In wave modeling, multiple-structured grids system is the classic computationally efficient approach to downscale the coarse grids (~10 km) in deep water nested to finer resolution grids in coastal areas (~200 m) where irregularities in shoreline and geometrical features should be represented appropriately to resolve physics accurately. Using unstructured meshes is a more advanced way to avoid multigrid approach over large scale numerical domains, retaining the same level of grid size variance and computational costs. Studies have shown improvement in the accuracy of the model due to better representation of geometrical features (i.e. shore line), forcing conditions and physics parameterization. However, it needs more sophisticated numerical schemes and grid optimization in order to reduce computational time and numerical diffusion.
Balancing the accuracy and stability of the model is a big challenge for model developers. In this study, we have implemented implicit scheme following the work of Roland, 2008 and extending it to be fully implicit in all spaces in WAVEWATCH III model with three different orders including Narrow stencil (N-Scheme), Positive Streamline Invariant (PSI) and Flux Corrected Transport (FCT) schemes, which reduce numerical diffusion and inversely increase computational time.
These improvements are assessed for Hurricane Ike (September 2008), which made landfall at Galveston, Texas. The model grid covers the entire Gulf of Mexico and extends into the Atlantic Ocean to the approximate longitude of 65W, allowing for appropriate generation of hurricane waves from atmospheric effects over a large region. We have tested three unstructured meshes including high- (overland grid resolution of approximately 50 m) mid (~200 m) and low (~2000 m) resolutions and on a regular grid (1/12 degree). The model is forced by high resolution wind fields derived from HWRF atmospheric model and water level and current fields from the ADCIRC tide and surge model.
We have quantified the performance of the WAVEWATCH III model with different numerical schemes for different grid resolutions and time steps. The model validation is done for wave observations at buoy locations and along satellite tracks. The time series and frequency spectrum analysis has been done showing the effectiveness and accuracy of the implicit scheme, especially for the case of the 50 m coastal resolution mesh, where the explicit scheme requires a smaller CFL time step, and hence longer run times. Improvement in the model output shows the necessity of high resolution model meshes in coastal areas where water level and current play a significant role in wave breaking, refraction and reflection.
The results clearly demonstrate that the discretization order of the various schemes in geographical space does not play a essential role in the forecast quality for the investigated cases when compared to the 3rd order scheme on structured grids. Further research is needed to properly access the influence of the order of the various schemes and dimensions in shallow water.