Probabilistic Modeling and Uncertainty Simulations of National-Scale Hydrostratigraphic Models: An Example from Denmark Rasmus Bødker Madsen, Frederik Alexander Falk, Ingelise Møller, Lars Troldborg, Anne-Sophie Høyer Mathematical Geosciences, 2026 Uncertainties in hydrological models arise primarily from the subsurface architecture and hydrological properties of each unit. This paper presents a method to simulate structural uncertainties in large-scale hydrostratigraphic or geological models by generating multiple realizations constrained by quantified uncertainties. The simulation is based on the geology-driven modeling (GDM) method. GDM requires quantified uncertainty estimates for each interpretation point and assumes that the model domain is sufficiently small for stationarity to hold. However, the stationarity assumption does not hold at the national scale. To address this limitation, an upscaling method for GDM is proposed, which subdivides the domain into regions with similar structural properties. These regions can be simulated independently using Gaussian simulation, then combined and layer-corrected to produce a cohesive three-dimensional model ensemble. This approach is computationally efficient, flexible, and scalable, making national-scale modeling feasible. The upscaled version, GDM-National, is introduced, and its effectiveness is demonstrated by generating an ensemble of realizations for Denmark’s national hydrostratigraphic layer model. The method provides a valuable tool for propagating interpretation uncertainties from hydrostratigraphic layers to hydrological models.
Operational flood forecasting in Denmark - integrating groundwater and surface water Jun Liu, Julian Koch, Simon Stisen, Lars Troldborg, Raphael Schneider Geus Bulletin, 2026 Most operational flood forecasting systems provide predictions of pluvial and fluvial floods, often neglecting groundwater flooding. Groundwater-induced floods can occur when prolonged rainfall, high river stages or elevated sea levels raise the groundwater table above the surface of the land, often occurring in low-lying areas or areas with specific soil and land-surface conditions. This study presents an operational, national-scale, integrated flood forecasting system that combines surface water and groundwater components – such as river discharge and high groundwater levels – to assess flood risk in Denmark. The system has been proven to effectively capture peak river flows and elevated groundwater levels, as it did across the country during the winter of 2024, and provide local-scale insights, as exemplified during a specific flood event in Varde, west Denmark. This study demonstrates how groundwater flooding, often neglected in operational forecasting, can be effectively incorporated at a national scale to support more informed flood management.
Bridging the 39Ar–14C Groundwater Dating Gap: A Dual-Permeability Transport Perspective Based on Numerical Modeling and Field Data S. L. Musy, K. Hinsby, D. Wachs, J. Sültenfuss, L. Troldborg, W. Aeschbach, O. S. Schilling, R. Purtschert Water Resources Research, 2025 Groundwater dating studies rely on environmental tracers to estimate residence times, but most available reliable tracers cover either short (days to decades; e.g., 222 Rn, 3 H/ 3 He, 85 Kr) or extended timescales (millennia to millions of years; e.g., 4 He, 36 Cl, 81 Kr). This leaves a critical gap in age information for intermediate residence times (50–30,000 years), which are essential for groundwater resources management. Argon‐39 ( t 1/2 = 269 years) and Carbon‐14 ( t 1/2 = 5,730 years) could fill this gap, yet apparent groundwater ages estimated with these tracers often show systematic discrepancies, with 39 Ar‐ages appearing younger than 14 C‐ages. While mixing and geochemical reactions have been suggested as possible explanations, these mechanisms alone do not fully resolve the observed differences. Despite numerous studies using 39 Ar– 14 C dating, no approach has fully reconciled these inconsistencies, particularly in dual‐permeability systems. This study addresses this gap by explicitly modeling tracer transport and production processes, integrating both numerical simulations and field observations to improve groundwater age interpretations. We combined explicit numerical simulations of reactive tracer transport with multi‐tracer field data from Denmark to systematically evaluate the physical and chemical processes affecting 39 Ar and 14 C activities. Our results demonstrate the systematic biases introduced by depth‐dependent underground production of 39 Ar, mixing processes, and diffusive exchange between mobile and immobile groundwater zones in dual‐permeability media. Thus, this study provides a quantitative framework to address transport biases in 14 C and 39 Ar groundwater dating, allowing for more accurate groundwater residence time estimation and better‐informed decision‐making in water management in both semi‐arid and humid regions.
CAMELS-DK: Hydrometeorological time series and landscape attributes for 3330 Danish catchments with streamflow observations from 304 gauged stations Jun Liu, Julian Koch, Simon Stisen, Lars Troldborg, Anker Lajer Højberg, Hans Thodsen, Mark F. T. Hansen, Raphael J. M. Schneider Earth System Science Data, 2025 Large samples of hydrometeorological time series and catchment attributes are critical for improving the understanding of complex hydrological processes, hydrological model development, and performance benchmarking. CAMELS (Catchment Attributes and Meteorology for Large-sample Studies) datasets have been developed in several countries and regions around the world, providing valuable data sources and test beds for hydrological analysis and new frontiers in data-driven hydrological modeling. Regarding the lack of samples from lowland, groundwater-dominated, small-sized catchments, we develop an extensive repository of a CAMELS-style dataset for Denmark (CAMELS-DK). This CAMELS addition is the first containing both gauged and ungauged catchments as well as detailed groundwater information. The dataset provides dynamic and static variables for 3330 catchments covering all of Denmark from various hydrogeological datasets, meteorological observations, and a well-established national-scale hydrological model. For 304 of those catchments, streamflow observations are provided, whereas simulated streamflow is provided for all 3330 catchments. The dataset contains time series spanning 30 years (1989–2019) with a daily time step, and the data will be updated once new observations and model simulations become available. The dense and full spatial coverage for all 3330 catchments, instead of only gauged catchments, together with the addition of various simulation data from a distributed, process-based model, enhances the applicability of such CAMELS data, for example, for the development of data-driven and hybrid physically informed modeling frameworks or other cases where consistent full spatial coverage is required. We also provide quantities related to the human impact on the hydrological system in Denmark, such as groundwater abstraction and irrigation. The CAMELS-DK dataset is freely available at https://doi.org/10.22008/FK2/AZXSYP (Koch et al., 2024).
Model and Ensemble Indicator-Guided Assessment of Robust, Exploitable Groundwater Resources for Denmark Hans Jørgen Henriksen, Lars Troldborg, Maria Ondracek Sustainability Switzerland, 2024 Groundwater constitutes 99% of the Earth’s liquid freshwater and is crucial for human health, economic development, and ecosystem sustainability. This study assesses groundwater sustainability in Denmark by employing a comprehensive hydrological model and a set of ensemble indicators. The paper describes the methodology and the results based on nine selected indicators. Three indicators focus on recharge capture and aquifer sustainability, one focuses on groundwater level and wetland capture, two focus on baseflow and drainage flow capture, and three focus on eco flow capture. Our findings highlight that while overall exploitable groundwater resources are estimated at 1.1 billion m3/year, significant regional disparities exist, with certain areas, notably Zealand, facing over-exploitation rates exceeding 250% of sustainable limits. The indicators developed not only provide a framework for assessing current groundwater resource limits, but also serve as a basis for future monitoring and adaptive management strategies. This research underscores the need for stakeholder engagement and integrated approaches to ensure the sustainability of groundwater resources in the face of growing anthropogenic pressures and climate change. Our work contributes to the ongoing discourse on sustainable water management and offers a robust methodology for assessing groundwater sustainability.
Modeling groundwater redox conditions at national scale through integration of sediment color and water chemistry in a machine learning framework Julian Koch, Hyojin Kim, Joel Tirado-Conde, Birgitte Hansen, Ingelise Møller, Lærke Thorling, Lars Troldborg, Denitza Voutchkova, Anker Lajer Højberg Science of the Total Environment, 2024 Redox conditions play a crucial role in determining the fate of many contaminants in groundwater, impacting ecosystem services vital for both the aquatic environment and human water supply. Geospatial machine learning has previously successfully modelled large-scale redox conditions. This study is the first to consolidate the complementary information provided by sediment color and water chemistry to enhance our understanding of redox conditions in Denmark. In the first step, the depth to the first redox interface is modelled using sediment color from 27,042 boreholes. In the second step, the depth of the first redox interface is compared against water chemistry data at 22,198 wells to classify redox complexity. The absence of nitrate containing water below the first redox interface is referred to as continuous redox conditions. In contrast, discontinuous redox conditions are identified by the presence of nitrate below the first redox interface. Both models are built using 20 covariate maps, encompassing diverse hydrologically relevant information. The first redox interface is modelled with a mean error of 0.0 m and a root-mean-squared error of 8.0 m. The redox complexity model attains an accuracy of 69.8 %. Results indicate a mean depth to the first redox interface of 8.6 m and a standard deviation of 6.5 m. 60 % of Denmark is classified as discontinuous, indicating complex redox conditions, predominantly collocated in clay rich glacial landscapes. Both maps, i.e., first redox interface and redox complexity are largely driven by the water table and hydrogeology. The developed maps contribute to our understanding of subsurface redox processes, supporting national-scale land-use and water management.
Groundwater resilience, security, and safety in the four largest cities in Denmark L. F. Jorgensen, L. Troldborg, M. Ondracek, I. K. Seidenfaden, J. Kidmose, C. Vangsgaard, K. Hinsby Acque Sotterranee Italian Journal of Groundwater, 2024 Denmark's complete reliance on groundwater for water supply presents a unique case study in management of natural resources, urban planning, and water resilience in the face of climate change. This paper examines the groundwater management strategies in Denmark in general, focusing on Denmark's four largest cities—Copenhagen, Aarhus, Odense, and Aalborg— each facing distinct challenges due to their demographic, geographical, hydrogeological, and economic characteristics. Through analysis of these cities' approaches to groundwater management, this research contributes to the global discourse on sustainable urban water supply systems. As coastal groundwater cities (CGC), these urban areas must navigate the complexities of sustaining growing populations, mitigating climate change impacts, and coastal processes while ensuring the long-term viability of their groundwater resources. Copenhagen and Aalborg, built atop semi-confined fractured and locally karstic carbonate rocks, highlights the specific challenges associated with karstic groundwater systems, while, Aarhus, and Odense built on glaciofluvial aquifers faces different issues. The different groundwater challenges in these cities underscores the importance of integrating urban development with water resource management and environmental sustainability, offering valuable insights and lessons learned for other regions facing similar challenges. This study, thus not only sheds light on Denmark's groundwater management practices, but also emphasizes the need for innovative solutions to ensure the resilience of urban water supply systems in a changing climate and increasing pressures of emerging organic contaminants and elevated concentrations of geogenic elements induced by water abstraction and fluctuating water tables. Advanced Danish monitoring and modelling tools applied to support decision-making and innovation within the water sector are continuously developed and improved to support resilient and sustainable management of the available water resources.
A national-scale hybrid model for enhanced streamflow estimation - consolidating a physically based hydrological model with long short-term memory (LSTM) networks Jun Liu, Julian Koch, Simon Stisen, Lars Troldborg, Raphael J. M. Schneider Hydrology and Earth System Sciences, 2024 Accurate streamflow estimation is essential for effective water resource management and adapting to extreme events in the face of changing climate conditions. Hydrological models have been the conventional approach for streamflow interpolation and extrapolation in time and space for the past few decades. However, their large-scale applications have encountered challenges, including issues related to efficiency, complex parameterization, and constrained performance. Deep learning methods, such as long short-term memory (LSTM) networks, have emerged as a promising and efficient approach for large-scale streamflow estimation. In this study, we have conducted a series of experiments to identify optimal hybrid modeling schemes to consolidate physically based models with LSTM aimed at enhancing streamflow estimation in Denmark. The results show that the hybrid modeling schemes outperformed the Danish National Water Resources Model (DKM) in both gauged and ungauged basins. While the standalone LSTM rainfall–runoff model outperformed DKM in many basins, it faced challenges when predicting the streamflow in groundwater-dependent catchments. A serial hybrid modeling scheme (LSTM-q), which used DKM outputs and climate forcings as dynamic inputs for LSTM training, demonstrated higher performance. LSTM-q improved the mean Nash–Sutcliffe efficiency (NSE) by 0.22 in gauged basins and 0.12 in ungauged basins compared to DKM. Similar accuracy improvements were achieved with alternative hybrid schemes, i.e., by predicting the residuals between DKM-simulated streamflow and observations using LSTM. Moreover, the developed hybrid models enhanced the accuracy of extreme events, which encourages the integration of hybrid models within an operational forecasting framework. This study highlights the advantages of synergizing existing physically based hydrological models (PBMs) with LSTM models, and the proposed hybrid schemes hold the potential to achieve high-quality large-scale streamflow estimations.
Evaluating the impact of muon-induced cosmogenic 39Ar and 37Ar underground production on groundwater dating with field observations and numerical modeling Stephanie Musy, Klaus Hinsby, Lars Troldborg, Hugo Delottier, Sophie Guillon, Philip Brunner, Roland Purtschert Science of the Total Environment, 2023 Groundwater dating by radioactive cosmogenic tracers such as 39Ar relies on the decay rate from a known initial atmospheric activity (100%modern). Thereby, it is assumed that cosmogenic 39Ar production in the subsurface is negligible at depths below the water table and that contributions from natural rock radioactivity are minor or missing. Here we present 39Ar data from aquifers located in quaternary glacial sediments and tertiary limestones in Denmark, which unequivocally demonstrate that cosmogenic production can induce considerable age biases. 39Ar values larger than 100%modern are observed at relatively shallow groundwater depths in non-radiogenic rocks. These activities are compared to calculations based on previously assessed depth-dependent production rates in rocks and realistic estimates of the emanated fractions to the water phase. The water residence time distribution with depth, which was determined by numerical flow modeling and particle tracking, underpinned the significance of muon-induced 39Ar production. The short-lived isotope 37Ar is produced by similar processes as 39Ar and demonstrated its usefulness as an indicator of local underground production in an aquifer. The significance of cosmogenic underground production in other possible recharge scenarios was then assessed by explicitly simulating the radioargon accumulation and decay in a 2D synthetical numerical model. These simulations demonstrated that underground production is negligible when the water infiltrates freely in a porous aquifer. However, in the presence of a confining layer impeding the infiltration at shallow depths (<30 m), as is the case in our study site in Denmark for instance, over-modern 39Ar activities (>100%modern) may occur. The age concluded from the dissolved activities is then possibly biased towards young values. Special attention should thus be paid to the recharge rates when using 39Ar for dating groundwater. 37Ar activities provide complementary information about the strength and mechanisms of underground production.
Post Audit of Groundwater Model Predictions under Changing Conditions Jacob Kidmose, Lars Troldborg, Jens Christian Refsgaard Water Switzerland, 2023 Post audits of hydrological or groundwater models are the last part of the modelling protocol, where the original model predictions are tested using new data obtained after a certain period. The evaluation of model predictions and associated predictive uncertainty was performed by comparing an original hydrological model, a model with post audited geology, and a model with post audited geology and calibrated against new types of observation data. The post audit showed original model predictions close to what was observed (in terms of abstracted volumes necessary to lower a shallow groundwater table). In contrast to the robust original model predictions, the original model underestimated the predictive uncertainty compared to the assessments of uncertainty using the new and updated post audit model. To ensure a robust model evaluation, we propose a four-step post audit protocol, including (1) testing the validity of the original model predictions with new data, (2) estimating the predictive uncertainty of the original model, (3) producing a new post audit model(s) based on revising the conceptual model and calibration, and (4) assessing the predictive uncertainty of the new post audit models. The work presented here was motivated by the lack of studies that, after a certain time, have re-evaluated model predictions (post audit) with new data.
Use of expert elicitation to assign weights to climate and hydrological models in climate impact studies Eva Sebok, Hans Jørgen Henriksen, Ernesto Pastén-Zapata, Peter Berg, Guillaume Thirel, Anthony Lemoine, Andrea Lira-Loarca, Christiana Photiadou, Rafael Pimentel, Paul Royer-Gaspard, Erik Kjellström, Jens Hesselbjerg Christensen, Jean Philippe Vidal, Philippe Lucas-Picher, Markus G. Donat, Giovanni Besio, María José Polo, Simon Stisen, Yvan Caballero, Ilias G. Pechlivanidis, Lars Troldborg, Jens Christian Refsgaard Hydrology and Earth System Sciences, 2022
Assessing urban groundwater table response to climate change and increased stormwater infiltration Geological Survey of Denmark and Greenland Bulletin, 2013
Water balance evaluation in Denmark using remote sensing-driven land surface modelling and spatially distributed hydrological modelling IAHS AISH Publication, 2007
