Model of the Long-Term Transport and Accumulation of Radionuclides in Future Landscapes

The main principles used for developing this model are generally the same that we applied in the development of the model described in Avila et al. (2006). Essentially, we consider that for a model to have all required capabilities mentioned above, it should describe the processes of transport and accumulation in the biosphere at a landscape level, rather than for each ‘biosphere object’ separately. The reasons for this are discussed in Avila et al. (2006).

A ‘biosphere object’ is defined as an area of the landscape that can receive radionuclide releases; either through discharge of deep groundwater (Berglund et al. 2013a) or in contaminated surface water, at any time during a glacial cycle (Lindborg et al. 2013). The identification of biosphere objects is described by Lindborg et al. (2013).

In our earlier model, we divided the potentially affected landscape into several interlinked biosphere objects. For each of these objects we used several radioecological models, since we expected that at different future times different ecosystem types will prevail in a biosphere object and a single radioecological model that could handle this was not available. By radioecological model we mean a model that can simulate the transfer and accumulation of radionuclides in an ecosystem. In that previous model we handled transitions between ecosystems by introducing discrete events, i.e., at a given time we substituted one radioecological model with another one during the simulations. We then transferred the accumulated inventory between the ecosystem models.

This created several problems, mainly because the different radioecological models had different compartments, which made it difficult to ensure mass balance at the transitions. Also, the transition between ecosystems is a continuous process and treating it as a discrete event creates unrealistic abrupt changes in predicted time series of inventories and concentrations, which are difficult to handle numerically. Another problem with the previous model was that we used existing radioecological models, although with some modifications (Avila 2006a, b) and some of these models did not include all relevant processes. In particular, processes related to the transport and accumulation of radionuclides in the lower regolith, e.g., till from the last glaciations, were not included.

The model that we describe in the “Results and Discussion” section is an attempt to solve the above-mentioned problems, by modeling each biosphere object with a single radioecological model that is applicable to all those ecosystem types that are of relevance for the given assessment context. We also impose the requirement that the model should be able to simulate transitions between ecosystems in a continuous manner, rather than as discrete events. As we show later in this paper, a main idea in this model is that it includes an aquatic and a terrestrial part that interact with each other, through fluxes of water and particles and processes related to biomass production.

Figure 1 shows an example of the landscape model at a specific point in time within a glacial cycle (Näslund et al. 2013). The boxes show the different biosphere objects and the arrows the fluxes of water and particles, as well as of radionuclides, between them. Since the biosphere objects are interconnected, the model can simulate the transport and accumulation of radionuclides in the whole landscape. In the terrestrial phase, when biosphere objects have emerged from the sea and have been converted to lakes and wetlands, the radionuclide fluxes from a biosphere object are directed to connected downstream objects. Hence, all downstream objects will receive inputs from one or several upstream objects. In the Sea Stage, when biosphere objects are still sea basins, these interact only with the outer coastal area (Öregrundsgrepen) via water exchange in both directions. From Öregrundsgrepen, radionuclides are finally discharged to the Baltic Sea.

Extensive site investigations at the site selected for a repository for spent nuclear fuel in Sweden, Forsmark, have resulted in a detailed description of the site and its development (SKB 2011). Data obtained from the site investigations together with a better understanding of the site has been the primary source for parameter values of the Radionuclide Model of the biosphere. Parameters represent the development of the individual biosphere objects, characteristics of the relevant ecosystems, and water flows within and between biosphere objects. There are also parameters describing the exposed individuals and dose coefficients for external exposure, inhalation, and ingestion of food and water. For each parameter, we derived a best estimate (BE) value using site and/or literature data, and to describe the uncertainty of parameter values we assigned a probability density function (PDF) to those parameters that are considered uncertain; i.e., to most parameters excluding those that are considered constants, such as the dose coefficients that relate radiation dose to intake of activity. In the safety assessment, we used the BE values in deterministic simulations to obtain baseline dose estimates (see below) and the PDFs in probabilistic simulations to assess the impact of parameter uncertainty on the dose estimates.

For most parameters, we selected BE values and PDFs using expert judgment as described by Avila et al. (2010). Two element-specific parameters, the distribution coefficients (K _d) and concentration ratios (CR), are known from previous safety assessments (SKB 2006) to have a large impact on the dose predictions. The K _d and CR are used to model radionuclide retention and biological uptake, respectively. For these parameters, we applied a more formalized approach for derivation of BE values and PDFs using Bayesian inference methods (Nordén et al. 2010). These methods allow combination of site and literature data in a systematic way and with a good theoretical basis. The site investigations included extensive measurements of K _d and CR values (Nordén et al. 2010) for a large number of elements, including those corresponding to the most important radionuclides, like ²²⁶Ra and ¹²⁹I. We retrieved literature data primarily through the EMRAS (IAEA 2010) and ERICA databases (Beresford et al. 2007). Where relevant values were missing in these databases, we used values compiled for previous SKB safety assessments (Karlsson and Bergström 2002). Finally, where appropriate data were not available from the site or from the open literature we used data for analog biota types or elements.

The model accepts time and spatially distributed releases as input. However, for the purpose of this specific safety assessment we performed simulations for unit releases of each radionuclide to obtain radionuclide-specific Dose Conversion Factors (annual doses per unit release rate), which we then multiplied by the actual releases of the corresponding radionuclide to obtain radiation dose values resulting from those releases. The Swedish regulations (SSM 2008a, b) require that annual dose averaged over the lifetime of the individuals be calculated for comparison with the risk criteria. This means that it is not necessary to calculate doses to different age groups, as this average can be adequately represented by the annual dose to an adult (ICRP 2000). Hence, in the derivation of Dose Conversion Factor values, we have calculated doses to adults averaged over a lifetime. The term dose is taken to mean ‘effective dose’, including, as appropriate, the committed dose from intakes of radionuclides and the contribution from external irradiation.

For this study we derived two different Dose Conversion Factors: (i) the Landscape Dose Conversion Factor (LDF) that is applicable to continuous long-term releases over hundreds to tens of thousands of years at a constant rate and is defined as the annual effective dose to a representative individual from the most exposed group resulting from a constant unit release rate of this radionuclide to the biosphere (the units are Sv a⁻¹ per Bq a⁻¹) and (ii) the Landscape Dose Conversion Factor for pulse releases (LDF pulse) that is applicable to a radionuclide release that reaches the biosphere in a pulse over years to hundreds of years and is defined as the annual effective dose to a representative individual from the most exposed group resulting from a unit pulse release of this radionuclide to the biosphere (the units are Sv a⁻¹ per Bq). The most exposed group is defined as the group of individuals exposed to the biosphere object with the potentially highest contamination, considering a glacial cycle from a submerged landscape to fully terrestrial conditions. A representative individual from the most exposed group is assumed to spend all time in this biosphere object, and get his/her entire supply of food and water from the object, but still considering constraints in water and food supply (Kautsky et al. 2013; Saetre et al. 2013). All potential exposure pathways are considered in the dose calculations, including external irradiation from radionuclides in the surrounding environment and internal irradiation from radionuclides incorporated into the human body by inhalation and via ingestion of food and water.

We calculated LDF values for three different periods of the reference glacial cycle (Näslund et al. 2013): the period of submerged conditions following the deglaciation, the interglacial period, and a prolonged period of periglacial conditions. Additionally, we calculated LDFs for a global warming climate case. The maximum LDF in the landscape during each time period was used in the dose calculations for the safety assessment.

The first part of the reference glacial cycle is represented by temperate conditions, i.e., climate conditions similar to those of today. This interglacial period is assumed to exist for 18 400 years (i.e., at the first occurrence from −9000 ad to 9400 ad, but then recurring in each glacial–interglacial cycle). When the period starts, the landscape is covered by the sea (submerged conditions). As land emerges sufficiently out of the sea, wetlands are first created and then possibly converted to arable land (Lindborg et al. 2013). The interglacial period with temperate conditions is followed by a period with periglacial conditions, representing a colder climate than today with deep permafrost. These conditions are assumed to prevail for 50 200 years (i.e., from 9400 ad to 59 600 ad at the first occurrence). During glacial conditions, when the repository is covered by an inland ice sheet, releases can only cause humans to be exposed to radionuclides through ingestion of sea food, when the ice margin is situated above or close to the repository. The resulting doses in this case are expected to be lower than maximum doses during temperate conditions, due to a larger dilution of radionuclides released to the sea. To estimate annual exposures from releases during glacial conditions, the LDFs from the open-sea stage (submerged period) obtained for temperate conditions are used in the assessment.

For the global warming climate case we assumed that global warming will extend the period of temperate conditions, which will prevail during the whole interglacial period (i.e., from −9000 ad to about 60 000 ad). LDFs for the global warming climate case represent the maximum during this period.

In deriving LDF values for the different periods of the reference glacial cycle we introduced several assumptions about the future evolution of the system, some of which were realistic and some other pessimistic. The model itself also includes a combination of realistic and cautious assumptions. LDF values obtained from deterministic simulations under these baseline assumptions are here called the baseline LDF values, which were used in the dose calculations for comparison with regulatory dose criteria.

Very briefly, we have studied system, model, and parameter uncertainties as well as numerical model integration uncertainties pertaining to the LDF values that we have derived. Furthermore, we carried out sensitivity analyses for time-independent parameters using the results from probabilistic simulations. A detailed description of the methods used is given in the Appendix (Electronic Supplementary Material).