A collective model for predicting the long-term behaviour of radionuclides in rivers

The Science of the Total Environment 201(1997) 17-29

A collective model for predicting the long-term behaviour of radionuclides in rivers Luigi Monte Istituto per la Radioprotezione,

ENEA

CR Casaccia,

CP 2400, 00100 Roma,

Italy

Received 8 October 1996; accepted 17 March 1997

Abstract Here I describea collective model to predict the long term behaviour of “Sr in river catchments.The model is appliedto 11 Italian rivers contaminatedby s”Sr due to nuclear explosionsin the atmosphereover past decades.The uncertainty at the 68% confidencelevel of the model,when usedasa generictool for evaluatingthe concentrationof the radionuclidein water, is a factor 1.8 aroundthe predictedvalues.The reliability of the model output is due to the mutual compensationeffects of different phenomenaoccurring in the catchmentsthat lead to ‘collective’ behaviours which are scantilyvariable and uncertain despitethe large range of catchmentcharacteristics.The model is basedon the assumptionthat the time behaviour of the ?Sr (Bq s-l) transported by water, following a single pulse of radionuclide deposition,is the sum of someexponential components.In the present paper the componentswere supposedcharacterisedby the following decay constants:A, = 2.3 X 10-r s-l, A, = 4.2 X lo-’ s-l and A3= 4.2 x lo-” s-r. The averagevalue of 90Srtransfer coefficient from the catchmentto the river, that, in the caseof a pulse deposition,is approximatelyequalto the ratio betweenthe radionuclideconcentration in water and the deposition,is estimatedto be 0.2 m-‘. 0 1997Elsevier ScienceB.V. Keywards: Collective models;Radionuclides;Rivers; Transfer function; Model uncertainty

1. Introduction

Following the Chernobyl accident, some international projects (BIOMOVS, 1991; IAEA, 1995) were launched to validate models for predicting the migration of radionuclide through the environment. These projects were based on validation exercises carried out using a great deal of contamination data gathered by a number of interna-

tional institutions. The collected experimental data were relevant to a variety of different ecosystems in the northern hemisphere. Special attention was devoted to the analysis of radionuclide migration through fresh water ecosystems. The investigations and the model validations have mainly concentrated on 137Cs. Indeed, data for the concentration of 137Cs in the components of fresh water ecosystems are copi-

0048-9697/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved. PI1 SOO48-9697(97)00081-S

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ously available. The lack of similar quantities of experimental data prevented modellers from undertaking equivalent extensive tests of models aimed to predict the environmental migration of other long living radionuclides. Among them 90Sr, which shows a high mobility through the aquatic environment and deserves particular attention due to its potential toxicity. In principle, models for predicting the behaviour of complex ecosystems may be ascribed to two ideal categories: ‘empirical’ and ‘conceptual’ models. Models belonging to the first category make use of empirical algorithms relating the output to the input variables. On the contrary, ‘conceptual’ models are based on a detailed and, at least in principle, complete knowledge of the whole set of fundamental processes controlling the environmental migration of the contaminant substances. The use of pure ‘empirical’ or pure ‘conceptual’ models have obvious advantages and disadvantages. Empirical models may be very simple and manageable although, in most cases, they make use of parameters that need site-specific values. As a result, they may be unreliable when the environmental conditions are markedly different from the ones relevant to the model calibration. Conceptual models may be very complex and need a tremendous amount of input data that, in most circumstances, are difficult to obtain. Conceptual models are powerful tools for understanding the dynamics and the behaviour of a system. They embed, at least in principle, the main processes occurring in the system in a mathematical framework. Obviously, the majority of the existing models are hybrids that take advantage of the features of both the above categories. Among the set of models that cannot be defined as pure empirical or pure conceptual, the ‘collective’ (Monte, 1996a) models play a peculiar role. This sort of model makes wide use of aggregatedstate variables and parameters. Collective models are based on the assumption that the mutual compensation effects of different phenomena occurring in a system can lead to collective behaviours that are less variable, and consequently may be predicted with less uncer-

201 (1997)

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tainty, than each single process. The systems that may be divided into sets of homogeneous sub-systems are the most obvious examples. Indeed, the processes originating as ‘ensemble averages’ over the class of these sub-systems show somewhat regular behaviour due to statistical effects (‘statistical aggregation’). A detailed description of the fundamental principles of the collective modelling is reported elsewhere (Monte, 1996a). The main aim of the present paper is to describe a simple and reliable collective model for predicting the migration of dissolved radioactive substances from catchments of large rivers. It will be demonstrated that the high performances of the model output are due not only to the ‘statistical aggregation’ of the migration processes, but also to some competitive effects that reduce the variability of the migration parameters despite the large ranges of environmental conditions. The model has been validated using data for “‘Sr concentrations in 11 Italian contaminated rivers following the fall-out from nuclear explosions in the atmosphere over past decades. Particular attention was devoted to this radionuclide to highlight an issue that has not been sufficiently investigated by the scientific literature. The data used for validation were collected by the ‘Laboratorio per lo Studio della Radioattivita Ambientale’ of the ‘Comitato Nazionale Energia Nucleare’ (CNEN, at present ENEA) and by the ENEA laboratories at Casaccia Institute (Rome). They cover the period from 1963 to 1994. 2. Radionuclide catchments

transfer functions from

The transfer of a toxic substance through a catchment is mainly controlled by the interaction of the pollutant dissolved in running water with the soil particles. Such a process is usually modelled by means of the so-called ‘partition coefficient’ (or ‘distribution coefficient’) that is defined as the ratio, at equilibrium, of the concentration of the radionuclide in particulate phase (Bq kg-’ ) divided by the concentration of the radionuclide in dissolved form (Bq rne31. It may be demonstrated (Joshi and Shukla, 1991) that the flux @$t) (g s-’ or Bq SK’) of pollutant through a

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catchment at time t, following a single pulse deposition D (g me2 or Bq m-‘1 and on the hypothesis that the partition coefficient (k,) and the other geological and hydrological characteristics are constant through the catchment, is, Qr,(t) = $e-

Spkr, where A is

the surface area of the catciment, .( is a constant depending on the characteristics of the catchment, and p is the soil density (kg mm3>. &

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In a large catchment the flux a#> of a pollutant may be calculated as follows: q,(t)

= DA

1

approximately,

201 (1997)

/%y 0

epkd) &d5pk,

where F( zJpkd) is the distribution in the catchment. By putting obtain

(1)

function of {pkd Spkd = l/0, we

is

the removal constant (s-l ). As the values of kt, p and 5 may vary through the catchment, the total flux of the pollutant is the sum of several exponential components. Each of them corresponds to the contribution of contaminant from a subcatchment characterised by specific values of the above parameters. In a previous paper (Monte, 1996a), the author demonstrated, by an intuitive, non-quantitative proof, that, during the time interval within the period of observation, from instant t, to instant t, after a pulse deposition event, if t, and t2 have the same order of magnitude. the component whose removal constant is of the order of l/t, (or l/t,) is the most significant. Indeed, if tpk, +C t, and t,, the relevant exponential component is negligible as the term I .~ e ‘Pi” is low. On the other hand, if tpkd z=-t, and t,, the component is ne ligible due to the low R value of the coefficients 5pk,. During the observation period, the significant exponential components of the pollutant flux are mainly related to the order of magnitude of t, and t, and are almost independent of all the other characteristics of the catchment. For example, as a quantitative illustration:

(2)

The radionuclide

flux is equal to the Laplace

transform of the function g( 0) = $ f i multi( 1 plied by AD. This result may help one to calculate cP,(t>.The effective removal constant obtained by a logarithmic fit of Qr(t> over the interval [t&l is:

A=---- l dd,tt) q,(t) dt r where t belongs to [t,,t,].Using Eq. (21, after calculations and an integration by parts, Eq. (3) becomes:

(4)

The second term in the right member of the previous equation may scarcely affect the order of magnitude of h. Indeed, due to the presence of the term g’(0), the integral of the numerator

Table 1 Measured values of some parameters of the TF from catchments (dissolved caesium) River Danube Rhine (Lobith)

0.89 0.74

95% up of (Y,

95% down of Ly2

A2 + 4 (s-1)

95%

up of A, + A, (s- ‘)

1.29 1.43

0.48 0.05

1.7

1.8 x 10-s x 10-s

2.3 2.3

x 10-s x lo- s

95% down

A?+A,(s-l) 1.2 x 10-s 1.2 x lo- 8

of

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L. Monte / The Science of the Total Environment 201 (1997) 17-29

may be very low when compared with the denominator. Notice that g’(e) reaches both positive and negative values that mutually compensate when the function is integrated over the interval [0, ~1, whereas g(e) is a non-negative function. Equation (4) shows that, on the previous hypotheses, A depends solely on t and is scarcely sensitive to the other characteristics of the catchment S,p,kd and A. Unfortunately, analytical integration of Eq. (2) is very difficult except when the function F((pkd) is particularly simple. This occurrence prevents one from demonstrating the previous result in a general way. A quantitative example using the following distribution function: nn

e 5pkd = r(n - 1) ( Epkdln (naY

F(bk,)

(5)

said before t, and t, are of the same order of magnitude) is of the order of l/t1 and is independent of the other parameters in Eq. (5) (therefore it is independent of the characteristics of the catchment). Similar results may be obtained by using other distribution functions of [pkd, such as hyperbolic and, under suitable hypothesis, constant functions over a finite interval. The radionuclide transfer function (TF) from a river catchment is the flux of radionuclide (Bq SK’ > transported by the river, following a single pulse deposition of radionuclide into the drainage area (Bq m-‘1, as function of the time and of the water flow. The mathematical form of the dissolved radionuclide transfer function proposed by the author (Monte, 1995) is the following: Qr(t) = ED ~~“i(t)P,Aie-‘“~‘“~)’

(7)

i

(coefficients were introduced integral of the function from tion (5) shows a maximum at when cpkd + CCand is equal The radionuclide flux is Qr(t> =AD(na)“-

‘(n - 1)

to assure that the 0 to CCis 1). Equa[pk, = a, tends to 0 to 0 when [pkd = 0. 1

(6)

(na + t)”

If n > 1, Eq. (5) may simulate a hypothetical distribution of (pk,. When n varies from > 1 to some units and if t > O.lna, it is easy to verify that the removal constant evaluated by a logarithmic fit of the Eq. (6) in the range t,-t, (as

QF is the radionuclide flux in Bq s-l, E is the transfer coefficient from the catchment (m-l>, D is the deposition per square metre (Bq rnw2), CDis the water flow (m3 s-l), pi (pi must be 1 when cyi= 1) are normalisation coefficients introduced to ensure that the units of Pi are m3 s-l, Ai is the relative weight of the ith component (CA, = l), A, is the radioactive decay constant aid A, + hi are the effective decay constants. The values of j3, may be chosen as follows: pi = @(OF az

(8)

Table 2 Measured values of some parameters of the TF from catchments (particulate caesium) River Danube Uzh Teterev Prypiat Dnieper Desna Rhine (Lobith) Geometric

2.44 1.02 1.34 1.52 1.24 1.11 1.12 1.34

95% up of Lyz

95% down of Lyz

A2

+4 (SC’)

95% up of A2 + A, (s-1)

95% down of A, + A, (SC’)

1.90 0.65 0.97 1.34 1. 0.83 0.27

2.98 1.39 1.77 1.70 1.37 1.39 1.97

1.4 x 1.1 x 1.2 x 1.4 x 1.2 x 8.9 x 1.7 x

2.2 x 1.8 x 1.8 x 1.6 1.4 x 1.3 x 2.4 x

6.7 x 4.0 x 6.0 x 1.3 x 1.1 x 4.7 x 1.0 x

10-s 10-s 10-s 10-s 10-s 1O-9 10-s

1.2 x 10-s

10-s 10-x 10-s IO-* 10-s 10-s 10-s

lo-” 10-9 1O-9 10-s 10-s 1o-y 10-s

L. Monte / The Science of the Total Environment 201 (1997) 17-29

where a(O) is the water flux at an arbitrary chosen initial time (t = 01. The introduction of coefficients pi is based on the hypothesis that the calculated products l Pi are independent of t,,, the instant when the deposition occurs. In a previous paper (Monte, 1995) the author evaluated the parameters of the TF for dissolved caesium and strontium of the Chernobyl origin in various European rivers: PO (Italy), Prypiat, Dnieper, Teterev and Uzh (Ukraine) and Rhine (Central Europe). Two exponential components were detected by fitting available experimental data collected over a period of approx. 5-6 years after the accident. A review of the values of the parameters of the TF is reported in previous papers (Monte, 1996b, 1995). Table 1 shows some new results obtained by analysing data of radionuclide concentration in two European rivers (Maringer, 1994). The results of the data analysed in Monte (1996b, 1995) are here summarised: the short effective decay component (h, + hi) ranges from 0.6 X 10e7 to 9.0 X lop7 s-‘(dissolved 137Cs, 90Sr and lo3Ru), the long effective decay component ranges from 7. x 10e9 to 2.7 x 10F8 s- ’ (‘37Cs) and from 3.6 x lo-’ to 5.9 x low9 s-l (90Sr). The effective decay constants, despite the tremendous differences in the geological, geographical, morphological and hydrological characteristics of the examined catchments, show low variability in agreement with the conclusions of the previous discussion. The exponent LY* for 137Cs ranges

21

from 0.53 to 1.08. Unfortunately, the scarcity of data and the large standard deviations associated do not allow to infer that this parameter is significantly lower than 1. The exponent a2 for “Sr ranges from 1.12 to 1.41 and is significantly higher than 1. As consequence the concentration of this a (t> radionuclide in water -& significantly ini 1 creases with the water flow. Coefficient A, is, on average, 20 times higher than A,. Due to the difficulty of getting reliable estimates of the mean radionuclide deposition onto the river catchments due to the Chernobyl accident, the evaluation of E is very uncertain. Table 2 shows the evaluation of some parameters of TF for particulate 137Cs carried out by using data of radionuclide concentrations from the international literature (Maringer, 1994; Kaniviets and Voitchekhovich, 1992). Equation (7) is valid for a single pulse deposition event. If the deposition is a function of time (D(t) = deposition rate Bq me2 s-l) the radionuelide flux may be evaluated as follows:

If Si is the amount of radioactive substance (Bq mv2> in the ith radionuclide storage compart-

Table 3 Characteristics of the examined rivers River

Am0 Flumendosa Ofanto Piavr PO Reno Simeto Tevere Ticino Tirso Voltumo

Length (km)

245 122 134 220 652 210 88 396 248 150 185

Area of drainage basin (km’)

82.50 1175 2764 4100 70000 4628 4186 17156 7228 3376 5617

Course Rise

outflow

Tuscan-Emilian Apennines Sardinian range Campanian Apennines East Alps West Alps Tuscan-Emilian Apennines Sicilian range of Apennines Tuscan-Emilian Apennines Central Alps Sardinian range Campanian Apennines

Ligurian Sea Tyrrhenian Sea Adriatic Sea Adriatic Sea Adriatic sea Adriatic Sea Ionian Sea Tyrrhenian Sea River PO Mediterranean Sea Tyrrhenian Sea

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L. Monte /The Science of the Total Environment 201 (1997) 17-29 Table 5 Values of E Cm-‘) “Sr (A, = 0.045)

ment of the catchment, we obtain

where Si are solutions of the following system of differential equations: dsi - - (Ai + h,)S, +/l@(t) dt

(11)

The radionuclide storage compartments may be schematically intended as the various soil layers and the vegetation cover in the catchment. Using ayi= 1 the model allows one to evaluate the average flux of radionuclide disregarding the seasonal effects due to the variations of the water flow during the year. For such a hypothesis we obtain from Eq. (10): Cw=E Es,

(12)

i

where C, is the concentration radionuclide in water: c

w

of the dissolved

= @r(t) @(t)

Equation (11) may be solved numerically by a variety of software tools such as Ithink (Software from High Performance Systems Inc., 45 Lyne Road, Nanover, New Hampshire, USA). The model neglects the migration of particulate 90Sr as this radionuclide is, mainly, in dissolved form. The present paper shows the results of the model validation. The experimental data of ‘OSr were measured in 11 Italian rivers (see Table 3). The watercourses and the relevant drainage areas Table 4 Values of the parameter used in the model Parameter

Value

Measurement units

Al ‘42 Al

0.935 0.045 2.3 x lo-’ 4.2 x 1O-9 4.2 x lo- lo

Dimensionless Dimensionless

A2

A3

s-1 s-1 s-1

Ofanto Flumendosa Tirso Volturno Simeto Aano Ticino Reno PO (Guarda V.) PO (Turin) Piave Tevere Geometric mean

E

4

0.30 0.15 0.22 0.15 0.35 0.26 0.15 0.29 0.18 0.13 0.14 0.16 0.20

13.50 x 6.75 x 9.90 x 6.75 x 15.80 x 11.70 x 6.75 x 13.10 x 8.10 x 5.85 x 6.30 x 7.20 x 9.00 x

lo- 3 1O-3 10-3 10-s 1O-3 10-s 1O-3 10-s 1O-3 1O-3 1O-3 1O-3 10-s

show a wide range of morphological, geological and hydrological characteristics. The values of the parameters used in model are reported in Table 4. The third exponential component was included in the model to account for the long term migration processes. Table 5 shows the value of E calculated by calibrating the model output using the available experimental data and the parameter values showed in Table 4. The geometric mean of E is 0.2 m-l. This value was used for the model simulations reported and discussed in the present paper. Some examples of the comparison of the model results with the experimental data are illustrated in Figs. l-4. The deposition of 90Sr on the river catchments was obtained from Giorcelli (1980). They represent estimates averaged over the Italian region (see Fig. 5). The model results were calculated using czi= 1 and, of course, they must be intended as average estimate of radionuclide concentration in water. Fig. 6 shows, as an example, the predicted 90Sr concentration in the river Arno evaluated when LY*= 1.4. The simulation was carried out using monthly averages of the water fluxes (Pulselli and Bagato, 1978). The model better predicts the time behaviour of the radionuclide concentration in connection with the seasonal maxima and minima of water flux. The aim of the following discussion is to evaluate the uncertainty of the model results and to charac-

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L. Monte /The Science of the Total Environment 201 (1997) 17-29

RIVER TEVERE 1OOA

b -

t 2boo

4000

6000

8000

10000

MODEL OUTPUT

12000

14000

r 16000

DAYS AFTER JANUARY 1ST 1954 Fig. 1. Comparison of the model output with the experimental data collected in river Tevere. Period of observation 1964-1994.

RIVER OFANTO 1oooa

c -MODEL

lOi 3000

3500

4000

4500

5000

OUTPUT

5500

6000

DAYS AFTER JANUARY 1ST 1954 Fig. 2. Comparison of the model output with the experimental data collected in river Ofanto. Period of observation 1963-

L. Monte / The Science of the Total Environment 201 (1997) 17-29

24

RIVER VOLTURNO L

a 100:

-

I

MODEL OUTPUT

M k

II

L 10: in z rE

2000 7

3500

4000

4500

5000

5500

6000

r

6500

DAYS AFTER JANUARY 1ST 1954 Fig. 3. Comparison of the model output with the experimental data collected in river Volturno. Period of observation 1963-1972

RIVER FLUMENDOSA 100

M ‘E 10 liz hi z

1 3500

-

4000

4500

5000

MODEL OUTPUT

5500

6000

6500

7000

DAYS AFTER JANUARY 1ST 1954 Fig. J. Comparison of the model output with the experimental data collected in river Flumendosa. Period of observation 196351972.

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L. Monte / The Science of the Total Environment 201 (1997) 17-29

gOSr MONTHLY DEPOSIT ION

DAYS AFTER JANUARY 1ST 1954 Fig. 5. The monthly deposition of WSr in Italy.

RIVER ARNO 1000

-

10 3000

3500

4000

4500

5000

MODELOUTPUT

5500

6000

6500

7000

DAYS AFTER JANUARY lST 1954 Fig. 6. Comparison of the experimental WSr concentration in water of river Amo with the model output obtained using 1y2= 1.4 The model can predict the seasonal variation of the radionuclide concentration in water due to the varying water flux.

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L. Monte /The Science of the Total Environment 201 (1997) 17-29

terise the performances of the model when it is used as a ‘generic tool’ (the radionuclide concentrations were calculated using, for all the rivers, the same values of the model parameters) for predicting the migration of 90Sr in rivers. 3. Empirically based uncertainty analysis (EBUA) applied to the model

The empirically based uncertainty analysis (EBUA) is a mathematical method for evaluating the uncertainty of model output by using the results of the model validation (Monte et al., 1996). EBUA may be applied when experimental evaluations of the quantities to be modelled are available at different sites. The goal of such a method is to assess the confidence limits of model predictions by analysing the results of the comparison of the model output with the experimental data sets. EBUA is based on the calculation of performance indices assessing the reliability of the model. Each index is characterised by an optimal value: the closer the value of the index to the optimal value, the better the model predicts the experimental behaviour. In some cases, the evaluation of the performance index allows one to calculate, by the statistical analysis of the index values, the confidence interval for the model predictions. Two indices were used in the present work: Table 6 Logarithmic distances (d) between the experimental data sets and the model predictions River

d

Flumendosa Po(Turin) Tirso Ofanto Piave Reno

0.279 0.53 0.274 0.373 0.494 0.235 0.347 0.499 0.158 0.215 0.256 0.202

AlllO

Simeto PO (G. Veneta) Tevere Ticino Volturno

Table 7 Correlation coefficients (r) between the logarithm of the experimental data and the logarithm of the predicted values River

r

Flumendosa PO (Turin) Tirso Ofanto Piave Reno

0.106 0.271 0.27 0.171 0.178 0.67 0.658 0.626 0.193 0.256 0.012 5.000 x 10-5

AIYIO

Simeto PO (G. Veneta) Tevere Ticino Volturno

1. the logarithmic average distance between the experimental data sets and the model predictions; and 2. the correlation coefficient, r, between the logarithm of the experimental data and the logarithm of the predicted values. The logarithmic as follows: d2

=

c

OnP,

-

i

average distance (d) is defined

lnOij2

n

(13)

where Pi is the ith predicted value, 0, is the ith observed value and n is the number of the observations at a specific site. The optimal values of d and r are, respectively, 0 and 1. The results of the calculation of d and r are given in Tables 6 and 7, respectively. Fig. 7 reports the histogram of the natural logarithm of the ratio predicted/observed values. The average value is 0.0316. The functional distance show a log-normal distribution (Fig. 8). It is possible to demonstrate (Monte et al., 1996) that, in such hypothesis, the standard deviation (+ of the above ratio may be calculated as follows:

CT=$(d2>

(14)

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HISTOGRAM

OF IdEXPERIMENTAL

201 (1997)

27

17-29

DATA /MODEL OUTPUT)

1601’ , 140. 120. 1oor = 8

80. 60 1

In (EXPERIMENTAL

0 1 DATA/MODEL OUTPUT)

2

3

Fig. 7. The histogram of the natural logarithm of the ratio observations/model predictions. The average value is close to 0. The shape of the histogram shows that the distribution of the ratio is approximately log-normal.

‘-1

-,g

-,8

-,7

-36

-,5

-,4

-,3

NATURAL LOGARITHM OF THE FUNCTIONAL DISTANCE Fig. 8. The percentile of the normal distribution vs. the logarithm of the functional distance d. As the figure shows the distribution of d is approximately log-normal.

28

L. Monte

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of the

where the brackets < > indicate the average value. Applying Eq. (14) above, we get (T = 0.567. The probability that the ratio ranges from e-” = 0.6 to epu = 1.8 is 68%. It is interesting to notice that the standard deviation of the ratio calculated directly by the data reported in the histogram is 0.563, in good agreement with Eq. (14). The comparison of the results reported in Tables 6 and 7 allow one to draw some conclusions: l

Rivers At-no, Reno, Simeto: the large values of the logarithmic distances show that the model output values are systematically biased: indeed, as Fig. 9 and Table 5 show, the experimental data are underestimated by the model and the calculated values of E for these rivers are higher than the generic value used in the model (E = 0.2 m-l 1 The high values of the correlation coefficient indicates that the model reliably predicts the time behaviour of the experimental data.

Total Environment l

l

l

201 (1997)

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River PO (Turin): the low value of Y is due to the relevant influence of the seasonal conditions on the water contamination. The logarithmic distance at Turin is higher than the logarithmic distance in Guarda Veneta. This is a further demonstration of the importance of the seasonal effects. Indeed at Turin, a town close to Alps where the river PO rises, the seasonal variation of the water flux due to the various hydrological conditions (rain in autumn, melting of ice in spring etc.) is very large and plays an important role, whereas at Guarda Veneta, close to the river mouth, these effects are less important. Rivers Piave, Tirso, Ofanto, Tevere and Flumendosa: as seasonal effects are important, the logarithmic distance is very high. Rivers Volturno and Ticino: although the logarithmic distances are less than for other rivers (such occurrence indicates a good agreement of the experimental and the predicted data) the correlation coefficients are

RIVERS ARNO, RENOAND SIMETO 1000

t ARNO o RENO l

%

A SIMETO

-

1J 3000

3500

4000

4500

5000

5500

MODEL OUTPUT

6000

6500

c 7000

DAYS AFTER JANUARY lST 1954 Fig. 9. Comparison of the model output with the observed “Sr concentration in rivers Arno, Reno and Simeto. The model systematically underestimates the experimental values when E = 0.2 m-’ (the ‘generic value’) is used.

L. Monte / The Science of the Total Environment 201 (1997) 17-29

very low. This occurrence is due to the feeble variation, during the period of observation (1964-1974) of the yearly average of radionuelide concentration in water. These slow variations are not sufficient to raise the level of r that are lowered by the data uncertainty and, mainly, by the seasonal fluctuations not predicted by the model when cy2= 1.

4. Conclusions

The use of a collective model based on the transfer function allows one to predict, for a long run, %Sr migration in catchment basins. The model shows an uncertainty of approx. 1.8 at the 68% confidence level when applied as a generic tool to predict the migration of radionuclide in water. The model described here shows the minimal structure necessary to predict some specific behaviour of 90Sr in water bodies. The values of its parameters are scantily variable despite the large ranges of characteristics of the rivers. This peculiarity makes the model usable in circumstances for which it was not calibrated before. The low uncertainty levels are due to collective effects arising from the mutual compensations of some processes occurring in catchment basins. The values of the TF parameters (A,, A,, A,, A, and A,) here used were obtained by means of a number of different attempts. Indeed no efforts were made to evaluate, by mathematical fitting of the experimental data, the parameters of the transfer function for the different watercourses due to the difficulties of such kind of fit that must be carried out using radionuclide deposition variable with the time and multi-exponential fitting functions.

29

Acknowledgements

This research was partially financed by the EC, Contract N” FI4P-(X96-0036, Project MOIRA. References BIOMOVS. On the Validity of Environmental Transfer Models. Symposium, Swedish Radiation Protection Institute, October 8-10, 1990. Stockholm, Sweden, 1991. Giorcelli F. Valutazione della dose alla popolazione Italiana derivante da esplosioni nucleari. CNEN-RT/PROT (80) 30, Rome, ENEA, 1980. IAEA. Environmental impact of radioactive releases. Proceedings of an International Symposium on Environmental Impact of Radioactive Releases. Vienna, Austria, May 1995:8-12. Joshi S.R., Shukla B.S. The role of the water/soil distribution coefficient in the watershed transport of environmental radionuclides. Earth Planet Sci Lett 1991;105:314-318. Kaniviets W, Voitchekhovich OV. Scientific report: radioecology of water systems in zone of consequences of the Chernobyl accident. Report of Ministry of Chernobyl Affairs of Ukraine, Contract N l/92 (in Russian). Maringer FJ. Das Verhalten von Radionukliden im Wasser, Schwebstoff und Sediment der Donau. Dissertation. Technischen Universitlt Wien, April 1994. Monte L. Evaluation of radionuclide transfer functions from drainage basins of fresh water systems.J Environ Radioact 1995;26:71-82. Monte L. Collective models in environmental sciences. Sci Total Environ 1996a;192:41-47. Monte L. Analysis of models assessing the radionuclide migration from catchments to water bodies. Health Physics 1996b;70:227-237. Monte L., Hikanson L., BergstrGm U., Brittain J., Heling R. Uncertainty analysis and validation of environmental models: the empirically based uncertainty analysis. Ecological Modelling 1996;91:139-152. Pulselli U, Bagato F. Elaborazione dei dati idrologici de1 bacino dell’Amo. In: Regimi delle Acque Superflciali. ENEL Studi e Ricerche. 1978.