Simple models efficiently predict free cadmium Cd2+ in the solutions of low-contaminated agricultural soils

Speciation of Cd in soil solutions strongly determines the fate of this toxic metal in the environment. Generally, in soil solutions, Cd predominantly binds to the dissolved organic matter (DOM). The determination of the quantity and reactivity of DOM that actually complexes Cd in soil solutions is challenging for operational purposes. Therefore, this study tested whether Cd²⁺ concentration in soil solutions could effectively be predicted by considering complexation with a single mean organic ligand assumed to be a fraction of DOM of unspecified nature or assumed to be purely fulvic acids (FA) with reactivity as described in WHAM VII. The reactivity of the unspecified ligand and the concentration of FA were modelled and fitted to experimental data from 76 agricultural soils with low Cd contents. The optimal reactivity and FA concentration that minimized the relative error (RE) of predictions of the concentration of Cd²⁺ in soil solutions were either considered constant across soils or modelled from soil properties by multiple linear regressions (MLR) or random forests (RF), giving 6 models, the predictive value of which was assessed by 10-folds cross-validation. When the reactivity of the mean ligand and the optimal FA concentration were considered constant across soils, the models were biased and 66.9% of predictions had relative errors below a factor of 2. By contrast, if the reactivity of the mean ligand or the optimal FA concentration were allowed to vary with soil characteristics, these performances increased to 95.5%, soil pH being the main predictor and RF being slightly more efficient than MLR. With more than 95% of the relative errors of prediction below a factor of 2, the models developed in this work could be valuable for assessing Cd speciation in the solution of soils having a low Cd content.