Geoffrey W. Cowles

FVCOM validation experiments : comparisons with ROMS for three idealized barotropic test problems

[1] The unstructured-grid Finite-Volume Coastal Ocean Model (FVCOM) is evaluated using three idealized benchmark test problems: the Rossby equatorial soliton, the hydraulic jump, and the three-dimensional barotropic wind-driven basin. These test cases examine the properties of numerical dispersion and damping, the performance of the nonlinear advection scheme for supercritical flow conditions, and the accuracy of the implicit vertical viscosity scheme in barotropic settings, respectively. It is demonstrated that FVCOM provides overall a second-order spatial accuracy for the vertically averaged equations (i.e., external mode), and with increasing grid resolution the model-computed solutions show a fast convergence toward the analytic solutions regardless of the particular triangulation method. Examples are provided to illustrate the ability of FVCOM to facilitate local grid refinement and speed up computation. Comparisons are also made between FVCOM and the structured-grid Regional Ocean Modeling System (ROMS) for these test cases. For the linear problem in a simple rectangular domain, i.e., the winddriven basin case, the performance of the two models is quite similar. For the nonlinear case, such as the Rossby equatorial soliton, the second-order advection scheme used in FVCOM is almost as accurate as the fourth-order advection scheme implemented in ROMS if the horizontal resolution is relatively high. FVCOM has taken advantage of the new development in computational fluid dynamics in resolving flow problems containing discontinuities. One salient feature illustrated by the three-dimensional barotropic winddriven basin case is that FVCOM and ROMS simulations show different responses to the refinement of grid size in the horizontal and in the vertical.

Parallelization of the Fvcom Coastal Ocean Model

The Finite Volume Coastal Ocean Model (FVCOM) is a publicly available software package for simulation of ocean processes in coastal areas. The unstructured grid approach used in the model is highly advantageous for resolving dynamics in regions with complex shorelines such as estuaries, embayments, and archipelagos. A growing user community and a demand for large-scale, high resolution simulations has driven the need for the implementation of a portable and efficient parallelization of the FVCOM core code. The triangular grid approach used in FVCOM precludes the utilization of schemes used previously in the parallelization of popular structured grid ocean models. This paper describes recent work on a SPMD parallelization of FVCOM. The METIS partitioning libraries are employed to decompose the domain. Parallel operations are programmed with the Message Passing Interface (MPI) standard interface. Updates for flow quantities near the interprocessor domain boundaries are performed using a mixture of halo and flux summation approaches to minimize communication overhead. Evaluation of the implementation efficiency is made on machines comprising several parallel architectures and interconnect types. The implementation is found to scale well on medium-sized (~ 256 processor) clusters. An execution time model is developed to expose bottlenecks and extrapolate the performance of FVCOM to increasingly available large MPP machines. Application to a model of water circulation in the Gulf of Maine shows that the parallelized code greatly increases the capabilities of the original core scheme by extending practical model simulation timescales and spatial resolution.

A nonhydrostatic version of FVCOM: 1. Validation experiments

[1] The unstructured grid finite volume coastal ocean model (FVCOM) system has been expanded to include nonhydrostatic dynamics. This addition uses the factional step method with both split mode explicit and semi‐implicit schemes. The unstructured grid finite volume method, combined with a correction of the final free surface from its intermediate value with inclusion of nonhydrostatic effects, efficiently reduces numerical damping and thus ensures second‐order accuracy of the solutions with local/global volume conservation. Numerical experiments have been made to fully validate the nonhydrostatic FVCOM, including surface standing and solitary waves in idealized flat‐ and sloping‐ bottomed channels in homogeneous conditions, the density adjustment problem for lock exchange flow in a flat‐bottomed channel, and two‐layer internal solitary wave breaking on a sloping shelf. The model results agree well with the relevant analytical solutions and laboratory data. These validation experiments demonstrate that the nonhydrostatic FVCOM is capable of resolving complex nonhydrostatic dynamics in coastal and estuarine regions.

Turbulent and numerical mixing in a salt wedge estuary : dependence on grid resolution, bottom roughness, and turbulence closure

The Connecticut River is a tidal salt wedge estuary, where advection of sharp salinity gradients through channel constrictions and over steeply sloping bathymetry leads to spatially heterogeneous stratification and mixing. A 3-D unstructured grid finite-volume hydrodynamic model (FVCOM) was evaluated against shipboard and moored observations, and mixing by both the turbulent closure and numerical diffusion were calculated. Excessive numerical mixing in regions with strong velocities, sharp salinity gradients, and steep bathymetry reduced model skill for salinity. Model calibration was improved by optimizing both the bottom roughness (z0), based on comparison with the barotropic tidal propagation, and the mixing threshold in the turbulence closure (steady state Richardson number, Rist), based on comparison with salinity. Whereas a large body of evidence supports a value of Rist 0.25, model skill for salinity improved with Rist 0.1. With Rist 5 0.25, numerical mixing contributed about 1/2 the total mixing, while with Rist 5 0.10 it accounted for 2/3, but salinity structure was more accurately reproduced. The combined contributions of numerical and turbulent mixing were quantitatively consistent with high-resolution measurements of turbulent mixing. A coarser grid had increased numerical mixing, requiring further reductions in turbulent mixing and greater bed friction to optimize skill. The optimal Rist for the fine grid case was closer to 0.25 than for the coarse grid, suggesting that additional grid refinement might correspond with Rist approaching the theoretical limit. Numerical mixing is rarely assessed in realistic models, but comparisons with high-resolution observations in this study suggest it is an important factor.

Preconditioning for dual-time-stepping simulations of the shallow water equations including Coriolis and bed friction effects

Diagonal preconditioners for implicit-unsteady and steady discretizations of the shallow water equations at low- and high-Rossby and drag-number limits are analyzed. For each case, sub and supercritical flow conditions are also considered. Based on the analysis, a preconditioner is derived for use with a multigrid cycle that performs as well as possible under all conditions. In addition, a streamwise-upwind Petrov-Galerkin discretization of the system is presented that is derived from the preconditioned system. Using this discretization, it is demonstrated that for most conditions, the preconditioner gives rapid convergence that is independent of the grid resolution and the flow parameters. Practical tests including an equatorial Rossby soliton and tide propagation over variable bathymetry are simulated to demonstrate the performance of this approach.

Critical Issues for Circulation Modeling of Narragansett Bay and Mount Hope Bay

Narragansett Bay is a medium-sized estuary located along the coast of the northeast United States with shoreline in bothMassachusetts andRhode Island. The bay covers 380 km, has an average water depth of 7.8 m, and a maximum depth of 56 m. Narragansett Bay contains three large islands—Aquidneck, Conanicut, and Prudence, all of which are oriented roughly north–south, and divide the bay into three interconnected channels—the West Passage, the East Passage, and the Sakonnet River (Fig. 9.1). The narrow linkages between these waterways control the water exchange among the various sectors of the bay. The connection to the sea is found in the southern reaches of the bay, where it opens onto the inner New England Shelf via Rhode Island Sound. In the northeast corner of the bay lies a semi-isolated shallow estuary called Mount Hope Bay. It is connected to the greater portion of Narragansett Bay through a narrow, deep channel of about 800 m in width and 25 m in depth. In view of water exchange dynamics, Narragansett Bay and Mount Hope Bay are an integrated inter-bay complex. In recent decades, intensive shortand long-term field measurements have been made in Narragansett Bay. These observations show that regional warming has caused a dramatic increase in the stratification of the water column (Hicks, 1959; Nixon et al., 2004). Annual mean water temperatures in the Narragansett Bay–Mount Hope Bay system underwent an increase of 28C from 1985 to 2001, following a decrease during 1972–1984 (Fig. 9.2a, dashed line), with a net increase of 1.18C overall (Fig. 9.2a, solid line). The warming trend was also observed in Woods Hole, Massachusetts (Nixon et al., 2004), and in coastal waters of the northeast United States (Oviatt, 2004). The bay, which remained vertically well mixed throughout the year in 1954–1955 (Hicks, 1959), has been strongly stratified since the summer of 1990.

Hydrodynamic and isotopic niche differentiation between juveniles of two sympatric cryptic bonefishes, Albula vulpes and Albula goreensis

We employed numerical wave models, GIS, and stable isotope analyses of otolith material to identify interspecific differences in habitat and resource use among juveniles of two sympatric and morphologically indistinct bonefishes, A. goreensis and A. vulpes in littoral zones of The Bahamas. Both species occurred in similar water temperatures; however, A. goreensis juveniles occupied habitats characterized by greater wave-driven flow velocities and closer proximity to coral reefs than A. vulpes. Likewise, A. goreensis was present across a broader range of flow environments and sampling stations than A. vulpes, which was typically confined to sheltered, low-flow habitats. The results of stable isotope analyses were consistent with the species’ relationships with environmental parameters, providing support for differential habitat and/or resource utilization. Otolith δ18O did not differ significantly between species, suggesting they experience comparable thermal regimes. However, δ13C varied substantially, with the otoliths of A. goreensis depleted in 13C relative to A. vulpes by approximately 1‰, potentially signifying a greater reliance on pelagic carbon sources by the former, in agreement with observed distinctions in habitat use. In linear models, otolith δ13C was negatively correlated with ambient flow velocity and positively related to distance from coral reef habitats, and these relationships did not vary across species. After accounting for the effects of these variables, species-specific differences in otolith δ13C remained, indicating that other unknown factors contributed to the observed disparities. Collectively, our findings suggest that niche partitioning between A. goreensis and A. vulpes is likely mediated by their differential abilities to compete across various flow environments, likely as a result of divergent behavioral and/or physiological adaptation.