Innovating the calibration of a national-scale integrated hydrological model
Authors: Schneider Raphael , Troldborg Lars , Højberg Anker Lajer , Ondracek Maria , Christiansen David Terpager , Stisen Simon 
Published: March 2024

The National Hydrological Model for Denmark (DK-model) is a distributed, integrated hydrological model coupling 3D groundwater flow to descriptions of root zone processes, overland flow and river routing, including anthropogenic interference with the hydrological cycle. It covers all of Denmark (~43,000km2) at 500m and 100m grid scale. Its constant development over the last three decades has both been driven by research projects and projects for public authorities. It is being used for various tasks such as water resource assessments, climate change impact assessments, hydrological real-time monitoring and nutrient transport studies.Recently, we endeavored novel ways to calibrate and parameterize the DK-model. The model is placed on the edge between research interest and practical applications, with a demand for adequately representing various aspects of the hydrological cycle across the entirety of the model domain. In combination with its large-scale distributed nature and high computational demand, conventional (groundwater) model optimization techniques are challenged: The complex nature and versatile applications of the DK-model require suitable parametrization schemes and inclusion of diverse calibration and evaluation data, beyond conventional groundwater head observations and streamflow. This also leads to trade-offs between the multiple objective functions. Hence, we moved beyond previously used single solution, gradient-based optimization algorithms.The Pareto Archived Dynamically Dimensioned Search (PADDS) algorithm allows us to use a global parameter optimization, effective even at a few hundred model runs. Another major advantage of PADDS is that it does not require the a-priori weighting of objective function groups &#8211; instead, it explores the tradeoffs (pareto front) between the different objective function groups, allowing weighting after gaining knowledge about tradeoffs during the optimization process. Also, all solutions explored during the optimization are stored and remain open to analysis after finished optimization. This not only sheds light on tradeoffs between different objective functions in a unique manner, but also supports understanding of parameter sensitivity and uncertainty in a manner which otherwise is hard to achieve due to computational constraints.Moreover, we included evapotranspiration patterns from satellite products as well as a machine learning based estimate of artificial drain flow as novel spatial data in the model evaluation. This helps us constraining some of the model processes crucial for e.g. nutrient transport, but otherwise poorly constrained by conventional data such as streamflow (305 stations) and groundwater heads (24,000 wells) covering practically the entire model domain.We explored the benefits of this optimization setup applied to the DK-model, advancing not only the calibration process itself, but also our understanding of model process representation and performance.