Tidal currents are a promising source for future power generation given their periodicity and predictability. Therefore, numerical hydrodynamic models are frequently utilized for resource assessments. However, the relevant scales of the simulations and hence modeling techniques depend on the problem at hand. This paper shows the potential of the grid refinement technique for the assessment of tidal current energy for particular sites given its relatively low computational expense and high accuracy for the regions with the refined resolution. Example applications are described for mapping the tidal resources near two facilities (Portsmouth Naval Shipyard in Maine and Key West Naval Station in Florida) for possible future deployments of Marine Hydro-Kinetic technologies. The grid refinement capability in the coupled ocean-atmosphere-wave-sediment transport modeling system is used to improve the spatial resolution in the regions of interest, and has shown significant advantage over the original simulation results for the tidal power assessment. The numerical simulation results from both the original coarse grids and the refined grids are validated with measured tidal constituents at available locations. This study demonstrates how the enhancement of a model system for a regional tidal energy with grid refinement can assist with the performance of site specific resource assessments with modest computational expense.

## I. INTRODUCTION

The increasing energy consumption and decreasing reserve of fossil fuels have led to growing interest in various types of renewable energy. Tides are a rich reservoir of both potential and kinetic energy. Tidal currents originate from the rise and fall of sea levels primarily due to the combined gravitational forcing from the sun and the moon. Therefore, tides vary periodically on different time scales ranging from hours to months. The tidal elevation can be approximated as the superposition of various tidal constituents given as

where $H$ is the tidal water level, $a0$ is the vertical offset, and $ai,\u2009\sigma i,\u2009\delta i$ are the amplitude, angular frequency, and phase angle of the *i*th tidal constituents.^{1} The classical method of tidal energy harvesting is to trap water during high tides using a dam or barrage, and release it later during low tide to generate electricity.^{2} The La Rance tidal barrage in France, the Annapolis Royal Generating Station in Nova Scotia, Canada, and the Jiangxia Station in China are all tidal energy facilities based on this working principle.^{3}

In addition to the tidal potential energy due to the vertical displacement of the water surface, the resulting horizontal motion of tidal currents is a form of kinetic energy which can be recovered as renewable energy. A current energy converter such as an underwater turbine extracts and converts the kinetic energy in the current into a transmittable energy form. The in-stream power per cross-sectional unit area, power density $P$, is calculated as a function of the current speed

where $Cp$ is the conversion coefficient, $\rho $ is the density of the fluid, and $V$ is the flow speed. Efficiencies of tidal power converters are reported to be typically between 16% and 50%.^{4,5}

Tidal streams with high velocities are considered a potentially promising alternative energy resource due to their deterministic nature created by periodic horizontal movement of the tides often magnified by narrow channels. The current understanding of tidal energy resources and emerging technologies of tidal stream power generation has been reviewed.^{6,7} In general, due to the deterministic nature of tidal flows, numerical hydrodynamic models are utilized for resource assessments. However, the relevant scales of the simulations depend on the problem at hand (e.g., Ref. 8). Therefore, the particular modeling methodology required for a resource assessment will greatly depend on the purpose of the resource assessment. The recently published IEC Technical Specification for tidal energy resource assessment^{9} provides guidance suggesting that feasibility studies utilize grid resolution less than 500 m. An example of a regional feasibility study is the geodatabase of tidal constituents developed using Regional Ocean Modeling System (ROMS) to present the regional assessment of tidal stream power resource and identify locations with considerably high kinetic power density in the USA.^{10} Frequent results from these types of models are used in conjunction with theoretical analysis of the maximum extractable power.^{11,12}

Resource assessments utilized for siting considerations require a much higher level of accuracy derived from higher model resolutions suggested by the IEC TS^{9} to be less than 50 m. Due to the tremendous effect of localized bathymetric variability, these models generally require grids with high resolution on the order of 100 m to capture the spatial flow variability. For example, Bomminayuni *et al*.^{13} used a model with an unstructured grid and therefore higher resolution in the region of interest to simulate the flows in tidal channels near Rose Dhu Island, Georgia. Recently, Lewis *et al*. simulated the Irish Sea with a structured grid model and determined that model resolution had a significant effect on the local resource assessment.^{14} They demonstrated that higher model resolutions (<500 m) is required for siting considerations.

Once a project location has been determined, resource assessments must use models that take into consideration the effect of energy extraction. To date, there have been numerous tidal power assessments performed with the effects of tidal power extraction around the world. For example, a 2-D tidally driven hydrodynamic numerical model was used to evaluate the tidal stream energy resources in Portland Bill, UK and optimize the location of turbine arrays at the site.^{15} Tidal stream energy resources in northwest Spain were modeled numerically and the impacts of tidal stream energy were assessed.^{16,17} The maximum tidal power potential of Johnstone Strait, British Colombia, Canada was studied by Sutherland *et al*. using a 2-D finite element model and the maximum extractable power in northwestern Johnstone Strait was estimated to be about 1300 MW.^{18} The available tidal power from in-stream turbines placed in the Minas Passage of the Bay of Fundy and the Passamaquoddy–Cobscook Bay located near the entrance to the Bay of Fundy was also examined.^{19,20} Polagye *et al*. studied and characterized the in-stream tidal energy potential of Puget Sound, Washington and quantified the far-field, barotropic effects of the energy extraction.^{21,22} The Kennebec River of the central Maine coast was found to contain narrow passages where mean tidal energy capacity is sufficient to meet the consumption needs of about 150 homes.^{23} The Tanana River at Nenana, Alaska was studied for its potential for installing and operating hydrokinetic turbines, and suitable locations were recommended.^{24}

As evident in the literature review, much work has focused on developing modeling techniques for modeling the effect of energy extraction on tidal flows. However, much less work has focused on how to best perform siting studies satisfying the IEC technical specifications requiring a high level of resolution. This may be accomplished with models using models with unstructured grids such as the recent resource assessment for New Jersey by Tang *et al*.^{25} Another study by Ramos *et al*.^{26} coupled several structured grids with varying grid resolutions in relatively simple estuary. However, frequently an initial feasibility study is completed using a relatively coarse grid and further siting studies may need to proceed based on those results. Therefore, the purpose of the present study is to demonstrate the use of a grid refinement technique for performing a resource assessment to determine the suitability of particular sites for tidal energy satisfying the requirements for the IEC Technical Specifications.^{9} Grid refinement is enabled to allow two-way communication between the coarser parent grid (outer grid) with greater spatial coverage and the finer child grid (inner grid) with higher spatial resolution. This allows the model to resolve full estuary scale features along with highly detailed small scale features in the particular region of interest with a reasonable computational expense.

The grid refinement technique provides a computationally efficient method for creating much finer resolution in a region of interest without having to increase the resolution of the entire parent grid. Performing simulations with grid refinement is also superior to simply simulating the inner grid alone with higher resolution, since the outer grid has boundaries far away from the inner refined grid and feeds instantaneous boundary conditions to the inner grid so that boundary effects of the inner grid are minimal. This method is also superior to one-way grid nesting because of the two-way interaction where the child grid affects the parent grid. Any additional tidal flows resolved in the higher resolution child grid are fed back directly into the coarser parent grid. While model grid nesting has long been part of oceanographic modeling and the grid refinement technique is more or less a fairly new improvement of traditional nesting, the application of this technique for performing tidal energy resource assessments is new.

The example application of this resource assessment technique is to evaluate the suitability of tidal energy for two locations near United States Navy facilities shown in Figure 1. One is the Portsmouth Naval Shipyard located near Seavey's Island in the Piscataqua River on the border between Maine and New Hampshire. The first comprehensive study of bottom stress and tidal energy dissipation for the area of Great Bay estuary, NH was performed by Swift and Brown^{27} and was considered a benchmark on the estuary tidal analysis. A subsequent study led by Carl Kammerer was performed in 2007 using more comprehensive instruments including Acoustic Doppler Current Profiler (ADCPs) and their data is made publicly available through NOAA's Tides and Currents website (http://co-ops.nos.noaa.gov/products.html). The other location of interest is the Key West Naval Station located on Stock Island of Key West in Florida. Significant tidal currents (>1 m/s) in the surrounding areas of these two locations are expected leading to interest in mapping their tidal resources.

These locations have been simulated at the regional scale as part of the earlier national resource assessment;^{10} however, the grid resolution is insufficient to resolve the flow details in the surrounding regions. In particular, there is low to no resolution for some tidal stream channels within the particular region of interest. Therefore, these are ideal candidates for demonstrating the usefulness of the grid refinement method for evaluating the suitability of specific sites for tidal energy. The simulations are performed using the Coupled Ocean-Atmosphere-Wave-Sediment Transport (COAWST) Modeling system,^{28} which has been widely used in numerous studies in meteorology and oceanography (e.g., Refs. 29–31). However, there are not any systematic studies of tidal power assessment that take advantage of its advanced grid refinement capability. Therefore, the present study seeks to exploit the technique of grid refinement within the COAWST modeling system for the purpose of tidal power assessment.

## II. NUMERICAL MODEL SETUP

The numerical simulations for the two selected locations were performed using the COAWST modeling system consisting of an ocean model ROMS, an atmosphere model Weather Research and Forecasting (WRF) model, a wave model SWAN and a sediment transport model.^{28} The WRF model is a next-generation mesoscale numerical weather prediction system and features two dynamical cores, a data assimilation system, and a software architecture facilitating parallel computation and system extensibility (http://www.wrf-model.org). SWAN is a third-generation wave model, developed at Delft University of Technology that computes random, short-crested wind-generated waves in coastal regions and inland waters (http://www.swan.tudelft.nl/). In this study, only the ocean component ROMS was activated since our primary interest is the characteristics of the tidal driven current flows. ROMS is a 3-dimensional, free surface, terrain-following numerical model that solves 3-D Reynolds-averaged (time-averaged based on Reynolds decomposition) Navier-Stokes (RANS) equations using hydrostatic and Boussinesq assumptions.^{32} ROMS uses finite-difference approximations on a horizontal curvilinear Arakawa C grid and vertical stretched terrain-following coordinates.^{33} Momentum and scalar advection and diffusive processes are solved using transport equations and an equation of state is used to compute the density field that accounts for temperature, salinity, and suspended sediment concentrations. The model is configured to run with multiple processors using distributed memory. In the simulation, the coastline data used to mask the land nodes was obtained from the National Ocean Service (NOS) Medium Resolution Coastline via the Coastline Extractor (http://www.ngdc.noaa.gov/mgg/shorelines/). Raw bathymetry was obtained from the NOS Hydrographic Surveys Database (http://maps.ngdc.noaa.gov/viewers/nos_hydro/). The ROMS tidal forcing file is generated by interpolating the ADCIRC tidal database (http://adcirc.org/) at the open boundary nodes of the ROMS grid. The harmonic constituents used for the forcing includes Q1, O1, K1, S2, M2, N2, K2, M4, and M6. The simulations are run for 32 days, with the first 2 days considered as model spin up and the last 30 days used for the tidal analysis.

For the Portsmouth location, the simulation used two nested grids shown in Figure 2. The parent grid is the same grid used by Define *et al*.^{10} with a horizontal resolution of approximately 250 m (grid size: 320 × 238). The child grid embedded within the parent grid has a horizontal resolution increased by a factor of 5 to about 50 m. Because of the increased resolution, the number of grid cells of the child is consistent with the parent facilitating the allocation of processors for the computation, although the area of the child grid is only about 1/20 of the parent. Figures 3(a) and 3(b) show the bathymetry of the original parent grid and refined child grid for the Portsmouth location. The area of interest is fairly shallow with maximum water depth around 20 m, and is connected to a number of narrow channeled streams. In the parent grid, most of the channeled streams are poorly resolved with only one or two grid points of resolution, while the refined child grid has much finer resolution with at least 5 grid points across the narrowest channel. Special treatment has been applied to the nested grid bathymetry so that boundary points of the child grid are adjusted to match the parent and the overlapping region in the parent is replaced with averaged bathymetry of the child.

Similarly, Figure 4 shows the domain boundaries for both the parent grid (blue) and child grid (red) for the Key West location. The area of interest is overall very shallow water with the maximum water depth not exceeding 20 m. The area is characterized by scattered small islands, and channeled streams between those islands. The west portion of the domain has a few underwater channels which also play a role in shaping the current structures in the area. Figures 5(a) and 5(b) show the corresponding model bathymetry for the two nested grids. The parent grid in Figure 5(a) has 601 × 150 grid points, while the child grid in Figure 5(b) has 327 × 332 grid points. The resolution of the parent grid is about 300 m on average and is refined to about 60 m in the child grid. Similar treatment on the grid bathymetry and mask described previously has also been applied here to ensure consistency of bathymetry between the parent and child grids. The parent grid (Figure 5(a)) has fairly poor resolution along the coastline of the several connected islands near the Key West Naval Station, and completely designates the Fleming Key land area as underwater. On the other hand, the child grid (Figure 5(b)) has a much more refined representation of the actual coastline and small channels between islands. Realistic representation of channels is important since high tidal velocities are expected in constrained channels due to local flow acceleration.

## III. MODELING RESULTS

It takes approximately about 1 h to simulate one day of the coarse grid model. It takes about 3 h to simulate one day of the refined grid model (coarse grid and refined child grid running simultaneously). This estimate is based on using 10 Intel Central Processing Unit (CPUs) on a HP Linux cluster. To provide an overview of the model results, figures with maps of the depth averaged monthly currents are provided. The depth averaged current speed from the original parent grid with no refinement and from the refined child grid at the Portsmouth location is shown in Figures 6(a) and 6(b), respectively. In the open ocean and the mouth of the estuary, the current is fairly weak, although still non-zero, due to the broad channel geometry. The current speed increases when it enters the narrow channels near the Seavey's Island (labeled in Figure 6(b)). Beyond just horizontal constrained channel geometry, sufficient water depth which will allow enough water mass to pass through is also essential for forming fast channeled current flow. This explains why rapidly accelerated current flow occurs on the deeper (∼15 m) north side of the New Castle Island (labeled in Figure 6(b)) but not on the south side because of the shallow water depth (∼2 m) on the south side.

The maximum mean current speed near the Portsmouth location exceeds 2 m/s, indicating very rich hydrokinetic energy resources in several hotspots. Although the currents from both the parent and child grids show similar areas of high current velocities, the child grid provides more details of the strong currents at various locations. Moreover, the higher resolution in the child grid allows the channel on the northern side of the Seavey's Island to be resolved, and results in strong currents within this channel. However, as seen in Figure 5(a), due to the coarse resolution of the parent grid, the same channel is not resolved, and therefore, no currents are shown in that channel (P4 in Figure 6(b)).

The depth averaged current speed from the Key West simulation is shown in Figure 7. The current structure comes from the local variation of the bathymetry and the coastline, which greatly affect the timing and tidal heights. For example, the tidal current tends to be much stronger in channels where the flow path is geographically constrained by the coastline. For the Key West location, the maximum mean current speed is slightly below 1.5 m/s, still fairly significant for the purpose of extracting tidal kinetic energy. Figures 7(a) and 7(b) show solutions from the original parent grid and the refined grid, respectively. Both simulations show similar large-scale flow characteristics, although the currents from the child grid shown Figure 7(b) are much better resolved with more details than the currents from the parent grid shown in Figure 7(a). In addition, the coastline is also more precisely represented for the child grid. Since initial tidal energy projects are very likely to be conducted close to the coast for easy device deployment and power transmission, accurate prediction of tidal currents along the coast is an important factor for successful tidal modeling in the context of recovering tidal current energy. The grid refinement solution shown in Figure 7(b) successfully resolves the channel between Fleming Key and Key West island (see Figure 1 for their locations), and predicts fairly strong (>1 m/s) currents in the channel. The simulation with grid refinement also predicts strong currents through the channel located at the northern tip of the Fleming Key. However for the parent grid shown in Figure 7(a), those aforementioned two channels and the Fleming Key are not resolved due to coarse resolution, and therefore, promising hotspots for tidal power extraction could have been overlooked by conducting the coarse simulation only. Hotspots for tidal power extraction can be visually identified in Figure 7(b) as mostly located at channels between islands. The region along the west end of the grid also features fairly strong current flow, which can be attributed to the existence of channels identifiable in Figure 5(b).

In order to validate the model, tidal constituents from the model are compared with locations where data are available. The methodology for the model verification used in a previous national assessment study^{10} was repeated here with the new model results. The model results are verified with measured harmonic constituents for water levels and current speeds as available. The parameters used for verification include Amplitude Difference (amd), and Phase Difference (phd) from measurements, defined as the following:

where $(ampm)k$ and $(ampc)k$ are the combined amplitudes of the kth harmonic constituent computed by the model output and the measured data, respectively. $(phdm)k$ and $(phdc)k$ are the phases of the kth harmonic constituent. For the Portsmouth location, measured harmonic constituents of tidal velocities were obtained from ports ADCP measurements for two different locations marked as P1 and P2 in Figure 6(b). The ADCPs are upward looking with 25 bins and a bin size of 1 m with a sampling frequency of 6 min. For the Key West location, the tidal harmonic constituents for water levels were obtained from NOAA's website (http://tidesandcurrents.noaa.gov/harcon.html?id=8724580) for point K1 shown in Figure 7(b). The results are presented in Tables I–III for three locations: P1, P2, and K1. In Tables I–III, model results from both the coarse grids and the refined grids were compared with their measurement counterparts, and the differences were calculated. In all 3 locations where comparisons were conducted, the constituent M2 with a period of 12.42 h is shown to dominate the tidal flows. The errors of refined grid simulations are shown to be generally smaller than those of the original coarse grids, especially for the leading tidal constituents.

P1 (70.707 W, 43.075 N) . | ||||||
---|---|---|---|---|---|---|

. | . | . | Simulation error . | |||

. | Measurements . | Coarse grid only . | Grid refinement . | |||

Constituent . | Period (h) . | amp (m/s) . | amd (m/s) . | phd (min) . | amd (m/s) . | phd (min) . |

M2 | 12.4206 | 0.72 | 0.09 | 23 | 0.02 | 26 |

N2 | 12.6583 | 0.16 | −0.02 | 98 | 0 | 103 |

M6 | 4.1402 | 0.04 | 0.06 | −21 | 0.07 | −22 |

S2 | 12 | 0.17 | −0.14 | −243 | −0.06 | −199 |

K1 | 23.9345 | 0.05 | −0.02 | 53 | −0.01 | 73 |

O1 | 25.8193 | 0.04 | 0.01 | 60 | 0.01 | 55 |

M4 | 6.2103 | 0.17 | −0.09 | −137 | −0.07 | −118 |

K2 | 11.9672 | 0.10 | −0.04 | −84 | −0.02 | −71 |

Q1 | 26.8684 | 0.01 | −0.01 | −376 | 0.01 | −376 |

P1 (70.707 W, 43.075 N) . | ||||||
---|---|---|---|---|---|---|

. | . | . | Simulation error . | |||

. | Measurements . | Coarse grid only . | Grid refinement . | |||

Constituent . | Period (h) . | amp (m/s) . | amd (m/s) . | phd (min) . | amd (m/s) . | phd (min) . |

M2 | 12.4206 | 0.72 | 0.09 | 23 | 0.02 | 26 |

N2 | 12.6583 | 0.16 | −0.02 | 98 | 0 | 103 |

M6 | 4.1402 | 0.04 | 0.06 | −21 | 0.07 | −22 |

S2 | 12 | 0.17 | −0.14 | −243 | −0.06 | −199 |

K1 | 23.9345 | 0.05 | −0.02 | 53 | −0.01 | 73 |

O1 | 25.8193 | 0.04 | 0.01 | 60 | 0.01 | 55 |

M4 | 6.2103 | 0.17 | −0.09 | −137 | −0.07 | −118 |

K2 | 11.9672 | 0.10 | −0.04 | −84 | −0.02 | −71 |

Q1 | 26.8684 | 0.01 | −0.01 | −376 | 0.01 | −376 |

P2 (70.752 W, 43.079 N) . | ||||||
---|---|---|---|---|---|---|

. | . | . | Simulation error . | |||

. | Measurements . | Coarse grid only . | Grid refinement . | |||

Constituent . | Period (h) . | amp (m/s) . | amd (m/s) . | phd (min) . | amd (m/s) . | phd (min) . |

M2 | 12.4206 | 1.51 | 0.63 | −372 | 0.07 | 2 |

N2 | 12.6583 | 0.21 | 0.14 | −379 | 0.06 | 6 |

M6 | 4.1402 | 0.15 | 0.07 | 112 | −0.01 | 108 |

S2 | 12 | 0.12 | −0.05 | 54 | −0.03 | 75 |

K1 | 23.9345 | 0.10 | 0.01 | 684 | −0.02 | 12 |

O1 | 25.8193 | 0.08 | 0.02 | −718 | 0.00 | 93 |

M4 | 6.2103 | 0.07 | 0.09 | 37 | 0.24 | −118 |

K2 | 11.9672 | 0.06 | 0.06 | 208 | 0.01 | −182 |

Q1 | 26.8684 | 0.01 | 0 | 803 | 0.01 | −724 |

P2 (70.752 W, 43.079 N) . | ||||||
---|---|---|---|---|---|---|

. | . | . | Simulation error . | |||

. | Measurements . | Coarse grid only . | Grid refinement . | |||

Constituent . | Period (h) . | amp (m/s) . | amd (m/s) . | phd (min) . | amd (m/s) . | phd (min) . |

M2 | 12.4206 | 1.51 | 0.63 | −372 | 0.07 | 2 |

N2 | 12.6583 | 0.21 | 0.14 | −379 | 0.06 | 6 |

M6 | 4.1402 | 0.15 | 0.07 | 112 | −0.01 | 108 |

S2 | 12 | 0.12 | −0.05 | 54 | −0.03 | 75 |

K1 | 23.9345 | 0.10 | 0.01 | 684 | −0.02 | 12 |

O1 | 25.8193 | 0.08 | 0.02 | −718 | 0.00 | 93 |

M4 | 6.2103 | 0.07 | 0.09 | 37 | 0.24 | −118 |

K2 | 11.9672 | 0.06 | 0.06 | 208 | 0.01 | −182 |

Q1 | 26.8684 | 0.01 | 0 | 803 | 0.01 | −724 |

K1 (81.807 W, 24.555 N) . | ||||||
---|---|---|---|---|---|---|

. | . | . | Simulation error . | |||

. | Measurements . | Coarse grid . | Grid refinement . | |||

Constituent . | Period (h) . | amp (m) . | amd (m) . | phd (min) . | amd (m) . | phd (min) . |

M2 | 12.4206 | 0.186 | 0.020 | −34 | 0.011 | −34 |

N2 | 12.6583 | 0.037 | −0.001 | −33 | 0.003 | −32 |

S2 | 12 | 0.052 | 0.010 | −41 | 0.004 | −37 |

K1 | 23.9345 | 0.090 | −0.004 | −25 | 0.003 | −18 |

O1 | 25.8193 | 0.094 | −0.002 | 27 | 0.001 | 28 |

M4 | 6.2103 | 0.009 | 0.020 | −71 | 0.013 | −68 |

K2 | 11.9672 | 0.015 | 0.003 | −47 | 0.000 | −42 |

Q1 | 26.8684 | 0.023 | −0.004 | 14 | 0.003 | 14 |

K1 (81.807 W, 24.555 N) . | ||||||
---|---|---|---|---|---|---|

. | . | . | Simulation error . | |||

. | Measurements . | Coarse grid . | Grid refinement . | |||

Constituent . | Period (h) . | amp (m) . | amd (m) . | phd (min) . | amd (m) . | phd (min) . |

M2 | 12.4206 | 0.186 | 0.020 | −34 | 0.011 | −34 |

N2 | 12.6583 | 0.037 | −0.001 | −33 | 0.003 | −32 |

S2 | 12 | 0.052 | 0.010 | −41 | 0.004 | −37 |

K1 | 23.9345 | 0.090 | −0.004 | −25 | 0.003 | −18 |

O1 | 25.8193 | 0.094 | −0.002 | 27 | 0.001 | 28 |

M4 | 6.2103 | 0.009 | 0.020 | −71 | 0.013 | −68 |

K2 | 11.9672 | 0.015 | 0.003 | −47 | 0.000 | −42 |

Q1 | 26.8684 | 0.023 | −0.004 | 14 | 0.003 | 14 |

For example, at location P1, the measured current speed of M2 constituent is 0.72 m/s. The original grid has a 0.09 m/s error while the refined grid has an error 0.02 m/s. Similarly, for location P2, the original grid has an error of 0.63 m/s while the refined grid has an error of 0.07 m/s. Tidal phases also agree reasonably well for leading tidal constituents considering that past modeling experience demonstrates it is difficult to predict tidal phases as accurately as tidal amplitudes. The phase shift does not change significantly between the coarse and refined grid, because unlike the amplitudes which depend heavily on the localized bathymetric features, the phase depends on the full estuary geometry. The largest phase shifts are for the smallest constituents that have negligible amplitudes and therefore much less influence on the overall superposition. Overall, the comparisons between model results and measurements show reasonable agreement for the dominant tidal constituents. The comparisons also clearly indicate the significant improvement of simulation accuracy by using the grid refinement technique.

## IV. TIDAL ENERGY ASSESSMENT

From a practical point of view, it is helpful to quantify the undisturbed kinetic power as an initial measure of the theoretical tidal resource. For a detailed resource assessment for particular turbines, the current speed at hub height should be used. However, because this study does not pertain to a particular turbine, the depth averaged current is used, although due to the shallow nature of the flow, the vertical structure is weak and the results are robust. A number of points in close proximity to the “hotspots” are chosen for the initial resource assessment (points P3, P4, and P5 in Figure 6(b) for the Portsmouth location, and points K2, K3, and K4 in Figure 7(b) for the Key West location). The average water depth and channel width for each location are given in Table IV. For each point, tidal constituents are calculated through harmonic analysis of the time series from the refined model results. The frequencies and amplitudes for the current velocity magnitude are shown in Tables V and VI.

. | Portsmouth . | Key West . | ||||
---|---|---|---|---|---|---|

. | P3 . | P4 . | P5 . | K2 . | K3 . | K4 . |

Avg. water depth (m) | 9 | 3 | 10 | 3 | 1 | 3 |

Avg. channel width (m) | 320 | 100 | 200 | 250 | 60 | 200 |

. | Portsmouth . | Key West . | ||||
---|---|---|---|---|---|---|

. | P3 . | P4 . | P5 . | K2 . | K3 . | K4 . |

Avg. water depth (m) | 9 | 3 | 10 | 3 | 1 | 3 |

Avg. channel width (m) | 320 | 100 | 200 | 250 | 60 | 200 |

Current velocity amplitude (m/s) . | ||||
---|---|---|---|---|

Constituents . | Period (h) . | Point P3 . | Point P4 . | Point P5 . |

M2 | 12.4206 | 2.888 | 1.879 | 4.050 |

N2 | 12.6583 | 0.456 | 0.304 | 0.690 |

S2 | 12 | 0.114 | 0.061 | 0.189 |

K1 | 23.9345 | 0.184 | 0.109 | 0.211 |

O1 | 25.8193 | 0.152 | 0.097 | 0.224 |

M4 | 6.2103 | 0.144 | 0.085 | 0.090 |

K2 | 11.9672 | 0.219 | 0.115 | 0.229 |

Q1 | 26.8684 | 0.024 | 0.012 | 0.035 |

Current velocity amplitude (m/s) . | ||||
---|---|---|---|---|

Constituents . | Period (h) . | Point P3 . | Point P4 . | Point P5 . |

M2 | 12.4206 | 2.888 | 1.879 | 4.050 |

N2 | 12.6583 | 0.456 | 0.304 | 0.690 |

S2 | 12 | 0.114 | 0.061 | 0.189 |

K1 | 23.9345 | 0.184 | 0.109 | 0.211 |

O1 | 25.8193 | 0.152 | 0.097 | 0.224 |

M4 | 6.2103 | 0.144 | 0.085 | 0.090 |

K2 | 11.9672 | 0.219 | 0.115 | 0.229 |

Q1 | 26.8684 | 0.024 | 0.012 | 0.035 |

Current velocity amplitude (m/s) . | ||||
---|---|---|---|---|

Constituents . | Period (h) . | Point K2 . | Point K3 . | Point K4 . |

M2 | 12.4206 | 1.496 | 1.731 | 1.514 |

N2 | 12.6583 | 0.240 | 0.228 | 0.213 |

S2 | 12 | 0.311 | 0.292 | 0.282 |

K1 | 23.9345 | 0.290 | 0.304 | 0.282 |

O1 | 25.8193 | 0.247 | 0.257 | 0.236 |

M4 | 6.2103 | 0.062 | 0.055 | 0.044 |

K2 | 11.9672 | 0.241 | 0.223 | 0.192 |

Q1 | 26.8684 | 0.045 | 0.032 | 0.029 |

Current velocity amplitude (m/s) . | ||||
---|---|---|---|---|

Constituents . | Period (h) . | Point K2 . | Point K3 . | Point K4 . |

M2 | 12.4206 | 1.496 | 1.731 | 1.514 |

N2 | 12.6583 | 0.240 | 0.228 | 0.213 |

S2 | 12 | 0.311 | 0.292 | 0.282 |

K1 | 23.9345 | 0.290 | 0.304 | 0.282 |

O1 | 25.8193 | 0.247 | 0.257 | 0.236 |

M4 | 6.2103 | 0.062 | 0.055 | 0.044 |

K2 | 11.9672 | 0.241 | 0.223 | 0.192 |

Q1 | 26.8684 | 0.045 | 0.032 | 0.029 |

Histograms of the current magnitude for different points at Portsmouth and Key West are shown in Figures 8 and 9. The left columns of Figures 8 and 9 show the histograms from the original coarse parent grids and right columns show the histograms from the refined child grids. Generally speaking, the refined grids have faster current speed than the coarse grids. The refined grid has fairly strong current speed (∼1.5 m/s) at point P4 located north of Seavey's Island; however, the coarse grid has no data from this location due to lack of resolution at this spot. The current speed at P5 is significantly weaker in the coarse grid than in the refined grid. However, the difference in current speed at P3 between the coarse grid and the refined grid is much smaller. This leads to a conclusion that refined grid tends to produce more improved solutions for areas with confined geometry due to larger relative changes in volume flux directly resulting from the higher resolution. Conversely, within larger channels, grid refinement produces much smaller relative changes in volume flux.

For all three locations (K2, K3, and K4) in the Key West, the refined grid produces similar but faster currents than the coarse grid. Current velocity is generally stronger in the streams at Portsmouth than at Key West possibly due to more constrained channel geometry with point P5 having the strongest current velocity. Current flows at P3 and P4 merge on the west of the Seavey's Island resulting in an even stronger current at P5. At Key West, the current velocity distributions are relatively consistent between all 3 points.

Hydrokinetic power from tidal currents are expected to be extracted with devices such as underwater turbines, which will further limit the power generation due to technological constraints such as turbine technology and power transmission. In the following analysis, the power generated by turbines is estimated by using:

where $V(t)$ is the depth averaged current speed, $Ef$ (45%) is the assumed turbine efficiency, and $As$ ($10\u2009m2$) is the total turbine sweep area. The values of $Ef$ and $As$ are assumed to be the same with a previous case study of tidal resource assessment by Bomminayuni *et al*.,^{13} and any modification in $Ef$ and $As$ will produce a linear change in the total power estimate. The time series of power produced for these parameters for all different points are presented in Figures 10 and 11. It is shown that the available power at spring tides and neap tides can differ significantly. For example, at point P3, the available power at spring tides is over 120 kW, but it is only about 20 kW at neap tides. In addition, a minimum “cut-in” speed required by the turbine to operate is specified as 1 m/s. Using the cut-in speed and integrating the instantaneous power over an entire year, the energy production is estimated to be approximately $250\u2009MW\u2009h$ (P3), $68\u2009MW\u2009h$ (P4), $710\u2009\u2009MW\u2009h$ (P5), $39\u2009MW\u2009h$ (K2), $61\u2009MW\u2009h$ (K3), and $40\u2009MW\u2009h$ (K4), respectively.

The estimates are based on assumed turbine parameters, which are obviously subject to uncertainty. However, any modification would produce a corresponding linear change in the total power estimate. These estimates also do not account for operational availability or downtime for maintenance and repairs, and are based on the undisturbed power density. A previous study of tidal power^{12} found that extraction devices could partially block the flow in the tidal stream channels backing up the water level, resulting in increased head and increased potential power. A simple method for computing the resulting potential power based on the undisturbed flow was derived; however, it assumes bodies of water connected by a single channel. In this study, we are looking at a multi-channel system, and cannot apply this method to the region of interest. To account for the back flow effect, the simulations numerical simulations would need to incorporate the effect of energy dissipation such as the method in Ref. 34.

Extracting power from tidal streams may alter the flow characteristics and result in environmental effects. A quick preliminary check of potential hydrodynamic effect is to compare the level of power extraction from the assumed turbine array with the total kinetic power through the entire transects. The total kinetic power through the entire transects for respective locations is shown in Figures 10 and 11. For most points selected for analysis, the extracted power is only a small fraction of the total available power in the transects. For example, the power extraction at P3 is about 5% of the total kinetic power in its transect, while the power extraction at P4 and P5 is less than 1% of the total kinetic power in their transects. Therefore, the hydrodynamic effects of power extraction at this level are expected to be minimal, although many other environmental effects would need to be evaluated and proportionally higher levels of extraction would also have more effects.

## V. CONCLUSIONS

In this study, due to strong interest expressed for possible large scale deployment of Marine Hydro-Kinetic (MHK) technologies near two Navy bases, a technique using grid refinement is utilized for the resource assessment to determine the suitability of these sites. One site is located near the Portsmouth Naval shipyard on Seavey's Island on the border between Maine and New Hampshire. The other site is located at the Key West Naval Station, Florida. A previous national tidal resource assessment with coarse grid resolution was used for the initial feasibility study identifying these two locations to be of interest. However the model is insufficient to resolve the flow details in the tidal stream channels. Therefore, simulation of higher resolution is necessary to produce more accurate prediction of potential tidal resources for those two locations. An integrated modeling system COAWST with grid refinement capability is used to perform the tidal simulation for these two sites satisfying resolution requirement of the IEC Technical Specification.^{9} Grid refinement allows simultaneous simulation of an enclosing parent grid and a refined child grid within the parent grid with much higher spatial resolution without significantly increasing the computational expense. It is also advantageous compared to modeling the inner grid at higher resolution alone, since the outer grid (parent grid) can provide the surrounding ocean state to the inner refined grid (child grid) as boundary conditions to minimize possible boundary effects.

Modeling results from both the original coarse grids and the refined child grids are validated against measured tidal constituents at available locations. Although both model simulations exhibit reasonable agreement with the measurements, the results from refined grids are significantly improved with reduced differences from the measurements, especially for areas with constrained geometry producing larger currents which is of primary importance for tidal stream energy. Simulations with refined grids have much better representation of the geographical features along the coasts, and are able to resolve narrow tidal streams not in the original grids due to the coarse resolution. Because of the improvement in model resolution, a number of “hotspots” with significant current velocities are identified as promising locations for future device deployment. One year of time series of current velocities in these “hotspots” are predicted with computed tidal constituents to provide histograms of current magnitudes. Comparing the histograms of current magnitudes from the original grids and the refined grids shows that the original coarse grids tend to produce lower current velocities than the refined grids, and therefore, underestimate the tidal power potential in some areas, especially in constrained tidal streams. The kinetic power potential of the “hotspots” is calculated from the solutions of the refined grids using hypothetical turbine parameters as an initial assessment of tidal energy resources. The power extracted by turbines is also compared with the total available kinetic power in the full channel cross-section. It is concluded that power extraction for parameters used is expected to have little hydrodynamic effects since the energy removal is only a small fraction of the total available kinetic power.

This study demonstrates a methodology for satisfying the IEC Technical Specification grid requirements for resource assessments^{9} for both feasibility and design studies using the grid refinement technique with lower computational expense (compared to increasing grid resolution uniformly) and higher accuracy (compared to the coarse resolution). The use of grid refinement allows for feasibility studies to be completed for large regions with relatively coarse grids followed by design studies with higher resolution building on the model framework already completed with less computational expense. This study also paves the path for more in-depth assessment to characterize a specific deployment site for tidal power extraction in those two selected locations. The next step will be to implement the extraction effects into the model at the child grid level in order to facilitate the layout design of the array and to determine the far field effects. In addition, further assessment will need to take into account various technological, economic, and environmental constraints, which will further determine the actual power availability. In the future, it will also be helpful to launch field campaigns to perform *in-situ* surveys for a specific deployment site to obtain more accurate measurement of the current velocity profiles.

## ACKNOWLEDGMENTS

This study was supported by National Renewable Energy Laboratory (AFC-4-42041-01). Any opinions, finding, and conclusions or recommendations expressed herein are those of the authors and do not necessarily reflect the views of the National Renewable Energy Laboratory.

## References

*Marine Energy - Wave, Tidal and Other Water Current Converters - Part 201: Tidal Energy Resource Assessment and Characterization*,