# Modeling Assessment of Tidal Energy Extraction in the Western Passage

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Study Site

**.**shows the model domain and bathymetry distribution. Bathymetric data were obtained from various data resources. Bathymetry in the large area of the Bay of Fundy and Gulf of Maine was interpolated from the National Oceanic and Atmospheric Administration’s (NOAA’s) ETOPO1 1-arc-minute Global Relief Model [36]. Inside the Passamaquoddy–Cobscook Bay archipelago, bathymetric data were digitized from NOAA and Canadian Hydrographic Service navigation charts and supplemented with multi-beam data for the Western Passage and Cobscook Bay [28]. Water depths in most of the coastal areas are generally shallow and less than 100 m. The deepest area in the model domain is near the open boundary and the southeast side of Grand Manan Island.

#### 2.2. Tidal Hydrodynamic Model

_{T}is the turbine thrust coefficient, A

_{s}is the flow-facing area swept by turbines, and $\overrightarrow{u}$ is the velocity vector at the turbine hub height.

#### 2.3. Model Configurations and Boundary Conditions

^{3}/s and 5.6 m

^{3}/s for the St. Croix River and Dennys River, respectively, which are relatively small compared to the model domain [28]. Wind-driven circulation in the archipelago system is also small compared to the strong tidal current. Therefore, similar to [28], the sea surface wind, salinity, and temperature effects are not considered in this study.

#### 2.4. Observation Data for Model Calibration and Validation

## 3. Results and Discussion

#### 3.1. Model Calibration

^{2}), were calculated to assess the model’s ability to reproduce the characteristics in the study domain. Model parameters, such as the bottom roughness, vertical layers, and open-boundary sponge layer (radius, and friction coefficient), were also adjusted iteratively during the calibration runs to achieve an overall satisfactory agreement between the model predictions and field observations. The final calibrated bottom roughness height was 0.005 m. The calibrated radius and friction coefficient of the open-boundary sponge layer were 1500 m and 0.001, respectively. Two model runs with 15 and 30 uniform sigma layers were conducted to evaluate the effect of the total number of vertical layers on model accuracy. The model results with 30 vertical layers showed little improvement in model performance error statistics over 15 vertical layers. Therefore, 15 vertical layers were selected in all the model runs to achieve better runtime efficiency while maintaining the same level of model accuracy.

^{2}) were persistently higher than 99% at all three stations (Table 2). The scatter indexes (SIs) were relatively small, indicating that the model was able to reproduce the water level accurately and consistently (Table 2).

^{2}) for the current predictions are all above 0.94, indicating that the model predictions are highly correlated to the measurements at all three stations.

#### 3.2. Model Validation

#### 3.3. Characteristics of Tidal Hydrodynamics

#### 3.4. Along-Channel Kinetic Energy Flux

^{2}) at any location or grid cell in the model, N is the total number of velocity output timesteps over the simulation period, $\rho $ is the seawater density (1025 kg/m

^{3}), and U is the current magnitude normal to the cross section (m/s).

^{2}, which is evenly distributed in the middle–bottom layers of the channel that are deep enough for device deployment (Figure 13a). XS2 and XS3 show a range of 1–2 kW/m

^{2}power density available near the surface (Figure 13b,c). The highest power density value, up to 3.0 kW/m

^{2}, was identified at XS4, which presented the strongest current at a magnitude of 2.5 m/s (Figure 13d).

_{xs}across a cross section can be estimated by multiplying the mean power density $\overline{{P}_{w}}$ with the grid cell area and integrating it over the entire cross section using the following formula:

_{cell}is the total number of model grid cells projected along the cross section, and A

_{cell}is the projected area for each grid cell. Based on Equation (3), the tidal kinetic energy flux P

_{xs}for each of the four cross sections was estimated to be 45.8 × 10

^{3}(kW) for XS1, 22.3 × 10

^{3}(kW) for XS2, 9.03 × 10

^{3}(kW) for XS2, and 48.6 × 10

^{3}(kW) for XS4, respectively.

#### 3.5. Energy Extraction in the Western Passage

_{t}tidal constituent amplitudes. Specifying γ = 0.22, $\rho $ = 1025 kg/m

^{3}, g = 9.81 m/s2, Q

_{max}= 74,388 m

^{3}/s, and ${a}_{i}\left(i=1,2,\dots ,9\right)$ from Table 4 into Equation (4) yields P

_{max}= 447,825 (kW). The P

_{max}value can be used as a reference (upper limit) for the development of tidal energy projects in the Western Passage. It should be noted that Equation (4) likely overestimates the P

_{max}value due to the simplification and assumptions made in the derivation of the equation [5].

## 4. Summary

_{max}estimate using theoretical analysis and numerical modeling approaches.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Model domain and bathymetry. The three blue circles represent the tide stations used for model calibration of the water level.

**Figure 3.**(

**a**) Model grid of the finite-volume community ocean model (FVCOM) for the model domain that consists of the Passamaquoddy–Cobscook Bay archipelago (blue box), Bay of Fundy, and northern Gulf of Maine; (

**b**) zoomed-in model grid with bathymetry for the Passamaquoddy–Cobscook Bay archipelago.

**Figure 5.**Comparison of the modeled and observed depth-averaged tidal currents (principal component) at (

**a**) EP0003, (

**b**) EP0004, and (

**c**) J02. A positive value denotes the flood current. Station locations are shown in Figure 1.

**Figure 6.**Comparison of the observed and modeled velocity time series through the water column at station WP1 in the Western Passage. (

**a**,

**b**) The observed east (u) and north (v) velocity components; (

**c**,

**d**) the modeled east (u) and north (v) velocity components.

**Figure 7.**Comparison of the observed and modeled vertical profiles of velocity percentiles at station WP1 in the Western Passage based on three months of records: (

**a**,

**b**) the observed east (u) and north (v) velocity components; (

**d**,

**e**) the modeled east (u) and north (v) velocity components; (

**c**,

**f**) the observed and modeled velocity magnitudes, with positive as the ebb current and negative as the flood current. Velocity percentiles were calculated as 10%, 25%, 50%, 75%, and 90%.

**Figure 8.**Depth-averaged velocity magnitudes in the Western Passage, Cobscook Bay, and Head Harbor Passage during (

**a**) peak flood and (

**b**) peak ebb tides in spring tide on April 28, 2017.

**Figure 9.**Normal velocity magnitudes at (

**a**) peak flood and (

**b**) peak ebb tides along cross section XS1 in the Western Passage. Positive velocity is away from the reader. The cross-section location is shown in Figure 1.

**Figure 10.**Normal velocity magnitudes at (

**a**) peak flood and (

**b**) peak ebb tides along cross section XS2 in the Western Passage. Positive velocity is away from the reader. The cross-section location is shown in Figure 1.

**Figure 11.**Normal velocity magnitudes at (

**a**) peak flood and (

**b**) peak ebb tides along cross section XS3 in Cobscook Bay. Positive velocity is away from the reader. The cross-section location is shown in Figure 1.

**Figure 12.**Normal velocity magnitudes at (

**a**) the peak flood and (

**b**) peak ebb tides along cross section XS4 in Head Harbor Passage. Positive velocity is toward the reader. The cross-section location is shown in Figure 1.

**Figure 13.**Predicted tidal power density along cross sections (

**a**) XS1 and (

**b**) XS2 in the Western Passage, (

**c**) XS3 in Cobscook Bay, and (

**d**) XS4 in Head Harbor Passage. The locations of the cross sections are shown in Figure 1.

Station | Type | Longitude | Latitude | Depth (m) | Year |
---|---|---|---|---|---|

Eastport, ME | Tide Gage | −66.985 | 44.903 | 6.7 | 2000 |

Cutler, ME | XTide | −64.967 | 45.567 | 5.9 | 2000 |

Port Greville, NS | XTide | −64.550 | 45.400 | 11.8 | 2000 |

EP0003 | ADCP | −66.996 | 44.888 | 34.1 | 2000 |

EP0004 | ADCP | −67.101 | 45.076 | 32.0 | 2000 |

JO2 | ADCP | −67.017 | 44.891 | 32.0 | 2001 |

WP1 | ADCP | −66.989 | 44.920 | 45.0 | 2017 |

Water Level | Cutler | Eastport | Port Greville |
---|---|---|---|

RMSE (m) | 0.15 | 0.26 | 0.41 |

SI | 0.12 | 0.15 | 0.13 |

R^{2} | 0.99 | 0.99 | 0.99 |

Depth-Average Velocity | EP0003 | EP0004 | J02 |
---|---|---|---|

RMSE (m/s) | 0.38 | 0.14 | 0.27 |

SI | 0.42 | 0.41 | 0.33 |

R^{2} | 0.97 | 0.94 | 0.96 |

Water Level (m) | M2 | N2 | S2 | K1 | O1 | P1 | Q1 | M6 | MK3 | MS4 |
---|---|---|---|---|---|---|---|---|---|---|

Data (WP1) | 2.72 | 0.38 | 0.54 | 0.09 | 0.14 | 0.06 | 0.06 | 0.15 | 0.02 | 0.18 |

Model | 2.62 | 0.38 | 0.52 | 0.08 | 0.15 | 0.06 | 0.02 | 0.17 | 0.02 | 0.09 |

Difference | −0.11 | 0.01 | −0.03 | −0.01 | 0.01 | 0.01 | −0.04 | 0.03 | 0.00 | −0.09 |

Percentage Error | 3.9 | 1.5 | 4.8 | 10.9 | 5.4 | 12.8 | 66.9 | 18.7 | 3.1 | 53.3 |

**Table 5.**Comparison of the observed and modeled tidal current constituents at WP1 in the Western Passage.

Current (m/s) | M2 | N2 | S2 | K1 | O1 | P1 | Q1 | M6 | MK3 | MS4 |
---|---|---|---|---|---|---|---|---|---|---|

Data (WP1) | 1.67 | 0.25 | 0.34 | 0.07 | 0.04 | 0.21 | 0.11 | 0.07 | 0.06 | 0.12 |

Model | 1.46 | 0.23 | 0.31 | 0.04 | 0.04 | 0.20 | 0.04 | 0.06 | 0.04 | 0.03 |

Difference | −0.21 | −0.02 | −0.03 | −0.02 | −0.01 | −0.01 | −0.07 | −0.01 | −0.02 | −0.09 |

Percentage Error | 12.4 | 8.5 | 7.8 | 32.1 | 13.9 | 3.9 | 62.9 | 13.2 | 26.6 | 71.9 |

Total Turbines | Turbine Spacing | Hub Height | Turbine Diameter | Avg. Extracted Power (kW) | Power per Turbine (kW) |
---|---|---|---|---|---|

19 | 80 m × 160 m | 15 m | 20 m | 4810 | 253 |

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**MDPI and ACS Style**

Yang, Z.; Wang, T.; Xiao, Z.; Kilcher, L.; Haas, K.; Xue, H.; Feng, X. Modeling Assessment of Tidal Energy Extraction in the Western Passage. *J. Mar. Sci. Eng.* **2020**, *8*, 411.
https://doi.org/10.3390/jmse8060411

**AMA Style**

Yang Z, Wang T, Xiao Z, Kilcher L, Haas K, Xue H, Feng X. Modeling Assessment of Tidal Energy Extraction in the Western Passage. *Journal of Marine Science and Engineering*. 2020; 8(6):411.
https://doi.org/10.3390/jmse8060411

**Chicago/Turabian Style**

Yang, Zhaoqing, Taiping Wang, Ziyu Xiao, Levi Kilcher, Kevin Haas, Huijie Xue, and Xi Feng. 2020. "Modeling Assessment of Tidal Energy Extraction in the Western Passage" *Journal of Marine Science and Engineering* 8, no. 6: 411.
https://doi.org/10.3390/jmse8060411