Satellite-based earth observations offer great opportunities to improve spatial model predictions by means of spatial-pattern-oriented model evaluations. In this study, observed spatial patterns of actual evapotranspiration (AET) are utilised for spatial model calibration tailored to target the pattern performance of the model. The proposed calibration framework combines temporally aggregated observed spatial patterns with a new spatial performance metric and a flexible spatial parameterisation scheme. The mesoscale hydrologic model (mHM) is used to simulate streamflow and AET and has been selected due to its soil parameter distribution approach based on pedo-transfer functions and the build in multi-scale parameter regionalisation. In addition two new spatial parameter distribution options have been incorporated in the model in order to increase the flexibility of root fraction coefficient and potential evapotranspiration correction parameterisations, based on soil type and vegetation density. These parameterisations are utilised as they are most relevant for simulated AET patterns from the hydrologic model. Due to the fundamental challenges encountered when evaluating spatial pattern performance using standard metrics, we developed a simple but highly discriminative spatial metric, i.e. one comprised of three easily interpretable components measuring co-location, variation and distribution of the spatial data. The study shows that with flexible spatial model parameterisation used in combination with the appropriate objective functions, the simulated spatial patterns of actual evapotranspiration become substantially more similar to the satellite-based estimates. Overall 26 parameters are identified for calibration through a sequential screening approach based on a combination of streamflow and spatial pattern metrics. The robustness of the calibrations is tested using an ensemble of nine calibrations based on different seed numbers using the shuffled complex evolution optimiser. The calibration results reveal a limited trade-off between streamflow dynamics and spatial patterns illustrating the benefit of combining separate observation types and objective functions. At the same time, the simulated spatial patterns of AET significantly improved when an objective function based on observed AET patterns and a novel spatial performance metric compared to traditional streamflow-only calibration were included. Since the overall water balance is usually a crucial goal in hydrologic modelling, spatial-pattern-oriented optimisation should always be accompanied by traditional discharge measurements. In such a multi-objective framework, the current study promotes the use of a novel bias-insensitive spatial pattern metric, which exploits the key information contained in the observed patterns while allowing the water balance to be informed by discharge observations.

The process of model evaluation is not only an integral part of model development and calibration but also of paramount importance when communicating modelling results to the scientific community and stakeholders. The modelling community has a large and well-tested toolbox of metrics to evaluate temporal model performance. In contrast, spatial performance evaluation does not correspond to the grand availability of spatial observations readily available and to the sophisticate model codes simulating the spatial variability of complex hydrological processes. This study makes a contribution towards advancing spatial-pattern-oriented model calibration by rigorously testing a multiple-component performance metric. The promoted SPAtial EFficiency (SPAEF) metric reflects three equally weighted components: correlation, coefficient of variation and histogram overlap. This multiple-component approach is found to be advantageous in order to achieve the complex task of comparing spatial patterns. SPAEF, its three components individually and two alternative spatial performance metrics, i.e. connectivity analysis and fractions skill score, are applied in a spatial-pattern-oriented model calibration of a catchment model in Denmark. Results suggest the importance of multiple-component metrics because stand-alone metrics tend to fail to provide holistic pattern information. The three SPAEF components are found to be independent, which allows them to complement each other in a meaningful way. In order to optimally exploit spatial observations made available by remote sensing platforms, this study suggests applying bias insensitive metrics which further allow for a comparison of variables which are related but may differ in unit. This study applies SPAEF in the hydrological context using the mesoscale Hydrologic Model (mHM; version 5.8), but we see great potential across disciplines related to spatially distributed earth system modelling.

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.

The paper analyzes the national DK-model hydrological information and prediction (HIP) system and HIP portal viewed as a ‘digital twin’ and how the introduction of real-time dynamic updating of the DK-model HIP simulations can make room for plug-in submodels with real-time boundary conditions made available from an HIP portal. The possible feedback to a national real-time risk knowledge base during extreme events (flooding and drought) is also discussed. Under climate change conditions, Denmark is likely to experience more rain in winter, more evapotranspiration in summer, intensified cloudbursts, drought, and sea level rise. These challenges were addressed as part of the Joint Governmental Digitalization Strategy 2016–2020 for better use and sharing of public data about the terrain, water, and climate to support climate adaptation, water management, and disaster risk reduction. This initiative included the development of a new web-based data portal (HIP portal) developed by the Danish Agency for Data Supply and Infrastructure (SDFI). GEUS delivered 5 terabytes of hydrological model data to the portal, with robust calibration methods and hybrid machine learning (ML) being key parts of the deliverables. This paper discusses the challenges and potentials of further developing the HIP digital twin with ‘plug-in digital twins’ for local river basins, including feedback to the national level.

Geological heterogeneity is a very important factor to consider when developing geological models for hydrological purposes. Using statistically based stochastic geological simulations, the spatial heterogeneity in such models can be accounted for. However, various types of uncertainties are associated with both the geostatistical method and the observation data. In the present study, TProGS is used as the geostatistical modeling tool to simulate structural heterogeneity for glacial deposits in a head water catchment in Denmark. The focus is on how the observation data uncertainty can be incorporated in the stochastic simulation process. The study uses two types of observation data: borehole data and airborne geophysical data. It is commonly acknowledged that the density of the borehole data is usually too sparse to characterize the horizontal heterogeneity. The use of geophysical data gives an unprecedented opportunity to obtain high‐resolution information and thus to identify geostatistical properties more accurately especially in the horizontal direction. However, since such data are not a direct measurement of the lithology, larger uncertainty of point estimates can be expected as compared to the use of borehole data. We have proposed a histogram probability matching method in order to link the information on resistivity to hydrofacies, while considering the data uncertainty at the same time. Transition probabilities and Markov Chain models are established using the transformed geophysical data. It is shown that such transformation is in fact practical; however, the cutoff value for dividing the resistivity data into facies is difficult to determine. The simulated geological realizations indicate significant differences of spatial structure depending on the type of conditioning data selected. It is to our knowledge the first time that grid‐to‐grid airborne geophysical data including the data uncertainty are used in conditional geostatistical simulations in TProGS. Therefore, it provides valuable insights regarding the advantages and challenges of using such comprehensive data.