A modelling study of tidally induced equilibrium sand balances in the North Sea during the Holocene

The present paper describes a depth-integrated modelling approach for tide-induced sediment transport, and its application to the North Sea for various cases during the Holocene sea level rise. The flow model is based on the shallow water equations, while the transport model is based on Galappatti’s asymptotic approach for rivers, now applied to tidal flow situations in two horizontal dimensions (Galappatti, 1983, Galappatti and Vreugdenhil, 1986). The empirical Engelund–Hansen formula for sedimentation / erosion is used as a closure for the sediment exchange term in the transport equation, while variation of the bed height is neglected. The various assumptions in the derivation of the sediment model, and their consequences are addressed step by step. The North Sea area considered in the application is the whole North west European continental shelf, as mapped onto the Dutch Continental Shelf Model. In a series of cyclic period simulations of the present day situation, the sensitivity to parameter variations such as diffusion, equilibrium concentration and adaptation time is analysed, as well as the effect of bathymetry smoothing. Using a suitable and fixed parameter setting, the North Sea tidally induced equilibrium sand balances are simulated for several epochs during the Holocene sea level rise. Both uniform sea level reductions (0, −5, −15, and −35 m. and non-uniform sea level reductions (8500 BP, 8100 BP are considered, based on Jelgersma’s geological uniform sea level curve, and glacio-hydro-isostatic rebound modelling results, respectively. It is concluded that the derived Galappatti model for 2D tidal flow is a feasible approach to get a first assessment of equilibrium sedimentation balance on North Sea scale, and of its possible changes due to the Holocene sea level rise under various simplified assumptions regarding the evolution of coastline and bathymetry, both uniform and non-uniform.