Development of a machine learning model to estimate biotic ligand model-based predicted no-effect concentrations for copper in freshwater

The copper biotic ligand model (BLM) has been used for environmental risk assessment by taking into account the bioavailability of copper in freshwater. However, the BLM-based environmental risk of copper has been assessed only in Europe and North America, with monitoring datasets containing all of the BLM input variables. For other areas, it is necessary to apply surrogate tools with reduced data requirements to estimate the BLM-based predicted no-effect concentration (PNEC) from commonly available monitoring datasets. To develop an optimized PNEC estimation model based on an available monitoring dataset, an initial model that considers all BLM variables, a second model that requires variables excluding alkalinity, and a third model using electrical conductivity as a surrogate of the major cations and alkalinity have been proposed. Furthermore, deep neural network (DNN) models have been used to predict the nonlinear relationships between the PNEC (outcome variable) and the required input variables (explanatory variables). The predictive capacity of DNN models in this study was compared with the results of other existing PNEC estimation tools using a look-up table and multiple linear and multivariate polynomial regression methods. Three DNN models, using different input variables, provided better predictions of the copper PNECs compared with the existing tools for four test datasets, i.e., Korean, United States, Swedish, and Belgian freshwaters. The adjusted r2 values in all DNN models were higher than 0.95 in the test datasets, except for the Swedish dataset (adjusted r2 > 0.87). Consequently, the most applicable model among the three DNN models could be selected according to the data availability in the collected monitoring database. Because the most simplified DNN model required only three water quality variables (pH, dissolved organic carbon, and electrical conductivity) as input variables, it is expected that the copper BLM-based risk assessment can be applied to monitoring datasets worldwide.