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Article

Improvements for the Western North Atlantic, Caribbean and Gulf of Mexico ADCIRC Tidal Database (EC2015)

1
School of Civil Engineering and Environmental Science, University of Oklahoma, 202 W. Boyd Room 334, Norman, OK 73019, USA
2
NOAA/Great Lakes Environmental Research Laboratory, 4840 South State Road, Ann Arbor, MI 48108, USA
3
NOAA/National Ocean Service/Coast Survey Development Laboratory, 1315 East-West Highway, Silver Spring, MD 20910, USA
4
Earth Resources Technology, Inc., 14401 Sweitzer Lane, Suite 300, Laurel, MD 20707, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Richard P. Signell
J. Mar. Sci. Eng. 2016, 4(4), 72; https://doi.org/10.3390/jmse4040072
Received: 17 July 2016 / Revised: 28 October 2016 / Accepted: 1 November 2016 / Published: 8 November 2016

Abstract

This research details the development and validation of an updated constituent tidal database for the Western North Atlantic, Caribbean and Gulf of Mexico (WNAT) region, referred to as the EC2015 database. Regional databases, such as EC2015, provide much higher resolution than global databases allowing users to more accurately define the tidal forcing on smaller sub-region domains. The database last underwent major updates in 2001 and was developed using the two-dimensional, depth-integrated form of the coastal hydrodynamic model, ADvanced CIRCulation (ADCIRC), which solves the shallow-water equations in the generalized wave continuity equation form. Six main areas of improvement are examined: (1) placement of the open ocean boundary; (2) higher coastal resolution using Vertical Datum (VDatum) models; (3) updated bathymetry from global databases; (4) updated boundary forcing compared using two global tidal databases; (5) updated bottom friction formulations; and (6) improved model physics by incorporating the advective terms in ADCIRC. The skill of the improved database is compared to that of its predecessor and is calculated using harmonic data from the National Oceanic and Atmospheric Administration Center for Operational Oceanographic Products and Services (NOAA CO-OPS) stations and historic International Hydrographic Organization (IHO) data. Overall, the EC2015 database significantly reduces errors realized in the EC2001 database and improves the quality of coastal tidal constituents available for smaller sub-regional models in the Western North Atlantic, Caribbean and Gulf of Mexico (WNAT) region.
Keywords: tidal constituent database; WNAT region; ADCIRC tidal constituent database; WNAT region; ADCIRC

1. Introduction

Small-scale regional hydrodynamic models are widely used to study many varied physical processes such as sediment transport [1,2,3]; storm surge inundation [4,5,6]; real-time surge forecast systems [7,8,9,10]; sea level rise [11,12,13,14]; passive fish and larval transport, as well as coupled ecological behavior [15,16,17]; combined hydrologic and hydrodynamic processes [9,18]; passive transport of oil spills [19] and coupled hydrodynamic-marsh interactions with biological feedback [20]. Each of these complex applications requires reliable tidal boundary forcing in order to provide accurate results. In particular, many coastal ocean models utilize tidal databases in order to specify the tidal boundary conditions in these regional studies. When no other data is available, the boundary conditions are often selected from global tidal databases. However, while global tidal databases are highly accurate in the deep ocean, they often lack the resolution over continental shelves and in the shallower near-shore regions to adequately resolve the astronomical and associated nonlinear tides in the immediate coastal regions [21]. Therefore, it is necessary to create smaller-scale tidal databases that are able to resolve the near-shore environment. Over the past 25 years, three such databases have been developed for the eastern coast of the United States [22,23,24]. These regional databases use the finite element ADvanced CIRCulation model (ADCIRC) forced with a global tidal database at the open ocean boundary to develop the tidal profile within the domain.
Historically, the eastern (and gulf) coast of the United States has been modeled with a large domain that encompasses the entire Western North Atlantic, Gulf of Mexico and Caribbean Sea, herein referred to as the WNAT domain, and has traditionally had the open ocean boundary located at the 60° W meridian [22,25,26]. This larger domain provides easier forcing as the boundary lies mostly in the deeper Atlantic Ocean and includes only a small portion of the continental shelves near the coastline.
The first tidal database for the WNAT region, EC1991, was state of the art for its time and had 19,858 nodes and 36,653 elements with elements ranging from 7 km at the coastline to about 140 km in the deeper ocean. The bathymetry was extracted from the Earth Topography 5 min gridded resolution (ETOPO5) global bathymetric database. The EC1991 database included elevation and velocity harmonics for the O1, K1, Q1, M2, S2, N2 and K2 constituents [22].
An updated version, EC1995, was created in order to take advantage of the National Ocean Service (NOS) hydrographic survey database for nearshore bathymetry, which has since been digitized [27]. The NOS bathymetric database includes raw sounding tracks from ship surveys and typically covers coastal areas out to the continental shelf in U.S. coastal waters. This updated version had 31,435 nodes and 58,369 elements and a minimum element size of 750 m in Perdido Bay between Alabama and Florida and a maximum element size of 105 km. The average coastal element size was about 5 km with regions of the Florida peninsula and the Gulf Coast west of the Mississippi River typically having 10 km resolution. The EC1995 database included elevation and velocity harmonics for the steady, O1, K1, M2, S2, N2, M4 and M6 constituents.
The next generation, EC2001, database utilized a grid with 254,565 nodes and 492,179 elements and had a minimum element size of 200 m in the Mississippi River Delta region and a maximum element size of 29 km. The New Orleans area was the most highly resolved with average element sizes of 1 km and some areas of finer 500 m resolution. However, the remainder of the domain had typical coastal element sizes closer to 2–3 km. The original EC2001 database included elevation and velocity harmonics for the O1, K1, Q1, M2, S2, N2 and K2 constituents [23]. As an intermediate update, a longer run of 410 days with additional P1 tidal boundary forcing was recomputed in 2008, ec2001_v2e [24], to provide the NOS suite of 37 tidal constituents [28] for both species.
In comparison, the latest version, EC2015, database has 2,066,216 nodes and 3,770,720 elements with a minimum element size of 13 m in the Puerto Rico and Long Island Sound regions (as well as some small Florida channels) and a maximum element size of 46 km near the open boundary. With a few exceptions, the entire WNAT coastline (United States water only) has typical resolutions of 250–500 m with even more detail in inland channels and inlets. As per the 2008 update to the EC2001 database, the EC2015 database provides the computed amplitude and phase of elevation and velocity for the 37 standard NOS tidal constituents. Table 1 summarizes the grid features of the WNAT domain tidal databases.
In the next sections, we present the improvements that have been incorporated into this latest generation tidal database and the remaining challenges. We summarize the development of the EC2015 tidal constituent database; present a skill assessment for global, regional and site specific locations; and discuss how the database can and should be used. Limitations of the database are also discussed. In the interest of brevity, we will only present the skill assessment for these 8 primary constituents: M2, S2, N2, K2, O1, K1, P1 and Q1.

2. Materials and Methods

2.1. ADCIRC Computational Model

2.1.1. General Model Details

As mentioned before, the enhancements to this database will employ the ADCIRC regional hydrodynamic model. ADCIRC utilizes the full non-linear St. Venant (shallow water) equations, using the traditional hydrostatic pressure and Boussinesq approximations. The depth-averaged generalized wave continuity equation is used to solve for the free surface elevation, along with the non-conservative form of the momentum equation for the velocity components. The equations are discretized horizontally in space using continuous Galerkin, linear finite elements with equal-order interpolating functions (linear C0), while time is discretized using an efficient, split-step, Crank-Nicholson algorithm with the nonlinear terms evaluated explicitly. There have been many papers written about the development and usage of the ADCIRC computational model, but basic details for the equations of ADCIRC can be found in [29,30,31].
One of the advances within ADCIRC since the East Coast database was last updated in 2001 is the addition of Manning’s n friction representations. Users are able to specify specific quadratic friction coefficients, Chezy friction coefficients or Manning’s n values throughout the domain [32]. For the Manning’s n implementation, the n values are converted to an equivalent quadratic friction coefficient within ADCIRC before the bottom stress is calculated [30]. This equivalent quadratic friction coefficient is calculated for each node at every time step as
C F ( t ) = g n 2 d e p t h + e t a ( t ) 3
where g is the gravitational constant (9.81 m/s2), n is the Manning’s coefficient, depth is bathymetric depth (m) and eta(t) is the water surface elevation at time t (m). Note that the computed quadratic friction coefficient, CF(t), can also be limited on the lower end by specifying the minimum CF value in the input file. Otherwise, the values can become quite small as the depth becomes large.

2.1.2. Model Input Parameters

Unless otherwise noted in the appropriate methods and results subsections, all of the ADCIRC model runs used the parameters in the following descriptions. The EC2015 tidal database was developed from a 410-day simulation run in order to capture the long-period non-linear tides. A smooth hyperbolic tangent ramp function is applied to both the boundary forcing and the tidal potential forcing functions for the first 25 days. Then the model is allowed to run for another 20 days before the internal ADCIRC harmonic analysis is started for the final 365 days of the simulation. A one-minute interval is used for the internal harmonic decomposition. Tidal potential forcing is applied to the interior of the domain for the O1, K1, Q1 and P1 diurnal constituents and the M2, N2, S2 and K2 semidiurnal constituents. In addition to these eight constituents, the open ocean boundary is also forced with the Mm, Mf, M4, MN4 and MS4 constituents. Nodal factors and equilibrium arguments were set for a 410-day run starting on November 17, 1991; this translates to the harmonic analysis occurring over the entire year of 1992, which is the middle of the current National Tidal Datum Epoch from 1983 to 2001. Unless otherwise noted, tidal forcing was extracted from the TPXO7.2 global tidal database [33].
A time-step of 1.0 s was used yielding a maximum Courant number of 0.76 in the U.S. Virgin Islands and of 0.3 along the Atlantic and Gulf coasts. The time weighting factors for the three-level implicit scheme in the GWCE form of the momentum equation are 0.35, 0.30 and 0.35 for the future, present and past time levels respectively. A two-level Crank-Nicholson scheme is used for the momentum equations. The lateral eddy viscosity coefficient was set equal to 5.0 m2/s and a non-linear quadratic bottom friction scheme with a constant value of 0.0025 was used for all runs except for the variable bottom-friction comparisons. Specific friction settings for the Manning’s n formulation and the variable CF runs are detailed in Section 2.2.5 below; for all variable friction tests, a lower limit of 0.0025 was used. A spatially variable but temporally constant GWCE, G or τ0, parameter was used such that G is dependent upon the local depth and is set as follows: if the depth is ≥10, G is set to 0.005, if the depth is <10, G is set to 0.020.
Due to the large overall mesh domain, variable Coriolis forces were enabled. The non-linear finite amplitude option was utilized with wetting and drying enabled. With the newly expanded open ocean boundary, it was possible to enable the advective terms, as detailed in Section 2.2.6 below.

2.2. Improvements for the ADCIRC Tidal Database

The WNAT domain has been improved upon bit by bit over the past 25 years. As technology has progressed in that time, larger computational domains have been possible. Additionally, with advances in remote data collection methods, more accurate and plentiful data is now available for the bathymetric profile of the world’s oceans and the location of coastlines. For the latest generation East Coast tidal database, six areas of improvement were examined:
  • Move the open ocean boundary out away from the Lesser Antilles
  • Improve the coastal resolution using the NOAA VDATUM product grids
  • Update the deep water bathymetry
  • Use the latest global tidal database products for forcing on the open ocean boundary
  • Compare three bottom friction schemes for improved accuracy
  • Improve the model physics by enabling the advective terms within ADCIRC
In the following subsections, we detail the methods used for each of these areas. Improvements realized in the harmonic constituent accuracy, as compared with CO-OPS and IHO field measurements, will be presented in the results section.

2.2.1. Open Ocean Boundary Placement

The open ocean boundary has been moved out from the traditional 60° W meridian that has been used for the past 25 years. Figure 1 shows the new extended model domain with the traditional boundary shown in red as a vertical line near the new boundary. The purpose of this expanded domain was to improve model stability by moving the open ocean boundary further away from the complexities of the Lesser Antilles island chain that separates the Caribbean Sea from the Atlantic Ocean. The traditional EC2001 domain becomes unstable near these islands when the quarter-diurnal constituents (M4, MS4, and MN4) are included in the boundary forcing. The EC2001_extended mesh was created at NOAA and has the same coastline and bathymetry in the interior as the EC2001 domain, but with a different boundary location.
There were two guiding principles for choosing this new open ocean boundary location: (1) to avoid any nearby amphidromic regions of the principal tidal constituents—M2, S2, N2, K1 and O1; and (2) to create a smooth boundary with gradually changing element size. For elements closer to the coast, the element size was chosen to be smaller and then to gradually increase in size away from the coast. The new boundary curves to the west near Nova Scotia in order to create a smooth transition, without sharp corners, from the ocean boundary to the land boundary. It also prevents the introduction of the Gulf of St. Lawrence into the model domain. One other important design feature was to avoid having too small of elements across shelf breaks, particularly in the southern part of the boundary near the Lesser Antilles.
After a suitable boundary location was found, a one-year fully non-linear tidal simulation was performed to confirm the stability and robustness of the new boundary location. All thirteen of the TPXO7.2 global tidal model constituents were used to force the open boundary (M2, S2, N2, K2, K1, O1, P1, Q1, Mf, Mm, M4, MS4, and MN4) during this stability test.

2.2.2. Increased Coastal Resolution

Each of the WNAT predecessors has gradually added more resolution along the coastline as data and computation capabilities were more readily available. However, this version marks a substantially increased level of coastal resolution for such a large study region. Recall from Table 1 that there are nearly 8 times the number of nodes in the EC2015 mesh when compared to the EC2001 mesh.
Over the past 15 plus years, NOAA has undertaken an ambitious study of the United States coastline to create a tool for transformation between different vertical datums. The VDatum (Vertical Datum) tool provides a single source for accurately and easily transforming geospatial data among different tidal, orthometric and ellipsoidal vertical datums along the United States coast. It allows the user to combine data from different horizontal and vertical reference systems into a common system in order to create integrated digital elevation models. The interested reader is referred to the VDatum website for more general information about the VDatum tool and for regional publications [34].
In order to create accurate tidal datum fields for the coastal regions, a series of highly resolved coastal grids were developed for each region of the East and Gulf Coast for the United States, as well as Puerto Rico and the U.S. Virgin Islands. Figure 1 shows the boundaries of the nine VDatum grids that are presently available in the WNAT domain, with the remainder of the EC2001_extended boundary shown to clearly illustrate the regions where VDatum meshes were used. Individual reports [35,36,37,38,39,40,41,42,43] for each of these domains are available on the VDatum website.
Notice that there are several areas of overlap between these regional VDatum subdomains. For each of these overlaps, the individual grids were carefully pieced together in such a way as to preserve the source grid with the highest coastal resolution. For the shelf regions within these overlaps, a transitional mesh was created at an appropriate distance from the shoreline that smoothly blended the triangulations of the two VDatum meshes. Finally, the bathymetry from the highest resolution source was reapplied onto the new triangulation. This process was repeated for each of the overlapping areas. A comparison of the East Coast of the United States from North Carolina to Maine in the EC2015 model and the previous EC2001 model is shown in Figure 2. Notice the inclusion of more inland channels, rivers and islands; as well as a more detailed shoreline.
It is important to note that the high-resolution meshes created for the VDatum project are in a Model Zero (MZ) vertical datum. The interested reader is referred to the VDatum Standard Operating Procedure manual [44]; but the basic idea is that small corrections are added/subtracted from the original charted bathymetry in an iterative manner until the simulation converges to a solution. The converged solution is verified against harmonic constituent data available within the region. This was necessary since the original bathymetric sources were all in different tidal datums and no tool existed to transform them into a unified vertical datum. The resulting vertical datum of the high resolution coastline is MZ. Although, model zero is not necessarily the same as mean sea level (MSL) due to non-linear dynamic effects, for our purposes, we have to assume that the VDatum coastline is approximately relative to MSL.
The next step was to replace the coastline of the newly created EC2001_extended mesh with this higher resolved coastline. During this step, we also compared localized truncation error analysis (LTEA) meshes of various resolution for the Florida South Atlantic Bight region as we transitioned from the VDatum coastline into the deeper waters [45]. While exploring the various options, it was discovered that several smaller channels along the Georgia and Carolina coasts had not been included in the original VDatum mesh. We decided not to pursue the LTEA meshing at this time, due to the large grid size and time involved to process the size functions. Instead, any hydrologically significant channels were added using NOAA National Ocean Service (NOS) charts and sounding data. However, because these areas were outside of the original VDatum “wet” area, the proper conversion from the NOS sounding datum (usually MLLW or MLW) to the common MSL datum was estimated from the nearest wet conversion points output from the VDatum tool, typically at the mouth of the channel. In order to extrapolate the conversions up the length of the new channels, the slope of the surrounding channel topography was examined and average slope values (for each stream reach) were used to “march” the sounding datum to MSL conversions upstream from the channel mouth. At points in the channel where the surrounding topographic slope changed, a new reach slope value was used to continue marching upstream.

2.2.3. Updated Global Bathymetry

Once the improved coastline was merged into the EC2001_extended model, the next task was to update the bathymetry of all the non-coastal U.S. waters, which had last been updated in 2001. Two different global bathymetry sources were examined: the ETOPO1 Global Relief Model from the National Geophysical Data Center and the SRTM30_PLUS model from the Scripps Institute of Oceanography.
The ETOPO1 product is a 1 arc-minute global relief model of the Earth’s surface. It integrates land topography and ocean bathymetry and was built from numerous regional and global data sets. Older two arc-minute and 5 arc-minute products are still available, although they have been deprecated by the latest model. The horizontal datum of ETOPO1 is WGS84 geographic and the vertical datum is sea level. “More specific vertical datums, such as mean sea level, mean high water, and mean low water, differ by less than the vertical accuracy of ETOPO1 (~10 m at best), and are therefore effectively equivalent” [46]. Various methods are available for obtaining the ETOPO1 product from their website [47].
The SRTM30_PLUS product is a 30 arc-second global relief model of the Earth’s surface, also derived from a wide variety of sources. However, rather than only being a compilation of existing bathymetric data sources, it also uses these data sources to modify global satellite bathymetry based on the latest altimeter-derived gravity models [48,49]. Depths are reported in meters and negative values indicate data points that are below sea level. Additionally, catalogs of the data sources and estimated errors in the depth and navigation for each point are available. Various methods of obtaining the data are available at their website [50].
After data was downloaded for each of these sources, the procedure was to create a bounding polygon of all water that was included in the various VDatum regional grids and only update the water that was outside of that polygon, see Figure 1 (all regions that are within the gray boundary but outside of the black boundaries were updated). This meant that most of the Gulf of Mexico and Caribbean coastline, including the southern coast of Cuba, Haiti and Jamaica had to be updated with global sources that were not necessarily meant to be used in shallow coastal regions. We compared both of the global sources and noticed that the ETOPO1 product resulted in a great deal of oscillations in shallower regions (checkerboard type pattern from one point to the next), particularly along the southern coast of Cuba. In comparison, the SRTM30_PLUS product did not suffer as much with this issue, although it did exhibit occasional oscillations in shallower regions. In general, both products were developed for deeper water not coastal areas and the resolution and depth accuracy is not high enough to adequately resolve shallow coastal waters—with average errors in the 10 m range, all depths below 10 m are suspect. Overall, it was decided to use a single source for the updated bathymetry and the SRTM30_PLUS database was used as it exhibited fewer oscillations in the shallower, near-shore regions. However, after interpolation of the global data set, there were nodes within the grid that were suspect—e.g., sharp change in bathymetry relative to surrounding nodes. The bathymetry at these suspect grid nodes was then hand-cleaned by interpolating from surrounding values in the mesh itself instead of directly from the global source. This removed most sharp oscillations along the non-US coastlines between topographic and bathymetric values, however, further inspection may reveal that some errors still exist.

2.2.4. Updated Open Ocean Forcing

Once an updated physical model had been developed for the entire WNAT region, it was necessary to extract tidal forcing information from available global tidal models at the open-ocean boundary. Since the last version of the East Coast ADCIRC tidal database in 2001, significant improvements have been made in the global tidal modeling community as well. Therefore, we compared two different choices for the boundary conditions: the TPXO7.2 model obtained from the Oregon State University Tidal Inversion Software (OTIS) and the Finite Element Solution FES2012 model from the French Tidal Group [33,51].
OTIS implements an efficient representer scheme for the general inversion calculation for tidal processing of TOPEX/Poseidon altimeter data going back to 2002. TPXO7.2 is a more recent version of a global model of ocean tides obtained from OTIS. The solution best fits, in a least-squares sense, the Laplace Tidal Equations and along-track averaged altimetry data [52,53]. TPXO products are updated as more altimetry and bathymetry data becomes available; since the beginning of the EC2001 project, they have since updated to TPXO8, but for consistency we wanted all of the model runs to have the same forcing so we continued to use TPXO7.2. Tides are provided as complex amplitudes of earth-relative sea-surface elevation for 13 constituents at a 1/4 degree resolution for the global ocean; software and accompanying data can be downloaded from their website [33].
Similarly, the French Tidal Group utilizes a global unstructured grid to model the tidal barotropic equations in a spectral configuration and then employs representer data assimilation from long-term satellite altimetry data to correct the tidal signals. FES products are provided on a 1/16 degree resolution for 32 tidal constituents over the global ocean. The most recent version is FES2012, which was produced by Noveltis, Legos and CLS Space Oceanography Division and is distributed by Aviso [51,54].
After extracting the tidal constituent information from each of these databases, a visual comparison was made of the amplitude and phase information that would be used as input into the ADCIRC model. Since the TPXO products only have information for 13 constituents, it was decided to use these same thirteen harmonic constituents to force the ocean boundary (diurnal—O1 K1 P1 Q1; semi-diurnal—M2 S2 N2 K2; quarter-diurnal—M4 MS4 MN4; and long term—Mf Mm) in order to maintain a comparable forcing suite. In general, there were very few visual differences between these two models, particularly for the diurnal, semi-diurnal and long term constituents. What differences did exist were typically concentrated at the northern boundary near Nova Scotia (refer to Figure 1 for geographic locations within the WNAT domain). Similarly, among the quarter-diurnal constituents, most of the amplitude differences were focused along the boundary as it approached the coast of Nova Scotia. However, the phasing of the quarter-diurnal constituents was significantly different all along the boundary; note that the amplitudes of these constituents are often on the order of 10−3 to 10−2 m. Additionally, the phasing of the Q1 constituent in each of the global products departed rapidly from each other as the boundary neared the Nova Scotia coast. A more quantitative comparison was made by calculating the maximum absolute difference in amplitude and phase over all 187 open ocean boundary nodes; these results are given in Table 2.
While interesting, this was not enough information to determine if one global model was better than the other. In the results section, we will present the actual ADCIRC harmonic differences due to the boundary forcing.

2.2.5. Bottom Friction Assignment

Finally, we examined three variations of the quadratic friction formulation for the EC2015 database: a constant CF version and two variable friction formulations. For the variable formulations, we used a merged combination of the CF values that had been developed for each of the VDatum regions and we also used the collaborative United States Geological Survey (USGS) usSEABED [55] database of core samples to assign appropriate Manning’s n friction values.
Of the nine VDatum grids that fall within the EC2015 model domain, five had a variable quadratic bottom friction scheme. It was not necessary to be as rigorous in combining these friction values, as the areas of grid overlap did not have any conflicting friction values. Therefore, each VDatum region was simply mapped onto the EC2015 model and then combined canonically.
The usSEABED database contains three files for each region: “EXT—numeric data extracted from lab-based investigations, PRS—numeric data parsed from word-based data and CLC—numeric data calculated from the application of models or empirical relationship files” [55]. Each of these datasets has limitations and describes the data in different ways; they can be combined to create a more extensive coverage of the seafloor characteristics. For the EC2015 study, we had to limit the richness of the dataset in order to make it tractable for such a large study area. Therefore a relatively simple approach wherein the grain distributions within the “Gravel”, “Sand”, “Mud” and “Clay” columns of the original usSEABEDS data were aggregated into a single description based upon percentages in each class. This created a verbal distinction only between gravel, sand and silt that did not worry about actual grainsize distributions. Each larger coastal area was then assigned a descriptive designation with an associated shelf Manning’s n value: muddy/silty: n = 0.015, sandy: n = 0.022 (upon visual examination, there were no large areas that were entirely gravel, just independent data points so no gravel appropriate Manning’s n values were assigned in this stage). After a region was classified by bed type, depth-dependent linear interpolation was used to assign Manning’s n values over each section of the coastal/shelf. For water depths between 5 m and 200 m, the shelf value was assigned; for depths greater than 200 m the post-Ike “deep ocean” value of 0.012 was assigned; finally, for depths less than 5 m, values were linearly interpolated from a value of 0.025 at zero depth to the shelf value at 5 m depth. This slightly larger zero-depth Manning’s n value is meant to take into account the impeded flow characteristics due to extremely shallow water. After this process was completed, smaller sub-regions were assigned estuary specific “shelf” values and very coarse sub-grids were defined over the sub-regions, then these sub-grids went through the linear depth interpolation process again with these new values. Only a few estuaries were assigned values different than their surrounding shelves. Table 3 provides the rough geographical shelf regions and specific estuaries that were used in this process, as well as the assigned shelf Manning’s n values.
This is a very simplified approach to assigning friction values given the rich dataset available. However, in the time available for the project, it was impossible to interpolate between each of the usSEABEDS data points and “smooth” the ensuing profile since there could be distances on the order of kilometers from a boulder site that was surrounded by sand. Without knowing the physical extents of the boulders, it is a judgement call how to transition from the one or two boulder indicated grainsizes to the surrounding sand bed. An area of future work would be an efficient interpolation scheme for such a diverse and scattered data set. Depending upon the water depth at an area of interest, it may not be as important as one might think however. If we look again at Equation (1) and note that initially eta(t) = 0, then we can compute the equivalent quadratic friction coefficient, as ADCIRC does internally. This allows a visual comparison between the Manning’s n friction representation and the assigned VDatum friction representation. Figure 3 and Figure 4 show regional views for the Gulf of Maine/New York Sound area and the Mississippi River delta area. For both Figures, panel (a) shows the bathymetric depth profile, panel (b) shows the assigned VDatum quadratic friction coefficients, panel (c) shows the simplified Manning’s n assignment, and panel (d) shows the computed equivalent quadratic friction coefficient associated with (a) and (c).
Note that in both figures, the scales for panels (b) through (d) are the same. However, owing to the difference in regional bathymetry, the bathymetry scales for panel (a) in each figure are different. For the deeper Atlantic coast region, notice that although there is some variation in the Manning’s n profile itself, the computed quadratic friction values do not show as much detail due to the overall deep bathymetry. Meanwhile, for the Louisiana region, the bathymetry scale is more abbreviated (from 0 m to 500 m with more detail in the first hundred meters) and there is more detail to the coastal CF values due to the shallower nature of that region.
Due to the inherent simplifications in the Manning’s n assignments, a sensitivity study of the computed harmonic constituents to the assigned Manning’s n values was conducted. The originally assigned Manning’s n values were multiplied by factors of 90% and 110% and the resulting harmonic responses were compared. More details of this sensitivity study are given in the results section.

2.2.6. Inclusion of ADCIRC Non-linear Advective Terms

The final effort was to include the non-linear advective terms in the ADCIRC formulation; the interested reader is referred to [56] for details about the development of these terms and equations. In practice, these terms enter in by activating two flags in the input file. In past versions of the East Coast tidal database, the location of the open ocean boundary near the Lesser Antilles island chain caused instabilities if these terms were activated. Therefore, until the boundary was moved as part of this study, it was not possible to include fully non-linear advection and compare how the tidal response varied due to these terms.

2.2.7. Summary of Tidal Database Improvements

Six different areas of improvement have been presented for the EC2015 tidal database. Where possible, each model improvement was isolated to determine the accuracy improvement that was due only to that component of the project. However, the improved coastal resolution and updated bathymetry were lumped into the final EC2015 release and were not studied individually. Table 4 provides a summary of the simulations that were completed for this study; including the run designation, description, mesh domain, inclusion of the advection terms, friction scheme and boundary forcing. For the boundary forcing, the textual label indicates which global tidal database was used and the number indicates how many constituents were used (e.g., TPXO-10 indicates that the TPXO7.2 global database was used with only 10 constituents—recall that the quarter-diurnal constituents create instability in the EC2001 domain for long-term simulations). For clarity, when reporting results, labeling figures and during the discussion, the results will be referred to by their run designation.
The EC2001 tidal database was rerun with the most recent version of ADCIRC to ensure that we could expect a fair comparison with the EC2015 results. Error analysis confirmed that the new version of ADCIRC was recreating the harmonic constituents from the 2008 updated tidal database [23]. In subsequent sections, all reference to the EC2001 model indicate that constituents were directly extracted from the previous version of the database at the same locations as the recent improvements. In order to test the affects due solely to the boundary location, a new input file that mimicked the 2008 update, but used the new expanded boundary, was created; this run designation is given by EC2001-ext. The only difference in the input file is that boundary forcing was extracted from the TPXO7.2 global tidal database at the new boundary node locations.
A series of runs using the final EC2015 model domain (boundary placement, updated bathymetry and improved coastal resolution all lumped together) were conducted; all seven of these used the full thirteen-constituent suite of boundary forcing and six of them include the advective terms. The OTIS1 and FES1 simulations differ only in whether the TPXO7.2 or FES 2012 global tidal databases were used for the boundary conditions; a constant bottom friction was utilized in order to isolate the boundary forcing. Additionally, four variable bottom friction runs were conducted to compare the harmonic response to various friction schemes; OTIS3 used the merged VDatum friction, OTIS4 used the original Manning’s n assignments, OTIS5 used the OTIS4 Manning’s n values scaled by 90%, and OTIS6 scaled these by 110%. Finally, in order to test the advective terms, the OTIS3noadv simulation mimics the OTIS3 simulation but with the advective terms turned off.

2.3. Validation of the Improved ADCIRC Tidal Database

Two sources of harmonic constituent data were used to validate the new EC2015 tidal database. The analysis techniques used to compute model errors are also discussed in this section.

2.3.1. Validation Data

The Center for Operational Oceanographic Products and Services (CO-OPS) keeps a record of tidal benchmarks and harmonic data at stations throughout the United States [57]. Tidal harmonic data was available at 404 such stations in the EC2015 domain. Additionally, historical data from the International Hydrographic Organization (IHO) was used to provide wider coverage, specifically in the deeper regions beyond the continental shelves [58]. There is a higher measure of uncertainty in the IHO data, as information about the source of the constituents (e.g., length of analysis and data records) is not available; furthermore, the three-decimal digits precision of longitude and latitude coordinates used to locate the stations are sometimes insufficient to determine the physical location of the data collection. At the request of some of the participating countries, the bank was removed from public distribution in about 2002 [59]. Of the about 4190 IHO stations available worldwide, 277 fall within the EC2015 domain. For skill assessment purposes, all 681 stations (404 from CO-OPS and 277 from IHO) were classified by regional location (Atlantic, Gulf of Mexico, Caribbean Sea), as well as coastal proximity versus deep ocean.
The overall locations of the available 681 data stations are shown in Figure 5a; while Figure 5b,c and Figure 6 show zoomed views of the various regions. In all of these figures, the gray boundary depicts the new EC2015 model domain while the green boundary depicts the old EC2001 model domain; the data locations from CO-OPS are shown in blue while IHO data locations are shown in red; data locations shown with a cyan circle surrounding them are not wet in the EC2001 domain and are excluded from any error comparisons that specifically say that only wet stations were used; finally, sample regional scatter plots are provided in Appendix B for the 10 stations that are shown with a black X and indicated by station number.
Of these 681 stations, only 367 were considered wet in the EC2001 model, where by wet we mean that they are either within the domain itself (280) or were near enough to the boundary in the main water bodies that nearest neighbor data extraction (87) was valid. Stations that were far inland or within small channels are not extracted from the EC2001 database as they were not physically represented in the older database. All stations shown in Figure 5 and Figure 6 without a cyan circle denote the location of these 367 stations where harmonics were extracted from the EC2001 database for comparison with the new EC2015 database. Appendix A provides a list of all 681 stations with the CO-OPS station designation (when applicable), lon/lat location, station name and assigned region (Table A1). Station numbers indicated with a single * are close enough to the boundary to use nearest element approximations within the EC2001 model, while those with a double ** are not located within the extents of the EC2001 model and are not used for statistics or station scatter plots when comparing results. Actual longitude and latitude coordinates were not shifted when extracting from the EC2001 database, as the nearest element is most likely where the station would have been manually shifted anyway.

2.3.2. Validation Methods

In order to determine which model best captured the tidal harmonic data at the available data stations, we looked at a variety of error measures. For each station, we examined scatter plots of measured and computed amplitude and phase for the eight primary tidal constituents (M2, S2, N2, K2, O1, K1, P1 and Q1). Ideally, the computed and measured values would have a one-to-one correspondence. Scatter plots were also made that included all 681 stations for each of these eight constituents and a least-squares linear regression was computed. Additionally, comparison scatters showing both the EC2001 and EC2015 models for these eight constituents were created using the 367 wet stations in the EC2001 tidal database.
In addition to these qualitative measures, three different error measures were calculated to quantify the skill of each model. For the phase, the mean absolute error was computed as
M A E = 1 8 n p e = 1 n p k = 1 8 | data e , k model e , k |
where errors are summed over the number of data points for a particular region (e) as well as the number of constituents (k). To calculate the mean errors for an individual constituent, the second sum would only be computed for k = 1 and the 8 is removed from the denominator.
Due to some constituents having very small amplitudes, the mean relative error was computed for amplitudes only as
M R E = 1 8 n p e = 1 n p k = 1 8 | data e , k model e , k | data e , k
where the same summation rules apply. Note that if the errors are on the same order of magnitude as the data, the relative errors will be close to 100%. Additionally, a composite root mean square (RMS) error, combining the phase and amplitude error for each constituent into a single error metric, was calculated at each station as
A E = 0.5 ( A m 2 + A o 2 ) A m A o cos ( π ( h m h o ) / 180 )
where Am is the modeled amplitude in meters, Ao is the observed amplitude in meters, hm is the modeled phase (degrees GMT) and ho is the observed phase (degrees GMT). As before, the mean errors are calculated by summing over the number of data points for any particular region as well as the number of constituents,
M e a n R M S E = 1 8 n p e = 1 n p k = 1 8 ( A E ) e , k
In order to compare the skill of the new EC2015 model versus the previous EC2001 database, harmonic constituents were extracted from the 2001 database (2008 updated) at the stations that were within (or close enough to) the bounds of the EC2001 model. Mean errors were then computed for both databases at those 367 locations. However, mean errors were also calculated at all 681 stations for the new EC2015 database. Table 5 provides the total number of stations in each region that were used for statistics for each model; parenthetical numbers include only the stations that were physically within the EC2001 domain, not the nearest neighbors.

3. Results

3.1. Results for the Various Improvements

In this section some of the model improvements are examined independently to determine how effective they are at increasing the tidal constituent accuracy. For brevity, only the regional mean RMS error comparisons are provided here. Full error analysis, as described in Section 2.3.2, will be provided in Section 3.2 when the EC2001 model is compared to the final release EC2015 model. Figure 7 presents the regional mean RMS errors for all nine simulations that were previously presented in Table 4. These mean errors were computed using only the 367 wet stations that are common to all model domains.

3.1.1. Boundary Placement

As described in Section 2.2.1, the open ocean boundary has been moved out away from the Lesser Antilles Islands and the historical 60° W meridian that has been used for over 25 years. In order to test how much of an affect the new boundary placement has on the extracted harmonic constituents, the new EC2001_extended model was run with an identical input file as was used for the 2008 updates to the EC2001 tidal database, ec2001_v2e, [23]: a larger time step of 5.0 s is possible with these coarser meshes, the non-linear advective terms were turned off and only 10 forcing frequencies were used on the open boundary—the three quarter-diurnal constituents were not used in order to match the EC2001 simulation. All other parameters are as described in Section 2.1.2.
Concentrating only on the EC2001 and EC2001-ext results in Figure 7, we note that simply moving the boundary out away from the Lesser Antilles does not significantly improve the overall accuracy, although it does help the stability of the model. The Atlantic and Caribbean regional errors are unchanged, while the global errors are only slightly reduced. A moderate error reduction is realized in the Gulf of Mexico region and the deep stations actually have slightly higher mean errors.

3.1.2. Comparison of Open Ocean Boundary Forcing

Two different global tidal databases have been examined as input to the EC2015 model: FES12 and TPXO7.2. Looking at the FES1 and OTIS1 bars in Figure 7, we note that for all regions the OTIS1 simulation has less error than the FES1 simulation; these error reductions are most significant in the Atlantic region and deep water stations. Although the differences are rather small, it is obvious that the TPXO global database is providing more accurate results than the FES12 database.

3.1.3. Comparison of Bottom Friction Schemes

In this study, three different bottom friction schemes are compared: constant CF = 0.0025, VDatum quadratic friction coefficients and Manning’s n formulation with n values estimated using the USGS usSEABEDS data. Due to the simplified assignment of the Manning’s n values, sensitivity to the actual Manning’s n specification was also examined.
Looking at the mean RMS errors for the OTIS1 through OTIS6 simulations (ignoring OTIS3noadv) in Figure 7, we note that there is actually very little difference in the mean errors for the Gulf of Mexico, Caribbean and Deep stations for any of the five friction simulations. Furthermore, we see that there is also little difference in the three Manning’s n simulations (OTIS4 through OTIS6) in any of the regions. This is encouraging as it means that there is very little to no model sensitivity to small perturbations in the Manning’s n values. Although a rather simplified approach for assigning these values was used, we should not be too concerned with the approach, assuming that representative values for each region were chosen carefully. Finally, we note that the VDatum friction scheme (OTIS3) has slightly higher mean errors in the Atlantic region.
Examination of the individual constituents indicate that there is very little difference in the mean errors for the various friction simulations. The exception is the M2 constituent which has slightly higher errors of about 0.3 cm for the OTIS3 simulation than all of the others. If one were to look at scatter plots of individual stations, then more substantial differences could be detected; however, on average, most constituents are insensitive to small changes in the bottom friction. Given the simplifications of the Manning’s n assignments and the prior validation of the VDatum CF values during the VDatum model development, for this release (EC2015) we have chosen to implement the VDatum friction values.

3.1.4. Inclusion of Advective Terms

Finally, when examining the OTIS3 and OTIS3noadv error bars, we note that very little difference can be seen between the errors in the Gulf of Mexico and Caribbean regions. However, there are noticeable differences in the Atlantic Ocean and Deep stations, with the OTIS3noadv bars having slightly higher error than their counterpart. From this, we conclude that the addition of the advective terms does reduce the mean errors in the tidal constituent harmonics, particularly in the Atlantic coastal regions. While not shown here, it is noteworthy that these differences are more significant when all 681 stations are used to calculate the mean errors; this is due to the higher percentage of stations in the shallower coastal regions and narrow channels where the advective processes are more dominant.

3.2. Comparison of EC2015 and EC2001

For the EC2015 tidal database release, the VDatum friction formulation and TPXO7.2 boundary forcing with all 13 constituents was used; all other model input parameters are as given above in Section 2.1.2. For results and discussion, when we refer to EC2001 we mean the updated 2008 version [24]. Scatter plots of computed versus measured amplitudes and phases (and their linear best-fit) for the EC2001 and EC2015 databases are shown in Figure 8 for the dominant diurnal and semi-diurnal tidal signals: K1 and M2. Additionally, Table 6 provides the best fit statistics for all eight primary constituents at the 367 validation stations that are common to both databases.
For a perfect fit of the validation data, both the slope and R2 values would have a value of unity. Notice that although the slope may not be improved for all eight constituents, the R2 value is closer to unity for all of them, indicating a tighter distribution. The larger apparent scatter in the diurnal amplitudes is due to their much smaller magnitudes, while the scatter in the semi-diurnal phases resides mostly in the Caribbean and Gulf of Mexico stations where the predominant constituents are diurnal. Additionally, many of the CO-OPS validation stations on Puerto Rico have data records that are significantly less than one year.
Similarly, if we look at scatter plots of individual stations, we can compare how each of the databases performs for that point. Since there are 681 validation stations, only a few representative stations are provided herein. Figure B1, Figure B2, Figure B3, Figure B4, and Figure B5 in Appendix B provide plots for the 10 stations that were shown by a black X in Figure 6 and Figure 7; plots are grouped together by region: Atlantic coast, Florida coast, Gulf of Mexico, Caribbean Sea and deep ocean stations. In order to illustrate the station differences due to the friction formulation, results for both the VDatum and Manning’s n friction formulations are shown in these plots. Other than the bottom friction itself, all other ADCIRC parameters are the same for these two data sets. First, note that the different friction formulations typically affect the amplitude response of the model more than the phase (with the exception of station 313 at Pilottown, LA and station 645 at Curacao Willemstad). Recall that there are no river boundary conditions in these simulations, they are purely tidally driven. Therefore, stations such as Pilottown, LA that are located on a major river will not exhibit the proper harmonic response as they do not include the effects of riverine flow. Generally, the new EC2015 model is within the 5%–10% error bars for amplitudes and 10°–20° error bars for phase. For stations that are not, such as station 348 at Galveston Bay Entrance, where some constituents are overestimated while others are underestimated, a thorough examination of the nearby bathymetry may be warranted. While every effort was made to use the most recent bathymetry data available by incorporating the VDatum models, for some regions the only available NOS charts can be around 100 years old.
It is also instructive to see if there are sub-regional patterns in the errors (at the individual water body scale), which can help to guide future efforts at improving the tidal database. Plots of relative amplitude and absolute phase errors for the EC2015 model at each of the 681 stations are provided in Figure C1, Figure C2, Figure C3, Figure C4, Figure C5, Figure C6 and Figure C7 in Appendix C for the M2 and K1 constituents (same zoom views given in Figure 5 and Figure 6). Plots are only provided for the dominant constituent in the sub regions: Gulf of Maine, Atlantic coast and Florida–M2 and Gulf of Mexico and Caribbean Sea—K1. Points shown in blue are underestimating the amplitudes (or exhibit a phase lag), while points shown in red are overestimating (exhibit a phase lead). The symbol shapes indicate to what degree the model is over/under estimating; we would like to see amplitude errors less than 10% and phase errors less than 20°. Several general trends can be gleaned from these plots:
  • The M2 amplitudes in the Gulf of Maine are slightly overestimated (generally less than 5% but a few as high as 20%) while those at the east end of Long Island Sound are overestimated about 10%–20%. Meanwhile stations along the remainder of the Atlantic coast down through Florida are underestimated by 5%–10% on average, with a few isolated stations overestimating. The Chesapeake Bay and Florida Key regions have several stations that are underestimated by more than 10%. For the 681 stations, 309 or roughly 45% of them have relative amplitude errors above the desired 10% threshold; most of these lie within the Gulf Coast and Caribbean regions where the semi-diurnal amplitudes are small and the remaining are fairly evenly distributed throughout the domain.
  • The M2 phases are generally lagged for the entire Atlantic coast and Florida region, with the exception of the Gulf of Maine (which exhibits slight 0%–5% phase leads). The most severe phase lags are often in the upper reaches of the estuaries, embayments and rivers. Of the 404 stations, only 111 (or 16%) have absolute phase errors greater than the desired 20°; most of these lie within the Chesapeake Bay, Gulf Coast and Caribbean regions.
  • The amplitudes for the diurnal K1 constituent are generally overestimated along the Gulf coasts and the Caribbean, although there are a few stations that are underestimated. While many of the Gulf of Mexico stations are outside of the desired 10% range, the majority of the Caribbean Sea stations are below this threshold. A higher number of the 681 stations (57%) fall outside of the desired 10% relative amplitude error range—of these stations, 60% are along the Atlantic coast where the semi-diurnal tides usually dominate and 30% are in the Gulf of Mexico with the remainder in the Caribbean Sea.
  • Meanwhile, the phases for the K1 constituent generally exhibit a phase lag in the Gulf of Mexico and Caribbean Sea basins and are typically more accurate. However, the stations along the northern Texas coast often exhibit phase leads. Only 8% fall outside of the desired 20° error range and two-thirds of those are along the Atlantic coast.
Finally, mean RMS errors for regions are shown in Figure 9, while mean absolute phase errors and mean relative amplitude errors are provided in Table 7. Looking primarily at the 367 validation stations that are common to both databases (blue diamonds for EC2001 and red circles for EC2015), we can draw several general conclusions.
  • Globally, the greatest overall RMS improvement is realized in the M2 constituent (1.1 cm reduction). All of the constituents (except Q1) exhibit 2°–4° reductions in mean absolute phase error and 1%–7% reductions in mean relative amplitude errors. Overall, there is a 4% reduction in amplitude errors and about 2° in phase errors.
  • For the Atlantic region, RMS error reductions of about 0.3 cm are gained in the O1, K1 and N2 constituents and 1.4 cm for the M2 constituent. In general, all of the constituents have 2°–3° reductions in mean absolute phase errors. However, the Q1 and K2 constituents actually have higher errors in the 2°–3° range. Additionally, with the exception of Q1 which is roughly unchanged, the diurnal constituents exhibit 1 to 8% reductions in relative amplitude errors while the semi-diurnal have 3%–8% reductions in error.
  • For the Gulf of Mexico, the greatest RMS error improvements are in the O1 and K1 (0.5 cm), M2 (1.0 cm) and S2 (0.3 cm) constituents. Mean absolute phase errors are improved by 1°–3° for the diurnal constituents and 3°–11° for the semi-diurnal (with the exception of S2 which exhibits little change). Meanwhile, mean relative amplitude errors are reduced by 2%–6% for the diurnal constituents and by 8%–13% for the semi-diurnal (with the exception of Q1 and M2 which exhibit error increases of 2%–3%).
  • For the Caribbean region, there are minor RMS error improvements of about 0.2 cm in the O1, K1 and S2 constituents and 0.4 cm for M2 while most of the other constituents are reduced by less than 0.1 cm. Mean absolute phase errors increase by 1°–2° for the diurnal constituents and decrease by 2°–9° for the semi-diurnal constituents. Mean relative amplitude errors decrease by 2%–11% for the diurnal constituents and 2% for M2; while N2 and K2 increase by about 1%. Given these erratic trends, it is instructive to note that the data records used at CO-OPS to generate the harmonic constituent data in the U.S. Virgin Islands and Puerto Rico are often as small as 29 days.

4. Discussion

Table 8 provides a summary of the global RMS errors for the eight primary constituents, as well as the mean regional errors summed over these constituents, for each of the nine model simulations done as part of this study (statistics computed using only the 367 common validation data points).
Notice that the placement of the boundary did not significantly change either the individual constituents (greatest change was a less than 0.2 cm reduction for O1) or the regional means, where the greatest difference was less than 0.1 cm. Recall from Section 2.2.1 that this improvement was included primarily to increase the model stability for the long-term simulations of 410 days that were necessary for this study. While the slight model improvement is appreciated, it was not expected or required.
Meanwhile, the inclusion of the advective terms did not significantly affect the mean errors either. The largest difference was in the M2 constituent, which exhibited 0.3 cm reductions of error when the advective terms were included in the simulation, and the largest regional change was for the Atlantic stations (less than 0.05 cm difference). While these are not significant error reductions, it is important to include as much of the model physics as possible. Furthermore, examination of scatter plots for individual stations shows that the inclusion of the advective terms can have significant influence on certain types of stations (rivers, channels, shallower estuaries, etc.) where we would expect the hydrodynamics to be more dominated by advection.
Turning now to the open ocean boundary forcing, we note that the simulation with TPXO 7.2 forcing is on average more accurate than the FES2012 forcing. The most significant difference is for the S2 constituent, which exhibits 0.6 cm less error when the TPXO 7.2 product is used as the boundary condition, with the only other noticeable improvement being in the P1 constituent (about 0.15 cm). Regionally, the reductions are about 0.15 cm for the deep and Atlantic stations. Interestingly, neither of these constituents has the highest phase or amplitude errors in Table 2. Visual examination of P1 amplitudes and phases along the open boundary indicate that the FES2012 product has a considerable phase lag, compared to TPXO 7.2, for this constituent along the entire length and a noticeable departure for the amplitudes near the coast of Nova Scotia. However, there are no significant differences visible for the S2 constituent. From this we infer that the non-linear interactions between the tides can indeed be very complex. Additionally, this highlights the need for accurate boundary conditions at any modeling level.
Finally, comparison of the various bottom friction schemes indicates that the bottom friction does not noticeably affect the overall statistical errors; there are very few differences across the OTIS1, OTIS3 and OTIS4 through OTIS6 simulations for constituents or regions. The exception to this is that the OTIS3 simulation is about 0.3 cm higher than all of the others for the M2 constituent, with most of these errors occurring (on average) in the Atlantic region. However, as shown in Appendix B, individual stations can be significantly affected when the bottom friction is varied, from which we infer that overall statistical improvement could be gained by optimizing the friction scheme in each coastal embayment and estuary.

5. Conclusions

The results indicate that most of the reduction in harmonic constituent errors are due to the increased coastal resolution and updated coastal bathymetry. On average, very little overall improvement was realized solely from the bottom friction representation, inclusion of advective terms or new open ocean boundary location. However, these do contribute to the overall stability and robustness of the model, as well as having localized effects on the harmonic accuracy.
To put the errors in context, we also computed the mean RMS error (for all eight primary constituents) between the CO-OPS station data and the IHO data for the 63 stations that were available in both data sets. The mean error for all 63 stations was 0.72 cm, while the minimum and maximum error over all stations were 0.19 cm and 2.94 cm, respectively. On average, one could expect the data itself to be in error by about 0.7 cm at a given station, which is about half of the global RMS errors reported in Table 8. The measured to computed error measures reported throughout the paper include these errors in the data; thus, a significant portion of the reported errors stem from the uncertainty in the data itself.
Future improvements to the WNAT tidal database could include better bottom friction representations in individual water bodies that have not been optimized (e.g., the upper reaches of Chesapeake Bay, marshy areas along the Florida coast and other regions indicated by the figures in Appendix C) and updated bathymetry for inlets and other important conveyances (e.g., Pamlico Sound inlets) as the VDatum models themselves are updated with more recent sounding data.
It is recommended that users of the EC2015 tidal database follow two basic guidelines: (1) choose your regional open ocean boundary location to be well outside of estuaries and bays and (2) make sure that your regional model bathymetry matches the database bathymetry at your boundary. Additionally, while harmonic information is available for 37 constituents, use caution when applying larger suites as only eight have been validated. Further guidelines and limitations are provided in Appendix D for the interested reader. The EC2015 tidal database is available on the ADCIRC website [24].

Acknowledgments

Funding for the project was provided by the National Oceanic and Atmospheric Administration. Additional resources were provided by the University of Oklahoma. The computing for this project was performed at the OU Supercomputing Center for Education & Research (OSCER) at the University of Oklahoma (OU). Any opinions, conclusions, or findings are those of the authors and are not necessarily endorsed by the funding agencies. We also thank the reviewers for their insightful and constructive comments during the review process.

Author Contributions

R.K, K.D. and J.F. conceived the project and decided upon the six areas of improvement; J.W. created and validated the new EC2001_extended model domain and provided VDatum model grids and the most recent approved CO-OPS tidal constituent data; C.S. created the new EC2015 model domain, performed all of the ADCIRC model simulations to test the various improvements and analyzed the model results; K.D. modified the ADCIRC source code to allow internal harmonic analysis for large grids and the full suite of 37 constituents; C.S. wrote the paper.

Conflicts of Interest

The authors declare no conflict of interest. J.F. as a representative of the funding sponsor, was involved in designing the study. The funding sponsors had no role in the analyses or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

Appendix A

The locations, names and regional classification of all 681 validation stations are given herein; the last 277 stations are marked with IHO in the CO-OPS ID column to indicate that they are from the IHO bank of tidal constituents. Stations marked with a single asterisk are considered “wet” in the EC2001 model even though they are approximated by their nearest neighbor. Meanwhile, those marked with a double asterisk are not included in scatter plots or statistical error metrics for the EC2001 database since they are well outside the domain of the boundary or are in channels and other features that are not represented in the EC2001 model. Abbreviations for the region designations are as follows: Atlantic Ocean—A, Gulf of Mexico—G, Caribbean Sea—C, Deep water—D.
Table A1. Geographic location, name and regional classification for available validation stations.
Table A1. Geographic location, name and regional classification for available validation stations.
IDCO-OPSLongitudeLatitudeStation NameRegion
12695540−64.7033132.37339Bermuda Esso Pier, St. Georges IslandA
28410140−66.9829044.90460Eastport, Passamaquoddy BayA
3 **8410714−67.1084044.87045Coffin Point, Coffin NeckA
4 **8410715−67.1300044.92330Garnet Point, Hersey NeckA
5 **8410834−67.1437545.12889Pettegrove Point, Dochet IslandA
6 **8410864−67.1516744.82333Gravelly Pt., Whiting BayA
78411060−67.2091744.65637Cutler Farris Wharf, Little RiverA
88411250−67.2967044.64170Cutler Naval Base, Machias BayA
9 **8412581−67.8750044.54000Milbridge, Narraguagus RiverA
10 **8413320−68.2050044.39170Bar Harbor, Frenchman BayA
118413825−68.4350044.17000Mackerel Cove, Swans IslandA
128414249−68.6209344.19231Oceanville, Deer IslandA
13 **8414612−68.7719044.78765Bangor, Penobscot RiverA
148414721−68.8133044.47170Fort Point, Penobscot RiverA
158414888−68.8884044.16080Pulpit Harbor, Penobscot BayA
16 **8415490−69.1017044.10500RocklandA
17 **8415709−69.1817044.07136Thomaston, St George RiverA
188417177−69.7850043.75500Hunniwell Point, Kennebec RiverA
19 **8417208−69.7970844.08721Richmond, Kennebec RiverA
20 **8417227−69.8088043.92500Bath, Kennebec RiverA
21 **8418150−70.2460143.65608Portland, Casco BayA
22 *8418445−70.3333043.54000Pine Point, Scarborough RiverA
23 *8418606−70.3817043.46170Camp Ellis, Saco RiverA
24 *8419317−70.5630343.31966Wells, Webhannet RiverA
25 **8419870−70.7417043.08000Seavey Island, Portsmouth HarborA
26 **8423898−70.7116743.07179Fort Point, Newcastle IslandA
27 **8440273−70.9080042.83600Salisbury Point, Merrimack RiverA
28 *8440452−70.8200042.81670Plum Island, Merrimack River Ent.A
29 **8440466−70.8733042.81500Newburyport, Merrimack RiverA
30 *8441551−70.6150742.66033Rockport HarborA
31 **8442645−70.8764942.52295Salem, Salem HarborA
32 **8443187−70.9433042.45830Lynn, Lynn HarborA
33 **8443970−71.0472042.35750Boston, Boston HarborA
348444162−70.8917042.32830Boston Light, Boston HarborA
35 **8444525−70.9533042.28000Nut Island, Quincy BayA
36 **8444788−70.9667042.24830Shipyard Point, Weymouth Fore RiverA
378445138−70.7247642.20099Scituate, Scituate HarborA
388446009−70.6387342.08330Brant Rock, Green Harbor RiverA
39 **8446121−70.1821642.04959Provincetown, Cape CodA
40 **8446166−70.6678942.03830Duxbury, Duxbury HarborA
41 *8446493−70.6617041.96000Plymouth, Plymouth HarborA
42 **8447173−70.5350041.77500Sagamore, Cape Cod CanalA
43 **8447191−70.5617041.77000Bournedale, Cape Cod CanalA
44 *8447241−70.1555041.75600Sesuit Harbor, East DennisA
45 **8447259−70.5934241.74585Bourne Bridge, Cape Cod CanalA
46 **8447270−70.6167041.74170Buzzards Bay, Cape Cod CanalA
47 **8447295−70.6242541.73500Gray Gables, Buzzards BayA
488447368−70.7150041.71170Great HillA
49 **8447386−71.1655041.70580Fall River, Hope BayA
508447416−70.7194141.69578Piney Point, Wings CoveA
51 *8447435−69.9488741.68847Chatham, Lydia CoveA
528447495−70.0567041.66478Saquatucket HarborA
538447712−70.8998141.59292New Bedford, Clarks PointA
548447842−70.9283041.53830Round Hill PointA
558447930−70.6717041.52330Woods Hole, Buzzards BayA
56 **8448157−70.5987041.45830Vineyard Haven, Vineyard Hvn HbrA
57 **8448558−70.5115041.38822Edgartown, Martha’s VineyardA
58 *8448725−70.7679541.35461Menemsha HarborA
59 **8449130−70.0943841.28503Nantucket Island, Nantucket SoundA
60 *8451552−71.2550041.63670Bristol FerryA
618452660−71.3267041.50500Newport, Narragansett BayA
628452944−71.3433041.71670Conimicut Light, Narragansett BayA
638453742−71.3867041.49670West JamestownA
64 **8454000−71.3997841.80786Providence, Providence RiverA
65 *8454049−71.4110041.58680Quonset PointA
66 **8454538−71.4434641.57384Wickford, Narragansett BayA
678455083−71.4900041.36330Point Judith, Harbor Of RefugeA
688458022−71.7617041.32830Weekapaug Point, Block Island SoundA
698459338−71.5562141.17404Block Island Harbor, Old HarborA
708459479−71.5800041.22830Sandy Point, Block Island SoundA
718459681−71.6106441.16330Block Island, Block Island SoundA
72 **8461490−72.0897541.36105New London, Thames RiverA
73 **8463701−72.5317041.26830Clinton, Clinton HarborA
74 **8465705−72.9083041.28330New Haven, New Haven HarborA
75 **8467150−73.1817041.17330Bridgeport, Bridgeport HarborA
76 *8467373−73.2133041.15670Black Rock Harbor, Cedar CreekA
77 **8467726−73.2828641.13249Southport, Southport HarborA
788468799−73.4800041.03830Long Neck Point, Long Island SoundA
798510321−71.8558641.07199Montauk Point LightA
80 *8510448−71.9350041.07330Lake Montauk (U.S.C.G.)A
81 **8510560−71.9600041.04830Montauk, Fort Pond BayA
828510719−72.0319141.25792Silver Eel Pond, Fishers IslandA
83 *8511171−72.1900041.03500Threemile Harbor EntranceA
848511236−72.2052141.17125Plum Island Plum Gut HarborA
858511671−72.3067041.13670Orient, Orient HarborA
868512668−72.5617041.01500Mattituck Inlet, Long IslandA
87 **8512735−72.5817040.93470South Jamesport, Great PeconicA
88 **8512769−72.5866740.81830Shinnecock Yacht Club, Penn. CreekA
89 *8512987−72.6450040.98170Northville Fuel Dock, Long IslandA
908513825−72.8683040.73830Smith Point Bridge, Narrow BayA
91 *8514322−73.0000040.74780Patchogue, Patchogue RiverA
92 *8514422−73.0433040.96500Cedar BeachA
93 **8515586−73.3533040.90000Northport, Northport BayA
948515786−73.4000040.95330Eatons Neck, Huntington BayA
95 **8515921−73.4317040.91000Lloyd Harbor LighthouseA
96 **8516061−73.4700040.87330Cold Springs HarborA
97 **8516299−73.5500040.90330Bayville Bridge, Oyster BayA
98 **8516614−73.6550040.86330Glen Cove Yacht Club, Long IslandA
99 **8516761−73.7033040.83170Port Washington, Manhassset BayA
100 *8516945−73.7649040.81030Kings Point, Long Island SoundA
101 **8516990−73.7817040.79330Willets Point, Little Bay, East RiverA
102 **8517276−73.8567040.78330College Pt, Ft. Of 110Th StA
103 **8517847−73.9951740.70374Brooklyn Bridge, East RiverA
1048518091−73.6717040.96170Rye Beach, Amusement ParkA
105 **8518639−73.9062540.80133Port Morris, East 138Th St.A
106 **8518668−73.9417040.77670Horns Hook, E. 90Th St. Hell GateA
107 **8518687−73.9583040.75830Queensboro Bridge, East RiverA
108 **8518699−73.9695640.71170Williamsburg BridgeA
109 **8518750−74.0143640.70020The Battery, New York HarborA
110 **8518903−73.9250040.87830Spuyten Duyvil Ck, Ent., Hudson R.A
111 **8518905−73.9167040.90330Riverdale, Hudson RiverA
112 **8518924−73.9633041.21830Haverstraw BayA
113 **8519483−74.1423040.63980Bergen Point West, Kill Van KullA
114 *8531680−74.0094040.46690Sandy HookA
1158534720−74.4183039.35500Atlantic City, Atlantic OceanA
1168534770−74.4767039.33500Ventnor City, Fishing PierA
117 *8534836−74.5333039.30830Longport, Risely ChannelA
118 *8536110−74.9600038.96833Cape May Canal, Delaware BayA
119 *8536581−74.8917039.12830Bidwell Creek Entrance, Del. BayA
120 *8536931−75.1750039.23830Fortescue CreekA
1218537121−75.3750039.30500Ship John Shoal, Delaware RiverA
122 **8538886−75.0430040.01194Tacony-Palmyra BridgeA
123 **8539094−74.8697040.08170Burlington, Delaware RiverA
124 **8539487−74.7367040.13670Fieldsboro, Delaware RiverA
125 **8539993−74.7550040.18830Trenton Marine TerminalA
126 **8540433−75.4100039.81170Marcus HookA
127 **8545240−75.1409139.93333Philadelphia (U.S.C.G.), Del. RiverA
128 **8545530−75.1383039.95330Philadelphia (Pier 11 North), Del. RA
129 **8548989−74.7517040.13670Newbold, Delaware RiverA
130 **8551762−75.5883039.58170Delaware City, Delaware RiverA
131 **8551910−75.5733139.55870Reedy Point, C&D CanalA
132 *8554399−75.4000039.18500Mahon River Entrance, Del. BayA
1338555889−75.1133338.98667Brandywine Shoal Light, Del. BayA
134 *8557380−75.1200038.78200Lewes, Ft. MilesA
135 *8558690−75.0700038.61000Indian River InletA
1368570280−75.0833038.32670Ocean City, Fishing PierA
137 **8570283−75.0916738.32833Ocean City InletA
138 **8570536−75.1890938.21516South Point, Chincoteague BayA
139 **8570649−75.2850038.14830Public Landing, Chincoteague BayA
140 **8571091−75.8633037.97670CrisfieldA
1418571117−76.0289537.99826Ewell, Smith IslandA
1428571421−76.0383038.22000Bishops Head, Hoopers StraitA
143 **8571559−76.0050038.30000Mccreadys Creek, Fishing BayA
144 *8571579−76.2650038.34170Barren Island, Chesapeake BayA
145 **8571773−75.8193038.48396Vienna, Nanicoke RiverA
146 **8571892−76.0681838.57354Cambridge, Choptank RiverA
147 *8572467−76.3733038.83670Kent Point, Chesapeake BayA
148 **8572669−75.9450038.91670Hillsboro, Tuckahoe CreekA
149 *8572770−76.3550038.95670MatapeakeA
1508572955−76.3011039.03170Love Point Pier, Kent IslandA
151 **8573349−75.9250039.24500Crumpton, Chester RiverA
152 *8573364−76.2457739.21333Tolchester Beach, Chesapeake BayA
153 *8573704−76.0633039.37170Betterton, Sassafras RiverA
154 **8573903−75.9167039.50330Town Point WharfA
155 **8573927−75.8100039.52766Chesapeake CityA
156 *8574070−76.0900039.53670Havre De Grace, Chesapeake BayA
157 **8574459−76.2550039.38830Pond Point, Bush RiverA
158 **8574680−76.5783339.26667Baltimore (Fort McHenry)A
159 **8574683−76.5850039.26170Fort McHenry Marsh, Patapsco RA
160 **8575512−76.4809938.98441U.S. Naval Academy, Severn RiverA
1618577004−76.4726138.46579Long Beach, Chesapeake BayA
162 *8577188−76.3964038.39340Cove PointA
163 **8577330−76.4516738.31667Solomons Island, Patuxent RiverA
164 **8579542−76.6833338.65500Lower Marlboro, Patuxent RiverA
165 **8579997−76.9392338.93240Bladensburg, Anacostia RiverA
166 **8594900−77.0216738.87333Washington, Potomac RiverA
167 **8630308−75.4051637.90701Chincoteague Channel, South EndA
1688632200−75.9884437.16519Kiptopeke, Chesapeake BayA
169 *8632366−76.0245037.26330Cape Charles Harbor (U.S.C.G.)A
1708632837−76.0150037.53830Rappahannock LightA
171 **8632869−75.9167037.55670Gaskins Pt., Occohannock CreekA
1728633532−75.9928837.82926Tangier Island, Chesapeake BayA
1738635150−76.9600038.25170Colonial Beach, Potomac RiverA
174 **8635257−77.2429738.21330Rappahannock BendA
175 **8635750−76.4644437.99590Lewisetta, Potomac RiverA
176 **8635985−76.7833037.87330Wares Wharf, Rappahannock RA
177 *8636580−76.2900037.61442Windmill Point, Rappahannock RA
178 **8636653−76.9899637.58327Lester ManorA
179 *8637289−76.2733037.34670New PointA
1808637590−76.2217037.25670New Point, Comfort ShoalA
181 **8637624−76.5000037.24670Gloucester Point, York RiverA
182 **8637689−76.4783337.22667Yorktown U.S.C.G. Training CenterA
183 **8638339−76.3991136.82322Western BranchA
184 **8638421−76.6683037.05670Burwell Bay, James RiverA
185 **8638424−76.6633037.22000Kingsmill, James RiverA
186 **8638433−76.7833037.18500Scotland, James RiverA
187 **8638445−76.9117037.40330Lanexa, Chicahominy RiverA
188 **8638450−76.9433037.23988Tettington, James RiverA
189 **8638489−77.3733837.26686Puddledock, Appomattox RiverA
190 **8638495−77.4206037.52451Richmond River Locks, James RiverA
191 *8638610−76.3300036.94667Sewells Point, Hampton RoadsA
192 **8638660−76.2920236.82168Norfolk Naval ShipyardA
1938638863−76.1133336.96667Chesapeake Bay Bridge TunnelA
1948639207−75.9698436.83180Inside Channel, Rudee InletA
195 **8639348−76.3017236.77804Money Point, S. Br. Elizabeth RiverA
1968651370−75.7466936.18331Duck, Frf PierA
197 **8652247−75.7689035.90370Manns Harbor, Croatan SoundA
198 **8652437−75.6564535.84482Oyster Creek, Croatan SoundA
199 **8652547−75.7000035.81170Roanoke Marshes Light, Croatan SA
200 **8652587−75.5493635.79429Oregon Inlet Marina, Pamlico SA
2018654400−75.6350035.22330Cape Hatteras Fishing PierA
202 **8654467−75.7041735.20950U.S.C.G. Hatteras, Pamlico SA
203 **8654792−75.9894535.11564Ocracoke IslandA
204 **8655875−76.3433034.87500Sea Level, Core SoundA
205 **8656483−76.6700034.72000Beaufort, Duke Marine LabA
2068656590−76.7117034.69330Atlantic Beach Triple S PierA
207 **8658120−77.9533034.22670Wilmington, Cape Fear RiverA
2088658163−77.7856634.21330Wrightsville BeachA
209 **8659084−78.0183033.91500SouthportA
2108659182−78.0817033.90170Oak Island, Atlantic OceanA
211 *8659897−78.5067033.86500Sunset Beach Pier, Atlantic OceanA
2128661070−78.9183033.65500Springmaid Pier, Atlantic OceanA
213 **8664022−79.9213833.00880Gen. Dynamics Pier, Cooper R.A
214 **8664545−79.8300032.92670Cainhoy, Wando RiverA
215 **8664941−79.7067032.85670South Capers Island, Capers CreekA
216 **8665099−80.0217032.83670I-526 Bridge, Ashley RiverA
217 **8665530−79.9237832.78170Charleston, Cooper River EntranceA
218 **8667633−80.7841032.50250Clarendon Plantation, Whale Br.A
219 **8668498−80.4650032.34000Hunting Island Pier, Fripps InletA
2208668918−80.7367032.26670Ribaut Island, Skull CreekA
221 **8670870−80.9017032.03373Fort Pulaski, Savannah RiverA
222 **8677344−81.3967031.13170St Simons LighthouseA
223 **8679511−81.5132330.79781Kings BayA
224 **8679758−81.4717030.76330Dungeness, Seacamp DockA
225 **8679964−81.5483030.72000St. Marys, St. Marys RiverA
226 **8720011−81.4650030.70830Cut 1N, St Marys River EntrA
2278720012−81.3017030.71670Cut 2N, St Marys River EntrA
228 **8720030−81.4653930.67171Fernandina Beach, Amelia RiverA
229 **8720051−81.5233030.64330Lanceford Creek, LoftonA
230 **8720098−81.5150030.56830Nassauville, Nassau River EastA
231 **8720211−81.4133030.40000Mayport (Naval Sta.) St Johns RA
232 **8720218−81.4300030.39670Bar Pilots Dock, St Johns RiverA
233 **8720219−81.5583030.38670Dames Point, St. Johns RiverA
234 **8720220−81.4317030.39330Mayport (Ferry) Saint Johns RA
235 **8720225−81.6340830.38337Phoenix ParkA
236 **8720242−81.6200030.36000Longbranch, St Johns RiverA
237 *8720291−81.3867030.28330Jacksonville BeachA
238 **8720357−81.6916430.19170I-295 Bridge, West End, St Johns RA
239 **8720503−81.6283029.97830Red Bay Point, St Johns RiverA
240 **8720554−81.3000029.91670Vilano Beach (ICWW)A
241 **8720582−81.3067029.86670State Road 312, Matanzas RiverA
2428720587−81.2633029.85670St. Augustine Beach, AtlanticA
243 **8720625−81.5483229.80165Racy Point, St Johns RiverA
244 **8720651−81.2583029.76830Crescent Beach, Matanzas RiverA
245 **8720692−81.2278629.70453State Road A1A BridgeA
246 **8720757−81.2050029.61500Bings Landing, Matanzas RiverA
247 **8720767−81.6817029.59500Buffalo Bluff, St. Johns RiverA
248 **8720774−81.6317029.64328Palatka, St. Johns RiverA
249 **8720832−81.6752029.47675Welaka, St. Johns RiverA
250 *8721020−81.0050029.22830Daytona Beach (Ocean)A
251 **8721604−80.5935028.41580Trident Pier, Port CanaveralA
252 **8721608−80.6015228.40871Canaveral Harbor EntranceA
253 **8722125−80.3717027.63170Vero Beach, Indian RiverA
254 **8722208−80.3250027.47170North Beach Causeway, Indian RA
255 **8722548−80.0667026.84330Pga Boulevard Bridge, Palm BeachA
256 **8722588−80.0509626.77000Port Of W. Palm Beach, Lake WorthA
257 **8722669−80.0467026.61330Lake Worth (ICWW)A
2588722670−80.0333026.61170Lake Worth Pier, Atlantic OceanA
259 *8723080−80.1200025.90330Haulover Pier, N. Miami BeachA
2608723170−80.1315425.76830Miami Beach (City Pier)A
2618723178−80.1300025.76330Miami Beach, Government CutA
2628723214−80.1618025.73140Virginia Key, Biscayne BayA
263 *8723962−81.0167024.71830Key Colony BeachG
264 *8723970−81.1050024.71170Vaca Key, Florida BayG
265 *8724580−81.8079024.55570Key WestG
2668724635−81.8783024.45330Sand Key LighthouseG
2678724671−81.9215324.71828Smith Shoal Light, FlG
2688724698−82.9200024.63170Loggerhead Key, Dry TortugasG
269 *8725110−81.8075026.13170Naples, Gulf Of MexicoG
270 **8725520−81.8712026.64770Fort Myers, Caloosahatchee RiverG
2718726347−82.7600027.60170Egmont Key, Tampa BayG
2728726364−82.7267027.61500Mullet Key, Tampa BayG
2738726384−82.5621027.63870Port Manatee, Tampa BayG
2748726520−82.6269027.76060St. Petersburg, Tampa BayG
275 *8726607−82.5537627.85778Port Tampa, Old Tampa BayG
276 **8726667−82.4250027.91333Csx Rockport, Mckay Bay EntranceG
2778726724−82.8317027.97830Clearwater Beach, Gulf Of MexicoG
278 **8726738−82.6850027.98830Safety Harbor, Old Tampa BayG
279 **8727235−82.6383028.69170Johns Island, Chassahowitzka BayG
280 **8727274−82.6383028.76170Mason Creek, Homosassa BayG
281 **8727277−82.6954028.77170Tuckers Island, Homosassa RiverG
282 **8727293−82.6033028.80063Halls River Bridge, Halls RiverG
283 **8727306−82.6583028.82500OzelloG
284 **8727328−82.6667028.86330Ozello NorthG
2858727333−82.7233028.87000Mangrove Point, Crystal BayG
286 **8727336−82.6350028.88170Dixie BayG
287 **8727348−82.6382928.90505Twin Rivers Marina, Crystal RiverG
288 **8727359−82.6917028.92330Shell Island, Crystal RiverG
2898727520−83.0317029.13500Cedar Key, Gulf Of MexicoG
290 *8728229−84.2900030.05870Shell Point, Walker CreekG
291 *8728360−84.5117029.91500Turkey PointG
292 **8728690−84.9813829.72670Apalachicola, Apalachicola RiverG
293 **8729108−85.6669430.15228Panama City, St. Andrew BayG
2948729210−85.8783030.21330Panama City Beach, Gulf Of MexicoG
295 **8729501−86.4933030.50330Valpariso, Boggy BayouG
2968729678−86.8650030.37670Navarre BeachG
297 **8729905−87.3567030.41860Millview, Perdido BayG
298 **8729941−87.4288130.38694Blue Angels Park, Perdido BayG
299 **8731439−87.6842830.27982Gulf Shores, IcwwG
300 *8733821−87.9345330.48664Point Clear, Mobile BayG
3018735180−88.0750030.25000Dauphin Island, Mobile BayG
302 **8735391−88.0880030.56517SH 163 Bridge, Dog RiverG
303 **8737048−88.0401030.70830Mobile State Docks, Mobile RiverG
3048741196−88.5333030.34000Pascagoula Point, Miss. SoundG
305 *8742221−88.6667030.23830Horn Island, Mississippi SoundG
306 **8743281−88.7983030.39170Ocean SpringsG
307 **8744117−88.9033030.41175Biloxi, Bay Of BiloxiG
3088745557−89.0817030.36000Gulfport Harbor, Mississippi SoundG
3098747437−89.3257830.32639Bay Waveland Yacht, Bay St. LouisG
3108747766−89.3667030.28170Waveland, Mississippi SoundG
3118760417−89.0444729.20075Devon Energy Facility, North PassG
3128760551−89.1400028.99000South PassG
3138760721−89.2583029.17830PilottownG
3148760849−89.3512029.27330Venice, Grand PassG
3158760922−89.4075028.93220Pilot Station East, SW PassG
3168760943−89.4183028.92500Pilot Station, SW PassG
317 *8761305−89.6732529.86811Shell Beach, Lake BorgneG
318 *8761529−89.8350029.94500Martello Castle, Lake BorgneG
3198761819−90.0383029.40170Texaco Dock, Hackberry BayG
320 *8761927−90.1134230.02717U.S.C.G. New Canal, Lake Pont.G
321 **8762075−90.2086029.11430Port Fourchon, Belle PassG
3228763535−90.9760029.17390Texas Gas Platform, Caillou BayG
323 **8764025−91.2300029.74330Stouts Pass At Six Mile LakeG
324 **8764044−91.2375029.66750Berwick, Atchafalaya River, LaG
3258764227−91.3381029.45500Lawma, Amerada PassG
3268764311−91.3850029.37170Eugene IslandG
3278765251−91.8800029.71336Cypremort PointG
328 *8767816−93.2216730.22364Lake Charles, Calcasieu RiverG
3298767961−93.3006930.19031Bulk Terminal #1G
3308768094−93.3428929.76817Calcasieu Pass, East JettyG
331 **8770475−93.9313029.86670Port Arthur, Sabine Naches CanalG
332 **8770520−93.8817029.98000Rainbow Bridge, Neches RiverG
333 **8770539−93.8950029.76670Mesquite PointG
334 **8770559−94.6904029.71330Round Point, Trinity BayG
335 **8770570−93.8701029.72840Sabine Pass NorthG
336 **8770597−93.7217030.09830Orange (Old Navy Base)G
337 **8770613−94.9850029.68170Morgans Point, Barbours CutG
338 **8770625−94.8683029.68000Umbrella Point, Trinity BayG
339 **8770733−95.0783029.76500Lynchburg Landing, San Jacinto RG
340 **8770743−95.0900029.75670Battleship Texas, Houston Ship ChG
341 **8770777−95.2658029.72580Manchester, Houston Ship ChG
3428770822−93.8369429.67806Texas Point, Sabine PassG
343 **8770933−95.0667029.56330Clear LakeG
344 **8770971−94.5133029.51500Rollover PassG
345 **8771013−94.9183029.48000Eagle Point, Galveston BayG
3468771081−93.6400029.49830Sabine OffshoreG
347 **8771328−94.7800029.36500Port Bolivar, Bolivar RoadsG
3488771341−94.7248329.35733Galveston Bay Ent North JettyG
349 **8771450−94.7933029.31000Galveston Pier 21G
3508771510−94.7894029.28530Galveston Pleasure Pier, GoMexG
351 **8772440−95.3083028.94830Freeport, Dow Barge CanalG
352 **8772447−95.3025028.94310U.S.C.G. Freeport, Entr ChannelG
353 **8773037−96.7117028.40800Seadrift, San Antonio BayG
354 **8773259−96.5950028.64000Port Lavaca, Lavaca CausewayG
355 **8773701−96.3883028.45170Port O’Connor, Matagorda BayG
356 **8774513−97.0217028.11830Copano Bay State Fishing PierG
357 **8774770−97.0467028.02170Rockport, Aransas BayG
358 **8775188−97.4750027.85830White Point BayG
359 **8775237−97.0733027.83890Port AransasG
3608775270−97.0500027.82670Port Aransas, H. Caldwell PierG
361 **8775283−97.2033027.82130Port Ingleside, Corpus Christi BayG
362 **8775296−97.3900027.81170Texas State Aquarium, CorpusG
363 **8775421−97.2800027.70500Corpus Christi Naval Air StationG
364 **8775792−97.2367027.63330Packery ChannelG
3658775870−97.2167027.58000Corpus Christi, Gulf Of MexicoG
366 **8779748−97.1767026.07670South Padre Island (U.S.C.G)G
3678779750−97.1567026.06830Padre Island, Brazos Santiago PassG
368 **8779770−97.2150026.06000Port Isabel, Laguna MadreG
3699500966−97.7805022.26200Madero, Tampico Harbor, MexicoG
3709650593−87.8700015.89300Puerto CortesC
3719710441−78.9970026.71000Settlement Point, Grand BahamasC
3729751309−64.7210018.36800Leinster Point (Bay), St. JohnC
373 *9751364−64.7050017.75000Christiansted, St. Croix IslandC
374 **9751373−64.7148018.34560St John’S Island, Coral HarborC
375 **9751381−64.7240018.31800Lameshur Bay, St. JohnC
3769751401−64.7541017.69500Lime Tree Bay, St CroixC
3779751467−64.8040018.36090Lovango Cay, St JohnC
3789751494−64.8180018.29700Dog Island, St ThomasC
379 **9751567−64.8690518.31870Benner BayC
3809751583−64.8640018.34870Water Bay, Saint ThomasC
381 *9751584−64.8840017.71300Fredericksted, St. Croix IslandC
382 **9751639−64.9203018.33570Charlotte Amalie, St. ThomasC
383 *9751768−64.9627018.37110Ruy Point, St ThomasC
384 *9751774−65.0350018.36300Botany Bay, St ThomasC
3859752235−65.3020018.30100CulebraC
3869752619−65.4440018.15300Isabel Segunda, Vieques IslandC
387 *9752695−65.4710018.09395Esperanza, Vieques IslandC
3889752962−65.5700018.34500Isla PalominosC
389 *9753216−65.6310018.33500Playa De FajardoC
390 *9753641−65.7110218.18700NaguaboC
391 *9754228−65.8330018.05500Yabucoa HarborC
392 **9755371−66.1160018.45900San Juan, La Puntilla, San Juan BayC
3939755679−66.1580017.92800Las MareasC
394 *9756639−66.4070017.95390Santa IsabelC
3959757809−66.7021018.48140Arecibo, Puerto RicoC
3969758053−66.7620017.97300Penuelas, Punta GuayanillaC
397 **9759110−67.0460317.97000Magueyes IslandC
398 **9759189−67.1890018.07500Puerto RealC
399 **9759197−67.1970017.95100Bahia SalinasC
400 *9759394−67.1608018.21790Mayaguez, Puerto RicoC
4019759412−67.1650018.45700Aguadilla, Crashboat BeachC
4029759421−67.1853018.16500Punta Guanajabo, MayaguesC
4039759938−67.9390018.09000Mona IslandC
404 *9761115−61.8210017.59040BarbudaC
405IHO−66.0500045.23330Partridge IslandA
406IHO−67.0499945.06667St AndrewsA
407IHO−66.8666745.04583Back BayA
408IHO−65.0666545.05000MargretsvilleA
409IHO−67.0171144.96622FairhavenA
410IHO−66.9833344.90000EastportA
411IHO−66.9535444.88334WelshpoolA
412IHO−62.7589644.77344Murphy CoveA
413 **IHO−66.7501044.76557North HeadA
414IHO−65.8333444.66667Deep CoveA
415IHO−63.5671244.64378HalifaxA
416IHO−66.7999944.60000Outer Wood IslandA
417IHO−63.9500144.49900Indian HarbourA
418 **IHO−66.1000144.46390Sandy CoveA
419 **IHO−68.2000144.40000Bar HarbourA
420IHO−68.0166644.40000Prospect HarbourA
421IHO−66.3999944.25000Lighthouse CoveA
422IHO−66.1666644.20000MeteghanA
423IHO−68.8833344.14642Pulpit HarbourA
424IHO−64.6621043.98320LiverpoolA
425IHO−65.1042043.66480LockeportA
426 **IHO−70.2466743.65667PortlandA
427IHO−65.7429043.52580Woods HarbourA
428IHO−66.0000043.50000Flat IslandA
429IHO−66.0000043.48333Seal IslandA
430 **IHO−70.7416743.08000Portsmouth (Navy Yard)A
431IHO−63.2000142.81667Fundy 1A/D
432IHO−63.9833442.78333SB2A/D
433IHO−64.3666742.61666Fundy 21A/D
434IHO−67.7166742.46667Fundy 6A/D
435 **IHO−71.0332642.35078Boston (Commonwealth Piers)A
436IHO−65.5000042.11666Fundy 22aA/D
437IHO−65.6333342.05000Fundy 22bA/D
438 **IHO−71.3969441.80080ProvidenceA
439 *IHO−70.5000041.77482E Cape Cod CanalA
440 **IHO−70.6166741.74072WCape Cod CanalA
441 **IHO−70.6251241.73333Buzzards BayA
442IHO−65.7999941.73333Fundy 3A/D
443 *IHO−70.8999941.60000New BedfordA
444IHO−71.3333441.50000NewportA
445IHO−70.6714341.52422Woods Hole (Ocean Inst)A
446 **IHO−72.0990041.34903New LondonA
447IHO−72.3500141.26667Connecticut River EntA
448 *IHO−73.1666641.16667BridgeportA
449IHO−72.2000141.16521Plum IslandA
450 *IHO−71.9666741.05000montaukA
451 **IHO−73.0672840.95027Port JeffersonA
452 *IHO−73.7833340.80000Willets PointA
453 **IHO−73.8500640.78285College PointA
454IHO−66.8333440.73333Fundy 4A/D
455 **IHO−73.2328040.71533Bayshore Long IslandA
456 **IHO−74.0166640.70000New York: BatteryA
457 **IHO−74.0166640.68333New York: Governor’s IslandA
458IHO−74.0333340.60000New York: Fort HamiltonA
459IHO−74.0166640.46833Sandy HookA
460IHO−67.7500040.36666Fundy 23A/D
461IHO−70.8999940.30000IAPSO: 30-1.2.32A/D
462IHO−68.6333340.11667IAPSO: 30-1.2.1A/D
463 **IHO−75.1333339.95000PhiladelphiaA
464IHO−71.3833339.95000IAPSO: 30-1.2.2A/D
465 **IHO−75.5833439.58333Delaware CityA
466 **IHO−75.5666539.55000Reedy PointA
467 **IHO−75.8166539.53140Chesapeake CityA
468 **IHO−75.8833339.51667Court House PointA
469 **IHO−75.9841939.43576Elk River EntranceA
470IHO−76.2666639.28333Pooles Island LightA
471 **IHO−76.5807039.26940BaltimoreA
472IHO−72.1666639.21667IAPSO: 30-1.2.17A/D
473IHO−71.3666739.16667IAPSO: 30-1.2.19A/D
474IHO−76.4166639.15000Seven Foot Knoll LightA
475IHO−76.3022139.04201Love Point LightA
476 **IHO−76.4819138.98550AnnapolisA
477 *IHO−74.9600038.96833Cape May Ferry TerminalA
478IHO−76.4333538.90000Thomas Point Shoal LightA
479 **IHO−77.0172538.86094Washington D.C.A
480 **IHO−75.1022038.78790Breakwater HarbourA
481 **IHO−75.0704538.60092Indian River InletA
482 **IHO−76.0634138.57254CambridgeA
483 **IHO−76.4500138.31667Solomons IslandA
484 **IHO−76.4166638.31667Drum Point LightA
485IHO−76.9500138.25000Colonial BeachA
486IHO−76.7500038.21667Colton PointA
487IHO−76.5333338.13334Piney PointA
488IHO−76.1000138.06667Holland Island Bar LightA
489IHO−76.2666637.80000Great Wicomico LightA
490IHO−76.2666637.56667Stingray Point LightA
491IHO−73.0833437.36666IAPSO: 30-1.2.16A/D
492 **IHO−77.2666637.31667City Point HopewellA
493 **IHO−76.0244937.26667Cape CharlesA
494 **IHO−76.4988237.24811Gloucester PointA
495IHO−76.2999937.00000Old Point ComfortA
496 **IHO−76.3333436.95000Hampton Roads (Sewall Pt.)A
497IHO−75.9666736.83333Virginia BeachA
498IHO−75.5000035.33333AvonA
499 *IHO−76.6833534.71667Morehead CityA
500 **IHO−77.9500134.23333WilmingtonA
501 *IHO−78.0166733.91500SouthportA
502IHO−78.8999933.66667Myrtle BeachA
503 **IHO−79.9166632.78333CharlestonA
504IHO−75.6166732.68333IAPSO: 30-1.2.3A/D
505IHO−64.6499932.36666St. Davids IslandA
506 **IHO−80.7827932.31757Port Royal SoundA
507IHO−64.8333432.31667Ireland IslandA
508 **IHO−80.8999532.03360Savannah River EntranceA
509IHO−64.4333532.01667IAPSO: 30-1.2.18A/D
510 **IHO−81.2005031.53659Sapelo SoundA
511 **IHO−88.0401030.70830MobileG
512IHO−76.4166630.43333IAPSO: 30-1.2.11A/D
513 **IHO−88.9033030.41175BiloxiG
514 **IHO−87.2166730.40000PensacolaG
515 *IHO−81.4325930.39928MayportA
516 **IHO−87.2642830.34872Warrington Navy YardG
517 **IHO−81.6166730.35000Jacksonville Dredger Dept.A
518IHO−90.2999930.29805Pass Nanchac LightG
519IHO−89.3333430.30000Bay St LouisG
520IHO−89.1666630.23333Cat IslandG
521 **IHO−88.0166630.23333Mobile Point LightG
522 **IHO−85.7473630.16939Alligator BayouG
523IHO−84.1833530.06667St Marks LightG
524IHO−90.1166730.02376West EndG
525 **IHO−90.0680329.91999New OrleansG
526IHO−93.3473629.78333Calcasieu Pass LightG
527 **IHO−94.6904029.71333Round PointG
528IHO−84.9833429.71667ApalachicolaG
529IHO−93.8500129.70000SabineG
530 **IHO−94.9833429.68333Morgan PointG
531 *IHO−94.4903829.51828GilchristG
532IHO−92.0349229.57862Lighthouse PointG
533 **IHO−91.5499929.51667Point ChevreuilG
534IHO−91.7671029.48820South PointG
535IHO−89.1666629.48333Breton IslandG
536 **IHO−91.2707729.51204Shell IslandG
537IHO−91.5973429.50966Rabbit Island PassG
538IHO−91.3850029.37170Eugene IslandG
539 **IHO−89.3333429.36667Jack BayG
540IHO−94.7000129.33333Galveston Bay EntranceG
541IHO−91.7500029.28667Point au FerG
542 **IHO−94.7833329.31667GalvestonG
543 **IHO−89.9666729.26667Bayou RigaudG
544IHO−89.6000129.25000Empire JettyG
545IHO−81.0000029.23333Daytona BeachA
546 **IHO−95.0000029.21667Carancahua ReefG
547IHO−89.0499929.21667Lonesome BayouG
548 **IHO−81.0000029.21667Daytona BeachA
549IHO−83.0316729.13333Cedar KayG
550IHO−89.0333329.11667Southeast PassG
551IHO−89.2666629.05000Joseph BayouG
552IHO−89.1666629.01667Port EadsG
553IHO−89.1333328.98333South PassG
554IHO−95.2999928.93333FreeportG
555IHO−89.4283328.93167Southwest PassG
556 *IHO−82.6687428.45132Indian BayG
557IHO−76.7999928.45000IAPSO: 30-1.2.15A/D
558IHO−67.5333328.23333IAPSO: 30-1.2.5A/D
559IHO−69.7500028.13333IAPSO: 30-1.2.4A/D
560 **IHO−97.0499928.01667RockportG
561IHO−76.7833328.01667IAPSO: 30-1.2.14A/D
562IHO−69.6666627.98333IAPSO: 30-1.2.8A/D
563IHO−69.6666627.96667IAPSO: 30-1.2.7A/D
564 **IHO−97.3999927.81493Nueces BayG
565IHO−82.6166727.76667St PetersburgG
566 *IHO−82.7329527.53391Anna MariaG
567 **IHO−82.2500026.71667South Boca GrandeG
568IHO−84.2500026.70000IAPSO: 30-1.2.13G/D
569 **IHO−81.8666726.65000Fort MyersG
570 **IHO−82.0666526.63333Matlacha PassG
571 **IHO−82.0808126.55000Tropical HomesitesG
572 **IHO−82.1833526.51667Captiva IslandG
573 **IHO−82.0833426.48333St James CityG
574 **IHO−82.0166626.48333Punta RassaG
575IHO−69.3333426.46667IAPSO: 30-1.2.13A/D
576 **IHO−81.9500126.45511Matanzas PassG
577 **IHO−81.9333526.45000Hurricane Bay San CarlosG
578IHO−69.3166526.45000IAPSO: 30-1.2.9A/D
579 **IHO−81.9095126.43333Estero Island Estero BayG
580 **IHO−81.8593826.43120Mound Key Estero BayG
581 **IHO−81.8924826.41690Ostego BayG
582 **IHO−81.8832426.40748Carlos Point Estero BayG
583 **IHO−97.3500126.35000North PointG
584 **IHO−97.2150026.06000Port IsabelG
585IHO−97.1499926.06667South Padre IslandG
586IHO−79.8999925.85000IAPSO: 30-1.2.12A/D
587IHO−79.2833325.55000Cat CayA
588IHO−77.3500125.08333NassauA
589IHO−77.9620825.04691Anros IslandA
590IHO−76.1500024.76667EleutheraA
591IHO−89.6499924.76667IAPSO: 30-1.2.6G/D
592IHO−80.9333524.76667Grassy KeyA
593 **IHO−81.0166624.71667Marathon ShoresA
594IHO−82.8833324.63333TortugasG
595IHO−81.7999424.54559Key WestG
596IHO−75.9663123.66719Steventon Great ExumaA
597IHO−82.3333423.17150HabanaG
598IHO−74.9500123.00000Long IslandA
599IHO−73.0499922.33333Start Point MayaguanaA
600IHO−97.7699022.25000TampicoG
601IHO−74.2999922.16667Datum BayA
602IHO−79.9790821.72682CasildaC
603IHO−82.9167721.44490CarapachibeyC
604IHO−71.1499921.43333Grand TurkA
605IHO−89.6500021.30000ProgresoG
606IHO−76.1086021.11580GibaraA
607IHO−74.4938020.36023BaracoaA
608IHO−75.1499919.89300Guantanamo BayC
609IHO−90.5531019.85580CampecheG
610IHO−70.6591019.78300Puerto PlataA
611 **IHO−69.3166519.19590SamanaA
612IHO−96.1116019.18333Vera CruzG
613 **IHO−64.3833318.72501AnegadaA
614IHO−72.3538418.55022Port au PrinceC
615 **IHO−69.8833318.46527Ciudad TrujilloC
616 **IHO−66.1160018.45900San JuanA
617 **IHO−64.6166718.42723TortolaC
618 **IHO−68.9500118.41036La RomanaC
619 *IHO−64.9333518.33333St ThomasC
620IHO−65.2833318.30000Great HarborC
621IHO−78.1333318.20000Savanna la MarC
622IHO−94.4166618.15805CoatzacoalcosG
623 **IHO−67.0460317.97000Magueyes IslandC
624 **IHO−61.8511117.12284St JohnsC
625IHO−64.8833316.53333IAPSO: 30-1.3.2C/D
626IHO−64.9166616.50000IAPSO: 30-1.3.1C/D
627 **IHO−61.5000016.38333Petit CanalC
628 *IHO−61.6994316.33476Sainte RoseC
629IHO−61.2666616.25000Saint FrancoisC
630IHO−61.5370216.23290Pointe a PitreC
631IHO−87.9500115.83333Puerto CortesC
632 *IHO−61.4666715.56667PortsmouthC
633IHO−61.0499914.58333Fort de FranceC
634IHO−83.3666714.01667Puerto CabezasC
635IHO−61.0011014.02240CastriesC
636IHO−61.2333413.13333Kingstown St VincentC
637 **IHO−59.6145413.08616Carlisle BayA
638IHO−61.1833512.83333Mustique Grand BayC
639IHO−61.3333412.70329Charlestown BayC
640IHO−61.3500112.63333Tobago CaysC
641IHO−70.0529012.60000Aruba Malmok BayC
642IHO−61.4177812.59252Clifton HarbourC
643IHO−70.0355412.51347Aruba OranjestadC
644IHO−61.4570912.48783Hillsborough BayC
645IHO−68.9333512.10000Curacao WillemstadC
646 *IHO−61.7565212.05000St GeorgesC
647IHO−68.6499912.00000Klein Curacao n.w. CoastC
648 *IHO−70.2166711.75000AmuayC
649 *IHO−60.7336011.16920ScarboroughA
650IHO−71.6465111.02353ZaparitaC
651IHO−71.5833411.00000MaleconC
652IHO−71.5666510.96667Zapara IslandC
653IHO−71.6166710.88333TablazoC
654IHO−60.9333510.83689TocoA
655IHO−71.6333310.81667Punta PalmasC
656 **IHO−61.6000110.68333Carenage BayC
657IHO−61.6499910.66667Gaspar GrandeC
658 *IHO−61.5169210.64955Port of SpainC
659IHO−66.9333510.61667La GuairaC
660IHO−62.0833410.61667Puerto de HierroC
661IHO−64.2047010.45000CumanaC
662IHO−61.0193210.40000Nariva RiverA
663IHO−75.5764010.38333CartagenaC
664IHO−61.4833410.36667Point LisasC
665IHO−61.7000110.18333Point FortinC
666 **IHO−62.6431010.12410Punta GordaC
667 *IHO−61.0166610.15000Guayaguayare BayA
668 *IHO−61.6499910.06667Erin BayC
669IHO−62.2000110.01667Rio PedernalesC
670IHO−83.0333310.00267Puerto LimonC
671IHO−79.916669.36667ColonC
672IHO−79.916669.35000Cristobal (Canal Zone)C
673 **IHO−59.799998.41667Waini PointA
674 **IHO−58.250006.95000Bluejacket BeaconA
675 **IHO−58.049996.95000Demerara BeaconA
676 **IHO−58.416666.86667ParikaA
677 *IHO−58.166666.83333GeorgetownA
678 **IHO−57.950016.78333BelfieldA
679 **IHO−58.616676.40000BarticaA
680 *IHO−57.016665.96667Nickerie River MouthA
681 **IHO−55.216675.98630Surinam River Entrance LightA
* Station is approximated by nearest neighbor for harmonic extraction since it is not within the actual bounds of the EC2001 model domain but is near the edge of the domain; ** Station is not included in EC2001 error measures or scatter plots as it is not physically within the EC2001 model domain and is far removed from the domain.

Appendix B

Scatter plots for the 10 stations shown by a black X in Figure 5 and Figure 6 are provided herein. Both the EC2015 Manning’s n and VDatum friction models are compared to the EC2001 model. Note that other than the Pilottown, LA station (313) and Curacoa, Willemstad (645) stations, the different friction formulations generally create more of a difference in the amplitude response than they do in the phase response. Plots are grouped according to region.
Figure B1. Scatterplots of computed versus measured harmonic data for representative stations along the Atlantic coast.
Figure B1. Scatterplots of computed versus measured harmonic data for representative stations along the Atlantic coast.
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Figure B2. Scatterplots of computed versus measured harmonic data for representative stations along the Florida coast.
Figure B2. Scatterplots of computed versus measured harmonic data for representative stations along the Florida coast.
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Figure B3. Scatterplots of computed versus measured harmonic data for representative stations along the Gulf of Mexico coast.
Figure B3. Scatterplots of computed versus measured harmonic data for representative stations along the Gulf of Mexico coast.
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Figure B4. Scatterplots of computed versus measured harmonic data for representative stations in the Caribbean Sea.
Figure B4. Scatterplots of computed versus measured harmonic data for representative stations in the Caribbean Sea.
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Figure B5. Scatterplots of computed versus measured harmonic data for representative deep IHO stations.
Figure B5. Scatterplots of computed versus measured harmonic data for representative deep IHO stations.
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Appendix C

The actual geographic distribution of errors for the K1 and M2 constituents are provided at all 681 validation stations in the following seven figures. Although the same regional views given in Figure 5 and Figure 6 are used herein, only the dominant constituent is shown in each subregion: Gulf of Maine, Atlantic Coast and Florida Coast—M2, Gulf of Mexico and Caribbean Sea—K1. Symbol shapes denote the magnitude of the errors while the colors represent whether the EC2015 model is over (red) or underestimating (blue) the amplitudes. Similarly, blue symbols denote locations where the model exhibits a phase lag while red symbols denote a phase lead.
Figure C1. Distribution of relative amplitude and absolute phase errors for the K1 constituent: global view.
Figure C1. Distribution of relative amplitude and absolute phase errors for the K1 constituent: global view.
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Figure C2. Distribution of relative amplitude and absolute phase errors for the K1 constituent: Gulf of Mexico.
Figure C2. Distribution of relative amplitude and absolute phase errors for the K1 constituent: Gulf of Mexico.
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Figure C3. Distribution of relative amplitude and absolute phase errors for the K1 constituent: Caribbean Sea.
Figure C3. Distribution of relative amplitude and absolute phase errors for the K1 constituent: Caribbean Sea.
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Figure C4. Distribution of relative amplitude and absolute phase errors for the M2 constituent: global view.
Figure C4. Distribution of relative amplitude and absolute phase errors for the M2 constituent: global view.
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Figure C5. Distribution of relative amplitude and absolute phase errors for the M2 constituent: Gulf of Maine and New York Bight.
Figure C5. Distribution of relative amplitude and absolute phase errors for the M2 constituent: Gulf of Maine and New York Bight.
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Figure C6. Distribution of relative amplitude and absolute phase errors for the M2 constituent: Atlantic coast from Delaware to Georgia.
Figure C6. Distribution of relative amplitude and absolute phase errors for the M2 constituent: Atlantic coast from Delaware to Georgia.
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Figure C7. Distribution of relative amplitude and absolute phase errors for the M2 constituent: Florida coast.
Figure C7. Distribution of relative amplitude and absolute phase errors for the M2 constituent: Florida coast.
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Appendix D

Herein we provide general applicability and usage guidelines for the EC205 tidal database. It is recommended that users read through these sections to understand the limitations of the database before they apply it to their own regions of interest.

Appendix D.1. Applicability Guidelines for the EC2015 Tidal Database

The EC2015 tidal database provides elevation amplitudes and phases throughout the WNAT domain for all 37 constituents frequently used by NOS. Although data for all 37 constituents are included in the database, care should be taken when deciding how many of these constituents are important for the user’s intended application. Often, accurate results can be obtained when using only the primary astronomic tides, particularly if the boundary of interest is in deeper water, far removed from the coastline.
This database does not provide information regarding responses associated with density effects, riverine driven circulation, wind and atmospheric pressure driven events and/or oceanic currents. Vertical and horizontal variations in density can set up steric level differences in sea surface elevation, can drive significant horizontal circulation patterns, and can cause variation in the vertical structure of the currents. These effects tend to be important in estuarine or delta systems with significant freshwater riverine inflows. Furthermore the seasonal heating of the upper layers of the ocean’s surface directly drives the expansion in the upper layer water volume that is associated with a seasonal fluctuation of water level. This can be especially significant in the Gulf of Mexico and the Caribbean Sea. It is noted that published tidal constituent data includes these seasonal sea surface expansions as long-term tidal constituents such as the Sa Solar annual and the Ssa Solar semiannual constituents. From a tidal hydrodynamics perspective these long-term constituents (with periods of a year and half a year respectively) are of astronomical origin and should appear as weak tides. They may also be generated through nonlinear interactions that lead to extremely weak responses. Nonetheless, in harmonically-decomposed measured field data, these constituents can appear as significant constituents since the driving radiational heating process is also an annual event. In the Gulf of Mexico, the Sa and Ssa elevation constituents can be almost as large as the dominant diurnal tides while current responses are much smaller due to the long-term period associated with these constituents. Thus it is emphasized that the EC2015 computations are entirely barotropic and do not include any of these density effects.
Rivers were not included in the EC2015 tidal database calculations. The barotropic pressure gradient and mass input effects of the river will be important in the immediate vicinity of the river outlet and will diminish away from the river outlet. Wind driven and/or atmospheric pressure driven effects such as coastal setup and storm surge and any basinwide modes that may be set up by these processes are also not included in the database. These effects can be significant on the shelf as well as within bays and estuaries. Major oceanic circulation patterns such as the Gulf Stream and the associated loop currents and other eddies, which are shed from it, are not included in the database. These currents tend to reside off the shelf in deep ocean waters but can be associated with fast flows in the 1 to 2 m/s range.
Finally the local accuracy of the EC2015 tidal computations will be affected by the accuracy of the geometry and bathymetry locally defined in the WNAT-based EC2015 grid. Geometric and bathymetric inaccuracies in the grid will especially affect the accuracy of the currents. Obviously a missing estuary or island or inaccurate bathymetry will greatly influence the database computations.

Appendix D.2. Usage Guidelines for the EC2015 Tidal Database

The EC2015 tidal constituent database can be applied anywhere within the defined WNAT domain. However, the prevailing hydrodynamics in a specific region will determine how accurately the currents will be predicted. If the surface elevation response and currents are indeed dominated by astronomical tides, then the database will provide an excellent prediction of the response. A good estimate of the accuracy of the EC2015 tides can be obtained by examining the regional error estimates given in Table 7 and Table 8, or by examining the error plots provided for the dominant constituents in Appendix C; although plots are only provided for the M2 and K1 constituents, in general, all four of the semi-diurnal constituents follow the same regional trends, as do the diurnal constituents. Furthermore how accurately the EC2015 grid and bathymetry describe the region of specific interest influences the accuracy and appropriateness of applying database values.
For locations that are tidally dominated and for which the EC2015 grid accurately describes both local geometry and bathymetry, the database can be directly applied to extract tidal elevations and currents. Because the thirty-seven constituents are computed at every node and are defined within the framework of a finite element grid, values at any point within the domain can be readily interpolated from the nodal values within which the point lies.
An extraction program, ADCIRC_db_extract.F90, together with the EC2015 finite element grid file, ec2012_v3d_chk.grd, accompany the tidal database. The user must supply an input file that provides the number of extraction points desired followed by the list of coordinates for those points. The extraction program will prompt the user for this input files as well as the name of the grid used to create the database. The program will also prompt the user whether they would like to produce the harmonic constituent output for elevations, velocities or both and then will produce the harmonic extraction output for amplitude and phase at the specified location(s) according to the user’s request. Elevation output is stored in elev_hc.out while velocity output is stored in vel_hc.out. Additionally, diagnostic output is written to tides.dia and provides the location of each extraction point in the global mesh as well as the interpolation weights used to calculate the harmonic constituents. The KDTREE2 search algorithms have been incorporated into the new extraction program to facilitate a speedier search response. Finally, the program takes advantage of dynamic allocation in order to avoid the old hardcoded array limitations found in previous extraction routines. The ADCIRC_db_extract.F90 program will work with any old ADCIRC databases that utilized the individual fort.53 and fort.54 file formats.
A time-history of response can be readily Fourier synthesized using the outputs in the elev_hc.out and vel_hc.out files. For example a time-history of water-surface elevation can be computed as
ζ ( x , y , t ) = A i ( x , y ) f i ( t 0 ) cos [ σ i ( t t 0 ) + V i ( t 0 ) h i ( x , y ) ]
where Ai(x,y) and hi(x,y) are the amplitude and phase, respectively, at the location (x,y) of interest for constituent i, which are provided by the EC2015 tidal database, and the frequency σi = 2π/Ti. The frequencies σi in rad/sec and periods Ti in hours for each of the 37 constituents included in the database are presented in Table D1. It is important to specify frequencies precisely, at least to eight significant figures. The nodal factor fi(t0) and the equilibrium argument, Vi(t0), relative to reference time t0 can be computed using program tide_fac.f, which is available as a utility program on the ADCIRC website [60].
Table D1. Frequencies and periods for EC2015 harmonic constituents.
Table D1. Frequencies and periods for EC2015 harmonic constituents.
ConstituentFrequency (Rad/s)Period (h)
M(2)0.000140518912.42
N(2)0.000137879712.66
S(2)0.000145444112.00
O(1)0.000067597725.82
K(1)0.000072921223.93
K(2)0.000145842311.97
L(2)0.000143158112.19
2N(2)0.000135240512.91
R(2)0.000145643211.98
T(2)0.000145245012.02
Lambda(2)0.000142804912.22
Mu(2)0.000135593712.87
Nu(2)0.000138232912.63
J(1)0.000075560423.10
M(1)0.000070282024.83
OO(1)0.000078244622.31
P(1)0.000072522924.07
Q(1)0.000064958526.87
2Q(1)0.000062319328.01
Rho(1)0.000065311726.72
M(4)0.00028103786.21
M(6)0.00042155674.14
M(8)0.00056207563.11
S(4)0.00029088826.00
S(6)0.00043633234.00
M(3)0.00021077848.28
S(1)0.000072722124.00
MK(3)0.00021344018.18
2MK(3)0.00020811668.39
MN(4)0.00027839866.27
MS(4)0.00028596306.10
2SM(2)0.000150369311.61
Mf0.0000053234327.86
Msf0.0000049252354.37
Mm0.0000026392661.31
Sa0.00000019918765.82
Ssa0.00000039824382.91
In locations and/or at times where the hydrodynamics is not tidally dominated and/or the EC2015 grid does not provide sufficient geometric and/or bathymetric detail, a regional model that interfaces with the EC2015 model will lead to a better representation of regional flows. Some examples of cases where this may be appropriate include: (a) bays or estuaries not included in the grid; (b) shallow nonlinearly-dominated inlets or estuaries; (c) coastal and/or estuarine regions barotropically and/or baroclinically influenced by a significant riverine discharge; (d) combined wind- and tidally-driven circulation on a shelf. The basic idea is to construct a domain/grid that extends onto or beyond the shelf within the EC2015 domain. The open ocean boundary is then forced using the tidal constituent data from the EC2015 tidal data base. The defined domain may also include additional regional detail in geometric and bathymetric definition, may include additional forcing functions on select boundaries or within the domain, and/or may include additional terms in the governing equations.
The regional model open ocean boundary should be placed away from the region of immediate interest, and its exact position and shape depends on the application. In no case should the boundary be placed at the mouth or entrance to an embayment of interest. The tidal constituents on the open ocean boundary nodes of the regional model are extracted in the same way as a simple point location. It may be necessary to add an additional forcing component to the boundary elevation and/or radiation forcing function to account for additional interior domain processes and forces. In the development of a regional model it is also recommended that the bathymetry along the open boundary match the bathymetry of the EC2015 grid. This will help ensure that the boundary condition extracted from the EC2015 database is physically consistent with the regional model. Failure to match bathymetries along the regional model open boundary can lead to unrealistic gyre formation and/or instabilities in the regional model computations. The bathymetry can depart from that comprising the EC2015 grid away from the open boundary area.
The EC2015 tidal database is available on the ADCIRC website as two separate compressed files: EC2015_elev-only_tidaldatabase.tar, which contains all of the extraction programs, grids, and sample notes but only has the fort.53 elevation harmonics; and EC2015_tidaldatabase.tar, which has everything given in the previous file with the addition of the fort.54 velocity harmonics [24]. You will only need to download one of the files depending upon whether you wish to have access to the velocity data as well.
In addition to the ADCIRC_db_extract.F90 extraction program, the database also includes another utility for “cutting” a portion of the global database out for visualization within SMS (or other tools). The HarmonicResultScope.f90 program works much the same way as ResultScope.f90, for those who are familiar with that ADCIRC utility program. Additional notes about the usage of each of these programs, as well as sample input and output files for each, are included in the TidalExtract/ directory within the database tar file.

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Figure 1. Location of new EC2001_extended model domain (shown in gray) compared to the traditional EC2001 boundary at the 60° W meridian (shown in red—remainder of shoreline is same as gray); and location of the nine VDatum domains (shown in black) used to update the coastal resolution and bathymetry in the EC2015 model. Note that the coarser gray shoreline is not visible underneath the black.
Figure 1. Location of new EC2001_extended model domain (shown in gray) compared to the traditional EC2001 boundary at the 60° W meridian (shown in red—remainder of shoreline is same as gray); and location of the nine VDatum domains (shown in black) used to update the coastal resolution and bathymetry in the EC2015 model. Note that the coarser gray shoreline is not visible underneath the black.
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Figure 2. Comparison of coastal resolution in the EC2001 (left) and EC2015 (right) models from North Carolina to Maine.
Figure 2. Comparison of coastal resolution in the EC2001 (left) and EC2015 (right) models from North Carolina to Maine.
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Figure 3. Comparison of bottom friction assignment for the Atlantic coastline from North Carolina to Maine: (a) bathymetry—scale from 0 m to 2500 m, (b) assigned Vertical Datum (VDatum) friction coefficient (CF) values, (c) assigned Manning’s n values and (d) computed CF values from bathymetry and assigned Manning’s n values.
Figure 3. Comparison of bottom friction assignment for the Atlantic coastline from North Carolina to Maine: (a) bathymetry—scale from 0 m to 2500 m, (b) assigned Vertical Datum (VDatum) friction coefficient (CF) values, (c) assigned Manning’s n values and (d) computed CF values from bathymetry and assigned Manning’s n values.
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Figure 4. Comparison of bottom friction assignment for the Louisiana coastline: (a) bathymetry—scale from 0 m to 500 m, (b) assigned VDatum CF values, (c) assigned Manning’s n values and (d) computed equivalent CF values from bathymetry and assigned Manning’s n values.
Figure 4. Comparison of bottom friction assignment for the Louisiana coastline: (a) bathymetry—scale from 0 m to 500 m, (b) assigned VDatum CF values, (c) assigned Manning’s n values and (d) computed equivalent CF values from bathymetry and assigned Manning’s n values.
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Figure 5. Locations for the stations available for validating the WNAT tidal databases: (a) global; (b) New York and Maine coast; and (c) Delaware down to Georgia. Blue points are from NOAA, red points are from IHO, cyan circles indicate stations that are in EC2015 (gray boundaries) but are not wet in EC2001 (green boundaries). Scatterplots are shown in Appendix B for points shown by an X.
Figure 5. Locations for the stations available for validating the WNAT tidal databases: (a) global; (b) New York and Maine coast; and (c) Delaware down to Georgia. Blue points are from NOAA, red points are from IHO, cyan circles indicate stations that are in EC2015 (gray boundaries) but are not wet in EC2001 (green boundaries). Scatterplots are shown in Appendix B for points shown by an X.
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Figure 6. Locations for the stations available for validating the WNAT tidal databases: (a) Florida, (b) Gulf of Mexico and (c) Caribbean Sea. Blue points are from NOAA, red points are from IHO, cyan circles indicate stations that are in EC2015 (gray boundaries) but are not wet in EC2001 (green boundaries). Scatterplots are shown in Appendix B for points shown by an X.
Figure 6. Locations for the stations available for validating the WNAT tidal databases: (a) Florida, (b) Gulf of Mexico and (c) Caribbean Sea. Blue points are from NOAA, red points are from IHO, cyan circles indicate stations that are in EC2015 (gray boundaries) but are not wet in EC2001 (green boundaries). Scatterplots are shown in Appendix B for points shown by an X.
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Figure 7. Comparison of regional root mean square (RMS) errors using the 367 wet stations for all nine study simulations summarized in Table 4.
Figure 7. Comparison of regional root mean square (RMS) errors using the 367 wet stations for all nine study simulations summarized in Table 4.
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Figure 8. Comparison of scatter plots for the dominant constituents (K1, M2) for the EC2001 and EC2015 tidal databases using the 367 common validation data stations.
Figure 8. Comparison of scatter plots for the dominant constituents (K1, M2) for the EC2001 and EC2015 tidal databases using the 367 common validation data stations.
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Figure 9. Mean RMS errors (cm) in harmonic constituents for the EC2001 and EC2015 ADCIRC tidal databases for each region of the WNAT model domain.
Figure 9. Mean RMS errors (cm) in harmonic constituents for the EC2001 and EC2015 ADCIRC tidal databases for each region of the WNAT model domain.
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Table 1. Summary of grid features for Western North Atlantic, Caribbean and Gulf of Mexico (WNAT) domain ADvanced CIRCulation model (ADCIRC) tidal databases.
Table 1. Summary of grid features for Western North Atlantic, Caribbean and Gulf of Mexico (WNAT) domain ADvanced CIRCulation model (ADCIRC) tidal databases.
Database Name# of Mesh Nodes# of Mesh ElementsAvg. Coastal Resolution (km)Min. Coastal Resolution (m)Max. Deep Ocean Resolution (km)
EC199119,85836,65371000140
EC199531,43558,3695750105
EC2001254,565492,1791 to 320029
EC20152,066,2163,770,7200.25 to 0.51346
Table 2. Maximum absolute differences along the entire EC2015 boundary between the TPXO7.2 and FES2012 global tidal database products.
Table 2. Maximum absolute differences along the entire EC2015 boundary between the TPXO7.2 and FES2012 global tidal database products.
ConstituentAmplitude (cm)Phase (Degrees)
O11.2820.20
K12.2610.95
P11.2534.62
Q10.55122.14
M22.031.10
N20.446.39
S21.317.95
K21.0010.01
M40.8634.49
MS40.9558.66
MN40.1116.22
Mf0.2139.85
Mm0.066.67
Table 3. Geographic regions used for Manning’s n assignment from usSEABEDS data.
Table 3. Geographic regions used for Manning’s n assignment from usSEABEDS data.
Geographic RegionBed DescriptionAssigned Shelf Value
Louisiana/Texasmuddy/silty0.015
Floridasandy0.022
Mexico/South America/Caribbean 1sandy0.022
Atlantic Coastsandy0.022
Delaware/Chesapeake Bayssilty0.015
Westernmost New York Soundsilty0.015
1 No data was available for these regions, so a general assumption was made.
Table 4. Summary of model parameters for the model simulations completed in this study.
Table 4. Summary of model parameters for the model simulations completed in this study.
Run DesignationDescriptionGridAdvectionFriction SchemeBoundary Forcing 1
EC2001EC2001 extractedEC2001Off0.0025TPXO-10
EC2001-extEC2001 extended meshEC2001_extOff0.0025TPXO-10
FES1FES 2012 EC2015On0.0025FES-13
OTIS1TPXO 7.2EC2015On0.0025TPXO-13
OTIS3EC2015 release versionEC2015OnVDatumTPXO-13
OTIS3noadvEC2015 advection offEC2015OffVDatumTPXO-13
OTIS4Manning nEC2015OnManning’s nTPXO-13
OTIS590% Manning nEC2015On90% ManningTPXO-13
OTIS6110% Manning nEC2015On110% ManningTPXO-13
1 The textual part of the label indicates which global tidal database was used, while the number indicates how many constituents were included.
Table 5. Total number of validation stations available in each region for the most recent East Coast models.
Table 5. Total number of validation stations available in each region for the most recent East Coast models.
ModelAtlantic OceanDeep Stations 2Gulf of MexicoCaribbeanGlobal
EC2001204 (151) 13190 (74)73 (55)367 (280)
EC20154143117889681
1 Numbers in parentheses indicate how many were actually within the EC2001 domain while the first number includes those stations approximated with nearest neighbors. 2 The deep stations are also included in the Atlantic and Gulf of Mexico regional numbers.
Table 6. Summary of best-fit linear statistics for the 367 common validation stations in the EC2001 and EC2015 tidal databases.
Table 6. Summary of best-fit linear statistics for the 367 common validation stations in the EC2001 and EC2015 tidal databases.
Harmonic Amplitudes
ModelBest-fitO1K1P1Q1M2S2N2K2
EC2001Slope1.0821.0530.9891.0651.0250.9380.9161.013
R20.9730.9640.9560.9590.9890.9590.9710.943
EC2015Slope1.0541.0241.0141.1061.0100.9460.9111.027
R20.9840.9780.9640.9600.9960.9750.9800.964
Harmonic Phases
ModelBest-fitO1K1P1Q1M2S2N2K2
EC2001Slope0.9880.9950.9810.9670.9800.9590.9760.960
R20.9940.9950.9950.9920.9720.9630.9790.946
EC2015Slope0.9830.9750.9880.9550.9860.9510.9860.964
R20.9970.9970.9970.9930.9840.9740.9870.962
Table 7. Comparison of mean relative amplitude and mean absolute phase errors by region for each of the eight primary harmonic constituents and summed over all eight constituents for the EC2001 and EC2015 tidal databases: only common 367 wet validation stations used in the summations.
Table 7. Comparison of mean relative amplitude and mean absolute phase errors by region for each of the eight primary harmonic constituents and summed over all eight constituents for the EC2001 and EC2015 tidal databases: only common 367 wet validation stations used in the summations.
Mean Relative Amplitude Errors (%)
ConstituentEntire DomainAtlantic OceanGulf of MexicoCaribbean Sea
EC2001EC2015EC2001EC2015EC2001EC2015EC2001EC2015
O118.9912.1218.6810.3518.1115.5920.9112.74
K119.5114.0218.9312.9618.4215.9722.4514.56
P118.4617.2717.0416.1918.2517.4222.8320.23
Q121.7921.0019.8920.3421.2624.5628.8617.50
M223.3920.6513.398.5038.3139.8132.9530.98
S223.7718.0817.0112.7637.8324.5425.3325.06
N222.5719.2014.7611.9739.7631.6023.6624.72
K231.4025.0620.0111.7861.8254.2833.7334.71
All 822.4018.2917.4212.9830.9027.2326.1622.49
Mean Absolute Phase Errors (deg)
ConstituentEntire DomainAtlantic OceanGulf of MexicoCaribbean Sea
EC2001EC2015EC2001EC2015EC2001EC2015EC2001EC2015
O110.378.4911.029.419.306.539.878.34
K18.877.479.217.738.446.278.498.25
P19.597.669.527.558.906.7110.699.17
Q113.7014.2215.2217.039.858.2014.8314.58
M215.4912.199.537.2423.5319.0522.2117.55
S216.2414.359.408.5326.6222.8122.6420.27
N217.1612.9810.407.5327.4517.9423.9522.72
K219.1119.5712.0615.7230.1925.0529.1725.67
All 813.7612.0010.729.9717.7213.7917.6015.65
Table 8. Summary of RMS errors (cm) for the 367 common validation stations: global means for the eight primary constituents and regional means summed over all eight primary harmonic constituents.
Table 8. Summary of RMS errors (cm) for the 367 common validation stations: global means for the eight primary constituents and regional means summed over all eight primary harmonic constituents.
Mean Global Constituent RMS Errors (cm)
Run DesignationO1K1P1Q1M2S2N2K2
EC20011.4111.6780.5370.3545.4451.4681.4400.558
EC2001-ext1.2311.6170.5740.3935.3501.4881.4880.603
FES11.1881.4950.6840.3794.0031.8781.3210.487
OTIS11.1091.4010.5190.3774.0221.2641.2820.510
OTIS31.0791.3810.5080.3794.3301.2721.2300.545
OTIS3noadv1.0481.3660.5040.3784.6531.2661.2080.534
OTIS41.1081.3750.5170.3733.9801.2631.2820.503
OTIS51.1041.3820.5160.3743.9721.2641.2750.506
OTIS61.1181.3720.5210.3724.0281.2641.2960.500
Mean Regional RMS Errors (cm)
Run DesignationGlobalAtlantic OceanGulf of MexicoCaribbean SeaDeep Ocean
EC20011.6551.9281.4191.1610.774
EC2001-ext1.6341.9251.3341.1670.848
FES11.4661.7441.1391.0671.035
OTIS11.3431.5751.0761.0020.874
OTIS31.3741.6321.0741.0010.867
OTIS3noadv1.4051.6911.0661.0000.888
OTIS41.3321.5771.0350.9950.875
OTIS51.3311.5691.0460.9990.873
OTIS61.3411.5931.0380.9910.878
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