Proceedings of the

The 33rd European Safety and Reliability Conference (ESREL 2023)
3 – 8 September 2023, Southampton, UK

A Case Study of Ecological Suitability of Mussel and Seaweed Cultivation using Bivariate Copula Functions

Rieke Santjer1,a, Patricia Mares-Nasarre2,c, Ghada El Serafy1,b and Oswaldo Morales-Nápoles2,d

1Marine and Coastal Systems, Deltares, Delft, The Netherlands Delft Institute of Applied Mathematics, Delft University of Technology, The Netherlands.

2Hydraulic Structures and Flood Risk, Delft University of Technology, Delft, The Netherlands.


Aquaculture is gaining importance in the current context of continuous growth population as a source of (local) food resources and its potential of being combined with other uses at sea (e.g.: offshore energy production or tourism). Consequently, within the European Horizon 2020 project UNITED, the combination of mussel and seaweed cultivation together with wind energy production in the German North Sea is investigated. Here, the feasibility of the mussel Mytilus edulis and seaweed Saccharina latissima based on their ecological needs is analysed. Ecological data from a three-dimensional hydrodynamic and ecological model covering the northwest European continental shelf is used. For each of the two species, three variables are selected as relevant, including in both of them the water temperature. In addition, chlorophyll-a and dissolved oxygen are considered for mussels, and dissolved inorganic nitrogen and phosphorus are selected for seaweed. Temperature is selected as dominant variable so its daily maxima for the growing months are selected together with the concomitants of the other variables. Gaussian Mixture distributions (see McLachlan and Peel (2000)) and truncated Gaussian kernel distributions (see Bowman and Azzalini (1997)) are used to model the marginal distributions of the random variables. Bivariate copulas are fitted for each pair of variables to describe their dependence structure. Finally, probabilities of being within the optimal ranges of the relevant variables are calculated. Chlorophyll-a concentration and temperature are the most limiting variables for mussels and seaweed, respectively. Relatively low probabilities are obtained, since ranges for optimal growth are considered. Generally, it is feasible to cultivate mussels and seaweed at this location based on the selected ecological variables, as the probability of variables reaching values outside growth limits for the species is low.

Keywords: aquaculture, Mussels, Seaweed, Feasibility, Multi-use, Marginal distribution, Copulas, Probability.

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