A weighted bootstrap method for the determination of probability density functions of freshwater distribution coefficients (Kds) of Co, Cs, Sr and I radioisotopes

Predicting the distribution coefficient of cesium in solid phase groups using machine learning

The migration and retention of radioactive contaminants such as 137Cesium (137Cs) in various environmental media pose significant long-term storage challenges for nuclear waste. The distribution coefficient (Kd) is a critical parameter for assessing the mobility of radioactive contaminants and is influenced by various environmental conditions. This study presents machine-learning models based on the Japan Atomic Energy Agency Sorption Database (JAEA-SDB) to predict the Kd values for Cs in solid phase groups. We used three different machine learning models: random forest (RF), artificial neural network (ANN), and convolutional neural network (CNN). The models were trained on 14 input variables from the JAEA-SDB, including factors such as the Cs concentration, solid-phase properties, and solution conditions, which were preprocessed by normalization and log-transformation. The performances of the models were evaluated using the coefficient of determination (R2) and root mean squared error (RMSE). The RF, ANN, and CNN models achieved R2 values greater than 0.97, 0.86, and 0.88, respectively. We also analyzed the variable importance of RF using an out-of-bag (OOB) and a CNN with an attention module. Our results showed that the environmental media, initial radionuclide concentration, solid phase properties, and solution conditions were significant variables for Kd prediction. Our models accurately predict Kd values for different environmental conditions and can assess the environmental risk by analyzing the behavior of radionuclides in solid phase groups. The results of this study can improve safety analyses and long-term risk assessments related to waste disposal and prevent potential hazards and sources of contamination in the surrounding environment.

Fresh Groundwater Discharge as a Major Source of 90Sr into the Coastal Ocean

The behavior and source of 90Sr in the coastal ocean remain uncertain. Here, we investigated the distributions of 90Sr in coastal fresh groundwater, river water, pore water, and seawater in three bays along the southeastern coast of China between 2019 and 2021 and evaluated the potential of submarine groundwater discharge (SGD) as a source of coastal 90Sr. The 90Sr activity in coastal fresh groundwater was higher than that in river water and seawater, while the 90Sr activity in pore water was comparable to that in adjacent seawater. In addition, nonconservative mixing behavior of 90Sr along the salinity gradient between river water and seawater was observed. These observations indicated that fresh SGD may serve as an additional source of 90Sr in coastal seawater. Combining our groundwater 90Sr data with the reported fresh SGD flux data, the estimated fresh SGD-derived 90Sr fluxes into the three bays were comparable to or even higher than those supplied by riverine sources. These results revealed that fresh SGD is a major but overlooked source of 90Sr in the coastal ocean. This subterranean pathway for transport of 90Sr to the coastal ocean should be considered in the monitoring and risk assessment of coastal areas, especially those near nuclear facilities.

A comprehensive probabilistic approach for integrating and separating natural variability and parametric uncertainty in the prediction of distribution coefficient of radionuclides in rivers

A geochemical speciation model was developed to predict Distribution coefficients (K_ds) of radionuclides (RNs) in rivers. The model takes into account complexation of RNs with inorganic ligands, sorption of RNs with hydrous ferric oxides, complexation of RNs with dissolved and particulate organic carbon (DOC and POC) and sorption and/or co-precipitation of RNs to carbonates. A sorption model of Cs onto clay was also integrated. The tool is also designed to conduct uncertainty and sensitivity analysis. Sensitivity analysis follows a stepwise structured approach, starting from computationally 'inexpensive' Morris method to most costly variance-based EFAST method. A nested Monte Carlo approach was also implemented to separate natural variability and lack of knowledge in global uncertainty assessment. As case studies, K_d distributions were estimated for Co, Mn, Ag and Cs in seven French rivers. Uncertainty analysis allowed to quantify K_d ranges that can be expected when considering all the sensitive parameters together.

Distribution Coefficient and Metal Pollution Index in Water and Sediments: Proposal of a New Index for Ecological Risk Assessment of Metals

The Lake of Texcoco is a closed basin with soils that confer salinity, conductivity, and alkalinity to it. It has undergone a reduction in size, incorporation of wastewater, and short-term desiccation, and includes temporary wetlands interconnected during the rainy season, some of which receive treated wastewater. Sediments contain metals, thus affecting water quality. Five artificial lakes were studied, and 12 metals (As, Ba, Cd, Cu, Cr, Fe, Mg, Mn, Hg, Ni, Pb, and Zn) were monitored bimonthly in water and sediments from June 2015 to March 2018. The Metal Pollution Index (MPI) and the Distribution Coefficient (Kd) were computed. Fe and Cd were the most and least stable metals in sediments, respectively (mean Log(Kd) = 4.24 and 2.079). Based on Log(Kd), metals were ranked as Fe > Mn > Zn > Cu > Mg > Cr > Ni > Ba > Pb > Hg > As > Cd. Log(Kd) values < 3 and > 5 indicate that metals occur mainly in water and sediments, respectively. The Mean Distribution Coefficient Log(Kd MPI) is a novel index proposed to assess ecological risk from metals in a water body. This index allows determining the phase (liquid or solid) where metals predominate, negatively affecting either free-swimming or benthic organisms. Log(Kd MPI) values indicated that metals occur primarily in the liquid phase in all lakes studied.

Extended Kd distributions for freshwater environment

Many of the freshwater K_d values required for quantifying radionuclide transfer in the environment (e.g. ERICA Tool, Symbiose modelling platform) are either poorly reported in the literature or not available. To partially address this deficiency, Working Group 4 of the IAEA program MODARIA (2012-2015) has completed an update of the freshwater K_d databases and K_d distributions given in TRS 472 (IAEA, 2010). Over 2300 new values for 27 new elements were added to the dataset and 270 new K_d values were added for the 25 elements already included in TRS 472 (IAEA, 2010). For 49 chemical elements, the K_d values have been classified according to three solid-liquid exchange conditions (adsorption, desorption and field) as was previously carried out in TRS 472. Additionally, the K_d values were classified into two environmental components (suspended and deposited sediments). Each combination (radionuclide x component x condition) was associated with log-normal distributions when there was at least ten K_d values in the dataset and to a geometric mean when there was less than ten values. The enhanced K_d dataset shows that K_d values for suspended sediments are significantly higher than for deposited sediments and that the variability of K_d distributions are higher for deposited than for suspended sediments. For suspended sediments in field conditions, the variability of K_d distributions can be significantly reduced as a function of the suspended load that explains more than 50% of the variability of the K_d datasets of U, Si, Mo, Pb, S, Se, Cd, Ca, B, K, Ra and Po. The distinction between adsorption and desorption conditions is justified for deterministic calculations because the geometric means are systematically greater in desorption conditions. Conversely, this distinction is less relevant for probabilistic calculations due to systematic overlapping between the K_d distributions of these two conditions.

A comprehensive probabilistic approach for integrating natural variability and parametric uncertainty in the prediction of trace metals speciation in surface waters

The main objectives of this study were to evaluate global uncertainty in the prediction of Distribution coefficients (Kds) for several Trace Metals (TM) (Cd, Cu, Pb, Zn) through the probabilistic use of a geochemical speciation model, and to conduct sensitivity analysis in speciation modeling in order to identify the main sources of uncertainty in Kd prediction. As a case study, data from the Loire river (France) were considered. The geochemical speciation model takes into account complexation of TM with inorganic ligands, sorption of TM with hydrous ferric oxides, complexation of TM with dissolved and particulate organic matter (i.e. dissolved and particulate humic acids and fulvic acids) and sorption and/or co-precipitation of TM to carbonates. Probability Density Functions (PDFs) were derived for physico-chemical conditions of the Loire river from a comprehensive collection of monitoring data. PDFs for model parameters were derived from literature review. Once all the parameters were assigned PDFs that describe natural variability and/or knowledge uncertainty, a stepwise structured sensitivity analysis (SA) was performed, by starting from computationally 'inexpensive' Morris method to most costly variance-based EFAST method. The most sensitive parameters on Kd predictions were thus ranked and their contribution to Kd variance was quantified. Uncertainty analysis was finally performed, allowing quantifying Kd ranges that can be expected when considering all the sensitive parameters together.

Potential utilization of the absolute point cumulative semivariogram technique for the evaluation of distribution coefficient

The classical solid/liquid distribution coefficient, K(d), for radionuclides in water-sediment systems is dependent on many parameters such as flow, geology, pH, acidity, alkalinity, total hardness, radioactivity concentration, etc. in a region. Considerations of all these effects require a regional analysis with an effective methodology, which has been based on the concept of the cumulative semivariogram concept in this paper. Although classical K(d) calculations are punctual and cannot represent regional pattern, in this paper a regional calculation methodology is suggested through the use of Absolute Point Cumulative SemiVariogram (APCSV) technique. The application of the methodology is presented for (137)Cs and (90)Sr measurements at a set of points in Keban Dam reservoir, Turkey.

Probabilistic distribution coefficients (K(d)s) in freshwater for radioisotopes of Ag, Am, Ba, Be, Ce, Co, Cs, I, Mn, Pu, Ra, Ru, Sb, Sr and Th: implications for uncertainty analysis of models simulating the transport of radionuclides in rivers

The objective of this study was to provide operational probability density functions (PDFs) for distribution coefficients (K(d)s) in freshwater, representing the partition of radionuclides between the particulate and the dissolved phases respectively. Accordingly, the K(d) variability should be considered in uncertainty analysis of transport and risk assessment models. The construction of PDFs for 8 elements (Ag, Am, Co, Cs, I, Mn, Pu and Sr) was established according to the procedure already tested in Durrieu et al. [2006. A weighted bootstrap method for the determination of probability density functions of freshwater distribution coefficients (K(d)s) of Co, Cs, Sr and I radioisotopes. Chemosphere 65 (8), 1308-1320]: (i) construction of a comprehensive database where K(d)s values obtained under various environments and parametric conditions were collected; (ii) scoring procedure to account for the 'quality' of each datapoint (according to several criteria such as the presentation of data (e.g. raw data vs mean with or without replicates), contact time, pH, solid-to-liquid ratio, expert judgement) in the construction of the PDF; (iii) weighted bootstrapping procedure to build the PDFs, in order to give more importance to the most relevant datapoints. Two types of PDFs were constructed: (i) non-conditional, usable when no knowledge about the site of concern is available; (ii) conditional PDFs corresponding to a limited range of parameters such as pH or contact time; conditional PDFs can thus be used when some parametric information is known on the site under study. For 7 other radionuclides (Ba, Be, Ce, Ra, Ru, Sb and Th), a simplified procedure was adopted because of the scarcity of data: only non-conditional PDFs were built, without incorporating a scoring procedure.