Journal of Marine Science and Engineering

Article Tidal Datum Changes Induced by Morphological Changes of North Carolina Coastal Inlets

Jindong Wang 1,2,* and Edward Myers 1 1 Coast Survey Development Laboratory, National Ocean Service, National Oceanic and Atmospheric Administration, 1315 East-West Highway, Silver Spring, MD 20910, USA; [email protected] 2 Earth Resources Technology, Inc., 14401 Sweitzer Lane, Suite 300, Laurel, MD 20707, USA * Correspondence: [email protected]; Tel.: +1-301-713-2809

Academic Editor: Richard P. Signell Received: 18 July 2016; Accepted: 12 November 2016; Published: 18 November 2016

Abstract: In support of the National Oceanic and Atmospheric Administration’s VDatum program, a new version of a tidal datum product for the North Carolina coastal waters has been developed to replace the initial version released in 2004. Compared with the initial version, the new version used a higher resolution grid to cover more areas and incorporated up-to-date tide, bathymetry, and shoreline data. Particularly, the old bathymetry datasets that were collected from the 1930s to the 1970s and were used in the initial version have been replaced by the new bathymetry datasets collected in the 2010s in the new version around five North Carolina inlets. This study aims at evaluating and quantifying tidal datum changes induced by morphological changes over about 40 to 80 years around the inlets. A series of tidal simulations with either the old or new bathymetry datasets used around five inlets were conducted to quantify the consequent tidal datum changes. The results showed that around certain inlets, approximately 10% change in the averaged depth could result in over 30% change in the tidal datum magnitude. Further investigation also revealed that tidal datum changes behind the barrier islands are closely associated with the cross-inlet tidal flux changes.

Keywords: VDatum; tidal datums; morphological changes; inlets; North Carolina

1. Introduction The software package VDatum, developed and maintained by the National Oceanic and Atmospheric Administration (NOAA), allows users to transform geospatial data among a variety of ellipsoidal, orthometric, and tidal datums [1]. For example, users can integrate the United States Geological Survey’s elevation data referenced to the North American Vertical Datum of 1988 (NAVD88) with NOAA’s sounding data referenced to Mean Lower Low Water (MLLW) to build a seamless bathymetry-topography Digital Elevation Model (DEM) dataset referenced to a common datum of Mean Sea Level (MSL) by using VDatum. The integrated DEM provides a basis for coastal inundation modeling and mapping [2]. As a critical part of VDatum, tidal datums are derived from water level time series simulated by a tide model. The tidal highs and lows from modeled water levels are used to calculate tidal datums: Mean Higher High Water (MHHW), Mean High Water (MHW), Mean Low Water (MLW), and Mean Lower Low Water (MLLW) [3]. Following the VDatum Standard Operating Procedures [4], we use the ADvanced CIRCulation (ADCIRC) model [5] to conduct tidal simulations for deriving tidal datums in VDatum. The ADCIRC model has been widely used for tidal simulations from the basin scale [6–8] to the regional scale [9–11]. The initial version of VDatum for North Carolina was released in 2004 [12]. An updated version has been developed to cover more areas and incorporate up-to-date tide, bathymetry, and shoreline

J. Mar. Sci. Eng. 2016, 4, 79; doi:10.3390/jmse4040079 www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2016, 4, 79 2 of 17 data. Around five main North Carolina inlets (Beaufort, Barden, Ocracoke, Hatteras, and Oregon Inlet), the bathymetry datasets collected from the 1930s to the 1970s were used in the initial version for tide modeling to derive tidal datums. These old bathymetry datasets have been replaced by the datasets collected in the 2010s around five inlets in the updated version. Tidal datum changes induced by morphological changes of the inlets need to be quantified to provide NOAA guidance for future updating of VDatum, installing new tide gauges, and conducting new hydrographic surveys in this region. Tidal inlets are typically dynamically active regions where tidal circulation and transport lead to continuous sediment movement and thus morphological changes. In general, the combination of tides and waves was considered to shape the inlet morphology into different types: flood-tidal delta and ebb-tidal delta [13–16]. Tidal distortion was found to affect net sediment transport [17,18]. Tidal prism and inlet cross-sectional area were also considered as important factors to affect the inlet morphology [19]. Around North Carolina’s Beaufort Inlet, a nearshore jet in tidal circulation was identified and simulated and was considered to be associated with the net transport through the inlet [20,21]. Sediment deposition and erosion around North Carolina inlets was investigated with the local dynamics by Inman and Dolan [22]. These previous studies have mainly been focused on how hydrodynamics (e.g., tides and waves) affect the morphology of the inlets. Little attention has been paid to the feedback of tides to morphological changes of the inlets. In this study, we aimed at evaluating and quantifying how morphological changes of the inlets affect tidal changes. This paper is organized as follows: following the introduction section, Section2 describes the sources of a variety of tide, shoreline, and bathymetry data, as well as the tide model setup, numerical experiment design, and model validation. The results will be described in Section3 followed by some discussions and conclusions in the last section.

2. Materials and Methods

2.1. Data Sources The water level data [23] and the observed tidal datums [24] provided by the Center for Operational Oceanographic Products and Services (CO-OPS) of NOAA were used for model validation. CO-OPS typically publishes one single value for a particular tidal datum (e.g., MHW) at one station. The tidal datums were typically derived from the water level time series for a certain time period (from a couple of months to years). The observed tidal datums were referenced to the current National Tidal Datum Epoch (NTDE) (1983–2001) [24]. In this paper, the observed tidal datums at 31 tide stations were compared with the modeled tidal datums to evaluate the general model performance in North Carolina coastal waters. Since the identification (ID) numbers of all North Carolina stations begin with 865, the 865 will be ignored when we describe station IDs in the following discussions. The locations of all 31 datum stations are shown in Figure1. Among these stations, the 4 outside stations 1370, 4400, 6590, and 6937 are located on the Atlantic Ocean coast. The other 27 inside stations are located behind the barrier islands and within the sounds and estuaries. Among the 31 datum stations, tidal harmonic constituents are also provided for 16 stations [25]. In addition, the hourly water level data collected from 1967 to 2016 at Beaufort Station (ID: 6483), about 4 km behind the Beaufort Inlet and Duck Station (ID: 1370) on the Atlantic coast, were used to evaluate the temporal variation of MHW. The development of the hydrodynamic model grid requires shoreline and bathymetry data. The National Geodetic Survey provided the up-to-date North Carolina shoreline data which combined NOAA Continually Updated Shoreline Product (CUSP) and the Office of Coast Survey (OCS) chart shoreline data [26]. The bathymetry data were mainly from three sources. The OCS sounding data collected from 1851 to 2012 were used for most of the North Carolina coastal regions. The particular areas covered by the datasets collected in a certain year can be found in a Bathymetry Data Viewer [27]. A global bathymetry-topography database SRTM30_PLUS from Scripps Institution of Oceanography J. Mar. Sci. Eng. 2016, 4, 79 3 of 17

J. Mar. Sci. Eng. 2016, 4, 79 3 of 17 was used for the far offshore region [28]. The sounding data collected since 2010 by the U.S. Army J. Mar.Corps theSci. U.S.Eng. Engineers’ 2016Army, 4, Corps79 Wilmington Engineers’ District Wilmington were used District for coastal were used inlets for and coastal intra-coastal inlets and waterways intra-coastal [29]. 4 of 17 Allwaterways the up-to-date [29]. All tide, the bathymetry, up-to-date tide, and shorelinebathymetry data, and have shoreline been applied data have to derive been theapplied updated to derive tidal have datumsthe the updated same used depths tidal by the datums currently interpolated used available by the from currently VDatum the same available tool. bathymetry VDatum tool. datasets described in Section 2.1. Therefore, the only difference between the old-bathy grid and the new-bathy grid was the bathymetry around the five inlets. The same model setup and tidal forcing were applied to the models using the old-bathy grid and the new-bathy grid. In the following discussions, we will use the old-bathy model and the new-bathy model to represent the models using the old-bathy grid and the new-bathy grid, respectively. Since Beaufort Inlet and Barden Inlet are close to each other, we made another two grids new-bathy-BE and new-bathy-BA to evaluate the tidal datum changes induced by the morphological changes of each individual inlet. For the new-bathy-BE grid, the new bathymetry data were used around Beaufort Inlet and the old bathymetry data were used for the other four inlets. Similarly, for the new-bathy-BA grid, the new bathymetry data were used around Barden

Inlet and the old bathymetry( adata) were used for the other four inlets.( bWe) will use the new-bathy-BE model and the new-bathy-BA model to represent tidal simulations using the new-bathy-BE grid and Figure 1. Map of North Carolina coastal waters and inlets and the locations of the National Oceanic Figure 1. Map of North Carolina coastal waters and inlets and the locations of the National Oceanic and the new-bathyand Atmospheric-BA grid, respectivelyAdministration, in(NOAA the following) water level discussions. stations (black dots): (a) Northern part; (b) Atmospheric Administration (NOAA) water level stations (black dots): (a) Northern part; (b) Southern The overviewSouthern part. of Pleasethe common note that thearea scale bathymetry in (b) is 4 times is shownlarger than in (aFigure). 2b. Most regions behind the part. Please note that the scale in (b) is 4 times larger than (a). barrier islands are shallower than 8 m. There are significant bathymetric differences between the 2.2. Model Setup old-bathy2.2. Model grid Setup and the new-bathy grid around the inlets, as shown in Figures 3–5. For example, around BeaufortThe ADCIRC Inlet [5](Figure Two- Dimensional3), the mean Depth depth Integrated has increased (2DDI) by version 44% wasfrom used the inold this-bathy study depth to of The ADCIRC [5] Two-Dimensional Depth Integrated (2DDI) version was used in this study to 5.0 msolve to the the new shallow-bathy water depth equations of 7.2 m. and In simulateaddition, tidal the water recent levels. deep The channel finite became amplitude deeper and and solve the shallow water equations and simulate tidal water levels. The finite amplitude and convection convection terms and the wetting and drying option were activated. The lateral viscosity was set as a widerterms relative and to the about wetting 60 and years drying ago. option These were morphological activated. The changes lateral viscosityaround wasBeaufort set as Inlet a constant, should be constant, 5.0 m·s−2, throughout the model domain. The quadratic bottom friction scheme was used mainly5.0 associated m·s−2, throughout with historical the model dredging domain. activities The quadratic [30]. bottomThe mean friction depths scheme increased was used by with 70%, a 22%, with a constant coefficient of 0.0025. The model was forced by a reconstructed tide at the ocean 4%, andconstant 11% coefficientfrom the ofold 0.0025.-bathy The grid model to the was new forced-bathy by a reconstructedgrid around tideBarden at the Inlet, ocean Ocracoke boundary Inlet, boundary (shown as blue lines in Figure 2a) using the harmonic constants of the five most significant Hatteras(shown Inlet, as and blue Oregon lines in FigureInlet, respectively.2a) using the harmonicThe morphological constants of parameters the five most for significant five inlets tidal are listed tidal constituents (M2, S2, N2, K1, and O1) from the EC2001 tidal database [7]. constituents (M ,S ,N ,K , and O ) from the EC2001 tidal database [7]. in Table 1.The time step2 2was2 set 1to be 1 s.1 Under this condition, the maximum Courant number is 0.67 over the smallest elements in the grid. This ensured model stability. The model simulations covered a time period of 40 days. The first 10 days were used for the tidal field to reach an equilibrium state. The 6-min water level time series at each node from the last 30 days of each simulation were then used to derive tidal datums and harmonic constants. The 15-min velocity time series at each node from the last 15 days of each simulation were used to calculate the flood and ebb fluxes across the inlets. A triangular mesh (Figure 2a) has been developed with a spatially varying resolution from 30 km offshore to 10 m inland to resolve important geographical features such as inlets, channels, estuaries, and bays. We used this mesh as a basis to generate the model grids by interpolating the old (1930s–1970s) and the new (2010s) bathymetry datasets around five North Carolina inlets (Beaufort, Barden, Ocracoke, Hatteras, and Oregon Inlet) onto the mesh. In the following discussions, we will use the old-bathy grid to represent the model grid using the old (1930s–1970s) bathymetry data and use the new-bathy grid to represent the model grid using the new (2010s) bathymetry data around the inlets. The particular collection(a) years for the old and new bathymetry(b) datasets around each inlet have been listed in Table 1. For the old-bathy grid, we combined the patched bathymetry datasets FigurecollectedFigure 2. (ina) 2. 1956The(a) The triangularand triangular 1962 around model model Ocracokegrid grid (the (the blue blueInlet lineslinesto represent delineatedelineate the the the general open open ocean oceanmorphology boundary; boundary; thein this green the region green linesin the linesdelineate mid delineate-20th the century. land the land boundary); For boundary); the new (b-)bathy (Modelb) Model grid, grid grid we bathymetry bathymetrycombined inthe in North Northbathymetry Carolina Carolina datasets coastal collecte waterswatersd (the in regions2014,(the 2015, deeper regions and than deeper2016 20 around than m use 20 m Hatterasthe use same the same Inlet blue blue and color; color; the the bathymetry the black black line showsdatasetsshows the the collected location location for in longitudinalfor 2014 longitudinal and 2016 profilesaroundprofiles in Oregon Figure in Figures s Inlet 15 and15 to and 16). represent 16 ). the recent morphology in these two regions. The detailed coverages of the old and the new bathymetry datasets are shown for Beaufort and Barden Inlet in FigureTable 3d, 1.Ocracoke Bathymetric and dataHatteras and Inletmorphological in Figure 4d,parameters and Oregon around Inlet five in FigureNorth Carolina5d. Other inlets. than the inlet regions delineated by the polygons in Figures 3–5, the old-bathy grid and the new-bathy grid Area with Mean Mean Collection Collection Width Changed Depth of Depth of Inlet Years of Old Years of New (km) Bathymetry Old-Bathy New-Bathy Bathymetry Bathymetry (km2) (m) (m) Beaufort 1.3 6.2 1953 5.0 2010 7.2 Barden 0.7 4.3 1955 1.7 2015 2.9 Ocracoke 2.4 8.8 1956, 1962 4.0 2013 4.9 Hatteras 2.2 8.7 1935 2.6 2014, 2015, 2016 2.7 Oregon 1.0 3.7 1975 3.6 2014, 2016 4.0

J. Mar. Sci. Eng. 2016, 4, 79 4 of 17

The time step was set to be 1 s. Under this condition, the maximum Courant number is 0.67 over the smallest elements in the grid. This ensured model stability. The model simulations covered a time period of 40 days. The first 10 days were used for the tidal field to reach an equilibrium state. The 6-min water level time series at each node from the last 30 days of each simulation were then used to derive tidal datums and harmonic constants. The 15-min velocity time series at each node from the last 15 days of each simulation were used to calculate the flood and ebb fluxes across the inlets. A triangular mesh (Figure2a) has been developed with a spatially varying resolution from 30 km offshore to 10 m inland to resolve important geographical features such as inlets, channels, estuaries, and bays. We used this mesh as a basis to generate the model grids by interpolating the old (1930s–1970s) and the new (2010s) bathymetry datasets around five North Carolina inlets (Beaufort, Barden, Ocracoke, Hatteras, and Oregon Inlet) onto the mesh. In the following discussions, we will use the old-bathy grid to represent the model grid using the old (1930s–1970s) bathymetry data and use the new-bathy grid to represent the model grid using the new (2010s) bathymetry data around the inlets. The particular collection years for the old and new bathymetry datasets around each inlet have been listed in Table1. For the old-bathy grid, we combined the patched bathymetry datasets collected in 1956 and 1962 around Ocracoke Inlet to represent the general morphology in this region in the mid-20th century. For the new-bathy grid, we combined the bathymetry datasets collected in 2014, 2015, and 2016 around Hatteras Inlet and the bathymetry datasets collected in 2014 and 2016 around Oregon Inlet to represent the recent morphology in these two regions. The detailed coverages of the old and the new bathymetry datasets are shown for Beaufort and Barden Inlet in Figure3d, Ocracoke and Hatteras Inlet in Figure4d, and Oregon Inlet in Figure5d. Other than the inlet regions delineated by the polygons in Figures3–5, the old-bathy grid and the new-bathy grid have the same depths interpolated from the same bathymetry datasets described in Section 2.1. Therefore, the only difference between the old-bathy grid and the new-bathy grid was the bathymetry around the five inlets.

Table 1. Bathymetric data and morphological parameters around five North Carolina inlets.

Width Area with Changed Collection Years of Mean Depth of Collection Years of Mean Depth of Inlet (km) Bathymetry (km2) Old Bathymetry Old-Bathy (m) New Bathymetry New-Bathy (m) Beaufort 1.3 6.2 1953 5.0 2010 7.2 Barden 0.7 4.3 1955 1.7 2015 2.9 Ocracoke 2.4 8.8 1956, 1962 4.0 2013 4.9 Hatteras 2.2 8.7 1935 2.6 2014, 2015, 2016 2.7 Oregon 1.0 3.7 1975 3.6 2014, 2016 4.0 J. Mar. Sci. Eng. 2016, 4, 79 5 of 17

(a) (b)

Figure 3. Cont.

(c) (d)

Figure 3. The morphological changes around Beaufort Inlet and Barden Inlet: (a) the old-bathy grid depths; (b) the new-bathy grid depths; (c) the depth difference between the new-bathy grid and the old-bathy grid; (d) the original bathymetry sounding data points (orange: data in 1953 around Beaufort Inlet and data in 1955 around Barden Inlet; blue: data in 2010 around Beaufort Inlet and data in 2015 around Barden Inlet). The black dotted polygons delineate the area with changed bathymetry.

(a) (b)

J. Mar. Sci. Eng. 2016, 4, 79 5 of 17 J. Mar. Sci. Eng. 2016, 4, 79 5 of 17

J. Mar. Sci. Eng. 2016, 4, 79 5 of 17

(a()a ) (b)

(c()c ) (d) Figure 3. The morphological changes around Beaufort Inlet and Barden Inlet: (a) the old-bathy grid FigureFigure 3. The 3. morphologicalThe morphological changes changes around around BeaufortBeaufort Inlet Inlet and and Barden Barden Inlet: Inlet: (a) the (a) old the-bathy old-bathy grid grid depths; (b) the new-bathy grid depths; (c) the depth difference between the new-bathy grid and the depths;depths; (b) the (b) new-bathy the new-bathy grid grid depths; depths; (c ()c) the the depthdepth difference between between the thenew new-bathy-bathy grid and grid the and the old-bathy grid; (d) the original bathymetry sounding data points (orange: data in 1953 around old-bathy grid; (d) the original bathymetry sounding data points (orange: data in 1953 around old-bathyBeaufort grid; (Inletd) the and original data in bathymetry1955 around soundingBarden Inlet; data blue: points data (orange:in 2010 around data in Beaufort 1953 around Inlet and Beaufort Beaufort Inlet and data in 1955 around Barden Inlet; blue: data in 2010 around Beaufort Inlet and Inlet anddata data in in2015 1955 around around Barden Barden Inlet). Inlet; The blue:black datadotted in polygons 2010 around delineate Beaufort the area Inlet with and changed data in 2015 data in 2015 around Barden Inlet). The black dotted polygons delineate the area with changed aroundbathymetry. Barden Inlet). The black dotted polygons delineate the area with changed bathymetry. bathymetry.

(a) (b) J. Mar. Sci. Eng. 2016, 4, 79 (a) (b) 6 of 17

(c) (d)

Figure 4. The morphological changes around Ocracoke Inlet and Hatteras Inlet: (a) the old-bathy grid Figure 4. The morphological changes around Ocracoke Inlet and Hatteras Inlet: (a) the old-bathy grid depths; (b) the new-bathy grid depths; (c) the depth difference between the new-bathy grid and the depths;old (b-bathy) the new-bathy grid; (d) the grid original depths; bathymetry (c) the depthsounding difference data points between (orange: the data new-bathy in 1956 and grid 1962 and the old-bathyaround grid; Ocracoke (d) the originalInlet and bathymetry data in 1935 soundingaround Hatteras data points Inlet; blue: (orange: data datain 2013 in 1956around and Ocracok 1962 arounde OcracokeInlet Inlet and data and in data 2014, in 2015, 1935 and around 2016 around Hatteras Hatteras Inlet; Inlet). blue: The data black in 2013dotted around polygons Ocracoke delineate Inlet the and data inarea 2014, with 2015, changed and 2016bathymetry. around Hatteras Inlet). The black dotted polygons delineate the area with changed bathymetry.

(a) (b)

(c) (d)

Figure 5. The morphological changes around Oregon Inlet: (a) the old-bathy grid depths; (b) the new-bathy grid depths; (c) the depth difference between the new-bathy grid and the old-bathy grid; (d) the original bathymetry sounding data points (orange: data in 1975 around Oregon Inlet; blue: data in 2014 and 2016 around Oregon Inlet). The black dotted polygons delineate the area with changed bathymetry.

J. Mar. Sci. Eng. 2016, 4, 79 6 of 17

(c) (d)

Figure 4. The morphological changes around Ocracoke Inlet and Hatteras Inlet: (a) the old-bathy grid depths; (b) the new-bathy grid depths; (c) the depth difference between the new-bathy grid and the old-bathy grid; (d) the original bathymetry sounding data points (orange: data in 1956 and 1962 around Ocracoke Inlet and data in 1935 around Hatteras Inlet; blue: data in 2013 around Ocracoke J. Mar. Sci. Eng. 2016, 4, 79 6 of 17 Inlet and data in 2014, 2015, and 2016 around Hatteras Inlet). The black dotted polygons delineate the area with changed bathymetry.

(a) (b)

(c) (d)

Figure 5. The morphological changes around Oregon Inlet: (a) the old-bathy grid depths; (b) the Figurenew 5. The-bathy morphological grid depths; (c) changesthe depth difference around Oregon between Inlet:the new (a-bathy) the grid old-bathy and the gridold-bathy depths; grid; (b) the new-bathy(d) the grid original depths; bathymetry (c) the depthsounding difference data points between (orange: the data new-bathy in 1975 around grid Oregon and the Inlet; old-bathy blue: grid; (d) thedata original in 2014 bathymetry and 2016 around sounding Oregon data Inlet). points The (orange: black dotted data polygons in 1975 delineate around Oregonthe area with Inlet; blue: data inchanged 2014 and bathymetry. 2016 around Oregon Inlet). The black dotted polygons delineate the area with changed bathymetry.

The same model setup and tidal forcing were applied to the models using the old-bathy grid and the new-bathy grid. In the following discussions, we will use the old-bathy model and the new-bathy model to represent the models using the old-bathy grid and the new-bathy grid, respectively. Since Beaufort Inlet and Barden Inlet are close to each other, we made another two grids new-bathy-BE and new-bathy-BA to evaluate the tidal datum changes induced by the morphological changes of each individual inlet. For the new-bathy-BE grid, the new bathymetry data were used around Beaufort Inlet and the old bathymetry data were used for the other four inlets. Similarly, for the new-bathy-BA grid, the new bathymetry data were used around Barden Inlet and the old bathymetry data were used for the other four inlets. We will use the new-bathy-BE model and the new-bathy-BA model to represent tidal simulations using the new-bathy-BE grid and the new-bathy-BA grid, respectively, in the following discussions. The overview of the common area bathymetry is shown in Figure2b. Most regions behind the barrier islands are shallower than 8 m. There are significant bathymetric differences between the old-bathy grid and the new-bathy grid around the inlets, as shown in Figures3–5. For example, around Beaufort Inlet (Figure3), the mean depth has increased by 44% from the old-bathy depth of 5.0 m to the new-bathy depth of 7.2 m. In addition, the recent deep channel became deeper and wider relative to about 60 years ago. These morphological changes around Beaufort Inlet should be mainly associated with historical dredging activities [30]. The mean depths increased by 70%, 22%, 4%, and 11% from the old-bathy grid to the new-bathy grid around Barden Inlet, Ocracoke Inlet, Hatteras Inlet, and Oregon Inlet, respectively. The morphological parameters for five inlets are listed in Table1. J. Mar. Sci. Eng. 2016, 4, 79 7 of 17 J. Mar. Sci. Eng. 2016, 4, 79 7 of 17 2.3. Model Validation

2.3. ModelComputed Validation tidal datums from both the old-bathy model and the new-bathy model were compared with the observed tidal datums at 31 stations. The root mean squared errors (RMSEs) of bothComputed models for tidal four datums tidal datums from both have the been old-bathy listed in model Table and 2. In the general, new-bathy both model models were had compared decent withperformances the observed relative tidal datums to the at observations. 31 stations. The The root new mean-bathy squared model errors had a (RMSEs) little higher of both overall models forperformance four tidal datums than the have old-bathy been listedmodel. in It Table should2. Inbe general, noted that both the models RMSEs had of the decent new- performancesbathy model relativeare slightly to the higher observations. than the uncertainty The new-bathy values model published had aon little the VDatum higher overall website performance [31]. This is mainly than the old-bathybecause the model. official It shouldVDatum be tidal noted datums that the were RMSEs calculated of the from new-bathy longer time model series are of slightly simulated higher water than thelevels. uncertainty values published on the VDatum website [31]. This is mainly because the official VDatum tidal datums were calculated from longer time series of simulated water levels. Table 2. The root mean squared errors of the modeled tidal datums relative to the observed ones. Table 2. The root mean squared errors of the modeled tidal datums relative to the observed ones. Mean Higher Mean High Mean Low Mean Lower High Water Model Mean Higher High Water WaterMean (MHW High Water) WaterMean (MLW Low Water) LowMean Water Lower Low Model (MHHW) (MHHW) (cm) (MHW)(cm) (cm) (MLW)(cm) (cm) (MLLWWater (MLLW)) (cm) (cm) Old-bathy Model 6.1(cm) 4.6 4.5 6.0 New-bathyOld-bathy Model Model 4.86.1 4.6 3.54.53.3 6.0 4.5 New-bathy Model 4.8 3.5 3.3 4.5 Since the four tidal datums have similar trend and patterns, only MHW will be discussed as an Since the four tidal datums have similar trend and patterns, only MHW will be discussed as an example in the rest of the paper. The result for MHW is shown in Figure6. The new-bathy model example in the rest of the paper. The result for MHW is shown in Figure 6. The new-bathy model outperformed the old-bathy model at particular stations. At the inside stations not too far away from outperformed the old-bathy model at particular stations. At the inside stations not too far away from the inlets (e.g., 2678, 6084, and 6483), the new-bathy model matched the observations very well while the inlets (e.g., 2678, 6084, and 6483), the new-bathy model matched the observations very well while the old-bathy model underestimated the observations by approximately 5% to 25%. This is because the old-bathy model underestimated the observations by approximately 5% to 25%. This is because tidaltidal datums datums at at these these stations stations hadhad changedchanged more dramatically than than other other stations stations and and the the new new-bathy-bathy modelmodel simulation simulation is is closer closer to to thethe currentcurrent NationalNational Tidal Datum Epoch Epoch (1983 (1983–2001)–2001) conditions. conditions. At At the the outsideoutside stations stations and and the the inside inside stations stations far far away away from from the the inlets inl (e.g.,ets (e.g., 1370, 1370, 3365, 3365, and and6590), 6590), the MHW the valuesMHW from values both from models both hadmodels very had small very differences. small differences.

0.8 Observed Old-bathy model 0.6 Errors of old-bathy model New-bathy model Errors of new-bathy model 0.4

0.2

MHW (m) MHW

0

-0.2

1370 1817 2232 2247 2437 2547 2587 2648 2678 2905 3215 3365 3951 4400 4467 4572 4792 5151 5875 6084 6201 6306 6467 6483 6502 6518 6539 6590 6612 6841 6937

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Station

FigureFigure 6. 6.Comparison Comparison of of MHW MHW at at 31 31 NOAA NOAA stations between between the the observations observations (black (black dots), dots), the the old-bathyold-bathy model model (red (red solid solid diamonds), diamonds), andand the the new-bathy new-bathy model model (blue (blue s solidolid squares). squares). The The blank blank diamondsdiamonds and and squares squares indicate indicate the the modelmodel errors.errors.

The amplitudes and phases of five principal tidal constituents (M2, S2, N2, K1, and O1) from both The amplitudes and phases of five principal tidal constituents (M2,S2,N2,K1, and O1) from both models were also compared with the observations at 16 stations. As an example, the results for M2 models were also compared with the observations at 16 stations. As an example, the results for M2 (Figures 7 and 8) indicate that the old-bathy model and the new-bathy model had decent (Figures7 and8) indicate that the old-bathy model and the new-bathy model had decent performance. performance. For some stations with small amplitude (e.g., 5875), the discrepancy between the For some stations with small amplitude (e.g., 5875), the discrepancy between the modeled phase and modeled phase and the observed phase could be relatively high because the obscured tidal signals in the observed phase could be relatively high because the obscured tidal signals in the observed water the observed water level time series led to high uncertainty in the observed phase itself. level time series led to high uncertainty in the observed phase itself.

J. Mar. Sci. Eng. 2016, 4, 79 8 of 17 J. Mar. Sci. Eng. 2016, 4, 79 8 of 17

At the inside stations not too far away from the inlets (e.g., 2678 and 6483), the new-bathy J. Mar. Sci.At Eng. the2016 inside, 4, 79 stations not too far away from the inlets (e.g., 2678 and 6483), the new-bathy8 of 17 model outperformed the old-bathy model. The old-bathy model had underestimated amplitudes model outperformed the old-bathy model. The old-bathy model had underestimated amplitudes and overestimated phases relative to the observations. and overestimated phases relative to the observations.

0.6 Observed Observed 0.6 Old-bathy model Old-bathy model Errors of old-bathy model Errors of old-bathy model 0.4 New-bathy model 0.4 New-bathy model Errors of new-bathy model Errors of new-bathy model 0.2 0.2

0 amplitude (m) amplitude 0

2

amplitude (m) amplitude

2

M

M -0.2 -0.2

1370 2247 2437 2547 2587 2678 3951 4400 4467 4792 5875 6201 6467 6483 6590 6841

1370 2247 2437 2547 2587 2678 3951 4400 4467 4792 5875 6201 6467 6483 6590 6841 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Station Station Figure 7. Comparison of the M2 amplitude at 16 NOAA stations between the observations (black FigureFigure 7. 7.Comparison Comparison of of the the M 2Mamplitude2 amplitude at 16at NOAA 16 NOAA stations stations between between the observationsthe observations (black (black dots), dots), the old-bathy model (red solid diamonds), and the new-bathy model (blue solid squares). The thedots), old-bathy the old model-bathy (redmodel solid (red diamonds), solid diamonds) and the, and new-bathy the new-bathy model model (blue (blue solid solid squares). squares). The blankThe blank diamonds and squares indicate the model errors. diamondsblank diamonds and squares and squares indicate indicate the model the model errors. errors.

120 120 Observed Observed Old-bathy model 90 Old-bathy model 90 Errors of old-bathy model Errors of old-bathy model New-bathy model New-bathy model 60 Errors of new-bathy model 60 Errors of new-bathy model 30 30 0 phase (deg) phase 0

2

phase (deg) phase

2

M

M -30 -30 -60 -60

1370 2247 2437 2547 2587 2678 3951 4400 4467 4792 5875 6201 6467 6483 6590 6841

1370 2247 2437 2547 2587 2678 3951 4400 4467 4792 5875 6201 6467 6483 6590 6841 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Station Station

Figure 8. Comparison of the M2 phase at 16 NOAA stations between the observations (black dots), FigureFigure 8. 8.Comparison Comparison of of the the M M22 phasephase atat 1616 NOAA stations between between the the observations observations (black (black dots), dots), the old-bathy model (red solid diamonds), and the new-bathy model (blue solid squares). The blank thethe old-bathy old-bathy model model (red (red solid solid diamonds), diamonds), andand thethe new-bathynew-bathy model model (blue (blue solid solid squares). squares). The The blank blank diamonds and squares indicate the model errors. diamondsdiamonds and and squares squares indicate indicate the the model model errors.errors.

Tidal datum changes induced by morphological changes of Beaufort Inlet can also be observed Tidal datum changes induced by morphological changes of Beaufort Inlet can also be observed fromAt Beaufort the inside Station stations (6483) not about too 4 far km away behind from the theBeaufort inlets Inlet (e.g., as 2678show andn in Figure 6483), 9a. the The new-bathy value from Beaufort Station (6483) about 4 km behind the Beaufort Inlet as shown in Figure 9a. The value modelof each outperformed black dot inthe the old-bathy figure model. came from The old-bathy the monthly model averaged had underestimated MHW. In addition amplitudes to the and of each black dot in the figure came from the monthly averaged MHW. In addition to the overestimated18.6-year-cycle phases and seasonal relative variations, to the observations. there was an obvious trend increasing from ~0.44 m in 1967 18.6-year-cycle and seasonal variations, there was an obvious trend increasing from ~0.44 m in 1967 to ~0.49Tidal m datum in 2016. changes The 18.6 induced-year-cycle by morphological variation is due changes to the changing of Beaufort locations Inlet can of the also sun be and observed the to ~0.49 m in 2016. The 18.6-year-cycle variation is due to the changing locations of the sun and the frommoon Beaufort relative Station to the earth (6483) [2]. about For 4the km model behind results the Beaufortaround the Inlet same as shownlocation, in MHW Figure increased9a. The value from of moon relative to the earth [2]. For the model results around the same location, MHW increased from each0.41 black m of dotthe old in the-bathy figure model came to from0.47 m the of monthlythe new- averagedbathy model, MHW. which In additionis largely toconsistent the 18.6-year-cycle with the 0.41 m of the old-bathy model to 0.47 m of the new-bathy model, which is largely consistent with the andobserved seasonal trend. variations, As a comparison, there was an for obvious Duck Station trend increasing(1370) on the from Atlantic ~0.44 mcoast, in 1967 MHW to ~0.49 also showed m in 2016. observed trend. As a comparison, for Duck Station (1370) on the Atlantic coast, MHW also showed Thethe 18.6-year-cycle 18.6-year-cycle variation and seasonal is due variations to the changing and a slightly locations decreasing of the sun trend and based the moon on the relative analyzed to the the 18.6-year-cycle and seasonal variations and a slightly decreasing trend based on the analyzed data in 1978–2016 (Figure 9b). This trend is not reflected in the model results because Duck Station is earthdata [2 in]. 1978 For the–2016 model (Figure results 9b). aroundThis trend the is same not location,reflected in MHW the model increased results from because 0.41 m Duck of the Station old-bathy is approximately 50 km away from the nearest Oregon Inlet and thus is not affected by the inlet modelapproximately to 0.47 m of 50 the km new-bathy away from model, the nearest which Oregon is largely Inlet consistent and thus with is not the affected observed by trend. the inlet As a bathymetry changes. comparison,bathymetry for changes. Duck Station (1370) on the Atlantic coast, MHW also showed the 18.6-year-cycle and seasonal variations and a slightly decreasing trend based on the analyzed data in 1978–2016 (Figure9b). This trend is not reflected in the model results because Duck Station is approximately 50 km away from the nearest Oregon Inlet and thus is not affected by the inlet bathymetry changes.

J. Mar. Sci. Eng. 2016, 4, 79 9 of 17 J. Mar. Sci. Eng. 2016, 4, 79 9 of 17

(a) (b)

Figure 9. Temporal changes for the last few decades of the monthly averaged MHW at two NOAA Figure 9. Temporal changes for the last few decades of the monthly averaged MHW at two NOAA stations: (a) Beaufort Station (ID: 6483); (b) Duck Station (ID: 1370). The red lines delineate the stations: (a) Beaufort Station (ID: 6483); (b) Duck Station (ID: 1370). The red lines delineate the linearly bestlinearly fit lines. best fit lines.

3. Results 3. Results

3.1. Tidal DatumDatum ChangesChanges DueDue toto MorphologicalMorphological ChangesChanges ofof thethe InletsInlets The MHWMHW from thethe new-bathynew-bathy modelmodel and thethe old-bathyold-bathy model and their differencesdifferences for thethe North CarolinaCarolina coastalcoastal waters waters are are shown shown in in Figures Figure 10s –1014–.14. In In general, general, MHW MHW had had higher higher values values on theon Atlanticthe Atlantic Ocean Ocean side andside lowerand lower values values behind behind barrier barrier islands. islands. The MHW The MHW values values were also were higher also behindhigher Beaufortbehind Beaufort Inlet than Inle thoset than behind those behind the other the four other inlets, four indicatinginlets, indicating that it that is much it is much easier easier for the for tides the tides to propagate from the ocean into the sounds through Beaufort Inlet. In addition, the waters toJ. propagate Mar. Sci. Eng. from 2016, 4 the, 79 ocean into the sounds through Beaufort Inlet. In addition, the waters10 behind of 17 Beaufortbehind Beaufort Inlet have Inlet smaller have areas smaller and deeper areas and depths deeper relative depths to Pamlico relative Sound to Pa behindmlico Ocracoke Sound behind Inlet, HatterasOcracokenew-bathy Inlet, Inlet,-BA and Hatteras model Oregon (Figure Inlet, Inlet. 11b).and Thus, Oregon The tidal extended Inlet. energy Thus part there , should tidal is much energy come less from there dissipated the is contributionmuch than less that dissipated of within the PamlicothanBeaufort that Sound. within Inlet changes. Pamlico Sound. As shown in Figure 10, if the morphological changes only occurred around Beaufort Inlet (i.e., the new-bathy-BE model), MHW has increased behind Beaufort Inlet in three directions: Newport River, Bogue Sound, and Back Sound. MHW in the entire Newport River has increased by ~15% from ~0.4 m to ~0.46 m. The increased MHW becomes smaller where it is farther away from the inlet entrance in both the Bogue Sound and Back Sound directions. The percentage of the increased MHW relative to the old MHW drops to 10% about 10 km away from the inlet entrance in the Bogue Sound direction and about 5 km in the Back Sound direction. Thus, the inlet morphological changes have more influence on MHW in the Newport River direction than the other two directions. This is probably because Newport River is a more enclosed area. As shown in Figure 11, if the morphological changes only occurred around Barden Inlet (i.e., the new-bathy-BA model), the increased MHW has a maximum of 0.06 m (22% of the old MHW) around Morgan Island. The percentage of the increased MHW relative to the old MHW drops to 10% 7 km away from Morgan Island in the Back Sound direction and 3 km in the Core Sound direction. Thus, the inlet morphological changes have more influence on MHW in the Back Sound direction than in the Core Sound(a ) direction. This is probably because tidal changes(b) induced by the inlet morphologicalFigure 10. changes The MHW are changes positively induced correlated only by thewith inlet tidal morphological range. Tidal changes range around is larger Beaufort due to less Figure 10. The MHW changes induced only by the inlet morphological changes around Beaufort Inlet: dampedInlet: tidal (a) energythe MHW in thedifference deeper between Back Sound the new relative-bathy-BE to modelCore Soundand the (see old- bathydepths model; in Figure (b) the 3a ,b and (a) the MHW difference between the new-bathy-BE model and the old-bathy model; (b) the MHW MHW MHWin Figure change 12a in,b). percentage relative to the old-bathy model MHW. The black dotted polygons change in percentage relative to the old-bathy model MHW. The black dotted polygons delineate the Indelineate fact, the the morphological area with changed changes bathymetry. occurred around both Beaufort Inlet and Barden Inlet. As shownarea in with Figure changed 12c, bathymetry. the increased MHW is almost the sum of that induced by individual inlet morphological changes. For example, the increased MHW in North River is about 0.04 m. About 0.02 m is Asfrom shown the morphol in Figureogical 10, if thechanges morphological of Beaufort changes Inlet only(Figure occurred 10a). The around other Beaufort 0.02 m Inlet is from (i.e., the new-bathy-BEmorphological model),changes MHW of Barden has increased Inlet (Figure behind 11a). Beaufort This is probably Inlet in three because directions: the tides Newport propagating River, Boguethrough Sound, Beaufort and Back Inlet Sound. interact MHW with in the the tides entire propagating Newport River through has increased Barden by Inlet ~15% in from the regions ~0.4 m tolocated ~0.46 inm. between The increased both MHWinlets. becomes In the Core smaller Sound where direction, it is farther the location away from of the inlet contour entrance of 10% in increase in MHW is 10 km (Figure 12d) away from Morgan Island, compared to 3 km in the

(a) (b)

Figure 11. The MHW changes induced only by the inlet morphological changes around Barden Inlet: (a) the MHW difference between the new-bathy-BA model and the old-bathy model; (b) the MHW change in percentage relative to the old-bathy model MHW. The black dotted polygons delineate the area with changed bathymetry.

J. Mar. Sci. Eng. 2016, 4, 79 10 of 17

new-bathy-BA model (Figure 11b). The extended part should come from the contribution of the Beaufort Inlet changes.

J. Mar. Sci. Eng. 2016, 4, 79 10 of 17

both the Bogue Sound and(a) Back Sound directions. The percentage of the increased(b) MHW relative to the old MHWFigure drops 10. The to 10% MHW about changes 10 km induced away only from by the the inlet inlet entrancemorphological in the changes Bogue around Sound Beaufort direction and about 5Inlet: km in(a) the the BackMHW Sound difference direction. between Thus, the new the- inletbathy morphological-BE model and the changes old-bathy have model; more (b influence) the on MHW inMHW the Newport change in River percentage direction relative than to the the other old-bathy two modeldirections. MHW. This The is black probably dotted because polygons Newport River isdelineate a more the enclosed area with area. changed bathymetry.

(a) (b)

Figure 11. The MHW changes induced only by the inlet morphological changes around Barden Inlet: Figure 11. The MHW changes induced only by the inlet morphological changes around Barden Inlet: (a) the MHW difference between the new-bathy-BA model and the old-bathy model; (b) the MHW (a) the MHW difference between the new-bathy-BA model and the old-bathy model; (b) the MHW change in percentage relative to the old-bathy model MHW. The black dotted polygons delineate the change in percentage relative to the old-bathy model MHW. The black dotted polygons delineate the area with changed bathymetry. area with changed bathymetry.

As shown in Figure 11, if the morphological changes only occurred around Barden Inlet (i.e., the new-bathy-BA model), the increased MHW has a maximum of 0.06 m (22% of the old MHW) around Morgan Island. The percentage of the increased MHW relative to the old MHW drops to 10% 7 km away from Morgan Island in the Back Sound direction and 3 km in the Core Sound direction. Thus, the inlet morphological changes have more influence on MHW in the Back Sound direction than in the Core Sound direction. This is probably because tidal changes induced by the inlet morphological changes are positively correlated with tidal range. Tidal range is larger due to less damped tidal energy inJ. the Mar. deeper Sci. Eng. Back 2016, Sound4, 79 relative to Core Sound (see depths in Figure3a,b and MHW in Figure11 12of 17a,b).

(a) (b)

Figure 12. Cont.

(c) (d)

Figure 12. The MHW changes induced by the inlet morphological changes around Beaufort Inlet and Barden Inlet: (a) MHW from the old-bathy model; (b) MHW from the new-bathy model; (c) the MHW difference between the new-bathy model and the old-bathy model; (d) the MHW change in percentage relative to the old-bathy model MHW. The black dotted polygons delineate the area with changed bathymetry.

The influence range of the morphological changes around Ocracoke Inlet, Hatteras Inlet, and Oregon Inlet are shorter than the distances between itself and its neighbor inlets. Thus, the morphological changes of these three inlets have independent effects on local tidal datum changes. For Ocracoke Inlet, water depths (Figure 4) have increased from ~4 m to ~9 m in the northeastern part of the ocean-side area of the inlet but have decreased from ~4 m to ~2 m in most sound-side areas of the inlet. As a result, MHW (Figure 13) has increased of ~20% from ~0.35 m to ~0.42 m in the middle of the inlet and the increased MHW is confined within the inlet. MHW has a sudden drop by ~20% from ~0.21 m to ~0.17 m on the northeastern side behind the inlet and the decreased MHW extends inside of Pamlico Sound. The percentage of the decreased MHW gradually drops to 10% about 6 km behind the inlet in the northeastern direction. Therefore the decreased water depths at the inside entrance play a key role in strengthening the tides within the inlet but weakening the tides behind the inlet.

J. Mar. Sci. Eng. 2016, 4, 79 11 of 17

J. Mar. Sci. Eng. 2016, 4, 79 11 of 17

(a) (b)

(c) (d)

FigureFigure 12. 12.The TheMHW MHW changes induced induced by by the the inlet inlet morpho morphologicallogical changes changes around around Beaufort Beaufort Inlet and Inlet Barden Inlet: (a) MHW from the old-bathy model; (b) MHW from the new-bathy model; (c) the and Barden Inlet: (a) MHW from the old-bathy model; (b) MHW from the new-bathy model; (c) the MHW difference between the new-bathy model and the old-bathy model; (d) the MHW change in MHW difference between the new-bathy model and the old-bathy model; (d) the MHW change in percentage relative to the old-bathy model MHW. The black dotted polygons delineate the area with percentage relative to the old-bathy model MHW. The black dotted polygons delineate the area with changed bathymetry. changed bathymetry. The influence range of the morphological changes around Ocracoke Inlet, Hatteras Inlet, and OregonIn fact, Inlet the are morphological shorter than changesthe distances occurred between around itself both and Beaufort its neighbor Inlet inlets. and BardenThus, the Inlet. Asmorphological shown in Figure changes 12c, theof these increased three inlets MHW have is almost independent the sum effects of that on local induced tidal bydatum individual changes. inlet morphologicalFor Ocracoke changes. Inlet, For water example, depths the increased(Figure 4) MHW have inincreased North River from is about~4 m 0.04to ~9 m. m About in the 0.02 mnortheastern is from the morphologicalpart of the ocean-side changes area of of Beaufort the inlet Inlet but have (Figure decreased 10a). The from other ~4 m 0.02 to ~2 m m is in from most the morphologicalsound-side areas changes of the of inlet. Barden As a Inlet result, (Figure MHW 11 (Figurea). This 13) is probablyhas increased because of ~20% the tidesfrom propagating~0.35 m to through~0.42 m Beaufort in the middle Inlet interact of the inlet with and the the tides increased propagating MHW through is confined Barden within Inlet the in inlet. the regions MHW has located a insudden between drop both by inlets. ~20% Infrom the ~0.21 Core m Sound to ~0.17 direction, m on the the northeastern location of theside contour behind the of 10% inlet increase and the in MHWdecreased is 10 km MHW (Figure extends 12d) inside away of from Pamlico Morgan Sound. Island, The comparedpercentage to of 3 the km decreased in the new-bathy-BA MHW gradually model (Figuredrops 11 tob). 10% The about extended 6 km part behind should the comeinlet in from the thenortheastern contribution direction. of the BeaufortTherefore Inlet the changes.decreased water depths at the inside entrance play a key role in strengthening the tides within the inlet but The influence range of the morphological changes around Ocracoke Inlet, Hatteras Inlet, weakening the tides behind the inlet. and Oregon Inlet are shorter than the distances between itself and its neighbor inlets. Thus, the morphological changes of these three inlets have independent effects on local tidal datum changes. For Ocracoke Inlet, water depths (Figure4) have increased from ~4 m to ~9 m in the northeastern part of the ocean-side area of the inlet but have decreased from ~4 m to ~2 m in most sound-side areas of the inlet. As a result, MHW (Figure 13) has increased of ~20% from ~0.35 m to ~0.42 m in the middle of the inlet and the increased MHW is confined within the inlet. MHW has a sudden drop by ~20% from ~0.21 m to ~0.17 m on the northeastern side behind the inlet and the decreased MHW extends inside of Pamlico Sound. The percentage of the decreased MHW gradually drops to 10% about 6 km behind the inlet in the northeastern direction. Therefore the decreased water depths at the inside entrance play a key role in strengthening the tides within the inlet but weakening the tides behind the inlet. For Hatteras Inlet, water depths (Figure4) have decreased from ~5 m to ~2 m on the eastern side of the inlet, which leads to a MHW (Figure 13) drop of ~30% from ~0.25 m to ~0.17 m. The decreased MHW also extends inside of Pamlico Sound. The percentage of the decreased MHW gradually drops to 10% about 4 km behind the inlet in the northeastern direction. Water depths have increased from ~1 m to ~4 m on the western side of the inlet, which leads to a MHW increase of ~20% from ~0.23 to ~0.28. The extension of the increased MHW is confined within a small area inside the inlet and may be due to the decreased water depths in the western part of the inside entrance. J. Mar. Sci. Eng. 2016, 4, 79 12 of 17 J. Mar. Sci. Eng. 2016, 4, 79 12 of 17

(a) (b)

(c) (d)

Figure 13. The MHW changes induced by the inlet morphological changes around Ocracoke Inlet Figure 13. The MHW changes induced by the inlet morphological changes around Ocracoke Inlet and Hatteras Inlet: (a) MHW from the old-bathy model; (b) MHW from the new-bathy model; (c) the and Hatteras Inlet: (a) MHW from the old-bathy model; (b) MHW from the new-bathy model; (c) the MHW difference between the new-bathy model and the old-bathy model; (d) the MHW change in MHW difference between the new-bathy model and the old-bathy model; (d) the MHW change in percentage relative to the old-bathy model MHW. The black dotted polygons delineate the area with percentage relative to the old-bathy model MHW. The black dotted polygons delineate the area with changed bathymetry. J. Mar.changed Sci. Eng. bathymetry. 2016, 4, 79 13 of 17 For Hatteras Inlet, water depths (Figure 4) have decreased from ~5 m to ~2 m on the eastern side of the inlet, which leads to a MHW (Figure 13) drop of ~30% from ~0.25 m to ~0.17 m. The decreased MHW also extends inside of Pamlico Sound. The percentage of the decreased MHW gradually drops to 10% about 4 km behind the inlet in the northeastern direction. Water depths have increased from ~1 m to ~4 m on the western side of the inlet, which leads to a MHW increase of ~20% from ~0.23 to ~0.28. The extension of the increased MHW is confined within a small area inside the inlet and may be due to the decreased water depths in the western part of the inside entrance. For Oregon Inlet, the inlet channel with ~8 m depth has shifted from the northwestern side in the old-bathy grid to the southeastern side in the new-bathy grid (Figure 5). The average depth around Oregon Inlet has increased from ~3.6 m of the old-bathy grid to ~4.0 m of the new-bathy grid. Unlike Ocracoke Inlet and Hatteras Inlet, MHW (Figure 14) has increased by ~50% from ~0.25 m to ~0.37 m across the interior of the inlet. The increased MHW extends inside of Pamlico Sound. The percentage of the increased MHW gradually drops to 10% about 6 km behind the inlet in almost all directions. This is probably because the presence of several deeper channels (Figure 5a,b) in Pamlico Sound behind Oregon Inlet favors tidal propagation in all directions. (a) (b)

Figure 14. Cont.

(c) (d)

Figure 14. The MHW changes induced by the inlet morphological changes around Oregon Inlet: (a) MHW from the old-bathy model; (b) MHW from the new-bathy model; (c) the MHW difference between the new-bathy model and the old-bathy model; (d) the MHW change in percentage relative to the old-bathy model MHW. The black dotted polygons delineate the area with changed bathymetry.

3.2. Tidal Harmonic Changes

The spatial pattern of the M2 amplitude in North Carolina coastal waters is similar to that of MHW because M2 is the dominant component of tidal constituents in this region; consequently, the M2 amplitude changes induced by the inlet morphological changes are also similar to the MHW changes. Figures 15a,b show the M2 amplitude and phase from the old-bathy model and the new-bathy model along a line (shown in Figure 2b) approximately 1 km behind the barrier islands. The M2 amplitude has increased from the old-bathy model to the new-bathy model behind Beaufort Inlet, Barden Inlet, and Oregon Inlet and has decreased behind Ocracoke Inlet and Hatteras Inlet. The M2 phase has slightly decreased from the old-bathy model to the new-bathy model behind Beaufort Inlet, Barden Inlet, and Oregon Inlet and has changed very little behind Ocracoke Inlet and Hatteras Inlet. These suggest that it becomes easier for the M2 tide to propagate through Beaufort Inlet, Barden Inlet, and Oregon Inlet relative to about 40 or 60 years ago. It becomes more difficult for the M2 tide to propagate through Ocracoke Inlet and Hatteras Inlet relative to about 50 or 80 years ago. As shown in Figure 15c,d, the K1 amplitude and phase changes induced by the inlet morphological changes are similar to the M2 amplitude and phase changes. However, when we

J. Mar. Sci. Eng. 2016, 4, 79 13 of 17

J. Mar. Sci. Eng. 2016, 4, 79 13 of 17

(a) (b)

(c) (d)

FigureFigure 14. 14.The The MHW MHW changeschanges induced induced by by the the inlet inlet morp morphologicalhological changes changes around around Oregon Oregon Inlet: Inlet:(a) (a)MHW MHW from from the the old-bathy old-bathy model; model; (b (b) )MHW MHW from from the the new-bathy new-bathy model; model; (c) ( cthe) the MHW MHW difference difference between the new-bathy model and the old-bathy model; (d) the MHW change in percentage relative between the new-bathy model and the old-bathy model; (d) the MHW change in percentage relative to to the old-bathy model MHW. The black dotted polygons delineate the area with changed the old-bathy model MHW. The black dotted polygons delineate the area with changed bathymetry. bathymetry.

3.2.For Tidal Oregon Harmonic Inlet, Changes the inlet channel with ~8 m depth has shifted from the northwestern side in the old-bathy grid to the southeastern side in the new-bathy grid (Figure5). The average depth around The spatial pattern of the M2 amplitude in North Carolina coastal waters is similar to that of Oregon Inlet has increased from ~3.6 m of the old-bathy grid to ~4.0 m of the new-bathy grid. Unlike MHW because M2 is the dominant component of tidal constituents in this region; consequently, the Ocracoke Inlet and Hatteras Inlet, MHW (Figure 14) has increased by ~50% from ~0.25 m to ~0.37 m M2 amplitude changes induced by the inlet morphological changes are also similar to the MHW across the interior of the inlet. The increased MHW extends inside of Pamlico Sound. The percentage changes. Figures 15a,b show the M2 amplitude and phase from the old-bathy model and the of thenew-bathy increased model MHW along gradually a line (shown drops to in 10% Figure about 2b) 6 approximately km behind the 1 inlet km behind in almost the all barrier directions. islands. This is probablyThe M2 amplitude because has the presenceincreased offrom several the old-bathy deeper channels model to (Figurethe new-bathy5a,b) in model Pamlico behind Sound Beaufort behind OregonInlet, InletBarden favors Inlet, tidal and propagationOregon Inletin and all has directions. decreased behind Ocracoke Inlet and Hatteras Inlet. The M2 phase has slightly decreased from the old-bathy model to the new-bathy model behind 3.2. Tidal Harmonic Changes Beaufort Inlet, Barden Inlet, and Oregon Inlet and has changed very little behind Ocracoke Inlet and

HatterasThe spatial Inlet. patternThese suggest of the that M2 amplitudeit becomes ineasier North for Carolinathe M2 tide coastal to propagate waters isthrough similar Beaufort to that of MHWInlet, because Barden MInlet,2 is theand dominantOregon Inle componentt relative to of about tidal 40 constituents or 60 years in ago. this It region;becomes consequently, more difficult the for M 2 amplitudethe M2 tide changes to propagate induced through by the inletOcracoke morphological Inlet and Hatteras changes Inlet are also relative similar to about to the 50 MHW or 80 changes.years ago. Figure 15a,b show the M2 amplitude and phase from the old-bathy model and the new-bathy model As shown in Figure 15c,d, the K1 amplitude and phase changes induced by the inlet along a line (shown in Figure2b) approximately 1 km behind the barrier islands. The M 2 amplitude hasmorphological increased from changes the old-bathy are similar model to the to theM2 new-bathyamplitude modeland phase behind changes. Beaufort However, Inlet, Barden when we Inlet, and Oregon Inlet and has decreased behind Ocracoke Inlet and Hatteras Inlet. The M2 phase has slightly decreased from the old-bathy model to the new-bathy model behind Beaufort Inlet, Barden Inlet, and Oregon Inlet and has changed very little behind Ocracoke Inlet and Hatteras Inlet. These suggest that it becomes easier for the M2 tide to propagate through Beaufort Inlet, Barden Inlet, and Oregon Inlet relative to about 40 or 60 years ago. It becomes more difficult for the M2 tide to propagate through Ocracoke Inlet and Hatteras Inlet relative to about 50 or 80 years ago. As shown in Figure 15c,d, the K1 amplitude and phase changes induced by the inlet morphological changes are similar to the M2 amplitude and phase changes. However, when we compared the percentage of the amplitude change relative to the old, we found that the K1 changes are less dramatic than the M2 changes behind Beaufort Inlet and Barden Inlet (Figure 16). The K1 changes in percentage have similar magnitudes to the M2 changes behind Ocracoke Inlet, Hatteras Inlet, and Oregon Inlet. J. Mar. Sci. Eng. 2016, 4, 79 14 of 17

J. Mar. Sci. Eng. 2016, 4, 79 14 of 17 compared the percentage of the amplitude change relative to the old, we found that the K1 changes

2 1 comparedare less dramatic the percentage than the of M the changes amplitude behind change Beaufort relative Inlet to theand old, Barden we found Inlet that(Figure the 16).K1 changes The K 2 arechangesJ. Mar. less Sci. dramaticin Eng. percentage2016, 4than, 79 havethe M similar2 changes magnitude behind sBeaufort to the M Inlet changes and Bardenbehind InletOcracoke (Figure Inlet, 16). Hatteras The14 of K 171 changesInlet, and in Oregon percentage Inlet. have similar magnitudes to the M2 changes behind Ocracoke Inlet, Hatteras

Inlet, and Oregon Inlet. 360 0.6 Old-bathy model Old-bathy model New-bathy model New-bathy model 360270 0.60.4 Old-bathy model Old-bathy model New-bathy model 270180 New-bathy model 0.40.2 Beaufort Hatteras

phase (deg) phase 90

amplitude (m) amplitude Beaufort 2 180

2

M M 0.20 Ocracoke Barden Oregon 0 BeaufortBarden Hatteras phase (deg) phase 90 amplitude (m) amplitude Ocracoke Oregon Beaufort Hatteras 2 2

M M 0 0 50 100 Ocracoke150 200 250 0 50 100 150 200 250 Barden Oregon 0 Barden km Hatteras kmOcracoke Oregon

0 50 100 150 200 250 0 50 100 150 200 250 (a)km (b)km

0.08 (a) Old-bathy model 300 (b) Old-bathy model New-bathy model New-bathy model 0.06 270 Ocracoke 0.08 Old-bathy model 300 Old-bathy model 0.04 New-bathy model 240 New-bathy model 0.06 270 Ocracoke 0.02 210 phase (deg) phase 240

amplitude (m) amplitude Barden

0.04 1

1 Beaufort

K K 0 Ocracoke 180 0.02 Barden Oregon 210 Beaufort Hatteras Oregon

Hatteras (deg) phase

amplitude (m) amplitude Barden

1

1 Beaufort

K K 0 0 50 100 Ocracoke150 200 250 180 0 50 100 150 200 250 Barden Oregon Beaufort Hatteras Oregon km Hatteras km

0 50 100(c) 150 200 250 0 50 100(d) 150 200 250 km km Figure 15. Longitudinal(c) variations of: (a) the M2 amplitude; (b) the M2 phase; (dc)) the K1 amplitude; (d) Figure 15. Longitudinal variations of: (a) the M2 amplitude; (b) the M2 phase; (c) the K1 amplitude; the K1 phase along a line (shown in Figure 2b) about 1 km behind the barrier islands. The red lines Figure(d) the 15. K1 Longitudinalphase along avariations line (shown of: (a in) the Figure M2 2amplitude;b) about 1 ( kmb) the behind M2 phase; the barrier (c) the islands.K1 amplitude; The red (d) indicate the results from the old-bathy model. The blues lines indicate the results from the new-bathy thelines K1 indicate phase along the results a line (shown from the in old-bathyFigure 2b) model. about 1 The km bluesbehind lines the indicatebarrier islands. the results The red from lines the indicatemodel.new-bathy themodel. results from the old-bathy model. The blues lines indicate the results from the new-bathy model.

40 M 2 40 MK Beaufort 20 12 Ocracoke K Beaufort 20 1 OcracokeHatteras 0 Barden Hatteras Oregon 0 Barden -20 Oregon -20

Amplitude change (%)change Amplitude -40

Amplitude change (%)change Amplitude -40 0 50 100 150 200 250 km 0 50 100 150 200 250 km Figure 16. Comparison between the M2 (red line) and K1 (blue line) in amplitude change between the new-bathy model and the old-bathy model relative to the old-bathy model along a line (shown in Figure 16. ComparisonComparison between between the the M M2 (red2 (red line) line) and and K1 K(blue1 (blue line) line) in amplitude in amplitude change change between between the newFigurethe new-bathy-bathy 2b) aboutmodel model 1 andkm and behindthe theold old-bathythe-bathy barrier model model islands. relative relative to tothe the old old-bathy-bathy model model along along a aline line (shown (shown in Figure 22b)b) aboutabout 11 kmkm behindbehind thethe barrierbarrier islands.islands. 4. Discussion and Conclusions 4. Discussion DiscussionThe model and and results Conclusions Conclusions validated with the observations show that tidal datums (represented by MHW)The and model model harmonic results results validated amplitudes validated with with have the the observationsincreased observations by show 10 % show– that35% tidalthat from datumstidal the datums old (represented-bathy (represented model by MHW) to the by MHW)newand- harmonicbathy and model harmonic amplitudes behind amplitudes Beaufort have increased Inlet, have Barden increased by 10%–35% Inlet, by and 10 from% Oregon–3 the5% old-bathy fromInlet. theTidal modelold datums-bathy to theand model new-bathy harmonic to the newamplitudesmodel-bathy behind model have Beaufort decreased behind Inlet, Beaufort by Barden 15% Inlet,–30% Inlet, Barden from and Oregonthe Inlet, old and-bathy Inlet. Oregon Tidalmodel datumsInlet. to the Tidal andnew datums harmonic-bathy modeland amplitudes harmonic behind amplitudesOcracokehave decreased Inlet have and by decreased 15%–30%Hatteras byInle from 15t.% theCompared–30% old-bathy from with the model theold -other tobathy the four new-bathymodel inlets, to the tidal model new datums behind-bathy around Ocracokemodel Oregonbehind Inlet OcracokeInletand Hatteras experienced Inlet Inlet. and the ComparedHatteras most dramaticInle witht. Compared the changes other four with (35%) inlets, the within other tidal datumsfoura shorter inlets, around time tidal Oregonperiod datums (1975 Inlet around experienced–2014). Oregon The Inletreasonthe most experienced needs dramatic to be the further changes most investigated. dramatic (35%) within changes In a addition, shorter (35%) time Beaufortwithin period a Inletshorter (1975–2014). has timethe largest period The reasonrange (1975 of– needs2014). influence toThe be reasonprobablyfurther needs investigated. due toto bethe further deeper In addition, investigated. waters Beaufort behind In Inletit.addition, has the Beaufort largest Inlet range has of the influence largest probably range of dueinfluence to the probablydeeperIt should waters due tobe behind the noted deeper it. that watersall four behind tidal datums it. (MHHW, MHW, MLW, and MLLW) are referenced to MSL.It should The MHHW, be noted MLW, that all and four MLLW tidaltidal datumsdatums changes (MHHW,(MHHW, induced MHW, MHW, by the MLW, MLW, inlet and morphologicaland MLLW) MLLW) are are referencedchanges referenced are to toveryMSL. MSL. similar The The MHHW, toMHHW, the MLW,MHW MLW, andchanges. and MLLW MLLW Tidal changes rangechanges induced is inducedan indicator by the by inletthe of tidalinlet morphological energy.morphological The changes morphological changes are very are very similar to the MHW changes. Tidal range is an indicator of tidal energy. The morphological similar to the MHW changes. Tidal range is an indicator of tidal energy. The morphological changes of the inlets affect the energy of the tides propagating through the inlets and thus tidal range behind the inlets. MHW and MLW are almost equal to half of the mean tidal range. MHHW and MLLW are J. Mar. Sci. Eng. 2016, 4, 79 15 of 17 almost equal to half of the diurnal tidal range. Therefore, all four tidal datums have similar changes in response to the morphological changes. To evaluate these tidal changes induced by morphological changes of the inlets, we calculated the flood and ebb volumes and durations across the inlets based on the velocity and elevation outputs from the old-bathy model and the new-bathy model. The results have been summarized in Table3. For Beaufort Inlet, the flood volume has increased by 18 × 106 m3 (16%) while the ebb volume has increased by 8 × 106 m3 (7%) from the old-bathy model to the new-bathy model, suggesting that more tidal energy and more water go into the sounds. Similarly, flood volumes have increased by 8 × 106 m3 (38%) and 11 × 106 m3 (15%) for Barden Inlet and Oregon Inlet, respectively. On the other hand, flood volumes have decreased by 5 × 106 m3 (4%) and 7 × 106 m3 (6%) for Ocracoke Inlet and Hatteras Inlet, respectively. These suggest that the cross-inlet tidal volume changes are closely related to tidal datum changes behind the inlets. The magnitude of the volume change is also positively correlated with the influence range.

Table 3. Flood and ebb volumes and durations across five North Carolina inlets from the old-bathy model and the new-bathy model.

Flood Volume Ebb Volume Tidal-Cycle Flood Ebb Inlet (106 m3) (106 m3) Residual (106 m3) Duration (h) Duration (h) Beaufort (old) 111.31 −113.60 −2.29 5.95 6.53 Beaufort (new) 129.37 −121.43 7.95 5.99 6.48 Barden (old) 21.72 −18.76 2.96 5.92 6.56 Barden (new) 30.02 −27.67 2.36 5.96 6.51 Ocracoke (old) 132.47 −141.34 −8.87 5.79 6.71 Ocracoke (new) 127.09 −132.91 −5.81 5.77 6.73 Hatteras (old) 122.12 −122.90 −0.78 5.80 6.70 Hatteras (new) 114.87 −113.74 1.13 5.80 6.70 Oregon (old) 73.07 −73.63 −0.56 5.82 6.67 Oregon (new) 84.52 −84.30 0.22 5.84 6.66

As mentioned in Section 2.2, for the common regions other than the inlet regions, the old-bathy grid and the new-bathy grid used the same bathymetry sounding datasets [27]. For the shallow areas within the sounds, most sounding data were collected before the 1980s and very limited sounding data were collected after the 2010s. Tidal changes induced by morphological changes within the sounds will be evaluated in future work upon the availability of new sounding data in these regions. Based on the numerical experiments in this paper, both the magnitude and geographical extension of the tidal datum changes behind the barrier islands can be easily evaluated by monitoring the inlet morphological changes induced by erosion or accumulation, dredging, or dumping. This can be used as a guidance for NOAA to make decisions on when to update VDatum tidal datums in this region and where to install new tide gauges. Furthermore, as the sea level may rise in the future, some new inlets may appear and the existing inlets may become wider and deeper. Under this circumstance, the spatial pattern of the tides behind the barrier islands may be dramatically changed, which will be evaluated in future work.

Acknowledgments: This study was supported by NOAA’s VDatum program coordinated by three NOAA offices: the Office of Coast Survey, the Center for Operational Oceanographic Products and Services, and the National Geodetic Survey. We sincerely thank the anonymous reviewers for providing insightful comments and suggestions to help substantial improvements of this manuscript. Author Contributions: J.W. and E.M. conceived and designed the experiments; J.W. performed the experiments and analyzed the data; J.W. and E.M. wrote the paper. Conflicts of Interest: The authors declare no conflict of interest. J. Mar. Sci. Eng. 2016, 4, 79 16 of 17

References

1. Parker, B.B.; Hess, K.W.; Milbert, D.G.; Gill, S. A national vertical datum transformation tool. Sea Technol. 2003, 44, 10–15. 2. Eakins, B.W.; Taylor, L.A. Seamlessly integrating bathymetric and topographic data to support tsunami modeling and forecasting efforts. In Ocean Globe; Bremen, J., Ed.; ESRI Press Academic: Redlands, CA, USA, 2010; pp. 33–86. 3. National Ocean Service. Tidal Datums and Their Applications; NOAA Technical Report NOS COOPS 1; Center for Operational Oceanographic Products and Services: Silver Spring, MD, USA, 2000; p. 112. 4. National Ocean Service. VDatum Manual for Development and Support of NOAA’s Vertical Datum Transformation Tool, VDatum. 2012; p. 119. Available online: http://vdatum.noaa.gov/docs/publication. html (accessed on 20 September 2016). 5. Luettich, R.A., Jr.; Westerink, J.J.; Scheffner, N.W. ADCIRC: An Advanced Three-Dimensional Circulation Model for Shelves Coasts and Estuaries, Report 1: Theory and Methodology of ADCIRC-2DDI and ADCIRC-3DL; Dredging Research Program Technical Report DRP-92-6; U.S. Army Engineers Waterways Experiment Station: Vicksburg, MS, USA, 1992; p. 137. 6. Westerink, J.J.; Luettich, R.A.; Muccino, J.C. Modeling tides in the Western North Atlantic using unstructured graded grids. Tellus A 1994, 46, 178–199. [CrossRef] 7. Mukai, A.Y.; Westerink, J.J.; Luettich, R.A.; Mark, D. Eastcoast 2001: A Tidal Constituent Database for the Western North Atlantic, Gulf of Mexico and Caribbean Sea; Technical Report, ERDC/CHL TR-02-24; US Army Engineer Research and Development Center, Coastal and Hydraulics Laboratory: Vicksburg, MS, USA, 2002; p. 201. 8. Hench, J.L.; Luettich, R.A.; Westerink, J.J.; Scheffner, N.W. ADCIRC: An Advanced Three-Dimensional Circulation Model for Shelves, Coasts, and Estuaries, Report 6: Development of a Tidal Constituent Database for the Eastern North Pacific; Dredging Research Program Technical Report DRP-92-6; U.S. Army Engineer Waterways Experiment Station: Vicksburg, MS, USA, 1994; p. 21. Available online: http://acwc.sdp.sirsi.net/client/search/asset/ 1004166 (accessed on 20 September 2016). 9. Blain, C.A.; Rogers, E. Coastal Tidal Prediction Using the ADCIRC-2DDI Hydrodynamic Finite Element Model; Formal Report NRL/FR/7322-98-9682; Naval Research Laboratory, Stennis Space Center: Hancock County, MS, USA, 1998; p. 92. Available online: http://www.dtic.mil/dtic/tr/fulltext/u2/a358752.pdf (accessed on 20 June 2016). 10. Luettich, R.A., Jr.; Carr, S.D.; Reynolds-Fleming, J.V.; Fulcher, C.W.; McNinch, J.E. Semi-diurnal seiching in a shallow, micro-tidal lagoonal estuary. Cont. Shelf Res. 2001, 22, 1669–1681. [CrossRef] 11. Burrows, R.; Walkington, I.A.; Yates, N.C.; Hedges, T.S.; Wolf, J.; Holt, J. The tidal range energy potential of the west coast of the United Kingdom. Appl. Ocean Res. 2009, 31, 229–238. [CrossRef] 12. Hess, K.; Spargo, E.; Wong, A.; White, S.; Gill, S. VDatum for Central Coastal North Carolina: Tidal Datums, Marine Grids, and Sea Surface Topography; NOAA Technical Report NOS CS 21; the National Oceanic and Atmospheric Administration: Silver Spring, MD, USA, 2005; p. 46. 13. Hayes, M.O. General morphology and sediment patterns in tidal inlets. Sediment. Geol. 1980, 26, 139–156. [CrossRef] 14. Hubbard, D.K.; Oertel, G.; Nummedal, D. The role of waves and tidal currents in the development of tidal-inlet sedimentary structures and sand body geometry: Examples from North Carolina, South Carolina, and Georgia. J. Sediment. Petrol. 1979, 49, 1073–1092. 15. Komar, P.D. Tidal-inlet processes and morphology related to the transport of sediments. J. Coast. Res. 1996, 23–45. 16. Cayocca, F. Long-term morphological modeling of a tidal inlet: The Arcachon Basin, France. Coast. Eng. 2001, 42, 115–142. [CrossRef] 17. Militello, A.; Zarillo, G.A. Tidal motion in a complex inlet and bay system, Ponce de Leon Inlet, Florida. J. Coast. Res. 2000, 16, 840–852. 18. Boon, J.D.; Byrne, R.J. On basin hyposmetry and the morphodynamic response of coastal inlet systems. Mar. Geol. 1981, 40, 27–48. [CrossRef] 19. Fitzgerald, D.M. Geomorphic variability and morphologic and sedimentologic controls of tidal inlets. J. Coast. Res. 1996, 47–71. J. Mar. Sci. Eng. 2016, 4, 79 17 of 17

20. Luettich, R.A., Jr.; Hench, J.L.; Fulcher, C.W.; Werner, F.E.; Blanton, B.O.; Churchill, J.H. Barotropic tidal and wind driven larvae transport in the vicinity of a barrier island inlet. Fish. Oceanogr. 1999, 8, 190–209. [CrossRef] 21. Churchill, J.H.; Blanton, J.O.; Hench, J.L.; Luettich, R.A., Jr.; Werner, F.E. Flood tide circulation near Beaufort Inlet, North Carolina: Implications for larval recruitment. Estuaries 1999, 22, 1057–1070. [CrossRef] 22. Inman, D.L.; Dolan, R. The Outer Banks of North Carolina: Budget of sediment and inlet dynamics along a migrating barrier system. J. Coast. Res. 1989, 5, 193–237. 23. NOAA Tides and Currents Website: Water Levels. Available online: http://tidesandcurrents.noaa.gov/ stations.html?type=Water+Levels (accessed on 20 September 2016). 24. NOAA Tides and Currents Website: Datums. Available online: http://tidesandcurrents.noaa.gov/stations. html?type=Datums (accessed on 20 September 2016). 25. NOAA Tides and Currents Website: Harmonic Constituents. Available online: https://tidesandcurrents. noaa.gov/stations.html?type=Harmonic+Constituents (accessed on 20 September 2016). 26. NOAA Shoreline Website. Available online: https://shoreline.noaa.gov (accessed on 20 September 2016). 27. National Centers for Environmental Information (NCEI) Bathymetry and Global Relief. Available online: https://www.ngdc.noaa.gov/mgg/bathymetry/relief.html (accessed on 20 September 2016). 28. Becker, J.J.; Sandwell, D.T.; Smith, W.H.F.; Braud, J.; Binder, B.; Depner, J.; Fabre, D.; Factor, J.; Ingalls, S.; Kim, S.-H.; et al. Global bathymetry and elevation data at 30 arc seconds resolution: SRTM30_PLUS. Mar. Geod. 2009, 32, 355–371. [CrossRef] 29. US Army Corps of Engineering Wilmington District Website: Hydrographic Surveys. Available online: http://www.saw.usace.army.mil/Missions/Navigation/Hydrographic-Surveys/ (accessed on 20 September 2016). 30. Olsen Associates, Inc. Inlet Dredging and Disposal. In Regional Sand Transport Study: Morehead City Harbor Federal Navigation Project Summary Report; Olsen Associates, Inc.: Jacksonville, FL, USA, 2006. Available online: http://www.carteretcountync.gov/DocumentCenter/View/268 (accessed on 20 June 2016). 31. NOAA VDatum Website: Estimation of Uncertainties. Available online: http://vdatum.noaa.gov/docs/est_ uncertainties.html (accessed on 20 September 2016).

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).