Tidally-induced sediment transport patterns in the upper Bay of Fundy: A numerical study

Continental Shelf Research 31 (2011) 2041–2053

Contents lists available at SciVerse ScienceDirect

Continental Shelf Research journal homepage: www.elsevier.com/locate/csr

Research papers

Tidally-induced sediment transport patterns in the upper Bay of Fundy: A numerical study Yongsheng Wu n, Jason Chaffey, David A. Greenberg, Keir Colbo, Peter C. Smith Coastal Ocean Science Section, Ocean Science Division, Fisheries and Oceans Canada, Bedford Institute of Oceanography, Dartmouth, Nova Scotia, Canada B2Y 4A2

a r t i c l e i n f o

abstract

Article history: Received 30 May 2011 Received in revised form 9 September 2011 Accepted 13 October 2011 Available online 28 October 2011

The Minas Basin, the eastern end of the Bay of Fundy, is well known for its high tide ranges and strong tidal currents, which can be exploited to extract electricity power. The properties of the tidally-induced sediment transport in the Minas Basin, where significant changes in tidal processes may occur due to a recently proposed tidal power project, have been studied with a three-dimensional hydrodynamic model, an empirical bed load sediment transport model and surface sediment concentrations derived from the remotely-sensed images. The hydrodynamic model was evaluated against independent observational data, which include tidal elevation, tidal current (in the full water column and bottom layer), residual current profile and tidal asymmetry indicators. The evaluation shows that the model is in good agreement with the observations. The sediment transport includes two components, bed load and suspended particulate load. The bed load is calculated using the modelled bottom shear stress and the observed grain size data. The estimated features of bed load transport roughly agree with the observed patterns of the erosion and deposition in the Minas Basin and Cobequid Bay. The transport of the suspended load is estimated using the modelled velocity fields and the surface sediment concentration derived from remote-sensing images. The comparisons between the modelled results and the limited observations illustrate that the observed directions of suspended sediment transport are basically reproduced by the model. The modelled net suspended sediment input into the Minas Basin through Minas Passage is 2.4  106 m3 yr  1, which is comparable to the observed value of 1.6  106 m3 yr  1. The variations of the bed load and the suspended load in space and time are also presented. The total net transport, defined as the mean value of the sum of bed and suspended load transports during the tidal cycle, shows strong spatial variability. The magnitude of the transport flux ranges from 0.1 to 0.2 kg m  1 s  1 in Minas Channel and Minas Passage, 0.1 kg m  1 s  1 in Cobequid Bay, to 0.01 kg m  1 s  1 in the central Minas Basin and Southern Bight. In Minas Channel, the sediment transport follows the structure of the tidal residual circulation, which features a large anticlockwise gyre. The sediment in Minas Passage moves eastward and deposits into the central Minas Basin. However, the sediment from the eastern part of the Basin moves westward and deposits in the central Minas Basin as well. In the Cobequid Bay, sediment moves eastward and deposits in the upper bay. Crown Copyright & 2011 Published by Elsevier Ltd. All rights reserved.

Keywords: Sediment transport Hydrodynamic model Model evaluation The upper Bay of Fundy

1. Introduction Tidal power is one of the important sources of renewable energy that has recently received considerable attention due to popular desire to reduce the public’s dependency on fossil fuels and limit CO2 emissions (Garrett and Cummins, 2004; Thresher and Musial, 2010). Compared to other renewable energy sources, such as solar energy, wave energy and wind energy, tidal power has many advantages, including high energy density, predictability and economical feasibility (Neill et al., 2009; Walkington and

n

Corresponding author. E-mail address: [email protected] (Y. Wu).

Burrows, 2009). In the Bay of Fundy, for example, the spring tides exchange more than 100 billion tonnes of water nearly twice a day and the associated energy, estimated as twice the mean potential energy released over half tidal period, can reach 10 GW, about 15 percent of the Canada’s current annual electrical power demand (Karsten et al., 2008). The Bay of Fundy, possibly the home of the world’s highest tides (Garrett, 1974), is located at the northeastern end of the Gulf of Maine between the Canadian provinces of New Brunswick and Nova Scotia (see Fig. 1). A number of studies reported that the tidal energy there can be exploited by using either the potential energy of the tidal range in the Minas Basin or the kinetic energy of the tidal current in Minas Passage. The environmental impacts based on the former approach have been investigated by many

0278-4343/$ - see front matter Crown Copyright & 2011 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.csr.2011.10.009

2042

Y. Wu et al. / Continental Shelf Research 31 (2011) 2041–2053

30’ Minas Passage

N

24’ S3 S1S4 A1 A2

el

18’

n an

h

C as

n

Mi

Cobequid Bay

A3 A4

Minas Basin

Scots Bay A6

A5 46°N

12’

ay ick B nsw ecto Bru n g i Ch dy un a fF o oti y a Sc B a v e No ain

Southern Bight

New

Cape Split 45°N

A

S.

U.

6’

fM

44°N

lf o

Gu

45°N

B

68W°

30’

15’

64°W

66W°

ic

nt

la

At

A

64W°

45’

62W°

30’

Fig. 1. Model domain (A) and study area (B). The red dots in (B) denote the locations of current data, and red dots in (A) denote the locations of tidal elevation data. The black straight line across Bay of Fundy in (A) indicates the western boundary of the model domain. The area of the red box in (A) indicates the study area (B). The blue and red contour lines in (B) represent the 20 m and 50 m isobaths, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

studies, including Garrett (1974), Garrett and Greenberg (1977), Greenberg (1977, 1979, 1983), Greenberg and Amos (1983), Sucsy et al. (1993) and Shaw et al. (2010), in which changes in physical characteristics of the tide, such as elevation and currents, in Gulf of Maine were examined by specifying reduced or no water flow into the Minas Basin. However, few studies discuss the impacts based on the presence of in-stream turbines in Minas Passage, except for Karsten et al. (2008), who found that a significant decrease of the tidal energy may lead to dramatic decrease of tidal level in the Minas Passage and Minas Basin, and thus affects a number of physical and biological processes. One of those processes is the transport of the bottom sediment, which is the focus of this paper. To date, the character of hydrodynamic tidal processes in the Bay of Fundy is well represented using either hydrodynamic models or field observations. However, knowledge of the sediment transport is quite limited. Most of our understanding of sediment transport is derived from a few field observations three decades ago (Amos and Joice, 1977; Long, 1979; Amos and Long, 1980). Recently, Li et al. (2010) described the bed load transport in the Bay of Fundy using numerical tidal current, wave parameters and general circulation features. However, this work was concentrated on conditions in the outer bay, not in the Minas Basin. In the present paper, the sediment transport in Minas Basin, including bed load and suspended load, is studied. The changes of sediment transport due to various arrangements of turbines will be examined in a sequel to this paper. The paper is organised as follows: Section 2 gives a description of the model and model setup, and a method for calculating the bottom drag coefficient is introduced in Section 3. In Section 4, the model results are compared with observations including tidal currents and tidal elevations. In Section 5, the horizontal patterns of the model results are presented, followed by a description of the sediment transport rates of bed load and suspended load in Section 6. The conclusions are given in Section 7.

2006, 2007; Cowles et al., 2008). FVCOM has a free surface, uses sigma coordinates in the vertical, and employs mode time split technology. The model also contains an embedded second-order turbulence closure scheme (Blumberg and Mellor, 1987), which takes into account the effects of both wind mixing and wave dissipation (Mellor and Blumberg, 2004). The vertical eddy viscosity is parameterized by a mixing length, the turbulence kinetic energy and a stability factor which depends on the vertical shear and buoyancy. The horizontal diffusion is estimated with the Smagorinsky diffusivity. To simulate the flooding/drying processes, a mass-conserving wet/dry point treatment was employed in the model. The model domain covers the upper Bay of Fundy, including Minas Basin, Minas Passage and Chignecto Bay (Fig. 1). The initial coastline and bathymetric data were obtained from a digital version of a Canadian Hydrographic Service nautical chart. Recent multibeam sonar data were used to supplement the bathymetry in Minas Passage and parts of Chignecto Bay. The model mesh has 4588 nodes and 8629 triangular elements and the resolution varies between approximately 7500 m in the outer part of the mesh and 100 m in Minas Passage. In the study area (see Fig. 1), the maximum water depth is about 120 m in Minas Passage and the area of tidal flat represents about 20% of the total study domain. There are 21 levels in the vertical, with enhanced resolution near the surface and bottom. The open boundary crosses the Bay of Fundy about halfway down the outer bay (Fig. 1). The open boundary conditions for tidal elevation were taken from WebTide, a software package for tidal prediction (Dupont et al., 2002). Amplitudes and phases of tidal elevation for the five largest constituents (M2, N2, S2, K1, O1) were interpolated to the open boundary nodes. The time step is 1.0 s. The model is forced by the boundary conditions and a 35-day model run from still water was used for spin up. The final results of the spin-up were then used as the initial conditions for a 29-day model run, and the hourly model output was used for model validation and analysis.

2. Model description and model setup

3. Bottom drag coefficient

The model used in this study is the Finite-Volume Coastal Ocean Model (FVCOM), which is a proven three-dimensional, finite-volume, unstructured grid ocean model that was developed at University of Massachusetts-Dartmouth (Chen et al., 2003,

Bottom drag coefficient is a key parameter for a tidal model since it has a significant influence on the calculation of velocity, shear stress, stratification in the near bottom layer, and thus the sediment transport properties (Davies and Jones, 1995; Lu and Zhang, 2006).

Y. Wu et al. / Continental Shelf Research 31 (2011) 2041–2053

In FVCOM, it is determined by matching to a logarithmic distribution at the bottom layer of the model grid, i.e. C d ¼ k2 =ðlnðzab =z0 ÞÞ2

ð1Þ

where z0 is the apparent roughness height, where velocity is zero. k is von Karman’s constant (k ¼0.40) and zab is the half height of the deepest model layer. An implicit condition is zab Zz0, according to the assumptions of the law of the wall. Based on Eq. (1), the bottom drag coefficient is determined by the ratio of the bottom model vertical grid scale to the bottom roughness z0. In the limit as zab approaches the bottom roughness, z0, the value of Cd approaches infinity. On the other hand, Cd approaches zero when z0 is much less than zab. For given bottom roughness, Eq. (1) indicates that the drag coefficient varies with the vertical scale of the bottom model grid. Thus a constant drag coefficient in the whole model domain may be possible if zab is properly specified. Hence, the Cd expressed in Eq. (1) is more like a numerical parameter rather than a physical one. So, the current profiles in the near bed region and hence the sediment transport are significantly influenced by both z0 and zab. In practice, the value of bottom roughness, z0, is usually defined as a function of grain size (Li and Amos, 2001; Werner et al., 2003; Warner et al., 2008). For this study, historical grain size observations (Amos and Joice, 1977) and the relationship between grain size and bottom roughness derived by Li and Amos (2001) will be used to estimate the bottom roughness. The maximum value of the drag coefficient is arbitrarily set at 0.5, while the minimum value is taken to be 2.5  10  3. The horizontal distributions of the grain size and the derived drag coefficient are shown in Fig. 2. The distribution of the grain size (D50) is patchy with strong horizontal variability in our study area, especially in the Minas Channel, where the observational data are quite scarce (Fig. 2A). Coarse sediment can be found in areas of Minas Channel, northern coast of Minas Passage, central and western Minas Basin. In contrast, the finer sediment can be seen in southern coast of Minas Basin and upper Cobequid Bay. The spatial structure of the drag coefficient has many similarities to that of the grain size (Fig. 2B). However, the relationship between them is not simply proportional because of the variability of the bottom model grid. A series of sensitivity tests did indicate that our variable roughness significantly improves the model performance, especially the tidal currents in Minas

2043

Passage, but the details of the sensitivity study are not given here since they are beyond the scope of this paper.

4. Model validation In this section, we compare model results to observational data. Two kinds of data are used; water level and current, which includes the ellipse parameters of M2, M4, tidal residual currents and total velocity. 4.1. Tidal elevation comparisons The statistical parameters of M2 constituent at 10 tidal stations (their locations are shown in Fig. 1) from model and observations are listed in Table 1. As it can be seen, the modelled results agree well with their observed counterparts. For example, the amplitude difference ranges from  0.04 to 0.24 m, the mean difference is 0.07 m, which is only 1.4% of the observed mean of 5.04 m. The phase difference ranges from 5.91 to 2.31 with a mean of  1.61. The root-mean-squares (r.m.s.) of the amplitude and the phase differences are 0.11 m and 2.71, respectively. The errors, defined as the magnitudes of the vector difference between model and observation at each station, vary from 0.08 to 0.45 m with mean of 0.22 m and r.m.s. of 0.25 m. A plot of amplitudes and phases of the observational and modelled M2 tidal elevation constituents is presented in Fig. 3. Model results are further compared to two previous model studies in the upper Bay of Fundy: Dupont et al. (2005) and Karsten et al. (2008). To make sure the same stations used in the comparison, the errors are recalculated according to the results reported in their papers. The magnitude of the r.m.s. vector error obtained by Dupont et al. (2005) is 0.28 m, whereas that of Karsten et al. (2008) is 0.38 m, both larger than the 0.25 m obtained in this study. One interesting feature of the comparison is that the phase differences range from  5.91 to 2.31 at 10 stations, among which the modelled phases lead the observed at 3 stations and lag at 7 stations. However, all the modelled phases of Karsten et al. (2008) lead the observations, whereas the results of Dupont et al. (2005) lag the observations (Fig. 3). 4.2. Tidal current comparisons The velocity observations used in comparisons were collected at 10 stations (see Fig. 1) with 300 kHz RDI workhorse Acoustic Doppler Current Profilers (ADCPs) installed in streamlined floats, with the transducer heads at approximately 4.5 m above the bottom Table 1 Observed and modelled amplitude and phase, and discrepancies of M2 tidal elevations. Stations

Fig. 2. Observed grain size (A) and derived bottom drag coefficient (B). The black dots in (A) denote the observation sites.

Isle Haute Chignecto Grindstone CumberlandBasin Cape d’Or Cobequid Bay Economy Minas Basin Blomidon Cape Sharp(new) Mean r.m.s.

Observed

Modelled

Difference

Ampl. (m)

Phase (deg.)

Ampl. (m)

Phase (deg.)

Ampl. (m)

Phase (deg.)

4.15 4.26 4.86 4.74 4.34 6.12 5.92 5.54 5.36 5.17 5.04 5.09

99.2 104.2 104.4 104.6 102.0 129.3 125.4 120.8 116.7 117.0 –

4.00 4.10 4.62 4.64 4.32 6.12 5.96 5.53 5.25 5.15 4.97 5.02

103.4 105.1 107.4 106.7 107.9 131.6 124.8 118.5 115.8 118.0 –

0.15 0.16 0.24 0.10 0.02 0.00  0.04 0.01 0.11 0.02 0.07 0.11

 4.2  0.9  3.0  2.1  5.9  2.3 0.6 2.3 0.9  1.0  1.6 2.7

Errors (m)

0.34 0.17 0.35 0.19 0.45 0.24 0.08 0.23 0.13 0.09 0.22 0.25

2044

Y. Wu et al. / Continental Shelf Research 31 (2011) 2041–2053

and profile bins set at 4 m resolution. The duration of the data records ranges from 21 to 41 days. All the records showed good data return with few gaps in the profile over the water column. In the data processing, bins that were clearly above highest observed water levels were discarded. Small gaps (o30 min) in the time series were linearly interpolated in time to give complete records (gaps less than 1% for all wet bins). A magnetic declination of  181270 was applied to the 2009 records and  181390 for the 2007 record. The time series were analysed using the tidal analysis package of Pawlowicz et al. (2002) to determine tidal constituents and the tidal residual flow. In the model-data comparisons, the modelled velocities are linearly interpolated to each observation site. The comparisons start with the harmonic constants of M2, the dominant constituent, based on a simple statistical analysis. A similar comparison of M4 is followed. We then present the residual currents comparisons. In the last subsection, time series comparison of the total currents, which are used to calculate the shear stress and the sediment transport pattern, are presented.

Fig. 3. Model-data comparison of water level M2 tidal constituent. The grey dots represent the observations and the dash lines indicate the difference from the corresponding model results (stars are from this paper; squares are from Dupont et al. (2005) and triangles are from Karsten et al. (2008)).

4.2.1. M2 ellipse parameters comparisons The comparisons of the depth-averaged results for M2 ellipse parameters (Table 2), analysed with T_Tide (Pawlowicz et al., 2002), indicate that model results are in reasonable agreement with the observations. For example, the magnitude of the mean difference between model results and observations of the semimajor axis velocities is 0.06 m s  1, less than 3% of the mean. The r.m.s. of difference is 0.2 m s  1, or 9% of the mean. Although the relative error of the semi-minor axis is large, all the rotation directions of the tidal currents from the model are consistent with those of observations. The difference of ellipse inclination lies in the range of  4.21 to þ1.21, with a mean of  1.11, and the mean discrepancy of phase is 0.201. The corresponding r.m.s. of the phase difference, however, reaches 4.71. This is mainly due to the pronounced differences at three stations; A3, where the modelled phase lags the observed value by 10.41, and two others, A4 and A6, where the modelled phases lead the observations by 6.41 and 5.51, respectively. As an indication of the variations in the vertical direction, the comparisons at sites A1 and A5 are shown in Fig. 4, we can find that the observed vertical distributions of the velocity parameters are generally reproduced by model. As an example, the modelled parameters with a constant bottom roughness (z0 ¼0.0005 m) were plotted in Fig. 4 as well. As we can see, at site A1, the semi-major axis is consistently better simulated from bottom to surface with the variable roughness. However, semiminor axis from the constant roughness is a little better than that from the variable roughness. The improvement of the inclination and phase varies with depth. At site A5, the result of the semimajor axis does not change much with the different bottom roughness. Significant improvements can be found in semi-minor axis and phase. A sample of the vertical profile of tidal ellipses at site A1 is given in Fig. 5.

4.2.2. M4 ellipse parameters comparisons The modelled and the observed tidal ellipse parameters of M4 is compared as well since M4 tidal current is an important mechanism resulting in the tidal asymmetry, which dominates the net sediment transport. The results are listed in Table 3. As we can see, the agreement between the model and the observations varies significantly from site to site. For instance, poor agreement can be seen at sites A2 and A4, where the difference of the phase reaches 1801 and 115.91, respectively. Generally, the agreement is reasonably good at sites (A1, A8, S1, S1, and S4) in the northern side of the Minas Passage, where the turbines will be installed, and sites (A5 and A6) in the Southern Bight. At the sites in the northern Minas Passage, the results of the semi-major axis from model agree well with those from observations although they are

Table 2 Observed and modelled tidal ellipse parameters for depth-averaged M2 currents at DFO and Fundy Ocean Research Centre for Energy (FORCE) mooring sites. Stations Observed

A1 A2 A3 A4 A5 A6 A8 S1 S3 S4 Mean r.m.s.

Modelled

Difference

Semi-major axis (m s  1)

Semi-minor axis (m s  1)

Inclination (deg.)

Phase (deg.)

Semi-major axis (m s  1)

Semi-minor axis (m s  1)

Inclination (deg.)

Phase (deg.)

Semi-major axis (m s  1)

Semi-minor axis (m s  1)

Inclination (deg.)

Phase (deg.)

2.87 1.93 2.13 2.19 0.93 0.94 3.08 3.23 2.61 2.67 2.25

 0.10  0.09 0.08  0.03  0.22  0.17  0.01  0.06  0.02  0.02  0.06

162.0 166.6 167.7 144.5 116.1 98.9 169.9 163.2 154.9 158.7 150.2

209.3 200.0 219.4 199.1 203.6 196.3 222.9 217.3 212.1 210.2 209.0

2.86 1.82 2.35 2.26 0.98 1.10 3.62 3.07 2.56 2.58 2.32

 0.17  0.10 0.14 0.00  0.32  0.19  0.03  0.03  0.02  0.05  0.08

162.2 165.4 168.8 145.9 118.4 98.5 171.0 165.3 159.1 158.8 151.3

207.3 200.2 229.8 192.7 202.8 190.8 222.7 220.5 210.7 210.8 208.8

0.01 0.10  0.22  0.07  0.07  0.16  0.54 0.16 0.05 0.09  0.06 0.20

0.07 0.01  0.06  0.03  0.05 0.02 0.02  0.03  0.00 0.03 0.01 0.04

 0.2 1.2  1.1  1.4  2.3 0.4  1.1  2.1  4.2  0.1  1.1 1.5

2.1  0.2  10.4 6.4 0.8 5.5 0.2  3.2 1.4  0.6 0.2 4.7

Y. Wu et al. / Continental Shelf Research 31 (2011) 2041–2053

2045

60 50

z (m)

40 30 20 10 0 0

2

4 −0.5

0

1

2

−0.2

0.5 155

160

165 200

115

120 180

210

220

200

220

30 25

z (m)

20 15 10 5 0 0

Semi−major Axis (m s−1)

−0.4

Semi−minor Axis (m s−1)

0 110

Inclination (°)

Phase (°)

Fig. 4. Depth-dependent M2 ellipse parameter comparisons between model results (thick black curves) and observations (black dots, thin black lines are the error bars of the observations) at site A1 (upper row) and A5 (lower row). The dash dot curves represent the model results with a constant bottom roughness (z0 ¼ 0.0005 m).

Davies and Lawrence, 1994). As an example, the depth dependent profiles of the comparison at A1 and A5 are shown in Fig. 6. At site A1, the model largely catches the vertical distribution of the observed semi-major axis, inclination and phase. The model obtains the right signs of the observed semi-minor axis; however, the magnitudes are clearly overestimated by model. At site A5, the vertical profiles of the inclination and phase are quantitatively simulated; however, obvious differences exist for semi-major axis and semi-minor axis.

Fig. 5. M2 tidal ellipses (14–54 m) from site A1 off Cape Sharp (see Fig. 1).

obviously over-estimated by model. The difference of phase varies from  12.91 to 2.21, and difference of inclination varies from 17.31 to 16.11. The reasons for the discrepancies between model and observations are many, for example, the simplicity of the tidal model and noise effects on the observations since the magnitudes of M4 are small compared to those of M2 (Davies et al., 1985;

4.2.3. Tidal residual currents comparisons In general, residual currents can be driven by many mechanisms, for example, nonlinear interaction between tides, bottom topography, geometry of the coastline, bottom friction, winds, waves, density variations and far field general circulations. The contributions of all these mechanisms are included in the field observations. However, some of them, for example, winds, waves, density variations and far field general circulations, are ignored in our tidal model and they account for at least part of the modelobservations difference. Two approaches are used for model-data comparisons in this subsection. One is based on qualitative comparison obtained by plotting the observed vectors on the background of current vectors from the model. The other is based on a simple statistical analysis in which the parameters based on pairs of observational and model velocities are compared and analysed. In Fig. 7, the black thick arrows represent recent depthaveraged data from profiles with the vertical resolution of 2 m from the surface to 7.5 m above the bottom, whereas the black thin arrows are derived from data with poor vertical resolution (one or two levels only). Fig. 8 shows a sample of the observed vertical profile of tidal residual currents at site A1. The vector fields of both model results and observations show a large scale

2046

Y. Wu et al. / Continental Shelf Research 31 (2011) 2041–2053

Table 3 Observed and modelled tidal ellipse parameters for depth-averaged M4 currents at DFO and Fundy Ocean Research Centre for Energy (FORCE) mooring sites. Stations Observed

A1 A2 A3 A4 A5 A6 A8 S1 S3 S4

Modelled

Difference

Semi-major axis (m s  1)

Semi-minor axis (m s  1)

Inclination (deg.)

Phase (deg.)

Semi-major axis (m s  1)

Semi-minor axis (m s  1)

Inclination (deg.)

Phase (deg.)

Semi-major axis (m s  1)

Semi-minor axis (m s  1)

Inclination (deg.)

Phase (deg.)

0.27 0.16 0.12 0.08 0.08 0.12 0.21 0.26 0.30 0.31

 0.001 0.063  0.010 0.032  0.022  0.059  0.014 0.007 0.022 0.038

137.7 15.4 14.9 158.0 165.1 99.4 30.5 149.5 149.6 154.3

296.0 264.1 141.4 292.2 201.4 207.1 104.8 284.6 316.4 318.3

0.29 0.53 0.24 0.05 0.17 0.21 0.32 0.30 0.39 0.40

 0.067 0.040  0.010  0.015 0.009  0.025 0.030  0.053  0.021  0.019

138.9 178.5 22.9 142.8 166.1 113.6 14.4 166.8 155.0 153.5

293.8 84.1 185.8 176.3 215.0 218.1 91.9 300.9 326.9 325.1

 0.02  0.37  0.12 0.03  0.07  0.09  0.11  0.04  0.09  0.09

0.066 0.023 0.000 0.047  0.031  0.034  0.044 0.060 0.043 0.057

 1.2  163.1  8.0 15.2  1.0  14.2 16.1  17.3  5.4 0.8

2.2 180.0  44.4 115.9  13.6  11.0 12.9  16.3  10.5  6.8

60 50

z (m)

40 30 20 10 0

0

0.5 −0.1

0

0.1 100

150

200250

300

350

30 25

z (m)

20 15 10 5 0 0

0.1 0.2−0.05 0 0.05 140 160 180 150 Semi−major Axis Semi−minor Axis Inclination (°) (m s−1) (m s−1)

200 250 Phase (°)

Fig. 6. Depth-dependent M4 ellipse parameter comparisons between model results (thick black curves) and observations (black dots, thin black lines are the error bars of the observations) at site A1 (upper row) and A5 (lower row). The dash dot curves represent the model results with a constant bottom roughness (z0 ¼ 0.0005 m).

30’ N 24’ 18’ 12’ 6’ 1.0 m/s 45°N 65°W

40’

20’

64°W

40’

20’

Fig. 7. Depth-averaged residual flow. The thick black vectors are derived from recent current profile observations with high vertical resolution, the thin black vectors are based on early data with only one or two vertical levels and the grey vectors are the model results.

Y. Wu et al. / Continental Shelf Research 31 (2011) 2041–2053

anticlockwise eddy-like feature in Minas Channel, plus a clockwise eddy in the Southern Bight with relatively weak intensity. Along the northern coast of Minas Passage, data reveal that the residual flows eastward, whereas it flows westward, for the most part, along the southern coast of the Passage. These features are qualitatively simulated by the model, though in some places the observed magnitudes are over- or underestimated by the model. The statistical results in Table 4 show that the modelled depthaveraged residual currents are in reasonable agreement with their observed counterparts, but some differences are apparent. For example, at S4, the observed velocity is well reproduced by model. The magnitude of the difference between model and data is 0.06 m s  1,

2047

which is less than 10% of the mean. At A2, however, the magnitude of the difference reaches 100% of the mean value. The reasons for this significant difference are many: it could be due to our simple model, in which the general circulation, wind and wave effects are ignored, or uncertainties resulting from high horizontal gradient of the topography, for example, at site A2.

4.2.4. Total velocity comparisons In this subsection, we document the model-data comparison of the total current, which is related to the calculation of bottom shear stress and horizontal transport patterns of suspended sediment. An example of the comparisons at S4 is shown in Fig. 9, which indicates that the observed current is successfully simulated by the model, except that the modelled ebb u component is slightly smaller than the observations. The parameters obtained in the bottom layer from the time series results are given in Table 5. The parameters include mean current speed in

u, v and |u| (m s−1)

6

u (Obs) u (Mod)

4

v (Obs) v (Mod)

|u| (Obs) |u| (Mod)

2 0 −2 −4

u, v and |u| (m s−1)

4 2 0 −2 −4 730

740

750 Time (hour)

760

770

Fig. 9. Tidal current comparisons at S4: (A) depth-averaged over range of 6 m to  46 m from bottom and (B) values at 6 m from bottom.

Fig. 8. Residual current vectors (12–46 m) at site A1.

Table 4 Observed and modelled depth-averaged tidal residual currents (u: zonal; v: meridional and juj is the magnitude) at DFO and Fundy Ocean Research Centre for Energy (FORCE) mooring sites. Stations

A1 A2 A3 A4 A5 A6 A8 S1 S3 S4 Mean r.m.s.

Observed

Modelled

Difference

u (m s  1)

v (m s  1)

9u9 (m s  1)

u (m s  1)

v (m s  1)

9u9 (m s  1)

u (m s  1)

v (m s  1)

9u9 (m s  1)

 0.01  0.27 0.18  0.29  0.10  0.14 0.46 0.25 0.47 0.48 0.10

 0.20  0.09 0.08 0.11  0.03 0.10 0.06  0.29  0.28  0.26  0.08

0.20 0.29 0.20 0.32 0.10 0.17 0.48 0.39 0.55 0.55 0.33

 0.14  0.52 0.36  0.29  0.17  0.15 0.59 0.43 0.54 0.53 0.12

 0.17  0.05 0.04 0.26  0.04 0.11  0.12  0.21  0.29  0.29  0.08

0.23 0.52 0.36 0.40 0.17 0.19 0.61 0.49 0.62 0.61 0.42

0.13 0.25  0.18 0.0 0.07 0.01  0.13  0.18  0.07  0.05  0.02 0.13

 0.03  0.04 0.04  0.15 0.01  0.01 0.19  0.08 0.01 0.03 0.00 0.08

 0.03  0.23  0.16  0.08  0.07  0.02  0.13  0.10  0.07  0.06  0.09 0.11

2048

Y. Wu et al. / Continental Shelf Research 31 (2011) 2041–2053

Table 5 Observed and modelled depth-averaged tidal current time series analysis at DFO and Fundy Ocean Research Centre for Energy (FORCE) mooring sites. Sations

A1 A2 A3 A4 A5 A6 A8 S1 S3 S4 Mean r.m.s.

Observed

Modelled

Difference

9u9f lood (m s  1)

9u9ebb (m s  1)

r

9u9f lood (m s  1)

9u9ebb (m s  1)

r

9u9f lood (m s  1)

9u9ebb (m s  1)

r

1.53 0.90 1.55 1.00 0.63 0.59 1.93 1.72 1.71 1.68 1.32

1.50 1.28 1.30 1.48 0.63 0.75 1.28 1.37 1.00 1.04 1.16

0.01  0.19 0.08  0.19  0.01  0.10 0.17 0.10 0.26 0.23 0.04

1.40 0.67 1.79 1.05 0.71 0.73 2.60 1.81 1.66 1.70 1.41

1.68 1.63 1.31 1.79 0.74 0.84 1.55 1.16 0.85 0.89 1.24

 0.09  0.41 0.15  0.25  0.01  0.06 0.25 0.22 0.32 0.31 0.04

0.14 0.23  0.24  0.06  0.07  0.14  0.67  0.10 0.05  0.02  0.09 0.25

 0.18  0.35  0.01  0.31  0.10  0.08  0.27 0.21 0.15 0.15  0.08 0.20

0.10 0.22  0.07 0.06 0.00  0.04  0.08  0.11  0.06  0.08 0.00 0.09

flood (9U9flood) and ebb (9U9ebb) flows and tidal asymmetry, r, defined as (9U9flood  9U9ebb)/(9U9flood þ 9U9ebb). The table shows that the model overestimates both the flood speed (by 0.09 m s  1) and the ebb speed (by 0.08 m s  1). The r.m.s. of the differences in flood and ebb are 0.25 and 0.20 m s  1, respectively. The discrepancies amount to 5% and 6% of their means, respectively. The signs of the tidal asymmetry from model agree with those from observations except at station A1, where the asymmetry is weak with a magnitude of 0.01. Also, both the observations and model results show that, at sites A8, S3, S4, the flooding current is clearly stronger than the ebbing, but weaker than the ebbing at A2 and A4. The model results are in general consistent with the tidal asymmetry from the observations.

5. Horizontal features of model results The features of the tidally-dominated flow in this region, such as tidal elevation, tidal currents and residual current, have been presented in many previous studies, for example, Tee (1976, 1977) and Greenberg (1977, 1983). In this section, we briefly describe the novel features of our model results because (1) there are many new inputs to our model, such as new bathymetry from recent multibeam survey data and extensive historical grain size data, and (2) it features exceptionally high model resolution, especially in the Minas Passage area.

Fig. 10. M2 tidal elevation parameters of (A) amplitude and (B) phase.

5.1. Tidal amplitudes and phases Horizontal variations of the tidal amplitude and phase of M2 constituent are shown in Fig. 10. As we can see, the amplitude rises rapidly at the entrance to Minas Passage and increases as the tide advances to the east, except for minima in some coastal areas due to the interactions between the incident and reflected waves. The maximum amplitude of 6–7 m occurs in Cobequid Bay. The horizontal variation of the phase is found to follow a similar trend. The phase increases steadily from west to east but with two pronounced increases at the entrances of Minas Passage and Cobequid Bay. 5.2. M2 tidal current The distributions of the depth-averaged semi-major axis and semi-minor axis of M2 are plotted in Fig. 11. The semi-major axis with high magnitudes mainly occur in areas, from west to east, including Minas Channel, Minas Passage, Minas Basin and lower Cobequid Bay. The maximum velocity is found in the Minas Passage, where the semi-major axis of M2 reaches 3–4 m s  1.

Fig. 11. Ellipse parameters of the depth-averaged tidal currents (M2): (A) semi-major axis and (B) semi-minor axis.

Compared to the semi-major axis, the magnitude of semi-minor axis is quite small (o0.1 m s  1) except in the Southern Bight and Scots Bay, where the sign of the semi-minor axis is negative,

Y. Wu et al. / Continental Shelf Research 31 (2011) 2041–2053

2049

ranging from  0.5 to 0.2 m s  1, and the middle Minas Channel, where minor axis shows positive, ranging from 0.1 to 0.3 m s  1. The magnitude of the semi-major axis in Minas Passage, especially in the northern side, is quite a bit larger than that of the semi-minor axis. This indicates that the tidal flow there is strongly rectilinear, and potentially suitable for the installation of the in-stream turbines to extract energy during both flood and ebb periods. 5.3. Tidal residual current field Since the net sediment transport in the tidally-dominated regions strongly depends on the intensity, direction and scale of the tidal residual flow (Dronkers, 1986; Aldridge, 1997; Sanay et al., 2007), we present the modelled residual current field in this subsection. The modelled depth-averaged tidal residual circulation (Fig. 7) reveals four prominent eddy-like structures in the study area. The first is an anticlockwise gyre stretching across the Minas Channel. The centre of the gyre is close to the centre line of Minas Channel and about 10 km west of Cape Split. The magnitude of the velocity near the outer edge in the northern part of the Channel reaches 0.8 m s  1, which is higher than that in the southern part (0.5 m s  1). The maximum speed occurs near the western tip of Cape Split with a magnitude of 1.2 m s  1. The second gyre is clockwise and located in Southern Bight of the Minas Basin. The magnitude of the velocity of this gyre is about 0.2–0.3 m s  1. In the Minas Passage, two eddies with a small spatial scale of about 2 km2 can be found. One is centred near the western entrance of the Minas Passage and flows in clockwise direction. The strength of the gyre is strongly asymmetric, with speeds of 1.5 m s  1 in the southern part contrasting the 0.7 m s  1 at the northern coast of the passage. The other gyre is anticlockwise and covers the northeastern part of the passage. These structures can also be found form the observational data (Fig. 7). 5.4. Bottom shear stress Bottom shear stress is a controlling factor for the sediment transport. It directly controls the intensity and pathway of the bed load transport. For suspended load, it dominates suspended concentration in an indirect way through its effects on the erosion and deposition processes between the seabed and water column. The magnitudes of the bottom shear stress averaged over the flood and ebb durations are plotted in Fig. 12. Flooding stress with high intensity can be found in Minas Channel, Minas Passage, central Minas Basin and Cobequid Bay. The maximum is found at western entrance of Minas Passage, where the stress reaches 20 Pa. The magnitude of the stress is around 5 Pa in Minas Channel and Cobequid Bay, and around 2 Pa in central Minas Basin. In the remaining areas, the stress is quite weak, usually less than 1.0 Pa (Fig. 12A). The main features of the stress during ebb are quite similar to those of the flood stress except that the location of the high stress in Minas Channel found during flood moves northward due to a difference of the pathways of the flood and ebb currents (Fig. 12B). When compared to the distribution of bottom sediment grain size, it is clear that the high shear stress is basically related to the coarse grain size, for example, in Minas Passage and northern Minas Channel. However, the relationship between the fine grain size and low stress level is not very clear, for instance, in the areas of upper Cobequid Bay and Southern Bight. This means that the influence of grain size on the stress is supplemented by other factors, such as topography and the character of the tide. To illustrate the relative dominance of the flood and ebb in the bottom stress, another asymmetry index is defined asð9tf lood 9 9tebb 9Þ=ð9tf lood 9þ 9tebb 9Þ, (where tf lood and tebb are the averaged

Fig. 12. Mean bottom stress vector during periods of flood (A) and ebb (B) and asymmetry indicator (C; see text Section 5.4). Note that the arrows in (A) and (B) indicate only the direction of the shear stress.

bottom stress magnitudes during flood and ebb, respectively). The positive values indicate that the stress during flood is stronger than that during ebb. Otherwise, the ebb stress outweighs the flood stress when the index is negative. Fig. 12C shows clearly that the flood stress is stronger than the ebb counterpart in Scots Bay, the western entrance of Minas Passage and Cobequid Bay, but weaker than the ebb stress in the northwest of Cape Split and the western part of the Southern Bight. In general, tidal asymmetry is mainly attributed to two factors, overtides (M4 and M6) and tidal residual flow (Aldridge, 1997; Friedrichs and Aubrey, 1988; Sanay et al., 2007). It is useful to distinguish the specific contribution from each factor. To do so, we decompose the total tidal velocity as the residual flow and seven main tides (O1, K1, N2, M2, S2, M4 and M6). The asymmetry indicator due to one factor (residual flow) can be estimated by removing the other factor (M4 and M6) in the total velocity. The contribution of overtide is further split into M4 and M6. The results are shown in Fig. 13. Fig. 13A clearly shows a strong spatial variation of the asymmetry indictor, which is induced by the tidal residual flow. The horizontal pattern is quite similar to that of the residual flow shown in Fig. 7. Under the action of the tidal residual flow, the bottom stress during flooding period is stronger than that during ebbing in western Scots Bay, western and eastern ends of the Minas Passage. However, in the northern part of the Minas Channel and western part of the Southern Bight, the stress during flooding period is weaker than that in ebb. The magnitude of the stress asymmetry induced by M4 is close to zero except in two places, upper Cobequid Bay and southern part of the Minas Channel. The nonlinear effect of M4 results in stronger stress than in flooding period in the former place, but an opposite consequence in the latter place (Fig. 13B). The important contribution of M6 mainly occurs in the upper Cobequid Bay and intensity is smaller than

2050

Y. Wu et al. / Continental Shelf Research 31 (2011) 2041–2053

Fig. 13. Asymmetry indicators induced by the tidal residual (A), M4 tide (B) and M6 tide (C).

that of M4 (Fig. 13C). Overall, the tidal residual flow dominates the bottom stress asymmetry in our study area except the upper Cobequid Bay, where the stress asymmetry is mainly attributed to the combination of M4 and M6.

6. Sediment transport pattern Theoretically, the transport of bed load and suspended sediment can be quantitatively described by a coupled hydrodynamic– sediment model, for example, Warner et al. (2008), in which the sediment transport is simulated by an advection–diffusion model, governed by a series of sediment parameters, such as grain size, settling velocity, critical shear stresses for erosion and deposition, etc. On one hand, the sediment moves from one place to another under the actions of current and waves. On the other hand, the displaced sediment changes the topography and density in the water column, which, in turn, affects the flow conditions. However, one of the problems confronting modellers is the definition of these parameters since they usually show strong temporal and spatial variations. In our study area, for instance, the grain size of the bottom sediment displays a wide range from large boulders in Minas Passage to fine-grained sediment in Southern Bight (Fig. 2). So, the parameters based on the assumption of the spatial uniformity are clearly unrealistic. The definition of the parameters is further complicated by the presence of the cohesive sediment, which has been found to be an important component in Minas Basin, because the transport mechanisms are not only related to the size and density of cohesive particles, but also their biological and chemical properties (Amos et al., 1988, 1992). For instance, Amos et al. (1988) observed that the shear strength of the sediment at southern part of Minas Basin showed a dramatic increase in mid-summer. Using remotely-sensed images, a recent

Fig. 14. Contour map of the bed load transport rate flux (per unit cross-sectional distance) averaged during flood (A), ebb (B) and entire flood–ebb cycle (C). The arrows indicate only the directions of the transport.

study showed that surface suspended sediment concentration presents a strong seasonal variation (G. Bugden, personal communication). The reasons leading to the seasonal variation are still not well understood. The interactions between the sediment and hydrodynamic processes are complicated, so it is reasonable to start with a simple approach. Thus, without considering the feedback of sediment to the hydrodynamics, the sediment transport is estimated with the hydrodynamic model results and sediment models reported in previous studies. It is worth to note that the contribution of surface waves to the bottom shear stress is not included in this study. The waves may play an important role in the sediment transport in some areas, especially in shallow waters though the mean significant wave height is generally less than 0.5 m and the period is about 4–5 s according to Li et al. (2010). 6.1. Bed load transport Using the bottom shear stress from the hydrodynamic model and the observed grain size, the bed load transport rate1 is calculated with the formula proposed by Huang (2010), which is a revised version of the equation derived by Meyer-Peter and ¨ Muller (1948). The results of the transport rate illustrate that during flood tides, the bed load transport rate shows a strong spatial variation (Fig. 14). Bed load movement is quite active in Minas Channel, Minas Passage, Cobequid Bay, and some coastal areas around Minas Basin (Fig. 14A). The maximum transport, of the order of 2.0 kg m  1 s  1, is found at the western entrance of 1 In this paper, sediment transport rate is defined as the total mass transport of sediment per unit length of lateral cross-section, which is normal to the vector transport. Hence the units are (kg s  1)/m¼ kg m  1 s  1. Integration of this quantity along a particular transect gives the total transport through the section.

Y. Wu et al. / Continental Shelf Research 31 (2011) 2041–2053

Minas Passage, where the rate is about 20 times higher than that in Cobequid Bay. The transport rates in the coastal waters, on the order of 0.01 kg m  1 s  1, are comparable. The figure clearly shows that the bed load transport in Southern Bight moves to northward, but the magnitude is quite weak. In Minas Passage, sediment moves into Minas Basin along the northern shelf. In Cobequid Bay, the sediment is transported eastward to the upper bay. During ebb, the locations with higher transport rates are similar to those during flood, except in Minas Passage, where the sediment transport occurs mainly on the southern shelf of the Passage, versus on the northern shelf during flood (Fig. 14B). The directions of sediment transport during ebb are nearly opposite to those during flood. In Minas Passage, the net transport rate, averaged over the entire flood–ebb cycle (Fig. 14C), is directed eastward and feeds into Minas Basin along the northern shelf of the Passage, whereas sediment leaves Minas Basin along the southern shelf. According to the horizontal distribution of the grain size in Minas Passage, it can be inferred that Minas Basin receives coarse sediment, which is originally from the Minas Channel and Minas Passage, but donates fine sediment which originates in the Southern Bight. The figure also shows that most of the coarse sand is deposited at the eastern outlet of Minas Passage and forms the sand bars there. Another source of the coarse sediment which is deposited in central Minas Basin may be found in the eastern Minas Basin, where the ebb current exceeds the flood and carries the net amount of sediment westward. So overall, central Minas Basin is a place for bed load deposition. This conclusion is supported by the field observations of Amos and Joice (1977), who observed that the ‘‘newly’’ formed sediment in the central Minas Basin reached 8 m and the depth of the bedrock below seabed there was as deep as 40 m. At the western tip of Cape Split, a strong divergence of the bed load transport can be found. This feature mainly results from the spatial variability of the flood and ebb currents. On the eastern side of the divergence, the flood current is much stronger than the ebb (Fig. 12C). However, the ebb component dominates the tidal currents on the western side. Another divergence where the sediment moves in the opposite direction is at the eastern edge of Minas Basin. In Cobequid Bay, the sediment moves to the upper Bay. This movement also agrees with the observations of Amos and Joice (1977), in which they showed the deposition depth in Cobequid Bay increased with the distance into the upper Bay, but the erosion depth showed an opposite trend. According to the mechanism of asymmetry of the bottom shear stress analysed above, it is not difficult to conclude that the tidal residual flow mainly dominates the spatial pattern of the bed load transport in the study area except the CObequid Bay, where the bed load transport properties is more controlled by the M4 and M6.

2051

related to the turbulence intensity of the flow, we assume that the concentration changes in time following: cs ðtÞ ¼ C s cos2 ðotjÞ

ð2Þ

where cs(t) is the time-dependent surface concentration, Cs is the magnitude of the maximum surface concentration, and o and j are the frequency and phase of the depth-averaged M2 currents. As we know, vertical profiles of the sediment concentration are dependent on the turbulence intensity in the water column and the settling velocity of the sediment particulates. In this equation, however, time lag between the tidal current and sediment concentration is assumed negligible. This assumption may not be right for some cases, for example, tidal pumping of fine sediment, which relies on the lags in settling and re-suspension and differential concentrations in the vertical. For simplicity, we further assume the vertical distribution of the sediment is uniform according to the observations of the vertical profiles of the suspended sediment in Minas Basin (Amos and Joice, 1977). Data from April 15, 2009 were selected to derive the surface amplitude, Cs, since they have both high levels concentration and good horizontal coverage. Thus, the suspended load transport rate can be calculated using the ‘‘observed’’ concentrations and the total velocity from our hydrodynamic model. The results are shown in Fig. 15. During flood tides, the suspended sediment advances eastward following the flood currents, and retreats westward during ebb with the ebb currents. The typical magnitude of the transport rate is about 0.5 kg m  1 s  1, but reaches 2.0 kg m  1 s  1 in western Minas Passage. However, the magnitude of the net transport of the suspended material within the tidal cycle shows a strong spatial

6.2. Suspended load transport The transport mechanism of the suspended load is much more complicated than that of the bed load because it is not only related to the physical characteristics of the sediment particles, but also to their chemical and biological properties, which are important factors for settling velocity of the particles and the exchange processes between the water column and seabed, namely erosion and deposition. To keep the calculation as simple as possible, the surface sediment data, derived from remotelysensed images obtained from MEdium Resolution Imaging Spectrometer (MERIS), are used to represent the suspended particulate concentration. The data have a maximum spatial resolution of about 300 m. However, the temporal resolution of the data is roughly one day, which is too large to describe the changes over a tidal cycle. Since the suspension capacity in the water column is

Fig. 15. Contour map of the suspended load transport rate flux (per unit crosssectional distance) averaged during flood (A), ebb (B) and over the entire cycle (C). The black thick vectors in (C) represent the observed fluxes. The green line in (C) indicates the locations of the cross section at the eastern outlet of Minas Passage used in text Section 6.2. The arrows in (A) and (B) indicate only the direction of the transport, but those in (C) indicate both magnitude and direction.

2052

Y. Wu et al. / Continental Shelf Research 31 (2011) 2041–2053

Fig. 16. Total sediment transport flux. The arrows indicate only the direction of the transport.

variation. At the same time, the magnitude of the net transport is clearly smaller than that in flood or ebb periods. In Minas Channel, Minas Passage and Scots Bay, the magnitude of the net transport is around 0.1 kg m  1 s  1 and only 0.01 kg m  1 s  1 in central Minas Basin and the Southern Bight. The plot (Fig. 15C) also shows that the features of the net transport of the suspended load have many similarities with those of the tidal residual currents except in Cobequid Bay, where the suspended material moves eastward, whereas the tidal residual currents flow westward. This means that the transport mechanism of the suspended load there is different from the tidal residual flow. Our analysis shows that the nonlinear interactions of M2 and M4 dominates the suspended load transport (results are not shown). The comparisons between the model results and observed transport of suspended load are difficult since the field measurements are scarce. Using the data available, a preliminary comparison is performed. The measurements are from Amos and Joice (1977) and results are plotted in Fig. 15C. It is worthwhile to note that the data were collected only over 1–2 complete tidal cycles. Generally, the comparison shows reasonable agreement between model results and the observations. For instance, both the model results and observations show the strong transport flux directed into Minas Basin at the eastern outlet of the Minas Passage. In Cobequid Bay, the observations show that the net sediment transport eastward, and a similar transport direction can be found in the model results. However, the differences in magnitudes are obvious. The model clearly overestimates the transport in the Minas Basin, but underestimates it in Cobequid Bay. The net suspended matter flowing into Minas Basin through Minas Passage is calculated at a cross section near the eastern end of the Passage (see green line in Fig. 15C) where the net input is estimated at 2.4  106 m3 yr  1, similar to the observed value of 1.6  106 m3 yr  1 (Amos et al., 1980) The map of total sediment transport rate, including both the bed load and the suspended load (Fig. 16), indicates that pronounced transport occurs mainly in the Minas Channel and Minas Passage with the magnitude of 0.1–0.2 kg m  1 s  1. In Minas Channel, the sediment movement shows an anticlockwise structure. The sediment in Minas Passage moves eastward into Minas Basin and deposits into the central Minas Basin. The sediment in the eastern end of the basin mainly moves to the central basin and deposits there as well. In Cobequid Bay, sediment moves eastward to the upper Bay.

7. Conclusions The properties of the Tidally-induced sediment transport in the upper Bay of Fundy, where significant changes in tidal processes may occur due to the recently proposed tidal power project, have been studied with a 3-D hydrodynamic model, an empirical sediment model and surface sediment concentration

derived from remotely-sensed images. In the calculation of the bottom shear stress, the observed grain size data are employed to derive the bottom drag coefficient. The model was evaluated against independent observational data, which include tidal elevation, tidal current (in the water column and bottom layer), tidal residual current and tidal asymmetry indicators. The evaluation shows that the model is in good agreement with the observations. For example, the magnitude of the difference of the mean semi-major axis velocity of M2 is 0.06 m s  1, less than 3.0% of the mean. The r.m.s. of the semi-major axis difference is 0.20 m s  1, or about 9% of the mean. All the signs of the modelled semi-minor axes of M2 are consistent with those of the observations as well. The difference of inclination in the M2 tidal ellipse lies in the range of 4.21 to þ1.2o. The mean discrepancy of M2 phase (time difference from the maximum velocity) is 0.201. The observed vertical distributions of the velocity parameters are also generally reproduced by the model. The horizontal features of the residual flow are also successfully simulated by model. The statistical results show that the modelled tidal residual currents are in reasonable agreement with the observations, but some differences are apparent. The model-data comparisons indicate that the observed total velocity is reproduced by model. The model overestimates the flood speed by 0.09 m s  1, but underestimates the ebb speed by 0.08 m s  1. The discrepancies amount to roughly 5% and 6% of their means, respectively. The signs of the tidal asymmetry from the model agree with those from observations. The r.m.s. differences of the flood and ebb speeds are 0.25 and 0.20 m s  1, respectively. The sediment transport includes two components, bed load and suspended load. The bed load is calculated using the modelled bottom shear stress and the observed grain size data, and the results roughly agree with the observed features of the historical erosion and deposition observations in Minas Basin and Cobequid Bay. The transport of the suspended load is estimated using the modelled velocity field and the remotelysensed surface sediment concentrations. The model-data comparison illustrates that the observed directions of suspension transport are basically reproduced by the model. The estimated net suspended load transport into Minas Basin through Minas Passage is 2.4  106 m3 yr  1, which is consistent with the observed level of 1.6  106 m3 yr  1. The transport rate of the bed load in the study domain shows a strong spatial variation. Strong sediment movement occurs mainly in Minas Channel, where the magnitude of the transport flux reaches 1.0–2.0 kg m  1 s  1. In central Minas Basin and Cobequid Bay, the magnitude is about 0.1 kg m  1 s  1. In the remaining areas, the magnitude is less than 0.001 kg m  1 s  1. Minas Basin is the deposition site for most of the bed load from Minas Passage and the eastern edge of the basin. In Cobequid Bay, the bed load transport is directed eastward to the upper Bay. During the flood and ebb periods, the transport direction of the suspended particulate load mainly follows the tidal currents. During flood tides, the suspension advances eastward with the currents, whereas during the ebb period, it retreats westward. The horizontal distribution of the transport during flood and ebb is relatively uniform. The typical magnitude is about 0.5 kg m  1 s  1 and reaches 1.0–2.0 kg m  1 s  1 in western Minas Passage. However, the magnitude of the net transport of the suspension over an entire tidal cycle shows a strong spatial variation, despite the fact that it is clearly smaller than those in the flood or ebb periods separately. In Minas Channel, Minas Passage and Scots Bay, the magnitude of the transport is around 0.1 kg m  1 s  1 and only 0.01 kg m  1 s  1 in central Minas Basin and the Southern Bight. The total transport of bed load plus suspended load is concentrated in the Minas Channel and Minas Passage, where the magnitude of the transport flux is about 0.1–0.2 kg m  1 s  1.

Y. Wu et al. / Continental Shelf Research 31 (2011) 2041–2053

In the remaining areas, the magnitude is relatively small around 0.01 m  1 s  1. In Minas Channel, the sediment movement shows an anticlockwise structure. The sediment in Minas Passage moves eastward into the Minas Basin. The sediment in the eastern Minas Basin mainly moves to the central basin. In the Cobequid Bay, the sediment transports to the upper bay. The sediment transport results are indeed strongly sensitive to the model parameters, for example, the bed load transport, in which the increase or decrease of the critical shear stress would exponentially decrease or increase the amount of the bed load transport. The uncertainties of the parameters can seriously overor underestimate the sediment budget. However, the spatial patterns of the sediment transport are generally realistic and the model results are sufficiently robust to be used in a future study of the impacts of the tidal power project on sediment transport in the upper Bay.

Acknowledgements This work was supported by OEER-OETR Associations of Nova Scotia. We thank P. Hill for providing the grain size data, R. Pettipas for providing the ADCP current data and G. Lazin for providing the surface sediment data. We also thank C. Hannah and J. Shaw for many helpful suggestions. T. Milligan and G. Bugden read an early version of the paper and gave helpful comments and suggestions for improvement. References Aldridge, J.N., 1997. Hydrodynamic model prediction of tidal asymmetry and observed sediment transport paths in Morecambe Bay. Estuarine and Coastal Marine Science 44, 39–56. Amos, C.L., Buckley, D.E., Daborn, G.R., Dalrymple, R.W., McCann, S.B., Rick, M.J., 1980. Trip23: Geomorphology and Sedimentology of the Bay of Fundy. Amos, C.L., Daborn, G.R., Christian, H.A., Atkinson, A., Robertson, A., 1992. In situ erosion measurements on fine-grained sediments from the Bay of Fundy. Marine Geology 108, 175–196. Amos, C.L., Joice, G.H.E., 1977. The sediment budget of the Minas Basin, Bay of Fundy, N.S. Bedford Institute of Oceanography. Data Series Report, BI-D-77-3, 274 pp. Amos, C.L., Long, B.F.N., 1980. The sedimentary character of the Minas Basin, Bay of Fundy. In: McCann, S.B. (Ed.), The Coastline of Canada: Littoral Processes and Shore Morphology. Geological Survey of Canada Papers, 80-10, pp. 123–152. Amos, C.L., Van Wagoner, N.A., Daborn, G.R., 1988. The influence of subaerial exposure on the bulk properties of fine-grained intertidal sediment from Minas Basin, Bay of Fundy. Estuarine and Coastal Marine Science 27, 1–13. Blumberg, A.F., Mellor, G.L., 1987. A description of a three-dimensional coastal ocean circulation model. In: Heaps, N. (Ed.), Three-Dimensional Coastal Ocean Models, vol. 4, American Geophysical Union, Washington, DC, pp. 1–16. Chen, C., Cowles, G., Beardsley, R.C., 2006. An Unstructured Grid, Finite Volume Coastal Ocean Model: FVCOM User Manual, second ed. SMAST/UMASSD Technical Report-06-0602, p. 315. Chen, C., Huang, H., Beardsley, R.C., Liu, H., Xu, Q., Cowles, G., 2007. A finite volume numerical approach for coastal ocean circulation studies: comparisons with finite difference models. Journal of Geophysical Research 112, C03018. doi:10.1029/2006JC003485. Chen, C., Liu, H., Beardsley, R.C., 2003. An unstructured grid, finite-volume, threedimensional, primitive equations ocean model: application to coastal ocean and estuaries. Journal of Atmospheric and Oceanic Technology 20, 159–186. Cowles, G.W., Lentz, S.J., Chen, C., Xu, Q., Beardsley, R.C., 2008. Comparison of observed and model-computed low frequency circulation and hydrography on the New England Shelf. Journal of Geophysical Research 113, C09015. doi:10.1029/2007JC004394. Davies, A.M., Jones, J.E., 1995. The influence of bottom internal friction upon tidal currents: Taylor’s problem in three dimensions. Continental Shelf Research 15, 1251–1285. Davies, A.M., Lawrence, J., 1994. A three-dimensional model of the M4 tide in the Irish Sea: the importance of open boundary conditions and influence of wind. Journal of Geophysical Research 99, 16227–17197.

2053

Davies, A.M., Saurel, J., Evans, J., 1985. Computing new coastal tidal dynamics from observations and a numerical model. Continental Shelf Research 4, 341–366. Dronkers, J., 1986. Tidal asymmetry and estuarine morphology. Netherlands Journal of Sea Research 20 (2/3), 117–131. Dupont, F., Hannah, C.G., Greenberg, D., 2005. Modelling the sea level of the upper Bay of Fundy. Atmosphere-Ocean 43, 33–47. Dupont, F., Hannah, C.G., Greenberg, D.A., Cherniawsky, J.Y., Naimie, C.E., 2002 Modelling System for Tides for the Northwest Atlantic Coastal Ocean. Canadian Technical Report of Hydrography and Ocean Science 221, viiþ 72 pp. Friedrichs, C.T., Aubrey, D.G., 1988. Non-linear tidal distortion in shallow wellmixed estuaries: a synthesis. Estuarine and Coastal Marine Science 27, 521–545. Garrett, C., 1974. Normal modes of the Bay of Fundy and Gulf of Maine. Canadian Journal of Earth Science 11, 549–556. Garrett, C., Cummins, P., 2004. Generating power from tidal currents. Journal of Waterway Port Coastal and Ocean Engineering 130, 114–118. Garrett, C.J.R., Greenberg, D., 1977. Predicting changes in tidal regime: the open boundary problem. Journal of Physical Oceanography 7, 171–181. Greenberg, D.A., 1977. Mathematical studies of tidal behaviour in the Bay of Fundy. Manuscript Report Series, 46, 127 pp. Greenberg, D.A., 1979. A numerical model investigation of tidal phenomena in the Bay of Fundy and Gulf of Maine. Marine Geodesy 2, 161–187. Greenberg, D.A., 1983. Modelling the mean barotropic circulation in the Bay of Fundy and Gulf of Maine. Journal of Physical Oceanography 13, 886–904. Greenberg, D.A., Amos, C.L., 1983. Suspended sediment transport and deposition modeling in-the Bay of Fundy, Nova Scotia—a region of potential tidal power development. Canadian Journal of Fisheries and Aquatic Sciences 40, 20–34. Huang, H.Q., 2010. Reformulation of the bed load equation of Meyer_peter_Muller in light of the linearity theory for alluvial channel flow. Water Resources Research 46, W09533. doi:10.1029/2009WR08924. Karsten, R.H., McMillan, J.M., Lickley, M.J., Haynes, R.D., 2008. Assessment of tidal current energy in the Minas Passage, Bay of Fundy. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 222, 493–507. Li, M.Z., Amos, C.L., 2001. SEDTRANS96: the upgraded and better calibrated sediment-transport model for continental shelves. Computers & Geosciences 27, 619–645. Li, M.Z., Hannah, C., Perrie, W., Tang, C., Prescott, R., Greenberg, D.A., 2010. Numerical model predictions of seabed shear stress, sediment mobility and sediment transport in the Bay of Fundy. Abstract with program, Atlantic Geoscience Society (AGS) Colloquium 2010, 5–6 February 2010, Wolfville, Nova Scotia. Long, B.F.N., 1979. The nature of bottom sediments in the Minas Basin system, Bay of Fundy. Bedford Institute of Oceanography Data Series, BI-D-79-4, vi, 101 pp. Lu, X., Zhang, J., 2006. Numerical study on spatially varying bottom friction coefficient of a 2-D tidal model with adjoint method. Continental Shelf Research 26, 1905–1923. Mellor, G.L., Blumberg, A.F., 2004. Wave breaking and ocean surface mixed layer thermal response. Journal of Physical Oceanography 34, 693–698. ¨ Meyer-Peter, E., Muller, R., 1948. Formulas for bed-load transport. In: Proceedings, 2nd Meeting, IAHR, Stockholm, Sweden, pp. 39–64. Neill, S.P., Litt, E.J., Couch, S., Davies, A.G., 2009. The impact of tidal stream turbines on large-scale sediment dynamics. Renewable Energy 34, 2803–2812. Pawlowicz, R., Beardsley, B., Lentz, S., 2002. Classical tidal harmonic analysis including error estimates in MATLAB using T-TIDE. Computers and Geosciences 28, 929–937. Sanay, R., Voulgaris, G., Warner, J.C., 2007. Tidal asymmetry and residual circulation over linear sandbanks and their implication on sediment transport: a process-oriented numerical study. Journal of Geophysical Research 112, c12015. doi:10.1029/2007JC004101. Shaw, J., Amos, C.L., Greenberg, D.A., O’Reilly, C.T., Parrott, D.R., Patton, E., 2010. Catastrophic tidal expansion in the Bay of Fundy, Canada. Canadian Journal of Earth Sciences 47, 1079–1091. Sucsy, V., Pearce, B.R., Panchang, V.G., 1993. Comparison of two- and three dimensional model simulation of the effect of a tidal barrier on the Gulf of Maine tides. Journal of Physical Oceanography 23, 1231–1248. Tee, K.T., 1976. Tide-induced residual current, a 2-D nonlinear numerical tidal model. Journal of Marine Research 31, 603–628. Tee, K.T., 1977. Tide-induced residual current-verification of a numerical model. Journal of Physical Oceanography 17, 396–402. Thresher, R., Musial, W., 2010. Ocean renewable energy’s potential role in supplying electrical energy needs. Oceanography 23, 16–41. Walkington, I., Burrows, R., 2009. Modelling tidal stream power potential. Applied Ocean Research 31 (4), 239–245. Warner, J.C., Sherwood, C.R., Signell, R.P., Harris, C.K., Arango, H.G., 2008. Development of a three-dimensional, regional, coupled wave, current, and sediment-transport model. Computers & Geosciences 34, 1284–1306. Werner, S.R., Beardsley, R.C., Williams III, A.J., 2003. Bottom friction and bed forms on the southern flank of Georges Bank. Journal of Geophysical Research 108 (C11), 8004. doi:10.1029/2000JC000692.