A robust and well-balanced finite volume solver for investigating the effects of tides on water renewal timescale in the Nador lagoon, Morocco

Coastal lagoons, particularly those not well-connected to the sea, are highly susceptible to continuous water retention, adversely affecting water quality and ecosystems. Understanding and quantifying the processes governing water renewal in such semi-enclosed regions is crucial. Using the principles of constituent-oriented age and residence time theory (www.climate.be/cart), we calculated timescales to explain the water renewal process in semi-enclosed areas. To improve our understanding and define the dynamics of the Nador lagoon, we use two distinct time scales: residence time and exposure time. Residence time indicates the length of time a parcel of water leaves the region of interest for the first time, while exposure time represents the overall length of time a parcel of water remains in that region, including any subsequent inflows. The modeling system adopts an Eulerian approach, including two interlinked model components: the shallow-water equations incorporating bottom friction, eddy viscosity, wind shear stresses, momentum diffusion, and Coriolis forces for modeling hydrodynamics, and a transport-diffusion equation utilized to simulate the advection and diffusion of the passive tracer concentration. The entire system is integrated into a high-order finite volume solver that employs unstructured meshes, upwind numerical fluxes, and slope limiters to achieve precise resolution of steep bathymetric gradients that may arise in the approximate solution. The scheme is non-oscillatory and preserves the conservation properties. In this research, we explore various situations related to the connection between the Mediterranean Sea and the Nador lagoon. Specifically, we suggest novel entry points that have the potential to significantly decrease the water residence within the lagoon.