Reliability of Radioactive Transfer Models

The International Atomic Energy Agency (IAEA) is preparing a Safety Series publication on practical approaches for evaluating the reliability of predictions made by environmental radiological assessment models. This IAEA document discusses factors that affect the reliability of model predictions and describes methods for quantifying uncertainty. Emphasis is placed on distinguishing between: (1) uncertainty due to stochastic variability and (2) uncertainty due to lack of knowledge. The document states that the best method for evaluating the accuracy in model predictions is the process of testing against data sets that are independent from those used to develop the model (model validation). For situations in which validation results are not available, analytical and numerical methods are presented for propagating the uncertainty in model parameters into a quantitative statement of uncertainty about the model prediction (parameter uncertainty analysis). The strengths and weaknesses of model intercomparison exercises are also discussed. It is recognized that quantitative statements about the reliability of model predictions must rely upon the use of expert judgment when models are applied to situations that are different from those under which they have been tested.

Some of the models available at NRPB for predicting radionuclide transfer through the environment are briefly described and the problems encountered in verifying and validating them are identified. It is suggested that models for transfer through the various parts of the environment can be ranked in terms of whether they can be validated quantitatively, or whether all that can be achieved is quantitative validation of their conceptual basis. Priorities for further NRPB work on model verification and validation are given.

BIOMOVS (BIOspheric MOdel Validation Study) is an international study where models used for describing the distribution of radioactive and nonradioactive trace substances in terrestrial and aquatic environments are compared and tested. The main objectives of the study are to compare and test the accuracy of predictions between such models, explain differences in these predictions, recommend priorities for future research concerning the improvement of the accuracy of model predictions and act as a forum for the exchange of ideas, experience and information.

The Sellafield nuclear fuel reprocessing plant, sited 0.5 km from the coast, emits 14C to atmosphere primarily from two 120m high stacks. Measurements of 14C in hawthorn berries (Crataegus) at a distance of 4 km over six years shows significant variations in the net 14C per kg carbon with direction from the site. The predicted variation with direction, taking into account carbon uptake rate as well as the pattern of wind bearing and dispersion conditions through the growing season, shows reasonable agreement in most cases. The 14C distributions are largely accounted for by angular wind frequency during the daylight hours growing season, which for this site is markedly affected by sea breezes. For the years when there is a marked disagreement between the measured and predicted profiles the most likely explanation is considered to be curvature of the plume due to the influence of the hilly terrain.

In January 1985, after each of three periods of snowfall, snow samples were collected repeatedly at 33 sampling locations in the vicinity of the Karlsruhe Nuclear Research Center and the concentration of tritium in the snow-water was measured. The results of measurement have been published (Radiation Protection Dosimetry, Vol. 16, Nos. 1–2, pp. 95-100 (1986), Nuclear Technology Publishing). By parallel measurements of the intensity of snowfall it was possible to determine the tritium impact on the soil due to snowfall, expressed in Bq/m2. The values obtained are considered here as the results of measurement of the tritium impact on the soil due to snowfall.A calculation model which takes account of the intensity of emissions of tritium into the atmosphere as well as of the meteorological situation was used to determine the tritium impacts on the soil at each of the 33 sampling locations and for each of the three periods of snowfall. the measured and calculated results are in good agreement.

The two main forms of tritium, elementary gas HT and tritiated water HTO do not only differ in their radiotoxicity but also in their radioecological behaviour. To predict the radioecological pathway of tritium in a specific local situation a technique easy to apply was tested. Mechanically undisturbed soil cores were collected in the field and exposed to HT in the laboratory. The deposition velocity sufficiently describes the first step of the radioecological pathway of HT after its distribution in the air. Numerous results of deposition velocities in field, pasture and forest soil have been obtained in Jülich, but a tritium release experiment only enabled us to confirm the technique proposed. Soil cores have been exposed to the HT plume in the field and the HT deposition velocity of soil samples from the exposure site has been determined in the laboratory. The field data confirm the applicability of our method and one may be able to propose a way of collecting representative data under accidental and under chronic conditions.Another important aspect of radioprotection is the reemission of the reaction product HTO from the soil. Laboratory measurements demonstrate a very rapid HTO reemission during the first hour directly after the HT/HTO turnover in the soil. Thereafter the HTO reemission decreases distinctly.

Modeling internal dose resulting from environmental transport of atomic weapons’ test fallout from the Nevada Test Site (NTS) USA, during the period 1951–1962, requires estimates of many important parameters for which little data exists. A retrospective dose assessment study for which model reliability is of great importance is now nearing completion. The study’s objectives are to estimate thyroid dose from ingestion of radioiodine in milk and vegetables to a cohort of over 3000 persons. The cohort that had potentially been exposed to NTS fallout were examined for thyroid abnormalities during 1965 and 1985. Model sensitivity analysis and parameter uncertainties were used to help establish priorities for research and uncertainty analysis. Numerous parameters were shown to substantially affect radioiodine concentrations in milk and uncertainty estimates, the most significant being the fraction of fallout intercepted by vegetation and the relative timing of dairy management practices and deposition events. Both parameters were subsequently researched and the results are discussed. Verification of model reliability was attempted by comparing predictions with limited literature data.

In this paper a diagnostic model is used to reconstruct the wind field on the basis of measurements: An initial wind field generated from available sparse measured data is corrected to satisfy mass conservation by solving a three-dimensional elliptic differential equation. The actual orography is taken into account by transforming this equation to a terrain-following coordinate system. For the solution of the transformed equation a fully vectorized fast elliptic solver is applied. By the aid of the obtained wind fields air parcel trajectories may be calculated to elucidate the prevailing atmospheric transport mechanisms. As an example, wind fields and air parcel trajectories are presented for the Athens basin. The results confirm the features of the sea breeze circulation hinted at by observations and by previous calculations. The identified air movements are discussed in view of the elevated pollution levels in Athens.

The estimation of the dispersion of an airborne radioactive release presupposes the knowledge of the windfield and the level of diffusion in the region under consideration.The presence of the sea breeze requires particular attention due to the development of circulation patterns and reduced mixing depths within the boundary layer.The present work constitutes a part of the effort to include the sea breeze capability in the ADREA-I code, a transient three dimensional transport code, under development in NRCPS “Demokritos”, and refers specifically to the sea breeze analysis along the Alaskan sea coast [1]. This case has been selected on the way of looking for a well documented sea breeze analytical study in the open literature suitable for comparisons with the model adopted in the present analysis.It is shown that the generalized three dimensional k-1 model introduced in ADREA-I, canbe also faithfully applied to sea breeze calculations.

Environmental measurements following the Chernobyl accident for selected locations in the United States and Europe were compared with model predictions of the transfer of 137Cs through the air-pasture-cow-milk pathway. The models include IAEA Safety Series No. 57, AIRDOS/EPA, NRC Regulatory Guides 1.109 and 1.111, the National Council on Radiation Protection and Measurements (NCRP) screening model, and the PATHWAY dynamic food-chain model. Time integrals of the 137Cs concentrations in air, pasture, and milk were estimated, and the predicted and observed grass/air, milk/air, and milk/grass concentration ratios were compared. Predictions of the transfer of 137Cs from air to pasture and from pasture to milk tended to exceed observations. Those of PATHWAY, however, consistently underpredicted the grass/air and milk/air concentration ratios due to the use of parameter values specific for the deposition of large particles and their interception and retention by vegetation. Where possible, parameter values were adjusted to the specific conditions determined for a location, which substantially reduced the discrepancy between predictions and observations.

When the BIOMOVS study started in 1985 a scenario (B1) for the transfer of I 131 via the air-pasture-cow-milk pathway was defined for model inter-comparison, as this is one of the most important pathways for radionuclide releases from nuclear power plants and probably the best investigated radioecological problem. The predictions for milk (except from the model PATHWAY) were all within a factor of 20 and generally the modelers were satisfied with their results, as all differences in the predictions could be explained by the individual assumptions or the model intentions, i.e. conservative results or best estimates.The comprehensive measurements of I 131 in the environment after the Chernobyl accident gave a unique opportunity to receive new and independent datasets for model validation. Since then the necessary site specific data have been assembled for 13 different locations that cover a large range of I 131 air contaminations, and have been offered to participants for calculation (scenario A4). The results will be discussed at the next BIOMOVS workshop in December 1987 in the USA, but the outlines of the study are presented.

Measurements of cesium from the Chernobyl accident in different environmental media are compared with respective model predictions. Especially the sub-models for the interception of washout by plantstime-dependence of the contamination of grasstransfer fodder — milktransfer fodder — meat are considered. Mean values and ranges of several model parameters are derived from our measurements for the post-Chernobyl situation.These parameter ranges are used as input data for a stochastic version of the radioecological model ECOSYS and a probability function of the activity intake by man is generated. The results are compared with the distribution functions of cesium content in persons actually measured with whole body counters.

The models most widely used in France for impact studies related to nuclear facilities have been consolidated into computerized reference under the code name “DUNE”.The environmental effects of radionuclides released during the Chernobyl accident allowed observations to be made with applications not only to accidental fallout but also to routine waste discharge.Two examples are considered which reveal the difficulties encountered in completely verifying a model: one involves the contamination of mutton, and the other concerns radionuclide migration in soils.Two questions are then raised: “How can a model which produces uncertain results be confronted with field measurements which are variable by nature?” and “Should existing models be modified in the light of the latest observations?”

The NRPB dynamic foodchain models, FARMLAND, are general models to simulate the transfer of radionuclides through terrestrial foodchains.In order to assess the ability of the models to represent general conditions, predictions have been compared with two sets of data. The first set are measurements made after the Chernobyl reactor accident of activity concentrations in milk, lamb and green vegetables. The suitability of the data for model validation, the problems encountered and any significant differences between predictions and measurements are identified and discussed. The second set is of UK average activity concentrations in milk from fallout due to weapons testing over the last thirty years.Model predictions have also been compared with site-specific data of levels in milk resulting from the Chernobyl accident, for two different cattle management regimes.

After the first peak of the radioactive cesium in the milk at the middle of May 1986 there has been occurred à second one during the winterseason. To describe these two peaks in the milk we have taken into consideration that the radioactivity of the fresh animal feed decreases exponentially and of the dry one is constant, exept the first year when it increases due to the storage of the most contaminated dry feed, The consumption rate of the freshes is derived as a proportional amount of the agricultural productivity that has been given by a Fourier series. The total consumption rate has been kept constant during the whole year. By use of the model it can be calculated the concentrations in milk for several years even by taking into consideration the root uptake of the pasture forage. The uncertatinty analysis has given confidence ranges of about one magnitude of the cesium content in the milk.

The accuracy of three radionuclide transfer models for predicting surficial radionuclide contamination levels in agricultural crops was investigated using Pu-labelled aerosols and soil particles. Transport processes included the interception and retention of atmospheric deposition and the resuspension of soil particles to plant surfaces. Crops included wheat, soybeans and corn. The models evaluated were: 1) FOOD, a relatively general model; 2) AGNS, a model developed for the southeastern United States; and 3) SRP, an empirical model derived from studies on the U. S. Department of Energy’s Savannah River Plant in South Carolina. Predicted concentrations were compared to independent field data. The three models generally predicted the surficial Pu concentrations due to the interception of deposition to within a factor of 3, but showed differential abilities to predict concentrations due to the resuspension of Pu-bearing soil particles to plant surfaces.

The large uncertainties which are associated with the values of the soil-to-plant transfer factors prompted the IUR (International Union of Radioecologists) some years ago to initiate a soil-to-plant transfer factor working group. This group is carrying out a joint project in which participate 20 research institutions. The aim of the project is to provide reliable estimates of the soil-to-plant transfer factors of different crops for different soils, environmental conditions, etc. Only data of experiments which met predefined criteria are included. Data of five years of experiments are now available.Expected values for transfer values have been derived statistically for a large number of combinations of different factors as radionuclides, crops and soils. The 95 percent confidence interval was derived for averaged estimates based on the observations present in the data set as well as the 95 percent confidence interval of single predicted values for specific combinations of factors. The latter confidence interval is much larger, due to the relatively limited number of data for many of the possible combinations of factors.

This paper summarises the current status of a programme of work involving the production of appropriate dynamic foodchain models and the acquisition of time-dependent data to validate and improve these. The models are used to derive equilibrium transfer factors for the assessment of ingestion doses from routine atmospheric releases and to derive time-dependent transfer factors for use in similar assessments for discrete releases arising both from normal operation and from hypothetical accidental atmospheric releases.The structure of two new dynamic foodchain models recently developed by CEGB to study the uptake of S-35 and C-14 by crops is described. These models are additional to the generic model for studying actinide and fission product transport in foodchains that has been published elsewhereThe use of dynamic models to derive equilibrium transfer factors requires validation against experiment of the time-dependent model predictions. This is also needed before the models can be used for discrete release studies. Thus details are provided of two further experiments, as follows: (i)a study aimed at measuring crop interception factors, and(ii)a study of the dynamics of radionuclide transport in soils and in plants using a system of lysimeters.Both the above studies utilise contracted experimental facilities and expertise in the Department of Pure and Applied Biology and the Reactor Centre at Imperial College. CEGB input has been in defining the objectives, in participating in the planning of the experiments and in the subsequent data analysis, particularly with regard to the implications for foodchain models.Finally, details will be provided of the objectives of a project, jointly funded by CEGB and the UK Ministry of Agriculture, Fisheries and Food (MAFF), which will study the uptake by lamb of a selection of radionuclides relevant to both routine and accidental releases. Details will also be provided of the objectives of a joint project with Studsvik aimed at studying the behaviour of Chernobyl deposition in soils.

The amounts of cesium-134 and -137 were measured in vegetables which were contaminated by the fall-out due to the Chernobyl reactor accident. In the case where the plants were sown or planted before this incident occurred they were contaminated almost entirely by deposition of the radionuclides on their exposed parts (stalks and foliage), plants which were sown or planted after 1st May, contamination occurred mainly by transfer from soil to plant via the roots.The activities found were in most cases too small to be either measured accurately or for real differences to be found in various parts of the plants. Some of the values were within the fluctuations of the background. A normal consumption of vegetables grown in Northern Switzerland could therefore not lead to a significant increase of ingested radioactivity. Some nuts, cereals and berries on the other hand contained considerably higher activities. This was surprising since the migration of cesium in soil is too slow to have reached the root areas. We assumed that the cesium must have been incorporated into the fruit via the leaves. To prove this, we applied aqueous solutions of the radionuclides cesium, strontium and iodine to the leaves of some vegetable plants and measured the resulting activity in the edible parts. In some cases we found a transfer of more than 40% of the total cesium applied to the leaf in the edible part of the plant.Further experiments, such as washing the leaves at certain intervals after the application, competition with other non-radioactive elements, influence of the experimental conditions as well as the structure of the leaf are under investigation.

Within the international BIOMOVS project a broad comparison and testing of assessment models is undertaken for different release and dispersion scenarios.One of these scenarios dealt with the turnover of Ra-226 and Th-266 in a lake ecosystem. This ecosystem is continuously contaminated by inflow from a river over a period of 100 years with a concentration of 1 Bq/1 of each nuclide.This paper discusses the results from seven models which have been used to calculate results for Ra-226. Best estimates and associated uncertainties of the concentration in fish, sediment and drinking water are compared as well as major contributions to the uncertainties. The reasons for discrepancies between the results from the different models are summarized. Some recommendations on how to improve the confidence in results and reduce the uncertainty are given.

A dynamic model of radium transfers between water, sediments and fish-flesh was developed to compare lakes that differ in their biological and physical characteristics. Results indicate that factors associated with differences in biological productivity between lakes can result in significant differences in the predictions and uncertainties of radium in various aquatic components.

The development and verification of a finite element model for delineating radioactive contaminant plumes via groundwater are described. The model is then used to predict the migration of 226Ra and U from the near-shore Port Granby waste management site to Lake Ontario. The model predicts that the continuous migration, via groundwater, of both contaminants toward Lake Ontario is likely to persist even after the waste is removed from the site.

To improve the reliability of environmental transport models an extensive validation effort is necessary. The deposition brought about by the Chernobyl accident gave new insights and possibilities for model validation. A dynamic compartment model DETRA is employed in this study for the consideration of radionuclide transport in a large watercourse taking into account both direct deposition and runoff from the terrestric environment. The results are shortly compared with the experimental observations, but a comprehensive quantitative analysis can be performed only after the careful evaluation of extensive raw data has been completed.

This paper is dealing with the uncertainty of dose assessments, due to the variability of transfer parameter values. Committed effective dose equivalents from the discharge of the liquid effluents of a nuclear waste treatment facility into a river are being considered. The radionuclides in those effluents, contributing most to the doses, include Cs-137, Co-60, Sr-90 and I-131. The value ranges of the transfer parameters, to which the dose assessment is very sensitive, have been derived from the literature.The median values and the uncertainty ranges (95 % confidence interval) of the doses are calculated, following a Latin Hypercube sampling procedure of the parameter values. The parameters, which contribute most to the dose uncertainty are identified and the influence of the introduction of site-specific values of these parameters on the uncertainty ranges is shown.

Several aquatic dispersion models have been developed for the North-East Atlantic seas in order to assess radiation doses to humans received via marine pathways due to radioactive wastes from nuclear installations. This paper describes a performance test of such a model. The model is an extended and adjusted version of the compartment model developed by the National Radiological Protection Board in the United Kingdom for the coastal seas around North-Western Europe. The model provides an improved simulation of the water transport fron the North Sea to the Baltic Sea. This improvement was obtained by calibrating the model to obtain the best possible agreement between predictions and observations of seawater concentrations of 137Cs. For the purpose of testing the performance of the model two other radionuclides have been studied: 134Cs and 99TC. Discharges from Sellafield and Cap de La Hague covering the time period 1966–85 have been used as source terms for the model predictions. These predictions are compared with environmental measurements of seawater concentrations in different water regions.

Radioactive releases of Iodine 129 are controlled with measurements of the radioactivity of the liquid effluents before to be released in sea from the outlet of the reprocessing plant of La Hague. The effects on marine environment are contolled with a radioactive survey of Technecium 99 and Iodine 129 in Fucus (common seaweed).This radioactivity is measured along north Coast of France from Roscoff in the west of Britany to Wimereux close to Belgium frontier. On other hand, the theoritical study of dispersion of radionuclides in the Channel has permitted to make a model of simulation of the transfer of pollutants and particularly Technecium 99 and Iodine 129.

The comparison of marine dispersion model results with measurements is an essential part of model development and testing. The results from two residual flow models are compared with seawater concentrations, and in one case with concentrations measured in marine molluscs. For areas with short turnover times, seawater concentrations respond rapidly to variations in discharge rate and marine currents. These variations are difficult to model, and comparison with concentrations in marine animals provides an alternative and complementary technique for model validation with the advantages that the measurements reflect the mean conditions and frequently form a useful time series.

A multi-compartmental box model of the Irish Sea has been developed to predict the distribution and radiological consequences of radionuclides discharged from the Sellafield reprocessing plant. The box structure was based on observations of radionuclide distributions in the sea bed and the water circulation was generated from extensive time-series data on 137Cs concentrations in seawater. Measurements of naturally-occurring nuclides provided both data on the extent and rate of these processes and a means to validate the model assumptions.The model structure is briefly outlined, comparisons are made between model predictions and field observation, and some of the difficulties in making such comparisons are discussed.

The radionuclides dispersion from the low-level waste drums dumped in the North Atlantic NEA site has been assessed by three independent box models developed in UK, in USA and in France within the international “Co-ordinated Research and Environmental Surveillance Programme”.These models take into account the time variations of the release rates of the nuclides out of the drums, a great deal of physical and geochemical marine processes and the transfer to man via various pathways. In order to assess the reliability of these complex transfer models, an intercomparison of UK and USA models had been performed on a benchmark problem.The french model has been run on this problem and the results were compared with UK and USA models results. Concentration differences of up to 2 or 3 orders of magnitude have been observed in boxes potentially important for the dose calculations. These differences originate in the different parameterizations of the scavenging by the particles and of the transfer at the water/sediment interface, the different vertical diffusion and advection by the ocean fluid, and the different geometry of the boxes.A simplified sensitivity analysis has been performed with the CEA model to crudely assess the reliability of the dose calculations. This allowed to identify the features of the CEA model which would require careful reconsideration if more precise and realistic dose assessment were requested: the sedimentation and resuspension of the particles, the nuclides transfer between the coastal and ocean boxes, the nuclides transfer within the sediment and the parameterization of specific coastal processes.

Radionuclides discharged into the sea may return to land in the marine aerosol. The extent and significance of this transfer around Sellafield has been assessed using a series of computer models.A marine model calculates the dispersion of radioactivity through the Eastern Irish Sea. Validation of the model is by comparison against the observed distributions of 241Am. Transfer of radionuclides to the land is empirically modelled using measured deposition. This simple model reproduces both current and cumulative deposition well. Validation of airborne activity against time series data is less good.The maximum dose to the average person in Seascale due to the transfer of actinides was calculated to be 24 μSv in 1973, which will reduce to 2 μSv in 2000. However, use of site-specific data may change these predictions.

This paper presents a comparison between two approaches of modelling radionuclide transport in soil. A scenario within the BIOMOVS study is chosen for the comparison. The scenario treats soil as recipient for contaminated water from the geosphere. The groundwater, containing I-129 and Np-237, reaches the soil below the root zone. This paper compares and discusses the concentration of nuclides in the root zone.One model is based on the compartment theory and is numerically solved by the code BIOPATH. Some input data to the model are obtained from a hydrological model (WATPATH) describing the dynamics of water in the unsaturated zone and saturated zone where important parameters are precipitation and mean air temperature. The BIOPATH approach considers the retention of nuclides in the different reservoirs. The uncertainty in the results due to the uncertainty in the parameter values are determined by the PRISM system.The other model is based on the advection-dispersion equation which is numerically solved by the computer code TRUMP. The model takes into consideration the transport of nuclides with groundwater and percolating precipitation, and transport by dispersion and diffusion. It also considers the retention of radionuclides by sorption to the soil. The model gives the possibility of a detailed description of the flow and distribution of radionuclides (one or two dimensional) in a section of a soil profile as a function of time. Input data to the model is water flow, dispersivity, diffusivity and sorption characteristics in the different parts of the soil profile.

A large number of different radiological assessment models exist which vary in structure and degree of sophistication depending on the purpose for which they are designed. In this paper the various applications of environmental transfer models are outlined and the differences between models for present day releases and releases from radioactive waste disposal are highlighted. The second part of the paper addresses the uncertainties associated with both types of assessment. It is concluded that the long timescales involved are the major contribution to the overall uncertainty in the prediction of consequences of releases from a waste repository. Ideas are presented for tackling this problem.

At the present development of knowledge of the second french disposal site, calculations of radiological consequences combined with a sensitivity analysis point out the main radionuclides to be taken into account, identify the sensitive parameters of the different barriers and evaluate the safety margins achieved through structural design and the application of general safety requirements. It will be possible to define the radiological capacity more accurately and derive guidance on the experimental studies.

This paper describes the approach being adopted to improve confidence in biosphere modelling for the assessment of the post-disposal radiological impact of disposal of low and intermediate solid radioactive waste at alternative sites proposed by UK Nirex Ltd.Release from a disposal facility may be precipitated by a number of mechanisms and ultimately result in release of activity into the surface environment, or biosphere. The range of potential receiving environments in the biosphere is discussed, and preliminary results for the consequences of unit release of relevant radionuclides are used to identify the most significant factors which lead to uncertainty or lack of confidence in results for biosphere modelling. The paper then goes on to consider the steps which might be taken to improve confidence in the predictions based on understanding of the relevant processes and mechanisms. These steps include the setting up of appropriate field and laboratory experiments and use of appropriate natural and other analogues to provide the best practicably obtainable database against which the biosphere model may be tested. The scope for such methods is discussed, noting the extended periods over which releases might occur, and the likely delays before they start.This work is funded by UK Nirex Ltd.

This paper presents details of the program package DIVIS which is to support the construction of subjective probability distributions and the specification of correlation coefficients for uncertain parameters of computational models. DIVIS provides graphical representations of selected distributions and of specified measures of correlation interactively so that the model expert may quickly judge how well they represent his knowledge base on the uncertain parameter.

One of the major steps of a probabilistic uncertainty and sensitivity analysis of model predictions is the generation of an experimental design, i.e. the selection of a multivariate sample of parameter values suitable to study the influence of parameter uncertainties on model predictions. In order to support the analyst in performing this task a computer program, named MEDUSA, has been written to generate the desired design after having received the necessary input data from the experts who are familiar with the various uncertain parameters. The paper presented describes the main features of this program.In MEDUSA two types of sample selection procedures are implemented: “simple random sampling” and “Latin Hypercube sampling”. The user can select from a set of several commonly used probability distributions for his uncertain parameters.In many practical cases some of the uncertain parameters cannot be regarded as independent and the problem arises how to express these dependences quantitatively and how to take them into account in the selection of the sample. Unlike the program in [1] MEDUSA offers for both design types two alternative methods to quantitatively express dependence between uncertain parameters. One of these methods, first introduced in ρ: ordinary correlation coefficientq: quadrant measureτ_K: Kendall’s τρ_S: Spearman’s pThese quantities are defined and interpreted in terms of population properties of bivariate distributions which seems to be more natural than a definition and interpretation in terms of empirical properties of bivariate samples.Additionally, MEDUSA contains a method to represent a kind of total dependence where there is some deterministic functional relationship between two parameters which complies with their marginal distributions.

Each parameter entering a model may have a different impact on the model outcome, depending on its intrinsic uncertainty. Therefore, ranking parameters according with their relevancy to the model outcome is an useful exercise for environmental modellers and model users as well. A sensitivity index is used to rank all parameters entering a model designed specifically to interpret the atom ratios 1-129/1-127 in terms of the retrospective dose commitment due to 1–131 absorbed in human thyroids as a consequence of nuclear tests in the atmosphere.