Journal of Marine Science and Engineering

Article A Tidal Hydrodynamic Model for Cook Inlet, Alaska, to Support Tidal Energy Resource Characterization

Taiping Wang and Zhaoqing Yang * Pacific Northwest National Laboratory, 1100 Dexter Avenue North, Suite 500, Seattle, WA 98109, USA; [email protected] * Correspondence: [email protected]; Tel.: +1-206-528-3057



Received: 21 March 2020; Accepted: 31 March 2020; Published: 4 April 2020


Abstract: Cook Inlet in Alaska has been identified as a prime site in the U.S. for potential tidal energy development, because of its enormous tidal power potential that accounts for nearly one-third of the national total. As one important step to facilitate tidal energy development, a tidal hydrodynamic model based on the unstructured-grid, finite-volume community ocean model (FVCOM) was developed for Cook Inlet to characterize the tidal stream energy resource. The model has a grid resolution that varies from about 1000 m at the open boundary to 100–300 m inside the Inlet. Extensive model validation was achieved by comparing model predictions with field observations for tidal elevation and velocity at various locations in Cook Inlet. The error statistics confirmed the model performs reasonably well in capturing the tidal dynamics in the system, e.g., R2 > 0.98 for tidal elevation and generally > 0.9 for velocity. Model results suggest that tides in Cook Inlet evolve from progressive waves at the entrance to standing waves at the upper Inlet, and that semi-diurnal tidal constituents are amplified more rapidly than diurnal constituents. The model output was used to identify hotspots that have high energy potential and warrant additional velocity and turbulence measurements such as East Foreland, where averaged power density exceeds 5 kw/m2. Lastly, a tidal energy extraction simulation was conducted for a hypothetical turbine farm configuration at the Forelands cross section to evaluate tidal energy extraction and resulting changes in far-field hydrodynamics.

Keywords: tidal energy; resource characterization; Cook Inlet; FVCOM; Forelands; hotspots

1. Introduction In recent decades, the interest in harnessing energy directly from tidal streams with marine hydrokinetic (MHK) devices has been renewed in many countries [1,2]. Compared to other renewable energy sources, such as wind and solar power, tidal energy is highly predictable in time and space [3]. It thus can potentially serve as a dependable, clean energy resource for suitable tidal systems. A growing number of studies that involve laboratory experiments, computational modeling, as well as field measurements and device testing have been conducted worldwide [4–11]. To date, however, very few tidal turbines have been deployed in the field to harness tidal energy from natural tidal flows for commercial or operational use, due to various reasons, including concerns of the high operational cost and potential environmental risk. The MeyGen project in Scotland [12] is among the pioneering projects in which extracting tidal energy from tidal streams becomes operational and is also connected to the electric grid. In comparison, most other efforts have been largely focused on the earlier stage of tidal energy development, such as characterizing available tidal energy resources using computational models and testing MHK devices in the laboratory and at representative field-testing sites [13–16]. In the U.S., the first nationwide assessment of tidal stream energy production potential was released in 2011 [17]. In this assessment, the Regional Ocean Modeling System (ROMS) was applied to more than 50 individual coastal subdomains along the U.S. coastline. The findings suggest that the

J. Mar. Sci. Eng. 2020, 8, 254; doi:10.3390/jmse8040254 www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2020, 8, 254 2 of 19 state of Alaska has the most abundant tidal energy resource in the country. For instance, the estimated theoretical available power for Cook Inlet alone exceeds 18 GW, which accounts for nearly one-third of the national total. Because of its great tidal energy potential, Cook Inlet is regarded as a prime site for future tidal energy project development; hence, it warrants more detailed site characterization using fine-resolution numerical modeling and monitoring practices. Coastal circulation models have been widely used to support earlier-stage tidal energy development by providing a large-scale assessment of theoretically and practically available tidal energy resources, as well as the potential physical impact of energy extraction [5,6,8,11,17–25]. In these studies, both structured-grid and unstructured-grid coastal circulation models have been used. However, models based on an unstructured-grid framework also have a unique advantage, because they can be readily refined at local scales to a spatial resolution comparable to marine and hydrokinetic (MHK) devices. For instance, in a study conducted by Rao et al. (2015) [26] to specifically investigate the tidal turbine farm efficiency in the Western Passage of the Gulf of Maine, the minimum grid size used for turbine arrays is about 20 m, the same as the turbine dimensions, while the maximum grid size reaches 5 km at the open boundaries. Therefore, the unstructured-grid models can provide an efficient solution for obtaining a more detailed resource characterization for top tidal energy candidate sites in the U.S. (e.g., Cook Inlet), which often require various levels of grid refinement at local scales to meet different research and project needs. The objective of this study was to develop and validate an unstructured-grid, tidal hydrodynamic model framework for Cook Inlet, Alaska to support tidal energy research in this energetic tidal system. Compared to the first nation-wide tidal energy resource assessment by Haas et al [17], this study uses an unstructured-grid modeling approach. The model grid can be easily refined on an as-needed basis at local scales to provide a higher-resolution representation of tidal velocity and energy resource distributions at potential energy hotspots. Thus, this model can serve as a flexible and useful tool to support a variety of tidal-energy related research activities in Cook Inlet. As the first step, this study summarizes the model development, calibration and validation processes. In the current phase, the tidal hydrodynamic model was calibrated using observational data for both tidal water level and currents, and then was used to characterize tidal dynamics and tidal energy distribution in Cook Inlet. In the future, the unstructured model grid will be further refined for top energy hotspots to provide device-resolution (e.g., on the order of meters) velocity and turbulence profiles to assist with turbine farm siting and field measurement planning.

2. Methods

2.1. Study Site Cook Inlet is a major estuary in the U.S. state of Alaska; it stretches roughly 300 km from the Gulf of Alaska to the Municipality of Anchorage (the largest city in Alaska) in south-central Alaska (Figure1). At its northern end, Cook Inlet branches into Knik and Turnagain Arms surrounding Anchorage. At its south entrance, the Inlet extends and merges into Shelikof Strait and the Gulf of Alaska. Cook Inlet has many glacial-fed tributaries that have carried enormous quantities of sediment into the estuary. The sediment formed intertidal mud flats, which are especially predominant near the northern end of the Inlet, including the Knik and Turnagain Arms and the Susitna River Delta [27], and also pose a challenge for acquiring accurate bathymetry datasets. The inlet has long been regarded as one of the top candidates for tidal energy development (e.g., [17,27,28]) because of its extremely large tidal ranges. For instance, the Turnagain Arm near the northern end has the largest tidal range in the U.S.; it has a mean of 9.2 m. Tidal fluctuations in the main body of Cook Inlet, while not as extreme as those in the shallow and narrow Turnagain Arm, regularly reach 7 m or higher during the spring tide. In addition, Cook Inlet has a distinct advantage in terms of tidal energy development potential because of its adjacency to Alaska’s industry and population J. Mar. Sci. Eng. 2020, 8, 254 3 of 19 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 3 of 20 populationcenters, as wellcenters, as the as state’swell as primary the state’s power primary grid—the power Railbelt grid—the power Railbelt grid power that powers grid that Anchorage, powers Anchorage,Fairbanks, and Fairbanks, Alaska’s and south-central Alaska’s south-central region [28]. region [28].

Figure 1. AA map showing the study site, Cook Inlet in Alaska, USA, and selected field field monitoring stations. The The bottom-right bottom-right inset inset provides provides a a zoom-i zoom-inn view view of of the the bathymetric features features and field field observational stations near the Forelands.

In Cook Inlet, water levels are continuously monitored by by three tidal gages operated by the National OceanicOceanic andand AtmosphericAtmospheric Administration Administration (NOAA). (NOAA). From From the the south south entrance entrance to the to norththe north end, end,these these three three stations stations are located are located near Seldovia, near Seldov Nikiski,ia, Nikiski, and Anchorage and Anchorage (Figure 1(Figure), and they1), and roughly they roughlycapture thecapture tidal the range tidal distributions range distributions inside Cook inside Inlet. Cook In addition,Inlet. In addition, NOAA has NOAA conducted has conducted a seriesof a seriescurrent of surveys current usingsurveys Acoustic using Acoustic Doppler Doppler Current ProfilersCurrent Profilers (ADCPs) (ADCPs) in the summer in the monthssummerbetween months between2005 and 2005 2012. and These 2012. surveys These covered surveys many covered locations many in locations the Cook Inletin the region, Cook includingInlet region, data including acquired datafrom acquired a total of from 39 stations a total inside of 39 Cookstations Inlet. inside For thisCook study, Inlet. we For chose this Yearstudy, 2005 we aschose the model Year 2005 calibration as the modelperiod, calibration because the period, current because survey inthe 2005 current has the survey best spatialin 2005 coverage has the best among spatial all the coverage years. In among addition, all thewe choseyears. Year In addition, 2012 as the we model chose validation Year 2012 period, as the becausemodel validation it provides period, the second-best because spatialit provides coverage the second-bestthat complements spatial those coverage survey stationsthat complements in Year 2005. those Table 1 surveysummarizes stations those in selected Year current2005. Table survey 1 summarizesstations used those for model-data selected current comparisons. survey Amongstations the used total for of model-data nine stations, comparisons. three stations Among (COI0501, the totalCOI0502, of nine and stations, COI0503) three are located stations in (COI0501, the Foreland COI0502, cross section and COI0503) (Figure1), are a natural located restriction in the Foreland formed crossby two section opposing (Figure peninsulas, 1), a natural namely restriction East and form Wested by Forelands, two opposing to capture peninsulas, the complex namely and East strong and Westcurrents Forelands, there. to capture the complex and strong currents there.

Table 1. The list of selected Acoustic Doppler Current Profilers (ADCP) stations for model-data comparisons. Table 1. The list of selected Acoustic Doppler Current Profilers (ADCP) stations for model-data Station Sample Year Longitude Latitudecomparisons. Depth (m) # of Bins Station Full Name COI0514 2005 152.93028 59.30180 80.2 20 Augustine Island − COI0511Sample 2005 152.12018 60.02327Depth 68.6 # 18of Cape Ninilchik, west of Station Longitude− Latitude Station Full Name COI0508 2005 151.67325 60.48295 51.5 11 Kalgin Island, east of Year − (m) Bins COI0501 2005 151.64690 60.72198 33.5 9 West Foreland − COI0514COI0502 2005 2005 −152.93028151.55733 59.30180 60.72067 80.2 33.8 20 7 Augustine The Forelands Island − COI0511COI0503 2005 2005 −152.12018151.43297 60.02327 60.71727 68.6 44.2 18 12 Cape EastNinilchik, Foreland west of − COI1210 2012 151.23268 60.88697 43.3 15 Middle Ground Shoal, east of COI0508 2005 −151.67325− 60.48295 51.5 11 Kalgin Island, east of COI1207 2002 150.36035 61.05660 53.3 19 Point Possession − COI0501COI1209 2005 2012 −151.64690150.20150 60.72198 61.18483 33.5 29.4 915 Fire West Island, Foreland north of − COI0502 2005 −151.55733 60.72067 33.8 7 The Forelands COI0503 2005 −151.43297 60.71727 44.2 12 East Foreland

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2.2. Hydrodynamic Model The hydrodynamic model used for this study is the unstructured-grid, finite-volume, community ocean model (FVCOM) [29,30]. As a general-purpose coastal ocean model, FVCOM simulates water surface elevation, velocity, salinity, temperature, and other scalar constituents in an integral form by computing fluxes between non-overlapping horizontal triangular grid cells. By using the unstructured-grid framework in the horizontal plane, and a sigma-stretched coordinate system in the vertical direction, the model is especially suitable for resolving the complex geometry in estuaries and coastal oceans [31–33]. It also provides the flexibility for refining computational grid locally in regions of interest, such as tidal energy hotspots. To simulate tidal energy extraction, a MHK module was implemented in the FVCOM model based on the momentum sink approach [10]. The MHK module was validated against the analytical solution [10] and laboratory experiments [34], and has also been subsequently applied to studying tidal energy extraction and associated environmental impacts [11,35,36]. The modified governing equations in FVCOM with added momentum sink terms due to tidal energy extraction have the following general form [10]: ! ∂u ∂u ∂u ∂u 1 ∂p ∂ ∂u M + u + v + w fv = + Km + Fx Fx (1) ∂t ∂x ∂y ∂z − −ρo ∂x ∂z ∂z − ! ∂v ∂v ∂v ∂v 1 ∂p ∂ ∂v M + u + v + w + fu = + Km + Fy Fy (2) ∂t ∂x ∂y ∂z −ρo ∂y ∂z ∂z − where (x, y, z) are the east, north, and vertical axes in the Cartesian coordinates; (u, v, w) are the three velocity components in the x, y, and z directions; (Fx, Fy) are the horizontal momentum diffusivity terms in the x and y directions; Km is the vertical eddy viscosity coefficient; ρ is water density; p is →M M M pressure; and f is the Coriolis parameter. F = (Fx , Fy ) are the turbine-induced momentum sink terms in the x and y directions and are defined as follows:

→M 1 CTA F = →u →u (3) 2 Vc where Vc is the momentum control volume, CT is the turbine thrust coefficient, A is the flow-facing area swept by turbines, and →u is the velocity vector at turbine hub height. The total extracted tidal power at any given time can be calculated using the following formula:

M   X 3  1  Ptotal = N ρCTA →u  (4)  × 2  i=1 i where N is the number of turbines in each grid element and M is the total number of elements containing turbines.

2.3. Model Configuration The Cook Inlet hydrodynamic model domain covers the entire Cook Inlet with grid resolution (i.e., side length of triangular grid cells) varying from about 1000 m at the entrance to less than 300 m inside the Inlet. In terms of element area, they are roughly equivalent to a side length of 660 m and 200 m, respectively, for equilateral structured-grid cells. In channels and areas that have steep bathymetry gradients, a finer grid resolution of 100–300 m was used. The model grid consists of approximately 120,000 nodes and 240,000 triangular elements in the horizontal plane. In the vertical direction, 10 uniform sigma layers were applied. Although higher spatial resolutions can be used in both the horizontal and vertical planes, the adopted resolutions are adequate to fulfill the need for this initial phase of tidal hydrodynamic model development and validation. Model bathymetry was interpolated from the NOAA Alaska Fisheries Science Center’s 50 m resolution Cook Inlet bathymetry data set [37]. J. Mar. Sci. Eng. 2020, 8, 254 5 of 19

The horizontal and vertical mixing schemes were based on the default Smagorinsky parameterization and Mellor-Yamada level 2.5 turbulent closure in FVCOM, respectively [38]. The bottom drag coefficient was calculated using the default option based on the logarithmic boundary layer assumption. The user-specified bottom roughness height and minimum bottom drag coefficient were treated as the calibration parameters with their values fine-tuned through the process of model calibration. To simulate tidal hydrodynamics and characterize the tidal energy resource in Cook Inlet, the prescribed open boundary tidal elevations were considered the primary external forcing in the model. Specifically, the open boundary tidal elevation time series were obtained from Oregon State University’s TPXO8-atlas tidal database [39], which consists of 13 major harmonic constituents, namely M2, S2, N2, K1, O1, P1, Q1, M4, MS4, MN4, Mm, and Mf. In addition, all model runs were conducted in the barotropic mode, without considering the effect of water density variation caused by salinity and temperature. River discharge and meteorological forcing were not included in the current study either. Although these factors/processes could be important in modulating the transport processes, their contribution to tidal hydrodynamics is generally small considering the extremely large tidal ranges in Cook Inlet.

3. Results and Discussion

3.1. Model Calibration Since this study is focused on tidal-driven hydrodynamics in Cook Inlet, model calibration was achieved by adjusting user-specified parameter values that directly control tidal wave propagation in the system through a series of iterative model runs. In FVCOM, these parameters include bottom roughness height and minimum bottom drag coefficient for the bottom boundary condition, as well as the sponge layer radius and friction coefficient for the open boundary condition. For instance, the sponge layer is typically specified as a damping zone weighted from the open boundary nodes to the interior, with a specified influence radius and a friction coefficient to ensure that the radiation boundary condition will also suppress the noise perturbation of wave energy reflected back to the computational domain [38]. During the model calibration, the sponge layer parameters were first adjusted to obtain an overall reasonable comparison between model predictions and field observations at three NOAA tidal gauges and six selected ADCP stations in Year 2005. The bottom roughness height and minimum bottom drag coefficient were further adjusted to fine-tune water level comparisons at individual tidal gauges and ADCP stations. Through the course of model calibration, to quantify the model’s performance and to help identify the best set of model calibration parameters, three representative error statistical parameters, the root-mean-square-error (RMSE), the scattered index (SI), and the coefficient of determination (R2), were calculated using the following equations for both water elevation and currents, following each iterative model run. The RMSE, or root mean square deviation, represents the sample standard deviation of the differences between predicted values and measured values. It is defined as s PN 2 = (Pi Mi) RMSE = i 1 − (5) N where N is the number of observations, Mi is the measured value, and Pi is the predicted value. The SI is defined as the normalized RMSE (i.e., NRMSE) by the average of all measured values. Because water level and velocity can both be negative, the absolute values were used in this study to calculate the mean of the measured values. RMSE SI = (6) M where the overbar indicates the mean of the measured values. J. Mar. Sci. Eng. 2020, 8, 254 6 of 19

J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 6 of 20 The R2 is a measure of the strength of the linear relationship between the predicted and measured The R is a measure of the strength of the linear relationship between the predicted and values. In this study, R2 was tested at the significance level of 0.05. measured values. In this study, R was tested at the significance level of 0.05. (∑ (𝑀PN−𝑀)(𝑃 −𝑃)) 2 Mi M Pi P R = 2 i=1 (7) R(∑= (𝑀 −𝑀))(∑−  (𝑃 −𝑃−))  (7) PN  2 P N  2 i=1 Mi M i=1 Pi P It was found that tidal range and current− speed in Cook− Inlet was very sensitive to open boundaryIt was sponge found thatlayer tidal parameterization. range and current A combinat speed inion Cook of Inleta uniform was very sponge sensitive layer to radius open of boundary 1500 m andsponge a friction layer parameterization. coefficient of 0.0012 A combinationproduced the of best a uniform overall sponge model-data layer radiuscomparisons of 1500 at m all and calibration a friction stations.coefficient The of 0.0012bottom produced roughness the height best overall and the model-data minimum comparisons bottom drag at coefficient all calibration tended stations. to affect The morebottom on roughness the tidal phase height and and magnitude the minimum toward bottom the drag upper coe Inlet.fficient The tended final toparameter affect more values on the for tidal the phasebottom and roughness magnitude height toward and minimu the upperm bottom Inlet. The drag final coefficient parameter were values both forset theas 0.005, bottom based roughness on the calibrationheight and results. minimum bottom drag coefficient were both set as 0.005, based on the calibration results.

3.1.1. Tidal Elevation Figure2 2 shows shows thethe time-seriestime-series comparisonscomparisons ofof FVCOMFVCOM predictionspredictions andand NOAANOAA observationsobservations atat three NOAA tidal gages during a two-week spring-neapspring-neap cycle in May 2005. As indicated by the error statistical parameters, the model-predicted tidal elevationselevations match NOAA predictions very well at all stations; the R2 isis greater than 0.98 at allall threethree gages.gages. The spring-neap tidal cycle was successfully reproduced byby thethe model. model. In In general, general, tides tides inside inside Cook Cook Inlet Inlet are are semi-diurnal—two semi-diurnal—two unequal unequal high high and andtwo two unequal unequal low low tides tides occur occur per per tidal tidal day day (24 (24 h andh and 50 50 min). min). The The tidal tidal range range alsoalso increasesincreases rapidly from Seldovia near the entrance to Anchorage in thethe upper Inlet. For instance, at Anchorage, the tidal range exceeds 10 m during the spring tide (Figure(Figure2 2c).c).

Figure 2. Time-seriesTime-series comparisons of model-predicted tidal elevations and National Oceanic and Atmospheric Administration (NOAA) observations at three tidal gages inside Cook Inlet, ( (aa)) Seldevia, Seldevia, (b) Nikiski, and (c) Anchorage. The The numbers numbers inside inside the the brac bracketskets are are root-mean-square-error root-mean-square-error (RMSE), (RMSE), scattered index (SI), and coecoefficientfficient ofof determinationdetermination (R(R22) values.

To further assess the model’s skills in capturing individual tidal constituents, harmonic analysis for majormajor tidaltidal constituentsconstituents waswas performed, performed, and and the the results results are are presented presented in in Figure Figu3re. First,3. First, there there is an is an overall good agreement between model predictions and field observations for both amplitude and phase at all three tidal gages. Second, the results confirmed that tides in Cook Inlet are dominated by

J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 7 of 20

semi-diurnal constituents, as indicated in Figure 2. For example, the form ratio (the ratio between the sum of the amplitudes of the two main diurnal constituents K1 and O1, and that of the two main semi-diurnal constituents M2 and S2) varies from to 0.30 at Seldevia to 0.23 at Anchorage, suggesting the increasing dominance of semi-diurnal tides toward the upper Inlet. There is a general trend suggesting the amplification in tidal amplitude from the Inlet entrance to the upper inlet was slightly over-predicted by the model. In Figure 3a, tidal amplitude for most tidal constituents is under-predicted at Seldevia, but becomes over-predicted at Anchorage. However, the differences between predicted and observed values are very small, and mostly are on

J.the Mar. order Sci. Eng. of 2020a few, 8, 254centimeters. For instance, the maximum difference is for the M2 constituent7 of 19at Anchorage, which is 0.21 m but only accounts for about 6% of the tidal amplitude. At Nikiski, there is a near perfect match between predicted and observed tidal amplitude for all seven tidal overallconstituents. good agreementInterestingly, between Figure model 3a shows predictions that the and amplification field observations in tidal for amplitude both amplitude responds and phasedifferently at all in three diurnal tidal and gages. semi-diurnal Second, the constituents. results confirmed In general, that the tides semi-diurn in Cook Inletal constituents are dominated become by semi-diurnalmuch more amplified constituents, than asthe indicated diurnal ones, in Figure which2. Forshould example, be largely the forma result ratio of (thethe basin ratio geometry between the(e.g., sum length of the and amplitudes depth) of ofCook the twoInlet. main The diurnalsame pattern constituents also holds K1 andfor the O1, tidal and thatphase. of theFor twoexample, main semi-diurnalthe phase lag constituentsbetween Seldevia M2 and and S2) Anchorage varies from for to the 0.30 M2 at Seldeviaconstituent to 0.23is nearly at Anchorage, 140 degrees, suggesting but it is theless increasing than 60 degrees dominance for the of K1 semi-diurnal constituent. tides toward the upper Inlet.

Figure 3. Model-dataModel-data comparisons comparisons of of major major tidal tidal constituen constituentsts at atthree three tidal tidal gages gages inside inside Cook Cook Inlet Inlet (a) (tidala) tidal amplitude amplitude and and (b) (tidalb) tidal phase. phase. There is a general trend suggesting the amplification in tidal amplitude from the Inlet entrance to Overall, the differences between predicted and observed tidal phases are mostly on the order of the upper inlet was slightly over-predicted by the model. In Figure3a, tidal amplitude for most tidal a few degrees for major tidal constituents. The error statistics suggest that model-predicted tidal constituents is under-predicted at Seldevia, but becomes over-predicted at Anchorage. However, the elevations match NOAA observations generally better than those (e.g., an average of 10% differences between predicted and observed values are very small, and mostly are on the order of a few over-prediction in M2 amplitude) reported in the earlier study [17]. For example, in the earlier study centimeters. For instance, the maximum difference is for the M2 constituent at Anchorage, which is [17], the amplitude difference for M2 constituent between model prediction and field observation at 0.21 m but only accounts for about 6% of the tidal amplitude. At Nikiski, there is a near perfect match Nikiski tidal gage was 0.17 m (or 7% less than the observed value). In comparison, the difference in between predicted and observed tidal amplitude for all seven tidal constituents. Interestingly, Figure3a this study was reduced to 0.01 m (or 0.4%). In addition, the same trend was found for phase shows that the amplification in tidal amplitude responds differently in diurnal and semi-diurnal predictions, i.e., a 12-minute phase difference in this study vs. a 25-min difference in the earlier study constituents. In general, the semi-diurnal constituents become much more amplified than the diurnal [17]. ones, which should be largely a result of the basin geometry (e.g., length and depth) of Cook Inlet. The same3.1.2. patternTidal Velocity also holds for the tidal phase. For example, the phase lag between Seldevia and Anchorage for the M2 constituent is nearly 140 degrees, but it is less than 60 degrees for the K1 constituent. Overall,The ADCP the data diff erencesin Cook between Inlet mainly predicted cover andthe middle-depth observed tidal bins, phases and are a substantial mostly on portion the order of ofthe a surface few degrees and bottom for major depths tidal is missing, constituents. likely as The a result error of statistics the removal suggest of bad-quality that model-predicted data during tidal elevations match NOAA observations generally better than those (e.g., an average of 10% over-prediction in M2 amplitude) reported in the earlier study [17]. For example, in the earlier study [17], the amplitude difference for M2 constituent between model prediction and field observation at Nikiski tidal gage was 0.17 m (or 7% less than the observed value). In comparison, the difference in this study was reduced to 0.01 m (or 0.4%). In addition, the same trend was found for phase predictions, i.e., a 12-minute phase difference in this study vs. a 25-min difference in the earlier study [17]. J. Mar. Sci. Eng. 2020, 8, 254 8 of 19

3.1.2. Tidal Velocity J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 8 of 20 The ADCP data in Cook Inlet mainly cover the middle-depth bins, and a substantial portion of thethe surfaceQA/QC and process. bottom To depths accurately is missing, compare likely model as a output result of with the removalobservations, of bad-quality the FVCOM data velocity during thewas QA interpolated/QC process. in Tospace accurately and time compare onto each model dep outputth bin withof the observations, ADCP data. the The FVCOM interpolated velocity model was interpolatedvelocity and in ADCP space data and timewere onto averaged each depth over binthe ofwater the ADCP depth data.and compared. The interpolated Error modelstatistics velocity were andcalculated ADCP to data quantify were averaged the model’s over perfor the watermance depth in simulating and compared. observed Error currents. statistics were calculated to quantifyFigure the 4 model’s shows performancethe scatterplot in simulatingcomparisons observed of depth-averaged currents. velocity at six representative ADCPFigure stations4 shows in Cook the scatterplot Inlet. At all comparisons stations except of depth-averaged for Station COI0501 velocity located at six representative near West Foreland, ADCP stationsthe model in Cookwas able Inlet. to At capture all stations current except magnitude for Station and COI0501 direction located reasonably near West well. Foreland, The results the model also wasindicate able that to capture at most current stations, magnitude currents tend and directionto flow in reasonablya well-defined well. direction The results (i.e., also along indicate the principal that at mostaxis) stations,that aligns currents with tendthe channel to flow inorientation, a well-defined especially direction at (i.e.,Station along COI0511. the principal In comparison, axis) that aligns tidal withcurrents the channelat Stations orientation, COI0514 especially and COI0502 at Station appear COI0511. to be more In comparison, in a circular tidal nature. currents The at observed Stations COI0514currents andat Station COI0502 COI0501 appear show to be moredistinct in aflow circular directions nature. between The observed flood currentsand ebb. atDuring Station the COI0501 flood, showthe currents distinct are flow generally directions toward between the northwest flood and di ebb.rection During while the during flood, the the ebb, currents currents are generallyare more towardtoward thethe northwest southwest direction direction. while The during model the was ebb, no currentst able to are accurately more toward capture the southwest the observed direction. flow Thepattern model there. was The not results able to accuratelyalso indicate capture that depth-averaged the observed flow maximum pattern there. current The magnitude results also exceeds indicate 2 thatm/s depth-averagedat nearly all the maximumstations except current for magnitude Station COI0514, exceeds which 2 m/s is at located nearly allnear the the stations entrance except of forthe StationInlet. COI0514, which is located near the entrance of the Inlet.

FigureFigure 4.4. Scatterplots of U andand VV velocityvelocity componentscomponents forfor model-predictedmodel-predicted depth-averageddepth-averaged tidaltidal currentscurrents andand NOAANOAA observationsobservations atat sixsix ADCPADCP locationslocations inside Cook Inlet (a) COI0514;COI0514; (b) COI0511; ((cc)) COI0508;COI0508; ((dd)) COI0501;COI0501; ((ee)) COI0502;COI0502; ((ff)) COI0503.COI0503. TheThe plotsplots werewere generatedgenerated fromfrom depth-averageddepth-averaged velocityvelocity timetime seriesseries forfor bothboth modelmodel predictionspredictions andand fieldfield observations.observations.

TheThe error statistics were were calculated calculated for for the the east east and and north north velocity velocity components, components, respectively, respectively, to toquantify quantify the the model’s model’s performance performance in in simulating simulating tidal tidal currents. currents. The The results results are are provided provided in in Table Table 22.. Overall,Overall, there is a very very good good correlation correlation between between model model predictions predictions and and observations, observations, i.e., i.e., 10 10of of12 12R2 Rvalues2 values are are greater greater than than or orequal equal to to 0.9. 0.9. As As expect expecteded from from the the scatterplot scatterplot comparisons comparisons in in Figure 44,, StationStation COI0501COI0501 hashas thethe worstworst correlationcorrelation forfor thethe easteast component,component, asas thethe modelmodel failedfailed toto capturecapture thethe flowsflows acrossacross thethe channelchannel (east-west(east-west direction).direction). By looking at the RMSE and SI valuesvalues together,together, thethe absoluteabsolute errorserrors (RMSE)(RMSE) tendtend toto bebe largerlarger forfor thethe majormajor velocityvelocity components,components, whilewhile thethe relativerelative errorserrors (SI)(SI) areare comparablycomparably smallersmaller atat mostmost stations.stations. For example, atat Station COI0503, wherewhere thethe north-southnorth-south velocityvelocity isis thethe majormajor velocityvelocity component,component, thethe correspondingcorresponding RMSERMSE isis biggerbigger thanthan thatthat ofof the east-west component.component. In In contrast, contrast, the the SI SI shows shows the the exact exact opposi oppositete result. result. This This suggests suggests that that the the model model tends tends to simulate velocity better in the main flow directions. Depending on the location of the station, the RMSE can vary from 0.07 m/s to as big as 0.31 m/s, but most RMSEs are under 0.2 m/s.

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J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 9 of 20 to simulate velocity better in the main flow directions. Depending on the location of the station, the RMSE can vary from 0.07 m/s to as big as 0.31 m/s, but most RMSEs are under 0.2 m/s. Table 2. Error statistics (RMSE, SI, and R2) for depth-averaged tidal currents at six ADCP survey stations inside Cook Inlet (The top row is for the east velocity (U) component and the bottom row is Table 2. Error statistics (RMSE, SI, and R2) for depth-averaged tidal currents at six ADCP survey for the north velocity (V) component). stations inside Cook Inlet (The top row is for the east velocity (U) component and the bottom row is for the north velocity (V) component).Vel. COI COI COI COI COI COI Station Comp 0514 0511 0508 0501 0502 0503 Vel. COI COI COI COI COI COI Station RMSE CompU 0.070514 0.090511 0.130508 0.450501 0.150502 0.170503 (m/s) V 0.08 0.11 0.20 0.24 0.17 0.31 RMSE U 0.07 0.09 0.13 0.45 0.15 0.17 U 0.62 0.23 0.43 1.35 0.42 0.82 (m/s)SI V 0.08 0.11 0.20 0.24 0.17 0.31 UV 0.29 0.62 0.17 0.23 0.18 0.43 0.20 1.35 0.14 0.42 0.18 0.82 SI VU 0.85 0.29 0.97 0.17 0.92 0.18 0.19 0.20 0.93 0.14 0.90 0.18 2 R U 0.85 0.97 0.92 0.19 0.93 0.90 2 V 0.95 0.98 0.98 0.98 0.99 0.99 R V 0.95 0.98 0.98 0.98 0.99 0.99 3.2. A Sensitivity Test on the Effect of Grid Resolution 3.2. A Sensitivity Test on the Effect of Grid Resolution The calibration results (Figure 5 and Table 3) show that the discrepancy between model predictionsThe calibration and field results observations (Figure5 and becomes Table3 )larger show thatat those the discrepancy three ADCP between stations model located predictions in the andForeland field observationsregion. This discrepancy becomes larger is especially at those a threepparent ADCP at Station stations COI0501—the located in the data Foreland indicate region. there Thisis a discrepancyclear rectilinear is especially misalignment apparent between at Station flood COI0501—the and ebb datacurrent indicate directions there is while a clear the rectilinear model misalignmentpredictions did between not reproduce flood and the ebb same current pattern. directions We suspected while the that model a grid predictions resolution did of not 200 reproduce m might thenot samebe adequate pattern. to We resolve suspected the complex that a grid channel resolution geometry of 200 there. m might Therefore, not be a adequatesensitivity to test resolve was theconducted complex by channel refining geometrythe grid resolution there. Therefore, to about 50 a m sensitivity in the Foreland test was region conducted to assess by if an refining increased the gridspatial resolution resolution to will about help 50 improve m in the current Foreland predictions. region to assessA model if an grid increased resolution spatial of 50 resolution m matches will the helpresolution improve of the current bathymetry predictions. dataset, A modeland was grid th resolutionus considered of 50 sufficient m matches to capture the resolution the geometry of the bathymetryfeature represented dataset, andby the was bathymetry thus considered data. The suffi sensitcientivity to capture test results the geometry for the same feature calibration represented period by thewere bathymetry compared data.with Thethe earlier sensitivity model test results results and for fi theeld same observations calibration and period presented were comparedin Figure 5 with and theTable earlier 3. model results and field observations and presented in Figure5 and Table3.

FigureFigure 5.5.Scatterplots Scatterplots comparisons comparisons of U andof VU velocity and V components velocity forcomponents model-predicted for model-predicted depth-averaged tidaldepth-averaged currents (including tidal currents both (inclu the baselineding both calibration the baseline run calibration and the sensitivity run and the test sensitivity run with refinedtest run modelwith refined grid) andmodel NOAA grid) observationsand NOAA observations at three ADCP at three locations ADCP in locations the Foreland in the region Foreland (a) region COI0501; (a) (COI0501;b) COI0502; (b) ( cCOI0502;) COI0503. (c The) COI0503. plots were The generated plots were from generated depth-averaged from depth-averaged velocity time series velocity for bothtime modelseries for predictions both model and predictions field observations. and field observations.

AsAs oneone can can see see from from Figure Figure5, the sensitivity5, the sensitivity test results test did results not show did any not substantial show any improvement substantial overimprovement the previous over model the previous results. Themodel new results. model The results new mostly model overlayresults mostly with those overlay in the with calibration those in run.the calibration The error run. statistics The error also statistics largely remainalso largely the sameremain (Table the same3). We(Table suspect 3). We this suspect should this be should due tobe thedue insu to thefficient insufficient accuracy accura of thecy bathymetryof the bathymetry dataset dataset in the Forelandin the Foreland region region and the and upper the upper Inlet. AlthoughInlet. Although the bathymetry the bathymetry dataset dataset used for used this studyfor this has study a relatively has a highrelatively nominal high spatial nominal resolution spatial ofresolution 50 m, it shouldof 50 m, be it notedshould that be thisnoted dataset that this was dataset largely was re-produced largely re-produced (or re-gridded) (or re-gridded) from historical from bathymetryhistorical bathymetry surveys in surveys Cook Inlet.in Cook Hence, Inlet. Hence, the bathymetry the bathymetry data couldn’tdata couldn’t suffi cientlysufficiently capture capture the the dynamic changes of bed morphology in the Foreland region contributed by the interplay of the large amount of sediment input and energetic tidal currents. It is reasonable to conclude that without

J. Mar. Sci. Eng. 2020, 8, 254 10 of 19 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 10 of 20 dynamicmore accurate changes bathymetry of bed morphology information, in the a further Foreland refinement region contributed of the model by the grid interplay resolution of the will large not amounthelp improve of sediment velocity input predictions. and energetic tidal currents. It is reasonable to conclude that without more accurate bathymetry information, a further refinement of the model grid resolution will not help improveTable velocity 3. Error predictions. statistics (RMSE, SI, and R2) for depth-averaged tidal currents at three ADCP survey stations in the Foreland region (The top row is for the east (U) velocity component and the bottom 2 Tablerow is 3. forError the statisticsnorth (V) (RMSE,velocity SI, component). and R ) for The depth-averaged model results tidal are from currents the sensitivity at three ADCP test. survey stations in the Foreland region (The top row is for the east (U) velocity component and the bottom row Vel. COI COI COI is for the north (V) velocityStation component). The model results are from the sensitivity test. Comp 0501 0502 0503 Vel. COI COI COI Station RMSE U 0.45 0.15 0.19 Comp 0501 0502 0503 (m/s) V 0.24 0.17 0.23 RMSE UU 0.45 1.37 0.42 0.15 0.90 0.19 (m/s) SI V 0.24 0.17 0.23 V 0.20 0.14 0.18 U 1.37 0.42 0.90 SI U 0.19 0.93 0.90 R2 V 0.20 0.14 0.18 V 0.98 0.99 0.99 2 U 0.19 0.93 0.90 R V 0.98 0.99 0.99 3.3. Model Validation 3.3. Model Validation Model validation is another important step in hydrodynamic modeling. In this study, we picked YearModel 2012 as validation model validation is another pe importantriod. Since step the in sensitivity hydrodynamic test using modeling. the refined In this model study, grid we pickeddid not Yearshow 2012 any as substantial model validation improvement period. in Sincevelocity the predictions, sensitivity testwe chose using to the use refined the same model model grid grid did used not showfor the any baseline substantial calibration improvement model inrun velocity for the predictions, validation werun. chose The tomodel use the predicted same model current grid velocities used for theat three baseline additional calibration ADCP model stations run for deployed the validation in Year run. 2012, The model and these predicted were current compared velocities with atNOAA three additionalobservations. ADCP The stations model-data deployed comparisons in Year 2012, were and summarized these were comparedin Figure with6 and NOAA Table observations.4. At Station TheCOI1210, model-data the model comparisons predictions were summarizedmatch field observations in Figure6 and nearly Table 4perfect. At Station over COI1210,a full-month the model period predictions(Figure 6a). match The model field observationsperformance nearlybecomes perfect worse over for athe full-month other two period ADCP (Figurestations6a). located Themodel further performanceupstream. For becomes example, worse the for results the other at Station two ADCP COI1207, stations the located velocity further magnitude upstream. is Forsubstantially example, theunder-predicted results at Station (Figure COI1207, 6b), which the velocity can be seen magnitude from the is substantiallylarge RMSE (0.58 under-predicted m/s) and SI (0.48) (Figure values.6b), whichDespite can of be underpredicting seen from the largecurrent RMSE magnitude, (0.58 m/ s)the and model SI (0.48) performs values. very Despite well in of predicting underpredicting current currentdirection. magnitude, At Station the COI1209 model performs(Figure 6c), very the well model in predicting was not able current to accurately direction. resolve At Station the moderate COI1209 (Figurerectilinear6c), themisalignment model was not between able to accuratelyflooding and resolve ebbing the moderate current rectilineardirections. misalignment A closer look between at the floodingbathymetry and feature ebbing near current these directions. two ADCP A closerstations look indicates at the bathymetry the mismatch feature between near model these twopredictions ADCP stationsand field indicates observations the mismatch is likely between due to model the inaccuracy predictions of and the field bathymetry observations dataset is likely (Figure due 7). to theFor inaccuracyexample, the of theexisting bathymetry bathymetry dataset dataset (Figure shows7). For the example, presence the of existing a shallow bathymetry sill in the dataset middle shows of the thechannel presence that of is aadjacent shallow to sill COI1207. in the middle This shallow of the channel sill will that reduce is adjacent tidal flows to COI1207. through This the channel shallow and sill willsubsequently reduce tidal contribute flows through to the theunderprediction channel and subsequentlyof current magnitude contribute at toCOI1207. the underprediction A high-quality, of currentground magnitude truthing bathymetry at COI1207. survey A high-quality, in the upper ground Cook truthing Inlet is bathymetry highly warranted survey into theimprove upper model Cook Inletpredictions. is highly warranted to improve model predictions.

FigureFigure 6.6. ScatterplotsScatterplots ofof UU andand VV velocityvelocity componentscomponentsfor formodel-predicted model-predicteddepth-averaged depth-averaged tidaltidal currentscurrents and and NOAA NOAA observations observations at at three three Year Year 2012 2012 ADCP ADCP survey survey stations stations located located in in the the upper upper Cook Cook InletInlet ( a(a)) COI1210; COI1210; ( b(b)) COI1207; COI1207; ( c(c)) COI1209. COI1209. TheThe plots plots were were generated generated fromfrom depth-averaged depth-averaged velocityvelocity timetime series series for for both both model model predictions predictions and and field field observations. observations.

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Table 4.4. ErrorError statisticsstatistics (RMSE(RMSE andand R2)R2) forfor depth-averageddepth-averaged tidaltidal currentscurrents atat selectedselected ADCPADCP stations inside Cook Inlet. (The (The top top row is for the east velocity (U) component and the bottom row is for the north (V) velocity component.).

Vel.Vel. COICOI COICOI COI COI Station Station CompComp 12101210 12071207 1209 1209 RMSE RMSE UU 0.12 0.12 0.58 0.58 0.37 0.37 (m/s) (m/s) VV 0.12 0.12 0.23 0.23 0.38 0.38 U 0.11 0.42 0.30 SI U 0.11 0.42 0.30 SI V 0.16 0.48 1.0 V 0.16 0.48 1.0 U 0.99 0.97 0.97 R2 U 0.99 0.97 0.97 R2 V 0.99 0.97 0.57 V 0.99 0.97 0.57

Figure 7. The bathymetric feature near ADCP Stations COI1207 and and COI1209 in in upper Cook Inlet. The location of a shallow sillsill nearnear StationStation COI1207COI1207 isis pointedpointed byby anan arrow.arrow.

3.4. Tidal Characteristics As shown in FigureFigure3 3,, tides tides in in Cook Cook Inlet Inlet are are dominated dominated by by semi-diurnal semi-diurnal constituents. constituents. ItIt isis important toto see see how how tides tides propagate propagate within within the systemthe system and amplifyand amplify toward toward the upper the Inlet upper to produceInlet to theproduce largest the tidal largest ranges tidal of ranges all U.S. of coastal all U.S. waters. coastal According waters. According to the co-tidal to the charts co-tidal (Figure charts8 a,b)(Figure for the8a,b) largest for the semi-diurnal largest semi-diurnal and diurnal and constituents diurnal constituents (M2 and (M2 K1), and M2 tideK1), isM2 more tide amplifiedis more amplified than K1, whichthan K1, also which agrees also with agrees earlier with observations earlier observations at three NOAA at three tidal NOAA gages tidal (Figure gages2). For(Figure the tidal 2). For phase the (Figuretidal phase8c,d), (Figure M2 tide 8c,d), shows M2 atide much shows greater a much phase greater change phase than change K1 constituent, than K1 constituent, which is consistent which is withconsistent the amplitude. with the amplitude. The co-phase The chartco-phase for M2chart tide for (FigureM2 tide8 c)(Figure suggests 8c) suggests the length the of length Cook of Inlet Cook is smallerInlet is smaller but close but to close the half to the wave half length wave oflength M2 constituent. of M2 constituent. Also, the Also, narrowed the narrowed Foreland Foreland cross section cross appearssection appears to be the to critical be the location critical thatlocation substantially that substantially affects tidal affects propagation tidal propagation in Cook Inlet. in Cook Above Inlet. the crossAbove section, the cross tidal section, amplitude tidal amplitude and phase and both phase change bo muchth change more much rapidly more than rapidly in the than lower in Inlet.the lower Inlet.The tidal stage plots (Figure9) provide additional information on the tidal characteristics in Cook Inlet. Together with the co-tidal charts (Figure8), the results suggest that tides are essentially progressive Kelvin waves in the lower Inlet, and that they propagate faster toward the right (east) side of the channel along with larger amplitudes. Tidal velocity tends to be in phase with the water level; the maximum tidal velocity occurs during low and high tides (Figure9a–c). The co-tidal lines also appear to lie perpendicular to co-range lines (Figure8). In the upper Inlet region above the Foreland cross section, tides behave more like standing waves; e.g., maximum velocities tend to occur toward the mean tidal level rather than during the low and high tides (Figure9d–f).

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Figure 8. Two-dimensional distributions of tidal amplitudeamplitude and phase inside Cook Inlet for the most dominant semi-diurnalsemi-diurnal (M2)(M2) and and diurnal diurnal (K1) (K1) constituents constituents (a )(a M2) M2 amplitude; amplitude; (b) ( K1b) K1 amplitude; amplitude; (c) M2(c) phase;M2 phase; and and (d) K1(d) phase. K1 phase. J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 13 of 20 The tidal stage plots (Figure 9) provide additional information on the tidal characteristics in Cook Inlet. Together with the co-tidal charts (Figure 8), the results suggest that tides are essentially progressive Kelvin waves in the lower Inlet, and that they propagate faster toward the right (east) side of the channel along with larger amplitudes. Tidal velocity tends to be in phase with the water level; the maximum tidal velocity occurs during low and high tides (Figure 9a–c). The co-tidal lines also appear to lie perpendicular to co-range lines (Figure 8). In the upper Inlet region above the Foreland cross section, tides behave more like standing waves; e.g., maximum velocities tend to occur toward the mean tidal level rather than during the low and high tides (Figure 9dfe).

Figure 9. Tidal stage (water level vs. velocity) curves at six ADCP stations along the main axis of Cook Figure 9. Tidal stage (water level vs. velocity) curves at six ADCP stations along the main axis of Inlet showing the propagation of tidal wave in the system (a) COI0514; (b) COI0511; (c) COI0508; (d) Cook Inlet showing the propagation of tidal wave in the system (a) COI0514; (b) COI0511; (c) COI0508; COI0502; (e) COI1210; and (f) COI1209. (d) COI0502; (e) COI1210; and (f) COI1209.

3.5. Spatial Variability of Tidal Currents Because optimal turbine siting (e.g., hub height) relies on detailed knowledge of vertical velocity structure, it is important to further examine vertical current profiles at potential tidal energy hotspots in Cook Inlet. The depth-averaged velocity comparisons (Figure 4) suggest that Station COI0503 near East Foreland appears to be the top hotspot because it has the strongest current magnitude of all the stations. Figure 10 shows the 2-D current vertical profile comparisons at Station COI0503 on 25 May 2005, during the spring tide. It should be mentioned that the currents have been projected along the principal-axis direction to better show the current magnitude. The model-data comparisons show an overall good match with respect to the vertical structure and timing. The model results indicate that maximum current magnitude exceeds 4 m/s during peak flood and ebb at depths close to the surface. There are visible velocity gradients especially during the peak flood and ebb stages; e.g., the maximum differences between surface and bottom velocities reaches 1.5 m/s during peak flood around noon on 25 May 2005.

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Figure 9. Tidal stage (water level vs. velocity) curves at six ADCP stations along the main axis of Cook J. Mar. Sci. Eng. 2020 8 Inlet showing, the, 254 propagation of tidal wave in the system (a) COI0514; (b) COI0511; (c) COI0508; (d13) of 19 COI0502; (e) COI1210; and (f) COI1209. 3.5. Spatial Variability of Tidal Currents 3.5. Spatial Variability of Tidal Currents Because optimal turbine siting (e.g., hub height) relies on detailed knowledge of vertical velocity Because optimal turbine siting (e.g., hub height) relies on detailed knowledge of vertical velocity structure, it is important to further examine vertical current profiles at potential tidal energy hotspots structure, it is important to further examine vertical current profiles at potential tidal energy hotspots in Cook Inlet. The depth-averaged velocity comparisons (Figure4) suggest that Station COI0503 near in Cook Inlet. The depth-averaged velocity comparisons (Figure 4) suggest that Station COI0503 near East Foreland appears to be the top hotspot because it has the strongest current magnitude of all the East Foreland appears to be the top hotspot because it has the strongest current magnitude of all the stations. Figure 10 shows the 2-D current vertical profile comparisons at Station COI0503 on 25 May stations. Figure 10 shows the 2-D current vertical profile comparisons at Station COI0503 on 25 May 2005, during the spring tide. It should be mentioned that the currents have been projected along the 2005, during the spring tide. It should be mentioned that the currents have been projected along the principal-axis direction to better show the current magnitude. The model-data comparisons show an principal-axis direction to better show the current magnitude. The model-data comparisons show an overall good match with respect to the vertical structure and timing. The model results indicate that overall good match with respect to the vertical structure and timing. The model results indicate that maximum current magnitude exceeds 4 m/s during peak flood and ebb at depths close to the surface. maximum current magnitude exceeds 4 m/s during peak flood and ebb at depths close to the surface. There are visible velocity gradients especially during the peak flood and ebb stages; e.g., the maximum There are visible velocity gradients especially during the peak flood and ebb stages; e.g., the differences between surface and bottom velocities reaches 1.5 m/s during peak flood around noon on maximum differences between surface and bottom velocities reaches 1.5 m/s during peak flood 25 May 2005. around noon on 25 May 2005.

Figure 10. Projected principal-axis (along channel) vertical velocity profile comparison of model prediction (a) and ADCP measurements (b) at Station COI0503 for 25 May 2005. The positive values indicate flooding currents flowing toward upstream.

A detailed understanding of the temporal distribution/variability of tidal velocity provides critical information for optimizing tidal turbine device selection and operation [40]. Figure 11a shows the histogram plot of the density/frequency distribution of depth-averaged current speed at Station COI0503 over a three-month simulation period. The corresponding probability of exceedance curve is provided in Figure 11b, with additional results at three depths—surface layer, middle layer, and bottom layer. The histogram plot (Figure 11a) shows that current speed mostly ranges from 1 m/s to 3 m/s at Station COI0503, and has a peak density between 2 and 2.5 m/s. The probability of exceedance plot (Figure 11b) suggests the current speed exceeds 1 m/s more than 75% of the time. In addition, comparing the probability of exceedance plots at different depths indicates that the current speed for the bottom layer is much smaller than at the other depths. This is consistent with what we observed in the vertical profile plot (Figure 10). The depth-averaged current speed distribution appears to be very close to that found at the middle depth. As expected, surface current is the strongest of all the depths—current speed exceeds 2 m/s for more than half of the time. J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 14 of 20

Figure 10. Projected principal-axis (along channel) vertical velocity profile comparison of model prediction (a) and ADCP measurements (b) at Station COI0503 for 25 May 2005. The positive values indicate flooding currents flowing toward upstream.

A detailed understanding of the temporal distribution/variability of tidal velocity provides critical information for optimizing tidal turbine device selection and operation [40]. Figure 11a shows the histogram plot of the density/frequency distribution of depth-averaged current speed at Station COI0503 over a three-month simulation period. The corresponding probability of exceedance curve is provided in Figure 11b, with additional results at three depths—surface layer, middle layer, and bottom layer. The histogram plot (Figure 11a) shows that current speed mostly ranges from 1 m/s to 3 m/s at Station COI0503, and has a peak density between 2 and 2.5 m/s. The probability of exceedance plot (Figure 11b) suggests the current speed exceeds 1 m/s more than 75% of the time. In addition, comparing the probability of exceedance plots at different depths indicates that the current speed for the bottom layer is much smaller than at the other depths. This is consistent with what we observed in the vertical profile plot (Figure 10). The depth-averaged current speed distribution appears to be J. Mar.very Sci. close Eng. 2020to that, 8, 254found at the middle depth. As expected, surface current is the strongest of all14 the of 19 depths—current speed exceeds 2 m/s for more than half of the time.

FigureFigure 11. 11.(a )(a histogram) histogram plot plot of of current current speed speed atat thethe middlemiddle depth depth of of Station Station COI0503 COI0503 over over the the three three monthsmonths of modelof model simulation simulation in summer in summer 2005; (b2005;) the corresponding(b) the corresponding cumulative cumulative frequency frequency distribution plotsdistribution of current plots speed of overcurrent various speed waterover various depths. water depths.

3.6.3.6. Tidal Tidal Energy Energy Extraction Extraction Potential Potential in in Cook Cook InletInlet

3.6.1.3.6.1. Tidal Tidal Energy Energy Resource Resource Distribution Distribution InIn the the previous previous sections, sections, we we demonstrated demonstrated thatthat thethe hydrodynamic model model was was able able to to capture capture the the tidaltidal hydrodynamics hydrodynamics in in Cook Cook Inlet. Inlet. For For this this reason, reason, the the model model simulation simulation results results werewere furtherfurther usedused to characterizeto characterize tidal tidal energy energy resource resource distribution distribution in thein the system. system. Figure Figure 12 12 shows shows the the 2-D 2-D distribution distribution of depth-averagedof depth-averaged tidal powertidal power density density (or energy (or energy density den flux)sity influx) the in entire the entire system system and in and the zoom-inin the areazoom-in near Foreland. area near The Foreland. 2-D plots The suggest 2-D plots that suggest the areas that that the have areas high that energy have high density energy (i.e., density>2000 W(i.e.,/m 2) are> mostly2000 W/m located2) arein mostly the upper located Inlet. in the The upper Foreland Inlet. areaThe appearsForeland toarea have appears the most to have abundant the most tidal energyabundant resources tidal inenergy the entire resources system, in both the inentire terms system, of magnitude both in andterms spatial of magnitude coverage, primarilyand spatial as a resultcoverage, of the muchprimarily narrower as a result cross sectionof the much due to na therrower presence cross of section two forelands. due to the More presence specifically, of two the forelands. More specifically, the area immediately adjacent to East Foreland has the strongest power area immediately adjacent to East Foreland has the strongest power density, which exceeds 5000 W/m2. density, which exceeds 5000 W/m2. Considering that water depth is typically on the order of 50 m in Considering that water depth is typically on the order of 50 m in this area, it should be the top hotspot this area, it should be the top hotspot for potential tidal energy harnessing. It has a substantially for potential tidal energy harnessing. It has a substantially larger tidal stream power density sustained larger tidal stream power density sustained over a very large area. This is consistent with previous over a very large area. This is consistent with previous findings by Haas et al. [17]. findings J.by Mar. Haas Sci. Eng. et 2020 al., 8[17]., x FOR PEER REVIEW 15 of 20

Figure 12. Two-dimensional distribution of time- and depth-averaged tidal power density inside Figure 12. Two-dimensionalCook Inlet based on a distribution three-month model of time- simula andtion. depth-averaged The inset shows tidalthe zoom-in power tidal density power inside Cook Inlet baseddensity on a three-monthdistribution near model the Foreland simulation. region. The The dashed inset line shows indicates the the zoom-in location of tidal the powertidal density distributionturbine near farm the transect. Foreland region. The dashed line indicates the location of the tidal turbine farm transect. 3.6.2. Assessing Tidal Energy Extraction Potential While the East Foreland region appears to be the most promising site for tidal energy harnessing, it is also important to assess the possibility of extracting tidal energy at a much broader spatial scale to effectively reduce the energy cost. As suggested by the inset plot in Figure 12, a substantial portion of the Foreland area has a power density exceeding 2000 W/m2. Therefore, a sensitivity test was conducted by deploying hypothetical turbine arrays along one single transect across the entire Foreland cross section. Two tidal turbine array scenarios were considered. In both scenarios, tidal turbines were assumed to extract energy from the middle depths (Layers 5 and 6 in the hydrodynamic model) of the water column. More specifically, in Scenario 1 (S1), a 5% blockage ratio of the entire cross-sectional area was used to determine the tidal array density along the transect. In Scenario 2 (S2), a much higher (20%) blockage ratio was used. It should be mentioned that in both scenarios, the blockage ratios are higher than typical values reported in the literature, because in our case tidal turbines are only considered to occupy one cross section. In both scenarios, the tidal turbine module was configured in a way similar to that in [20]; e.g., a thrust coefficient (CT) of 0.5 was used, and no cut-in and cut-out speed limit was considered [20]. Figure 13 shows the instantaneous extracted tidal power time series under both energy extraction scenarios. The extracted power was calculated using Equation 4. The extracted tidal power time series exhibit strong temporal variability over spring and neap tidal cycles. The extracted power during the spring tide is nearly an order of magnitude higher than that during the neap tide. The maximum instantaneous power rate during the spring tide is close to 180 MW and 800 MW for S1 and S2, respectively. The mean power rate for S1 and S2 is approximately 46 MW and 181 MW, respectively. The extracted power rate in S2 is considerably larger than that in S1. It should be noted that this power extraction rate is only a theoretical value calculated by the hydrodynamic model.

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3.6.2. Assessing Tidal Energy Extraction Potential While the East Foreland region appears to be the most promising site for tidal energy harnessing, it is also important to assess the possibility of extracting tidal energy at a much broader spatial scale to effectively reduce the energy cost. As suggested by the inset plot in Figure 12, a substantial portion of the Foreland area has a power density exceeding 2000 W/m2. Therefore, a sensitivity test was conducted by deploying hypothetical turbine arrays along one single transect across the entire Foreland cross section. Two tidal turbine array scenarios were considered. In both scenarios, tidal turbines were assumed to extract energy from the middle depths (Layers 5 and 6 in the hydrodynamic model) of the water column. More specifically, in Scenario 1 (S1), a 5% blockage ratio of the entire cross-sectional area was used to determine the tidal array density along the transect. In Scenario 2 (S2), a much higher (20%) blockage ratio was used. It should be mentioned that in both scenarios, the blockage ratios are higher than typical values reported in the literature, because in our case tidal turbines are only considered to occupy one cross section. In both scenarios, the tidal turbine module was configured in a way similar to that in [20]; e.g., a thrust coefficient (CT) of 0.5 was used, and no cut-in and cut-out speed limit was considered [20]. Figure 13 shows the instantaneous extracted tidal power time series under both energy extraction scenarios. The extracted power was calculated using Equation 4. The extracted tidal power time series exhibit strong temporal variability over spring and neap tidal cycles. The extracted power during the spring tide is nearly an order of magnitude higher than that during the neap tide. The maximum instantaneous power rate during the spring tide is close to 180 MW and 800 MW for S1 and S2, respectively. The mean power rate for S1 and S2 is approximately 46 MW and 181 MW, respectively. The extracted power rate in S2 is considerably larger than that in S1. It should be noted that this power J.extraction Mar. Sci. Eng. rate 2020 is, 8 only, x FOR a theoreticalPEER REVIEW value calculated by the hydrodynamic model. 16 of 20

FigureFigure 13. 13. TimeTime series series of of extracted extracted power power rate rate for for two two hypothetical hypothetical tidal tidal turbine turbine farm farm scenarios scenarios (S1 (S1 andand S2). S2). It is important to investigate the system’s response to energy extraction. One potential response is It is important to investigate the system’s response to energy extraction. One potential response the changes (i.e., sensitivity-baseline) in tidal regime. We calculated the changes in tidal amplitude and is the changes (i.e., sensitivity-baseline) in tidal regime. We calculated the changes in tidal amplitude phase for major tidal constituents between power extraction scenarios and the baseline condition at all and phase for major tidal constituents between power extraction scenarios and the baseline condition three NOAA tidal gages in Figure1. The results suggest that the resulting changes at the two southern at all three NOAA tidal gages in Figure 1. The results suggest that the resulting changes at the two gages, Seldovia and Nikiski, are minimal. In addition, the changes for S1 are barely detectable. Hence, southern gages, Seldovia and Nikiski, are minimal. In addition, the changes for S1 are barely only the results for S2 and at the Anchorage tidal gage are presented here to illustrate the potential detectable. Hence, only the results for S2 and at the Anchorage tidal gage are presented here to impact of energy extraction (Figure 14). illustrate the potential impact of energy extraction (Figure 14). Figure 14a shows that extracting tidal energy from the Foreland transect reduced tidal amplitude Figure 14a shows that extracting tidal energy from the Foreland transect reduced tidal amplitude in the upper inlet. However, the magnitude of change is very small for the energy extraction rate in S2. in the upper inlet. However, the magnitude of change is very small for the energy extraction rate in The M2 constituent experiences the maximum amplitude drop of all constituents, but the reduction S2. The M2 constituent experiences the maximum amplitude drop of all constituents, but the is only on the order of 1 cm. Compared to its amplitude, the reduction ratio is only about 0.3%. reduction is only on the order of 1 cm. Compared to its amplitude, the reduction ratio is only about 0.3%. The higher-frequency constituents, which include four semi-diurnals (M2, S2, N2, and K2) and one quarter-diurnal (M4), exhibit a larger amplitude drop than the four diurnal ones (K1, O1, P1, and Q1). This is expected, considering that higher-frequency tidal currents tend to be dampened faster by friction force, or turbine drag in this case. Interestingly, the changes in tidal phase (Figure 14b) also shows a similar pattern in which semi-diurnal and quarter-diurnal constituents respond differently from the diurnal ones. Specifically, the negative changes in tidal phase for semi-diurnal and quarter-diurnal constituents suggest these tidal constituents propagate faster than the baseline condition. In contrast, all the diurnal constituents experience a phase lag, meaning they propagate slower than the baseline condition. However, the changes in tidal phase are also very small—all are less than a quarter degree.

J. Mar. Sci. Eng. 2020, 8, 254 16 of 19

The higher-frequency constituents, which include four semi-diurnals (M2, S2, N2, and K2) and one quarter-diurnal (M4), exhibit a larger amplitude drop than the four diurnal ones (K1, O1, P1, and Q1). This is expected, considering that higher-frequency tidal currents tend to be dampened faster by friction force, or turbine drag in this case. Interestingly, the changes in tidal phase (Figure 14b) also shows a similar pattern in which semi-diurnal and quarter-diurnal constituents respond differently from the diurnal ones. Specifically, the negative changes in tidal phase for semi-diurnal and quarter-diurnal constituents suggest these tidal constituents propagate faster than the baseline condition. In contrast, all the diurnal constituents experience a phase lag, meaning they propagate slower than the baseline J.condition. Mar. Sci. Eng. However, 2020, 8, x FOR the PEER changes REVIEW in tidal phase are also very small—all are less than a quarter degree. 17 of 20 The reduction in tidal amplitude affects tidal prism in the upper inlet, which is also reflected in the tidal flux across the Foreland transect. Figure 15 shows the changes in tidal flux between two energy extraction scenarios and the baseline condition. Compared to tidal flux under the baseline condition that varies between 1.7 106 m3/s across the Foreland transect, the changes in tidal flux for ± × both energy extraction scenarios is much smaller. For instance, the maximum flow reduction typically occurs during the peak and ebb flood stages when the tidal flux is highest. J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 17 of 20

Figure 14. The changes in tidal amplitude (a) and phase (b) at the NOAA tidal gage near Anchorage, Alaska, as a result of power extraction in S2.

The reduction in tidal amplitude affects tidal prism in the upper inlet, which is also reflected in the tidal flux across the Foreland transect. Figure 15 shows the changes in tidal flux between two energy extraction scenarios and the baseline condition. Compared to tidal flux under the baseline condition that varies between ±1.7 × 106 m3/s across the Foreland transect, the changes in tidal flux for bothFigure Figureenergy 14. 14. extraction TheThe changes changes scenarios in in tidal tidal amplitudeis amplitude much smaller. (a ()a )and and phaseFor phase instance, (b (b) )at at the the the NOAA NOAA maximum tidal tidal gage gageflow near nearreduction Anchorage, Anchorage, typically occursAlaska,Alaska, during as as a athe result result peak of of poweran powerd ebb extraction extraction flood stages in in S2. S2. when the tidal flux is highest.

The reduction in tidal amplitude affects tidal prism in the upper inlet, which is also reflected in the tidal flux across the Foreland transect. Figure 15 shows the changes in tidal flux between two energy extraction scenarios and the baseline condition. Compared to tidal flux under the baseline condition that varies between ±1.7 × 106 m3/s across the Foreland transect, the changes in tidal flux for both energy extraction scenarios is much smaller. For instance, the maximum flow reduction typically occurs during the peak and ebb flood stages when the tidal flux is highest.

Figure 15. The changechange in in tidal tidal flux flux across across the the tidal tidal farm farm transect transect near near the Forelands the Forelands as a result as a ofresult energy of energyextraction extraction for two for hypothetical two hypothetical tidal turbine tidal turbine farm scenarios farm scenarios (S1 and (S1 S2). and S2).

4. Summary In this study, an unstructured-grid based tidal hydrodynamic model was developed for Cook Inlet, Alaska, to assist tidal energy resource characterization in the estuary. The model-data comparisons indicated that the model has very promising skills in capturing the major tidal Figure 15. The change in tidal flux across the tidal farm transect near the Forelands as a result of characteristics of Cook Inlet; e.g., a semi-diurnal tidal regime with tidal range rapidly amplifying energy extraction for two hypothetical tidal turbine farm scenarios (S1 and S2). toward the upper Inlet. The model simulated tidal energy density distribution confirms the abundant 4.tidal Summary energy potential in Cook Inlet especially in the East Foreland region where time- and depth-averaged power density exceeds 5 kw/m2. This region should be considered as the most promisingIn this tidalstudy, energy an unstructured-grid hotspot in Cook based Inlet. tidalFurt hermore,hydrodynamic a model model test waswith developed a hypothetical for Cook tidal Inlet,turbine Alaska, farm configurationto assist tidal in theenergy Foreland resource cross chsectaracterizationion indicates thein theupper estuary. Inlet is The most model-data sensitive to comparisons indicated that the model has very promising skills in capturing the major tidal characteristics of Cook Inlet; e.g., a semi-diurnal tidal regime with tidal range rapidly amplifying toward the upper Inlet. The model simulated tidal energy density distribution confirms the abundant tidal energy potential in Cook Inlet especially in the East Foreland region where time- and depth-averaged power density exceeds 5 kw/m2. This region should be considered as the most promising tidal energy hotspot in Cook Inlet. Furthermore, a model test with a hypothetical tidal turbine farm configuration in the Foreland cross section indicates the upper Inlet is most sensitive to

J. Mar. Sci. Eng. 2020, 8, 254 17 of 19

4. Summary In this study, an unstructured-grid based tidal hydrodynamic model was developed for Cook Inlet, Alaska, to assist tidal energy resource characterization in the estuary. The model-data comparisons indicated that the model has very promising skills in capturing the major tidal characteristics of Cook Inlet; e.g., a semi-diurnal tidal regime with tidal range rapidly amplifying toward the upper Inlet. The model simulated tidal energy density distribution confirms the abundant tidal energy potential in Cook Inlet especially in the East Foreland region where time- and depth-averaged power density exceeds 5 kw/m2. This region should be considered as the most promising tidal energy hotspot in Cook Inlet. Furthermore, a model test with a hypothetical tidal turbine farm configuration in the Foreland cross section indicates the upper Inlet is most sensitive to tidal energy extraction; higher-frequency tidal constituents (e.g., semi-diurnal and quarter-diurnal) experience more impact than low frequency (diurnal) constituents, although the overall impact on tidal dynamics is minimum for the hypothetical energy extraction scenario considered in this study. Compared to the earlier tidal resource assessment by Haas et al. [17], the unstructured-grid modeling approach provides an additional flexibility for future grid refinement at any local scales and resolutions on an as-needed basis. The model results also suggest that, to better capture the spatial variability of currents in areas that have complex geometry and are also subject to dynamic morphological changes, higher-quality bathymetry survey data are warranted. These areas are mostly located in the upper inlet, where river discharge and associated sediment load become increasingly important in modulating water circulation and geomorphology. In addition, sea-ice can also form during cold months. It should be taken into consideration for more accurate tidal energy resource characterization during the winter. While the model has reasonably captured the general tidal wave characteristics in Cook Inlet, more research needs to be conducted to understand the mechanisms responsible for the rapid tidal amplification toward the upstream, such as the resonant effects. In the future, the model will be more comprehensively improved to include the effects of river input, sediment transport, and sea-ice, as these processes have been shown to be increasingly important, especially in the upper Inlet [41].

Author Contributions: Conceptualization, T.W. and Z.Y. Methodology, T.W. and Z.Y. Validation, T.W. Formal analysis, T.W. and Z.Y. Investigation, T.W. and Z.Y. Resources, Z.Y. Data curation, T.W. Writing—original draft preparation, T.W. Writing—review and editing, T.W. and Z.Y. Visualization, T.W. Supervision, Z.Y. Project administration, Z.Y. Funding acquisition, Z.Y. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Water Power Technology Office of the U.S. Department of Energy’s Office of Energy Efficiency and Renewable Energy, under Contract DE-AC05-76RL01830 to the Pacific Northwest National Laboratory. Acknowledgments: We would like to thank the technical steering committee, chaired by Bryson Robertson of Oregon State University, for providing external oversight for, input to, and review of this modeling study. Steering committee members include Henrique Alves of the National Oceanic and Atmospheric Administration; Brian Polagye of Pacific Marine Energy Center at University of Washington; James Behrens of the Coastal Data Information Program at the University of California San Diego; Pukha Lenee-Bluhm of Columbia Power; Bill Staby of Resolute Marine Energy, and Sean Anderton of Ocean Renewable Power Company. Thanks also go to Simon Waldman at The University of Hull for helpful discussion during this study. The model computations were performed using resources available through Research Computing at PNNL. PNNL is operated by Battelle for the U.S. Department of Energy under Contract DE-AC05-76RL01830. Conflicts of Interest: The authors declare no conflicts of interest.

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