Journal of Environmental Radioactivity 69 (2003) 177–205www.elsevier.com/locate/jenvrad

Review and assessment of models used topredict the fate of radionuclides in lakes

Luigi Monte a,∗, John E. Brittainb, Lars Hakansonc,Rudie Helingd, Jim T. Smithe, Mark Zheleznyakf

a ENEA CR Casaccia, via P. Anguillarese, 301, 00100 Rome, Italyb LFI, Natural History Museums & Botanical Garden, University of Oslo, Norway

c Institute of Earth Sciences, Uppsala University, Swedend NRG, Arnhem, The Netherlandse CEH Dorset, United Kingdom

f Institute of Mathematical Machines and System Problems (IMMSP), Academy of Sciences,Kiev, Ukraine

Received 11 November 2002; received in revised form 1 January 2003; accepted 2 March 2003

Abstract

A variety of models for predicting the behaviour of radionuclides in fresh water ecosystemshave been developed and tested during recent decades within the framework of many inter-national research projects. These models have been implemented in Computerised DecisionSupport Systems (CDSS) for assisting the appropriate management of fresh water bodies con-taminated by radionuclides. The assessment of the state-of-the-art and the consolidation ofthese CDSSs has been envisaged, by the scientific community, as a primary necessity for therationalisation of the sector. The classification of the approaches of the various models, thedetermination of their essential features, the identification of similarities and differences amongthem and the definition of their application domains are all essential for the harmonisation ofthe existing CDSSs and for the possible development and improvement of reference modelsthat can be widely applied in different environmental conditions. The present paper summarisesthe results of the assessment and evaluation of models for predicting the behaviour of radio-nuclides in lacustrine ecosystems. Such models were developed and tested within major pro-jects financed by the European Commission during its 4th Framework Programme (1994–1998). The work done during the recent decades by many modellers at an international levelhas produced some consolidated results that are widely accepted by most experts. Nevertheless,

∗ Corresponding author. Tel.:+39-0-630-484645; fax:+39-0-630-486716.E-mail address: monte@casaccia.enea.it (L. Monte).

0265-931X/03/$ - see front matter 2003 Elsevier Science Ltd. All rights reserved.doi:10.1016/S0265-931X(03)00069-9

178 L. Monte et al. / J. Environ. Radioactivity 69 (2003) 177–205

some new results have arisen from recent studies and certain model improvements are stillnecessary. 2003 Elsevier Science Ltd. All rights reserved.

Keywords: Lakes; Modelling; Radionuclides; Decision systems

1. Introduction

The appropriate management of fresh water ecosystems contaminated by radio-nuclides requires the assessment of the costs and the benefits of countermeasure andrestoration strategies aimed at reducing doses to man. Any environmental inter-vention may cause, indeed, non-desirable effects of ecological, economic and socialnature. Consequently, critical evaluations of alternative management strategies arenecessary to determine which of these reach the optimal balance between the relatedbenefits and costs.

Such an assessment requires the development of models for predicting the behav-iour of radionuclides in the fresh water environment, the effects of the countermeas-ure interventions (restoration actions) on the levels of pollution and the ecological,the social and the economic impacts of such interventions.

In the past decades a variety of models for predicting the behaviour of radio-nuclides in fresh water ecosystems were developed in the frame of many internationalprojects of research. Some of these models were implemented in ComputerisedDecision Support Systems (CDSS). Such CDSSs are software codes showing a highdegree of complexity and which address problems of great relevance for the practicalmanagement of the aquatic environment. These software products reach certaindefined goals running quantitative evaluations, simulating the consequences of selec-ted interventions, calculating costs and analysing benefits. They organise and struc-ture the knowledge of experts and allow decision makers to use many different typesof models appropriate for different environmental, social and economic situationsand for each specific contamination scenario.

Due to the wide variety of developed models and CDSSs, the scientific communityhas envisaged the review and the assessment of the whole sector as a primary necess-ity in order to classify the approaches of the various models, to determine theiressential features, to identify similarities and differences among them and to definetheir application domains in view of possible improvements and of the rationale ofthe entire sector.

The assessment of the state-of-the-art and the consolidation of existing DecisionSupport Systems has been one of the topical activities in the European Commission’s5th Framework Programme (1998–2002) on radiation protection (Schulte et al.,2002).

The main aim of the thematic network EVANET-HYDRA (“Evaluation and Net-work of EC-Decision Support Systems in the field of Hydrological Dispersion Mod-els and of Aquatic radioecological Research” ) is the completion of the above review

179L. Monte et al. / J. Environ. Radioactivity 69 (2003) 177–205

and assessment. The network is financed by the European Commission (CONTRACTN° FIGE-CT-2001-20125).

In the most trivial and general way a Decision Support System may be definedas any tool based on the organic structuring of expert knowledge to help decision-making. In principles, models for predicting the behaviour of radionuclides in thefresh water environment may be, therefore, obvious examples of DSS if they areaimed at answering specific demands from environmental managers or other poten-tial users.

CDSSs aimed at assessing the appropriateness of suitable and feasible countermea-sures for restoring aquatic environment contaminated by radionuclides are based,essentially, on

� a complete set of models for predicting the time behaviour of radionuclides inthe fresh water environment, the effects of the countermeasure interventions(restoration actions) on the levels of pollution and the ecological, the social andthe economical impacts of such interventions; and

� methodologies for ranking the different applicable countermeasures according totheir effectiveness when the benefits due to the dose reductions and the ecologic,the social and the economic detriments are accounted for.

As predictive models are essential components of CDSS for the management ofthe environment, it is of paramount importance to provide a critical analysis of theirfeatures in order to identify common approaches, overlaps and significant differencesamong them, to pinpoint shortcomings and to plan further improvements.

The present paper describes the results of the assessment and evaluation of modelsfor predicting the behaviour of radionuclides in lacustrine ecosystems. Such modelswere developed and tested within the frame of the most important projects financedby the European Commission during the 4th framework programme (1994–1998) ororganised by other international institutions (Table 1):

� ECOPRAQ: models were developed for 137Cs (137Cs-ECOPRAQ) and for 90Sr(90Sr-ECOPRAQ);

� MOIRA: 137Cs-ECOPRAQ was implemented in the MOIRA ComputerisedDecision Support System; a specific model for 90Sr was implemented in thepresent version of MOIRA (90Sr-MOIRA); MOIRA makes also use of a model(137Cs-MARTE) for predicting the behaviour of 137Cs in lakes or reservoirs incomplex river/catchment systems;

� AQUASCOPE: models for 137Cs (137Cs-AQUASCOPE) and 90Sr (90Sr-AQUASCOPE) were developed;

� RODOS: the RODOS Computerised Decision Support System includes the modelLAKECO for predicting radionuclide behaviour in lakes together with other mod-els aimed at assessing the non-homogeneous radionuclide dispersion in large orstratified water bodies (THREETOX);

� BIOMOVS, BIOMOVS II and VAMP: models were tested by applications toselected scenarios of lake contamination.

180 L. Monte et al. / J. Environ. Radioactivity 69 (2003) 177–205

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181L. Monte et al. / J. Environ. Radioactivity 69 (2003) 177–205

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182 L. Monte et al. / J. Environ. Radioactivity 69 (2003) 177–205

Among the models and the software codes developed in the frame of the previousprojects, the CDSSs RODOS and MOIRA show a high degree of complexity.

The CDSS RODOS comprises a complex set of models for predicting themigration of radionuclides through the environment. An Atmospheric DispersionModule assesses the radionuclide fall-out by accounting for the meteorological situ-ation. The Hydrological Dispersion Module aims at evaluating the subsequent disper-sion of the radionuclides through the aquatic environment. Doses to man from thecontamination of both the aquatic and terrestrial environments are therefore assessed.RODOS provides tools for processing and managing a large variety of differenttypes of information, including meteorology, radiology, economy, emergency actionsand countermeasures.

The CDSS MOIRA is a user-friendly software tool that allows decision makersto choose optimal countermeasure strategies for different kinds of aquatic ecosystemscontaminated by radionuclides, taking into account ecological, social and economicconsequences. MOIRA is structured to guide decision makers to approach problems,and to manage different solutions by “navigation” through different possible options(Appelgren et al., 1996).

The present paper is not aimed at supplying detailed descriptions of the assessedmodels. On the other hand, a copious scientific literature is available to provideextensive information about the features of the models object of the assessment.Nevertheless, some particular aspects of the models are circumstantially reported tosupport the general conclusions of the paper rather than to illustrate in detail, likea handbook, the characteristics of each model.

2. Basic structure of the models

137Cs-ECOPRAQ, 90Sr-ECOPRAQ (Comans et al., 2001), 90Sr-MOIRA, 137Cs-MARTE (Monte, 1998; Monte et al., 2002; Monte, 2001), 137Cs-AQUASCOPE, 90Sr-AQUASCOPE (Smith et al., 2002) and LAKECO (Heling, 1997; IAEA, 2000) (thislast is implemented in RODOS) supply predictions of radionuclide concentrationsin water averaged over the entire volume of the lake water and of sediment (lumpedmodels). The other models in RODOS are aimed at predicting radionuclide concen-trations at different points or depths in the water body (distributed models).

The models are aimed at supplying predictions of radionuclide concentrations inthe abiotic and the biotic components of a lacustrine system. Moreover, some ofthem allow one to assess the effects of selected countermeasures on contaminationlevels. Basically, they all comprise three main sub-models:

1. a sub-model for predicting radionuclide migration from catchment to water body;2. a sub-model for predicting the behaviour of radionuclides in the abiotic compo-

nents of the aquatic system; and3. a sub-model for predicting the behaviour of radionuclides in the biotic components

of the lake.

These sub-models are linked by a ‘one-way’ fl ux of input data. Sub-model b)

183L. Monte et al. / J. Environ. Radioactivity 69 (2003) 177–205

(abiotic lake components) makes use of data (radionuclide flux from the lakecatchment) calculated by means of sub-model a) (catchment) and supplies to sub-model c) the necessary input data (concentration in the abiotic components of thelake) for evaluating the concentrations of radionuclide in biota. Therefore compari-sons and assessments of model features can be done separately for each sub-model.

Our focus shifts now to assess the methodologies for predicting the behaviour ofradionuclides within the lake components (internal processes: sub-models b and c).

3. Modelling the behaviour of radionuclides in the abiotic components of lakeecosystems

The most important hydrological processes occurring in a lacustrine system thatinfluences the behaviour of radionuclides in the lake is obviously the outflow ofwater from the outlet. Such a process is, indeed, responsible of the removal of radio-nuclides from the water body. The process is usually modelled according to thefollowing formula:

�r � �Cw (1)

where �r is the flux of radionuclide (Bq s�1) removed by the outlet, � is the outletflux (m3 s�1) and Cw is the radionuclide concentration in the lake water (Bq m�3).The other processes of radionuclide migration involve the complex interaction ofdissolved radionuclide in water with suspended particles and bottom sediments.

137Cs-ECOPRAQ, 90Sr-ECOPRAQ, 90Sr-MOIRA, 137Cs-MARTE and LAKECOare typical first-order models. They comprise three or four compartments correspond-ing to the radionuclide in the lake water and in two or three layers of bottom sedi-ment. The structures of the above models do not show substantial differences. Themodels developed in the frame of the AQUASCOPE project although, at first sight,seem based on a different approach are substantially similar to the other box models.AQUASCOPE models are indeed based on the evaluation of the response of watercontamination to a single pulse deposition input of radionuclide.

The radionuclide concentration in water at instant t following a single pulse depo-sition event at instant t is

Cw(t) � DG(t�t) (2)

where G(t�t) is the response to a deposition pulse of 1 Bq m�2 and D (Bq m�2)is the radionuclide deposition per square metre. The radionuclide concentration Cw(t)for deposition processes depending on time (D(t) = radionuclide deposition rate Bqm�2 s�1) is:

Cw(t) � �t

0

D(t)G(t�t)dt. (3)

It is well known that any linear model such as 137Cs-ECOPRAQ, 90Sr-ECOPRAQ,90Sr-MOIRA, 137Cs-MARTE and LAKECO is characterised by a function G(t�t)

184 L. Monte et al. / J. Environ. Radioactivity 69 (2003) 177–205

that allows one to evaluate the radionuclide concentration in water (or in any othertarget variable) by Eq. (3). From now on we will call G(t�t) the Green Function(GF) of the model. It is instructive to start our analysis by considering 90Sr behaviourin the water-sediment sub-system of a lake. We compare, for instance, the model90Sr-AQUASCOPE with the 90Sr-MOIRA model.

The 90Sr-MOIRA model for predicting the migration of radionuclide from waterto sediments is composed of two active boxes (Fig. 1):

1. radionuclide dissolved in water (Water, Cw, Bq m�3);2. radionuclide deposited in sediment (Bottom sediment, Ds, Bq m�2);

and a ‘passive box’ (Deep sediment) representing the radionuclide subject to non-reversible removal processes from the active deposit.

The equations controlling the radionuclide migration processes are the following:

Fig. 1. Structure of the 90Sr-MOIRA box sub-model for predicting 90Sr migration from water to sedi-ments (internal processes).

185L. Monte et al. / J. Environ. Radioactivity 69 (2003) 177–205

dCw

dt� �

vws

hCw �

Ksw

hDs�lrCw (4)

dDs

dt� vwsCw�(Ksw � Kds)Ds�lrDs

where h is the average depth (m) of the lake, vws is the migration velocity (m s�1)of radionuclide to the bottom sediment, Ksw is the migration rate (s�1) from bottomsediment to water, Kds is the removal rate (s�1) of radionuclide from the bottomsediment, lr is the radioactive decay constant (s�1) and t is the time (s).

The solution of the previous equation system, following a deposition pulse D (Bqm�2) at time 0 (GF of the MOIRA model), is

Cw(t) �Dh

�l2�vws

h �(l2�l1)

e�(l1+lr)t �Dh

�vws

h�l1�

(l2�l1)e�(l2+lr)t (5)

where l1 and l2 are as follows:

l1,2 � �

��vws

h� Ksw � Kds� � ��vws

h� Ksw � Kds�2

�4vwsKds

h

2. (6)

90Sr-AQUASCOPE predicts 90Sr concentration in the water of so-called “closed”lakes by the following equation for a pulse deposition input at initial time t = 0

C(t) � Ae�(K+lr)t � Dhe�(g+lr)t (7)

where K, g and h are empirical parameters and A�Dh

.

A shallow lakes is defined by Smith et al. (2002) as “closed lake” if it is character-ised by a long mean water- residence time ( � 1 year). The response functions forradiocaesium and radiostrontium were obtained as simplified semi-empirical modelswhich have been extensively calibrated and tested for Chernobyl-derived radio-nuclides in several European lakes.

We are here considering the radionuclide behaviour in closed lakes as the hypoth-eses of:

� negligible contribution of radionuclides from the lake catchment; and� negligible removal of radionuclides by lake outlet;

offer the opportunity of assessing the model performances in relation to the prevail-ing processes occurring within the sub-system ‘water-sediment’ (internal processes).Moreover, in shallow lakes a more significant interaction of radionuclide in the watercolumn with bottom sediment can be hypothesised.

Radionuclide concentration predicted by 90Sr-AQUASCOPE model is the sum oftwo exponential components and depends on four independent parameters (h, K, hand g) (Eq. (7)) as the 90Sr-MOIRA model (Eq. (5)).

186 L. Monte et al. / J. Environ. Radioactivity 69 (2003) 177–205

Comparing Eqs. (5) and (7) we obtain

K � l2 (8)

g � l1 (9)

and

h�1h

�l2�vws

h �(l2�l1)

. (10)

Therefore, the above models are, essentially, equivalent. Indeed, they supply simi-lar output for a suitable choice of their parameters. Supposing vws = 1.04 × 10�7

m s�1, Ksw = 5.62 × 10�9 s�1 and Kds = 8.79 × 10�10 s�1, the values of K, g andh calculated by formulae (8), (9) and (10) are close to the estimates of Smith et al.(2002): K = 1.2 × 10�7 /h (h is in metres and K in s�1); g = 7.9 × 10�10 s�1; h =5 × 10�2 m�1.

Therefore, we expect that both models for shallow closed lakes supply similarresults for an appropriate choice of the values of the model parameters. It is worth-while to notice that we have used here improved evaluations of previous approximateestimates of vws, Ksw and Kds (Monte, 2001). Fig. 2 reports an example of comparison

Fig. 2. Comparison of the results (concentration in water of 90Sr) of models 90Sr-AQUASCOPE and90Sr-MOIRA. The models were applied to a hypothetical scenario of a shallow closed lake having depth=2m contaminated following a deposition of 1 Bq m�2 of 90Sr. The parameter values are as follows: vws

= 1.04 × 10�7 m s�1, Ksw = 5.62 × 10�9 s�1, Kds = 8.79 × 10�10 s�1, K = 6 × 10�8 s�1, g = 7.9 ×10�10 s�1 and h = 5 × 10�2 m�1.

187L. Monte et al. / J. Environ. Radioactivity 69 (2003) 177–205

of the model outputs. The models were applied to a hypothetical scenario of a shal-low lake (depth = 2 m) contaminated following a deposition of 1 Bq m�2 of 90Sr.From the figure we can conclude that, over a period of ten years following thedeposition, the two models supply solutions that are practically the same. The relativedifference “�r = 100∗ (Aquascope output-Marte output)/Aquascope output” is lowerthan 10% and decreases rapidly with time.

The model 137Cs-AQUASCOPE for ‘closed’ lakes is based on three exponentialcomponents:

C(t) � Ae�(K+lr)t � Dh1e�(K2+lr)t � Dh2e�(K3+lr)t (11)

where, as usual, A�Dh

and K, K2, h1 and h2 are empirical parameters.

The suggested values of parameters in Eq. (11) are as follows:

K2 � 1.3 � 10�8 s�1 K3 � 6.3 � 10�10 s�1 h1 � 4.0 � 10�2 m�1

h2 � 8.5 � 10�3 m�1.

K is the effective decay constant of radionuclide in water due to the removalprocesses from the water column. Smith et al. (2002) suggests four different formulaeto calculate K according to the levels of detail of the input data. The followingoptions are considered:

a) only the deposition is known;b) the deposition and the lake depth are known;c) the deposition, the lake depth and the sedimentation velocity of the matter sus-

pended in water are known;d) the deposition, the lake depth, the sedimentation velocity and the potassium con-

centration in water are known.

We will assess option b) that corresponds to the application of a ‘generic model’ (amodel that does not make use of site specific information).

K is calculated by the following equation:

K �Ah

� B (12)

where A = 2.5 × 10�7 m s�1 and B = 3.2 × 10�8 s�1.Neglecting the third component it is possible to compare the features, on the

medium term ( 10 years), of 137Cs-AQUASCOPE and 137Cs-MARTE models.Table 2 reports the values of vws, Kds and Ksw used by model 137Cs-MARTE and thecorresponding values calculated by solving, respect to vws, Kds and Ksw, Eqs. (8), (9)and (10) applied to the parameters of the first and second components of 137Cs-AQUASCOPE model (11).

The model 137Cs-MARTE relates the values of the parameters controlling themigration of radionuclide from water to sediment and vice-versa to certain hydrolog-

188 L. Monte et al. / J. Environ. Radioactivity 69 (2003) 177–205

Table 2Model parameter values for 137Cs in lakes and reservoirs

Parameter MARTE (lakes) MARTE (reservoirs) AQUASCOPE

Dynamic Dynamic Dynamic Dynamic Depth 2 m Depth 10 mratio 1000 ratio � ratio 1000 ratio �

1000 1000

vws (m s�1) 5.9 × 10�7 1.2 × 10�6 9.3 × 10�7 1.6 × 10�6 2.9 × 10�7 3.9 × 10�7

kds (s�1) 5.8 × 10�9 1.2 × 10�8 1.2 × 10�8 1.2 × 10�8 1.4 × 10�8 1.9 × 10�8

ksw (s�1) 3.0 × 10�8 1.5 × 10�8 1.5 × 10�8 1.5 × 10�8 1.1 × 10�8 1.2 × 10�8

ical characteristics of the water bodies. Different values are used for lakes, riversand reservoirs. The migration velocities depend on the so called “dynamic ratio”that represents a measure of the intensity of interaction between the water and thebottom sediment. The dynamic ratio Dr is defined as follows (Hakanson and Jans-son, 1983):

Dr ��S

h(13)

where S is the surface (m2) of the water body and h is the lake average depth.The values of the model parameters (Table 2) show similar orders of magnitude.

It is quite obvious that, like for 90Sr, models 137Cs-AQUASCOPE and 137Cs-MARTEsupply similar results for such a choice of their parameters.

The model MARTE, in a very crude way, accounts, also, for the processes ofrapid adsorption of radiocaesium onto bottom sediment. It is assumed that a thinlayer of sediment (interface layer) strongly interacts with radionuclide dissolved inwater and that radionuclide concentration in such a layer quickly reaches the equilib-rium with the radionuclide in water. Such a rapid process corresponds to a very fastexponential component (effective decay– � �).

Like MARTE, the ‘box model’ ECOPRAQ for predicting the behaviour of 137Csin lakes is based on the assessment of radionuclide balance in the lacustrine system.

According to the ECOPRAQ modelling approach, the lake is divided in threecomponents:

� the water column;� the sediment A-area;� the sediment ET-Area.

The A-area and ET-Area are, respectively, the bottom sediment areas where theprocesses of sediment accumulation (A) and of erosion-transport (ET) prevail.Fig. 3 shows the structure of the model.

The fluxes are related, as usual, to the total amount of radionuclide in each com-partment by proportionality factors (the rates). These rates are calculated by sub-

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Fig. 3. Structure of model ECOPRAQ (abiotic components of the sediment-water system). The radio-nuclide fluxes are as follows: FWA=flux from water to A-area (bottom sediment area where sedimentaccumulation processes prevail). FAW=flux from A-area to water; FWET=flux from water to ET-Area(bottom sediment area where erosion-transport processes prevail); FETW=flux from ET-area to water;FETA= flux from ET to A-area; FAPS= flux from A-area to deeper, passive sediments.

models that account for the most important processes controlling the radionuclidemigration in different environmental situations. As the descriptions of such sub-models can be very complex the interested reader can find further information in thescientific literature (Hakanson, 2002; Hakanson et al., 1996). The ECOPRAQ modelis therefore based on process and parameter aggregation and on the attempt of relat-ing the values of the latter to the prevailing environmental characteristics of the site.

We deem it sufficiently demonstrated that, although AQUASCOPE models arebased, in principle, on a particular methodology (evaluation of the response function)all the assessed models show equivalent structures.

As previously stated, box models are based on the evaluation of the time dependentbalance of radionuclide in the various compartments of an environmental system byaccounting for the radionuclide fluxes among these compartments.

The complex processes of radionuclide migration through the water-sediment sys-tem are often schematised in terms of the following processes:

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� molecular diffusion of radionuclide through sediment porewater;� sedimentation (particle scavenging) of contaminated particles in water and conse-

quent removal of radionuclide from the water column and transport to sediment;� sediment mixing due to physical processes and bioturbation; and� burial mechanisms and other non reversible processes of radionuclide interaction

with bottom sediments.

The model LAKECO makes use of the following equations for predicting the rateconstants of the migration processes (Table 3 reports a list of symbols):

a) Migration from water to top sediment layer:

kws � �Dm

ds1h�eRwf1

h�

Rwr1Kd1(1�f1)h

�sKdw

h � 11 � KdwL

. (14)

The four terms on the right side of the previous equation are:

� the rate constant of diffusion from water to sediment porewater;� the rate constant for radionuclide transfer from surface water to pore water in

sediment due to physical mixing and bioturbation;� the rate constant for radionuclide transfer from the water column to top sediment

layer due to physical mixing and bioturbation; and� sedimentation.

b) Migration from top sediment to water column:

ksw � � Dm

d2s1f1

� eRw

ds1� f1

f1 � Kd1r1(1�f1)�

Rw

ds1

Kd1r1(1�f1)f1 � Kd1r1(1�f1)

. (15)

The terms on the right side are:

� The rate constant for the radionuclide diffusion from sediment to water;� The rate constant for radionuclide transfer from sediment porewater to water col-

umn due to physical mixing and bioturbation;

Table 3List of symbols in Eqs. (14)–(18) (Model LAKECO)

h is the average depth of the water column;L is the suspended sediment concentration;Kdw, Kd1, Kd2 are the values of the distribution coefficient in water, in the top sediment layer and inthe deep sediment layer, respectively;Dm is the diffusion coefficient in the pore water;ds1, ds2 are the thickness of the top sediment layer and of the deep sediment layer;f1, f2 are the values of the porosity of the top sediment layer and of the deep sediment layer;r1, r2 are the density of the top sediment layer and of the deep sediment layer;Rw is the sediment reworking rate;e is a proportionality constant;s is the sedimentation rate.

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� The rate constant for radionuclide transfer from top sediment layer to the watercolumn due to physical mixing and bioturbation.

c) Migration from the top sediment layer to the deep sediment layer:

ks1s2 �Dm

ds1ds2f1

f1

f1 � Kd1r1(1�f1)�

sr1(1�f1)ds1

Kd1r1(1�f1)f1 � Kd1r1(1�f1)

. (16)

The terms on the right side are:

� The rate constant for diffusion from the top to the deep sediment layer;� The rate constant for the migration from the top to the deep sediment layer due

to burial mechanisms.

d) Migration from the deep to the top sediment layer:

ks2s1 �Dm

d2s2f2

f2

f2 � Kd2r2(1�f2). (17)

e) Finally, radionuclide burial from the deep sediment layer:

ks2�� �s

r2(1�f2)ds2

Kd2r2(1�f2)f2 � Kd2r2(1�f2)

. (18)

The five radionuclide fluxes of LAKECO model are controlled by the five aggre-gated rate constants kws, ksw, ks1s2, ks2s1 and ks2– �. The model structure correspondsto a three components exponential function representing the radionuclide concen-tration in water following a pulse event of contamination. The model calculates thevalues of the rate constants by 14 primary parameters most of which are related tofundamental processes like the molecular diffusion of the radionuclide through waterand the interaction of the radionuclide in dissolved form with sediment particles. Inprinciple the reliability of the model is strictly dependent on the accuracy of thevalues of these primary parameters. LAKECO is “ fundamental process specific” asit relates the behaviour of radionuclides in the environment to specific physical andchemical fundamental processes. LAKECO is a so called “ reductionistic model” . Inother words, it includes, at least in principle, as many relevant details as reasonablypossible by modelling them according to primary laws from fundamental disciplinessuch as physics and chemistry.

On the contrary, MARTE, AQUASCOPE and ECOPRAQ models are based on aholistic approach. They are “environmental process specific” , that is, they relate thebehaviour of radionuclides in the environmental systems to relevant environmentalcharacteristics and processes. As such they aggregate a great deal of elementary,fundamental processes of physical, chemical, geochemical, biological etc. nature.

Holism and reductionisms are elements of an irresolvable controversy in eco-system theory (Muller, 1997).

We summarise one of the main criticisms to the reductionistic approach from theholistic point of view. As seen from the description of LAKECO, the reductionistic

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approach is based on the development of many sub-models that require additionalparameter values. Unfortunately, this means that knowledge of a great many environ-mental parameters is needed, and these are often difficult to measure and evaluate.As a consequence, these models, often, cannot be used in practical circumstances.On the other hand, model complexity does not guarantee, necessarily, the accuracyof results. Model uncertainty can increase if more and more parameters are accountedfor modelling the system (IAEA, 2000). Indeed, the overall model uncertaintyincreases as result of the contribution of non-negligible uncertainties from a largenumber of parameters as many environmental modellers have experienced(Kirchner, 1990).

To decide whether the effort for developing complex models is really justified inview of the uncertainty of the model results is a crucial point for structuring environ-mental models. Many modellers are convinced that simple, empirically based modelsare, usually, a much better guide to the behaviour of environmental systems(Smith, 2000).

Therefore, it is wiser to develop models that synthetise, at a macroscopic level,the behaviour of “aggregated” environmental components to search for quantitative,experimentally based relationship among their emergent properties. This can be achi-eved by searching for ecosystem structures based on “atomic” elements or “holons”that are the elementary “building blocks” of a “hierarchically organised” greaterwhole (the system) (Patten et al., 1976).

It holds a fundamental point of view of methodological and philosophical naturethat was clearly summarised by Jørgensen and Mejer (1983):

... The direction of approach is more pragmatic, and it is based on the experiencesof ecological modelling. Not only from a computer point of view is it impossibleto cope with the ecosystem complexity in a direct way but also from the biologicalpoint of view. To describe in detail all the individual subunits and their behaviourunder all possible circumstances and to know all the parameters involved in sucha detailed description exceeds man’s possibility. It implies that other methodswhich we could name holistic methods have to be found....

On the other hand, the main criticisms from the followers of the reductionisticapproach to holism in ecology are based on the considerations that holism detractsfrom a deep insight into the fundamental properties of natural systems, circumventsthe understanding of processes and phenomena and worsen the model quality(Muller, 1997).

Obviously, aggregation influences the uncertainty of the model output. An overag-gregated model may ignore some details of importance for a reliable prediction ofthe behaviour of a system. Nevertheless, it is easier to manage aggregated modelshaving simple structure especially for practical applications.

Although the conflict seems insoluble, it is worthwhile to notice that the assessedmodels are often hybrids showing characteristics that can be attributed to both philo-sophical approaches. The experience gained during the last decades suggests oftaking advantage from aggregation and from the application of empirically based

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sub-models for predicting some parameters that can be hardly evaluated by areductionistic methodology.

4. Predicting radionuclide transport and diffusion in large, deep lakes

The previous assessed models are aimed at predicting the average behaviour ofcontaminant in water over intervals of time that are, approximately, of the order ofthe Time Resolving Power (TRP) of the model on the hypothesis of the completemixing of radionuclide through the water body.

Three-dimensional models are used to simulate the diffusion and the transport ofradionuclides in lakes when more detailed time and spatial resolutions are required.These models are based on the well-known formulae:

� � �K∂C∂x

� � vC (19)

where � is the radionuclide flux (Bq m�2 s�1), C is the radionuclide concentration(Bq m�3) and K (m2 s�1) and v (m s�1) are the diffusion constant and the translationvelocity, respectively.

Diffusion and advection Eqs. (19) are used to predict the dynamics of suspendedmatter in water as well. The resulting diffusion-transport model is linked to theequation controlling the mechanisms of interaction of dissolved radionuclide withsuspended matter and the sedimentation/resuspension processes to simulate thebehaviour of the contaminant in the complex system ‘water, suspended matter, sedi-ment’ .

The THREETOX model (Margvelashvily et al., 1997), which includes the aboveprocesses to simulate radionuclide dispersion in large water bodies, is one of thecomputer codes of RODOS CDSS. The model is constructed from basic physicalconsiderations to predict the dispersion of radionuclides in water bodies with compli-cated geometry and time-dependent and spatially non-homogeneous water flows.THREETOX is aimed at assessing the water body contamination levels for generalapplications. It has been developed for predictions of the pollution dynamics duringboth the emergency and non-emergency (intermediate and long term effects) phasesof an accident. The model simulates the three-dimensional hydrodynamic field onthe basis of fundamental physical equations (Blumberg and Mellor, 1983) assumingthat the water body is incompressible and hydrostatic. The relevant equations arecomplex and require many data for the description of the boundary conditions. Themodel is an illustrative example of application of reductionistic methodologies.

Deep lakes and reservoirs may show stratified thermal structures in connectionwith specific seasonal conditions. The behaviour of dissolved substances in suchwater bodies is influenced by these stratification phenomena related to the verticalprofile of water temperature and to the relevant differences in the water density. Thediffusion of dissolved substances through the water column shows marked seasonalvariation as a function of the presence or absence of a vertical gradient in tempera-ture.

194 L. Monte et al. / J. Environ. Radioactivity 69 (2003) 177–205

Such a process, generally, is simulated by subdividing the water column into spe-cific layers, namely the epilimnion (the upper layer), the thermocline (intermediatelayer) and the hypolimnion. The seasonal variation of pollutant diffusion throughthe water column is modelled by assuming that the radionuclide transfer parameterfrom contiguous layers is a function of time (Monte, 1991).

Like the holism-reductionism controversy, the question about the necessity ofdeveloping models for predicting, in sufficient detail, the spatial distribution of acontaminant within a water body has given rise to a heated debate involving twomain points of view:

a) Models predicting spatial distribution—A polluted water body can show variablespatial and time dependent concentrations of contaminant. During the early phaseof an accident, in large and deep lakes contamination may be non-homogeneouslydistributed. Therefore, for the proper management of the aftermath of an accidentit is necessary to predict the spatial distribution of the pollutant concentrations.

b) Models predicting lumped averages—It is quite obvious that concentration levelscan show, in the short term, a significant non-homogeneous spatial distributionin large water bodies. Unfortunately, in water bodies such a distribution is con-trolled by a variety of processes that are difficult to predict. For instance, themovement of surface water is strongly influenced by the wind whose intensityand direction can never be reliably predicted with sufficient accuracy. Conse-quently, the deterministic prediction of contaminant distribution can be veryuncertain. The choices of small values of the spatial (and time) resolution of amodel can be illusory for the accuracy of the model results, as the lack of knowl-edge of the dynamics and spatial dependence of many processes at such resolutionlevels reaches critical levels of model uncertainty. The impossibility of modellingin sufficient detail (both in time and space) the natural processes is the main factorcontrolling Time Resolving Power (TRP) and the Spatial Resolving Power (SRP)of a model. The predictions of a model are meant to be values averaged over theTRP and SRP intervals. To ask the question “what is the predicted value of aquantity averaged over a certain region of space and over a certain interval oftime?” seems more prudent and realistic than to ask “what is the value of a quan-tity at a certain instant at a specific point of the space?” .

It is obvious that both kinds of models can properly support the decision-makingprocess if they are wisely and carefully applied by considering their features.

From the practical point of view, models b) can be profitably used for predictions,on the medium and long term, of quantities averaged over space and time. On theother hand, models a) can make model users aware of the time and space heterogen-eity of contamination in the short, medium and long-term period.

More generally, reductionistic models include, in an organised whole, the state-of-the-art, available knowledge relevant to the behaviour of radionuclides in the aquaticenvironment. They are the only possible tools for guessing predictions of environ-mental radioactive contamination when exhaustive experimental experiences, at asystemic level, of the behaviour of a contaminant substance are not available. Such a

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Table 4Main characteristics of lakes Constance and Lugano

Lake Average depth (m) Mean water retention time(years)

Constance 85 4.1Lugano 55 2.5

circumstance, indeed, forces the modeller to make use of knowledge that is obtained,generally, in controlled or laboratory conditions. Nevertheless, for practicalapplications, their results must be carefully assessed mainly in relation to the dif-ficulty of evaluating their uncertainty.

5. Quantitative assessment of the time behaviour of radionuclides in lakewater

Section 3 clearly shows that, following a pulse deposition accident, the time behav-iour of radionuclide concentration in lacustrine water can be successfully analysedin terms of few exponential components. These kinds of analyses have been carriedout by many authors. For instance Zibold et al. (2001) calculated the constant ratesof the exponential components of radiocaesium concentration in water of lakes Con-stance, Vorsee and Lugano. As Constance and Lugano are deep lakes with longmean water retention times, it is possible to hypothesise that the contributions fromthe lake catchments do not affect significantly the balance of pollutant in the lakes.

Formula (6), after a slight modification to account for the mean water retentiontime, allows one to calculate the above rates. Table 4 shows the values of the para-meters necessary to evaluate l1 and l2.

The values of l2 and l1 were obtained from the experimental half-lives (T1/2)

measured by Zibold et al. (2001) (l =0.693T1/2

).

The calculated values are reported in Table 5 In the same table the corresponding

Table 5Values of the effective decay rates of 137Cs in water of lakes Constance and Lugano

Lake Short component l2 (s�1) Long component l1 (s�1)Experimental Model MARTE Experimental Model MARTE(Zibold et al., (Zibold et al.,2001) 2001)

Constance 5.6 × 10�8 4.3 × 10�8 7.8 × 10�9 7.4 × 10�9

Lugano – 4.9 × 10�8 9.1 × 10�9 1.1 × 10�8

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values calculated by using the parameter values of model MARTE (Table 1) arereported.

6. Comparison and assessment of sub-models for predicting the behaviour orradionuclide in the biotic components of lake systems

The behaviour of radionuclides in lacustrine biota is determined by a variety ofprocesses and factors of biological, ecological and environmental nature. Manyexperimental studies have demonstrated that the bioaccumulation of radionuclidesin biota depends on trophic level, water chemical characteristics, water temperatureand fish weight.

All the assessed models are based on the fundamental assumption that the timebehaviour of a radionuclide in a biota species (CB) can be modelled accounting forthe radionuclide excretion from the biota and the radionuclide uptake via ingestionor direct transfer from water. Moreover it is assumed that excretion is a first orderprocess and the uptake is proportional to the radionuclide concentration in the precur-sor compartment (CP) of the food chain or in water:

dCB

dt� �(lr � lB)CB � KCP (20)

where lB is the excretion rate and K is the uptake coefficient. The main differencesamong the models are essentially the methodological approach (reductionistic orholistic) for determining the values of the parameters in Eq. (20) and the detail ofanalysis of the food chain.

Some models (MOIRA-ECOPRAQ for 137Cs and AQUASCOPE) use the abovestructure for predicting the behaviour of radionuclides in fish. In contrast LAKECOconsiders several components of a complex food web: phytoplankton, zooplankton,filter feeders, deposit feeders, and different levels of prey and predatory fishes. Theuptake processes within this complex food web are modelled, at least in principle,by quantitative assessments of the radionuclide fluxes from every precursor “node”to the successor on the basis of theoretical considerations. For instance the uptakeby a predator is calculated as the product of radionuclide concentration in food, thefood consumption rate and the food extraction efficiency. The direct uptake fromwater is calculated as the product of the radionuclide concentration in water, thewater ‘extractability’ and the water uptake. This is a typical reductionistic approach.Nevertheless, some of the above listed parameters are estimated by sub-models usingmeasurable characteristics of the water body, such as the potassium content in water,due to the difficulty of a complete application of the reductionistic methodology.

Generally, the biological half lives of phytoplankton and zooplankton are shortcompared with the corresponding values for prey and predatory fish species. Thisimplies that the radionuclide concentrations in phytoplankton and zooplankton reachsteady state conditions in intervals of time that are short compared with the biologicalturn-over time of radionuclides in fish. Therefore, phytoplankton and zooplankton

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components scarcely influence the time behaviour of radionuclides in biota occupy-ing higher levels of the food chain.

In other words, if the rate lB of the radionuclide excretion process in a species(S1) is significantly larger than the similar parameters for other species in the food-web, the concentration of radionuclide in that species quickly reaches the steadystate equilibrium:

CB �K

(lr � lB)CP. (21)

It is possible to demonstrate, by simple mathematical considerations, that the timebehaviour of radionuclide concentration in the food-chain successor (S2) of suchbiota species can be related by a first-order Eq. (20) to the precursor (S0) of S1.This is a kind of ‘cancellation’ law that allows one to simplify the structure of food-chain models. This principle is applied by models such as AQUASCOPE and ECOP-RAQ.

AQUASCOPE and MOIRA-ECOPRAQ models predict the uptake of 137Cs byfish by a simple one-compartment structure:

dCF

dt� �(lr � lB)CF � KCw (22)

where CF is the concentration in fish and Cw is the concentration in water. Such astructure was, essentially, the same as used by models assessed in the VAMP (IAEA,2000) and BIOMOVS projects. It is important to notice that MOIRA-ECOPRAQconsiders also the uptake of radionuclide from sediment layers. The models that donot include such a pathway are based on the implicit assumption that, due to theslow dynamics of pollutant content in lake water, the overall uptake of radionuclideby fish is approximately controlled, in the short and medium term, by the contami-nation levels of water. Such an assumption is not generally valid in the case of fastdynamic behaviour of pollutants in water bodies. For instance, temporary dischargesof radionuclide in lakes with a small water retention time may result in levels ofsediment contamination that persist even when the pollutant concentration in waterbecomes negligible. In such circumstances, the migration pathway from sediment tofish (for instance through the benthic compartment) may significantly contribute tothe fish contamination.

AQUASCOPE and some of the VAMP project models relate the parameters inEq. (22) to certain properties of the water and to the trophic level of the biota. For137Cs biouptake K is inversely related to the concentration of potassium in water (Ck)

K �ACk

. (23)

For 90Sr, K is related to the concentration of Ca in water:

K �A

CnCa

(24)

where CCa is the calcium concentration and n is an exponent. Other similar equations

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have been suggested in the literature (IAEA, 1994). The values of the parametersin Eqs. (23) and (24) are also related to the trophic level of the biota (predatory andnon-predatory fish).

The MOIRA-ECOPRAQ models assess the 137Cs concentration in fish by relatingthe biouptake and excretion fluxes to several relevant environmental characteristicsof the ecosystem.

The fluxes of radionuclide through the food chain are indeed calculated byaccounting for many processes occurring at an ecological level. Biouptake is relatedto the allochthonous and autocthonous production, to the concentration of potassiumin water, to the level occupied by the biota in the food web, to the size of the outflowarea, to the total phosphorous, to the fish weight and, obviously, to the concentrationof radionuclide in water. Excretion is calculated by accounting for the water tempera-ture and the fish weight.

As in the case of sub-model for predicting the radionuclide behaviour in abioticcomponents of the lacustrine environment, MOIRA-ECOPRAQ aims at assessingthe migration process in an ecological perspective. MOIRA-ECOPRAQ is mainlybased on the so called ecometric sub-models (Hakanson and Peters, 1995) for pre-dicting the radionuclide fluxes within the mass-balance model. Ecometric modelsdescribe the empirical relations among ecological effects, contaminant loads andsystem sensitivity.

Some models for predicting the behaviour of toxic substances in the environmentare based on the assumption that radionuclides such as 137Cs and 90Sr show chemical(and bio-chemical) behaviours similar, respectively, to potassium and calcium. Themodel ECOMOD (Sazykina, 1994) belongs to this category. Therefore, as the radio-active nuclides and the corresponding natural stable homologues are indistinguishablefrom living organisms, the share of radionuclide in the transfer processes is equalto the relative share of radionuclide in the common pool of this element(radionuclide+stable analogues). ECOMOD can be classified within the category ofreductionistic models.

7. Discussion

7.1. Modelling radionuclide migration through lacustrine abiotic and bioticcomponents

AQUASCOPE, MARTE, ECOPRAQ, LAKECO and THREETOX are well-known examples of models for predicting the behaviour of radionuclides in lacustrineecosystems. Most models focus mainly on radiocaesium and radiostrontium as theseradionuclides are of particular importance for their long radioactive decay times andthe consequent persistence in the environment. Despite their seeming differences theassessed models show, at least in principle, many similarities.

MARTE, ECOPRAQ and LAKECO are compartment models (first order) basedon the assessment of radionuclide balance within the components of the lacustrineenvironment. On the contrary, AQUASCOPE is based on the “ response function”

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of the water-sediment sub-system to a pulse deposition event. It was demonstratedthat, from the mathematical point of view, the approaches are equivalent.

The main difference among the models is relevant to the approach for assessingthe fluxes from the compartments. In LAKECO the values of the transfer parameters(rates) are predicted from basic processes, such as the Fick’s law, that are assumedto control the migration of radionuclide through the lacustrine environment.

The models MARTE and AQUASCOPE are based on a more pragmatic approach.Indeed, these models use generic values for the transfer parameters. The applicationto many different lacustrine systems suggested that the time behaviour of radio-nuclides in the water column can be predicted with reasonable accuracy by thesegeneric models. In ECOPRAQ the rates, rather than to the fundamental processes andthe relevant laws like in LAKECO, are related to the environmental characteristics ofthe lake. The model is characterised by a deeper insight into the most importantemerging behaviours controlling the radionuclide migration through the complexaquatic ecosystem.

Models like THREETOX are based on fundamental equations and are the mostrepresentative example of reductionistic models.

As MARTE, ECOPRAQ, LAKECO and AQUASCOPE show some similarity itis reasonable to encourage an effort for harmonising the methodologies, theapproaches and, possibly, the models themselves.

The bioaccumulation of radionuclides in fish is controlled by many physical,chemical, biological and ecological processes. Therefore, the development of modelsfor predicting the migration of radioactive substances through the biotic componentsof the lacustrine system is a real challenge for modellers.

To have an idea of how variable the bioaccumulation is in relation to differentkind of radionuclides, it is sufficient to look at the range of concentration factorsmeasured in different environmental conditions (IAEA, 1994).

Recently, researchers have profited from many experimental results relevant to themigration of 137Cs and 90Sr in complex lacustrine systems. Several EC projects aswell VAMP and BIOMOVS gave the opportunity to many scientists of extendingknowledge and experience to develop more reliable models for predicting the behav-iour of these radionuclides in the components of lake biota.

Some of the models examined here are aimed at predicting the behaviour of 137Csand 90Sr for general environmental conditions and circumstances. These models,being of general application, can be very helpful tools for the management of anycontaminated lacustrine systems. Nevertheless, it is quite obvious that site-specificcalibrated models can show significantly higher accuracy. Therefore, it seems wiseto encourage studies and research aimed at customising the models to site-specificconditions of European lakes by profiting from newly acquired data and informationand from recently gained experience.

In spite of the great deal of studies for developing 137Cs and 90Sr models, compara-tively limited deployment of models for assessing the migration of other radio-nuclides (Joshi, 1991; Shukla, 1993) in the lacustrine environment has been under-taken by modellers at an international level of co-operation.

The occurrence that different models show similar features is not surprising.

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Indeed, most parts of the assessed models were developed according to traditionalapproaches (compartment models) and taking advantage of the great deal of experi-ence and knowledge gained during past decades at an international level.

Moreover, international projects such as VAMP and BIOMOVS, gave the opport-unity for significant exchange of this knowledge and experience among modellersof many countries. It was possible to analyse and assess the performances of manymodels by comparison with experimental information from the environmental con-tamination following the Chernobyl accident. These were the grounds for the devel-opment of common and empirically substantiated approaches.

7.2. What is really old, what is really new and what is there to do?

As previously stated most of the assessed models for predicting the behaviour ofradionuclides in the abiotic components of a lake are basically comprised of 2 or 3active compartments and a passive compartment that simulate the water column, thebottom sediment layers and the deep sediment. They belong to the category of theso called “ fully mixed” hydrological dispersion models that have been well describedin the scientific literature (e.g. IAEA, 1985).

Indeed, before the Chernobyl accident, much research was focused to the develop-ment of models for assessing the behaviour of radionuclides in surface waters. Theresults were summarised in many reports (NCRP, 1984). Therefore, it seems quiteobvious that the scientific community has reached a general agreement on the struc-ture of the models for predicting the radionuclide migration through the system“water column–bottom sediment” . Validation studies carried out in the frame ofproject BIOMOVS II (Davis et al., 1999) also reached similar conclusions (Kryshevet al., 1999).

Unfortunately, there was not a similar agreement concerning the values of theparameters controlling the processes of migration. Whereas the dispersion fluxes ofradionuclides through the water compartment are described at a satisfactory level inmany important international publications (IAEA, 2001; IAEA, 1985), the analysisof available literature (IAEA, 1982; IAEA, 1994) suggests that little information wasavailable about the values of the migration parameters controlling such fluxes. Sucha gap has been partially abridged for radiocaesium and radiostrontium following theresearch carried out during this last decade.

The validation exercise carried out in the frame of project BIOMOVS clearlyenlightened the difficulties that modellers came across in choosing appropriate valuesof the transfer parameters. The exercise was aimed at assessing model predictionsutilising experimental data of 137Cs and stable caesium concentration in three lakesystems (BIOMOVS, 1991): a) East Twin Lake (USA) contaminated by stable caes-ium for research purposes; b) Lake Hojsjoen (Norway) and c) Lake Hillesjon(Sweden) contaminated by 137Cs introduced in the environment following the Cher-nobyl accident.

The following models were used:

1. BILTH (Laboratory of Radiation Research at the National Institute for PublicHealth and Environmental Protection, the Netherlands)

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2. BIOLAKE (Chalk River Nuclear Laboratory, Canada)3. BIOPATH (Studsvik Eco&Safety AB, Sweden)4. DETRA (Technical Research Centre of Finland)5. JAERI (Japan Atomic Energy Research Institute)6. RISO (Riso National Laboratory, Denmark)7. NRIRR (National Research Institute for Radiology and Radiohygiene, Hungary).

Table 6 shows the values of the parameters used by each model. The values ofthe migration velocity to sediments vws ranged from 5.50 × 10�10 to 7.13 × 10�7

m s�1. The migration rate from sediment to water Ksw ranged from 3.17 × 10�11 to1.93 × 10�7 s�1. The migration rate from bottom sediment to deep sediment Kds

ranged from 2.85 × 10�10 to 1.17 × 10�8 s�1.The ranges of variation of the parameters are therefore of the order of one thousand

and more. It is quite obvious that such large ranges significantly influence the uncer-tainty of the model output. It is worthwhile to notice that modellers estimated theuncertainty ranges of these parameters were one order of magnitude and more

Table 6Values of migration parameters for 137Cs used by models included in a BIOMOVS test exercise(BIOMOVS, 1991)

Lake East Twinvws (m s�1) Ksw (s�1) Kds (s�1)

8.77 × 10�9 1.05 × 10�8

3.91 × 10�8 3.49 × 10�8 2.31 × 10�9

3.49 × 10�9 3.17 × 10�11 2.85 × 10�10

3.70 × 10�8 9.51 × 10�10 3.17 × 10�9

1.06 × 10�7 6.34 × 10�9 1.17 × 10�8

Lake Hillesjonvws (m s�1) Ksw (s�1) Kds (s�1)

5.35 × 10�8 8.24 × 10�9

1.64 × 10�8 1.05 × 10�8

2.40 × 10�7 1.52 × 10�8 1.14 × 10�9

1.98 × 10�7 2.41 × 10�9 1.14 × 10�9

1.23 × 10�8 2.22 × 10�10 1.59 × 10�9

7.13 × 10�7 1.93 × 10�7

Lake Hojsjoenvws (m s�1) Ksw (s�1) Kds (s�1)

3.51 × 10�9 1.05 × 10�8

5.07 × 10�9 1.90 × 10�8 7.61 × 10�10

5.50 × 10�10 3.17 × 10�11 3.01 × 10�10

3.68 × 10�9 9.51 × 10�10 1.17 × 10�8

202 L. Monte et al. / J. Environ. Radioactivity 69 (2003) 177–205

(Togawa and Homma, 1990). The research carried out following the Chernobyl acci-dent and in the frame of the EC projects considered in the present assessment allowedthe improvement of model performances by more accurate assessment of the transferparameters on the basis of many different experimental evaluations at a systemiclevel. Unfortunately, at present such studies have only been done for 137Cs and 90Sr.There are no similar extensive and reliable data for other radionuclides. The improve-ment of the quality of the results of models for predicting the migration of radio-nuclides other than 137Cs and 90Sr can be achieved by a better knowledge of therelevant transfer parameters. This can be a wise objective for future research activi-ties. It is indeed reasonable to assume that the model parameter uncertainty for theseradionuclides is similar to the large uncertainty of the parameters for radiocaesiumand radiostrontium estimated before the better assessments of these last years.

For instance, an exercise of intercomparison of model for predicting the behaviourof 226Ra and 230Th in lakes (BIOMOVS, 1988; Sundblad, 1991) demonstrated that theranges of some transfer rate parameters of these radionuclides cover several orders ofmagnitude. Such variability is reflected in the estimated uncertainty of the modelresults over long term periods.

The simple structures of the assessed models suggest that the “data assimilation”procedures can be readily applied to obtain more reliable predictions in the mediumand long term. Data assimilation procedure is a technique that enables one to improvethe accuracy of predictions taking advantage from the monitoring data acquired. Forthe assessed models it seems very easy and practical to implement computer sub-programmes for the “ real time” calibration of the models in CDSSs (Rojas Palma,2002).

A real step forward could be represented by the development of suitable sub-models that allow one to assess the values of the transfer parameter for differentenvironmental circumstances. For assuring the reliability of models for practicalapplications, it is important to relate these values to environmental and geographicalinformation that can be easily obtained. This means that, instead of developing sub-models based on fundamental laws and quantities, it is wiser to study the relationshipexisting among the aggregated transfer rates, such as vws, ksw and kds, and environ-mental conditions. These can be important topics for further studies relevant to thebehaviour of radionuclides and, more generally, of toxic substances through the freshwater environment.

8. Conclusions

The work done during the past decades by many modellers at an internationallevel has produced some consolidated results that are, generally, widely accepted bymost experts. Nevertheless, some new results have been obtained by recent studiesand some model improvements are still necessary.

� The structures of models for predicting the migration of radionuclides through

203L. Monte et al. / J. Environ. Radioactivity 69 (2003) 177–205

the biotic and the abiotic components of the lacustrine environment have beenclearly identified and are widely accepted by the scientific community;

� Recently, many experimental studies following the most significant nuclear acci-dents (Chernobyl, Kyshtym) have provided the opportunity for a quantitativeevaluation of the most important transfer parameters for radiocaesium and radios-trontium through lacustrine ecosystems. Consequently the uncertainty of theseparameters and, thus of the models, has become considerably lower than the adecade ago;

� 137Cs and 90Sr models based on the previous structures and parameters show levelsof uncertainty of a factor of 2 or 3 when applied as generic tools for predictingthe behaviour of radionuclides in the abiotic components of the lacustrine environ-ment. Nevertheless, it is possible that lacustrine systems in extreme environmentalconditions cannot be modelled within similar narrow uncertainty ranges. More-over, a larger uncertainty is expected for predictions relevant to the biotic compo-nents of the lacustrine environment;

� As the structures of the models include a few exponential components, dataassimilation procedures can be easily applied and can be helpful for improvingprediction relevant to the contamination behaviour in the medium and long termfollowing a nuclear accident;

� For the same reason, the widespread assessment of site-specific values of themodel parameters may be of importance for improving the model performancesfor many practical applications;

� For several important radionuclides similar information is not yet available andfurther assessment is necessary mainly in relation to the evaluation of modeluncertainties;

� It is wise to perform further efforts to harmonise the results of recent projects inorder to develop a reference lake model that can be widely applied throughoutEurope and that can be implemented in Computerised Decision Support Systemsfor the management of post-accident consequences.

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