Welsch et al. (2026) The importance of system interactions in hydrodynamic models of parts of complex interconnected deltas

Identification

• Journal: Environmental Modelling & Software
• Year: 2026
• Date: 2026-01-06
• Authors: Niels M. Welsch, Jord Jurriaan Warmink, Suzanne Jmh Hulscher, Denie C.M. Augustijn
• DOI: 10.1016/j.envsoft.2025.106838

Research Groups

• University of Twente, Enschede, Netherlands
• Deltares, Delft, Netherlands (Software developer, model collaborator)
• Dutch Water Authority (Rijkswaterstaat), Netherlands (Model maintainer, data provider, funder)

Short Summary

This study investigates how downstream boundary conditions of hydrodynamic models for parts of interconnected river deltas are affected by external changes. It demonstrates that the impact on water levels depends on distance to boundaries and relative upstream discharge, propagating significantly upstream, thus highlighting the critical need for appropriate boundary selection in such models.

Objective

• To assess to what extent the stage–discharge relation at the downstream boundary of a model representing part of an interconnected river delta is impacted by changing conditions outside the modelled domain, specifically considering sea level rise as a downstream change and more extreme river discharge (increase and decrease) as upstream changes.

Study Configuration

• Spatial Scale: The Dutch river delta, encompassing the Rhine branches, the Meuse, and the Rhine–Meuse–Estuary. The study uses one-dimensional (1D) hydrodynamic models of these river networks.
• Temporal Scale: Validation was performed for the period between 1 June 2021 and 1 January 2023. Scenario analysis involved steady (time-independent) upstream river discharges and downstream sea levels.

Methodology and Data

• Models used:
  • SOBEK 3 (version 3.7.25.55022), developed by Deltares, which numerically solves the 1D shallow water equations.
  • D-RTC (Real-Time Control) module for managing hydraulic structures.
  • Three submodels (Rhine, Meuse, Estuary) were combined into a single, larger model to explicitly resolve internal hydraulic conditions.
• Data sources:
  • Hydrodynamic models and model set-up data: Obtained from the Dutch Water Authority (Rijkswaterstaat) via iplo.nl (specific versions: sobek-rijn-j226-v1a1, sobek-maas-j236-v1a1, sobek-rmm-vzm-j15_5-v4).
  • Water level and discharge data for validation: Acquired from the Dutch Water Authority via waterinfo.rws.nl (observations).
  • Stage–discharge relationships for Rhine submodel boundaries: Derived from results of a two-dimensional (2D) Estuary model (van der Wijk, 2022).
  • Synthetic series for analysis scenarios:
    • Rhine discharge (upstream): 500 cubic metres per second (m³/s) to 18000 m³/s.
    • Meuse discharge (upstream): 30 m³/s (low), 300 m³/s (reference), 3000 m³/s (high).
    • Sea level (downstream): -1.00 metres (m) NAP (low), 0.45 m NAP (reference), 1.50 m NAP (high), 5.10 m NAP (storm surge).

Main Results

• The stage–discharge relationships at the downstream boundaries of submodels are significantly impacted by external conditions, such as sea level and discharge in confluencing rivers.
• The impact on water levels depends on the distance to the boundaries and the relative upstream discharge in the considered rivers.
• Extreme sea levels (e.g., storm surge) cause water level deviations of decimetres to metres, which propagate far upstream (e.g., over 91 kilometres for the Waal at low Rhine discharge).
• For increasing Rhine discharges, the influence of downstream conditions on water levels at location A1 (Waal) diminishes, becoming more discharge-dominated.
• At location A2 (Lek), the impact of downstream conditions (sea level) remains relatively constant and less dependent on Rhine discharge, showing a continuous bias.
• At location A3 (Meuse), water levels are influenced by all three considered boundary conditions (Rhine discharge, Meuse discharge, sea level) to a similar extent, with their relative effects being interdependent.
• The combined model, which explicitly resolves system interactions, provides a more accurate representation of responses to changing downstream conditions compared to submodels relying on static stage–discharge relations.
• Errors introduced by inappropriate boundary conditions can propagate substantially upstream, potentially altering discharge distribution at bifurcations.

Contributions

• Provides a quantitative assessment of how changing external conditions (e.g., climate change impacts like sea level rise and extreme river flows) affect the accuracy and applicability of stage–discharge relations used as boundary conditions in hydrodynamic submodels of interconnected river deltas.
• Demonstrates the significant spatial extent of these impacts, showing that errors can propagate far upstream and influence critical hydraulic processes like discharge distribution at bifurcations.
• Highlights the limitations of using isolated submodels with static boundary conditions for large-scale studies or scenarios outside their original calibration scope.
• Offers a quantitative foundation for modellers to make informed decisions regarding model domain selection and boundary condition definition, advocating for the expansion of model domains to explicitly resolve complex interconnectivity and reduce inherent uncertainties.

Funding

• Rijkswaterstaat as part of the Kennisimpuls Klimaatadaptatie.

Citation

@article{Welsch2026importance,
  author = {Welsch, Niels M. and Warmink, Jord Jurriaan and Hulscher, Suzanne Jmh and Augustijn, Denie C.M.},
  title = {The importance of system interactions in hydrodynamic models of parts of complex interconnected deltas},
  journal = {Environmental Modelling & Software},
  year = {2026},
  doi = {10.1016/j.envsoft.2025.106838},
  url = {https://doi.org/10.1016/j.envsoft.2025.106838}
}