Marine Ecosystem Dynamics Modeling Laboratory

Tidal Simulation

In the last decade the tide-, river discharge- and wind-induced circulation in Narragansett Bay (NB)/Mt. Hope Bay (MHB) has been examined using various structured grid models (Gordon and Spaulding, 1987, Swanson and Jayko, 1987, Spaulding et al., 1999). Gordon and Spaulding (1987) applied a traditional finite-difference model to simulate the tidal motion in NB. Forced by M2 and M4 tidal constituents at the open boundary, their model reproduced the M2 and M4-induced tidal waves in good agreement with observations at tidal gauges. A similar effort was also made by Spaulding et al (1999), who included 37 tidal constituents for the purpose of improving the accuracy of tidal simulation. Due to poor resolving irregular coastline of islands, estuaries, and channels and sharp gradient of the local bathymetry in the deep channel, previous models failed to resolve strong tidal flushing and eddy formation through MNB-NB channel and MNB-SR channel. Failure to resolve these dynamic structures makes those models unable to accurately estimate and simulate the water exchange between MNB and its adjacent regions. This is one of critical reasons that we have introduced the unstructured grid FVCOM to MHB/NB.

The tidal simulation made by FVCOM in NB/MHB was described in detail in Zhao et al. (2006). A brief summary of our results are presented here to elucidate the capability of FVCOM in resolving the complex tidal dynamics in this region.

FVCOM successfully reproduces a tidal induced inertial gravity surface wave propagating into NB/MHB from the inner shelf dominated by the M2 frequency.  Due to Coriolis effects, at the same latitude, the tidal amplitude is slightly higher on the right-side coast than on the left-side coast. Consistently, the wave phase propagates slightly faster on the right side than on the left side (see Fig. 1).  The tidal amplitude is about 46-48 cm at the entrance of the bay and increases gradually to 58-59 cm at the northern end, while the phase difference from the entrance to the northern end is 8 degree, about 17 minute lag for the M2 tidal wave to arrive at the northern end from the entrance. The tidal phase in MHB is only 1-2o different from that in the upper NB, indicating that it takes only 2-4 minutes for a tidal wave from upper NB to reach the upper end of MHB. Such a small difference in phase implies that NB and MHB links closely with respect to the tidal process, so that they act like an integrated dynamic system.

A direct comparison between computed and observed amplitudes and phases of five major tidal constituents was made at five tidal gauges available around the coast of NB/MHB. The standard deviations between model-predicted and observed amplitudes and phases are 0.22 cm and 0.16oG for M2 tide, 1 cm and 0.66oG for S2, 0.06 cm and 0.69oG for N2, 0.11 cm and 0.66oG for K1, and 0.05 cm and 0.84oG for O1, all of which are within the range of the measurement uncertainty (Table 1). Computed ratio of tidal constituents is 0.22 for S2/M2; 0.25 for N2/M2; 0.12 for K1/M2; 0.09 for O1/M2, indicating that M2 tide accounts for about 70-90% energy of the tidal motion in the bay.

Unlike previous structured grid finite-difference models, FVCOM uses an unstructured triangular mesh with a horizontal resolution of less than 50 m in the deep channel of NB/MHB and MHB/Sakonnet River (SR).  This model captures a remarkable jump in both the amplitude and phase of the M2 tide on the northern and southern side of the Sakonnet River Narrows (SRN), which were not resolved in previous modeling efforts in this region (Zhao et al., 2006). SRN is 1500 m in length and 7 m in the mean water depth, characterized by two necks with a width of about 70 m at Sakonnet River Bridge (SRB) and 120 m at Stone Bridge (SB), respectively. The fact that FVCOM succeed in capturing the sharp jump of the tidal elevation in this channel demonstrates that geometric flexibility of FVCOM makes it practical for applications to the near shore region characterized with complex coastal geometry.

Animation of the sea level and near-surface tidal currents in the Mt. Hope Bay. This animation was made using the coarse resolution model results. To make the current field viewable, the grids are re-sampled and only parts of currents points are selected. Clike the image on the right to view the animation in the full-size.

Forced by five tidal constituents (M2, N2, S2, O1 and K1), FVCOM also captures the spring and neap tidal cycles in NB/MHB. An example was given for March-April 2001 in Zhao et al. (2006), which shows that the model is sufficiently robust to reproduce the fortnightly and monthly variation of tidal elevation measured at tidal gauges(dash line with blue color). A slight difference was found between observed and computed tidal elevations during the period with a large river discharge.  This bias is a result of the sea level rise around the time of peak river discharge, which was not taken into account in tidal simulation.

 

Posted on January 16, 2014