Physics-based sizing functions for ocean-to-estuary shallow-water models

Abstract

Modeling ocean processes requires a discrete representation of the system geometry, which itself contains multiple degrees of freedom, especially for systems of large geographical scale. This paper assesses the unstructured meshing requirements for a large-scale, astronomic-tide model domain of the western North Atlantic Ocean, Gulf of Mexico and Caribbean Sea with telescopic focus of the South Atlantic Bight (United States southeastern seaboard) and its estuaries. The methodologies of localized truncation error analysis (LTEA), which account only for the model interior and LTEA plus complex derivatives (+CD), which account for the model interior and boundary, are exploited due to their foundations stemming directly from tidal physics. LTEA and LTEA+CD are applied for the M2 tidal harmonics resulting from linear and nonlinear solutions of the ADCIRC (advanced circulation) model based on a highly resolved uniform mesh. The resultant target element size distributions are interrogated distinctively for the inshore (estuarine) region of the South Atlantic Bight, the inlet-punctuated coastline, the shelf-slope-rise triad and deep ocean, and the open-ocean boundary. The relatively large size of the LTEA computational molecule makes it the suitable choice for the deep ocean, offshore and shelf regions where the tidal dynamics are predominantly linear and smoothly changing in space. LTEA+CD is the logical choice for the shallows and estuaries because of the spatial coverage afforded by the combined utility of interior and boundary estimators (computational molecules), as well as its accounting for the nonlinearities in the evaluation of local truncation error. The combination of the two methods enables an almost complete coverage of the domain for generating spacing requirements, with LTEA+CD extending beyond the interior-only definition of LTEA to capture the inshore regions and model boundaries. Implementing the approach with LTEA and LTEA+CD to target finer resolution in areas with sharper gradients in the hydrodynamics, while relaxing resolution in areas with smoother hydrodynamics, resulted in a mesh with a far-reduced number of elements (∼1.3M) relative to an overly resolved uniform mesh (>10M elements) that is comparable in accuracy with ±5% tidal amplitude error for 99% of the domain.