Modelling of the shallow water table at high spatial resolution using random forests

Machine learning provides great potential for modelling hydrological variables at a spatial resolution beyond the capabilities of physically based modelling. This study features an application of random forests (RF) to model the depth to the shallow water table, for a wintertime minimum event, at a 50 m resolution over a 15 000 km² domain in Denmark. In Denmark, the shallow groundwater poses severe risks with respect to groundwater-induced flood events, affecting both urban and agricultural areas. The risk is especially critical in wintertime, when the shallow groundwater is close to terrain. In order to advance modelling capabilities of the shallow groundwater system and to provide estimates at the scales required for decision-making, this study introduces a simple method to unify RF and physically based modelling. Results from the national water resources model in Denmark (DK-model) at a 500 m resolution are employed as covariates in the RF model. Thus, RF ensures physical consistency at a coarse scale and fully exhausts high-resolution information from readily available environmental variables. The vertical distance to the nearest water body was rated as the most important covariate in the trained RF model followed by the DK-model. The evaluation test of the trained RF model was very satisfying with a mean absolute error of 76 cm and a coefficient of determination of 0.56. The resulting map underlines the severity of groundwater flooding risk in Denmark, as the average depth to the shallow groundwater is 1.9 m and approximately 29 % of the area is characterized as having a depth of less than 1 m during a typical wintertime minimum event. This study brings forward a novel method for assessing the spatial patterns of covariate importance of the RF predictions that contributes to an increased interpretability of the RF model. Quantifying the uncertainty of RF models is still rare for hydrological applications. Two approaches, namely random forests regression kriging (RFRK) and quantile regression forests (QRF), were tested to estimate uncertainties related to the predicted groundwater levels.