Efficient representation of transient tidal overheight in a coastal groundwater flow model using a phase-averaged tidal boundary condition

Ocean tides cause water table overheight near the seaward boundary of coastal aquifers which can have a large impact on groundwater flows and saltwater intrusion. Despite this, regional-scale coastal groundwater flow models often neglect the effects of ocean tides or alternatively assume that the influences of ocean tides and sea level are constant over time. These simplifications are often required because simulation of the phase-resolved tidal signal at a coastal boundary is computationally demanding. Our objective was to derive a phaseaveraged tidal boundary condition for application along gently sloping coastlines that enables simulation of real, complex tidal signals combined with sea-level changes due to meteorological effects. The boundary condition extends an existing analytical solution of tidal overheight by including an empirical correction function for conditions where the assumptions of the existing solution are violated. The correction function was developed by conducting a parametric study on an idealized two-dimensional cross-sectional coastal aquifer model and considering the effects of parameters including horizontal hydraulic conductivity, vertical anisotropy, specific yield, aquifer thickness, and beach slope. The performance of the new phase-averaged tidal boundary condition was assessed using a three-dimensional groundwater flow model of the island of Spiekeroog, Northwest Germany, which comprises complex coastal morphology with non-planar beach slopes. Simulations applying the new boundary condition were compared to simulations that adopted a phase-resolved tidal boundary condition and to observed groundwater levels. Accounting for time-varying changes in the tidal signal and sea level was found to be critical to simulate observed data and to adequately reproduce the transient tidal overheight simulated by the phase-resolved model. The performance of the new phase-averaged boundary condition in the regional-scale model varied depending on how the coastal morphology was represented in the boundary condition with local morphological features increasingly important for lower intertidal vertical infiltration capacity (low isotropic hydraulic conductivity or high vertical anisotropy) or specific yield. In conclusion, the new boundary condition presented overcomes current limitations in simulating transient tidal overheight in regionalscale groundwater models.