Elsevier

Ocean Modelling

Volume 147, March 2020, 101563
Ocean Modelling

A modeling study of estuarine–shelf circulation using a composite tidal and subtidal open boundary condition

https://doi.org/10.1016/j.ocemod.2019.101563Get rights and content

Highlights

  • A tidal-subtidal open boundary condition is used for simulating ocean circulations.

  • The TST-OBC is capable to resolve tidal and subtidal disturbances simultaneously.

  • A consistent usage of active scheme for all variables improves numerical downscaling.

Abstract

We investigated the performance of a tidally and subtidally forced open boundary condition (TST-OBC) on the estuarine–shelf circulation in a limited-area, down-scaling numerical modeling system for the northern South China Sea. We forced the modeling system with amplified tidal forces and subtidal forcing of spatiotemporally variable wind and river discharge. TST-OBC numerically and physically accommodates the circulation driven by the regional tides, subtidal forces, external forcing from its upscale solution, and internally generated disturbances. The advantages of TST-OBC are the separation of fast tidal and slow subtidal modes, active and dual-wave transmitting schemes, consistent treatment of barotropic and baroclinic circulation, and thermodynamic variables, which enable the model to capture observed circulation characteristics. The results differ from the results obtained using the Flather-type OBC, which over-restores internal to external solutions with a notable accumulation of spurious disturbances along the open boundaries. Disturbances with both tidal and subtidal signals that arrive at the open boundaries are well-treated by adopting TST-OBC, although it is currently feasible for the one-way downscaling applications.

Introduction

In numerical simulations of ocean circulation in a size-limited area, the open boundary condition (OBC) crucially impacts the interior solutions. However, implementing the OBC is an “ill-posed” problem (Oliger and Sundström, 1978). The reduced physics and simplified mathematics have led to improperly imposed “external” forces and reflective evacuation of “internal” disturbances at the open boundaries. A wrongly adapted OBC prevents a sensible connection between the internal and external forces and distorts the interior solution. This distorted solution is greater in shelf simulations where strong tidal and subtidal forces drive the hydrodynamically complex circulation (Bourret et al., 2005).

Sommerfeld (1949) originally proposed the radiation condition and Orlanski (1976), further generalized this condition. The radiation condition is the foundation of the most widely used conditions in modern ocean models. This Orlanski-type condition parameterizes propagating information across the open boundaries as nondispersive and unforced shallow water waves. Its equation is: ϕt+CϕN=0,where C is the propagation speed of the dependent variable, ϕ, and the subscripts, t and N, represent partial differentiation in time and horizontal space (usually in the cross-boundary direction), respectively.

The Orlanski-type condition inspired numerous different schemes, as summarized by Chapman, 1985, Tsynkov, 1998,  Palma and Matano, 1998, Palma and Matano, 2000, and Marsaleix et al. (2006). These schemes, in most cases, are used to solve circulation without tidal forcing, and their dynamics are defined by how C in Eq. (1) is determined, and how the disturbances arriving at the open boundaries are treated (Blayo and Debreu, 2005).

Properly including the exterior solution with a sensible scheme for C, with respect to the characteristics of the arriving disturbances, facilitates a less-reflective connection between the interior and exterior circulation, and forms “active” radiation OBCs (Gan and Allen, 2005, Gan et al., 2005). Schemes that exclude the exterior solution (forcing) are “passive” radiation OBCs (Blayo and Debreu, 2005). Gan and Allen (2005) suggested subtracting the exterior solution from the model’s variables, and solving for the “global” solution by using the Orlanski-type radiation in Eq. (1). The radiation OBC was valid only for unforced flow, in principle, and effective for slow subtidally forced currents at the open boundary. The radiation OBC cannot solve for the circulation in an estuary or coastal waters where tidal forcing is amplified and where tidal and subtidal currents exist simultaneously.

Reid and Bodine (1968) presented that a wave propagating across a boundary can be sensibly simulated by specifying C=gh in the two-dimensional, depth-averaged momentum equation. g is the gravitational acceleration, and h is the water depth over the open boundary. Flather (1976) advanced Reid and Bodine’s approach by including the tidal current. Oey and Chen (1992) further included the subtidal elevation and current to form the widely-used “active” Flather-type boundary condition (FLA-OBC) for a barotropic current flowing perpendicular to an open boundary.

While FLA-OBC effectively transmits tidal waves across the open boundary in a less reflective manner (Carter and Merrifield, 2007), the adaptability of the FLA-OBC in simulating the subtidal currents (for example, wind and buoyancy discharges) is questionable (Oddo and Pinardi, 2008) because of the dynamics on which FLA-OBC is based. The elevation and barotropic velocities are over-specified by FLA-OBC, and spurious kinetic energy accumulates at the open boundaries to create “rim currents” that prevent a sensible connection between the interior and exterior solutions in the computational domain (Mason et al., 2010). In addition, FLA-OBC has limited “noise” tolerance in the exterior solution and distorts the solutions in the baroclinic mode (Liu and Gan, 2016).

The inability of the Orlanski-type and Flather-type OBCs to sensibly resolve tidally and subtidally forced circulation across open boundaries in a limited-area simulation motivated the development of “active” schemes that overcame the drawbacks of FLA-OBC and the Orlanski-type OBC. Mason et al. (2010) proposed an improved FLA-OBC that separates the circulation at the open boundaries into components generated by internally and externally sourced surface gravity waves. They solve the internally sourced surface gravity waves by using “passive” schemes and the externally sourced ones by using “active” schemes with a specified C=gh. In this paper, the Mason et al. (2010) scheme is called MAS-OBC.

The tidally and subtidally forced open boundary condition (TST-OBC), developed by Liu and Gan (2016), resolves tidal and subtidal wave propagation across the open boundaries in a different way that is more physically sensible. This research resolves tidal and subtidal signals by recognizing concurrently propagating tidal waves and subtidally generated disturbances and adapting the numerical and physical advantages of the OBCs of Oey and Chen (1992) and Gan and Allen (2005), respectively. The separate treatment of tidally and subtidally forced currents allows TST-OBC to be an “active and dual-wave transmitting” scheme, in which both tidal and subtidal (“dual-wave transmitting”) disturbances are sensibly transmitted through the open boundary, while the exterior solution from the upscale simulation is imposed. However, in Liu and Gan’s study, the TST-OBC was based on steady, constant, and spatially uniform wind and tidal forcing. The reliability of TST-OBC in solving the tidal current and subtidal circulation driven by regional and remote forcing with extensive spatiotemporal variability was not investigated.

In our current study, a multi-domain downscaling simulation system that focuses on the circulation in the Pearl River Estuary and adjacent shelf waters (L2 domain in Fig. 1) is developed to investigate the adaptability and accuracy of TST-OBC. Both field observations and circulation dynamics are used to validate the simulation system.

The study area is in the northern South China Sea (L1 domain in Fig. 1a), which has a complicated coastline and bathymetry that stretches northeastward along the coast of Guangdong Province, China. The water depth in the L2 domain (Fig. 1b) is generally shallower than 70 m, and the depth decreases shoreward. The interior circulation and hydrodynamics in our domain are regulated by energetic spatially and temporally variable tidal (Zu et al., 2008) and subtidal (wind and river discharge) forces (Gan et al., 2009a, Gan et al., 2009b) and external forces from the large-scale slope and basin circulation of the connected L1 simulation (Gan et al., 2016). These jointly imposed forces produce complicated circulation patterns in the area (Zu and Gan, 2015).

Implementing the OBC so that the processes in the limited-area domain could communicate with the processes in the larger scale domain is critical and challenging in this multi-domain downscaling simulation system. In this study, the numerical and physical responses of TST-OBC to the spatiotemporally variable forcing of energetic and multi-constituent tidal forcing, strong shelf currents, winds, and buoyancy from river discharge are investigated. It is shown that TST-OBC has advantages in simulating shelf and estuarine circulation, when the circulation is jointly driven by spatiotemporal variable wind, buoyancy forcing, and tides.

Section snippets

Ocean model

The Regional Ocean Modeling System (ROMS; Shchepetkin and McWilliams, 2005; Rutgers branch, http://www.myroms.org) is used for the downscaling simulations. ROMS solves the three-dimensional primitive equations in an Arakawa C-grid system. In ROMS, barotropic and baroclinic mode splitting effectively computes the external and internal motions. The level-2.5 turbulent kinetic energy equations from Mellor and Yamada (1982) parameterize the vertical mixing of the sub-model, and a third-order

The forcing conditions

Fig. 2a and b show the horizontal distribution of wind vectors at 10 m above the sea surface and the standard deviation of the wind magnitude (95% confidence interval). The wind field in Fig. 2a is the average over the field cruise period (July 1 to August 15, 2015). Fig. 2c illustrates the time series of zonal and meridional wind speed and the time series of its alongshore component averaged over the L2 domain. A positive alongshore wind blew northeastward (22.8°to the east). The time series

Rationale of OBCs

In this section, the performance of TST-OBC’s response to variable forcing (Fig. 2) for the cruise period is detailed. To rationalize the success of TST-OBC in simulating tidal and subtidal currents, two additional sensitivity experiments in the L2 domain are conducted by using FLA-OBC and MAS-OBC in the Rutgers ROMS to solve for the barotropic velocities (Table 3). Unlike EROMS, TST-OBC is used to solve for the baroclinic velocities, temperature, and salinity in these new experiments to avoid

Conclusions

A set of limited-area numerical experiments is conducted to validate the performance of a recently developed “active” TST-OBC for estuarine–shelf circulation jointly driven by spatiotemporally variable wind, buoyancy forcing and tides in the northern South China Sea. TST-OBC is different from the frequently adopted OBC schemes in ROMS because it separates the tidal and subtidal currents by recognizing their distinguishing characteristics, and TST-OBC solves for the tidal and subtidal currents

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by the Theme-based Research Scheme (T21-602/16-R, OCEAN_HK project) of the Hong Kong Research Grants Council . We thank the insightful suggestions from two anonymous reviewers. We are grateful to the National Supercomputer Center of Tianhe-1 (Tianjin) and Tianhe-2 (Guangzhou). The model data for this study are produced by the community model ROMS (https://www.myroms.org/). The data used in the study are found on the web site, https://ocean.ust.hk/data/.

References (35)

Cited by (0)

View full text