Optimized Prediction of Shallow-Water Tides with the Global Ocean Tide Model TiME
Authors: Sulzbach Roman , Dobslaw Henryk , Thomas Maik 
Published: March 2024

Usually, the most accurate ocean tide atlases are produced by incorporating satellite altimetry observations into the modeling process. This strategy works best for large amplitude, i.e., major, ocean tides, which prominently appear in satellite observations. However, in the case of sparsely available observations or reduced observation precision (e.g., small-amplitude tides), purely numerical ocean tide models can provide valuable constraints for improving tidal predictions. For example, third-degree ocean tides, and several radiational tides were successfully predicted and identified in geodetic records by employing barotropic ocean models (e.g., Sulzbach et al. 2022; doi: 10.1007/s00190-022-01609-w), while they are hard to identify in altimetric records.A further complex facet of ocean tidal dynamics is shallow-water tides (SWTs), which are not directly generated by celestial bodies, but through the non-linear interaction of ocean tides in shallow waters. While appearing relatively small in amplitude in the deep ocean, SWTs exhibit more prominent signals in shallow waters and are also relevant for the processing of geodetic satellite observations, e.g., altimetry and gravimetry. The responsible non-linear tide-generating processes depend on several spatially variable characteristics of the ocean, e.g., seafloor roughness and ocean depth, and the accurate incorporation of major tides into the ocean model. Therefore, their excitation mechanism is only approximately known in contrast to gravitationally-excited tides. This uncertainty poses an additional challenge to the numerical modeling process.Here, we reapproach the simulation of shallow-water tides with the ocean tide model TiME by readressing the parameterization of potentially non-linear ocean-bottom friction. The barotropic ocean tide model has been refined to incorporate updated energy dissipation mechanisms by topographic wave drag and sea ice friction, possesses a truly global grid based on the rotation of the numerical poles, and operates at a relatively high resolution of 1/12&#176;. Most importantly, the effect of Self-Attraction and Loading (SAL) is modeled based on fast decomposition into Spherical Harmonic Functions at each time step. Thus, the model does not rely on prior estimates of the SAL effect, which are only weakly constrained for the SWTs, but estimates SAL self-consistently in real-time.The ocean tide model is optimized to simultaneously depict an accurate prediction of the major lunar tide M2, as well as its overtides in shallow waters (e.g., M4). Validation relies on geodetic data sets of complementary characteristics and focuses on a densely observed focus region: the European Shelf Sea. Based on multiple validation metrics, probing the sea surface height anomaly and the gravitational field of the SWTs, the effect of the improved bottom friction parameterization and the self-consistent effect of SAL are investigated. The simulations indicate that incorporating the self-consistent SAL effect for nonlinear tides significantly affects tidal propagation in the open ocean, similar to diurnal and semi-diurnal tides. Further, tuning of linear and nonlinear bottom friction effectively allows the reduction of the combined RMS for linear and nonlinear tides.