National-scale modelling of spatially heterogeneous groundwater concentrations of selected geogenic elements to predict local-scale concentration-inputs to surface waters in Denmark

Accurate national-scale modelling of surface water concentrations of trace elements requires accounting for both anthropogenic and geogenic inputs. In Denmark, groundwater concentrations of geogenic elements show pronounced spatial variability, making the natural groundwater component a potentially important contributor to the variability of surface water quality. However, quantifying groundwater–surface water interactions and groundwater-derived geogenic element concentrations at large spatial scales remains challenging due to limited data availability, model resolution constraints, and conceptual uncertainty.

This study aims to estimate the potential input of groundwater concentrations of selected geogenic elements (As, Ba, Cd, Cr, Cu, Ni, Pb, and Zn) to surface waters across Denmark. The resulting concentration estimates are intended as inputs to a nationwide surface water model. Therefore, the target spatial unit is the ID15 catchment, the smallest unit used in Danish national water management, representing topographic catchments with an average area of 15 km² (n = 3351).

To enable national-scale application, the complex three-dimensional groundwater–surface water system was simplified into a hierarchical structure with three levels: (1) well-screens, (2) groundwater bodies, and (3) ID15 catchments. Groundwater chemistry observations were available at the well-screen level. Well-screens were assigned to groundwater bodies with hydraulic contact to streams and lakes and thus feeding water into individual ID15 catchments.

We applied a hierarchical mixed-effects modelling framework to estimate typical (latent) concentrations of geogenic elements in groundwater bodies at depths relevant for groundwater–surface water contact. The model quantified the influence of hydrogeochemical and geological factors while accounting for spatial grouping within groundwater bodies and repeated measurements at individual well-screens. Each element was modelled separately, and concentrations were log-transformed prior to analysis.

The expected latent log-concentrations were described using a linear predictor with fixed and random effects. Fixed effects included redox class, pH class, geology, and depth, with interaction terms between redox and pH. Random effects were specified for groundwater bodies and well-screens. Measurements reported below detection limits were treated as left-censored observations and incorporated directly into the likelihood using cumulative log-normal probabilities.

Model parameter values including standard errors were estimated by minimising the joint negative log-likelihood using the R software package RTMB (R Template Model Builder), which is a high-performance statistical modelling tool. Model selection was based on Akaike’s Information Criterion. The model predicted latent groundwater concentrations at the depth assumed representative for groundwater–surface water contact: 3 m for groundwater bodies and 1 m for shallow near-surface groundwater not part of a groundwater body. Predicted log-concentrations were then aggregated to derive typical groundwater concentration inputs for each ID15 catchment.

We present a hierarchical modelling framework for estimating depth-dependent geogenic element concentrations at the groundwater body and ID15 catchment scales, enabling national-scale integration with surface water models, while interpreting and contextualising key model parameters and discussing limitations and future directions.