Incorporating Spatial Information for Regionalization of Environmental Parameters in Machine Learning Models

Abstract Machine learning models have gained popularity for environmental variable predictions due to their capacity to capture complex relationships and automate learning. However, incorporating spatial information as covariates into these models remains a challenge, as they may struggle to recognize spatial structures or autocorrelation without explicit training. In this study, we address this challenge by integrating spatial information into a random forest model, enhancing nitrate concentration predictions in groundwater. Using a dataset from 1,550 well locations in Baden-Wuerttemberg, Germany, spanning 2016 through 2019, we consider various environmental covariates including climate data, topography, land cover, soil properties, and hydrology. To incorporate spatial information, we employ eight techniques leveraging spatial coordinates (geographic coordinates, polynomial geographic coordinates, oblique geographic coordinates) or distances (Wendland transformed coordinates, Euclidean distance fields, Euclidean distance matrix, principal component analysis, eigenvector spatial filtering). Results are compared with a baseline model and a univariate ordinary kriging benchmark, evaluated through leave-one-out cross validation, various error metrics, and Moran’s I of residuals. Our findings highlight that integrating spatial information significantly enhances random forest model accuracy in predicting groundwater nitrate concentrations. Distance-based methods, like the Euclidean distance matrix, outperform coordinate-based approaches, albeit with higher computational requirements. Employing a dimension-reduced matrix strikes a balance between performance and accuracy. This study advances groundwater management and demonstrates the effectiveness of machine learning models in environmental studies.