Barrier coast systems connect oceanic and inland waters and support essential ecological functions. Their shallow subtidal and intertidal zones provide key ecosystem services, making it crucial to understand the nonlinear mechanisms driving water motion in these regions, particularly in terms of overtides, mean sea surface elevation, and residual flow. This study introduces a new interpretation framework for analyzing nonlinear processes in tidal systems with shallow regions, extending the established framework by Parker (1991) to account for wetting and drying dynamics. To illustrate this framework, it is applied to a model of the Marsdiep-Vlie double-inlet system in the Wadden Sea, governed by the cross-sectionally averaged shallow water equations, including the Defina (2000) approach to account for wetting and drying. The one-dimensional model bathymetry and planform feature a topographical high and varying channel widths, respectively. We assess contributions of nonlinear forcings to overtides and residual flow, and conduct sensitivity analyses on the effects of longitudinal variations in bottom elevation and channel width. Results confirm that Parker’s findings hold in deeper systems with minimal width variation; however, in systems with intertidal areas, distinct nonlinear processes emerge. Specifically, in these shallow regions, the Water Storage term, Nonlinear Continuity term, and Elevation Effect of the Friction term contribute greatly to generation, while the Nonlinear Continuity term strongly contributes to generation. For mean sea surface elevation, several nonlinear terms are equally important, while residual velocities are predominantly driven by the Nonlinear Continuity term.

Nonlinear tidal processes in water motion, which generate overtides and residual dynamics, are crucial not only for the morphodynamic evolution of tidal systems, but also for the transport of contaminants, nutrients and biogeochemical tracers. Traditional approaches, such as that of Parker (1991), explain these nonlinear processes using perturbation methods that assume a small tidal amplitude-to-depth ratio. While these methods effectively detect nonlinear mechanisms, quantifying their relative importance in practical applications remains challenging. Moreover, this assumption limits their applicability in very shallow and intertidal areas, where it is violated. To address this limitation, we propose a new methodology to assess the relative importance of overtide generation mechanisms. This approach is based on the fully nonlinear shallow water equations, combined with Defina’s (2000) wetting and drying approach to account for subgrid-scale topography. As a first validation step of this methodology, we applied it to a schematization of the Delaware estuary, the same case studied by Parker (1991), where very shallow or intertidal areas are absent. This setup allows for a direct comparison, particularly for the cases where an M₂ tidal constituent was imposed at the seaward boundary. Our analysis confirms the dominant role of the nonlinear continuity term in the M₄ overtide generation, while the combined velocity and sea surface elevation nonlinearity in bed friction plays a secondary role. For the M6 overtide, the quadratic velocity friction term, which accounts only for velocity nonlinearity, plays a pivotal role. Additionally, the combined velocity and sea surface elevation nonlinearity in bed friction is the main driver of mean sea level generation. The inclusion of mean Delaware River runoff enhances the M4 generation while slightly reducing the amplitudes of the M6 tidal constituent, and it leads to an increase in mean sea surface elevation. The observations above are consistent with Parker's results. In future research, the new methodology will be further explored for tidal systems with extensive intertidal areas, where Parker’s approach is no longer applicable.