Development and validation of a model for whole course aging of nickel added to a wide range of soils using a complementary error function

Abstract After water-soluble nickel (Ni) is added to soils, its bioavailability/toxicity, isotopic exchangeability, and extractability decline over time. Two separate semi-mechanistic models (Sqrt-model and Ln-model), have been developed to predict short- and long-term aging of Ni added to soils. To continuously predict Ni aging in one model, a semi-mechanistic model (Erfc-model) was developed in the present study where the description of the diffusion process was based on a complementary error function. The Erfc-model for whole course aging predicted short- and long-term Ni aging continuously with regression coefficients (R 2 ) of 0.87 and 0.94, which were comparable with the Sqrt-model (0.91) and Ln-model (0.89). Based on the Erfc-model, soil pH and aging time were two important factors influencing the Ni aging processes. An additional 45 soils covering short and long terms of aging were applied to validate the model. A strong correlation (R 2  = 0.85) was found between the measured and the predicted lability of Ni in soils with root-mean-square-error (RMSE) of 8.97%, illustrating that the Erfc-model could continuously predict short- and long-term aging processes of Ni added to soils. The model could be used as an alternative to normalize ecotoxicological data for driving soil environmental quality standards.