chapter 9

modeling the M₂S₂N₂ Tidal Flow in Great Bay

In this chapter, the Great Bay system is forced with an M₂S₂N₂ tidal elevation time series  at the boundary transect in Little Bay. In order to resolve the spring and neap tides in M₂S₂N₂ tidal forcing, the simulation is run for 108 M₂ tidal cycles, which corresponds to 1341.36 hrs. The details of the boundary forcing time series is given in Chapter 6. The space-variable, depth dependent bottom friction coefficient distribution used in the M₂ simulation is modified for the M₂S₂N₂ simulation. The modification was done by decreasing the bottom friction coefficient values by 7% at each node. The simulation parameters are given in Table 9-1.

Table 9-1. Simulation parameters for the M₂S₂N₂ forcing in Great Bay.

Description	Parameters
Bathymetry range
Porous layer thickness	h0 = 1.00m
Hydraulic conductivity	k  =  0.0003162
Bottom friction coefficient	See Simulation C
Time increment
Time steps per tidal period	300
Tidal periodicity	T =12.42 hrs
Length of simulation
Numerical implicity
Number of nonlinear iterations	4

9.1.            Results for the M₂S₂N₂ Forcing without Eelgrass

The simulation results are examined in two parts: Spring tide Neap tide. For this purpose, two windows are chosen on the M₂S₂N₂ tidal forcing time series. The time steps between  17100-17400 correspond to the Neap tide and the time steps between 22500-22800 correspond to the Spring tide .

·        During Spring tide, the water surface area of Great Bay is 19.70 km² (10336 elements) at  high water with an average depth of 2.80m and 8.16 km² (3755 elements) at  low water with an average depth of 2.27m. Thus, during Spring tide, 59% of the surface area in Great Bay dries at low water and 36586227 m³ water is discharged during that drying process.

·        During  Neap tide, the water surface area in Great Bay is 18.90 km² (9632 elements) at high water with an average depth of 2.50m and is 12.21 km² (5563 elements) at low water with an average depth of 1.82m. During  Neap tide, 35% of the surface area dries at low water.

 The high water and low water boundaries for the M₂S₂N₂ tide during the Spring and the Neap tides are shown in Figure 9-1.

 

 

Figure 9-1. High water and low water boundaries for the M₂S₂N₂ tide. The high water boundary is shown in green and the low water boundary is shown in red for the spring tide. The high water boundary is shown in pink and the low water boundary is shown in blue for the neap tide.

 

The model results at specified stations are compared with the tidal analysis predicted time series. The statistical analysis results for the comparison of the surface elevation time series at stations  T-UNH and T-19 and  the comparison of cross-section averaged velocity time series at station C-131 are given in Table 9-2.  The model predictions compare well with the tidal analysis predicted data at those stations.

 

Table 9-2. Statistical analysis results for M₂S₂N₂ forcing in Great Bay.

	Station T-UNH	Station T-19	Station C-131
Correlation Coef.	0.99	0.99	0.96
Skill	0.99	0.98	0.93
RMSN	0.12	0.16	0.27

9.2.            Eelgrass Effects on the M₂S₂N₂ Tidal Flow in Great Bay

The same 1990 eelgrass distribution explained in Chapter 7 is used for the M₂S₂N₂ simulation.  The following effects are observed:

·        During Spring tide, the water surface of Great Bay covers 19.70 km² (10336 elements) at high water and 8.62km² (3988 elements) at low water. The average depth is 2.80m for high water and 2.16m for low water. The average depth at low water with eelgrass is 11cm lower than the average depth at low water without any eelgrass. Also the water surface area at low water with eelgrass is 0.45 km² (233 elements) larger than the water surface area at low water without eelgrass. There was no significant change in the surface area and the average depth values at high water.

Figure 9-2. High water and low water boundaries for the M₂S₂N₂ tide with eelgrass. The high water boundary is shown in green and the low water boundary is shown in red for the spring tide. The high water boundary is shown in pink and the low water boundary is shown in blue for the neap tide.

 

·        During Neap tide, the water surface of Great Bay covers 18.90 km² (9632 elements) at high water and 13.47 km² (6094 elements) at low water. The average depth is 2.50m for high water and 1.66m for low water. The average depth at low water with eelgrass is 16cm lower than the average depth at low water without any eelgrass. Also the water surface area at low water with eelgrass is 1.26 km² (531 elements) larger than the water surface area at low water without eelgrass. There was no significant change in the surface area and the average depth values at high water.

 

The difference in the water volume time series between the simulation without eelgrass and the simulation with eelgrass is shown in Figure 9-3.

 

Figure 9-3. The difference in water volume time series between the simulation with eelgrass and the simulation without eelgrass for M₂S₂N₂ tide. Flood is in the negative direction.

 

When there is no eelgrass distribution, 820000 m³  more water enters and 750000 m³ more water exits the system at spring tide. This again shows that the eelgrass blocks the water entering the system, and once the high water stage is reached eelgrass holds the water and blocks it from exiting the system.

 

9.2.1.      Eelgrass Effects on the M₂S₂N₂ Tidal Flow at Spring Tide

  The previous twenty-seven (27) arbitrary stations in Great Bay are used in order to observe the frictional effects of eelgrass on the M₂S₂N₂ tidal flow during the spring tide. The changes in velocity magnitudes and directions are shown in Figure 9-4 through Figure 9-6 for the Spring cycle.

 

Figure 9-4. M₂S₂N₂ forcing: Comparison between model-predicted velocity vectors with eelgrass and the model-predicted velocity vectors without eelgrass at stations 1-9 for the spring tide. Eelgrass simulation results are shown with blue vectors.

 

Stations 1-13 and station 26 are all on the tidal flats. The velocities at those stations are decreased and change direction towards the deep channels when there was eelgrass on the tidal flats. Station 15 is in the Furber Strait far from the eelgrass effects and no velocity change due to eelgrass is observed at this station. The velocities at stations 16-27, except station 26, are increased as they are located in the channels.

 

Figure 9-5. M₂S₂N₂ forcing: Comparison between model-predicted velocity vectors with eelgrass and the model-predicted velocity vectors without eelgrass at stations 10-18 for the spring tide. Eelgrass simulation results are shown with blue vectors.

 

 

Figure 9-6. M₂S₂N₂ forcing: Comparison between model-predicted velocity vectors with eelgrass and the model-predicted velocity vectors without eelgrass at stations 19-27 for the spring tide. Eelgrass simulation results are shown with blue vectors.

 

9.2.2.      Eelgrass Effects on the M₂S₂N₂ Tidal Flow at Neap Tide

The changes in velocity magnitudes and directions are shown in Figure 9-7 through Figure 9-9 for the Neap cycle.

 

Figure 9-7. M₂S₂N₂ forcing: Comparison between model-predicted velocity vectors with eelgrass and the model-predicted velocity vectors without eelgrass at stations 1-9 for the neap tide. Eelgrass simulation results are shown with blue vectors.

 

Stations 1-13 and station 26 are on the tidal flats. The velocities at those stations are decreased directed towards the deep channels when there was eelgrass on the tidal flats. Station 15 is in the Furber Strait far from the eelgrass effects and no velocity change due to eelgrass is observed at this station. The velocities at stations 16-27, except station 26, are increased as they are located in the channels.

 

Figure 9-8. M₂S₂N₂ forcing: Comparison between model-predicted velocity vectors with eelgrass and the model-predicted velocity vectors without eelgrass at stations 10-18 for the neap tide. Eelgrass simulation results are shown with blue vectors.

 

Figure 9-9. M₂S₂N₂ forcing: Comparison between model-predicted velocity vectors with eelgrass and the model-predicted velocity vectors without eelgrass at stations 19-27 for the neap tide. Eelgrass simulation results are shown with blue vectors.