Chemical analogues and probabilistic functions to derive distribution coefficients of radium in soils

The existing data gaps in the sorption and desorption parameters of naturally occurring radionuclides (e.g., radium (Ra)) challenge the use of radioecological risk assessment models. We present two alternatives for deriving Ra distribution coefficients (K_d (Ra)) in soils when the physicochemical information on the solid and liquid phases involved is too scarce to apply parametric prediction models: the deduction of sorption parameters from those of chemical analogues (such as Ba and Sr) and the proposal of best estimate K_d (Ra) values deduced from probabilistic distribution functions of data grouped according to relevant factors affecting K_d (Ra) variability. Regarding the use of chemical analogues, partial least squares regression analysis and univariate linear correlations revealed that Ba and Ra sorption in soils was governed by the same soil properties (K_d (Ca + Mg) and Mn_am), related to exchangeable sites on the soil surface. The derivation of K_d (Ra) values from K_d (Ba) and also K_d (Sr) is feasible by applying suitable correction factors. Furthermore, several K_d (Ra) best estimates were derived from the distribution functions of K_d (Ra) datasets obtained from own and literature data. Statistical differences were noticed for the sorption and desorption datasets (the latter significantly affected by data from native Ra), leading to the proposal of distinct K_d (Ra) values (870 and 2760 L kg^-1, respectively) for uptake and remobilisation scenarios. Regarding the desorption data, diverse K_d (Ra) best estimates were suggested for acidic (1540 L kg^-1) and alkaline (6440 L kg^-1) soils. For the sorption data, statistically different K_d (Ra) best estimates were suggested according to pH (100 and 1240 L kg^-1 for pH < 4.5 and pH ≥ 7, respectively) and water-soluble Ca + Mg content, allowing for the selection of the most appropriate best estimate values for use in risk assessment models depending on the available information.