Introduction
Estuaries worldwide have been closed off from marine influence for flood protection and freshwater supply management. While effective for these societal needs, this strategy significantly alters estuarine ecosystems by eliminating tidal dynamics and disrupting marine-freshwater interactions, leading to blocked fish migration routes and reduced biodiversity. Consequently, there is growing interest in reintroducing controlled saltwater inflows to restore estuarine functions without compromising freshwater availability.
A key challenge in this approach is to establish a dynamic equilibrium in which saltwater inflow and outflow balance over a tidal cycle. Achieving this balance is critical to preventing salt intrusion into upstream freshwater zones. It requires detailed insight into complex hydrodynamic processes – such as stratification, mixing, and the flow dynamics in (former) tidal channels – that govern the salinity distribution in the estuary. Understanding these processes is essential for developing effective management strategies
This study focuses on the Haringvliet, a former estuary in the Rhine-Meuse Delta in the Netherlands, where controlled saltwater inflow has been reintroduced via regulated sluice operations. These trials are supported by extensive ecological monitoring and measurements of hydrodynamics and salinity. Observations show that flushing salt from the estuary’s channels is difficult (Kranenburg et al., 2023), emphasizing the need for optimized sluice management.. However, presently it is still unknown what saltwater inflow duration and timing result in acceptable or excessive salt intrusion.
To address this, we investigate the conditions needed to establish a dynamic equilibrium in the Haringvliet. An approach is developed that combines a detailed 3D numerical model with a simplified analytical model. The analytical model serves two major purposes: (1) to develop a sluice operation protocol that optimizes controlled saltwater inflow while preserving upstream freshwater conditions, and (2) to enhance understanding of the stratified hydrodynamics in the Haringvliet, offering valuable knowledge for future estuarine restoration and management efforts.
Methods
The field measurements from the saltwater reintroduction trials, especially salinity and velocity profiles in the deeper pit structures, provided critical insights into the estuary’s response (Kranenburg et al., 2023). Achieving a stable dynamic equilibrium during these trials proved challenging. Therefore, the field data are not used directly to define equilibrium states but instead serve to validate controlled 3D numerical simulations, which allow for a systematic exploration of equilibrium states under known and reproducible conditions.
A detailed 3D D-HYDRO model of the Haringvliet (Deltares, 2023) was used, a hydrostatic model with an unstructured horizontal mesh (typical cell side lengths of 60 m) and a combined z-sigma vertical grid (z-layer resolution of 0.125 m) to accurately resolve halocline dynamics. The model was validated against field data and used to simulate various combinations of sluice operations and sea salinity conditions with steady tidal forcing, to systematically explore conditions that lead to dynamic equilibrium. Due to the high computational cost, only a limited number of scenarios could be explored.
To overcome this limitation, a simplified analytical model of the Haringvliet system was developed, enabling broader exploration of the parameter space. The estuary is schematized horizontally into pits and channels, connected by sills of fixed height, each with a defined hypsometry. Vertical stratification is represented by a two-layer system, with denser saltwater down in the channels and pits and freshwater above. The model simulates three processes: (1) saltwater inflow through the sluices, using dilution relationships derived from the 3D model; (2) vertical mixing at the salt–freshwater interface, parameterized using the Richardson number and calibrated with 3D model outputs; and (3) outflow of the upper layer. With this approach, the analytical model computes the salt intrusion length for the dynamic equilibrium state in the estuary based on an inflow, outflow and sea salinity conditions.
Results
Using the 3D model, 59 simulations were conducted, covering six distinct sea salinity levels (1,000–10,000 mg/L), inlet volumes ranging from 1.3 to 20 million m³ per tide, and outflow volumes between 10 and 80 million m³ per tide. For each simulation, the establishment of a dynamic equilibrium was assessed, along with the extent of salt intrusion into the system. Results align well with field trial observations. The 3D model allowed partial filling of the parameter space and provided insight into how equilibrium location depends on system parameters. However, due to limited resolution in the simulated parameter space, these relationships remain approximate.
The analytical model was calibrated with the vertical mixing parameter using 3D model results. The calibrated mixing intensity varies with outflow volume: stronger mixing for lower outflows and reduced mixing at higher outflows. The calibrated model closely reproduced both the presence of equilibrium and the salt intrusion length observed in the 3D simulations and field data, making it a fast and reliable alternative for predicting system behaviour without the computational cost of 3D modelling.
After calibration, the analytical model was used to perform nearly 10,000 simulations, enabling high-resolution exploration of the parameter space – something not feasible with the 3D model alone.
Both models showed that the formation of a dynamic equilibrium is highly sensitive to sea salinity levels. At higher salinities, equilibrium can only be maintained with small inflow volumes and is generally confined to the first pit in the system. Once inflow volumes become large enough for saltwater to pass the first sill, salt intrusion becomes difficult to control, regardless of outflow capacity. In contrast, at lower sea salinities, equilibrium can be sustained over a broader range of inflow volumes. In such cases, salt intrusion may extend farther upstream, requiring sufficiently large outflow volumes to maintain control.
Conclusions
This study demonstrates that achieving a dynamic equilibrium in former estuarine systems with controlled saltwater inflow critically depends on the interplay between sea salinity, inflow and outflow volumes. By calibrating an analytical model using results from a detailed 3D numerical model, we identified the parameter ranges under which salt intrusion can be effectively managed.
The analytical model captures key physical processes, including vertical stratification, and closely reproduces both 3D model results and field observations. It offers a fast and practical tool for designing sluice operation protocols, without the need for extensive computational resources.
These findings support to the development of effective management strategies for estuarine restoration, while safeguarding upstream freshwater resources, with broader applicability to similar modified estuarine systems worldwide.
