NOAA Technical Report NOS CS 21 

VDATUM FOR CENTRAL COASTAL NORTH 

CAROLINA: TIDAL DATUMS, MARINE GRIDS, 

AND SEA SURFACE TOPOGRAPHY 

Silver Spring, Maryland 

December 2005 

n 0 a a National Oceanic and Atmospheric Administration 

U.S. DEPARTMENT OF COMMERCE 

National Ocean Service 

Office of Coast Survey 

Coast Survey Development Laboratory 
Office of Coast Survey 

National Ocean Service 

National Oceanic and Atmospheric Administration 

U.S. Department of Commerce 

The Office of Coast Survey (CS) is the Nation's only official chartmaker. As the 

oldest United States scientific organization, dating from 1807, this office has a 

long history. Today it promotes safe navigation by managing the National 

Oceanic and Atmospheric Administration's (NOAA) nautical chart and 

oceanographic data collection and information programs. 

There are four components of CS: 

The Coast Survey Development Laboratory develops new and efficient 

techniques to accomplish Coast Survey missions and to produce new and 

improved products and services for the maritime community and other 

coastal users. 

The Marine Chart Division collects marine navigational data to construct 

and maintain nautical charts, Coast Pilots, and related marine products 

for the United States. 

The Hydrographic Surveys Division directs programs for ship and shorebased hydrographic survey units and conducts general hydrographic 

survey operations. 

The Navigation Services Division is the focal point for Coast Survey 

customer service activities, concentrating predominantly on charting 

issues, fast-response hydrographic surveys and Coast Pilot updates. 
NOAA Technical Report NOS CS 21 

VDATUM FOR CENTRAL COASTAL NORTH CAROLINA: 

TIDAL DATUMS, MARINE GRIDS, AND SEA SURFACE 

TOPOGRAPHY 

Kurt W. Hess 

Emily A. Spargo 

Adeline Wong 

Office of Coast Survey 

Stephen A. White 

National Geodetic Survey 

Stephen K. Gill 

Center for Operational Oceanographic Products and Services 

December 2005 

n 0 a a National Oceanic and Atmospheric Administration 

U.S. DEPARTMENT 

OF COMMERCE 

Carlos Gutierrez, Secretary 

Office of Coast Survey 

National Oceanic and 

Atmospheric Administration 

Conrad C. Lautenbacher, Jr., 

VADM USN (Ret.), Under Secretary 

Captain Roger L. Parsons, NOAA 

National Ocean Service 

Charles W. Challstrom, Acting 

Assistant Administrator 

Coast Survey Development 

Laboratory 

Mary Erickson 
NOTICE 

Mention of a commercial company or product does not constitute an 

endorsement by NOAA. Use for publicity or advertising purposes of 

information from this publication concerning proprietary products or the tests 

of such products is not authorized. 
iii

TABLE OF CONTENTS

LIST OF FIGURES ............................................................................................................ v 

LIST OF TABLES ............................................................................................................. vi

ABSTRACT ...................................................................................................................... vii 

1. INTRODUCTION .......................................................................................................... 1 

2. BATHYMETRIC, TIDAL, AND COASTLINE DATA ................................................ 3 

2.1. Bathymetric Data ..................................................................................................... 3 

2.2. Tidal Data ................................................................................................................ 5 

2.3. Digitized Coastline .................................................................................................. 9 

3. TIDAL AND HYDRODYNAMIC MODELING ........................................................ 11 

3.1. The Hydrodynamic Model ..................................................................................... 11 

3.2. Model Grid Development ...................................................................................... 12 

3.3. Population of the Model Grid with Bathymetric Data ........................................... 13 

3.4. Ocean Boundary Forcing ....................................................................................... 14 

3.5. Results of Model Water Level Simulations ........................................................... 15 

3.6. Corrections to the Modeled Tidal Datum Fields ................................................... 18 

4. THE TIDAL MARINE GRIDS .................................................................................... 21 

4.1. Grid Point Location ............................................................................................... 21 

4.2. Population of the Marine Grids ............................................................................. 22 

4.3. Illustration of Problems at Barrier Islands ............................................................. 23 

4.4. The Bounding Polygons ......................................................................................... 25 

4.5. Assessment of Errors in the Marine Grid .............................................................. 28 

5. SEA SURFACE TOPOGRAPHY ................................................................................ 31 

6. SUMMARY AND CONCLUSIONS ........................................................................... 33 

ACKNOWLEDGEMENTS .............................................................................................. 34 

REFERENCES ................................................................................................................. 35

APPENDIX A. BATHYMETRIC DATA SOURCES ..................................................... 37 

APPENDIX B. WATER LEVEL STATION DATA ....................................................... 39 

APPENDIX C. HYDRODYNAMIC MODEL PARAMETERS ..................................... 41 

APPENDIX D. SUMMARY OF HYDRODYNAMIC MODEL ERRORS .................... 43 

APPENDIX E. SUMMARY OF VDATUM ERRORS ................................................... 45 
iv
v

LIST OF FIGURES 

Figure 1. The area of North Carolina around Pamlico Sound for which VDatum was 

developed. ........................................................................................................................... 2 

Figure 2. Dates of NOS surveys. ........................................................................................ 4 

Figure 3. Location of NOS soundings. ............................................................................... 4 

Figure 4. Locations of water level stations (red squares) in the study area. Only the last 

four digits of the station numbers are shown; the first three digits are 865 for all stations 

except for the northernmost, where they are 863. See Appendix B for further information.

............................................................................................................................................. 7 

Figure 5. Locations of water level stations (red squares) around Oregon inlet. Only the 

last four digits of the station numbers are shown; the first three digits are 865. See 

Appendix B for further information. ................................................................................... 8 

Figure 6. Locations of water level stations (red squares) around Beaufort Inlet. Only the 

last four digits of the station numbers are shown; the first three digits are 865. See 

Appendix B for further information. ................................................................................... 8 

Figure 7. Sample of extracted vector shoreline for MHW (black) and MLLW (green). .... 9 

Figure 8. Finite element grid for the regional model. ....................................................... 12 

Figure 9. Model finite element grid with DEM boundary (dark black box) and MHW 

coastline (blue line). .......................................................................................................... 13 

Figure 10. Time series of water levels over 21 days with extrema noted. ........................ 15 

Figure 11. Time series of water levels for 40 hours at a grid node with a depth of 0.22 m 

above model zero elevation. When total water depth falls to 10 cm or less, the cell 

becomes inactive. .............................................................................................................. 16 

Figure 12. Comparison of (a) the MHHW and MLLW datums (m) and (b) MHW and 

MLW datums obtained from observations (horizontal axis) and from the hydrodynamic 

model (vertical axis). RMS error for all datums is 5.2 cm. .............................................. 17 

Figure 13. Mean sea level, as computed by the hydrodynamic model. MSL is relative to 

the model's zero elevation. ................................................................................................ 17

Figure 14. Diurnal tide range (the difference between MHHW and MLLW) as computed 

by the hydrodynamic model. ............................................................................................. 18 

Figure 15. Error (modeled value minus observed value) in the MHHW datum field as 

interpolated by the TCARI method. .................................................................................. 19 

Figure 16. Sample region with marine grid points (solid squares) and their numerical 

datum values (cm), hydrodynamic model grids (large triangles) with datum values at their 

vertices (cm), narrow barrier island (gray area), and test points A and B. ...................... 24 
vi

Figure 17. Sample region with marine grid points (solid squares) and their datum values 

(cm), hydrodynamic model grids (large triangles) with their MHHW to MSL datum 

values (cm) at the vertices, a narrow barrier island (curved lines), and the bounding 

polygon (solid line inside barrier island). ......................................................................... 24 

Figure 18. The bounding polygons for the Coastal North area (purple line), Coastal 

Central area (green line), and Pamlico Sound area (blue line). Also shown are shoreline 

(gray) line, the hydrodynamic model’s offshore boundary (dashed black line) and the 25 

nmi limit (dotted black line). ............................................................................................ 26 

Figure 19. Area around Oregon Inlet showing the locations of the tidal marine grid points 

for the Pamlico Sound grid (blue squares) and the Coastal North grid (purple squares). 

The plus signs represent null points for each grid. The value (cm) of the tidal datum (here 

the difference between MHHW and MSL) is shown next to the non-null points. Points 

along a track crossing the bounding polygon are shown as black squares. ...................... 27 

Figure 20. Datum values along a 10-point track from northeast to southwest (see Figure 

19) from (a) both grids having equal spacing of approximately 0.24 nmi (open squares), 

and (b) a Pamlico grid with spacing of 0.24 nmi and a coastal grid with spacing of 0.48 

nmi (plus signs). Notice the discontinuity of 0.11 m at an along-track distance of 0.25 

nmi. ................................................................................................................................... 27 

Figure 21. The computed sea surface topography (TSS). Elevations are in meters. ........ 32 

LIST OF TABLES 

Table 1. Diurnal range values at stations where data from the 1960-1978 epoch and the 

1983-2001 epoch are both available. Ranges and differences are in meters. ..................... 6 

Table 2. Sample of tidal constituents and their harmonic constants at a boundary node in 

the regional grid. ............................................................................................................... 15 

Table 3. Parameters for the North Carolina tidal marine grids. Latitude is positive 

northward, and longitude is positive eastward. ................................................................. 22 

Table 4. Observed values of NAVD 88 relative to LMSL. The data are based on the most 

recent National Tidal Datum Epoch (1983-2001) unless noted, and a positive value 

means that the NAVD 88 elevation lies above the LMSL surface. .................................. 31 

Table 5. Parameters for the initial North Carolina sea surface topography (TSS) grid. 

Latitude is positive North, longitude is positive East. ...................................................... 32 
vii

ABSTRACT 

VDatum, a software tool for vertical datum transformation, has been developed for a 

portion of the North Carolina coastal area. To support VDatum, gridded fields 

representing the conversion between various tidal datums and mean sea level, and 

between mean sea level and the North American Vertical Datum of 1988, were created. 

Initial fields of tidal datum transformations (such as the difference between mean higher 

high water and mean sea level) were generated by the two-dimensional, barotropic, finiteelement numerical tidal model, ADCIRC. The model grid covers the central portion of 

the North Carolina coast including Currituck, Albemarle, Pamlico, Core, Back, and 

Bogue Sounds, as well as their offshore areas. Digitized coastline was available from the 

Extracted Vector Shoreline project, and depths were taken from historical Coast Survey 

hydrographic surveys. The hydrodynamic model was forced by a reconstructed tide at the 

ocean boundary, using harmonic constants from a basin-scale tidal model. After a 37-day 

model run, the 6-minute water level time series at each model node for the last 30 days 

was analyzed for high and low waters, then averaging produced the initial tidal datum 

fields. When the model’s tidal datums were compared to values at 45 historical tide 

stations, the RMS error for all datums was 5.2 cm. To reduce this error, a twodimensional correction field was constructed by spatial interpolation of the error values at 

each tide station using the TCARI method. When the correction fields were added to the 

hydrodynamic model’s tidal datum fields to get the final datum fields, the datum values 

closely matched the historical values at the tide stations. The final corrected datum field 

values were then transferred to a set of three regular marine grids. These grids have a 

uniform spacing in latitude and longitude. Three grids were needed to accurately 

represent the effect of the barrier islands and to keep file sizes small. The datum values 

from the marine grids match the observed datums to within 1.1 cm RMS. The sea surface 

topography (TSS), or difference between local mean sea level and the NAVD 88 

geopotential surface, was generated by a minimum curvature algorithm using data at 18 

historical tide stations with benchmark data. The TSS field values were then transferred 

to the same three regular marine grids. 

Key Words: tides, tidal datums, North Carolina, Pamlico Sound, North American 

Vertical Datum of 1988, mean sea level, spatial interpolation, coast line. 
viii
1

1. INTRODUCTION 

The National Ocean Service (NOS) of the National Oceanic and Atmospheric 

Administration (NOAA) requires tidal datum information such as Mean High Water 

(MHW) and Mean Lower Low Water (MLLW) to support nautical charting, navigational 

safety, shoreline photogrammetry, and marine boundary determination. In addition, tidal 

datum information is needed for referencing NOS’ bathymetric data (which is referenced 

to MLLW) to any one of the other vertical elevation reference systems. A software tool 

under development at NOS called VDatum (Milbert, 2002; Parker, 2002) is designed to 

transform among approximately 30 vertical reference datums. For example, using 

VDatum, ellipsoidal elevations can be converted, by parametric equations, to elevations 

relative to the North American Datum of 1983 (NAD 83); NAD 83 elevations can be 

converted to elevations relative to the North American Vertical Datum of 1988 (NAVD 

88) using a gridded geoid model such as Geoid99; NAVD 88 elevations can be converted 

to elevations relative to Local Mean Sea Level (LMSL) using a gridded field called the 

sea surface topography; and LMSL elevations can be converted to elevations relative to 

other tidal datums, such as MLLW, by using gridded tidal datum fields. 

Because the tides and the sea surface topography vary widely throughout the coastal 

region, each geographic area of VDatum application requires a unique set of gridded 

data. To date, tidal datum and sea surface topography fields for VDatum have been 

produced by NOS for Tampa Bay (Hess, 2001), coastal southern Louisiana (Hess et al., 

2004), the New York Bight (Hess, 2001), central coastal California (Myers, 2001), 

Delaware Bay (Hess et al., 2003), Puget Sound (Hess and Gill, 2003; Hess and White, 

2004), and Lake Calcasieu (Spargo and Woolard, 2005). VDatum for Tampa Bay was 

employed to integrate elevation data from a variety of sources into a bathymetrictopographic Digital Elevation Model for use in coastal GIS applications (Parker et al., 

2003; Gesch and Wilson, 2001). VDatum was also used for testing a method of 

processing the hydrographic data from a kinematic-GPS hydrographic survey in 

Delaware Bay (Hess et al., 2003). 

NOS routinely collects water level observations at shore-based stations along U.S. coasts 

and analyzes them to produce tidal datums. As described above, there is an important 

need to obtain two-dimensional tidal datum fields that cover the coastal waters between 

the water level stations. This paper discusses the process of obtaining (1) tidal datum 

fields in coastal North Carolina by the combined use of a hydrodynamic model and 

spatial interpolation of errors, and (2) the sea surface topography by spatial interpolation. 

VDatum in North Carolina grew from a study of the impacts of long-term sea level rise 

on the coastal ecosystems in the sounds and nearby estuaries of North Carolina (Hess et 

al., 2004). The study is being led by the Center for Sponsored Coastal Ocean 

Research/Coastal Ocean Program (CSCOR/COP) of NOS’ National Centers for Coastal 

Ocean Science. Technical support is provided by NOS’ Office of Coast Survey (OCS), 

National Geodetic Survey (NGS), and the Center for Operational Oceanographic 

Products and Services (CO-OPS), which are cooperating to develop data sets, modeling 
2

tools, and maps that will be useful to coastal managers. Based on project resources, the 

area of VDatum was selected to focus on Currituck, Albemarle, Pamlico, Core, Back, and 

Bogue Sounds (Figure 1). 

Figure 1. The area of North Carolina around Pamlico Sound for which VDatum was developed. 

The following sections describe the technical approach and the accomplishments in the 

major components of the study: 

 Access of historical NOS bathymetric, coastline, and tidal data, 

 Development of the hydrodynamic grid and model, 

 Creation of the tidal marine grid, and 

 Generation of the sea surface topography. 

The appendices include a discussion of the bathymetric data and the locations and names 

of the water level stations and their tidal datum values. 
3

2. BATHYMETRIC, TIDAL, AND COASTLINE DATA

Water level model development for the Pamlico Sound region requires three types of 

data: bathymetry, tidal data, and coastline data. Historical bathymetric, or sounding, data 

are available from NOS and other sources. Model validation depends on comparisons to 

datums based on observed water levels. Updated tidal datums were therefore derived for 

several local tide stations, and a new tide station was installed in Core Sound. Historical 

water levels were re-analyzed to determine updated estimates of long-term sea level rise. 

A digital coastline was accessed and used to delineate land and water areas. 

2.1. Bathymetric Data 

Several sources of bathymetric data for the North Carolina coast were evaluated and 

processed for the development of the water level model. Sounding values were 

initially selected from the NOS Office of Coast Survey (OCS) hydrographic database

maintained at the National Geophysical Data Center (NGDC), which developed 

the interactive GEOphysical DAta System (GEODAS) to assimilate, store and manage 

geophysical data. The NOS OCS bathymetric database contains soundings digitized from 

smooth sheets of hydrographic surveys completed between the years 1851 and 1965, as 

well as digital soundings acquired by survey ships since 1965. Lead line measurements 

are assumed for surveys before 1940. Water depths are recorded by digital echo sounders 

from 1940 onward. For some regions of the coastal United States, the NOS OCS 

bathymetric database includes high-density multibeam sonar depth measurements 

processed from hydrographic surveys since 1980. 

Accuracies reported for survey data apply the rigorous standards specified by the 

International Hydrographic Office (IHO) since the 1800s. The horizontal accuracy of 

the NOS sounding datasets ranges from 2 to 15 m nearshore and from 20 to 75 m 

offshore, with improved accuracy of recent surveys that employ a differential 

global position system (DGPS). NGDC's GEODAS Hydrographic Survey Database 

System archives the original depth units (feet, fathoms or meters) as tenths of 

meters. To establish a common horizontal reference, the original horizontal 

datum of each survey was transformed to North American Datum 1983(1986) 

[NAD 83(86)] using the North American Datum Conversion utility (NADCON) 

developed at NOS. For surveys before 1927, horizontal coordinates were 

transformed using a single pair of datum latitude/longitude shift values for the 

entire survey to approximate North American Datum 1927 (NAD 27), which 

NADCON further transformed to NAD 83(86). 

The NOS sounding data are referenced to one of several vertical datums; each 

sounding has associated metadata that lists whether the depth value is 

referenced to Mean Low Water (MLW), MLLW, or the low water datum (LWD), 

which is defined for North Carolina as 0.5 feet (0.15 meters) below the local 

Mean Water Level (MWL). MWL is the average water level over the available 
4

record. Analysis of tidal data included in NOAA hydrographic reports reveals that 

LWD is usually used for surveys within Pamlico Sound at locations far from 

inlets. The vertical accuracy of NOS soundings conform to IHO standards: 0.3 m 

in 0 to 20 m of water, 1.0 m in 20 to 100 m of water, and 1% of the water depth in 

waters deeper than 100 m. 

More than 200 NOS hydrographic surveys were conducted within the North Carolina 

project area between 1851 and 2002. Approximately 1,980,120 soundings from 158 

surveys were accessible and processed from GEODAS. NOS soundings were sorted, 

and then merged by year and by original vertical (tidal) datum. Soundings in each 

survey were checked against adjacent and overlapping surveys to ensure 

continuous coverage. Thirty-four separate spatial-temporal filters, consisting of 

raster layers resolved by date and sounding density, were generated to compile 

the best historical bathymetry retrievable from the NOS hydrographic survey 

database. The map below shows the dates, location, and density distribution of 

sounding data compiled from NOAA ENCs and historical NOS surveys (Figures 2 

and 3). Appendix A contains further information on the sounding data.

Figure 2. Dates of NOS surveys. 

Figure 3. Location of NOS soundings. 

1998-2001

1974-1981

1970-1971

1962-1965

1953-1955

1942-1943

1932-1936

1920-1927

1913-1917

1869-1877

ENC soundings 

NOS Hydrographic Surveys 
5

Multibeam sonar data from surveys conducted in 2002 and later and sounding data from 

at least 40 older surveys (the majority in the 1800s) were unavailable for distribution via 

GEODAS. Because these data had been processed and validated for publication by OCS, 

sounding values were collected from the 2004 editions of NOAA ENCs at map scales up 

to 1:50:000 or larger. Originally digitized from NOAA raster nautical charts, ENCs 

comprise the official charting database provided in IHO native S-57 vector format, which 

is the data standard developed by the IHO to be used for the exchange of digital 

hydrographic data. 

 

Historical NOS bathymetry data are also available in an interpolated, gridded format as 

part of NOAA’s Coastal Relief Model (CRM) at NGDC. CRM gridded bathymetry are 

available at a horizontal spacing of 3 arc-seconds, or approximately 90 m, while seafloor 

elevations are resolved to 0.1 m. However, CRM depths have not been corrected from 

their original horizontal datum or vertical datum (MLW, MLLW, or LWD). 

Recent bathymetry data from the U.S. Army Corps of Engineers (USACE) originate from 

54 inlet and channel surveys conducted between 1997 and 2003. Sounding data provided 

by the USACE are regularly published in the latest editions of NOAA nautical charts. 

Survey data were processed to 61,573 soundings whose horizontal coordinates were 

converted from NC State Plane (feet) to NAD 83 with Geodetic Reference System 1980 

ellipsoid (decimal degree), which closely corresponds to World Geodetic System 1984. 

The vertical datum for USACE surveys were recorded as local MLW. Soundings in feet 

were converted to depth in meters. Where applicable, USACE channel soundings blend 

with or supersede the historical NOS bathymetry (see Section 3.3). 

2.2. Tidal Data 

The NOS bathymetric data to be used by the hydrodynamic model is referenced to a tidal 

datum, so they must be adjusted to mean sea level. Tidal datum values at NOS water 

level stations are routinely computed and are available to the public in the form of the 

station benchmark sheets. Tidal datums at water level stations are elevation values that 

are determined from a time series of observations. For stations located along the coasts of 

the U.S. (except for the Great Lakes), the analysis starts with the identification of all the 

tidal extrema (highs and lows) in the record, and continues with the selection (within a 

25-hour time period) of the higher of the two highs and the lower of the two lows. If only 

one high water is present in the time period, it is categorized as a higher high. Thus, for 

high water (for example), each day has either a lower high and a higher high, or a single 

higher high. The average of all the lower highs and the higher highs is the MHW, and the 

average of just the higher highs is the MHHW. The process for producing Mean Low 

Water (MLW) and MLLW from the low waters is similar. The average of the MHW and 

the MLW is called the Mean Tide Level (MTL) and the average of the MHHW and the 

MLLW is called the Diurnal Tidal Level (DTL). Mean Sea Level (MSL) is the average 

of the hourly water levels. Where MSL is not computed, the MTL or DTL can be used as 

approximations. For further information on tidal datums, see Gill and Schultz (2001). 
6

Tidal datums derived from observations made in a limited time period are adjusted to 

represent equivalent values for a 19-year National Tidal Datum Epoch (NTDE). The 

present NTDE of 1983-2001 was implemented in April 2003 and replaced the previous 

1960-1978 NTDE period. This recent epoch will give more accurate datums for locations 

where apparent sea levels are changing rapidly due to local land subsidence caused by 

mineral and ground water extraction, isostatic rebound following the last ice age, or 

tectonic motion. Although tidal data throughout the U.S. are in the process of being 

updated to the new epoch, not all stations will be included in the update. Nevertheless, 

datums from older epochs may be useful in developing the hydrodynamic model and the 

datum fields. The data in Table 1 shows values at stations where data from the 1960-1978 

epoch and the 1983-2001 epoch are both available for comparison. For these stations, the 

mean range for the newer epoch is 0.90 m, the ratio of the mean tide range for the new 

epoch to the range for the older epoch is 1.014, the mean difference is 2.4 cm, and the 

mean of the percentage differences is 3.9% (the percentage difference at each station is 

100 times the absolute value of the difference divided by the average range). Therefore, 

because the differences are relatively small, it was decided to use datums from the 

previous epoch if only they, and not the newer datums, were available. 

Table 1. Diurnal range values at stations where data from the 1960-1978 epoch and the 1983-2001 

epoch are both available. Ranges and differences are in meters. 

______________________________________________________________________________________ 

No. Station Epoch Range Epoch Range Ratio Diff %Diff 

 1 8651370 1960 1.143 1983 1.124 0.983 -0.019 1.676 

 2 8652587 1960 0.350 1983 0.356 1.017 0.006 1.700 

 3 8652678 1960 0.675 1983 0.687 1.018 0.012 1.762 

 4 8653215 1960 0.241 1983 0.299 1.242 0.058 21.567 

 5 8654400 1960 1.076 1983 1.056 0.981 -0.020 1.871 

 6 8656306 1960 1.042 1983 1.065 1.022 0.023 2.183 

 7 8656394 1960 0.195 1983 0.203 1.041 0.008 3.983 

 8 8656483 1960 1.061 1983 1.079 1.017 0.018 1.710 

 9 8656502 1960 1.043 1983 1.065 1.021 0.022 2.087 

10 8656518 1960 0.963 1983 0.979 1.017 0.016 1.648 

11 8656539 1960 0.812 1983 0.830 1.022 0.018 2.192 

12 8656590 1960 1.305 1983 1.264 0.969 -0.041 3.157 

13 8656841 1960 1.353 1983 1.391 1.028 0.038 2.747 

14 8656937 1960 1.170 1983 1.201 1.026 0.031 2.578 

Means: 0.888 0.900 1.014 0.024 3.633 

 

The locations of the tidal stations used in this study are shown in Figures 4, 5, and 6. 

Station locations and tidal datum values are given in Appendix B. 
7

Figure 4. Locations of water level stations (red squares) in the study area. Only the last four digits 

of the station numbers are shown; the first three digits are 865 for all stations except for the 

northernmost, where they are 863. See Appendix B for further information.
8

Figure 5. Locations of water level stations (red squares) around Oregon inlet. Only the last four 

digits of the station numbers are shown; the first three digits are 865. See Appendix B for 

further information.

Figure 6. Locations of water level stations (red squares) around Beaufort Inlet. Only the last four 

digits of the station numbers are shown; the first three digits are 865. See Appendix B for further 

information. 
9

2.3. Digitized Coastline 

Digital files containing the MHW and the MLLW lines were obtained from the Coast 

Survey’s Extracted Vector Shoreline (EVS) project. The digital files contain points 

defining the coastline that were extracted from digital images of NOS’ nautical charts, 

and were used for identifying the land-water boundary. A sample is shown in Figure 7. 

 Figure 7. Sample of extracted vector shoreline for MHW (black) and MLLW (green). 
10
11

3. TIDAL AND HYDRODYNAMIC MODELING

As part of the tidal model development, a high-resolution finite element hydrodynamic 

model was created for the study area, and historical bathymetry from NOS and other 

sources was used to populate the grid with depths. The model was run numerous times to 

simulate astronomical tides, and further revised and calibrated until it produced relatively 

accurate tidal datum information. Tidal datum fields have been produced, and bathymetry 

was re-referenced to MSL. 

3.1. The Hydrodynamic Model 

Hydrodynamic water level modeling was accomplished using ADCIRC, the ADvanced 

CIRCulation model for oceanic, coastal and estuarine waters. The model runs in twodimensional (i.e., barotropic) mode on an unstructured grid composed of triangular 

elements; this type of grid is ideally suitable for representing complex coastlines to any 

desired resolution, and can be easily modified to add spatial resolution in any geographic 

area with little effort. The grid must then be populated by bathymetry to represent the 

region, and boundary forcing must be added to simulate tides and other types of water 

level variability. 

The ADCIRC model was developed by Rick Luettich at the University of North Carolina 

at Chapel Hill, Institute of Marine Sciences, and Joannes Westerink at the University of 

Notre Dame, Department of Civil Engineering and Geologic Sciences (Luettich, et al., 

1992; Luettich and Westerink, 2004). This model is a system of computer programs that 

solves time-dependent, free surface circulation and transport problems in two and three 

dimensions. The ADCIRC Two-Dimensional Depth Integrated (2DDI) version, used for 

the North Carolina area studies, is the barotropic version of the model. ADCIRC utilizes 

the finite element method in space, taking advantage of highly flexible, irregularly spaced 

grids. Numerous studies have shown this model to be robust throughout the Eastern 

North Atlantic and Gulf of Mexico regions (Luettich and Westerink, 1995; Mukai, et al., 

2000) and the West Coast (Spargo, 2003). 

ADCIRC has a wetting and drying algorithm that works as follows. When the water level 

at any node drops to less that a user-specified depth (here 10 cm), that node becomes 

temporarily inactive. When surrounding water levels are sufficiently high to push water 

into the nodal area to make the water level rise above the 10 cm value, the node is 

reactivated. During the model runs, some nodes become ‘ponded’ when their depths are 

at or near 10 cm, because the surrounding nodes were inactive and there was not a 

sufficient gradient for the water to flow out of them. 

The modeling of bottom friction and other parameters are discussed in detail in Appendix 

C. 
12

3.2. Model Grid Development 

The modeling strategy was to create a regional grid (Figure 8) by taking a portion of a 

larger scale grid, in this case, the western North Atlantic grid (Luettich and Westerink, 

1995). Then, grid elements covering Pamlico and Albemarle Sounds and Beaufort Inlet 

developed by Luettich et al. (1999) were incorporated. Finally, additional elements were 

added by NOS to parts of the region within the DEM area where more resolution was 

needed, including the Intracoastal Waterway. A portion of the high-resolution part of the 

grid around Beaufort is shown in Figure 9. The grid contains 36,409 nodes, and the 

smallest elements in that area have a node spacing on the order of 13 m. At the request of 

the U.S. Army Corps of Engineers in Wilmington, North Carolina, the Intracoastal 

Waterway was explicitly included in the grid wherever possible. 

Figure 8. Finite element grid for the regional model. 
13

 Figure 9. Model finite element grid with DEM boundary (dark black box) and MHW coastline (blue 

line). 

3.3. Population of the Model Grid with Bathymetric Data 

The bathymetric data used to populate the model grid came from five different sources. 

These data are: (1) Post-Hurricane Isabel (September 18, 2003) U.S. Army Corps of 

Engineers (USACE) sounding data, (2) Pre-Hurricane Isabel USACE sounding data, (3) 

NOS historical sounding data, (4) CRM depth data, and (5) manually digitized values 

appearing on NOAA paper nautical charts. The Post-Hurricane Isabel sounding data, 

henceforth, POST-ISA, is referenced to MLW. The Pre-Hurricane Isabel sounding data, 

henceforth referred to as PRE-ISA, is referenced to MLLW. The NOS sounding data is 

referenced to one of several datums; each sounding has associated metadata that lists 

whether the point is referenced to MLW, MLLW, or a low water datum (LWD). The 

CRM data is referenced to MLW. The NOAA paper nautical chart data, digitized 15 

years ago at the University of North Carolina, are referenced to MLW; these data points 

were incorporated into the finite element grid. 

The grid was filled with depth data from these sources, and at some locations, data were 

available from several sources. Priority was given first to the POST-ISA data, then to 

PRE-ISA data, then to NOS soundings, then to CRM data, and finally to the digitized 

NOAA chart data. At the start of the fill, all POST-ISA points within the DEM region 

were used. The nodal depth value was taken as the average depth of all points that fell 

within the triangular elements adjacent to the node. For filling from the remaining 

sources, a tolerance distance of 0.0004 (44.4 m) was set. Then, the data with the next 

highest priority (the PRE-ISA data) were examined and any points that fell within the 

tolerance distance from any previously–filled data point were eliminated; points that were 

beyond the tolerance distance were retained and used to fill nodal values. The process 

was repeated for the remaining data sources. Additionally, CRM data with 0.0 or 
14

-99999.0 depth values were eliminated, since these two values were only used in the 

CRM as “placeholders”. 

 

The depths were adjusted to MSL by an iterative process. Initially, a MSL-to-LWD 

difference of 15 cm in the portions of Pamlico Sound where LWD was used, and 

estimated MSL-to-MLW and MSL-to-MLLW differences of 50 cm were applied 

elsewhere to the bathymetric depths. After the first and each subsequent 30-day tide 

simulation, the computed MSL-to-MLW, MSL-to-MLLW, and MSL-to-LWD 

differences were averaged for each triangular element and applied to the bathymetric 

depths from the original sources within that element. Depth adjustments at most locations 

converged to within 1 cm of their final values after three to five simulations. Note that the 

modeled MSL, determined by averaging hourly values at each node, differs from the 

model’s zero elevation in Pamlico Sound by approximately 5 cm. 

Inter-tidal areas often did not have depth values, since neither NOS nor USGS measures 

depths there and Lidar data is usually not collected when the water level is at or below 

MLLW. Therefore, depths in the inter-tidal areas, which in the Sounds are usually 

vegetated, were assumed to be everywhere 10 cm below MSL. 

3.4. Ocean Boundary Forcing 

The outer coastal boundary of the regional grid (Figure 8) is forced with periodic water 

level variations to astronomical tides. The water level, relative to the model’s zero 

elevation, at the outer boundary is 

 H = ho + ∑ fn An cos ( ωn t + [Vo + u]n – κn) 

where H is the total water level (m), ho represents a constant offset (here taken to be zero), 

and the remaining term represents the astronomical tide. An is the constituent amplitude 

(m), ωn is the constituent speed (degrees/hr), t is the time relative to some reference time, 

[Vo + u]n is the equilibrium angle (degrees), and κn is the phase relative to Greenwich 

time (degrees). There is a unique set of harmonic constants at each grid node along the 

coastal boundary; a sample is shown in Table 2. 

For the simulation of water levels that are to be used to generate tidal datums, as opposed 

to simulating the tide for a specific date, the day and year of the simulation is not 

important. Therefore, for the following model runs the lunar node factor, fn, was set to 1.0 

and the equilibrium angle [Vo + u]n was set to 0.0. 
15

Table 2. Sample of tidal constituents and their harmonic constants at a boundary node in 

the regional grid. 

 Constituent Amplitude (m) Phase (deg) 

 An κn

 

K1 0.091433 177.978 

O1 0.068979 191.636 

Q1 0.012528 177.459 

M2 0.408000 351.313 

S2 0.074515 10.154 

N2 0.096141 336.247 

K2 0.017007 16.020 

3.5. Results of Model Water Level Simulations 

The model was run to simulate astronomical tides by forcing with the elevation equation 

discussed in the previous section, and the time series of water levels were saved at 6-min 

intervals at all grid nodes. The water level amplitudes were linearly increased from zero 

to their full values over the first 5 days, and the total simulation period was 37 days. 

The time series were analyzed to determine tidal datums. The datums at each node in the 

grid were found by extracting the high and low waters from the last 30 days of the 37-day 

simulation, categorizing them as highs, higher highs, lows, or lower lows, then averaging. 

Figure 10 shows a sample time series with the tidal extrema denoted. 

Figure 10. Time series of water levels over 21 days with extrema noted. 
16

For nodes that have gone dry (Figure 11) or have ‘ponded’ (i.e., have a non-zero depth 

but are within an area encircled by dry nodes), low water in the time series does not 

accurately reflect a tidal datum. Therefore, for these points, the tidal datums from the 

closest non-drying nodes were used. 

Figure 11. Time series of water levels for 40 hours at a grid node with a depth of 0.22 m above model 

zero elevation. When total water depth falls to 10 cm or less, the cell becomes inactive. 

After each run, the computed datum fields were used to adjust the water depths from the 

original sounding datum (MLLW, MLW, or LWD) to the model zero elevation. After 

three runs, the datum adjustments converged to repeating values. 

 

Then the computed datums were compared to those derived from observations. Several 

sets of runs were completed to make the tides more realistic; these involved alterations in 

the grid to better represent geographic features or modifications in the method used in 

assigning bathymetric values to grid nodes. For the final run, the root mean square (RMS) 

difference between the modeled and observed MHHW, MHW, MLW, and MLLW datum 

values, relative to MSL, was 5.2 cm (Appendix D). A plot of the MHHW and MLLW 

comparisons is shown in Figure 12. The modeled fields for MSL and diurnal range are 

shown in Figures 13 and 14, respectively. 

River flows for the Pamlico, Neuse, and Tar Rivers were added to the water level model 

to assess their influence on mean levels. The differences between the tide-only and the 

tide-plus-rivers computed water levels were negligible, except in the upper reaches on the 

rivers, where differences on the order of less than 1 cm were found. 
17

 (a) (b) 

Figure 12. Comparison of (a) the MHHW and MLLW datums (m) and (b) MHW and MLW datums 

obtained from observations (horizontal axis) and from the hydrodynamic model (vertical axis). RMS 

error for all datums is 5.2 cm.

 Figure 13. Mean sea level, as computed by the hydrodynamic model. MSL is relative to the model's 

zero elevation. 

 
18

 

Figure 14. Diurnal tide range (the difference between MHHW and MLLW) as computed by the 

hydrodynamic model.

3.6. Corrections to the Modeled Tidal Datum Fields 

The tidal datum fields as computed by the hydrodynamic model match closely, but not 

exactly, to the datums at the stations based on observed water levels. The RMS error for 

the four tidal datum fields (MHHW, MHW, MLW, and MLLW) was 5.2 cm. Plots of the 

errors for MHHW and MLLW, and for MHW and MLW, are shown in Figure 12. 

Therefore, the four datum fields were ‘corrected’ by subtracting the interpolated error 

field. The interpolated error field was generated by taking the error at each individual 

water level station, and creating an interpolated field using the Tidal Constituent And 

Residual Interpolation (TCARI) model (Hess, 2002; Hess, 2003). A sample error field is 

shown in Figure 15. The corrected fields closely match the observed datums at the water 

level stations. 
19

Figure 15. Error (modeled value minus observed value) in the MHHW datum field as interpolated by 

the TCARI method.
20
21

4. THE TIDAL MARINE GRIDS 

The tidal marine grid for a specific region consists of points with uniform spacing in the 

longitudinal and latitudinal directions. Points designated as water are populated by tidal 

datums, while other points are designated as land and given the default, or null, value of 

−88.8888. The tidal datums used to populate the marine grid are produced by the 

hydrodynamic model and corrected by spatial interpolation. The datum values are then 

spatially interpolated to the points in the marine grid. The sea surface topography is 

interpolated to another marine grid and is described in Section 5. 

It is important to note that, in the VDatum software, the final datum conversion values at 

any geographic point within the marine grid are determined by a distance-weighted 

average of the datum values at the surrounding four points. Therefore, if even one of the 

four surrounding points is non-null, a datum value will be returned. Hence, the marine 

grid’s point spacing puts a limit on the size of geographic features that can be recognized. 

However, the region in North Carolina consisting of Pamlico and Albemarle Sounds is 

separated from the ocean by a series of narrow barrier islands which have significantly 

different tidal datums on each side. Some islands are so narrow that the marine grid 

spacing would have to be in the order of 10s of meters to represent them. Therefore, the 

entire VDatum region was divided into two separate areas, each with a distinct marine 

grid. Having two marine grids eliminates the possibility that VDatum points representing 

the ocean and the sound might be adjacent in the same grid. The border between the 

regions was defined by a set of points approximating the centerline of the barrier islands. 

The grid covering the sounds is called the Pamlico Sound Grid and the grids representing 

the area oceanward of the barrier islands are called the Coastal North Grid and the 

Coastal Central Grid. 

4.1. Grid Point Location 

The location of the points in each marine grid is completely defined by the geographic 

coordinates of the origin (i.e., the most southwesterly point), the latitude and longitude 

spacing between points, and the maximum number of points in the eastward and 

northward directions. The grid origin is at latitude0 and longitude0, and extends to 

latitude1 and longitude1. The longitudinal spacing between points is delx, and the 

latitudinal spacing is dely. The VDatum grid consists of points as defined by 

longitudei = longitude0 + (i - 1)delx 

latitudej = latitude0 + (j - 1)dely 

 

where the index i denotes longitude and index j denotes latitude. The range of i is 1 to 

imax and the range of j is 1 to jmax, where 
22

imax = 1+ ( longitude1 - longitude0 )/delx 

jmax = 1+ ( latitude1 - latitude0 )/dely 

For the North Carolina coastal area in the present study, three separate grids were needed 

to (a) properly represent the influence of the narrow barrier islands and (b) to keep file 

sizes small (under one million points in the grid). The values for the grids, called the 

Pamlico Sound, Coastal Central, and Coastal North, are given in Table 3. 

 Table 3. Parameters for the North Carolina tidal marine grids. Latitude is positive northward, and 

longitude is positive eastward.

Region latitude0

(degrees) 

longitude0

(degrees) 

dely 

(degrees) 

delx 

(degrees) 

Jmax Imax 

Pamlico 

Sound Grid 

34.594 282.745 

(-77.255) 

0.002 0.0025 639 723 

Coastal 

Central Grid 

34.026 282.745 

(-77.260) 

0.002 0.0025 640 965 

Coastal North 

Grid 

35.296 284.050 

(-75.950) 

0.002 0.0025 732 443 

4.2. Population of the Marine Grids 

There are two main steps in creating and populating the marine grids. In the first step, all 

points in the marine grid are given a latitude and longitude (using values given in Table 

3), and then set to be either land or water. Points are set to water if they are located within 

a half a grid spacing of a coastline segment that defines either the mainland or an island; 

otherwise they are land (see Hess and White, 2004, for a detailed discussion). This step is 

accomplished by the Fortran program vgridder5.f. 

The next step consists of filling the water values with the tidal datum values. For the 

North Carolina region, the datum values have been generated by the hydrodynamic 

model and corrected to match the station data (Section 3). Recall that each cell in the 

hydrodynamic model’s unstructured mesh is defined by the three nodes which form the 

vertices, and each node is the vertex of one or more elements. For each water point, the 

closest node in the unstructured grid is found. If the water point lies inside a 

hydrodynamic model grid element, the value for the marine grid is linearly interpolated 

from the values at the nodes. If the water point lies outside all hydrodynamic model cells, 

it is filled by one of two methods. In the first method, if the closest node is less than a 

user-specified distance (the variable radius, here 0.002 deg) from the water point, the 

datum value is defined as the distance-weighted (by inverse square) mean of the values at 

the vertices of all elements which have the closest node in common. In the second 

method, if the closest node is not less than the user-specified distance, the water point is 

filled by an iterative procedure. At each iteration, all water points (in this category) are 

set to the mean of the surrounding water point values. The iterative procedure is complete 
23

when the maximum value over the entire marine grid of the difference between the new 

value at a point and its preceding value (for points in this category) falls below a given 

level (5 x 10-5 m). Note that a few marine water points cannot be filled by any of these 

methods because they are too distant from the hydrodynamic model grid or are physically 

separated from the filled water points by intervening land; these points remain unfilled. 

This second step in the process is accomplished by the Fortran program vpop11.f.

4.3. Illustration of Problems at Barrier Islands 

To illustrate the problem of filling a marine grid that crosses a barrier island, consider the 

filling of a single marine grid that covers both the sound side and the ocean side of a 

barrier island. In Figure 16, three values of the difference between MHHW (relative to 

MSL) in two rows of the marine grid have been filled by the methods described above. In 

the upper row the values are 13.7, 30.0, and 58.0 cm, and in the lower they are 14.1, 14.4, 

and 57.9 cm. The first and last values in each row were filled by interpolation from the 

values at the hydrodynamic model’s nodes, since they lie inside a model cell. These 

values adequately represent the hydrodynamic model values, which reflect the large tide 

range to the east of the barrier island and the small tide range to the west. Note that the 

middle value in the upper row, 30.0 cm, was determined by the mean of the surrounding 

values. However, it is not realistic because it averages values from both sides of the 

barrier island. 

Consider how VDatum would interpolate to find the values at Points A and B in Figure 

16. At A, the interpolated datum (using the values at the four surrounding water points) is 

approximately 22 cm, which is too large for the small tide range on the western side (the 

correct value should be 14 cm). At B, the value is approximately 42 cm, which is too 

small for the eastern side (the correct value should be 57 cm). A simple way to correct 

this problem is to use a dividing line to restrict vpop11.f’s selection of nodes in the 

hydrodynamic model. 

Suppose that the centerline of the barrier island in Figure 16 was a dividing line. When 

the selection of nodes is carried out, the marine grid points to the left of the line will use 

only hydrodynamic nodes to the left of that line, and similarly for the points and nodes to 

the right of the line. Then the marine grid values selected will be as shown in Figure 17. 

The values are now much more realistic. Note that the middle value in the upper row, 

which without the dividing line was 30.0 cm, is now 13.3 cm. Again, consider Points A 

and B in Figure 17. At A, the interpolated datum (using the values at the four surrounding 

water points) is approximately 14 cm, and at B, the value is approximately 58 cm; these 

are much more realistic values. The concepts in the dividing line are now extended to the 

bounding polygons. 
24

Figure 16. Sample region with marine grid points (solid squares) and their numerical datum values 

(cm), hydrodynamic model grids (large triangles) with datum values at their vertices (cm), narrow 

barrier island (gray area), and test points A and B.

 

Figure 17. Sample region with marine grid points (solid squares) and their datum values 

(cm), hydrodynamic model grids (large triangles) with their MHHW to MSL datum values 

(cm) at the vertices, a narrow barrier island (curved lines), and the bounding polygon (solid 

line inside barrier island). 
25

4.4. The Bounding Polygons 

As mentioned above, the presence of barrier islands can lead to the marine grid being 

filled with erroneous values. This problem can be rectified by introducing one or more 

bounding polygons that limit the selection of hydrodynamic model nodes when filling the 

marine grid. For the barrier islands of North Carolina, we generated three polygons. First, 

we created a line that approximated the centerline of the barrier islands. To create the 

offshore, or coastal ocean, polygons, the upper end of the centerline line was extended 

eastward to a distance somewhat beyond 25 nmi (the outer limit of coverage of national 

VDatum). To this were added five straight line segments that approximately followed the 

25 nmi line and stayed within the hydrodynamic model grid (Figure 18). The final line 

segment joined the westernmost point of the centerline. This polygon was the divided 

into two parts, the Coastal Northern and the Coastal Central polygons, separated at 

35.30°. 

To create the Pamlico Sound polygon, a point on the centerline just north of Oregon Inlet 

was selected. The latitude of the point, 35° 35.78′, ensures that Albemarle Sound is 

excluded from the polygon. This exclusion was necessary because the astronomical tides 

in this area are so small that wind tides may be dominant, in which case a tidally-defined 

shoreline may not be meaningful. Next, a line segment was extended westward to the 

longitude of the westernmost point of the centerline, and another line segment was 

extended southward to meet the centerline. From this initial polygon three areas were 

excluded. The areas were the Alligator River on the north border of the polygon, since it 

is part of Albemarle Sound; the southwest corner west of White Oak River, since that 

area is not in the hydrodynamic model grid; and a section of the Harlowe Canal which 

also is not in the hydrodynamic model grid. This polygon is shown in Figure 18. Since 

the sstronomical tides in Albemarle and Currituck Sound are so small and there is so little 

tidal data for these areas, no marine grid was developed to cover them. 

The bounding polygons were then used to create and populate the final marine grids. As 

before, during the gridding process (using program vgridder5.f), points within land 

polygons were set to land. Also, points outside the bounding polygon were also set to 

land. During the population process (using program vpop11.f), water points were filled 

with values from the hydrodynamic model. However, nodes in the hydrodynamic model 

had to be within the bounding polygon to be used. An exception to this restriction is that 

if any of the nodes defining the elements vertices fell within the bounding polygon, the 

remaining vertices could be used. A plot of the marine grid and values around Oregon 

Inlet are shown in Figure 19.

To test the continuity of datums, values of MHHW were extracted at points along a track 

that crossed the bounding polygon. The 10 points in the track are shown in Figure 19. 

The extracted tidal datums were plotted in Figure 20, along with values extracted from a 

coastal marine grid with twice the point spacing. The smaller spacing eliminates the 

discontinuity in datum values at the boundary. 
26

Figure 18. The bounding polygons for the Coastal North area (purple line), Coastal Central 

area (green line), and Pamlico Sound area (blue line). Also shown are shoreline (gray) line, 

the hydrodynamic model’s offshore boundary (dashed black line) and the 25 nmi limit 

(dotted black line). 
27

Figure 19. Area around Oregon Inlet showing the locations of the tidal marine grid points 

for the Pamlico Sound grid (blue squares) and the Coastal North grid (purple squares). The 

plus signs represent null points for each grid. The value (cm) of the tidal datum (here the 

difference between MHHW and MSL) is shown next to the non-null points. Points along a 

track crossing the bounding polygon are shown as black squares. 

 

Figure 20. Datum values along a 10-point track from northeast to southwest (see Figure 19) 

from (a) both grids having equal spacing of approximately 0.24 nmi (open squares), and (b) 

a Pamlico grid with spacing of 0.24 nmi and a coastal grid with spacing of 0.48 nmi (plus 

signs). Notice the discontinuity of 0.11 m at an along-track distance of 0.25 nmi. 
28

4.5. Assessment of Errors in the Marine Grid 

Probable errors in the VDatum tidal transformation fields are extremely difficult to assess 

in a direct way. However, they may be assessed indirectly by three methods: (1) 

analyzing the errors in the tidal hydrodynamic model results, (2) analyzing the 

interpolated fields of errors, and (3) comparing values in the marine grids with known 

datums at the tide stations. The most conservative method is the first, and it yields a 

probable RMS error of about 5 cm. In all likelihood, since an error correction field has 

been added to the hydrodynamic model output, the RMS error is less than 5 cm. 

For the first method, as was discussed in Section 3.5, the mean RMS error from the 

hydrodynamic model at the 44 stations used in the comparison (Appendix B) was 5.2 cm. 

The RMS errors for each individual datum were 5.8 cm for MHHW, 5.0 cm for MHW, 

5.1 cm for MLW, and 4.7 cm for MLLW. Maximum absolute errors in MHHW and 

MHW (20.7 cm and 19.0 cm, respectively) occurred at the Harkers Island Bridge tide 

station (865-6503), although the errors in the MLW and MLLW datums for that location 

were under 5.0 cm. Maximum absolute error in the MLW datum, 20.4 cm, occurred at 

Spooners Creek tide station (865-6467), although the errors in the other datums at that 

location were under 5.5 cm. The maximum absolute error in the MLLW datum, 12.9 cm, 

occurred at Cape Lookout Inside tide station (865-6841). The absolute errors in the other 

datums there were all between 10 and 12 cm. Errors in the hydrodynamic model’s datum 

values probably result from using coastline, bathymetry, and tidal observations from 

several different time periods. 

The second method is the assessment of the fields of interpolated error. Recall that 

hydrodynamic model errors were compensated for by subtracting from the modeled field 

of values an interpolated error field that matches the error value at the tide stations. This 

compensation process eliminates the error at the tide stations, but the effect on errors 

elsewhere is not precisely known. However, Figure 15 shows that the error field for 

MHHW is spatially consistent within the outer coastal area, Pamlico Sound, and the 

Beaufort Inlet area. Negative values in Pamlico Sound indicate that the hydrodynamic 

model under-predicts the tidal datum there, while positive values around Beaufort Inlet 

indicate that the model over-predicts the datum there. Therefore, even accounting for the 

fact that the interpolated error field may be somewhat unrealistic around some of the 

input locations, the overall effect is probably to reduce the errors in the datum fields. An 

examination of the values in the fields shows that the RMS value of the interpolated error 

field is 3.9 cm for MHHW, 3.1 cm for MHW, 4.2 cm for MLW, and 3.4 cm for MLLW, 

for an overall value of 3.7 cm. 

As a final assessment of error, the datum values extracted from the tidal marine grid at 

the locations of the tide stations were compared (using program cp3.f) to the tidal datums 

obtained from observations. This assesses errors that may occur when transferring the 

corrected tidal model results to the uniformly-spaced marine grid. Errors may arise 

because the model values are represented at the nodes in an unstructured mesh with 

triangular elements of varying sizes. Transfer of values is accomplished by spatial 

interpolation or extrapolation, or by the iterative solution of Laplace’s Equation, 
29

depending on the closeness of the marine grid point to points in the unstructured mesh. 

The results (Appendix E) show that the mean RMS error for the 40 tide stations within 

the three marine grids and all four datums was 1.1 cm, with the maximum error of 3.7 cm 

at Sea Level, Core Sound (865-5875). 

As a consistency check, we can examine the maximum point-to-point differences in 

values in the marine grid using program cp3.f. Differences are generally small except in 

regions near the inlets, where differences in adjacent point values can be as much as 15 

cm. These differences are reasonable, given the rapid spatial changes in tidal water levels 

in these regions. 

 
30
31

5. SEA SURFACE TOPOGRAPHY

VDatum requires a gridded Topography of the Sea Surface (TSS), which is defined here 

as the elevation of the North American Vertical Datum of 1988 (NAVD 88) relative to 

local mean sea level (LMSL). The TSS links the tidal datums with NAVD 88 and thus to 

land-based elevation reference systems. Values at the tide stations that were used to 

create the gridded field are shown in Table 4. Except for a single station, these values 

have been updated to the latest tidal datum epoch. The general picture shows that NAVD 

88 is about 13 cm above MSL in the offshore area (e.g., Duck Pier), but only 1 or 2 cm 

above MSL inside the sounds (e.g., Rodanthe). Thus MSL in Pamlico Sound may be 

about 12 cm higher than MSL outside the barrier islands, probably due to water density 

differences and non-linear effects. 

Table 4. Observed values of NAVD 88 relative to LMSL. The data are based on the most recent 

National Tidal Datum Epoch (1983-2001) unless noted, and a positive value means that the NAVD 88 

elevation lies above the LMSL surface. 

 N Station Name NOS Number NAVD 88 Notes 

 

 1 Virginia Bch, Rudee Inlet 863-9208 0.206 

 2 Duck Pier 865-1370 0.128 

 3 Oyster Creek, Croatan Snd 865-2437 0.012 

 4 Oregon Inlet Marina 865-2587 0.026 

 5 Rodanthe 865-3215 0.009 

 6 Cape Hatteras Pier 865-4400 0.135 

 7 Ocracoke Is. 865-4792 0.027 Older Epoch 

 8 Cedar Island 865-5151 -0.003 

 9 New River, Jacksonville 865-6394 0.020 

10 Beaufort (Duke Lab) 865-6483 0.112 

11 Morehead Cty Harbor 865-6502 0.118 

12 Harkers Is. Brdg. 865-6503 0.066 

13 Taylor Creek 865-6518 0.126 

14 Lenox Pt, N. River Chnl. 865-6539 0.085 

15 Atlantic Bch SSS Pier 865-6590 0.133 

16 Calico Jacks Marina 865-6612 0.094 

17 Wilmington Bch 865-8559 0.216 

An initial gridded TSS data set was generated as follows. First a uniform grid, which has 

the attributes shown in Table 5, was created. Then, with Surfer® software, a minimum 

curvature algorithm interpolated the values at the tide stations on to the uniform grid. In 

the interpolation, contours on the outer-coastal region were separated from those in the 

Pamlico Sound region by the use of break lines. The break lines were a series of line 

segments running along the middle of the barrier islands, and having gaps at the inlets. 

This line was constructed from the barrier island centerline described in Section 4.3. 

Because of the problem with interpolating across the barrier islands and the limits on file 
32

size, the bounding polygons that were used in the tidal datum grid (Section 4.3) were 

used to create three new, smaller TSS grids. The attributes of the new TSS grids, two for 

the outer coastal area and one for the Sounds, are the same as those in Table 5. The three 

TSS fields are plotted in Figure 21. 

Table 5. Parameters for the initial North Carolina sea surface topography (TSS) grid. Latitude is 

positive North, longitude is positive East.

Region latitude0

(degrees) 

longitude0

(degrees) 

dely 

(degrees) 

delx 

(degrees) 

Jmax Imax 

 Initial TTS 

Grid 

34.000 282.700 (-77.300) 0.001 0.001 2801 2501 

 

Figure 21. The computed sea surface topography (TSS). Elevations are in meters.
33

6. SUMMARY AND CONCLUSIONS 

In support of the national VDatum program, tidal datums in North Carolina were 

generated from a hydrodynamic model (ADCIRC). The tidal model used NOS 

bathymetry, corrected by an iterative procedure to compute water depths relative to MSL, 

and to the model’s zero elevation. Digital coastline was used to create the finite element 

grid. Tidal datums from the model were compared to NOS data at tide stations and 

corrected with the TCARI spatial interpolation. The datums were then transferred to three 

regular VDatum grids, two for the coastal ocean area (Coastal North and Coastal Central) 

and one covering Pamlico, Core, Back, and Bogue Sounds. The topography of the sea 

surface (TSS) was computed by spatially-interpolating the values at tide stations onto an 

initial, uniform grid. The final TSS grids were created for three areas, two for the coastal 

ocean and one for the sounds. 

Tidal datum values for the most recent available epoch were obtained from CO-OPS. A 

potential problem came with the use of tidal data from different tidal datum epochs. To 

decide whether older data could be used, we compared datums at stations in the North 

Carolina region which had values for both the most recent (1983 to 2001) and the 

previous (1960 to 1978) epochs. Since the datums have changed only a few percent 

between these two periods, we chose to use the older values when newer ones were not 

available. However, we recognize that there will be a few stations where significant 

changes are possible. 

The RMS error of the tidal model was computed to be 5.2 cm for 44 stations and four 

datums. The largest errors (10 to 20 cm for MHHW) occurred at the U.S. Coast Guard 

Station at Oregon inlet, Harkers Island, and inside Cape Lookout. The most probable 

reason for these errors is that the tidal data were collected several decades ago, while the 

hydrodynamic model uses coastline and bathymetry representing more recent conditions. 

Since the tidal data were collected, there have been numerous changes in channel position 

and depth (Oregon Inlet), intertidal areas (Harkers Island), and spit shoal areas (Cape 

Lookout). The hydrodynamic model’s datums were corrected by subtracting an error 

field for each datum field. The error field was constructed by interpolating the error 

values at the tide stations throughout the grid 

The division into three grids was necessitated by the existence of North Carolina’s barrier 

islands, which are too narrow to be represented adequately in the marine grids, and on a 

limit on the number of points in a marine grid (under 1 million). The solution was the 

creation of the three bounding polygons that were used to separate the regions on each 

side of the narrow barrier islands. The polygons were based on the break lines used in 

making the TSS fields; the break lines were hand-extracted from the digitized coastline 

data set. To create the bounding polygons, the break line segments were joined at the 

inlets to create the centerline. 

It has been decided that VDatum will cover navigable waters for which the NOAA 

nautical charts shows depth values, and will range from the heads of estuaries and bays 
34

out past the oceanic coastline to a distance on 25 nmi from that coastline. This 

requirement helped to determine the outer boundary of the coastal ocean polygon. 

Because there are three separate grids, there may be a small mismatch in datum 

conversion values at locations where the two meet, usually at the inlets (see Figures 12 

and 21). Recall that VDatum performs a distance-weighted averaging of the non-null 

values in the marine and TSS grids. At these marine grid cells, often there will be only 

two or three non-null values, a situation which makes the interpolation less accurate. In 

addition, at the inlets the spatial gradients in the tidal fields are large and changing 

rapidly. 

Albemarle and Currituck Sounds have not been included in this application of VDatum 

because astronomical tides are small there. Typical tide ranges are 10 cm or less. Wind 

tides in these sounds, however, can be quite large. Therefore, VDatum for this sound will 

have to be postponed until a relationship between charted MHW and water level 

fluctuations is established. 

Future work may include extending VDatum to more of the southern coast of North 

Carolina, and extending the grids to Albemarle and Currituck Sounds. 

ACKNOWLEDGEMENTS 

Digital coastline was provided by CSDL’s Annimeke Raymond, working in the Extracted 

Vector Shoreline project begun by CSDL’s Roger Johnson. Dennis Milbert of NOS’ 

National Geodetic Survey (NGS) provided insights into generating, populating, and 

testing the VDatum grid, and provided NGS benchmark data. Carol Auer of NOS’ 

National Centers for Coastal Ocean Science provided partial funding through the sea 

level rise program. 
35

REFERENCES 

Gesch, D. and R. Wilson, 2001: Development of a Seamless Multisource Topographic/ 

Bathymetric Elevation Model for Tampa Bay. Marine Technology Society Journal, 

35(4): 58-64, Winter 2001/2002. 

Gill, S. K., and J. R. Schultz, 2001: Tidal Datums and Their Applications. Silver Spring, 

Maryland: U.S. Department of Commerce, National Oceanic and Atmospheric 

Administration, Silver Spring, Maryland. NOAA Special Publication NOS CO-OPS 1, 

111 pp + appendix. 

Hess, K. W, 2001: Generation of Tidal Datum Fields for Tampa Bay and the New York 

Bight. U.S. Department of Commerce, National Oceanic and Atmospheric 

Administration, Silver Spring, Maryland, NOAA Technical Report NOS CS 11, 43 pp. 

___, 2002: Spatial interpolation of tidal data in irregularly-shaped coastal regions by 

numerical solution of Laplace’s equation. Estuarine, Coastal and Shelf Science, 54(2), 

175-192. 

 ___, 2003: Water level simulation in bays by spatial interpolation of tidal constituents, 

residual water levels, and datums. Continental Shelf Research, 23(5), 395-414. 

___, S. A. White, J. Sellars, E. A. Spargo, A. Wong, A. K., Gill, and C. Zervas, 2004. 

North Carolina Sea Level Rise: Interim Project Report. NOS Technical Memorandum

NOS CS 5, 26 pp. 

__, D. G. Milbert, S.K. Gill, and D.R. Roman, 2003: Vertical Datum Transformations for 

Kinematic GPS Hydrographic Surveys. Proceedings, U.S. Hydrographic Conference, 

March 24 – 27, 2003. Biloxi, Mississippi. 8 pp. 

 ___, and S. K. Gill, 2003: Puget Sound Tidal Datums by Spatial Interpolation. 

Proceedings, Fifth Conference on Coastal Atmospheric and Oceanic Prediction and 

Processes. Am. Meteorological Soc., Seattle, August 6-8, 2003. Paper 6.1, 108 - 112. 

___, and S. A. White, 2004: VDatum for Puget Sound: Generation of the Grid and 

Population with Tidal Datums and Sea Surface Topography. U.S. Department of 

Commerce, National Oceanic and Atmospheric Administration, Silver Spring, Maryland, 

NOAA Technical Memorandum NOS CS 4, 27 pp. 

___, R. Wilson, D. Roman, and D. Milbert, 2004: Final Report on NOAA’s Work on the 

Southern Louisiana Coastal Topographic/bathymetric Project. Coast Survey 

Development Laboratory, Office of Coast Survey, National Ocean Service, Silver Spring, 

Maryland. Unpublished manuscript, 12 pp. 
36

 ___, and E. Spargo (in preparation): TideSheet: An Updatable Astronomical Tide 

Database. Coast Survey Development Laboratory, Office of Coast Survey, National 

Ocean Service, Silver Spring, Maryland. 48 pp. 

Luettich, R.A. and J.J. Westerink, 1995: Continental Shelf Scale Convergence Studies 

with a Barotropic Tidal Model. In Quantitative Skill Assessment for Coastal Ocean 

Models, D.R. Lynch and A.M. Davies, Editors, Coastal and Estuarine Studies Series, 47, 

American Geophysical Union, Washington, D.C., 1995. 

___, 2004: Theory Report: Formulation and Numerical Implementation of the 2D/3D 

ADCIRC finite element model version 44.XX. Available at 

www.marine.unc.edu/C_CATS/adcirc/adcirc_theory_2004_05_14.pdf. 

Luettich, Jr., R. A., J. L. Hench, C. W. Fulcher, F. E. Werner, B. O. Blanton, and J. H. 

Churchill, 1999: Barotropic tidal and wind driven larval transport in the vicinity of a 

barrier island inlet. Fisheries Oceanography, 33 (April), 913 – 932. 

Milbert, D.G., 2002: Documentation for VDatum (and VDatum Tutorial); Vertical Datum 

Transformation Software. Ver. 1.06 (nauticalcharts.noaa.gov/bathytopo/vdatum.htm). 

Mukai, A., J.J. Westerink, R.A. Luettich, and D. Mark, 2000: A Tidal Constituent 

Database for the Western North Atlantic Ocean, Gulf of Mexico and Caribbean Sea. 

Technical Report, U.S. Army Engineer Research and Development Center, Vicksburg 

Mississippi, September 2001. 

Myers, E., 2001: Generation of Tidal datums for Central California. Coast Survey 

Development Laboratory, Office of Coast Survey, National Ocean Service, Silver Spring, 

Maryland. Unpublished manuscript, 13 pp. 

Parker, B. P., 2002: The integration of bathymetry, topography, and shoreline, and the 

vertical datum transformations behind it. International Hydrographic Review (3) 3 

(November 2002). 

Parker, B., K. W. Hess, D. Milbert, and S. K. Gill, 2003: A national vertical datum 

transformation tool. Sea Technology, v. 44. no. 9 (Sept. 2003), 10 - 15. 

Spargo, E. A., and J. W. Woolard, 2005. VDatum for the Calcasieu River from Lake 

Charles to the Gulf of Mexico, Louisiana: Tidal Datum Modeling and Population of the 

Grid. NOS Technical Report NOS CS 19, 26 pp. 

Spargo, E. A., 2003: Using a Finite Element Model of the Shallow Water Equations to 

Model tides in the Eastern North Pacific Ocean. Masters Thesis, University of Notre 

Dame, South Bend, Indiana. 224 pp. 
37

APPENDIX A. BATHYMETRIC DATA SOURCES 

 * Although CRM grids are distributed in NAD83 and Mean Sea Level, point soundings 

 were not uniformly georeferenced prior to gridding. 

 # Evaluated but not used. 

 # SPO's reported accuracies do not account for errors resulting from mixing the various 

 georeference systems of soundings compiled to create bathymetric grids. 

 # Although SPO grids are distributed in North American Datum 1927 and MLW, 

 point soundings were not uniformly georeferenced prior to gridding. 

Table A.1. Sources of bathymetric data that were evaluated and processed for the development of 

the water level model and VDatum marine grid. 

Accuracies reported for point soundings datasets employ the rigorous standards specified by the 

International Hydrographic Office. Where possible, the original horizontal coordinates of sounding 

points were converted to North American Datum of 1983 (NAD83) with the Geodetic Reference System 

1980 ellipsoid, which closely corresponds to World Geodetic System 1984. Vertical datums are 

expressed as tidal Mean Low Water (MLW), Mean Lower Low Water (MLLW) or local Low Water 

Datum (LWD). The gridded bathymetric datasets were generated by interpolating water depths without 

common re-referencing of the various original horizontal and vertical datums; i.e, bathymetric grids were 

derived from non-uniformly geo-referenced soundings. 

Horizontal Horizontal Vertical Vertical Horizontal Vertical

Format Source Resolution Accuracy Resolution Accuracy Datum Datum

Point Soundings National Ocean Service (NOS) various 2-15m nearshore various 0.3m at 0-20m depth NAD83 by survey

 Hydrographic Survey Database 20-75m offshore 0.5-1m at 20-100m depth MLLW

1% of depth > 100m MLW

LWD

Point Soundings U. S. Army Corps of Engineers various 3m nearshore various 0.3m at 0-20m depth NAD83 MLW

 Regional channel surveys 20-75m offshore 0.5-1m at 20-100m depth

Point Soundings NOAA Nautical Charts - Digitized various 2-15m nearshore various 0.3m at 0-20m depth NAD83 by chart

20-75m offshore 0.5-1m at 20-100m depth MLLW

1% of depth > 100m MLW

LWD

Structured Grid National Geophysical Data Center ~90m grid undetermined 0.1-1m undetermined mixed* mixed*

 Coastal Relief Model (CRM) NAD83 MLLW

other MLW

LWD

Structured Grid NOS Special Projects Office (SPO) ~30m grid ~3m nearshore# 2m ~2% of depth# mixed# mixed#

 Estuarine Bathymetry# ~90m grid NAD83 MLLW

other MLW

LWD
38
39

APPENDIX B. WATER LEVEL STATION DATA 

Tidal data were extracted from the CSDL database TideSheet101, which has the latest 

CO-OPS tidal datums as of April 2005. 

Table B.1. Tidal and orthometric datums (meters) and tidal datum epochs for the North 

Carolina stations used in this study. All datums are referenced to local mean sea level. -

9.999 denotes a missing value. Where the tidal epoch is unknown, the values ‘0-0’ are shown 

for the years. An ‘*’ following the epoch indicates that only the NAVD88 values were used. 

No. Station Latitude Longitude MHHW MHW MLW MLLW NAVD88 Epoch 

 1 8639208 36 49.90 -75 58.10 0.573 0.487 -0.514 -0.551 0.206 1983-2001 * 

 2 8651370 36 11.00 -75 44.80 0.585 0.487 -0.495 -0.539 0.128 1983-2001 

 3 8651375 36 10.40 -75 45.50 0.021 0.012 -0.012 -0.021 -9.999 0- 0 

 4 8652226 35 54.60 -75 35.50 0.609 0.518 -0.488 -0.549 -9.999 0- 0 

 5 8652232 35 54.60 -75 40.20 0.082 0.066 -0.026 -0.060 -9.999 1960-1978 

 6 8652247 35 54.20 -75 46.20 0.058 0.050 -0.044 -0.066 -9.999 1983-2001 

 7 8652437 35 50.70 -75 39.30 0.090 0.064 -0.062 -0.093 -9.999 1983-2001 

 8 8652547 35 48.70 -75 42.00 0.088 0.062 -0.061 -0.093 -9.999 1983-2001 

 9 8652587 35 47.70 -75 32.90 0.180 0.135 -0.137 -0.176 0.026 1983-2001 

 10 8652591 35 47.90 -75 35.00 0.092 0.061 -0.061 -0.091 -9.999 0- 0 

 11 8652648 35 46.50 -75 34.90 0.135 0.095 -0.102 -0.140 -9.999 1983-2001 

 12 8652657 35 46.40 -75 33.50 0.214 0.183 -0.183 -0.213 -9.999 0- 0 

 13 8652659 35 46.40 -75 32.30 0.336 0.275 -0.305 -0.335 -9.999 0- 0 

 14 8652678 35 46.10 -75 31.60 0.366 0.305 -0.294 -0.321 0.158 1983-2001 

 15 8652715 35 45.40 -75 31.90 0.274 0.244 -0.275 -0.305 -9.999 0- 0 

 16 8652737 35 44.90 -75 33.20 0.153 0.122 -9.999 -0.152 -9.999 0- 0 

 17 8652905 35 41.90 -75 46.40 0.094 0.068 -0.072 -0.103 -9.999 1983-2001 

 18 8653215 35 35.70 -75 28.30 0.168 0.115 -0.105 -0.131 0.009 1983-2001 

 19 8654400 35 13.40 -75 38.10 0.564 0.455 -0.456 -0.492 0.135 1983-2001 

 20 8654792 35 6.90 -75 59.30 0.199 0.161 -0.140 -0.159 0.030 1983-2001 

 21 8655151 35 1.20 -76 18.60 0.082 0.071 -0.042 -0.045 -0.003 1983-2001 

 22 8655875 34 52.50 -76 20.60 0.100 0.088 -0.087 -0.120 -9.999 1983-2001 

 23 8656084 34 49.40 -76 41.40 0.407 0.336 -0.308 -0.334 -9.999 1960-1978 

 24 8656225 34 47.50 -76 36.50 0.330 0.284 -0.256 -0.280 -9.999 1960-1978 

 25 8656298 34 46.00 -76 41.20 0.606 0.515 -0.430 -0.491 -9.999 1960-1978 

 26 8656306 34 46.10 -76 40.30 0.560 0.472 -0.467 -0.505 -9.999 1983-2001 

 27 8656394 34 44.70 -77 26.20 0.091 0.080 -0.084 -0.112 0.020 1983-2001 * 

 28 8656451 34 43.70 -76 40.10 0.531 0.451 -0.472 -0.518 -9.999 1960-1978 

 29 8656467 34 43.50 -76 48.20 0.229 0.195 -0.021 -0.204 -9.999 1960-1978 

 30 8656483 34 43.20 -76 40.20 0.558 0.470 -0.477 -0.521 0.112 1983-2001 

 31 8656486 34 43.20 -76 45.30 0.354 0.302 -0.302 -0.332 -9.999 1960-1978 

 32 8656495 34 43.20 -76 41.70 0.552 0.470 -0.487 -0.533 -9.999 1960-1978 

 33 8656499 34 43.10 -76 44.20 0.457 0.396 -0.336 -0.366 -9.999 1960-1978 

 34 8656502 34 43.20 -76 43.60 0.541 0.458 -0.481 -0.524 0.118 1983-2001 

 35 8656503 34 42.90 -76 34.70 0.145 0.095 -0.224 -0.248 0.066 1983-2001 

 36 8656518 34 42.70 -76 38.70 0.496 0.419 -0.440 -0.483 -9.999 1983-2001 

 37 8656539 34 42.50 -76 37.20 0.428 0.356 -0.365 -0.402 -9.999 1983-2001 

 38 8656554 34 42.20 -76 37.20 0.360 0.299 -0.311 -0.341 -9.999 1960-1978 

 39 8656566 34 42.00 -76 46.10 0.268 0.225 -0.257 -0.287 -9.999 1960-1978 

 40 8656569 34 41.90 -76 39.90 0.634 0.542 -0.433 -0.494 -9.999 1960-1978 

 41 8656571 34 41.90 -76 40.90 0.546 0.464 -0.487 -0.533 -9.999 1960-1978 

 42 8656590 34 41.60 -76 42.70 0.654 0.550 -0.563 -0.610 0.147 1983-2001 

 43 8656612 34 41.20 -76 32.00 0.318 0.257 -0.266 -0.295 0.094 1983-2001 

 44 8656841 34 36.80 -76 32.30 0.722 0.614 -0.620 -0.669 -9.999 1983-2001 

 45 8656937 34 36.50 -76 31.70 0.629 0.520 -0.527 -0.572 -9.999 1983-2001 

 46 8657419 34 27.10 -77 29.70 0.735 0.637 -0.642 -0.690 -9.999 1960-1978 

 47 8658559 34 1.90 -77 53.60 0.747 0.643 -0.639 -0.686 0.216 1983-2001 * 
40

Table B.2. NOS Water Level Station Names.

 No. Station Name 

 

 

 1 8639208 VIRGINIA BEACH RUDEE INL 

 2 8651370 DUCK FRF PIER 

 3 8651375 CURRITUCK SOUND NO 1 NC 

 4 8652226 JEANETTES PEIR NC 

 5 8652232 MANTEO SHALLOWBAG BAY 

 6 8652247 MANNS HARBOR CROATAN SOU 

 7 8652437 OYSTER CREEK CROATAN SOU 

 8 8652547 ROANOKE MARSHES LIGHT CR 

 9 8652587 OREGON INLET MARINA NC 

 10 8652591 ROANOKE SOUND CHANNEL NC 

 11 8652648 OLD HOUSE CHANNEL NC 

 12 8652657 OREGON INLET CHANNEL NC 

 13 8652659 OREGON INLET BRIDGE NC 

 14 8652678 USCG LIFEBOAT STATION ORE 

 15 8652715 PEA ISLAND #2 NC 

 16 8652737 DAVIS SLOUGH NC 

 17 8652905 LAKE WORTH STUMPY POINT 

 18 8653215 RODANTHE PAMLICO SOUND NC 

 19 8654400 CAPE HATTERAS FISHING PIE 

 20 8654792 OCRACOKE ISLAND 

 21 8655151 CEDAR ISLAND NC 

 22 8655875 SEA LEVEL CORE SOUND 

 23 8656084 CORE CREEK BRIDGE NC 

 24 8656225 NORTH RIVER BRIDGE BETTIE 

 25 8656298 NEWPORT RIVER NC 

 26 8656306 MOREHEAD-BEAUFORT Y C NEW 

 27 8656394 NEW RIVER JACKSONVILLE NC 

 28 8656451 GALLANT CHANNEL NC 

 29 8656467 SPOONERS CREEK NC 

 30 8656483 BEAUFORT DUKE MARINE LAB 

 31 8656486 N C A R STATE FISHERIES N 

 32 8656495 PORT TERMINAL NC 

 33 8656499 ATLANTIC BEACH BRIDGE NC 

 34 8656502 MOREHEAD CITY HARBOR HARB 

 35 8656503 HARKERS ISLAND BRIDGE NC 

 36 8656518 BEAUFORT TAYLOR CREEK NC 

 37 8656539 LENOXVILLE POINT NORTH RI 

 38 8656554 CHANNEL MARKER LIGHT #59 

 39 8656566 CORAL BAY ATLANTIC BEACH 

 40 8656569 BEAUFORT INLET CHANNEL RA 

 41 8656571 FORT MACON NC 

 42 8656590 ATLANTIC BEACH TRIPLE S P 

 43 8656612 CALICO JACKS MARINA NC 

 44 8656841 CAPE LOOKOUT (INSIDE) NC 

 45 8656937 CAPE LOOKOUT ATLANTIC OC 

 46 8657419 OCEAN CITY FISHING PIER 

 47 8658559 WILMINGTON BEACH NC 

 
41

APPENDIX C. HYDRODYNAMIC MODEL PARAMETERS 

C.1. Bottom Friction 

The ADCIRC model allows for several different methods of implementing bottom stress. 

Generally, bottom stress is expressed as bx=U* and by=V*, where U and V are the 

velocity terms and * is the bottom friction coefficient. For the linear option, 

*  Cf 

where Cf is the user specified bottom friction coefficient (and is constant in time, but may 

vary in space). For the quadratic friction option, 

H

Cf U V 2

1 2 2

*

(  )

  , 

where H is the bathymetric depth at the node. For the so-called hybrid friction, the same 

formula for * is used, although Cf is not assigned by the user but is calculated by the 

following formula: 





















 



 



  

H

H C C break

f f min 1 . 

In this equation, Hbreak (the so-called break depth) is a specified by the user such that in 

waters deeper than Hbreak, Cf approaches Cfmin, and in shallower waters (where H < Hbreak) 

Cf approaches Cfmin(Hbreak/H) The exponent  determines how quickly Cf approaches the 

asymptotic limit, and  determines how quickly the friction coefficient increases as the 

water depth decreases. This formulation allows for increasing values of bottom friction 

coefficients in very shallow water. 

For the North Carolina tidal simulations, the hybrid quadratic formulation was used, with 

values as follows: Cfmin = 0.0025, Hbreak = 2 m,  = 10, and  = 4/3. Effective values of Cf 

for various depths are shown in the table below. 

Depth (m) 0.1 0.5 2.0 5.0 10.0 

 Cf 0.1357 0.0159 0.0027 0.0025 0.0025 

C.2. Other Parameters 

A time step of 3 s was used, with a linear ramp-up time for tidal forcing of 5 days. The 

dimensionless tau0 value, which increases mass conservation, was set to 0.005 for water 

depths greater than 10 m, and 0.020 elsewhere. 
42
43

APPENDIX D. SUMMARY OF HYDRODYNAMIC MODEL ERRORS 

Table D.1. Summary of errors (modeled value minus observed value) at stations within the 

model grid. Values are in m. RMSE is root mean square error for the four datums at that 

station, and Amax is the maximum absolute error. Mean RMS error = 0.052 m. 

 n NOS MHHW MHW MLW MLLW RMSE Amax 

 1 8651370 -0.013 -0.007 0.010 0.036 0.020 0.036 

 2 8651375 -0.015 -0.007 0.007 0.014 0.012 0.015 

 3 8652226 -0.055 -0.058 0.023 0.067 0.054 0.067 

 4 8652232 -0.032 -0.022 -0.012 0.018 0.022 0.032 

 5 8652247 -0.017 -0.013 0.010 0.027 0.018 0.027 

 6 8652437 -0.002 0.014 -0.018 0.007 0.012 0.018 

 7 8652547 -0.002 0.015 -0.017 0.009 0.012 0.017 

 8 8652587 0.004 0.018 -0.029 0.002 0.017 0.029 

 9 8652591 0.008 0.024 -0.033 -0.009 0.021 0.033 

 10 8652648 0.057 0.066 -0.075 -0.046 0.062 0.075 

 11 8652657 -0.002 -0.005 -0.010 0.011 0.008 0.011 

 12 8652659 -0.086 -0.060 0.044 0.063 0.065 0.086 

 13 8652678 -0.108 -0.085 0.044 0.061 0.079 0.108 

 14 8652715 -0.055 -0.061 0.076 0.097 0.074 0.097 

 15 8652737 0.031 0.031 -9.999 -0.028 0.030 0.031 

 16 8652905 0.006 0.024 -0.015 0.008 0.015 0.024 

 17 8653215 -0.070 -0.024 0.019 0.035 0.042 0.070 

 18 8654400 -0.030 -0.017 0.014 0.028 0.023 0.030 

 19 8654792 -0.093 -0.066 0.034 0.040 0.063 0.093 

 20 8655151 -0.048 -0.052 0.023 0.023 0.039 0.052 

 21 8655875 0.031 0.012 -0.012 -0.001 0.018 0.031 

 22 8656084 0.048 0.039 -0.007 0.003 0.031 0.048 

 23 8656225 0.034 0.006 -0.024 -0.018 0.023 0.034 

 24 8656298 -0.040 -0.043 0.021 0.064 0.044 0.064 

 25 8656306 0.005 -0.001 0.057 0.077 0.048 0.077 

 26 8656451 0.047 0.035 -0.005 0.016 0.030 0.047 

 27 8656467 0.051 0.023 -0.204 -0.053 0.109 0.204 

 28 8656483 0.024 0.021 -0.010 0.008 0.017 0.024 

 29 8656486 0.016 0.001 -0.015 -0.022 0.015 0.022 

 30 8656495 0.037 0.029 -0.021 -0.003 0.026 0.037 

 31 8656499 -0.009 -0.022 -0.049 -0.051 0.038 0.051 

 32 8656502 -0.031 -0.028 0.036 0.048 0.036 0.048 

 33 8656503 0.207 0.190 -0.042 -0.046 0.144 0.207 

 34 8656518 -0.021 -0.021 0.029 0.043 0.030 0.043 

 35 8656539 0.039 0.036 -0.039 -0.032 0.037 0.039 

 36 8656554 0.097 0.084 -0.089 -0.089 0.090 0.097 

 37 8656566 0.046 0.025 -0.007 -0.011 0.027 0.046 

 38 8656569 -0.045 -0.041 -0.084 -0.050 0.058 0.084 

 39 8656571 0.039 0.031 -0.024 -0.006 0.028 0.039 

 40 8656590 -0.022 -0.015 0.021 0.042 0.027 0.042 

 41 8656612 0.048 0.040 -0.023 -0.021 0.035 0.048 

 42 8656841 -0.117 -0.104 0.107 0.129 0.115 0.129 

 43 8656937 -0.083 -0.069 0.074 0.094 0.080 0.094 

 44 8657419 -0.048 -0.050 0.052 0.072 0.056 0.072 
44
45

APPENDIX E. SUMMARY OF VDATUM ERRORS 

Error summary for all 40 tide stations: avg. rmse = 0.01100, max. rmse = 0.03699, 

avg. std = 0.00964, and max. std = 0.03627. The following tables show the errors in 

the Pamlico Sound region (Table E.1), the Coastal Central region (Table E.2) and the 

Coastal North region (Table E.3). 

Table E.1. Pamlico Sound Tide Station Comparisons (Errors in m). 

 

 

 n NOS lat lon rmse std 

 

 1 8652437 35.84500 -75.65500 0.00210 0.00209 

 2 8652547 35.81167 -75.70000 0.00236 0.00202 

 3 8652587 35.79500 -75.54833 0.00148 0.00145 

 4 8652591 35.79833 -75.58334 0.00637 0.00633 

 5 8652648 35.77500 -75.58167 0.00691 0.00683 

 6 8652657 35.77333 -75.55833 0.00208 0.00207 

 7 8652659 35.77333 -75.53833 0.00636 0.00308 

 8 8652678 35.76833 -75.52666 0.01175 0.00769 

 9 8652715 35.75667 -75.53167 0.01495 0.01387 

 10 8652737 35.74833 -75.55334 0.02171 0.02173 

 11 8652905 35.69833 -75.77333 0.00582 0.00193 

 12 8653215 35.59500 -75.47166 0.00267 0.00260 

 13 8654792 35.11500 -75.98833 0.02651 0.02643 

 14 8655151 35.02000 -76.31000 0.00067 0.00061 

 15 8655875 34.87500 -76.34333 0.03699 0.03627 

 16 8656084 34.82333 -76.69000 0.01552 0.01522 

 17 8656225 34.79167 -76.60833 0.01232 0.01191 

 18 8656298 34.76667 -76.68667 0.01612 0.01278 

 19 8656306 34.76833 -76.67167 0.00737 0.00606 

 20 8656451 34.72833 -76.66833 0.00352 0.00209 

 21 8656467 34.72500 -76.80334 0.01393 0.01253 

 22 8656483 34.72000 -76.67000 0.00267 0.00236 

 23 8656486 34.72000 -76.75500 0.00289 0.00288 

 24 8656495 34.72000 -76.69500 0.00524 0.00522 

 25 8656499 34.71833 -76.73666 0.01478 0.00738 

 26 8656502 34.72000 -76.72667 0.02297 0.02145 

 27 8656503 34.71500 -76.57833 0.02064 0.01485 

 28 8656518 34.71167 -76.64500 0.01316 0.01257 

 29 8656539 34.70833 -76.62000 0.00286 0.00286 

 30 8656554 34.70333 -76.62000 0.01765 0.01764 

 31 8656566 34.70000 -76.76833 0.00888 0.00607 

 32 8656569 34.69833 -76.66500 0.00764 0.00271 

 33 8656571 34.69833 -76.68166 0.01550 0.01114 

 34 8656612 34.68667 -76.53333 0.00159 0.00128 

 35 8656841 34.61333 -76.53833 0.01776 0.01776 

 

Error summary for tide Pamlico Sound stations 

 number = 35 

 avg. rmse = 0.01062 max. rmse = 0.03699 at n= 15 

 avg. std = 0.00919 max. std = 0.03627 at n= 15 
46

Table E.2. Coastal Central Tide Station Comparisons (Errors in m). 

 

 n NOS lat lon rmse std 

 1 8654400 35.22333 -75.63500 0.00072 0.00069 

 2 8656590 34.69333 -76.71167 0.03077 0.02792 

 3 8656937 34.60833 -76.52834 0.03140 0.03137 

Error summary for Coastal Central tide stations 

 number = 3 

 avg. rmse = 0.02096 max. rmse = 0.03140 at n= 3 

 avg. std = 0.02000 max. std = 0.03137 at n= 3 

 

 

Table E.3. Coastal North Tide Station Comparisons (Errors in m). 

 

 n NOS lat lon rmse std 

 

 1 8651370 36.18333 -75.74667 0.00196 0.00183 

 2 8652226 35.91000 -75.59167 0.00221 0.00213 

 

Error summary for Coastal North tide stations 

 number = 2 

 avg. rmse = 0.00209 max. rmse = 0.00221 at n= 2 

 avg. std = 0.00198 max. std = 0.00213 at n= 2