On the Comparison of Implicit with Explicit Schemes in Wave Watch III

WAVEWATCH III (WW3) as a spectral wave model has been known for its applicability in large-scale modeling of wave climate from large rectilinear grids offshore to high-resolution unstructured grids in coastal zones. The irreplaceable benefits of unstructured grids has made it a proper candidate to substitute the traditional multi-grid approach, where various regular grids are nested internally to represent the offshore domain with a less computationally expensive coarse grid, while the nearshore is run at a high resolution. The latter has been in forecast operation for a long time. Despite the known limitations of spectral models, solving the equations with explicit schemes in WAVEWATCH III requires a trade-off between spatial resolution and computational time. For operational applications, this limits the resolution to about 200 m in coastal waters. Recent advances in coastal circulation shed light on the need for incorporation of wave-surge coupling in nearshore regions. The fact that nonlinear shallow water equation models such as ADCIRC and FVCOM are comparatively faster than spectral wave models like WAVEWATCH III compels us to improve the numerical approach in wave model.

In this regard, we have implemented a new domain decomposition algorithm in WW3, which allows us to distribute the workload to a large number of computational nodes. As a result, high-resolution unstructured grids with millions of grid cells are no longer a limitation, as it is scalable on supercomputers. Unlike explicit schemes, a newly-implemented implicit scheme allows us to refine the nearshore region down to street level resolution. This scheme integrates the Wave Action Equation efficiently in time. This new scheme solves all propagation dimensions without any splitting between the various dimensions, and integrates the source terms directly based on Patankar rules. Therefore, the model can resolve offshore and nearshore physics at once with larger dynamically adjusted time steps compared to explicit ones. In this work, we have performed a validation study that compares the implicit scheme on various unstructured grids (2 km and 200 m resolutions near the US East Coast) with a regular grid with 10 km spatial resolution as well as with the results of the default explicit splitting scheme. The extreme conditions during Hurricane Sandy allowed us to evaluate the model capabilities in detail. The validation results for the investigated scales shows identical results between implicit and explicit methods on unstructured grids and structured grid in deep water and superior results from implicit scheme in nearshore region where structured grid is not able to resolve the coastline and geographical features properly. Incorporation of water level and current fields from a surge model in the inter-tidal zone together with the better solving of nearshore bathymetry and wave processes clearly improves the modeled wave field, with the implicit scheme overcoming the computational costs.