NOAA Technical Report NOS CS 25 

VDATUM FOR THE SAN JUAN ISLANDS AND 

THE STRAIT OF JUAN DE FUCA WITH UPDATES 

FOR PUGET SOUND: TIDAL DATUM 

MODELING AND POPULATION OF THE GRIDS 

Silver Spring, Maryland 

March 2006 

n 0 a a National Oceanic and Atmospheric Administration 

U.S. DEPARTMENT OF COMMERCE 

National Ocean Service 

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 shore-based 

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 25 

VDATUM FOR THE SAN JUAN ISLANDS AND THE STRAIT OF 

JUAN DE FUCA WITH UPDATES FOR PUGET SOUND: TIDAL 

DATUM MODELING AND POPULATION OF THE GRIDS 

Emily A. Spargo 

KurtW. Hess 

Office of Coadst Survey 

Stephen White 

National Geodetic Survey 

March 2006 

n 0 a a National Oceanic and Atmospheric Administration 

U.S. DEPARTMENT National Oceanic and National Ocean Service 

OF COMMERCE Atmospheric Administration John H. Dunnigan, 

Carlos Gutierrez, Secretary Conrad C . Lautenbacher, Jr., Assistant Administrator 

VADM USN (Ret.), Under Secretary 

Office of Coast Survey 

Captain Steven Barnum, NOAA 

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. STRAIT OF JUAN DE FUCA REGION TIDAL DATUM MODELING ................................ 3 

2.1. Selecting a Model ................................................................................................................ 3 

2.2. Original Model Results ........................................................................................................ 3 

2.3. Comparison to NOS Water Level Stations and Model Correction ...................................... 4 

3. NORTHERN PUGET SOUND TIDAL DATUM MODELING ............................................. 11 

4.1. Input Tidal Datum Values .................................................................................................. 17 

4.2. Generation of Tidal Datum Fields ..................................................................................... 21 

5. GENERATION AND POPULATION OF VDATUM MARINE GRIDS ............................... 23 

5.1. Generation of the VDatum Marine Grids .......................................................................... 23 

5.2. Population of the VDatum Marine Grids with Tidal Datums ............................................ 23 

5.3. Errors in the Marine Grid ................................................................................................... 25 

6. TOPOGRAPHY OF THE SEA SURFACE ............................................................................. 27 

ACKNOWLEDGEMENTS .......................................................................................................... 32 

REFERENCES ............................................................................................................................. 32 

APPENDIX A. STATION INFORMATION AND ERROR ANALYSIS ................................. 33 

APPENDIX B. VDATUM MARINE GRID WITH DATUMS ................................................... 49 
iv
v

LIST OF FIGURES 

Figure 1. VDatum region with border between the United States and Canada delineated. ............ 1 

Figure 2. Section of the Foreman grid used for computing the tidal datums for the VDatum grid 

with the MHW shoreline. ................................................................................................................ 4 

Figure 3. MHW coastline with (a) the location of NOAA tide gages and (b) a zoomed view, with 

the last four digits of the station identification number listed. The first three digits of this number 

are “944”. ........................................................................................................................................ 6 

Figure 4. (a) Modeled MLLW (meters) field, (b) spatially interpolated error between modeled 

results and NOS water level station MLLW values (meters), and (c) corrected MLLW (meters) 

field over the Foreman model domain. ......................................................................................... 10 

Figure 5. Finite element mesh for the TCARI model for the (a) entire northern Puget Sound area 

with the MHW shoreline in blue, and (b), (c) zoomed views of the mesh. .................................. 12 

Figure 6. MWH coastline with (a) the location of NOAA tide gages (in blue) referenced by the 

last 4 digits of the station identification number where the first 3 digits are “944” and boundary 

forcing points (in red) labeled from one to thirty, and (b), (c), and (d) zoomed views of the other 

forcing stations. ............................................................................................................................. 13 

Figure 7. MLLW tidal datum field (in meters) from the TCARI model using 56 input data 

stations (30 nodes along the boundary and 26 interior points at NOS water level gages). .......... 15 

Figure 8. The 65 water level stations in the Puget Sound region used in developing the TCARI 

solution are shown in blue, and the additional 2 stations used for final model evaluation are 

shown in green. Only the last four digits of the station numbers are shown; the first three digits 

are “944”. The locations of the 158 points along the boundary of the TCARI model grid are 

shown in red. ................................................................................................................................. 18 

Figure 9. VDatum marine grid populated with MLLW tidal datum field (in meters) for the 

southern Puget Sound area. ........................................................................................................... 22 

Figure 10. VDatum bounding polygon (blue line) for Southern Puget Sound. ............................ 24 

Figure 11. The area of the VDatum marine grid populated by the corrected Strait of Juan de Fuca 

model results outlined by the red bounding polygon and the area populated by the Northern 

Puget Sound spatial interpolation model results outlined by the blue bounding polygon. ........... 25 

Figure 12. Location of tidal benchmarks and tide stations used to compute the San Juan Islands 

and Puget Sound TSS grid. ........................................................................................................... 27 

Figure 13. Combined Strait of Juan de Fuca, Northern Puget Sound and Southern Puget Sound 

gridded TSS. ................................................................................................................................. 31 
vi

LIST OF TABLES 

Table 1. Station point numbers shown in Figure 3 with station name, station identification 

number and location. Station numbers marked with an asterisk (*) indicate stations that have 

been updated to the 1983-2001 National Tidal Datum Epoch. ....................................................... 7 

Table 2. Great diurnal range of tidal datums from 1960-1978 NTDE and 1983-2001 NTDE for 

15 stations, with ratio of range, difference, and absolute average percent difference. ................... 8 

Table 3. Stations shown in Figure 6 (as blue dots) with station name and identification number, 

and location. Stations marked with an asterisk (*) indicate stations that have been updated to the 

1983-2001 National Tidal Datum Epoch, and station numbers marked with a plus (+) indicated 

stations that duplicate those listed in Table 1. .............................................................................. 14 

Table 4. Great diurnal range of tidal datums from 1960-1978 NTDE and 1983-2001 NTDE for 

10 stations in Northern Puget Sound, with ratio of range, difference, and absolute average 

percent difference. ......................................................................................................................... 15 

Table 5. Identification numbers, names, and location of stations in southern Puget Sound. 

Station ID numbers marked with an asterisk (*) indicate stations that are referenced to the 1983-

2001 National Tidal Datum Epoch, and with a plus (+) were not used in generating the TCARI 

tidal datums but for model comparison. ....................................................................................... 19 

Table 6. Great diurnal range of tidal datums from 1960-1978 NTDE and 1983-2001 NTDE for 

22 stations, with ratio of range, difference, and absolute average percent difference. ................. 21 

Table 7. Derived residual values for each tidal datum at NGS benchmarks from the combined 

Strait of Juan de Fuca and Northern Puget Sound Tidal Grids. .................................................... 28 

Table 8. Derived NAVD 88-to-LMSL values for each tidal datum at NGS benchmarks from the 

Southern Puget Sound Tidal Grids. .............................................................................................. 29 
vii

ABSTRACT 

The generation and population of the VDatum marine grids for the Strait of Juan de Fuca, 

Northern Puget Sound and Southern Puget Sound are discussed. For the Strait of Juan de 

Fuca region, the tidal datum information used to populate the VDatum marine grids came 

from a harmonic constant data set derived from a hydrodynamic model of the area developed 

at Fisheries & Oceans Canada Institute of Ocean Sciences. For the northern and southern 

reaches of Puget Sound, beyond the extent of the hydrodynamic model, a spatial 

interpolation of the datums computed at NOAA water level stations was used to determine 

tidal datum fields. The model of southern Puget Sound is an update to a previously 

generated spatial interpolation from 2004. All three sources were then used to populate the 

VDatum marine grids for those regions. A continuous topography of the sea surface was 

calculated across the three regions for inclusion in the VDatum software package.

Key Words: tides, tidal datums, San Juan Islands, Strait of Juan de Fuca, Puget Sound, 

North American Vertical Datum of 1988, mean sea level, spatial interpolation. 
viii
1

1. INTRODUCTION 

A vertical datum transformation tool called VDatum is being developed by the National 

Ocean Service (NOS) to allow for the transformation between ellipsoidal, orthometric, and 

tidal datums (Milbert, 2002; Parker, 2002). The ellipsoidal and orthometric datum fields, and 

the transformations between these two types of datums, have already been established on 

national-scale grids. The transformations among tidal datums relative to Local Mean Sea 

Level (LMSL) and the transformations between LMSL and the North American Vertical 

Datum of 1988 (NAVD 88) are under development. This paper discusses the continuing 

work on the tidal datum transformations and the connection between LMSL and NAVD 88 

for the following areas: 

 the Strait of Juan de Fuca (including the San Juan Islands and the southern Strait of 

Georgia), 

 Northern Puget Sound (including Padilla Bay, Deception Pass, Skagit Bay, Saratoga 

Passage, and Port Susan), and 

 Southern Puget Sound (including Admiralty Inlet, Possession Sound, Hood Canal, 

East Passage, Colvos Passage, The Narrows, Cast Inlet, and Carr Inlet). 

These areas are shown in Figure 1. 

 Figure 1. VDatum region with border between the United States and Canada delineated. 
2

For the Strait of Juan de Fuca region, the tidal datums were computed from a harmonic 

constant database derived from a two-dimensional model of the region. The harmonic 

analysis results were used to construct a water level time series at each node in the model 

grid. These water level records were then analyzed to compute the tidal datums for that 

point. The modeled tidal datum fields were corrected to match datum information at NOS 

water level stations using a spatial interpolation method. Details of this process will be 

discussed in section 2 of this report. For both Puget Sound regions, a spatial interpolation 

method was used to compute the tidal datum fields directly from the NOS water level 

stations in the areas. The datums created from the spatial interpolation in both Northern and 

Southern Puget Sound were adjusted to match the corrected tidal datums in the Strait of Juan 

de Fuca region. This guaranteed there were no discontinuities at the boundaries. Section 3 

of this report details the modeling efforts in Northern Puget Sound, and the model of the 

Southern Puget Sound region is discussed in Section 4. 

After the modeling efforts were completed, the VDatum marine grids, used in the VDatum 

software package, were created and populated with the final model results. Two regularly 

spaced VDatum marine grids were created; one that combined the Strait of Juan de Fuca and 

Northern Puget Sound modeling efforts and a second marine grid was populated with tidal 

datum fields from the Southern Puget Sound model. Details of this process will be discussed 

in Section 5 of this report. 

To complete the files need for the VDatum transformation software, a gridded Topography of 

the Sea Surface (TSS) was created for each of the VDatum marine grids using the available 

benchmark data. The two surfaces were checked to guarantee a continuous surface across the 

interface of the two grids. This process is explained in Section 6. 
3

2. STRAIT OF JUAN DE FUCA REGION TIDAL DATUM MODELING 

2.1. Selecting a Model 

Sets of harmonic constants from three different shelf-scale hydrodynamic models of the 

Eastern North Pacific Ocean were available for use in this study. These models will be 

referred to as the Foreman model (Foreman et al., 2000), the Myers model (Myers and 

Baptista., 2001), and the Spargo model (Spargo et al., 2004). These models all covered 

approximately the same area: the northern boundaries run along the Aleutian Islands in 

Alaska and they all cover the western Canadian and U.S. shorelines. They are all finite 

element models; the Foreman model ran the FUNDY5SP code and the other two models ran 

the ADCIRC 2DDI code. The Foreman model assimilated TOPEX/POSEIDON data, the 

Myers model used an inversion technique to incorporate the same data, and the Spargo model 

did not use any data assimilation techniques. 

Twenty-two NOS water level stations with tidal datum values were found that reside within, 

or very near to the boundaries of, the areas common to all three models or very near to the 

boundaries of one or more of the models. A root mean square (RMS) error analysis was 

conducted of the model results as compared to the station data for the four main tidal datums 

(Mean Higher High Water (MHHW), Mean High Water (MHW), Mean Low Water (MLW), 

and Mean Lower Low Water (MLLW)). The Foreman model had the lowest RMS error (15.1 

cm), the Myers model had a slightly larger error (17.9 cm), and the Spargo model had the 

largest error (28.3 cm). An analysis of the absolute average error between the models and the 

station data at the same 22 locations for the four main datums provided another metric for 

model comparison. Again, the Foreman model performed the best with the lowest absolute 

average error (13.2 cm). This time the Spargo model was the second best (22.0 cm) and the 

Myers model had the largest error (31.6 cm). Due to the results of these analyses, the 

Foreman model results were chosen to be used for this project. The errors at each of the 22 

stations are listed in Appendix A, Table A.1. 

2.2. Original Model Results 

The Foreman model was originally run for a tidal modeling study of the northeast Pacific 

Ocean. This model assimilated tidal harmonics computed from the analysis of 

TOPEX/Poseidon satellite altimeter observations. Details of the model set-up and run for the 

original study can be found in Foreman et al. (2000). The triangulated mesh for this model 

covered the coastal and open ocean waters along the southern side of the Aleutian Islands, 

Alaska, in the north down to southern California in the south. A subsection of the larger grid 

was extracted for this project (Figure 2). This smaller mesh contains 13,656 nodes and 

22,900 elements. The MHW shoreline, also shown in Figure 2, is the Extracted Vector 

Shoreline (EVS) along the U.S. coastline and the World Vector Shoreline (WVS) from the 

National Geophysical Data Center (NGDC) along the Canadian coastline. As evident by the 

figure, the Foreman model domain did not cover the entire VDatum region; it only provided 

coverage for the Strait of Juan de Fuca and the San Juan Islands regions. 
4

Figure 2. Section of the Foreman grid used for computing the tidal datums for the VDatum 

grid with the MHW shoreline. 

The Foreman model provided amplitude and Greenwich phase values of the following 

harmonic constants at every node in the mesh: K1, O1, P1, Q1, M2, S2, N2, and K2. A Center 

for Operational Oceanographic Products and Services’ (CO-OPS) prediction program 

(pred.f) was used to construct 30-day long, 6-minute interval water surface elevation time 

series for each node in the mesh from this data (Zervas, 1999). The equilibrium arguments 

and node factors for the time series were set to match those for the end of 1992, which is the 

middle year of the 1983 – 2001 National Tidal Datum Epoch when the node factors for the 

major harmonic constants is close to 1.0. Each time series was then analyzed to calculate the 

tidal datums at every node by picking off the higher-high, lower-high, higher-low, and lowerhigh waters. The datums computed were MHW, MHHW, MLW and MLLW, all relative to 

MSL. 

2.3. Comparison to NOS Water Level Stations and Model Correction 

Initially, all NOS water level stations within the Foreman model boundary were selected 

from a Coast Survey Development Laboratory (CSDL) database from August 2005. For this 

task, the boundary was defined as a box between 48.0o N and 49.0o N latitude and between 

126.3o W and 122.4o W longitude. If more than one station occupied the same location, the 

station with the largest NOS identification number (presumably having the most recent or 

longest-running record) was kept and the other stations were eliminated. In total, 41 stations 

were found. These stations were then compared to the Foreman model mesh, and stations 

that were more than 800 m from the boundary of the grid as compared to the nearest grid 
5

point were eliminated. Thirty-one NOS water level stations remained. Next, station data 

were examined for completeness and redundancy. The Argyle North Bay station (#9449822) 

on San Juan Island was eliminated from this group because of incomplete data: there is tidal 

datum information for MHHW, MHW, MLW, and MLLW, but no reference for MSL, Mean 

Tide Level (MTL) or Diurnal Tide Level (DTL). The Shannon Point station (#9448773) was 

also eliminated due to its redundancy with the Ship Harbor, Fidalgo Island station 

(#9448772). These two stations have the same datums, and are in close proximity to each 

other. The remaining 29 stations are shown in Figure 3. The points are labeled with the last 

four digits of the station identification number. (The first three digits of this number are 

“944”.) The locations and names are listed in Table 1, and tidal datum values are listed in 

Appendix A, Table A.2. 

Of the 29 stations in this region, 15 stations have been updated to the 1983-2001 NTDE from 

the 1960-1978 NTDE. (For more information about the updating process see NOAA’s 

Center for Operational Oceanographic Products and Services (CO-OPS) website at: 

http://140.90.121.76/datum_update.shtml.) Although it would be best to use only data from 

the latest tidal epoch, it was assumed that if the adjustment to the new epoch was small 

enough, then the older epoch were still valid, and could be used for model validation and 

correction. To find that adjustment, the 15 stations with datum records from both epochs 

were compared. Table 2 shows the results of this analysis. The great diurnal tidal range, 

which is MHHW minus MLLW, was calculated for each epoch. The ratio of the new range 

versus the old range, the differences between the two, and the absolute average percent 

difference were computed as well. The average absolute average percent difference is 0.43%. 

This is considered to be an insignificant change and it was decided that all the data could be 

used, no matter which epoch it was associated with. 
6

Figure 3. MHW coastline with (a) the location of NOAA tide gages and (b) a zoomed view, 

with the last four digits of the station identification number listed. The first three digits of this 

number are “944”. 

a

b
7

Table 1. Station point numbers shown in Figure 3 with station name, station identification 

number and location. Station numbers marked with an asterisk (*) indicate stations that have 

been updated to the 1983-2001 National Tidal Datum Epoch. 

Point 

Number 

Station ID 

Number Station Name Latitude (degrees) 

Longitude 

(degrees) 

1 9442861 Mukkaw Bay 48.2967 -124.6717 

2 9443090* Neah Bay 48.3683 -124.6167 

3 9443361* Sekiu Clallam Bay 48.2633 -124.2967 

4 9443644 Twin Rivers 48.1750 -123.9500 

5 9443826* Crescent Bay 48.1617 -123.7250 

6 9444090* Port Angeles 48.1250 -123.4400 

7 9444122* Ediz Hook 48.1367 -123.4083 

8 9444705 Gardiner Landing 48.0583 -122.9167 

9 9447951 Whidbey Island, Sunset Beach 48.2833 -122.7283 

10 9447985 Smith Island 48.3167 -122.8367 

11 9447995 Whidbey Island, Coronet Bay 48.4017 -122.6233 

12 9448601 Yokeko Point 48.4133 -122.6150 

13 9448614* Reservation Bay 48.4150 -122.6517 

14 9448772 Fidalgo Island, Ship Harbor 48.5067 -122.6767 

15 9448967 Sinclair Island 48.6150 -122.6917 

16 9449161* Lummi Island 48.7167 -122.7083 

17 9449211* Bellingham 48.7450 -122.4950 

18 9449292* Lummi Bay 48.7900 -122.7083 

19 9449424* Cherry Point 48.8633 -122.7583 

20 9449679* Blaine 48.9917 -122.7650 

21 9449704 Patos Island 48.7867 -122.9700 

22 9449771 Orcas Island 48.6467 -122.8700 

23 9449802 Stuart Island 48.6883 -123.2367 

24 9449828* Hanbury Point 48.5817 -123.1700 

25 9449880* Friday Harbor 48.5467 -123.0100 

26 9449911 Lopez Isl., Upright Head 48.5717 -122.8850 

27 9449932* Armitage Island 48.5350 -122.7967 

28 9449982* Lopez Island, Richardson 48.4467 -122.8983 

29 9449994 Lopez Island, Aleck Bay 48.4250 -122.8533 
8

Table 2. Great diurnal range of tidal datums from 1960-1978 NTDE and 1983-2001 NTDE 

for 15 stations, with ratio of range, difference, and absolute average percent difference. 

Station Range(m) Epoch Range(m) Epoch Ratio Diff(m) Pct 

9443090 2.425 1960 2.425 1983 1.000 0.000 0.00% 

9443361 2.286 1960 2.286 1983 1.000 0.000 0.00% 

9443826 2.134 1960 2.151 1983 1.008 -0.017 0.81% 

9444090 2.143 1960 2.153 1983 1.005 -0.010 0.48% 

9444122 2.124 1960 2.135 1983 1.005 -0.011 0.50% 

9448614 2.338 1960 2.352 1983 1.006 -0.014 0.60% 

9449161 2.627 1960 2.637 1983 1.004 -0.010 0.37% 

9449211 2.579 1960 2.594 1983 1.006 -0.015 0.60% 

9449292 2.734 1960 2.749 1983 1.005 -0.015 0.55% 

9449424 2.774 1960 2.788 1983 1.005 -0.014 0.51% 

9449679 2.89 1960 2.905 1983 1.005 -0.015 0.53% 

9449828 2.307 1960 2.325 1983 1.008 -0.018 0.76% 

9449880 2.353 1960 2.364 1983 1.005 -0.011 0.46% 

9449932 2.387 1960 2.391 1983 1.002 -0.004 0.17% 

9449982 2.181 1960 2.185 1983 1.002 -0.004 0.18% 

Average = 1.004 0.011 0.43% 

The differences between the model results and the data at all 29 NOS water level stations 

were used to create a spatially interpolated error field. The error for each tidal datum was 

defined as the difference between the published NOS datum compared to mean sea level (i.e. 

MHHW-MSL, MHW-MSL, MLW-MSL, and MLLW-MSL) and the modeled datum 

compared to MSL. The error field was computed using the Tidal Constituent And Residual 

Interpolation (TCARI) program. TCARI solves Laplace’s Equation and takes landforms into 

account to create smooth, interpolated fields (Hess, 2002). For all runs discussed, the 

boundary condition parameter () was set to the recommended value of 0.9. A finite element 

implementation of the TCARI program was used so that the spatial interpolation could be 

computed directly on the section of the unstructured mesh that was extracted from the 

Foreman model grid. The input to the TCARI program was the error values at the nodes 

nearest the NOS station locations and the output was the error fields, which were defined at 

every node in the mesh. 

The model results and the station data for every station and every datum are listed in 

Appendix A, Table A.2. The highest errors are at Yokeko Point (#9448601) and Coronet 

Bay on Whidbey Island (#9447995), which are both at the very edge of the grid in Deception 

Pass. The model underpredicts the measured datums by between 22 and 42 cm (or about 

26% to 37% of the tidal signal). If these two stations are excluded from the analysis, the 

average absolute difference is 8.2 cm for MHHW, 7.4 cm for MHW, 5.6 cm for MLW, and 

3.7 cm for MLLW. Based on experience from the development of other models for the 

VDatum project, it has been decided that an absolute average difference error less than 10 cm 

is acceptable; and ideally, there would be less than 5 cm of error at every station for every 

datum. 
9

The final tidal datum fields were computed by subtracting the spatially interpolated error 

results from the Foreman model results. These results will be called the corrected Foreman 

model results. Figure 4 shows the modeled MLLW field, the error field resulting from the 

TCARI interpolation of the MLLW error at 29 stations, and the corrected MLLW field. 

After all the corrected datum fields were computed, the MTL and DTL fields were created by 

calculating MTL and DTL at every node in the mesh based on the following formulas: 

MTL=1/2[MHW + MLW] and DTL=1/2[MHHW + MLLW]. 
10

(a) 

 (b) 

 (c) 

Figure 4. (a) Modeled MLLW (meters) field, (b) spatially interpolated error between 

modeled results and NOS water level station MLLW values (meters), and (c) corrected 

MLLW (meters) field over the Foreman model domain. 
11

3. NORTHERN PUGET SOUND TIDAL DATUM MODELING 

As Foreman model does not extend into Northern Puget Sound (nor do the Myers and Spargo 

tide models), another approach for computing tidal datums was developed for this area. The 

TCARI method, briefly discussed in the previous section, was applied in this region. In the 

previous section, the TCARI method was used to spatially interpolate the error between the 

hydrodynamic model results and the NOS water level station data. For the Northern Puget 

Sound region, TCARI was used to spatially interpolate the actual tidal datums directly from 

NOS water level data throughout the domain. The resulting datum fields match the datums at 

the NOS water level station locations and follow the solution to Laplace’s Equation 

elsewhere. 

Since the TCARI model can be implemented using the finite element method, a triangular 

mesh was created for this region which includes all of the Northern Puget Sound Region (i.e. 

Padilla Bay, Deception Pass, Skagit Bay, Saratoga Passage, and Port Susan. See Figure 1 for 

locations) and extends further south into Southern Puget Sound to include Possession Inlet 

and Admiralty Inlet. The triangulated mesh and the EVS MHW shoreline are shown in 

Figure 5. The elements range in size from about 1 km down to 50 m with an average node to 

node spacing of 550 m. The nodal locations of the boundaries in Admiralty Inlet, Padilla Bay 

and in the Strait of Juan de Fuca just west of Deception Pass match those on the Foreman 

model mesh. 

To identify NOS water level stations available for the TCARI model, a region was defined by 

the area between 47.72o N and 48.51o N latitude and between 122.80o W and 122.18o W 

longitude using a CSDL database from August 2005. If more than one station occupied the 

same location, the station with the largest NOS identification number (presumably having the 

most recent or longest-running record) was kept and the other stations were eliminated. In 

total, 33 stations were found. These stations were then compared to the triangulated mesh 

developed for this area, and stations that were more than 800 m off the grid were eliminated. 

Twenty-six NOS water level stations remained. These stations are shown as blue dots in 

Figure 6 labeled with the last 4 digits of the station identification number. (The first three 

digits of this number are “944”.) The location and names of these stations are listed in Table 

3, and the 3 stations that are duplicates of those in the Foreman model region (as listed in 

Table 1) are marked as such. In order to make sure that the TCARI model output matched 

the corrected Foreman model discussed in the previous section, the tidal datum results from 

the corrected Foreman model were used at the northern boundaries (in Admiralty Inlet, west 

of Deception Pass and in Padilla Bay) as data points for the TCARI model run. (No data 

points were used at the southern boundary into southern Puget Sound.) These boundary 

points are shown as red dots in Figure 6 and are numbered from one to thirty. Only the 

locations of the NOS water level stations (blue dots in Figure 6) are listed in Table 3. The 

locations of the other points, as well as the datum information used for every point shown in 

Figure 6, are listed in Appendix A, Table A.3. 
12

Figure 5. Finite element mesh for the TCARI model for the (a) entire northern Puget Sound 

area with the MHW shoreline in blue, and (b), (c) zoomed views of the mesh. 

a 

b

c
13

Figure 6. MWH coastline with (a) the location of NOAA tide gages (in blue) referenced by 

the last 4 digits of the station identification number where the first 3 digits are “944” and 

boundary forcing points (in red) labeled from one to thirty, and (b), (c), and (d) zoomed 

views of the other forcing stations. 

b 

a

d

c
14

Table 3. Stations shown in Figure 6 (as blue dots) with station name and identification 

number, and location. Stations marked with an asterisk (*) indicate stations that have been 

updated to the 1983-2001 National Tidal Datum Epoch, and station numbers marked with a 

plus (+) indicated stations that duplicate those listed in Table 1. 

 Station ID 

 Number Station Name Longitude (degrees) 

Latitude 

(degrees) 

1 9444900* Port Townsend 48.1117 -122.7500 

2 9445016 Foulweather Bluff 47.9267 -122.6167 

3 9445017 Port Ludlow 47.9250 -122.6800 

4 9445526* Hansville 47.9183 -122.5450 

5 9445639 Apple Tree Cove 47.7967 -122.4933 

6 9445683 Point Jefferson 47.7467 -122.4767 

7 9447427 Edmonds 47.8133 -122.3833 

8 9447659* Everett 47.9800 -122.2233 

9 9447725 Ebey Slough 48.0450 -122.2100 

10 9447773 Tulalip Bay 48.0650 -122.2883 

11 9447814* Glendale 47.9400 -122.3567 

12 9447827 Double Bluff 47.9783 -122.5500 

13 9447854* Bush Point 48.0333 -122.6067 

14 9447855 Holly Harbor Farms 48.0267 -122.5433 

15 9447856 Sandy Point 48.0350 -122.3767 

16 9447883 Greenbank 48.1050 -122.5700 

17 9447929 Coupeville Penn Cove 48.2233 -122.6900 

18 9447952* Crescent Harbor 48.2867 -122.6167 

19 9447993 Ala Spit 48.3967 -122.5867 

20 9447995+ Coronet Bay 48.4017 -122.6233 

21 9448094 Port Susan 48.1367 -122.3667 

22 9448558* Swinomish Slough 48.3917 -122.4967 

23 9448576* Sneeoosh Point 48.4000 -122.5483 

24 9448601+ Yokeko Point 48.4133 -122.6150 

25 9448614*+ Reservation Bay 48.4150 -122.6517 

26 9448657* Turner Bay 48.4450 -122.5550 

Of the 26 stations in this region, 10 stations have been updated to the 1983-2001 NTDE from 

the 1960-1978 NTDE. The 10 stations with datum records from both epochs were compared. 

Table 4 shows the results of this analysis. The great diurnal tidal range, which is the 

difference between MHHW and MLLW, was calculated for each epoch. The ratio of the new 

range versus the old range, the differences between the two and the absolute average percent 

difference were computed as well. The average absolute mean percent difference is 0.26%. 

This was considered to be an insignificant change and it was decided that all the data could 

be used, no matter which epoch it was associated with. 

The TCARI model was run once for each tidal datum with input stations at the 26 NOS water 

level gage locations and the 30 Foreman model nodes. Once these datum fields were 

computed, the MTL and DTL fields were calculated as: MTL=1/2[(MHW)+( MLW)] and 

DTL=1/2[(MHHW)+( MLLW)]. 
15

Table 4. Great diurnal range of tidal datums from 1960-1978 NTDE and 1983-2001 NTDE 

for 10 stations in Northern Puget Sound, with ratio of range, difference, and absolute average 

percent difference. 

Station Range(m) Epoch Range(m) Epoch Ratio Diff(m) Pct 

9444900 2.576 1960 2.596 1983 1.008 -0.020 0.77% 

9445526 3.182 1960 3.18 1983 0.999 0.002 0.06% 

9447659 3.386 1960 3.38 1983 0.998 0.006 0.18% 

9447814 3.359 1960 3.364 1983 1.002 -0.005 0.15% 

9447854 2.848 1960 2.85 1983 1.001 -0.002 0.07% 

9447952 3.551 1960 3.554 1983 1.001 -0.003 0.08% 

9448558 3.152 1960 3.154 1983 1.001 -0.002 0.06% 

9448576 3.377 1960 3.369 1983 0.998 0.008 0.24% 

9448614 2.338 1960 2.352 1983 1.006 -0.014 0.60% 

9448657 3.165 1960 3.152 1983 0.996 0.013 0.41% 

Average = 1.001 0.008 0.26% 

The results from the spatially interpolated MLLW field are shown in Figure 7. The TCARI 

model results match the data from the corrected Foreman model at the boundaries in 

Admiralty Inlet, west of Deception Pass and in Padilla Bay . 

Figure 7. MLLW tidal datum field (in meters) from the TCARI model using 56 input data 

stations (30 nodes along the boundary and 26 interior points at NOS water level gages).
16
17

4. SOUTHERN PUGET SOUND TIDAL DATUM MODELING

In response to the development of VDatum for the Strait of Juan de Fuca and Northern Puget 

Sound, the existing tidal datum fields initially generated for Southern Puget Sound (Hess and 

White, 2004) were updated using input data from (1) the new tidal datum fields in Admiralty 

Inlet from the corrected Strait of Juan de Fuca regional model and in Saratoga Passage, and 

Port Susan from the Northern Puget Sound regional model (see Figure 1), and (2) the data at 

tide stations with updates to the latest National Tidal Datum Epoch (1983-2001) in the 

interior of the domain. Using these new input stations at the boundary and the updated 

datums at stations in the interior of the domain, revised tidal datum fields were generated by 

TCARI spatial interpolation for the Southern Puget Sound region. 

4.1. Input Tidal Datum Values 

A CSDL database (from June 2005) of NOS water level stations was searched to select all 

available stations between 47.0167o N and 48.1833o N latitude and between 123.1833o W and 

122.1667o W longitude. Seventy total stations were found. Revised datum values (from 

January 2006) were used for the station at Bush Point (#9447854) because the older datums 

appeared to be inconsistent when compared to datums at nearby stations. Also, the location 

of the Holly Harbor Farms station (#9447855) was revised slightly (from a longitude of 

122.54333° W to 122.53333° W) to ensure that it is in the grid. Two additional stations, 

those at Duwamish River (#9447029) and Ebey Slough, Qwuloolt (#9447729), were not used 

because they were too far up narrow rivers. Another station, at Gardiner Landing 

(#9444705), was not used since it was outside the model area. In total, 67 stations remained. 

The locations of these stations are shown in Figure 8 and the station identification number, 

name, and location are listed in Table 5. Two stations that were not used for the TCARI 

model runs, but were used in the final evaluation process at Commencement Bay (#9446484) 

and Tacoma (#9446545), are specially delineated in both Figure 8 and Table 5. To guarantee 

matching datums at the interface with the other models, an additional 158 nodes along the 

northern boundary of the grid were used in the TCARI model runs with datum information 

extracted from the corrected Strait of Juan de Fuca and Northern Puget Sound model results 

for all four datums (MHHW, MHW, MLW, and MLLW). The locations of these nodes are 

also shown in Figure 8. The tidal datum information for all 67 NOS stations are listed in 

Appendix A, Table A.4. Note that Lake Washington was not included in the VDatum area 

since water levels there are not strictly tidal because it is separated from Puget Sound proper 

by a system of locks. 
18

Figure 8. The 65 water level stations in the Puget Sound region used in developing the 

TCARI solution are shown in blue, and the additional 2 stations used for final model 

evaluation are shown in green. Only the last four digits of the station numbers are shown; the 

first three digits are “944”. The locations of the 158 points along the boundary of the TCARI 

model grid are shown in red. 
19

Table 5. Identification numbers, names, and location of stations in southern Puget Sound. 

Station ID numbers marked with an asterisk (*) indicate stations that are referenced to the 

1983-2001 National Tidal Datum Epoch, and with a plus (+) were not used in generating the 

TCARI tidal datums but for model comparison. 

N Station ID Station Name Latitude Longitude 

1 9444900 * PORT TOWNSEND ADMIRALTY INLET 48.1117 -122.7500 

2 9445016 FOULWEATHER BLUFF TWIN SPITS 47.9267 -122.6167 

3 9445017 PORT LUDLOW ADMIRALY INLET 47.9250 -122.6800 

4 9445059 PORT GAMBLE HOOD CANAL WA 47.8583 -122.5800 

5 9445088 LOFALL WA 47.8150 -122.6583 

6 9445133 * BANGOR 47.7483 -122.7267 

7 9445246 * WHITNEY POINT 47.7617 -122.8500 

8 9445269 ZELATCHED POINT DABOB BAY 47.7117 -122.8217 

9 9445272 * QUILCENE DABOB BAY HOOD CANAL 47.8000 -122.8583 

10 9445293 PLEASANT HARBOR HOOD CANAL 47.6650 -122.9117 

11 9445296 * SEABECK HOOD CANAL 47.6417 -122.8283 

12 9445326 TRITON HEAD WA 47.6033 -122.9700 

13 9445388 AYOCK POINT WA 47.5083 -123.0517 

14 9445441 LYNCH COVE DOCK WA 47.4183 -122.9000 

15 9445478 * UNION HOOD CANAL 47.3583 -123.0983 

16 9445526 * HANSVILLE 47.9183 -122.5450 

17 9445639 KINGSTON APPLE TREE COVE 47.7967 -122.4933 

18 9445683 POINT JEFFERSON PUGET SOUND 47.7467 -122.4767 

19 9445719 * POULSBO 47.7250 -122.6383 

20 9445753 PORT MADISON BAINBRIDGE ISLAND 47.7050 -122.5250 

21 9445832 * BROWNSVILLE 47.6517 -122.6150 

22 9445882 EAGLE HARBOR BAINBRIDGE ISL 47.6200 -122.5150 

23 9445901 TRACYTON DYES INLET PUGET 47.6100 -122.6600 

24 9445913 PORT BLAKELY PUGET SOUND 47.5967 -122.5100 

25 9445938 CLAM BAY WA 47.5733 -122.5433 

26 9445958 * BREMERTON WA 47.5617 -122.6233 

27 9445993 SOUTH COLBY-HARPER YUKON 47.5233 -122.5167 

28 9446025 POINT VASHON WA 47.5117 -122.4633 

29 9446248 DES MOINES WA 47.4000 -122.3283 

30 9446273 BURTON QUARTERMASTER HBR 47.3867 -122.4650 

31 9446281 * ALLYN 47.3833 -122.8233 

32 9446291 WAUNA CARR INLET PUGET SOUND 47.3783 -122.6400 

33 9446366 VAUGHN CASE INELT PUGET SOUND 47.3417 -122.7750 

34 9446369 GIG HARBOR PUGET SOUND WA 47.3400 -122.5883 

35 9446375 NEILL POINT WA 47.3333 -122.5067 

36 9446451 * GREEN POINT 47.3017 -122.6817 

37 9446484 * + TACOMA COMMENCEMENT BAY 47.2667 -122.4133 

38 9446486 TACOMA NARROWS BRIDGE WA 47.2717 -122.5517 

39 9446489 WALKERS LANDING WA 47.2817 -122.9233 

40 9446491 * ARLETTA 47.2800 -122.6517 

41 9446545 * + TACOMA 47.2550 -122.4317 

42 9446583 BALLOW 47.2467 -122.8617 

43 9446628 SHELTON OAKLAND BAY WA 47.2150 -123.0833 

44 9446638 LONGBRACH FILUCE B PUGET SOUND 47.2100 -122.7533 
20

Table 5. Continued 

N Station ID Station Name Latitude Longitude 

45 9446666 ARCADIA TOTTEN INLET WA 47.1967 -122.9383 

46 9446671 DEVIL'S HEAD WA 47.1667 -122.7633 

47 9446705 * YOMAN POINT ANDERSON ISLAND 47.1800 -122.6750 

48 9446714 STEILACOOM WA 47.1733 -122.6033 

49 9446742 * BARRON POINT 47.1583 -123.0083 

50 9446800 DOFFLEMEYER POINT WA 47.1417 -122.9033 

51 9446807 * BUDD INLET , GULL HARBOR 47.1000 -122.8967 

52 9446828 DUPONT NISQUALLY REACH WA 47.1183 -122.6650 

53 9446969 * OLYMPIA BUD INLET PUGET SOUND 47.0600 -122.9033 

54 9447110 * LOCKHEED SHIPYARD 47.5850 -122.3617 

55 9447130 * SEATTLE PUGET SOUND WA 47.6050 -122.3383 

56 9447265 MEADOW POINT WA 47.6883 -122.4033 

57 9447427 EDMONDS 47.8133 -122.3833 

58 9447659 * EVERETT WA 47.9800 -122.2233 

59 9447725 EBEY SLOUGH POSSESSION SOUND 48.0450 -122.2100 

60 9447773 TULALIP BAY WA 48.0650 -122.2883 

61 9447814 * GLENDALE POSSESSION SOUN 47.9400 -122.3567 

62 9447827 DOUBLE BLUFF ADMIRALTY IN 47.9783 -122.5500 

63 9447854 * BUSH POINT WHIDBEY ISLAND 48.0333 -122.6067 

64 9447855 HOLLY HARBOR FARMS WA 48.0267 -122.5333 

65 9447856 SANDY POINT SARATOGA PASS 48.0350 -122.3767 

66 9447883 GREENBANK WHIDBEY ISLAND 48.1050 -122.5700 

67 9448094 KAYAK PT PORT SUSAN WA 48.1367 -122.3667 

Of the 67 stations in southern Puget Sound, only 23 stations are referenced to the 1983-2001 

NTDE. By comparing the mean tide range, which is assumed to be representative of all tidal 

datums, from the previous NTDE (1960-1978) to the present (1983-2001) at stations in Puget 

Sound where both are available, it was determined that the mean change was 0.5 cm, which 

is only 0.14% of the mean range, 3.624 m. It was decided to use all data, even if it came from 

an older National Tidal Datum Epochs, since changes in range since the previous tidal epoch 

were small. See Table 6 for the comparison at 22 stations (since one station, #9446742, was 

installed recently, it is referenced only to the current 1983-2001 NTDE.) 
21

Table 6. Great diurnal range of tidal datums from 1960-1978 NTDE and 1983-2001 NTDE 

for 22 stations, with ratio of range, difference, and absolute average percent difference. 

Station Range(m) Epoch Range(m) Epoch Ratio Diff(m) Pct 

9444900 2.576 1960 2.596 1983 1.008 -0.020 0.77% 

9445133 3.375 1960 3.374 1983 1.000 0.001 0.03% 

9445246 3.52 1960 3.523 1983 1.001 -0.003 0.09% 

9445272 3.475 1960 3.468 1983 0.998 0.007 0.20% 

9445296 3.514 1960 3.504 1983 0.997 0.010 0.28% 

9445478 3.609 1960 3.613 1983 1.001 -0.004 0.11% 

9445526 3.182 1960 3.18 1983 0.999 0.002 0.06% 

9445719 3.578 1960 3.575 1983 0.999 0.003 0.08% 

9445832 3.603 1960 3.607 1983 1.001 -0.004 0.11% 

9445958 3.575 1960 3.578 1983 1.001 -0.003 0.08% 

9446281 4.316 1960 4.334 1983 1.004 -0.018 0.42% 

9446451 4.109 1960 4.105 1983 0.999 0.004 0.10% 

9446484 3.604 1960 3.605 1983 1.000 -0.001 0.03% 

9446491 4.057 1960 4.055 1983 1.000 0.002 0.05% 

9446545 3.609 1960 3.605 1983 0.999 0.004 0.11% 

9446705 4.105 1960 4.108 1983 1.001 -0.003 0.07% 

9446807 4.415 1960 4.414 1983 1.000 0.001 0.02% 

9446969 4.438 1960 4.438 1983 1.000 0.000 0.00% 

9447130 3.459 1960 3.462 1983 1.001 -0.003 0.09% 

9447659 3.386 1960 3.38 1983 0.998 0.006 0.18% 

9447814 3.359 1960 3.364 1983 1.002 -0.005 0.15% 

9447854 2.848 1960 2.85 1983 1.001 -0.002 0.07% 

Average = 1.000 -0.005 0.14% 

4.2. Generation of Tidal Datum Fields 

The finite difference version of the TCARI model was used to generate the datum fields for 

Southern Puget Sound. A structured grid similar to the original model grid was created (Hess 

and White, 2004). The new grid was generated using the newer EVS shoreline. The grid 

spacing was 0.075 nmi (about 140 m) in the northward and eastward directions and covered 

water areas of Southern Puget Sound. The grid has 109,252 water cells. 

The TCARI model was run once for each tidal datum with input stations at the NOS water 

level gage locations and the 158 boundary nodes. Two of the 67 stations were not used to 

generate the tidal fields because they were too far up rivers: #9446484 and #9446545. Once 

the MHHW, MHW, MLW and MLLW datum fields were computed, the MTL and DTL 

fields were calculated as: MTL=1/2[MHW + MLW] and DTL=1/2[MHHW + MLLW]. 

 
22

The results from the spatially interpolated MLLW field are shown in Figure 9. The TCARI 

model results match the data from the corrected Foreman model at the boundary in Admiralty 

Inlet, and the results match the Northern Puget Sound TCARI model results in Saratoga 

Passage and Port Susan. 

Figure 9. VDatum marine grid populated with MLLW tidal datum field (in meters) for the 

southern Puget Sound area. 
23

5. GENERATION AND POPULATION OF VDATUM MARINE GRIDS 

The VDatum software program requires regularly spaced (in arc degrees) input grids that 

cover both land and water in a given region. Due to a current restraint with the software, the 

grid files must contain less than 1 million points. A grid with approximately 200m x 200m 

resolution that covers all three regions (the Strait of Juan de Fuca, Northern Puget Sound and 

Southern Puget Sound) would have over 1 million points, so this area was divided into two 

sub-regions. The Northern Puget Sound and Strait of Juan de Fuca regions were combined to 

create one VDatum marine grid that covers both of those regions. Another VDatum marine 

grid was created for Southern Puget Sound. The following sections will discuss the VDatum 

marine grid generation and then the population of those grids. 

5.1. Generation of the VDatum Marine Grids 

The VDatum marine grids were generated using a program which requires a MHW coastline 

and a bounding polygon input file. This program creates a grid array for a user-specified 

area, then identifies nodes as land or water points. Only nodes completely within the 

bounding polygon or up to one half of a cell size outside the coastline are delineated as water 

nodes. All nodes outside the bounding polygon or those more than one half of a cell size 

away from the coastline are marked as land nodes. (A further description of this process can 

be found in the paper by Hess and White (2004) describing the VDatum process for the 

original Southern Puget Sound grid.) 

Both of the grids have a zonal spacing of 0.0025o and a meridional spacing of 0.00175o (for, 

approximately, a spacing of 0.1 nmi or 200 m in each direction). The first grid covers the 

Strait of Juan de Fuca and Northern Puget Sound. The origin of the grid is at 47.9897o N and 

122.3483o W, which is the southwest corner of the grid. The resulting grid has a width of 

1,577 nodes and a height of 578 nodes for a total of 911,506 nodes. The second grid covers 

only Southern Puget Sound; and the origin is at 47.016667° N and 123.183333° W, which 

again is the southwest corner of the grid. The resulting grid has a width of 408 nodes and a 

height of 668 nodes for a total of 275,544 nodes. 

5.2. Population of the VDatum Marine Grids with Tidal Datums 

5.2.1. Population of the Southern Puget Sound Marine Grid 

The grid used to generate the tidal datum fields in Southern Puget Sound using the TCARI 

program had a denser spacing and a different configuration than the VDatum marine grid 

created for the region. Values in the marine grid for the locations within the bounding 

polygon (Figure 10) were obtained by bi-linearly interpolating the four surrounding TCARI 

grid values for MHHW, MHW, MLW, and MLLW. If there were three or fewer surrounding 

values, inverse distance squared weighting was used for the interpolation. The fields for 

MTL and DTL were generated by averaging the MHW and MLW fields and the MHHW and 

MLLW fields, respectively. 
24

Figure 10. VDatum bounding polygon (blue line) for Southern Puget Sound. 

5.2.2. Population of the Combined Juan de Fuca and Northern Puget Sound Marine Grid

Population of the VDatum marine grid with the final tidal datum fields for the Juan de Fuca 

and Northern Puget Sound areas was done by a two-step process. First, the large marine grid 

was divided into two smaller regions (marked by two bounding polygons as shown in Figure 

11) to delineate where the corrected Juan de Fuca hydrodynamic model results would be used 

and where the Northern Puget Sound spatial interpolation results would be used. The regions 

do not exactly match the boundaries of either of the two model grids, but most closely follow 

the boundary of the grid used for the TCARI spatial interpolation of the datums in Northern 

Puget Sound. 
25

Figure 11. The area of the VDatum marine grid populated by the corrected Strait of Juan de 

Fuca model results outlined by the red bounding polygon and the area populated by the 

Northern Puget Sound spatial interpolation model results outlined by the blue bounding 

polygon. 

Values in the marine grid for locations within the Northern Puget Sound bounding polygon 

were obtained by linearly averaging the values for MHHW, MHW, MLW, and MLLW at the 

unstructured grid nodes attached to the cluster of elements that surround the marine grid 

node. If the marine grid node was outside of the boundary of the unstructured grid (but still 

within the Northern Puget Sound bounding polygon), the tidal datum value at the nearest 

node in the unstructured grid was used as the value of the marine grid node. The fields for 

MTL and DTL were generated by averaging the MHW and MLW fields and the MHHW and 

MLLW fields, respectively. For the values in the marine grid at locations within the Strait of 

Juan de Fuca bounding polygon, the same process was followed using values from the 

corrected Strait of Juan de Fuca model results. 

The results from both the Southern Puget Sound VDatum marine grid and the combined 

Northern Puget Sound and Strait of Juan de Fuca marine grid are shown together in 

Appendix B. 

5.3. Errors in the Marine Grid 

Possible errors in the VDatum tidal transformation fields can be traced to several sources. 

Errors in the hydrodynamic model results and the interpolation of those errors at the tide 

stations can be evaluated in the Foreman model (the Strait of Juan de Fuca region) only. For 

all of the models, the error associated with the interpolation of the model results onto the 

VDatum marine grid can be examined. 

The error in the Foreman hydrodynamic model results, which cover the Strait of Juan de 

Fuca region, has been examined in Section 2.1, and the RMS error for four datums at 22 

stations is 15.1 cm. An expansion of this analysis to all of the 29 stations in just the Foreman 

model domain (versus the Myers or Spargo model domains) lowers the RMS error to 10.9 

cm. The error in the TCARI models or Northern and Southern Puget Sound cannot be 

quantified in the same way since the models were designed to match the datums at every 

node. 

Errors in the Foreman model results were compensated for by subtracting an interpolated 

error field that matches the error value at the tide stations. This makes a nearly exact match 
26

right at each tide station, but the effect on the error throughout the rest of the domain is 

unknown. It can be noted, though, as shown in Figure 4, that the error field created (in this 

figure for the MLLW datum) is generally smooth, which is desirable to create smooth final 

tidal datum fields. 

Another source of error can be introduced when transferring the modeled datums from their 

native grids onto the structured VDatum marine grid. A check was done to compare the 

combined datum field results as projected onto the VDatum marine grid with datum 

information at the NOS water level stations in the region. The root mean squared error 

(RMSE) and standard deviation were computed for the four datums (MHHW, MHW, MLW, 

and MLLW) at each station. For the combined Northern Puget Sound and Strait of Juan de 

Fuca marine grid, the maximum RMSE was 1.83 cm at Sneesh Point in Skagit Bay (station 

#9448576). The average RMSE was 0.54 cm. The stations used for this analysis are shown 

in Figures 3 and 6 and listed in Tables 1 and 3, and the RMSE and standard deviation for 

each individual station are listed in Appendix A, Table A.5. For the Southern Puget Sound 

marine grid, the results were compared to the 67 tide gages shown in Figure 8 and listed in 

Table 5. The mean RMS difference was under 0.06 cm, and the maximum RMS difference 

at a single station was 2 cm. The results for each station are shown in Appendix A, Table 

A.6. 

This error was eliminated through a final adjustment of all water nodes (up to four) in the 

marine grid surrounding a tide station location so the values match the observed datum at that 

station. This way the RMSE and standard deviation for each NOS station was reduced to 

zero since the average of the datums at the water nodes surrounding a given NOS station 

would exactly equal the datum value at that station. 

Another check was done to look for maximum point-to-point differences in the marine grid. 

The maximum point-to-point difference in the combined Northern Puget Sound and Strait of 

Juan de Fuca marine grid was found in the MLLW datum and was 1.1 cm. All other datums 

had maximum differences less than 1 cm. The maximum point-to-point differences in the 

Southern Puget Sound marine grid occurred at the southern end of Marrowstone Island east 

of the Quimper Penninsula. Differences over the 0.1 nmi cell spacing for the MHHW field 

were 3.4 cm, in the MHW field were 2.4 cm, in the MLW were 4.2 cm, and in the MLLW 

field were 5.3 cm. 

For the Southern Puget Sound VDatum marine grid, the new results can be compared to the 

previously published results (Hess and White, 2004). The maximum changes in any one 

datum field were from 14 to 17 cm, depending on the datum. The maximum changes were 

located in the northern portion of Admiralty Inlet, where two significant changes in input 

data occurred. The revised tidal datums from Bush Point were used in the new tidal datum 

interpolation, and input values were used at the boundary with the Strait of Juan de Fuca. 

These changes account for the differences between the VDatum marine grid results. 
27

6. TOPOGRAPHY OF THE SEA SURFACE 

The Topography of the Sea Surface (TSS) is a gridded surface that models the elevation of 

the North American Vertical Datum of 1988 (NAVD 88) relative to local mean sea level 

(LMSL). The gridded TSS surface was generated by interpolating the observed values using 

commercial contouring software. In the Strait of Juan de Fuca-Puget Sound area, the 

observed values at various locations range from approximately -1.4 to -0.9 m. A positive 

value specifies that the NAVD 88 reference value is further from the center of the Earth than 

the local mean sea level surface. All data are based on the most recent National Tidal Datum 

Epoch (1983-2001). The location of tide stations and tidal benchmarks used are illustrated in 

Figure 12. 

Figure 12. Location of tidal benchmarks and tide stations used to compute the Juan de Fuca 

and Puget Sound TSS grid. 

The TSS grid was generated as follows. At each NGS benchmark location, there is a set of 

four TBMdatum values, each of which is the elevation at the Tidal Benchmark of a datum 
28

relative to MLLW (i.e., Datum – MLLW). Also, from the four tidal datum grids (see Section 

5), there is a set of VDdatum values, each of which is the difference between the tidal datum 

and MSL (i.e., Datum – MSL). 

For the first step, four residuals were computed. The residual, R, for each datum is defined 

as: 

Rdatum = TBMnavd88 – TBMdatum – VDdatum

Note that the VD values were interpolated to the location of the benchmark. The four 

residuals at the benchmark were averaged to produce the mean. Note that this mean is an 

estimate of the quantity MSL – NAVD88. The residuals are listed in Tables 7 and 8. 

Table 7. Derived residual values for each tidal datum at NGS benchmarks from the 

combined Strait of Juan de Fuca and Northern Puget Sound Tidal Grids.

Benchmark Latitude 

(deg) 

Longitude 

(deg) 

From 

MLLW 

(m) 

From 

MLW 

(m) 

From 

MHW 

(m) 

From 

MHHW 

(m) 

Average 

(m) 

Std. 

Dev. 

(m) 

TR0790 48.12333 -123.44472 -1.1629 -1.1542 -1.1682 -1.1629 -1.1621 0.0058 

TR0789 48.12722 -123.45777 -1.1621 -1.1470 -1.1724 -1.1634 -1.1612 0.0105 

TR0782 48.14000 -123.40194 -1.1792 -1.2161 -1.1699 -1.1976 -1.1907 0.0205 

TR0783 48.14000 -123.40138 -1.1789 -1.2163 -1.1698 -1.1980 -1.1908 0.0207 

TR0784 48.14055 -123.40888 -1.1749 -1.2171 -1.1694 -1.2014 -1.1907 0.0225 

TR0785 48.14055 -123.40972 -1.1740 -1.2174 -1.1692 -1.2021 -1.1907 0.0230 

TR0779 48.14055 -123.40250 -1.1776 -1.2163 -1.1699 -1.1991 -1.1907 0.0211 

TS0156 48.36555 -124.61666 -1.0543 -1.0426 -1.0757 -1.0676 -1.0601 0.0146 

TS0161 48.36555 -124.62083 -1.0545 -1.0479 -1.0674 -1.0625 -1.0581 0.0086 

AF8871 48.36583 -124.61722 -1.0574 -1.0482 -1.0747 -1.0681 -1.0621 0.0117 

TS0154 48.36638 -124.61138 -1.0551 -1.0422 -1.0768 -1.0682 -1.0606 0.0152 

TS0152 48.36694 -124.60416 -1.0597 -1.0477 -1.0769 -1.0691 -1.0634 0.0126 

TS0340 48.36694 -124.61944 -1.0546 -1.0484 -1.0665 -1.0620 -1.0579 0.0080 

TS0340 48.36694 -124.61944 -1.0546 -1.0484 -1.0665 -1.0620 -1.0579 0.0080 

TS0150 48.36694 -124.60416 -1.0597 -1.0477 -1.0769 -1.0691 -1.0634 0.0126 

AF8872 48.36805 -124.62388 -1.0577 -1.0530 -1.0666 -1.0636 -1.0602 0.0061 

AF8873 48.36805 -124.62666 -1.0550 -1.0511 -1.0614 -1.0595 -1.0568 0.0046 

TS0171 48.36833 -124.62305 -1.0577 -1.0529 -1.0666 -1.0636 -1.0602 0.0061 
29

Table 8. Derived NAVD 88-to-LMSL values for each tidal datum at NGS benchmarks from 

the Southern Puget Sound Tidal Grids.

Benchmark Latitude 

(deg) 

Longitude 

(deg) 

From 

MLLW 

(m) 

From 

MLW 

(m) 

From 

MHW 

(m) 

From 

MHHW 

(m) 

Average

(m) 

Std. 

Dev. 

(m) 

SY0868 47.05000 -122.90138 -1.3021 -1.3038 -1.3057 -1.3036 -1.3038 0.0015 

SY0865 47.05166 -122.90250 -1.3111 -1.3128 -1.3147 -1.3126 -1.3128 0.0015 

SY0866 47.05194 -122.90388 -1.3141 -1.3158 -1.3177 -1.3156 -1.3158 0.0015 

SY0536 47.26416 -122.41194 -1.3613 -1.3568 -1.3311 -1.3326 -1.3455 0.0158 

SY0920 47.56305 -122.62527 -1.3030 -1.3030 -1.3030 -1.3030 -1.3030 0.0000 

SY5718 47.56305 -122.62416 -1.3180 -1.3180 -1.3180 -1.3180 -1.3180 0.0000 

SY0270 47.57444 -122.36277 -1.2990 -1.2980 -1.2991 -1.2981 -1.2986 0.0006 

SY0271 47.57833 -122.36277 -1.2960 -1.2950 -1.2961 -1.2951 -1.2956 0.0006 

SY0272 47.58194 -122.36277 -1.2960 -1.2950 -1.2961 -1.2950 -1.2955 0.0006 

SY0273 47.58416 -122.36250 -1.2990 -1.2980 -1.2990 -1.2980 -1.2985 0.0006 

SY0283 47.60194 -122.33388 -1.3071 -1.3081 -1.3059 -1.3069 -1.3070 0.0009 

SY0286 47.60305 -122.33444 -1.3100 -1.3110 -1.3090 -1.3100 -1.3100 0.0008 

SY0290 47.60388 -122.33750 -1.3100 -1.3110 -1.3090 -1.3100 -1.3100 0.0008 

SY0289 47.60444 -122.33500 -1.3100 -1.3110 -1.3090 -1.3100 -1.3100 0.0008 

SY0959 47.74666 -122.72638 -1.2500 -1.2500 -1.2490 -1.2500 -1.2498 0.0005 

SY0128 47.81138 -122.38250 -1.3190 -1.3180 -1.3190 -1.3200 -1.3190 0.0008 

SY0126 47.81305 -122.38027 -1.3219 -1.3209 -1.3220 -1.3230 -1.3220 0.0009 

TR2726 48.11138 -122.76166 -1.1950 -1.1865 -1.1897 -1.1863 -1.1894 0.0041 

TR0559 48.11583 -122.75194 -1.1951 -1.1892 -1.1965 -1.1948 -1.1939 0.0032 

Next, a gridded sea surface topography field was generated. The mean residuals at all 

benchmarks were merged with values of the quantity NAVD88 – MSL at CO-OPS’ water 

level stations to produce input data for contouring. The tide stations and associated elevation 

information used in the computation of the TSS are presented in Table 9. A mesh covering 

the entire area of benchmarks and water level stations with a spatial resolution similar to that 

of the tidal marine grids was created. Break lines were inserted to represent the influence of 

land. A sea surface topography field was generated using the Surfer© software’s minimum 

curvature algorithm to create a surface that honors the data as closely as possible. The 

maximum allowed departure value used was 0.0001 meters. To control the amount of 

bowing on the interior and at the edges of the grid, an internal and boundary tension value of 

0.3 was utilized. Once the gridded topography field was generated, null values were 

obtained from the marine tidal grids and were inserted to denote the presence of land. The 

continuous surface produced this way is shown in Figure 13. 

Then a set of ‘Delta’ values were computed. Delta represents the difference between the 

observed tidal datum and the datum as computed by the gridded fields. If S represents the 

value of the quantity NAVD88 – MSL obtained from the sea surface topography grid, then 

Delta (D) for each tidal datum is computed as: 

-Ddatum = TBMnavd88 – TBMdatum – VDdatum - S 
30

The averaged Delta at each benchmark should be less than 0.01 m. If it is not, the input data 

and grids must be checked, appropriate changes made, and the Deltas recomputed until the 

criterion is met. 

Table 9. Location and elevation information for NOAA tide gages used to create the TSS. 

All datums are in meters and are relative to MLLW. Data are from CO-OPS. Station numbers 

marked with an asterisk have NAVD 88 elevations from NGS. 

Station 

Number 

Latitude 

(deg) 

Longitude 

(deg) MHHW MHW LMSL MLW NAVD88 LMSLNAVD88 

9440574 46.27333 -124.07167 2.361 2.156 1.246 0.374 0.077 -1.169 

9442396* 47.91333 -124.63667 2.651 2.43 1.423 0.428 0.258 -1.165 

9443090 48.36833 -124.61667 2.425 2.167 1.315 0.486 0.256 -1.059 

9443361 48.26333 -124.29667 2.286 2.03 1.269 0.545 0.176 -1.093 

9443826* 48.16167 -123.72500 2.151 1.971 1.285 0.659 0.127 -1.158 

9444090 48.12500 -123.44000 2.153 1.987 1.295 0.586 0.129 -1.166 

9444122 48.14000 -123.41333 2.135 1.926 1.282 0.684 0.097 -1.185 

9444900* 48.11167 -122.75833 2.596 2.389 1.522 0.76 0.3325 -1.1895 

9445133* 47.74833 -122.72667 3.374 3.103 1.978 0.877 0.728 -1.25 

9445246 47.76167 -122.85000 3.523 3.229 2.067 0.916 0.814 -1.253 

9445478 47.35833 -123.09833 3.613 3.312 2.122 0.917 0.865 -1.257 

9445958 47.56167 -122.62333 3.578 3.31 2.08 0.868 0.769 -1.311 

9446281* 47.38333 -122.82333 4.334 4.05 2.492 0.929 1.2285 -1.2635 

9446484 47.26667 -122.41333 3.605 3.336 2.094 0.87 0.758 -1.336 

9446491* 47.28000 -122.65167 4.055 3.78 2.316 0.898 1.202 -1.114 

9446545 47.25500 -122.43167 3.605 3.337 2.097 0.873 0.795 -1.302 

9446969 47.06000 -122.90333 4.437 4.129 2.546 0.935 1.227 -1.319 

9447110 47.58500 -122.36167 3.47 3.206 2.028 0.867 0.727 -1.301 

9447130 47.60500 -122.33833 3.462 3.198 2.023 0.864 0.715 -1.308 

9447427 47.81333 -122.38333 3.333 3.069 1.959 0.857 0.637 -1.322 

9447659 47.98000 -122.22333 3.38 3.114 1.976 0.854 0.62 -1.356 

9447814* 47.94000 -122.35667 3.364 3.108 1.976 0.86 0.6205 -1.3555 

9447952 48.28667 -122.61667 3.554 3.281 2.072 0.855 0.675 -1.397 

9448558* 48.39167 -122.49667 3.154 2.874 1.817 0.822 0.461 -1.356 

9448576 48.40000 -122.54833 3.369 3.108 1.946 0.781 0.615 -1.331 

9448657 48.44500 -122.55500 3.152 2.888 1.812 0.761 0.465 -1.347 

9449211 48.74500 -122.49500 2.594 2.375 1.51 0.718 0.147 -1.363 

9449424* 48.86333 -122.75833 2.788 2.535 1.61 0.796 0.293 -1.317 

9449679 48.99167 -122.76500 2.905 2.643 1.67 0.81 0.31 -1.36 
31

Figure 13. Combined Strait of Juan de Fuca, Northern Puget Sound and Southern Puget 

Sound gridded TSS.

The TSS grid was created to assure a continuous field across the boundary of the Strait of 

Juan de Fuca and Northern Puget Sound area with the Southern Puget Sound region. For use 

in the VDatum utility, however, this continuous TSS field was subdivided into two separate 

TSS grid files with boundaries that correspond with those used to divide the tidal datum 

fields. 

Quality control was carried out by comparing observed benchmarks values to those 

predicted. After the TSS was created, it was incorporated into VDatum. For the first test, 

conversions between NAVD 88 and the tidal datums MLLW, MLW, MHW, and MHHW at 

tidal benchmarks were computed. All Delta values tabulated for both the Southern Puget 

Sound TSS and the Strait of Juan de Fuca and Northern Puget Sound TSS are listed for each 

station in Appendix A, Table A.7. The RMS error was 1.03 cm. For the second test, the mean 

difference between known NAVD 88 to MSL relationships and that predicted by VDatum 

was computed. For the San Juan Islands VDatum the RMS difference was 0.125 cm, the 

mean was 0.03 cm, and the standard deviation was 0.12 cm, and for the Puget Sound 

VDatum, the RMS difference was 0.091 cm, the mean difference was 0.020 cm, and the 

standard deviation was 0.02 cm. Individual station results are listed in Appendix A, Table 

A.8 and Table A.9. 
32

ACKNOWLEDGEMENTS 

Dr. Mike Foreman of Fisheries & Oceans Canada, Institute of Ocean Sciences generously 

provided the results from his Eastern North Pacific assimilated tidal model. Dr. Edward 

Myers of NOAA/NOS/OCS/CSDL provided the results for the Eastern North Pacific inverse 

tidal model. Ms. Adeline Wong of CSDL and Ms. Animieke Raymond (formerly of CSDL) 

provided the EVS coastline data. 

REFERENCES 

Foreman, M.G.G., W.R. Crawford, and J.Y. Cherniawsky, 2000: A high-resolution 

assimilating tidal model for the northeast Pacific Ocean. J. of Geophysical Research, 

105(C12), 28629-28651. 

Hess, K.W. and S.A. White, 2004: VDatum for Puget Sound: generation of the grid and 

population with tidal datums and sea surface topography. NOAA Technical Memorandum, 

NOS CS4, 27 pp. 

Hess, K.W., 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. 

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

Transformation Software. Ver.1.06 (hppt://nauticalcharts.noaa.gov/bathytopo/vdatum.html). 

Myers, E.P. and A.M. Baptista, 2001: Inversion for tides in the Eastern North Pacific Ocean. 

Advances in Water Resources, 24, 505-519. 

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). 

Spargo, E.A., J.J. Westerink, R.A. Luettich, D.J. Mark, 2004: ENPAC 2003: A Tidal 

Constituent Database for the Eastern North Pacific Ocean. Department of the Army Technical 

Note, TR-04-12. 

Zervas, C., 1999: Tidal Current Analysis Procedures and Associated Computer Programs. 

NOAA Technical Memorandum, NOS CO-OPS 0021, 103 pp. 
33

APPENDIX A. STATION INFORMATION AND ERROR ANALYSIS 

Table A.1. Station identification number, location, and error (difference between model 

results {for the Foreman, Myers, and Spargo models} and station data) for four datums at 22 

NOS water level stations. Total RMS and absolute average error for each model is also 

given. 

 Station 

ID 

Longitude 

(deg) 

Latitude 

(deg) 

MHHW 

Error 

(cm) 

MHW 

Error 

(cm) 

MLW 

Error 

(cm) 

MLLW 

Error 

(cm) Model 

1 9442861 -124.668317 48.294021 

-4.14 -9.72 -24.02 18.55 Foreman 

45.91 3.17 5.51 -20.33 Myers 

-20.74 -16.86 -21.77 -8.16 Spargo 

2 9443090 -124.621009 48.363939 

11.75 7.50 -6.12 33.90 Foreman 

60.26 19.74 22.16 -6.12 Myers 

-7.64 -1.21 -5.94 1.50 Spargo 

3 9443361 -124.299453 48.261804 

15.76 14.63 -1.18 30.04 Foreman 

83.85 41.13 38.69 5.78 Myers 

9.36 10.11 3.62 6.17 Spargo 

4 9443644 -123.945229 48.164904 

19.13 17.57 6.15 23.59 Foreman 

79.37 34.28 35.34 -3.28 Myers 

26.81 20.81 15.11 11.97 Spargo 

5 9443826 -123.708153 48.167967 

24.39 16.72 8.01 23.31 Foreman 

70.57 23.81 33.39 -13.29 Myers 

34.38 23.39 24.82 14.75 Spargo 

6 9444090 -123.439732 48.112821 

18.08 15.35 5.64 14.07 Foreman 

74.15 25.83 26.79 -12.32 Myers 

13.91 12.29 2.07 10.16 Spargo 

7 9444122 -123.408964 48.151134 

16.29 20.05 22.40 13.17 Foreman 

94.43 46.94 50.30 2.77 Myers 

48.76 43.46 45.35 26.46 Spargo 

8 9447951 -122.724501 48.296276 

17.23 17.97 9.40 4.73 Foreman 

55.37 11.77 11.91 -43.81 Myers 

12.41 15.31 8.83 -4.56 Spargo 

9 9447985 -122.831746 48.327882 

30.94 24.11 8.58 21.21 Foreman 

74.36 29.85 33.21 -18.84 Myers 

45.74 38.35 35.31 15.64 Spargo 

10 9448614 -122.653705 48.418655 

12.33 9.06 2.75 6.65 Foreman 

58.62 14.65 26.26 -29.32 Myers 

4.71 6.86 7.91 -6.38 Spargo 

11 9448772 -122.682335 48.504810 

0.84 7.54 2.35 -16.72 Foreman 

88.74 40.24 35.58 -22.55 Myers 

3.39 8.35 1.59 -16.00 Spargo 

12 9448967 -122.697502 48.617693 

0.14 5.16 -5.37 -12.32 Foreman 

51.97 12.32 16.12 -41.01 Myers 

-2.62 3.82 -4.81 -13.96 Spargo 

13 9449161 -122.727517 48.718246 

-14.94 -7.57 -1.64 -17.45 Foreman 

16.94 -18.66 -7.54 -69.75 Myers 

-12.08 -5.49 -0.32 -17.49 Spargo 
34

Table A.1. (Continued)

 Station 

ID 

Longitude 

(deg) 

Latitude 

(deg) 

MHHW 

Error 

(cm) 

MHW 

Error 

(cm) 

MLW 

Error 

(cm) 

MLLW 

Error 

(cm) Model 

14 9449211 -122.518051 48.712912 

-11.07 -7.26 -9.51 -15.48 Foreman 

37.93 -3.10 8.52 -44.51 Myers 

-27.48 -21.17 -28.70 -50.08 Spargo 

15 9449424 -122.772523 48.842827 

-18.58 -12.47 -12.22 -23.36 Foreman 

32.99 -5.14 9.53 -51.12 Myers 

-0.52 -8.20 3.38 -15.35 Spargo 

16 9449704 -122.984318 48.778176 

-12.39 -5.67 -5.83 -33.57 Foreman 

38.31 -2.52 5.47 -55.28 Myers 

-8.39 -8.27 -18.80 -25.55 Spargo 

17 9449802 -123.249872 48.683484 

6.01 7.89 5.45 -18.16 Foreman 

50.82 8.05 13.56 -44.56 Myers 

-3.03 -4.43 -15.48 -53.22 Spargo 

18 9449828 -123.168774 48.592953 

-2.97 -2.38 7.03 -17.78 Foreman 

51.16 8.42 21.81 -30.19 Myers 

20.35 6.82 7.39 6.50 Spargo 

19 9449880 -123.014674 48.549839 

-0.60 -3.36 1.60 -18.25 Foreman 

49.79 6.47 19.09 -31.78 Myers 

57.65 32.62 34.20 49.69 Spargo 

20 9449932 -122.773907 48.533452 

7.71 -2.41 1.17 -17.39 Foreman 

36.11 -8.98 0.81 -54.73 Myers 

-57.02 -46.98 -41.83 -90.17 Spargo 

21 9449982 -122.907732 48.429925 

30.51 18.00 19.59 5.05 Foreman 

46.84 -3.91 3.43 -47.49 Myers 

69.06 39.66 35.72 57.08 Spargo 

22 9449994 -122.850802 48.414931 

37.80 33.71 30.76 3.18 Foreman 

62.20 20.63 24.07 -33.22 Myers 

73.73 49.63 42.59 52.12 Spargo 

 15.32 Foreman 

Total RMS error (cm) 18.25 Myers 

 28.87 Spargo 

13.23 Foreman 

Total Absolute Average Error (cm) 31.61 Myers 

 22.07 Spargo 
35

Table A.2. Station identification numbers (as shown in Figure 3 plus the “944” beginning 

digits), station name, and tidal datums for NOAA tide gages, the hydrodynamic model results 

at that location, the difference between the two, and the absolute average percent difference. 

Station ID 

Number Station Name MHHW (cm) 

MHW 

(cm) 

MLW 

(cm) 

MLLW 

(cm) Data 

9442861 Mukkaw Bay 

124.30 101.00 -98.90 -145.00 NOAA 

123.20 97.71 -94.76 -143.38 Model 

-1.10 -3.29 4.14 1.62 Difference 

0.89% 3.31% 4.28% 1.12% % Diff 

9443090 Neah Bay 

111.00 85.20 -82.90 -131.50 NOAA 

117.71 89.00 -87.19 -136.35 Model 

6.71 3.80 -4.29 -4.85 Difference 

5.87% 4.36% 5.04% 3.62% % Diff 

9443361 Sekiu Clallam 

Bay 

100.30 74.40 -74.40 -128.30 NOAA 

104.61 75.79 -72.57 -124.81 Model 

4.31 1.39 1.83 3.49 Difference 

4.21% 1.85% 2.49% 2.76% % Diff 

9443644 Twin Rivers 

88.10 67.30 -67.10 -125.60 NOAA 

97.10 74.64 -70.50 -120.45 Model 

9.00 7.34 -3.40 5.15 Difference 

9.72% 10.34% 4.94% 4.19% % Diff 

9443826 Crescent Bay 

86.60 68.60 -62.60 -128.50 NOAA 

92.83 73.22 -72.83 -118.92 Model 

6.23 4.62 -10.23 9.58 Difference 

6.94% 6.52% 15.11% 7.74% % Diff 

9444090 Port Angeles 

85.80 69.20 -70.90 -129.50 NOAA 

91.31 74.89 -72.55 -125.14 Model 

5.51 5.69 -1.65 4.36 Difference 

6.22% 7.90% 2.30% 3.42% % Diff 

9444122 Ediz Hook 

85.30 64.40 -59.80 -128.20 NOAA 

91.21 76.63 -73.47 -124.93 Model 

5.91 12.23 -13.67 3.27 Difference 

6.70% 17.34% 20.51% 2.58% % Diff 

9444705 Gardiner 

Landing 

94.50 73.20 -73.10 -146.30 NOAA 

101.15 81.05 -71.22 -141.32 Model 

6.65 7.85 1.88 4.98 Difference 

6.80% 10.18% 2.61% 3.46% % Diff 

9447951 Whidbey Island, 

Sunset Beach 

86.50 65.80 -65.20 -138.70 NOAA 

99.22 80.03 -69.18 -137.64 Model 

12.72 14.23 -3.98 1.06 Difference 

13.70% 19.52% 5.92% 0.77% % Diff 

9447985 Smith Island 

83.20 63.10 -62.80 -134.10 NOAA 

97.33 79.24 -69.69 -135.52 Model 

14.13 16.14 -6.89 -1.42 Difference 

15.65% 22.68% 10.40% 1.05% % Diff 
36

Table A.2. (Continued) 

Station ID 

Number Station Name MHHW (cm) 

MHW 

(cm) 

MLW 

(cm) 

MLLW 

(cm) Data 

9447995 Whidbey Island, 

Coronet Bay 

131.10 103.70 -97.50 -179.80 NOAA 

100.68 81.29 -70.80 -139.95 Model 

-30.42 -22.41 26.70 39.85 Difference 

26.25% 24.23% 31.73% 24.93% % Diff 

9448601 Yokeko Point 

138.00 107.60 -102.80 -182.00 NOAA 

100.68 81.30 -70.80 -139.95 Model 

-37.32 -26.30 32.00 42.05 Difference 

31.27% 27.85% 36.87% 26.12% % Diff 

9448614 Reservation Bay 

94.20 74.40 -66.40 -141.00 NOAA 

100.74 81.36 -70.83 -140.08 Model 

6.54 6.96 -4.43 0.92 Difference 

6.71% 8.94% 6.46% 0.65% % Diff 

9448772 Fidalgo Island, 

Ship Harbor 

95.10 72.50 -72.30 -150.30 NOAA 

106.53 83.46 -69.15 -147.65 Model 

11.43 10.96 3.15 2.65 Difference 

11.34% 14.05% 4.45% 1.78% % Diff 

9448967 Sinclair Island 

100.60 76.20 -76.20 -152.40 NOAA 

110.99 85.32 -70.61 -151.81 Model 

10.39 9.12 5.59 0.59 Difference 

9.82% 11.29% 7.62% 0.39% % Diff 

9449161 Lummi Island 

111.30 86.90 -74.70 -152.40 NOAA 

116.06 89.03 -73.22 -158.34 Model 

4.76 2.13 1.48 -5.94 Difference 

4.19% 2.42% 2.00% 3.82% % Diff 

9449211 Bellingham 

108.40 86.50 -79.20 -151.00 NOAA 

114.14 87.21 -71.38 -155.31 Model 

5.74 0.71 7.82 -4.31 Difference 

5.16% 0.82% 10.39% 2.81% % Diff 

9449292 Lummi Bay 

116.30 91.50 -79.70 -158.60 NOAA 

120.68 91.18 -75.07 -163.12 Model 

4.38 -0.32 4.63 -4.52 Difference 

3.70% 0.35% 5.98% 2.81% % Diff 

9449424 Cherry Point 

117.80 92.50 -81.40 -161.00 NOAA 

122.75 92.70 -76.78 -165.40 Model 

4.95 0.20 4.62 -4.40 Difference 

4.12% 0.22% 5.84% 2.70% % Diff 

9449679 Blaine 

123.50 97.30 -86.00 -167.00 NOAA 

126.02 95.35 -79.70 -169.40 Model 

2.52 -1.95 6.30 -2.40 Difference 

2.02% 2.02% 7.60% 1.43% % Diff 

9449704 Patos Island 

103.60 82.30 -79.30 -158.50 NOAA 

120.16 91.28 -74.88 -163.55 Model 

16.56 8.98 4.42 -5.05 Difference 

14.80% 10.35% 5.73% 3.14% % Diff 
37

Table A.2. (Continued) 

Station ID 

Number Station Name MHHW (cm) 

MHW 

(cm) 

MLW 

(cm) 

MLLW 

(cm) Data 

9449771 Orcas Island 

97.50 76.20 -73.20 -149.40 NOAA 

105.95 82.24 -68.06 -145.55 Model 

8.45 6.04 5.14 3.85 Difference 

8.31% 7.62% 7.28% 2.61% % Diff 

9449802 Stuart Island 

85.30 67.00 -67.10 -143.30 NOAA 

107.23 84.87 -73.25 -149.19 Model 

21.93 17.87 -6.15 -5.89 Difference 

22.78% 23.53% 8.76% 4.03% % Diff 

9449828 Hanbury Point 

95.80 75.60 -65.80 -136.70 NOAA 

101.59 84.45 -82.20 -141.37 Model 

5.79 8.85 -16.40 -4.67 Difference 

5.87% 11.06% 22.16% 3.36% % Diff 

9449880 Friday Harbor 

97.70 78.00 -68.90 -138.70 NOAA 

103.88 84.55 -76.54 -143.57 Model 

6.18 6.55 -7.64 -4.87 Difference 

6.13% 8.06% 10.51% 3.45% % Diff 

9449911 Lopez Island, 

Upright Head 

91.40 70.10 -70.10 -146.30 NOAA 

104.99 82.45 -71.68 -144.27 Model 

13.59 12.35 -1.58 2.03 Difference 

13.84% 16.19% 2.23% 1.40% % Diff 

9449932 Armitage Island 

96.90 78.20 -71.40 -142.20 NOAA 

103.73 83.77 -74.60 -143.43 Model 

6.83 5.57 -3.20 -1.23 Difference 

6.81% 6.88% 4.38% 0.86% % Diff 

9449982 Lopez Island, 

Richardson 

87.20 71.00 -67.60 -131.30 NOAA 

95.94 80.04 -74.65 -133.58 Model 

8.74 9.04 -7.05 -2.28 Difference 

9.54% 11.97% 9.91% 1.72% % Diff 

9449994 Lopez Island, 

Aleck Bay 

85.40 64.00 -64.00 -140.20 NOAA 

96.36 79.33 -73.06 -134.95 Model 

10.96 15.33 -9.06 5.25 Difference 

12.06% 21.39% 13.22% 3.82% % Diff 
38

Table A.3. Station identification number or node number (as shown in Figure 5), station 

name, location in longitude and latitude (in degrees), and datum information (in cm). 

Station ID/ 

Node 

Number 

Station Name Longitude

(degrees) 

Latitude 

(degrees)

MHHW

(cm) 

MHW 

(cm) 

MLW 

(cm) 

MLLW

(cm) 

9444900 Port Townsend -122.7500 48.1117 107.4 86.7 -76.2 -152.2 

9445016 Foulweather Bluff -122.6167 47.9267 125.3 99.7 -99.7 -184.4 

9445017 Port Ludlow -122.6800 47.9250 122.0 97.6 -97.5 -179.8 

9445526 Hansville -122.5450 47.9183 133.5 107.7 -100.4 -184.5 

9445639 Apple Tree Cove -122.4933 47.7967 137.5 111.6 -111.5 -197.5 

9445683 Point Jefferson -122.4767 47.7467 135.9 109.7 -109.8 -194.2 

9447427 Edmonds -122.4767 47.7467 137.4 111.0 -110.2 -195.9 

9447659 Everett -122.3833 47.8133 140.4 113.8 -112.2 -197.6 

9447725 Ebey Slough -122.2233 47.9800 139.6 113.7 -114.0 -190.5 

9447773 Tulalip Bay -122.2100 48.0450 143.2 115.8 -112.8 -195.1 

9447814 Glendale -122.2883 48.0650 138.8 113.2 -111.6 -197.6 

9447827 Double Bluff -122.3567 47.9400 128.0 95.1 -94.8 -179.2 

9447854 Bush Point -122.5500 47.9783 143.3 119.5 -59.3 -141.7 

9447855 Holly Harbor 

Farms -122.6033 48.0333 145.4 118.3 -118.3 -203.3 

9447856 Sandy Point -122.5433 48.0267 142.8 116.0 -114.4 -200.4 

9447883 Greenbank -122.3767 48.0333 143.2 115.8 -115.9 -201.2 

9447929 

Coupeville Penn 

Cove -122.6900 48.2233 146.3 118.9 -118.9 -204.2 

9447951 Sunset Beach -122.7283 48.2833 148.2 120.9 -121.7 -207.2 

9447952 Crescent Harbor -122.6167 48.2867 137.1 109.7 -100.6 -182.9 

9447985 Smith Isl. -122.8367 48.3167 131.1 103.7 -97.5 -179.8 

9447993 Ala Spit -122.5867 48.3967 141.1 114.3 -116.2 -201.5 

9448094 Port Susan -122.3667 48.1367 133.7 105.7 -99.5 -181.7 

9448558 Swinomish Slough -122.4967 48.3917 142.3 116.2 -116.5 -194.6 

9448576 Skagit Bay -122.5483 48.4000 138.0 107.6 -102.8 -182.0 

9448601 Yokeko Point -122.6150 48.4133 94.2 74.4 -66.4 -141.0 

9448657 Turner Bay -122.5550 48.4450 134.0 107.6 -105.1 -181.2 

1 -122.6890 48.1800 101.5 75.0 -68.6 -154.9 

2 -122.6940 48.1780 101.2 75.0 -68.5 -154.8 

3 -122.7000 48.1750 100.9 75.0 -68.4 -154.8 

4 -122.7110 48.1680 100.7 75.0 -68.2 -154.7 

5 -122.7240 48.1610 100.0 74.8 -68.0 -154.4 

6 -122.7330 48.1570 99.8 74.8 -67.9 -154.4 

7 -122.7440 48.1510 99.6 74.7 -67.7 -154.3 

8 -122.7550 48.1450 99.9 74.7 -67.6 -154.2 

9 -122.6770 48.4440 93.9 73.4 -70.3 -144.2 

10 -122.6900 48.4450 93.6 73.2 -70.0 -143.9 

11 -122.7100 48.4410 92.8 72.5 -69.2 -143.9 

12 -122.7260 48.4310 91.6 71.5 -68.0 -142.6 

13 -122.7290 48.4190 91.1 71.5 -69.8 -141.2 

14 -122.7180 48.4090 91.2 71.0 -67.5 -141.3 

15 -122.7080 48.4000 91.5 71.2 -67.6 -142.3 

16 -122.6990 48.3900 91.8 71.4 -67.8 -141.8 

17 -122.6910 48.3790 91.8 71.4 -67.7 -141.9 

18 -122.6730 48.3810 92.6 72.0 -68.3 -142.5 

19 -122.6650 48.3810 92.8 72.2 -68.5 -142.7 

20 -122.4850 48.5080 102.6 79.3 -74.8 -150.9 
39

Table A.3. (Continued) 

Station ID/ 

Node 

Number 

Station Name Longitude

(degrees) 

Latitude 

(degrees)

MHHW 

(cm) 

MHW 

(cm) 

MLW 

(cm) 

MLLW

(cm) 

21 -122.4920 48.5080 102.5 79.2 -74.7 -150.8 

22 -122.5000 48.5100 102.5 79.3 -74.7 -150.8 

23 -122.5100 48.5090 102.5 79.2 -74.7 -150.8 

24 -122.5180 48.5080 102.5 79.2 -74.6 -150.7 

25 -122.5250 48.5080 102.4 79.1 -74.6 -150.7 

26 -122.5330 48.5070 102.4 79.1 -74.6 -150.7 

27 -122.5410 48.5060 102.3 79.0 -74.5 -150.6 

28 -122.5480 48.4150 102.2 79.0 -74.4 -150.6 

29 -122.5560 48.4450 102.0 78.8 -74.3 -150.4 

30 -122.5570 48.2233 102.2 78.9 -74.4 -150.6 
40

Table A.4. Station identification number (as shown in Figure 8), station name, location in 

longitude and latitude (in degrees), and datum information (in cm). 

Station 

ID Station Name 

Latitude 

(degrees)

Longitude 

(degrees) 

MHHW 

(cm) 

MHW 

(cm) 

MLW 

(cm) 

MLLW 

(cm) 

9444900 PORT TOWNSEND 48.1117 -122.7500 107.4 86.7 -76.2 -152.2 

9445016 FOULWEATHER 47.9267 -122.6167 125.3 99.7 -99.7 -184.4 

9445017 PORT LUDLOW 47.9250 -122.6800 122.0 97.6 -97.5 -179.8 

9445059 PORT GAMBLE 47.8583 -122.5800 128.0 100.6 -103.6 -185.9 

9445088 LOFALL WA 47.8150 -122.6583 133.2 106.1 -106.0 -193.2 

9445133 BANGOR 47.7483 -122.7267 139.6 112.5 -110.1 -197.8 

9445246 WHITNEY POINT 47.7617 -122.8500 145.6 116.2 -115.1 -206.7 

9445269 ZELATCHED POINT 47.7117 -122.8217 146.3 115.8 -115.8 -204.2 

9445272 QUILCENE DABOB 47.8000 -122.8583 141.4 115.6 -115.8 -205.4 

9445293 PLEASANT 47.6650 -122.9117 146.3 115.8 -118.9 -207.3 

9445296 SEABECK HOOD 47.6417 -122.8283 144.6 115.6 -114.6 -205.8 

9445326 TRITON HEAD WA 47.6033 -122.9700 143.0 116.1 -115.8 -203.9 

9445388 AYOCK POINT WA 47.5083 -123.0517 141.5 112.5 -112.4 -205.1 

9445441 LYNCH COVE 47.4183 -122.9000 153.3 122.5 -122.5 -215.8 

9445478 UNION HOOD 47.3583 -123.0983 149.1 119.0 -120.5 -212.2 

9445526 HANSVILLE 47.9183 -122.5450 133.5 107.7 -100.4 -184.5 

9445639 KINGSTON APPLE 47.7967 -122.4933 137.5 111.6 -111.5 -197.5 

9445683 POINT JEFFERSON 47.7467 -122.4767 135.9 109.7 -109.8 -194.2 

9445719 POULSBO 47.7250 -122.6383 149.4 122.6 -121.0 -208.1 

9445753 PORT MADISON 47.7050 -122.5250 146.3 118.8 -115.9 -201.2 

9445832 BROWNSVILLE 47.6517 -122.6150 149.7 122.9 -121.9 -211.0 

9445882 EAGLE HARBOR 47.6200 -122.5150 140.2 115.8 -115.8 -204.2 

9445901 TRACYTON DYES 47.6100 -122.6600 155.5 128.0 -128.0 -210.3 

9445913 PORT BLAKELY 47.5967 -122.5100 146.3 118.9 -118.9 -204.2 

9445938 CLAM BAY WA 47.5733 -122.5433 144.8 118.6 -118.5 -204.5 

9445958 BREMERTON WA 47.5617 -122.6233 149.8 123.0 -121.2 -208.0 

9445993 SOUTH COLBY- 47.5233 -122.5167 149.4 121.9 -118.9 -204.2 

9446025 POINT VASHON 47.5117 -122.4633 145.4 118.9 -118.8 -206.0 

9446248 DES MOINES WA 47.4000 -122.3283 147.5 120.4 -120.7 -207.9 

9446273 BURTON 47.3867 -122.4650 154.2 126.4 -125.3 -213.1 

9446281 ALLYN 47.3833 -122.8233 184.2 155.8 -156.3 -249.2 

9446291 WAUNA CARR 47.3783 -122.6400 170.7 143.3 -143.3 -228.6 

9446366 VAUGHN CASE 47.3417 -122.7750 182.9 155.4 -155.5 -246.9 

9446369 GIG HARBOR 47.3400 -122.5883 149.4 125.0 -125.0 -210.3 

9446375 NEILL POINT WA 47.3333 -122.5067 151.2 124.4 -124.0 -211.2 

9446451 GREEN POINT 47.3017 -122.6817 175.1 147.1 -144.9 -235.4 

9446484 TACOMA 47.2667 -122.4133 151.1 124.2 -122.4 -209.4 

9446486 TACOMA 47.2717 -122.5517 161.2 133.8 -134.1 -222.5 

 
41

Table A.4. (Continued) 

Station 

ID Station Name 

Latitude 

(degrees) 

Longitude 

(degrees) 

MHHW 

(cm) 

MHW 

(cm) 

MLW 

(cm) 

MLLW 

(cm) 

9446489 WALKERS 47.2817 -122.9233 183.8 155.4 -155.5 -247.5 

9446491 ARLETTA 47.2800 -122.6517 173.9 146.4 -141.8 -231.6 

9446545 TACOMA 47.2550 -122.4317 150.8 124.0 -122.4 -209.7 

9446583 BALLOW 47.2467 -122.8617 181.8 153.1 -151.5 -243.2 

9446628 SHELTON 47.2150 -123.0833 199.6 169.1 -154.0 -233.2 

9446638 LONGBRACH 47.2100 -122.7533 176.8 149.3 -146.3 -234.7 

9446666 

ARCADIA 

TOTTEN INLET 47.1967 -122.9383 189.0 158.5 -158.5 -249.9 

9446671 DEVIL'S HEAD 47.1667 -122.7633 185.6 152.1 -152.1 -246.6 

9446705 YOMAN POINT 47.1800 -122.6750 175.7 147.5 -145.4 -235.1 

9446714 STEILACOOM 47.1733 -122.6033 174.1 146.3 -146.0 -236.8 

9446742 BARRON POINT 47.1583 -123.0083 189.9 160.3 -160.7 -252.7 

9446800 DOFFLEMEYER 47.1417 -122.9033 185.9 157.6 -157.9 -252.1 

9446807 

BUDD INLET 

GULL HARBOR 47.1000 -122.8967 187.9 159.1 -159.8 -253.5 

9446828 DUPONT 47.1183 -122.6650 175.0 146.6 -146.9 -236.8 

9446969 OLYMPIA BUD 47.0600 -122.9033 190.8 159.7 -159.7 -253.0 

9447110 LOCKHEED 47.5850 -122.3617 144.2 117.9 -116.1 -202.7 

9447130 SEATTLE 47.6050 -122.3383 143.9 117.5 -115.9 -202.3 

9447265 MEADOW 47.6883 -122.4033 140.5 114.3 -114.7 -200.3 

9447427 EDMONDS 47.8133 -122.3833 137.4 111.0 -110.2 -195.9 

9447659 EVERETT WA 47.9800 -122.2233 140.4 113.8 -112.2 -197.6 

9447725 EBEY SLOUGH 48.0450 -122.2100 139.6 113.7 -114.0 -190.5 

9447773 TULALIP BAY 48.0650 -122.2883 143.2 115.8 -112.8 -195.1 

9447814 GLENDALE 47.9400 -122.3567 138.8 113.2 -111.6 -197.6 

9447827 DOUBLE BLUFF 47.9783 -122.5500 128.0 95.1 -94.8 -179.2 

9447854 BUSH POINT 48.0333 -122.6067 114.0 90.2 -88.6 -1.710 

9447855 HOLLY 48.0267 -122.5333 145.4 118.3 -118.3 -203.3 

9447856 SANDY POINT 48.0350 -122.3767 142.8 116.0 -114.4 -200.4 

9447883 GREENBANK 48.1050 -122.5700 143.2 115.8 -115.9 -201.2 

9448094 KAYAK PT 48.1367 -122.3667 141.1 114.3 -116.2 -201.5 
42

Table A.5. Errors in the VDatum tidal fields at water level stations. Station identification 

number, location, RMSE (cm) and standard deviation (cm) for all 35 stations in the combined 

Northern Puget Sound and Strait of Juan de Fuca VDatum domain. 

 

Station 

ID # 

Latitude 

(degrees) 

Longitude 

(degrees) 

RMSE 

(cm) 

Standard 

Deviation 

(cm) 

9442861 48.296700 -124.671700 0.3020 0.3010 

9443090 48.368330 -124.616670 1.1250 1.0570 

9443361 48.263300 -124.296700 0.9450 0.8850 

9443644 48.175000 -123.950000 0.2550 0.2230 

9443826 48.161700 -123.725000 0.5130 0.5120 

9444090 48.125000 -123.440000 0.3520 0.3310 

9444122 48.136670 -123.408330 1.0670 1.0100 

9444705 48.058330 -122.916660 0.6390 0.6300 

9447929 48.223330 -122.690000 0.0120 0.0110 

9447951 48.283330 -122.728330 0.2850 0.2080 

9447952 48.286700 -122.616700 0.4750 0.4640 

9447985 48.316670 -122.836670 0.6260 0.6150 

9447993 48.396670 -122.586670 0.6950 0.5990 

9447995 48.401670 -122.623340 0.2760 0.2670 

9448558 48.391700 -122.496700 0.6030 0.5830 

9448576 48.400000 -122.548300 1.8340 1.7350 

9448601 48.413330 -122.615000 0.8150 0.8030 

9448614 48.415000 -122.651700 0.3930 0.3570 

9448657 48.445000 -122.555000 0.1000 0.0960 

9448772 48.506670 -122.676670 0.5820 0.0860 

9448967 48.615000 -122.691670 0.5750 0.1190 

9449161 48.716700 -122.708300 0.8550 0.2700 

9449211 48.745000 -122.495000 0.4920 0.4510 

9449292 48.790000 -122.708300 0.1370 0.0950 

9449424 48.863330 -122.758330 0.0880 0.0660 

9449679 48.991700 -122.76500 0.5380 0.4850 

9449704 48.786670 -122.970000 0.6950 0.3740 

9449771 48.646670 -122.870000 0.1770 0.1760 

9449802 48.688330 -123.236660 1.3560 1.0700 

9449828 48.581700 -123.170000 0.6900 0.4130 

9449880 48.546660 -123.010000 0.2760 0.0220 

9449911 48.571670 -122.885000 0.3040 0.1610 

9449932 48.535000 -122.796670 0.4090 0.0780 

9449982 48.446670 -122.898330 0.3020 0.1410 

9449994 48.425000 -122.853330 0.1260 0.1180 
43

Table A.6. Errors in the VDatum tidal fields at water level stations. Station identification 

number, location, RMSE (cm) and standard deviation (cm) for all 66 stations in the Southern 

Puget Sound VDatum domain. 

Station 

ID 

Number 

Latitude 

(degrees)

Longitude 

(degrees) 

RMSE

(cm) 

Standard 

Deviation 

(cm) 

9444900 48.1117 -122.7500 0.041 0.029 

9445016 47.9267 -122.6167 0.000 0.000 

9445017 47.9250 -122.6800 0.001 0.001 

9445059 47.8583 -122.5800 0.000 0.000 

9445088 47.8150 -122.6583 0.000 0.000 

9445133 47.7483 -122.7267 0.018 0.015 

9445246 47.7617 -122.8500 0.006 0.006 

9445269 47.7117 -122.8217 0.000 0.000 

9445272 47.8000 -122.8583 0.014 0.012 

9445293 47.6650 -122.9117 0.000 0.000 

9445296 47.6417 -122.8283 0.000 0.000 

9445326 47.6033 -122.9700 0.012 0.011 

9445388 47.5083 -123.0517 0.001 0.001 

9445441 47.4183 -122.9000 0.000 0.000 

9445478 47.3583 -123.0983 0.000 0.000 

9445526 47.9183 -122.5450 0.000 0.000 

9445639 47.7967 -122.4933 0.002 0.002 

9445683 47.7467 -122.4767 0.000 0.000 

9445719 47.7250 -122.6383 0.000 0.000 

9445753 47.7050 -122.5250 0.012 0.012 

9445832 47.6517 -122.6150 0.000 0.000 

9445882 47.6200 -122.5150 0.000 0.000 

9445901 47.6100 -122.6600 0.000 0.000 

9445913 47.5967 -122.5100 0.005 0.005 

9445938 47.5733 -122.5433 0.004 0.004 

9445958 47.5617 -122.6233 0.000 0.000 

9445993 47.5233 -122.5167 0.000 0.000 

9446025 47.5117 -122.4633 0.000 0.000 

9446248 47.4000 -122.3283 0.000 0.000 

9446273 47.3867 -122.4650 0.000 0.000 

9446281 47.3833 -122.8233 0.000 0.000 

9446291 47.3783 -122.6400 0.026 0.026 

9446366 47.3417 -122.7750 0.000 0.000 

9446369 47.3400 -122.5883 0.001 0.001 

9446375 47.3333 -122.5067 0.004 0.004 

9446451 47.3017 -122.6817 0.006 0.006 
44

Table A.6. (Continued) 

Station 

ID 

Number 

Latitude 

(degrees)

Longitude 

(degrees) 

RMSE

(cm) 

Standard 

Deviation 

(cm)

9446484 47.2667 -122.4133 1.794 1.574 

9446486 47.2717 -122.5517 0.018 0.018 

9446489 47.2817 -122.9233 0.000 0.000 

9446491 47.2800 -122.6517 0.000 0.000 

9446545 47.2550 -122.4317 1.768 1.652 

9446583 47.2467 -122.8617 0.000 0.000 

9446628 47.2150 -123.0833 0.000 0.000 

9446638 47.2100 -122.7533 0.000 0.000 

9446666 47.1967 -122.9383 0.001 0.001 

9446671 47.1667 -122.7633 0.000 0.000 

9446705 47.1800 -122.6750 0.015 0.008 

9446714 47.1733 -122.6033 0.000 0.000 

9446742 47.1583 -123.0083 0.043 0.042 

9446800 47.1417 -122.9033 0.029 0.026 

9446807 47.1000 -122.8967 0.000 0.000 

9446828 47.1183 -122.6650 0.003 0.003 

9446969 47.0600 -122.9033 0.000 0.000 

9447110 47.5850 -122.3617 0.000 0.000 

9447130 47.6050 -122.3383 0.000 0.000 

9447265 47.6883 -122.4033 0.000 0.000 

9447427 47.8133 -122.3833 0.009 0.008 

9447659 47.9800 -122.2233 0.000 0.000 

9447725 48.0450 -122.2100 0.009 0.009 

9447773 48.0650 -122.2883 0.000 0.000 

9447814 47.9400 -122.3567 0.000 0.000 

9447827 47.9783 -122.5500 0.000 0.000 

9447855 48.0267 -122.5333 0.002 0.002 

9447856 48.0350 -122.3767 0.003 0.003 

9447883 48.1050 -122.5700 0.000 0.000 

9448094 48.1367 -122.3667 0.029 0.013 
45

Table A.7. QA/QC Delta values, or differences between modeled and observed tidal datums, 

at NOS geodetic benchmarks from the Strait of Juan de Fuca and Northern Puget Sound 

(North) regional and the Southern Puget Sound (South) regional TSS grid and the four tidal 

datum grids. The PID is the benchmark identification number. The Std. Dev. is the standard 

deviation about the mean of the four Deltas at the individual benchmark. 

PID Latitude 

(deg) 

Longitude 

(deg) 

MHHW 

Delta 

(cm) 

MHW

Delta 

(cm) 

MLW 

Delta 

(cm) 

MLLW 

Delat 

(cm) 

Avg. 

(cm) 

Std. 

Dev. 

(cm) 

Reg. 

TS0171 48.36833 -124.62305 -0.10 -0.40 0.97 0.49 0.0024 0.0061 North 

AF8873 48.36805 -124.62666 0.26 0.07 1.10 0.71 0.0053 0.0046 North 

AF8872 48.36805 -124.62388 -0.03 -0.32 1.04 0.56 0.0031 0.0061 North 

TS0340 48.36694 -124.61944 -0.03 -0.48 1.32 0.71 0.0038 0.0080 North 

TS0152 48.36694 -124.60416 -0.05 -0.84 2.08 0.88 0.0052 0.0126 North 

TS0150 48.36694 -124.60416 -0.05 -0.84 2.08 0.88 0.0052 0.0126 North 

TS0154 48.36638 -124.61138 -0.04 -0.91 2.56 1.27 0.0072 0.0152 North 

AF8871 48.36583 -124.61722 -0.05 -0.70 1.95 1.03 0.0056 0.0117 North 

TS0161 48.36555 -124.62083 0.53 0.04 1.99 1.33 0.0097 0.0086 North 

TS0156 48.36555 -124.61666 -0.01 -0.82 2.50 1.33 0.0075 0.0147 North 

TR0785 48.14055 -123.40972 -0.05 3.24 -1.58 2.76 0.0109 0.0230 North 

TR0784 48.14055 -123.40888 0.06 3.25 -1.51 2.71 0.0113 0.0224 North 

TR0779 48.14055 -123.40250 -0.10 2.83 -1.81 2.06 0.0075 0.0211 North 

TR0782 48.14000 -123.40194 0.03 2.80 -1.81 1.88 0.0073 0.0205 North 

TR0783 48.14000 -123.40138 -0.01 2.81 -1.84 1.90 0.0071 0.0207 North 

TR0789 48.12722 -123.45777 0.04 -0.86 1.68 0.17 0.0026 0.0105 North 

TR0790 48.12333 -123.44472 0.11 -0.42 0.98 0.11 0.0020 0.0058 North 

TR0559 48.11583 -122.75194 0.06 -0.11 0.61 0.03 0.0015 0.0032 South 

TR2726 48.11138 -122.76166 0.32 -0.02 0.30 -0.55 0.0001 0.0041 South 

SY0126 47.81305 -122.38027 -0.10 0.01 0.11 0.01 0.0001 0.0009 South 

SY0128 47.81138 -122.38250 -0.04 0.06 0.16 0.06 0.0006 0.0008 South 

SY0959 47.74666 -122.72638 0.02 0.12 0.02 0.02 0.0005 0.0005 South 

SY0289 47.60444 -122.33500 -0.01 0.09 -0.11 -0.01 -0.0001 0.0008 South 

SY0290 47.60388 -122.33750 -0.09 0.01 -0.19 -0.09 -0.0009 0.0008 South 

SY0286 47.60305 -122.33444 -0.01 0.09 -0.11 -0.01 -0.0001 0.0008 South 

SY0283 47.60194 -122.33388 0.14 0.24 0.02 0.12 0.0013 0.0009 South 

SY0273 47.58416 -122.36250 0.12 0.02 0.12 0.02 0.0007 0.0006 South 

SY0272 47.58194 -122.36277 0.29 0.18 0.29 0.19 0.0024 0.0006 South 

SY0271 47.57833 -122.36277 0.19 0.09 0.20 0.10 0.0015 0.0006 South 

SY0270 47.57444 -122.36277 0.06 -0.04 0.07 -0.03 0.0002 0.0006 South 

SY0920 47.56305 -122.62527 0.77 0.77 0.77 0.77 0.0077 0.0000 South 

SY5718 47.56305 -122.62416 -0.72 -0.72 -0.72 -0.72 -0.0072 0.0000 South 

SY0536 47.26416 -122.41194 0.84 0.99 -1.58 -2.03 -0.0045 0.0158 South 

SY0866 47.05194 -122.90388 -0.23 -0.44 -0.25 -0.08 -0.0025 0.0015 South 

SY0865 47.05166 -122.90250 -0.06 -0.27 -0.08 0.09 -0.0008 0.0015 South 

SY0868 47.05000 -122.90138 0.27 0.06 0.25 0.42 0.0025 0.0015 South 
46

Table A.8. Comparison of modeled TSS and observed values at NOS benchmarks in the 

Northern Puget Sound and Strait of Juan de Fuca region. The PID is either the water level 

station number or the benchmark identification number. 

PID Latitude 

(deg) 

Longitude 

(deg) 

Observed 

NAVD 88 to 

MSL (m) 

TSS Modeled 

Value (m) 

Difference 

(cm) 

9443090 48.36833 -124.61667 -1.0590 -1.0607 0.17 

9443361 48.26333 -124.29667 -1.0930 -1.0933 0.03 

9443826 48.16167 -123.72500 -1.1580 -1.1581 0.01 

9444090 48.12500 -123.44000 -1.1660 -1.1668 0.08 

9444122 48.14000 -123.41333 -1.1850 -1.1852 0.02 

9444900 48.11167 -122.75833 -1.1895 -1.1899 0.04 

9447952 48.28667 -122.61667 -1.3970 -1.3960 -0.10 

9448558 48.39167 -122.49667 -1.3560 -1.3563 0.03 

9448576 48.40000 -122.54833 -1.3310 -1.3313 0.03 

9448657 48.44500 -122.55500 -1.3470 -1.3470 0.00 

9449211 48.74500 -122.49500 -1.3630 -1.3632 0.02 

9449424 48.86333 -122.75833 -1.3170 -1.3173 0.03 

9449679 48.99167 -122.76500 -1.3600 -1.3622 0.22 

TR0790 48.12333 -123.44472 -1.1629 -1.1640 0.11 

TR0789 48.12722 -123.45777 -1.1634 -1.1638 0.04 

TR0782 48.14000 -123.40194 -1.1976 -1.1980 0.04 

TR0783 48.14000 -123.40138 -1.1980 -1.1979 -0.01 

TR0784 48.14055 -123.40888 -1.2014 -1.2020 0.06 

TR0785 48.14055 -123.40972 -1.2021 -1.2016 -0.05 

TR0779 48.14055 -123.40250 -1.1991 -1.1982 -0.09 

TS0156 48.36555 -124.61666 -1.0676 -1.0675 -0.01 

TS0161 48.36555 -124.62083 -1.0625 -1.0678 0.53 

AF8871 48.36583 -124.61722 -1.0681 -1.0677 -0.04 

TS0154 48.36638 -124.61138 -1.0682 -1.0678 -0.04 

TS0152 48.36694 -124.60416 -1.0691 -1.0685 -0.06 

TS0340 48.36694 -124.61944 -1.0620 -1.0617 -0.03 

TS0340 48.36694 -124.61944 -1.0620 -1.0617 -0.03 

TS0150 48.36694 -124.60416 -1.0691 -1.0685 -0.06 

AF8872 48.36805 -124.62388 -1.0636 -1.0634 -0.02 

AF8873 48.36805 -124.62666 -1.0595 -1.0621 0.26 

TS0171 48.36833 -124.62305 -1.0636 -1.0626 -0.10 
47

Table A.9. Comparison of modeled TSS and observed values at NOS benchmarks in the 

Southern Puget Sound region. The PID is either the water level station number or the 

benchmark identification number. 

PID Latitude 

(deg) 

Longitude 

(deg) 

Observed 

NAVD 88 

to MSL (m) 

TSS 

Modeled 

Value (m) 

Difference 

(cm) 

9444900 48.11167 -122.75833 -1.1895 -1.1899 0.04 

9445133 47.74833 -122.72667 -1.2500 -1.2503 0.03 

9445246 47.76167 -122.85000 -1.2530 -1.2530 0.00 

9445478 47.35833 -123.09833 -1.2570 -1.2571 0.01 

9445958 47.56167 -122.62333 -1.3110 -1.3110 0.00 

9446281 47.38333 -122.82333 -1.2635 -1.2633 -0.02 

9446484 47.26667 -122.41333 -1.3360 -1.3362 0.02 

9446491 47.28000 -122.65167 -1.1140 -1.1163 0.23 

9446545 47.25500 -122.43167 -1.3020 -1.3023 0.03 

9446969 47.06000 -122.90333 -1.3190 -1.3191 0.01 

9447110 47.58500 -122.36167 -1.3010 -1.3002 -0.08 

9447130 47.60500 -122.33833 -1.3080 -1.3081 0.01 

9447427 47.81333 -122.38333 -1.3220 -1.3223 0.03 

9447659 47.98000 -122.22333 -1.3560 -1.3561 0.01 

9447814 47.94000 -122.35667 -1.3555 -1.3554 -0.01 

SY0868 47.05000 -122.90138 -1.3038 -1.3063 0.25 

SY0865 47.05166 -122.90250 -1.3128 -1.3120 -0.08 

SY0866 47.05194 -122.90388 -1.3158 -1.3133 -0.25 

SY0536 47.26416 -122.41194 -1.3455 -1.3410 -0.45 

SY0920 47.56305 -122.62527 -1.3030 -1.3107 0.77 

SY5718 47.56305 -122.62416 -1.3180 -1.3108 -0.72 

SY0270 47.57444 -122.36277 -1.2986 -1.2987 0.01 

SY0271 47.57833 -122.36277 -1.2956 -1.2970 0.14 

SY0272 47.58194 -122.36277 -1.2955 -1.2979 0.24 

SY0273 47.58416 -122.36250 -1.2985 -1.2992 0.07 

SY0283 47.60194 -122.33388 -1.3070 -1.3083 0.13 

SY0286 47.60305 -122.33444 -1.3100 -1.3099 -0.01 

SY0290 47.60388 -122.33750 -1.3100 -1.3091 -0.09 

SY0289 47.60444 -122.33500 -1.3100 -1.3099 -0.01 

SY0959 47.74666 -122.72638 -1.2498 -1.2502 0.05 

SY0128 47.81138 -122.38250 -1.3190 -1.3196 0.06 

SY0126 47.81305 -122.38027 -1.3220 -1.3221 0.01 

TR2726 48.11138 -122.76166 -1.1894 -1.1895 0.01 

TR0559 48.11583 -122.75194 -1.1939 -1.1954 0.15 
48
49

APPENDIX B. VDATUM MARINE GRID WITH DATUMS 

a 

b 

c 
50

Figure B.1. Combined Northern Puget Sound and Strait of Juan de Fuca, and Southern Puget 

VDatum marine grids populated by (a) MHHW, (b) MHW, (c) MLW, (d) MLLW, (e) MTL, 

and (f) DTL tidal datum fields. 

d 

e 

f