Climate change is raising the wave energy that reaches the coast. Sea level rise deepens the water near the shore, so larger and longer waves can travel further before they break, and warming oceans weaken coral reefs that once absorbed this energy. At the same time, coastal communities ask for protection that keeps the natural view of the sea. Submerged breakwaters meet both needs. They keep their crest below the water level, so they stay out of sight and let only part of the wave energy pass over the crest.

Design practice describes this transmission with a single bulk transmission coefficient 𝐾𝑡, the ratio of the transmitted to the incident significant wave height. This one number scales the whole sea state down at once. It says nothing about the individual waves that reach the water behind the structure, and nothing about the transmitted wave period. A structure behind the breakwater, such as a moored vessel or a revetment, responds to individual waves, and often to waves that are both high and long. Thus, a single coefficient hides the information that such a structure needs.

This study proposes a wave-by-wave model of the transmission over a submerged breakwater, built with a vine copula. The model is developed using the 32 small-scale physical model tests of van Gent et al. (2023). In each test, the incident and the transmitted individual waves are matched by a zero-crossing procedure, which pairs 30,924 of the 33,533 incident waves (92.2%). Each matched pair gives four normalized variables, the incident and transmitted wave heights and periods. The model is built in two parts. First, a marginal distribution is fitted to each of the four variables and its parameters are regressed on the bulk sea state. Second, a regular vine copula is selected to describe the dependence between the four variables, a single copula family is fitted at each of its edges, and the copula parameters are regressed on the bulk sea state as well. Both parts are driven by the same four bulk parameters of the sea state, so the joint distribution of the transmitted height and the transmitted period can be obtained for a new sea state without measuring its individual waves.

The predicted marginal distributions reconstruct the wave heights well, with 𝑅² = 0.99, and the wave periods less well. The selected vine is a D-vine, and it reproduces the measured four-dimensional dependence with 𝑅² = 0.99 on the rank scale. Compared against the single coefficient, the model shows that 𝐾𝑡 misallocates the transmission across the wave heights. It understates the transmission of the smallest waves, at 1.78 𝐾𝑡, and overstates that of the largest waves, at 0.83 𝐾𝑡, which break over the crest. Applied to every incident wave, the coefficient therefore over-predicts the largest transmitted waves, here the transmitted 𝐻2% by 9%. The model predicts the individual transmitted height more accurately than 𝐾𝑡 in all 32 tests, with a median 𝑅² of 0.57 against 0.38, and its 90% interval contains about 90% of the waves. It also predicts the transmitted period and the joint behaviour of the height and the period, which a single coefficient cannot. Note that the dependence between the transmitted height and the period makes a wave that is both high and long about 1.5 times as likely as it would be under independence. In a design example, accounting for this dependence doubles the estimated number of damaging waves.

It is concluded that a vine copula turns the single transmission coefficient into a full joint distribution of the transmitted wave height and period, and keeps the wave-to-wave variability and the dependence that a single coefficient discards. Thus, the model allows a probabilistic design of the water behind a submerged breakwater, and gives the transmitted period that current practice leaves out.
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The completion of a fourth sea dike (Binh Minh 4) in Kim Đông, Ninh Bính, in Vietnam will reshape local hydrodynamics and will result in land reclamation. Thus, the balance between mangrove forest health, flood protection, local livelihoods and development goals will be changed. This report addresses the impacts and fills knowledge gaps regarding the completion of this fourth dike on hydrodynamics in Kim Đông, and examines hydrodynamic, ecological, governance, and social factors in relation to the mangrove ecosystems in the region.

To achieve this, a governance analysis and system analysis are combined with a hydraulic analysis and a conceptual hydrodynamic model in Delft3D. This approach is supported by literature and institutional reviews, expert interviews, a community survey, and hydraulic data, including satellite-derived wave and wind records, as well as field measurements. Together, these elements shape the model set-up, boundary conditions and interpretation. The modelling framework compares a baseline situation without a dike with two with-dike scenarios, simulating both storm and regular weather conditions. Physical changes in the model are linked to drivers of ecological change, allowing an assessment of their impact on mangrove forests and socio-economic conditions in the area.

Findings from the conceptual Delft3D model indicate that the completion of a fourth dike is likely to reduce tidal connectivity and sediment supply to the enclosed area, leading to longer inundation times and lower water levels. These change in conditions drive mangrove squeeze, reducing habitat, shelter and carbon storage potential. At the same time, land reclamation creates development opportunities for aquaculture. Interventions to mitigate the effects of the fourth dike are presented using a COCD box, and evaluated via a multi-criteria analysis. Suitable interventions are further elaborated on their trade-offs and implementation process.

Decision-making in Vietnam, and in Kim Ðông especially, is highly hierarchical, which limits involvement of local authorities and residents even though they are most affected. Conflicting priorities among sustainability, economic growth and climate adaptation further complicate this involvement in decision making. Additionally, limited data availability and experience with nature-based solutions also constrain adaptive management and long-term monitoring. With this in mind, four potential interventions are assessed: adaptive gate management, mangrove co-management with incentives, sustainable aquaculture \\certification, and a digital monitoring platform. No single measure resolves all challenges. However, co-management with incentives and sustainable aquaculture emerge as promising options that couple ecological restoration with socio-economic benefits, supported by adaptive gate operations and a digital platform to improve coordination and transparency. ... Read more