay constant; a"j#k (the , sum of the physical decay constant j and the mass turnover rate k), instead of k in the exponents, a formal solution would be: F(t) " ¹ (t) Ph(t) V V (separately valid for each region and branching case x).
(A4)
The structure of this fractional equation is the same for each isotope, but the e!ective decay coe$cient a di!ers, depending on the physical constants and the actual urnover rates operating in that speci"c area. As an example, a set of possible values for local parameters that may be used in the compartment model with two bu!er branches that "ts our data is summarised in Table 4. A numeric approximation of the transfer function ¹ (t) can be calculated from these data. The results are shown graphically in Fig. 5. Another way of characterising the transport properties is to use the concept of relative transfer coe$cient P , given as the relationship between the in"nite 1, concentration integral of radioactivity in the nutrient compartment (N) to that of the input (deposition) rate from the source compartment (S). The equations used for Table 4 A reasonable set of parameters "tting the data observed Factors
Lauvsj+en
k (source turnover rate) +4.3 (year\) k (nutrition turnover rate) 0.33 (year\) , k (bu!er 1 rating) 3.5 (year\) k (bu!er 2 rating) 2.5 (year\) t (delay time bu!er 1) 2.7 (year\) t (delay time bu!er 2) 5.1 (year\) e /e (unknown distribution quantities which have to be proposed) e /e (rel. distribution) 3.48 e /e (rel. distribution) 0.76 (year) P 1.97 1,
Luru +27 (year\) 0.28 (year\) 2.7 (year\) 1.9 (year\) 2.1 (year\) 5.2 (year\) 0.78 0.08 (year) 1.65
167
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Fig. 5. Diagram showing the transferred content of radioactivity according to our ompartment model (ecological processes only), based on the data given in Table 4.
these calculations, based on the model with two bu!ers compartments (B1 and B2), are P "H /H #H /H 1, The theoretically in"nite integral characters are
(A5)
H "(e #e #e ) k [0.65/a #0.35/a ], H "0.65e k [1#(e /e ) (k /a )#(e /e ) (k /a )]/a a , H "0.35e k [1#(e /e ) (k /a )#(e /e ) (k /a )]/a a . The coe$cients included in the equations are as follows: a "j #k , a "j #k , a "j #k , a "j #k , a "j #k , a "j #k , a "j #k , a "j #k , (number 1 refers to isotope Cs and number 2 to isotope Cs).
,
,
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