Global and coastal ocean surface water elevation prediction skill has advanced considerably with improved algorithms, more refined discretizations and high-performance parallel computing. Model skill is tied to mesh resolution, the accuracy of specified bathymetry/topography, dissipation parameterizations, air-sea drag formulations, and the fidelity of forcing functions. Wind forcing skill can be particularly prone to errors, especially at the land-ocean interface. The resulting biases and errors can be addressed holistically with a machine-learning (ML) approach. Herein, we weakly couple the Temporal Fusion Transformer to the National Oceanic and Atmospheric Administration’s (NOAA) Storm and Tide Operational Forecast System (STOFS 2D Global) to improve its forecasting skill throughout a 7-day horizon. We demonstrate the transformer’s ability to enrich the hydrodynamic model’s output at 228 observed water level stations operated by NOAA’s National Ocean Service. We conclude that the transformer is a rapid way to correct STOFS 2D Global forecasted water levels provided that sufficient covariates are supplied. For stations in wind-dominant areas, we demonstrate that including past and future wind-speed covariates make for a more skillful forecast. In general, while the transformer renders consistent corrections at both tidally and wind-dominant stations, it does so most aggressively at tidally-dominant stations. We show notable improvements in Alaska and the Atlantic and Pacific seaboards of the United States. We evaluate several transformers instantiated with different hyperparameters, covariates, and training data to provide guidance on how to enhance performance.

This study showcases a global, heterogeneously coupled total water level system wherein salinity and temperature outputs from a coarse-resolution ($\sim$12 km) ocean general circulation model are used to calculate density-driven terms within a global, high-resolution ($\sim$2.5 km) depth-averaged total water level model. We demonstrate that the inclusion of baroclinic forcing in the barotropic model requires careful treatment of the internal wave drag term in order to maintain the fidelity of tidal results from the purely barotropic model. By accurately capturing the internal tide dissipation within the coupled system, the resulting heterogeneously coupled model has deep-ocean tidal errors of 2.27 cm, outperforming global, depth-resolving ocean models in representing global tides. Moreover, global median root mean square errors as compared to observations of total water levels, 30-day sea levels, and non-tidal residuals improve by 1.86, 2.55, and 0.36 cm respectively. The drastic improvement in model performance highlights the importance of including density-driven effects within global hydrodynamic models and will help to improve the results of both hindcasts and forecasts in modeling extreme and nuisance flooding. With only an 11\% increase in computational time as compared to the fully barotropic total water level model, this efficient approach paves the way for high resolution coastal water level and flood models to be used directly alongside climate models, improving operational forecasting of total water levels.

Coastal interfaces blend processes dominated by upland region hydrology and ocean hydrodynamics (tides, winds, waves, baroclinic fluctuations, among others). These areas tend to be vulnerable to flooding, a matter of concern considering that around 40% of the world’s population lives within 100 km of the ocean. Specifically, The US East and Gulf of Mexico Coasts are heavily affected by extratropical storms every year with catastrophic consequences. Models that integrate the dynamics of both oceans and river networks are needed in order to better improve flood forecast systems in coastal areas. Due to their spatial and temporal scale differences, traditional models solve river and ocean hydrodynamics independently. As a first step toward unifying coastal interface modeling, we designed an ADCIRC-based model that uses unstructured, highly variable-sized triangular meshes that can accurately represent both ocean basins and inland river networks. This meshing technique allows for incorporating features that control the dynamics of the nearshore area, such as barrier islands, jetties, and dredged channels. We analyze how mesh design impacts water level estimations in the deep ocean as well as inland rivers. Accuracy in the deep ocean is sensitive primarily to bathymetry in areas with high energy dissipation, whereas water level prediction within river networks depends on both bathymetry and resolution. While a minimum resolution in the order of a hundred meters is enough to accurately predict water level for most rivers with tidal influence, smaller tributaries require resolutions down to tens of meters. Future research will use these findings to build precipitation and rainfall-runoff into the model for a more comprehensive understanding of the coastal interface hydrodynamics.

The mechanisms and geographic locations of tidal dissipation in barotropic tidal models is examined using a global, unstructured, finite element model. From simulated velocities and depths, the total dissipation within the global model is estimated. This study examines the effect that altering bathymetry can have on global tides. The Ronne ice shelf and Hudson Bay are identified as a highly sensitive region to bathymetric specification. We examine where dissipation occur and find that high boundary layer dissipation regions are very limited in geographic extent while internal tide dissipation regions are more distributed. By varying coefficients used in the parameterizations of both boundary layer and internal tide dissipation, regions that are highly sensitive to perturbations are identified. Particularly sensitive regions are used in a simple optimization technique to improve both global and local tidal results. Bottom friction coefficients are high in energetic flow regions, across the arctic ocean, and across deep ocean island chains such as the Aleutian and Ryuku Islands. Global errors of the best solution in the $M_2$ are 3.10 \si{cm} overall, 1.94 \si{cm} in areas deeper than 1000 \si{m}, and 7.74 \si{cm} in areas shallower than 1000 \si{m}. In addition to improvements in tidal amplitude, the total dissipation is estimated and compared to astronomical estimates. Greater understanding of the geographical distribution of regions which are sensitive to friction allows for a more efficient approach to optimizing tidal models.