A new analytical framework for assessing the effect of sea-level rise and dredging on tidal damping in estuaries

This paper explores different analytical solutions of the tidal hydraulic equations in convergent estuaries. Linear and quasi-nonlinear models are compared for given geometry, friction, and tidal amplitude at the seaward boundary, proposing a common theoretical framework and showing that the main difference between the examined models lies in the treatment of the friction term. A general solution procedure is proposed for the set of governing analytical equations expressed in dimensionless form, and a new analytical expression for the tidal damping is derived as a weighted average of two solutions, characterized by the usual linearized formulation and the quasi-nonlinear Lagrangean treatment of the friction term. The different analytical solutions are tested against fully nonlinear numerical results for a wide range of parameters, and compared with observations in the Scheldt estuary. Overall, the new method compares best with the numerical solution and field data. The new accurate relationship for the tidal damping is then exploited for a classification of estuaries based on the distance of the tidally averaged depth from the ideal depth (relative to vanishing amplification) and the critical depth (condition for maximum amplification). Finally, the new model is used to investigate the effect of depth variations on the tidal dynamics in 23 real estuaries, highlighting the usefulness of the analytical method to assess the influence of human interventions (e. g. by dredging) and global sea-level rise on the estuarine environment.