Improving Barotropic Tide Modeling in MPAS-Ocean and Estimating Changes in Future Tides

Abstract

Modeling the ocean is critical for understanding both present and future risks posed by climate change on coastal communities. Ocean tides in these regions will continue to change over the following decades, yet tides are seldom resolved in climate models; historically, tides have been modeled separately from the oceanic general circulation. This work seeks to improve barotropic tidal modeling in the Department of Energy's Model for Prediction Across Scales, or MPAS-Ocean, and to use the resulting tide capabilities to examine potential future changes to tides. We first describe the implementation of an inline self-attraction and loading (SAL) calculation into MPAS-Ocean. When the sea-surface height over a column of ocean moves up and down, this change in mass loading causes small deformations of the Earth's crust. This deformation, along with changes in the gravitational potential of the deformed Earth and ocean, are known as "self-attraction and loading." We implement an inline SAL calculation using the fast spherical-harmonic transform package SHTns and compare the resulting tidal errors to the more common (and computationally cheaper) scalar approximation. We also compare the model's performance on quasi-uniform meshes and a variable-resolution mesh. We examine the root-mean-square error of our modeled tides when compared to a benchmark tidal dataset called TPXO8 and show that the variable resolution mesh and inline SAL calculations reduce the errors. We also find that the computational cost of SAL can be reduced by updating the term as infrequently as 10-15 minutes without sacrificing tidal error. The next improvement to the tidal model is carefully selecting a parameterized topographic wave drag (TWD). TWD occurs as tides flow over the ocean floor, leading to energy dissipation into the baroclinic tide. This process cannot be resolved directly in our single-layer barotropic model and must be parameterized. We compare three methods of parameterization. Two are scalar methods, based upon papers by Jayne and St. Laurent ac{JSL} and Zaron and Egbert (ZAE); one is a tensor method: Local Generation Formula (LGF). The main difference between the first two schemes lies in how the floor roughness is incorporated: JSL uses the standard deviation of topography, while ZAE uses the gradients. The tensor scheme is a simplification of the Nycandar formulation, which has the most thorough physical justification of the three schemes. We find that the most significant improvements in tides came from the ZAE scheme, leading to an improvement of 1.6cm over the JSL scheme, with LGF landing in the middle. Finally, using the results of this model development, we examine how tides might look in a future climate by running simulations in MPAS-Ocean with sea-level change, ice-shelf cavity geometry, and landfast ice. We adopt regionally varying sea-level and ice shelves from moderate and extreme future scenarios. The sea-level changes exert the most influence in near-shore regions, while the ice shelves have more impact on the global ocean. However, some near-shore areas see more or comparable impact from ice shelves than sea-level rise, indicating the importance of accounting for cavity geometry in future tide simulations.