Some considerations on the dependence to numerical schemes of Lagrangian radionuclide transport models for the aquatic environment.

Lagrangian models present several advantages over Eulerian models to simulate the transport of radionuclides in the aquatic environment in emergency situations. A radionuclide release is simulated as a number of particles whose trajectories are calculated along time and thus these models do not require a spatial discretization (although it is always required in time). In this paper we investigate the dependence of a Lagrangian model output with the grid spacing which is used to calculate concentrations from the final distribution of particles, with the number of particles in the simulation and with the interpolation schemes which are required because of the discrete nature of the water circulation data used to feed the model. Also, a Lagrangian model may describe the exchanges of radionuclides between phases (liquid and solid), which is done in terms of transition probabilities. The dependence of these probabilities with time step is analyzed as well. It was found that the optimum grid size used to calculate concentrations should be carefully checked, and that temporal interpolation is more significant than spatial interpolation to obtain a more accurate solution. A method to estimate the number of particles required to have a certain accuracy level is proposed. Finally, it was found that for low sediment concentrations and small radionuclide kd, exact equations for the transition probabilities should be used; and that phase transitions introduce a stability condition as in Eulerian models.

The transport, effective half-lives and age distributions of radioactive releases in the northern Indian Ocean.

A Lagrangian model which describes radionuclide transport in the northern Indian Ocean is described. Water circulation is obtained from HYCOM ocean model for year 2017. The model includes advection by currents, turbulent mixing and radionuclide interactions between water and sediments, described in a dynamic way using kinetic transfer coefficients. Hypothetical releases from five coastal nuclear power plants operating in the northern Indian Ocean were simulated. Releases were supposed to start both during the winter and summer monsoons, to study reversing circulation effects. Age distributions of releases were calculated, which adds information about circulation and radionuclide pathways. It was found that, for some of the NPPs, radionuclide distributions resulting from releases starting in both seasons were not as different as could be expected from the opposed circulation schemes during each monsoon. Effective 137Cs half-lives in the ocean surface were calculated and results were two orders of magnitude below previous estimations.

Development of a dynamic food chain model for assessment of the radiological impact from radioactive releases to the aquatic environment.

The software tool POSEIDON-R was developed for modelling the concentration of radionuclides in water and sediments as well as uptake and fate in the aquatic environment and marine organisms. The software has been actively advanced in the aftermath of the Fukushima Dai-ichi accident. This includes development of an uptake model for the benthic food chain, a kinetic-allometric compartment model for fish and recent advancements for the application of 3H. This work will focus on the food chain model development and its extension to key artificial radionuclides in radioecology such as 3H. Subsequently, the model will be applied to assess the radiological dose for marine biota from 3H, 90Sr, 131I, 134Cs and 137Cs released during and after the Fukushima Dai-ichi accident. The simulation results for 3H, 90Sr, 131I, 134Cs and 137Cs obtained from the coastal box (4-4 km) located at the discharge area of the Fukushima Dai-ichi NPP, and the surrounding regional box (15-30 km) are compared with measurements. The predictions are by and large consistent with experimental findings, although good validation for 3H, 90Sr and 131I is challenging due to lack of data. On the basis of the model predictions a dose assessment for pelagic and benthic fish is carried out. Maximum absorbed dose rates in the coastal box and the regional box are respectively 6000 and 50 µGy d-1 and are found in the pelagic non-piscivorous fish. Dose rates exceeding ICRP's derived consideration levels of 1 mGy d-1 are only found in the direct vicinity of the release and shortly after the accident. During the post-accidental phase absorbed dose rates consistently fall to levels where no deleterious effects to the marine biota are expected. The results also demonstrate the prolonged dose rate from 134Cs and 137Cs, particularly for benthic organisms, due to caesium's affinity with sediment, re-entry of caesium from the sediment into the food chain and external exposure from its high energetic gamma emissions. Uptake of non-organic tritium (HTO) and organically bound tritium (OBT) is modelled and shows some accumulation of OBT in the marine organism. However, dose rates from tritium, even during the accident, are low.

Models for predicting the transport of radionuclides in the Red Sea.

Two radionuclide transport models for the Red Sea are described: a Lagrangian model to deal with emergency situations and a Eulerian model better suited to longer term simulations, as for instance required in case of chronic radionuclide releases. Baroclinic circulation is obtained for both transport models from HYCOM ocean model. The Lagrangian model also includes tides, which are obtained from a standard tidal model customized to the Red Sea, and currents induced by local winds. Both models describe exchanges of radionuclides between water and sediments. A number of simulations were carried out to illustrate capabilities of the models. Additionally, flushing times over the Red Sea were evaluated with the Eulerian model, as another example of model use.

Fukushima 137Cs releases dispersion modelling over the Pacific Ocean. Comparisons of models with water, sediment and biota data.

A number of marine radionuclide dispersion models (both Eulerian and Lagrangian) were applied to simulate 137Cs releases from Fukushima Daiichi nuclear power plant accident in 2011 over the Pacific at oceanic scale. Simulations extended over two years and both direct releases into the ocean and deposition of atmospheric releases on the ocean surface were considered. Dispersion models included an embedded biological uptake model (BUM). Three types of BUMs were used: equilibrium, dynamic and allometric. Model results were compared with 137Cs measurements in water (surface, intermediate and deep layers), sediment and biota (zooplankton, non-piscivorous and piscivorous fish). A reasonable agreement in model/model and model/data comparisons was obtained.

The marine kd and water/sediment interaction problem.

The behavior of marine distribution coefficients is analyzed with the help of numerical experiments and analytical solutions of equations describing kinetic models for uptake/release of radionuclides. The difficulties in measuring true kd in a marine environment perturbed by an external radionuclide source are highlighted. Differences between suspended matter and bed sediment kd are analyzed. The performances of different kinetic models (1-step/2step; single-layer/multi-layer) are studied in model/model and model/experiment comparisons. Implications for the use of models to assess radioactive contamination after an emergency are given; as well as recommendations when kd data are compiled in order to create a useful database.

The behaviour of 236U in the North Atlantic Ocean assessed from numerical modelling: A new evaluation of the input function into the Arctic.

A numerical model, previously validated with other radionuclides, was applied to simulate the dispersion of 236U released from European nuclear fuel reprocessing plants in the North Atlantic and Shelf Seas using a published reconstruction of Sellafield and La Hague releases. Model results are in better agreement with observations if the lowest estimation of such releases are used. This implies that approximately 40kg of 236U has been discharged from Sellafield. It was found that adsorption of 236U on bed sediments of the shallow European Shelf Seas plays an essential role in its dispersion patterns. This contrasts strongly with the more conservative behaviour of 129I in the same area. This has two important implications in the use of 236U as oceanographic tracer; i) special care must be taken in coastal areas, as sediments might act as sinks and sources of 236U; ii) the annual input function of 236U into the Arctic is not directly controlled by the annual discharges from Sellafield and La Hague, since sediments from the Irish, Celtic and North Sea modulate and smooth the signal. Only 52% of the total releases enter into the Arctic Ocean.

The behaviour of 137Cs in the North Atlantic Ocean assessed from numerical modelling: Releases from nuclear fuel reprocessing factories, redissolution from contaminated sediments and leakage from dumped nuclear wastes.

A Lagrangian model which simulates the dispersion of 137Cs in the North Atlantic has been developed. The model includes water/sediment interactions. It has been tested comparing calculated and measured 137Cs concentrations in water and sediments of the European Shelf resulting after the releases from the nuclear fuel reprocessing plants of Sellafield and La Hague. Some additional numerical experiments have been carried out. First, the redissolution of 137Cs from contaminated sediments after the reduction in releases from the reprocessing plants has been studied. This allowed to calculate effective half-lives of 137Cs in several sub-basins. Later, potential leakage of 137Cs from dumped nuclear wastes in several locations of the Atlantic has been investigated. Even in worst-case scenarios, these leakages should not lead to any radiological implications.

Modelling of marine radionuclide dispersion in IAEA MODARIA program: Lessons learnt from the Baltic Sea and Fukushima scenarios.

State-of-the art dispersion models were applied to simulate (137)Cs dispersion from Chernobyl nuclear power plant disaster fallout in the Baltic Sea and from Fukushima Daiichi nuclear plant releases in the Pacific Ocean after the 2011 tsunami. Models were of different nature, from box to full three-dimensional models, and included water/sediment interactions. Agreement between models was very good in the Baltic. In the case of Fukushima, results from models could be considered to be in acceptable agreement only after a model harmonization process consisting of using exactly the same forcing (water circulation and parameters) in all models. It was found that the dynamics of the considered system (magnitude and variability of currents) was essential in obtaining a good agreement between models. The difficulties in developing operative models for decision-making support in these dynamic environments were highlighted. Three stages which should be considered after an emergency, each of them requiring specific modelling approaches, have been defined. They are the emergency, the post-emergency and the long-term phases.

Inter-comparison of dynamic models for radionuclide transfer to marine biota in a Fukushima accident scenario.

We report an inter-comparison of eight models designed to predict the radiological exposure of radionuclides in marine biota. The models were required to simulate dynamically the uptake and turnover of radionuclides by marine organisms. Model predictions of radionuclide uptake and turnover using kinetic calculations based on biological half-life (TB1/2) and/or more complex metabolic modelling approaches were used to predict activity concentrations and, consequently, dose rates of (90)Sr, (131)I and (137)Cs to fish, crustaceans, macroalgae and molluscs under circumstances where the water concentrations are changing with time. For comparison, the ERICA Tool, a model commonly used in environmental assessment, and which uses equilibrium concentration ratios, was also used. As input to the models we used hydrodynamic forecasts of water and sediment activity concentrations using a simulated scenario reflecting the Fukushima accident releases. Although model variability is important, the intercomparison gives logical results, in that the dynamic models predict consistently a pattern of delayed rise of activity concentration in biota and slow decline instead of the instantaneous equilibrium with the activity concentration in seawater predicted by the ERICA Tool. The differences between ERICA and the dynamic models increase the shorter the TB1/2 becomes; however, there is significant variability between models, underpinned by parameter and methodological differences between them. The need to validate the dynamic models used in this intercomparison has been highlighted, particularly in regards to optimisation of the model biokinetic parameters.

A comparison of marine radionuclide dispersion models for the Baltic Sea in the frame of IAEA MODARIA program.

Four radionuclide dispersion models have been applied to simulate the transport and distribution of (137)Cs fallout from Chernobyl accident in the Baltic Sea. Models correspond to two categories: box models and hydrodynamic models which solve water circulation and then an advection/diffusion equation. In all cases, interactions of dissolved radionuclides with suspended matter and bed sediments are included. Model results have been compared with extensive field data obtained from HELCOM database. Inventories in the water column and seabed, as well as (137)Cs concentrations along 5 years in water and sediments of several sub-basins of the Baltic, have been used for model comparisons. Values predicted by the models for the target magnitudes are very similar and close to experimental values. Results suggest that some processes are not very relevant for radionuclide transport within the Baltic Sea, for instance the roles of the ice cover and, surprisingly, water stratification. Also, results confirm previous findings concerning multi-model applications.

The behaviour of ¹²9I released from nuclear fuel reprocessing factories in the North Atlantic Ocean and transport to the Arctic assessed from numerical modelling.

A quantitative evaluation of the fate of (129)I, released from the European reprocessing plants of Sellafield (UK) and La Hague (France), has been made by means of a Lagrangian dispersion model. Transport of radionuclides to the Arctic Ocean has been determined. Thus, 5.1 and 16.6 TBq of (129)I have been introduced in the Arctic from Sellafield and La Hague respectively from 1966 to 2012. These figures represent, respectively, 48% and 55% of the cumulative discharge to that time. Inventories in the North Atlantic, including shelf seas, are 4.4 and 13.8 TBq coming from Sellafield and La Hague respectively. These figures are significantly different from previous estimations based on field data. The distribution of these inventories among several shelf seas and regions has been evaluated as well. Mean ages of tracers have been finally obtained, making use of the age-averaging hypothesis. It has been found that mean ages for Sellafield releases are about 3.5 year larger than for La Hague releases.

Numerical modeling of the releases of (90)SR from Fukushima to the ocean: an evaluation of the source term.

A numerical model consisting of a 3D advection/diffusion equation, including uptake/release reactions between water and sediments described in a dynamic way, has been applied to simulate the marine releases of (90)Sr from the Fukushima power plant after the March 2011 tsunami. This is a relevant issue since (90)Sr releases are still occurring. The model used here had been successfully applied to simulate (137)Cs releases. Assuming that the temporal trend of (90)Sr releases was the same as for (137)Cs during the four months after the accident simulated here, the source term could be evaluated, resulting in a total release of 80 TBq of (90)Sr until the end of June, which is in the lower range of previous estimates. Computed vertical profiles of (90)Sr in the water column have been compared with measured ones. The (90)Sr inventories within the model domain have also been calculated for the water column and for bed sediments. Maximum dissolved inventory (obtained for April 10th, 2011) within the model domain results in about 58 TBq. Inventories in bed sediments are 3 orders of magnitude lower than in the water column due to the low reactivity of this radionuclide. (90)Sr/(137)Cs ratios in the ocean have also been calculated and compared with measured values, showing both spatial and temporal variations.

Local scale marine modelling of Fukushima releases. Assessment of water and sediment contamination and sensitivity to water circulation description.

The dispersion of (137)Cs released from Fukushima nuclear power plant to the sea after the March 11th 2011 tsunami has been studied using numerical models. The 3D dispersion model consists of an advection/diffusion equation with terms describing uptake/release reactions between water and seabed sediments. The dispersion model has been fed with daily currents provided by HYCOM and JCOPE2 ocean models. Seabed sediment (137)Cs patterns obtained using both current data set have been compared. The impact of tides and of atmospheric deposition has been evaluated as well. It has been also found that a 2-step kinetic model (two consecutive reversible reactions) for describing water/sediment interactions produces better results than a 1-step model (one single reversible reaction).

Modelling the environmental behaviour of pollutants in Algeciras Bay (south Spain).

An environmental study of Algeciras Bay is carried out through numerical modelling. First, a 2D barotropic model is applied to calculate tides and mean circulation. Results of this model are used by a sediment transport model which provides suspended matter concentrations and sedimentation rates in the Bay. It includes three particle classes. An effective diffusion coefficient has been calibrated simulating temperature distribution inside the Bay. An additional validation is obtained from an independent nitrate dispersion simulation. Then heavy metal dispersion patterns are investigated using a model which includes water-sediment metal interactions and uses the outputs of the hydrodynamic and sediment transport models. The metal transport model has been applied to simulate the dispersion of Zn, Cu and Ni. Results from the hydrodynamic, sediment and metal transport models have been compared with measurements. Model results also indicate that transport inside the Bay is relatively weak. Numerical experiments have been carried out to determine flushing times for conservative and non-conservative pollutants. Flushing time is about 20 days for a conservative tracer, and this value is mainly due to the M(2) residual current. Tides are not effective in removing pollutants.

A set of rapid-response models for pollutant dispersion assessments in southern Spain coastal waters.

Three rapid-response Lagrangian particle-tracking dispersion models have been developed for southern Spain coastal waters. The three domains cover the Gulf of Cádiz (Atlantic Ocean), the Alborán Sea (Mediterranean), and the Strait of Gibraltar with higher spatial resolution. The models are based on different hydrodynamic submodels, which are run in advance. Tides are calculated using a 2D barotropic model in the three cases. Models used to obtain the residual circulation depend on the physical oceanography of each region. Thus, two-layer models are applied to Gibraltar Strait and Alborán Sea and a 3D baroclinic model is used in the Gulf of Cádiz. Results from these models have been compared with observations to validate them and are then used by the particle-tracking models to calculate dispersion. Chemical, radioactive and oil spills may be simulated, incorporating specific processes for each kind of pollutant. Several application examples are provided.

Contamination and restoration of an estuary affected by phosphogypsum releases.

The Huelva Estuary in Huelva, Spain, has been one of the most studied environmental compartments in the past years from the point of view of naturally occurring radioactive material (NORM) releases. It has been historically affected by waste releases, enriched in radionuclides from the U-decay series, from factories located in the area devoted to the production of phosphoric acid and phosphate fertilizers. Nevertheless, changes in national regulations forced a new waste management practice in 1998, prohibiting releases of phosphogypsum into the rivers. The input of natural radionuclides from phosphate factories to rivers was drastically reduced. Because of this there was a unique opportunity for the study of the response of a contaminated environmental compartment, specifically an estuary affected by tidal influences, after the cessation of the contaminant releases to, in this case, the Huelva Estuary (henceforth referred to as the Estuary). To investigate the environmental response to this new discharge regime, the specific activities of radionuclides 226Ra and 210Pb in water and sediment samples collected in four campaigns (from 1999 to 2005) were determined and compared with pre-1998 values. From this study it is possible to infer the most effective mechanisms of decontamination for the Estuary. Decontamination rates of 210Pb and 226Ra in the sediments and water have been calculated using exponential fittings and corresponding half-lives have been deduced from them. The cleaning half-life in the whole area of the Estuary is about 6 and 3.5 years for 226Ra and 210Pb respectively. The observed trend clearly shows that contamination of the Estuary by natural radionuclides is now decreasing and radioactive levels in waters and sediments are approaching the natural background references. This work attempts to evaluate whether it can be expected that the decontamination of the enhanced levels of natural radioactivity in the Estuary can be performed via natural processes.

Characteristic times in the English Channel from numerical modelling: supporting decision-making.

A numerical model that simulates the dispersion of radionuclides in the English Channel has been applied to study the dispersion of conservative and non-conservative radionuclides released from the La Hague nuclear fuel reprocessing plant. The model is based upon previous work and now is able to simulate dispersion over long timescales (decades), explicitly including transport by instantaneous tidal currents and variable wind conditions. Wind conditions are obtained from meteorological statistics using a stochastic method. Outputs from the model are treated using time-series analysis techniques. These techniques allow the determination of characteristic times of the system, transport velocities and dispersion factors. This information may be very useful to support the decision-making process after an emergency situation. Thus, we are proposing that time-series analysis can be integrated with numerical modelling for helping decision-making in response to an accident. The model is first validated through its application to actual releases of 99Tc and 125Sb, comparing measured and computed concentrations, and characteristic times for three radionuclides are given next: a perfectly conservative one, a very reactive one ((239,240)Pu) and 137Cs, which has an intermediate behaviour. Characteristic transport velocities and dispersion factors have been calculated as well. Model results are supported by experimental evidence.

Environmental modelling in the Gulf of Cadiz: heavy metal distributions in water and sediments.

The Gulf of Cadiz (GoC) connects the Atlantic Ocean and the Mediterranean Sea. An environmental study of the GoC is carried out through numerical modelling. First, a 3D baroclinic model is used to obtain the residual circulation and a 2D barotropic model is applied to calculate tides. The results of these models are used by a 3D sediment transport model which provides suspended matter concentrations and sedimentation rates in the GoC. Then heavy metal dispersion patterns are investigated using a 3D model which includes water-sediment metal interactions and uses the outputs of the hydrodynamic and sediment transport models. The metal transport model has been applied to simulate the dispersion of Zn, Cu and Ni introduced into the GoC from three rivers draining the Iberian Pyrite Belt, in the southern Iberian Peninsula. Results from the hydrodynamic, sediment and metal transport models have been compared with measurements in the GoC. In particular, the contamination of sediments collected along the southern coast of Spain is well reproduced by the model. Metal plumes reach the Strait of Gibraltar, thus the three rivers constitute a source of pollutants into the Mediterranean Sea.

Occupational dosimetric assessment (inhalation pathway) from the application of phosphogypsum in agriculture in South West Spain.

Phosphogypsum (PG) has been traditionally applied as Ca-amendment in saline marsh soils in SW Spain, where available PG has 710+/-40Bqkg(-1) of 226Ra. This work assesses the potential radiological risk for farmers through 222Rn exhalation from PG-amended soils and by inhalation of PG-dust during its application. A three-year field experiment was conducted in a commercial farm involving two treatments: control and 25tPGha(-1) with three replicates (each 0.5ha plots). The 222Rn exhalation rate was positively correlated with potential evapotranspiration, which explained 67% of the variability. Statistically significant differences between the control and PG treatments were not found for 222Rn exhalation rates, and mean values were within the lowest quartile of the typical range for 222Rn exhalation from soils. Airborne dust samples were collected during the application of PG and sugar-beet sludge amendments. The highest PG-attributable 226Ra concentration in the dust samples was 3.3x10(2)microBqm(-3), implying negligible dose increment for exposed workers.