Modelling depth of the redox interface in high resolution at national scale using machine learning and geostatistics

The transport of excess nitrate from agricultural fields to surface waterbodies, groundwater and marine waters constitutes a significant problem for environmental and human health across the globe. In consequence, the management of water resources needs robust methods to further reduce nitrate loads. Natural removal of nitrate occurs during the transport from source areas which is referred to as denitrification. Previous research has investigated the environmental and economic gains of spatially targeted measures, which are, opposed to uniform regulations, spatially differentiated with respect to the natural denitrification potential. This potential can be estimated based on combined knowledge on subsurface flowpaths and the depth to the redox interface, i.e. the location of the uppermost reduced (anaerobic) zone, below which denitrification takes place. In this study, we explored the opportunity to use a machine learning technique to model redox depth across Denmark in 100m resolution based on 13000 boreholes.

Random Forest (RF) is a powerful machine learning technique, which can be tied to geostatistical methods to further increase accuracy and to facilitate an uncertainty assessment. We applied random forest regression kriging (RFRK) in which sequential Gaussian simulation (sGs) was selected to model the RF residuals. An R² score of 0.48 was reached by the RF model for an independent validation test. Conditional sGs was performed to estimate the RF residuals which increased the R² to 0.83 and the spread of 800 realizations was utilized to map uncertainty. Emphasize was put on adequate handling of non-stationarities in the variance and spatial correlation of the RF residuals as both varied across the modelling domain. The residuals were found to be spatially correlated in the complex hill island landscape where crucial covariates are likely missing in the RF model. For the remaining part of the country no spatial correlation was evident and a local variance scaling method was applied to account for the non-stationary variance. Moreover, we presented and exemplified a framework where newly acquired field data can easily be integrated into RFRK to quickly update local models.