NOAA Technical Memorandum OAR PMEL-122

Tidal Datum Distributions in Puget Sound,

Washington, Based on a Tidal Model

H.O. Mofjeld1, A.J. Venturato2, V.V. Titov2, F.I. Gonz ́alez1, J.C. Newman2

1Pacific Marine Environmental Laboratory

7600 Sand Point Way NE

Seattle, WA 98115

2Joint Institute for the Study of the Atmosphere and Ocean (JISAO)

University of Washington

Box 351640

Seattle, WA 98195

November 2002

Contribution 2533 from NOAA/Pacific Marine Environmental Laboratory
NOTICE

Mention of a commercial company or product does not constitute an endorsement by

NOAA/OAR. Use of information from this publication concerning proprietary products

or the tests of such products for publicity or advertising purposes is not authorized.

Contribution No. 2533 from NOAA/Pacific Marine Environmental Laboratory

For sale by the National Technical Information Service, 5285 Port Royal Road

Springfield, VA 22161

ii
Contents iii

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2. Harmonic Constant Datum Method . . . . . . . . . . . . . . 5

3. Puget Sound Channel Tide Model . . . . . . . . . . . . . . . 6

3.1 Description of the channel tide model ............. 6

3.2 Adjustments for computing the tidal datums . . . . . . . . . 7

4. Computational Procedures . .................. 14

5. Results and Products . . . . . . . . . . . . . . . . . . . . . . . 15

5.1 Spatial distributions of the model datums . . . . . . . . . . . 15

5.2 Comparison of model and observed datums . . . . . . . . . . 15

5.3 Geodetic datums . . . . . . . . . . . . . . . . . . . . . . . . . 16

5.4 Available products . . . . . . . . . . . . . . . . . . . . . . . . 16

6. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

7. Summary .............................. 29

8. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . 30

9. Appendix: Tidal harmonic constants in Puget Sound . . . 30

10. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

List of Figures

1.1 Bathymetric map of Puget Sound showing major basins and channels,

cities, and NOAA tide stations. ..................... 3

1.2 Official tidal datums and sample observations of water at the 9447130

Seattle tide gage (47◦ 36.3

N 122◦ 20.3W), relative to MLLW. . . . 4

3.1a Map of Admiralty Inlet showing segments from the Puget Sound

channel tide model (Lavelle et al., 1988). . ............... 8

3.1b Map of Whidbey Basin showing segments from the Puget Sound

channel tide model (Lavelle et al., 1988). . ............... 9

3.1c Map of Hood Canal showing segments from the Puget Sound channel

tide model (Lavelle et al., 1988). . . . . . . . . . . . . . . . . . . . . 10

3.1d Map of the Main Basin showing segments from the Puget Sound

channel tide model (Lavelle et al., 1988). . . . . . . . . . . . . . . . . 11

3.1e Map of the South Sound showing segments from the Puget Sound

channel tide model (Lavelle et al., 1988). . . . . . . . . . . . . . . . . 12

5.1 Map of Puget Sound showing sections along which profiles of harmonic constants and tidal datums will be shown. . . . . . . . . . . . 17

5.2 Profiles of tidal datums, relative to MSL, down the main axis of Puget

Sound. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5.3 Profiles of MHW relative to MLLW the main axis of Puget Sound,

Whidbey Basin and Hood Canal. . . . . . . . . . . . . . . . . . . . . 19

5.4a Map of mean high water (MHW) relative to MLLW in Admiralty Inlet. 20

5.4b Map of mean high water (MHW) relative to MLLW in Whidbey Basin. 21

5.4c Map of mean high water (MHW) relative to MLLW in Hood Canal. 22

5.4d Map of mean high water (MHW) relative to MLLW in the Main Basin. 23

5.4e Map of mean high water (MHW) relative to MLLW in the South

Sound. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

A.1 Profiles of O1, K1, M2 and M4 tidal amplitudes down the main axis

of Puget Sound. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
iv Contents

A.2 Profiles of O1, K1, M2 and M4 tidal phase lags down the main axis

of Puget Sound. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

List of Tables

3.1 Indices of channel segments and junctions of the Puget Sound channel

tide model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

5.1 Model datum levels at the ends of major sections of Puget Sound. . 25

5.2 Net changes and spatial gradients of model MHW. . . . . . . . . . . 26

5.3 Ratio (%) of model MSL relative to MLLW. . . . . . . . . . . . . . . 26

5.4 Differences (cm) between model and observed datums. . . . . . . . . 27

5.5 Observed heights of tidal datums and the geodetic datums NAVD29

and NAVD88. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

A.1 Observed tidal harmonic constants in Puget Sound. . . . . . . . . . . 33

A.2 Percentage changes in the observed amplitudes H relative to the corresponding values at Port Townsend. . . . . . . . . . . . . . . . . . . 33

A.3 Differences in the observed phase lags G relative to the corresponding

values at Port Townsend. . . . . . . . . . . . . . . . . . . . . . . . . 34

A.4 Ratios of observed amplitudes H. . . . . . . . . . . . . . . . . . . . . 34

A.5 Differences in the observed phase lags G relative to the corresponding

values at Port Townsend. . . . . . . . . . . . . . . . . . . . . . . . . 34
Tidal Datum Distributions in Puget Sound, Washington, Based

on a Tide Model

H.O. Mofjeld1, A.J. Venturato2, V.V. Titov2, F.I. Gonz ́alez1, J.C. Newman2

Abstract. To improve the spatial estimates of tidal datums in Puget Sound, Washington, the

harmonic constant datum method has been applied to the harmonic constants from a channel

tide model of the Sound. This was done using the FORM180 Version 1.8 program. The model

datums, harmonic constants, and associated geospatial information are available on the website

www.pmel.noaa.gov/tsunami/TIME/. Focusing on mean high water (MHW) relative to mean lower

low water, it increases in height from 2.16 m at Port Townsend to 4.10 m at Olympia and 4.17 m

at the head of Oakland Bay. Larger increases per km occur in Admiralty Inlet (1.66 cm/km) and

the Tacoma Narrows (2.92 cm/km); smaller gradients occur in the Main Basin (0.44 cm/km) and

South Sound (0.70 cm/km). The model MHW in Hood Canal closely follows MHW along the main

axis with distance away from the main entrance to the Sound, to a maximum of 3.23 m at the head

of Lynch Cove. This is also true for MHW in Whidbey Basin, except for a maximum of 3.17 m in

southern Skagit Bay before decreasing northward toward Deception Pass. The model datums relative to MLLW tend to be slightly less than values derived from tide gage observations. For MHW,

an average deviation of −3.6 cm occurs in the Main Basin, with smaller deviations in Admiralty

Inlet (−1.1 cm) and the South Sound (−1.8 cm) and larger ones in Whidbey Basin (−7.8 cm) and

Hood Canal (−8.5 cm). Further improvements to the datums should include adjusting the model

datums to tide gage observations and applying high-resolution models to high-current areas and

large tideflats.

1. Introduction

This technical memorandum focuses on improving the estimates of tidal datums in Puget Sound, Washington. It is part of a project undertaken by the

NOAA/Center for Tsunami Inundation Modeling Efforts (TIME) in support of Washington State’s ongoing tsunami mitigation program. The goal

of the project is to map potential tsunami inundation in and near communities bordering the Sound. The tsunami inundation maps are created from

the results of numerical models that simulate the behavior of real tsunamis.

Essential to the accuracy of these simulations are high-resolution digital elevation models (DEMs) that approximate the water depths and coastal land

elevations over which the tsunami waves propagate. The DEMs are formed

by merging high-resolution grids of depth and elevation. Since the available

land elevations are referenced to mean high water (MHW) and the water

depths to mean lower low water (MLLW), an accurate estimate of the difference in height between these datums is required at each grid point, in order

to develop the DEM for the region of interest. Puget Sound (Fig. 1.1) is

a region in which the tides, and hence the tidal datums, vary considerably

with location. Descriptions of the tides in Puget Sound have been published

by Mofjeld and Larsen (1984) and Lavelle et al. (1988). Figure 1.2 shows

an example of tides and tidal datums for the Seattle tide station, which is

1NOAA/Pacific Marine Environmental Laboratory, 7600 Sand Point Way NE, Seattle,

WA 98115 2Joint Institute for the Study of the Atmosphere and Ocean (JISAO), University of

Washington, Box 351640, Seattle, WA 98195
2 H.O. Mofjeld et al.

the primary reference station for Puget Sound. A general discussion of tidal

datums is given by Marmer (1951) and NOAA/NOS (2000).

To estimate the distribution of tidal datums in the Sound, we applied

the harmonic constant datum (HCD) method. As input to the method, we

used the distribution of harmonic constants from the channel tide model

of Lavelle et al. (1988). This model divides Puget Sound into 545 segments

that extend across individual channels or form junctions between them. The

tidal datums, harmonic constants, and associated geospatial information are

available on the website www.pmel.noaa.gov/tsunami/TIME/, with the understanding that they are for research purposes only. A description of the

NOAA/TIME Center’s activities (www.pmel.noaa.gov/tsunami/) and the

U.S. National Tsunami Hazard Mitigation Program (www.pmel.noaa.gov/

tsunami-hazard/) that funds this work can be found on the World Wide

Web.

This memorandum is organized into the following sections: 1. Introduction, 2. Harmonic Constant Datum Method, 3. Channel Tide Model, 4. Computational Procedures, 5. Results and Products, 6. Discussion, 7. Summary,

8. Acknowledgments, 9. Appendix, and 10. References.
Tidal Datum Distributions in Puget Sound 3

Figure 1.1: Bathymetric map of Puget Sound showing major basins and channels, cities, and NOAA tide

stations. The station locations and datums were taken from the NOAA/NGS (www.ngs.noaa.gov) and

NOAA/NOS/CO-OPS (www.co-ops.nos.noaa.gov) websites.
4 H.O. Mofjeld et al.

Seattle Tide Gage

- 1

0

1

2

3

4

1 6 11 16 21 26 31

October 2002

Water Level (m)

MHHW

MHW

MTL

MSL

MLW

NAVD 88

MLLW

Figure 1.2: Official tidal datums and sample observations of water at the 9447130

Seattle tide gage (47◦ 36.3

N 122◦ 20.3W), relative to MLLW. The datums were

computed from the 19-year tidal epoch 1960–1978, and the water levels were sampled every 6 minutes. The values were taken from the NOAA/NOS/CO-OPS

(www.co-ops.nos.noaa.gov) website.
Tidal Datum Distributions in Puget Sound 5

2. Harmonic Constant Datum Method

The harmonic constant datum (HCD) method estimates the heights of tidal

datums relative to mean sea level from tidal harmonic constants (Harris,

1894; C&GS, 1952; Mofjeld et al., in review). The method is based on the

fact that these heights are most often controlled by the M2, K1, and O1

tides, with smaller contributions from the other constituents. These three

constituents form a fixed pattern in time, called the average tidal curve.

This is because the sum of the K1 and O1 frequencies exactly equals that

of the M2 tide. Averaged over a 19-year tidal epoch, the high and low

waters associated with the average tidal curve dominate the values of the

tidal datums. The HCD method uses explicit corrections for P1, N2, S2,

μ2, M4, and M6, while the effects of the other constituents are included via

empirical coefficients. The theory underlying the method is given in detail

by Harris (1894) and C&GS (1952). One merit of this method is that it is

very efficient, since it does not require the generation of long time series in

order to compute tidal datums.

Developed well before the advent of computers, the HCD method was

rendered into the C&GS Form 180 to guide the calculations. Associated

with the form are look-up tables that use various amplitude ratios and phase

differences as input; C&GS (1952) provides listings of these tables. The form

and tables have been converted into a set of Fortran subroutines. Except for

its Table 17, each of the tables is replaced by an iterative process derived

from the original implicit formulas in C&GS (1952). The computer code has

been verified by comparison with the examples provided by C&GS (1952).
6 H.O. Mofjeld et al.

3. Puget Sound Channel Tide Model

3.1 Description of the channel tide model

The Puget Sound channel tide model (Lavelle et al., 1988) divides the Sound

into 545 segments (Fig. 3.1). The linearized equations of motion with friction are used in finite difference form. The instantaneous water level is

approximated by its average value within a given segment, and the tidal

current between adjacent segments by its cross-sectional average. Assuming

sinusoidal forms for time dependence, the model separately estimates the

spatial distributions of the tidal and current harmonic constants for each of

the major tidal constituents O1, P1, K1, N2, M2, and S2, as well as the M4

tide.

Solving the one-dimensional equations in each of the 79 channels representing Puget Sound produces two sets of conditions at the 43 junctions that

lie between three or more channels. The first set is that the instantaneous

water level is the same in a given junction as it is in the channel segments

immediately adjacent to it. The second is that the sum of the instantaneous

tidal transport into the junction must equal the time rate of change of the

water level within the junction times its surface area. A boundary condition

of no horizontal transport is used at the heads of embayments.

All these conditions are solved simultaneously to give the spatial distribution for the complex amplitudes throughout the Sound, relative to a

given constituent’s amplitude at the northern end of Admiralty Inlet and

Deception Pass (Fig. 1.1). Admiralty Inlet is the main entrance by which

the tides enter Puget Sound from the Strait of Juan de Fuca. Deception Pass

is a much smaller entrance at the northern end of Whidbey Basin which affects the local tides in the northern part of Skagit Bay. The model neglects

the tidal exchange through Swinomish Channel, a very narrow (minimum

width of 100 m) and shallow (navigation channel control depth of 3 m below

MLLW) that is also at the northern end of Whidbey Basin.

The tuning of the friction coefficients was done on the M2 tide. After

setting the friction coefficient to a uniform value, the entrance M2 harmonic

constants and the friction coefficients in the high-current channel were adjusted to match the observed M2 harmonic constants. This was done at

47 tide stations (Fig. 1.1) throughout the Sound. M2 is the largest tidal

constituent in the region and dominates the tidal currents; it therefore controls the frictional effects on the other constituents. Using this same distribution of friction coefficients, the entrance harmonic constant of the other

constituents were then adjusted to get a best fit to their observed values at

the tide stations. The modulus of the complex amplitude is the amplitude

of the harmonic constants while its phase gives the phase lag. The details

of the model equations, the fitting procedures, and the comparison with observations are given by Lavelle et al. (1988). A brief summary of the tidal

distributions is provided in the Appendix.
Tidal Datum Distributions in Puget Sound 7

3.2 Adjustments for computing the tidal datums

Because the segment indices used by Lavelle et al. (1988) are often nonsequential within individual channels, it was necessary to develop the new

index scheme shown in Fig. 3.1 and Table 3.1. The two-digital integer indices

for the junctions were not changed. Internally within the database, 10000 is

added to the indices (e.g., the internal index of junction 43 is 10043 and that

of the channel segment 5601 is 15601) so that the index of each junction and

channel segment has five significant figures. For efficiency of presentation

and clarity of figures and tables, this prefix is left off the indices shown in

figures and tables.

Since there is a close relationship between P1 and K1 (separated in frequency by two cycles per year), we use the following formulas to compute

the P1 amplitude and phase lag based on the observed tides at Seattle

P1 = 0.303 K1 (1)

P1◦ = K1◦ − 0.128(K1◦ − O1◦) (2)

The HCD method also requires estimates of the small μ2 harmonic constant. For μ2, we also estimate its amplitude and phase lag on the following

relationships at Seattle:

μ2=0.030 M2 (3)

μ2◦ = S2◦ − 6.309(S2◦ − M2◦) (4)

where 360◦ is added to S2◦ when S2◦<M2◦ .

While the channel tide model estimates the distribution of the M4 harmonic constants, there are significant deviations between the model and

observed M4 harmonic constants, particularly in the South Sound. For this

reason the computation of datums presented here used average observed M4

values for the basins, while smooth transitions were used in the channels

connecting these basins. The small M6 tide is assumed to have a negligible

effect on the datums in Puget Sound, and its amplitude was set to zero in

the input to the HCD method.
Figure 3.1a: Map of Admiralty Inlet showing segments from the Puget Sound channel tide model (Lavet al., 1988).
Figure 3.1b: Map of Whidbey Basin showing segments from the Puget Sound channel tide model (Lavet al., 1988).
Figure 3.1c: Map of Hood Canal showing segments from the Puget Sound channel tide model (Lavell

al., 1988).
Tidal Datum Distributions in Puget Sound 11

Figure 3.1d: Map of the Main Basin showing segments from the Puget Sound channel tide model (Lavelle

et al., 1988).
Figure 3.1e: Map of the South Sound showing segments from the Puget Sound channel tide model (Lavet al., 1988).
Tidal Datum Distributions in Puget Sound 13

Table 3.1: Indices of channel segments and junctions of the Puget Sound channel tide model. The indices

have been modified from those used by Lavelle et al. (1988).

Name Channel Segments Junctions

ADMIRALTY INLET

Admiralty Inlet 6501–6506,6301–6312,6001–6002,5801–5808 33,30,41,29

Port Townsend 6401,6104–6110 33,31

Kilisut Harbor 6201–6207 31

Oak Bay 6101–6103 41

WHIDBEY BASIN

Deception Pass 6801–6802 34

Skagit Bay 6803–6805,6901,7001,7101–7115 34,35,32

Crescent Harbor 6705–6707 32

Penn Cove 6701–6704

Saratoga Passage 7201–7210,7401–7411 32,24,26

Holmes Harbor 7301–7308 24

Possession Sound 7601,7701–7704,7801–7803,8001–8006, 5901–5905 26,27,28,25,29

Port Susan 7501–7515 27

Snohomish Delta 7901–7902 28

HOOD CANAL

Hood Canal 5701–5732, 5301–5334 30,42

Quilcene Bay 5401–5402 43

Dabob Bay 5501–5504,5601–5604 43,42

MAIN BASIN

Puget Sound Main Reach 5201–5211,5101–5106,4601–4602,4501–4502, 29,39,40,38,20,36

3801–3804,3901,4001

Port Madison 5005–5007 39

Agate Passage 5003–5004 23

Liberty Bay 4901–4906 23

Port Orchard 5001–5002,4801–4808,4301–4302 23,22,21

Rich Passage 4401–4405 20,22

Sinclair Inlet 4101–4104 21

Dyes Inlet 4201–4205

Port Washington Narrows 4206–4209 21

Elliott Bay 4701–4703 40

Colvos Passage 3501–3518 38,19

East Passage 3701–3719 37,18

Quartermaster Harbor 3601–3609 18

Commencement Bay 3401–3403 18

Dalco Passage 3301–3302 18,19

SOUTH SOUND

The Tacoma Narrows 3201–3216 19,15

Hale Passage 3001–3007 15,14

Carr Inlet 2801–2811,2901–2905 14,17

Off Steilacoom 3101–3103,2301,2701 15,17,16,12

Pitt Passage 2501–2503 14,13

Balch Passage 2601–2602 16,13

Drayton Passage 2201–2204 11,13

Cormorant Passage 2401–2402 16,12

Nasqually Reach 2101–2108 12,11

Dana Passage 1201–1202,901 10,4,1

Case Inlet 1501–1507,1601,1701–1702,1801,1901–1905,2001–2002 7,8,9,10,11

Pickering Passage 1401–1411 7,6

Peale Passage 1101–1107 6,4

Squaxin Passage 1001–1003,501,601,701,801 5,2,3,4

Oakland Bay 401–406

Hammersley Inlet 407–417 5

Henderson Inlet 1301–1304 10

Budd Inlet 301–309 1

Eld Inlet 201–211 1

Totten Inlet 101–112 2
14 H.O. Mofjeld et al.

4. Computational Procedures

The FORM180 Version 1.8 program was used to compute the tidal datums

from the channel model harmonic constants. Since the type of tide in Puget

Sound is mixed semidiurnal or mixed diurnal, issues do not arise concerning

the effects of datums of spatial transitions between mixed and diurnal tides

(Mofjeld et al., in review). For definiteness the logical variable ‘diurnal’ in

the program was set to .false., in principle requiring that the mixed tidal

algorithms be used exclusively.

To provide the geospatial information for the GIS database, each channel

segment and junction was considered to be a polygon object defined by its

vertices. This is consistent with the straight shorelines and cross-channel

sections defining the segments and junctions. The centroids of the segments

were also computed for plotting variations along major and side channels of

Puget Sound. All locations are in digital degrees. The tidal datums, the

input channel model harmonic constants, and the geospatial information

were then imported into ArcView for graphical display and further analyses.
Tidal Datum Distributions in Puget Sound 15

5. Results and Products

5.1 Spatial distributions of the model datums

To summarize the general variations of the tidal datums in Puget Sound, it

is convenient to plot them along its main channels (Fig. 5.1) and to tabulate

datum values at the ends of various sections. Relative to mean sea level

(MSL), the high and low waters (Fig. 5.2) diverge from each other along

the Main Axis of Puget Sound, as the tidal range increases from the main

entrance to Olympia in the South Sound. However, the differences in heights

between the high waters remain relatively constant, as do the height differences between the low waters. The spread is substantially greater within

the low waters. Mean tide level (MTL) is slightly above MSL, decreasing

from 4.5 cm at the Main Entrance to 0.1 cm at Olympia. The relationships between datums are summarized in Table 5.1–5.3. Relative to MHW,

MHHW is almost constant (0.29–0.33 m) in Puget Sound with the exception of northern Admiralty Inlet. This is also true for MLW (0.79–0.83 m)

relative to MLLW, and the percentage MSL/MHW ratio (61–63%).

Focusing in more detail on MHW relative to MLLW, it increases southward (Fig. 5.3 and Table 5.1) from 2.16 m at the main entrance to 4.10 m

at Olympia in the South Sound. The increases in MHW per unit distance

(Table 5.2) are largest in Admiralty Inlet and the Tacoma Narrows and more

gradual in the Main Basin and the South Sound. MHW along a side channel

connecting the Main Basin with the head of Dyes Inlet essentially follows

the MHW profile in the Main Basin. The largest value (4.17 m) of MHW

in the Sound occurs in Oakland Bay, at the southwestern end of the South

Sound.

In Hood Canal, there is also a progressive increase in MHW from 2.76 m

at its entrance to 3.23 m at the head of Lynch Cove. The strongest spatial

gradients of MHW in Hood Canal occur seaward of its junction with Dabob

Bay. In Whidbey Basin, MHW increases from 3.00 m at its southern entrance

to a maximum of 3.17 m in southern Skagit Bay. It then decreases to values

around 3.00 m in the eastern approaches to Deception Pass. Limitations of

the channel tide model in the immediate vicinity of Deception Pass make

the tidal datum estimates less accurate there than in the rest of the Sound.

The detailed distributions of the model MHW are shown in Fig. 5.4.

5.2 Comparison of model and observed datums

The model MHW heights (Table 5.4) tend to be slightly less than those

observed at 47 tide stations (Fig. 1.1) located throughout Puget Sound. At

Seattle, the primary reference tide station for the Sound, the deviation for

MHW is −4.0 cm and is therefore close to the average (−3.6 cm) value for

the Main Basin. The average MHW deviation varies from lesser values in

Admiralty Inlet (−1.1 cm) and the South Sound (−1.8 cm) to larger values

in Whidbey Basin (−7.8 cm) and Hood Canal (−8.5 cm). The largest singlestation deviation (−15.0 cm) occurs at a 1-month long station at the head

of Lynch Cove. A discussion of the accuracy of observed tidal datums in

relation to the length of the time series is given by Swanson (1974).
16 H.O. Mofjeld et al.

In terms of percentage deviations, the model MHW is only 0.8% smaller

than the observed value (3.20 m) at Seattle. The small size of this difference

is due to the careful tuning of the channel model and to the accuracy of the

HCD method. For many purposes, the datums presented here are sufficiently

accurate; one example is the construction of a digital elevation model for use

in tsunami inundation studies. However, it should be noted that the model

datums are unofficial products and that official datums are available from

NOAA/NGS and NOAA/NOS.

5.3 Geodetic datums

The observed NGVD29 datum (Table 5.5) varies from 10–13 cm below MTL

in Hood Canal to 17–22 cm below in the other major regions. Again, northern Admiralty Inlet is an exception (7 cm at Port Townsend). NAVD88 is

1.04–1.14 m below NGVD29 with the largest values in Whidbey Basin and

northern Admiralty Inlet. Along the main axis of Puget Sound, NAVD88 increases from 0.37 m above MLLW at Port Townsend, through the Main Basin

(0.70–0.90 m) and the South Sound (1.12–1.27 m) to 1.27 m at Olympia. It

has comparable values to the Main Basin in Whidbey Basin (0.67–0.73 m)

and Hood Canal (0.79–0.92 m). MSL is not reported at many of the tide

gages in Table 5.5. However, the model MTL-MSL values (e.g., Table 5.1)

can be used to estimate MSL relative to the NGVD29 and NAVD88.

To account for mean sea level rise and changes in the tidal regime caused

by harbor development or other factors, the tidal datums are defined for

particular 19-year tidal epochs that corresponds to individual nodal cycles

of the moon’s orbit. The tidal datums reported here are for the 1960–1978

epoch. For Puget Sound, the long-term trend in sea level is monitored by

the permanent tide gage at Seattle. At that gage, the rate of sea level rise

(Zervas, 2001) is 2.11 ± 0.1 mm/yr for 1898–1999 and 2.26 ± 0.30 mm/yr

over the recent 50-year period 1950–1999. In the near future, NOS will adopt

a new 1980–1998 epoch. When this occurs, the values of the geodetic datums

relative to MLLW will change to accommodate the rise in relative MSL.

5.4 Available products

Full distributions of the tidal datums, as well as the harmonic constants, are

available at the website www.pmel.noaa.gov/tsunami/TIME/. Also available are the geospatial data for the channels and junctions. These consist of

polygon vertices for each model segment and locations of the polygon centroids. All locations are in digital degrees. For convenience and portability,

comma-delimited ASCII formats are used with the segment index as the first

column. A metadata file accompanies each data file, describing its contents.
Tidal Datum Distributions in Puget Sound 17

Figure 5.1: Map of Puget Sound showing sections along which profiles of harmonic constants and tidal

datums will be shown.
18 H.O. Mofjeld et al.

Tidal Datums Along Main Axis of Puget Sound

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

0 50 100 150 200

Distance From Entrance (km)

Height (m)

MHHW

MHW

MLHW

MTL

MHLW

MLW

MLLW

Relative to MSL

Figure 5.2: Profiles of tidal datums, relative to MSL, down the main axis of Puget Sound as computed from

the harmonic constants of the Puget Sound channel tide model using the harmonic constant datum method.
Tidal Datum Distributions in Puget Sound 19

 MHW Along Puget Sound Channels 

0.0

1.0

2.0

3.0

4.0

5.0

0 50 100 150 200

Distance From Entrance (km)

Difference (m)

Main Axis Hood Canal

Whidbey Basin

Oakland Bay

Dyes Inlet

Relative to MLLW

Figure 5.3: Profiles of MHW relative to MLLW the main axis of Puget Sound, Whidbey Basin and Hood

Canal. Also shown are profiles of MHW from the main axis to the heads of Dyes Inlet, Main Basin, and

Oakland Bay, South Sound.
Figure 5.4a: Map of mean high water (MHW) relative to MLLW in Admiralty Inlet, Puget Soundcomputed from the harmonic constants of the Puget Sound channel tide model (Lavelle et al., 1988).
Figure 5.4b: Map of mean high water (MHW) relative to MLLW in Whidbey Basin, Puget Soundcomputed from the harmonic constants of the Puget Sound channel tide model (Lavelle et al., 1988).
Figure 5.4c: Map of mean high water (MHW) relative to MLLW in Hood Canal, Puget Sound, as compufrom the harmonic constants of the Puget Sound channel tide model (Lavelle et al., 1988).
Tidal Datum Distributions in Puget Sound 23

Figure 5.4d: Map of mean high water (MHW) relative to MLLW in the Main Basin, Puget Sound, as

computed from the harmonic constants of the Puget Sound channel tide model (Lavelle et al., 1988).
Figure 5.4e: Map of mean high water (MHW) relative to MLLW in the South Sound, Puget Soundcomputed from the harmonic constants of the Puget Sound channel tide model (Lavelle et al., 1988).
Tidal Datum Distributions in Puget Sound 25

Table 5.1: Model datum levels relative to various reference levels at the ends of major sections of Puget

Sound and in two side channels.

Datum

Index MHW MHHW MTL MSL MLW

Reference Level: MLLW MHW MSL MLLW MLLW

(m) (m) (cm) (m) (m)

MAIN AXIS OF PUGET SOUND

Main Entrance 6506 2.16 0.24 4.5 1.40 0.73

N. Main Basin 29 3.00 0.29 2.6 1.88 0.80

N. Tacoma Narrows 19 3.35 0.30 2.2 2.07 0.83

S. Tacoma Narrows 15 3.68 0.32 2.1 2.25 0.85

Head of Budd Inlet 0301 4.10 0.33 0.1 2.49 0.88

WHIDBEY BASIN

S. Entrance 29 3.00 0.29 2.6 1.88 0.80

S. Saratoga Passage 26 3.07 0.30 2.5 1.91 0.81

S. Skagit Bay 32 3.17 0.30 2.5 1.96 0.82

Similk Bay 6804 3.02 0.31 2.8 1.89 0.81

Head of Lynch Cove 5301 3.23 0.30 0.4 2.03 0.83

HOOD CANAL

Canal Entrance 30 2.76 0.28 2.6 1.75 0.79

Dabob Bay Entrance 42 3.12 0.30 1.7 1.95 0.82

Head of Lynch Cove 5301 3.23 0.30 0.4 2.03 0.83

RICH PASSAGE THROUGH DYES INLET

E. Rich Passage 20 3.20 0.30 2.3 1.99 0.82

S. Port Wash. Narrows 21 3.25 0.31 2.3 2.02 0.82

Head of Dyes Inlet 4201 3.23 0.31 3.1 2.00 0.82

SQUAXIN CHANNEL THROUGH OAKLAND BAY

E. Squaxin Inlet Entrance 04 4.05 0.33 1.4 2.45 0.88

E. Hammersley Inlet Entrance 05 4.12 0.34 1.2 2.49 0.89

Head of Oakland Bay 0401 4.17 0.35 1.0 2.52 0.89
26 H.O. Mofjeld et al.

Table 5.2: Net changes and spatial gradients of model MHW relative to MLLW along the same sections of

Puget Sound as shown in Table 5.1.

Net Net Change Gradient

Length Change Gradient Indices Indices

(km) (m) (cm/km)

MAIN AXIS OF PUGET SOUND

Admiralty Inlet 55.2 0.84 1.66 6506-29 6506-5803

Main Basin 79.3 0.34 0.41 29-19 29-18

The Narrows 11.6 0.34 2.92 19-15 19-15

South Sound 49.3 0.41 0.70 15-0301 17-0301

Total 195.3 1.94

WHIDBEY BASIN

Possession Sound 21.0 0.06 0.31 29-26 29-26

Saratoga Passage 33.2 0.09 0.27 26-32 26-32

Skagit Bay 24.3 −0.08 −0.32 32-35 32-35

Deception Pass and Similk Bay 9.0 −0.14 −1.54 35-6801 35-6801

Total 87.5 −0.06

HOOD CANAL

Northern 48.1 0.36 0.74 30-42 30-42

Southern 61.1 0.12 0.19 42-5301 42-5301

Total 109.2 0.47

GREATER RICH PASSAGE—DYES INLET

Greater Rich Passage 16.6 0.05 0.47 20-21 20-21

Port Wash. Nrws and Dyes Inlet 10.6 −0.02 −0.24 21-4201 21-4201

Total 27.2 0.03

GREATER SQUAXIN PASSAGE—OAKLAND BAY

Squaxin Passage 5.8 0.07 1.25 04-05 04-05

Hammers. Inlet and Oakland Bay 16.3 0.05 0.29 05-0401 05-0401

Total 22.1 0.12

Table 5.3: Ratio (%) of model MSL at the ends of major sections

in Puget Sound. Both model datums are relative to MLLW.

Index MSL/MHW

(%)

MAIN AXIS

Main Entrance 6506 65

N. Main Basin 29 63

N. Tacoma Narrows 19 62

S. Tacoma Narrows 15 61

Head of Budd Inlet 0301 61

WHIDBEY BASIN

S. Entrance 29 63

S. Saratoga Passage 26 62

S. Skagit Bay 32 62

Similk Bay 6804 63

HOOD CANAL

Canal Entrance 30 63

Dabob Bay Ent. 42 63

Head of Lynch Cove 5301 63
Tidal Datum Distributions in Puget Sound 27

Table 5.4: Differences (cm) between model and observed datums at tide stations (Fig. 1.1) in Puget

Sound. All datums are relative to MLLW. Also shown are the averages for the major regions of the

Sound. The model values are taken from the segment adjacent to the tide station or an average of values when the tide station lies on the boundary between segments. In computing the observed datums

the control for all stations was Seattle, except that Friday Harbor was the control for Sneeoosh Point and

Port Townsend for Clam Bay. The observed datums are taken from the NOAA/NOS/CO-OPS Website

http://www.co-ops.nos.noaa.gov/bench mark.shtml?region=wa.

Model Station Model — Observed Differences

Index ID Tide Station Name MHHW MHW MTL MLW MLLW Length

(cm) (cm) (cm) (cm) (cm)

ADMIRALTY INLET

31,6401 9444900 Port Townsend 2.6 −1.3 −2.2 −2.9 0.0 12 yrs

30 9447827 Double Bluff −2.3 2.2 −1.7 −5.9 0.0 1 mo

5806 9445526 Hansville −1.0 −4.3 −4.8 −5.0 0.0 13 mos

Average: −0.3 −1.1 −2.9 −4.6 0.0

WHIDBEY BASIN

35 9448576 Sneeoosh Point, Skagit Bay 1.0 −2.1 −1.0 0.1 0.0 90 days

6705 9447952 U.S. Navy Pier, Crescent Harbor −8.9 −11.9 −7.7 −3.5 0.0 1 mo

7411 9447856 Sandy Point, Saratoga Passage −5.6 −8.9 −6.9 −4.8 0.0 1 mo

7301 9447855 Holly Harbor Farms, Holmes Harbor −6.0 −8.9 −6.2 −3.5 0.0 1 mo

8003 9447659 Everett, Possession Sound −3.7 −7.2 −5.6 −4.4 0.0 10 mos

5902,5903 9447814 Glendale, Possession Sound −3.5 −7.8 −6.4 −4.9 0.0 1 mo

Average: −4.5 −7.8 −5.6 −3.5 0.0

HOOD CANAL

5730 9445016 Foulweather Bluff −1.1 −4.0 −5.0 −5.9 0.0 2 mos

5718 9445088 Lofall −5.5 −7.4 −7.4 −7.3 0.0 1 mo

5401 9445272 Quilcene, Dabob Bay −4.7 −6.5 −7.0 −7.6 0.0 3 mos

5601 9445246 Whitney Point, Dabob Bay −9.5 −10.1 −10.1 −9.7 0.0 1 mo

5708 9445133 Bangor Wharf −8.9 −10.6 −9.4 −8.0 0.0 10 mos

5701 9445296 Seabeck, Seabeck Bay −11.3 −12.1 −11.0 −10.0 0.0 1 mo

5330 9445326 Triton Head −2.9 −6.0 −6.0 −6.2 0.0 43 days

5324 9445388 Ayock Point −0.3 −1.3 −6.0 −10.6 0.0 1 mo

5312,5313 9445478 Union −11.4 −11.7 −10.4 −9.1 0.0 5 mos

5301,5302 9445441 Lynch Cove Dock −15.4 −15.0 −12.8 −10.6 0.0 1 mo

Average: −7.1 −8.5 −8.5 −8.5 0.0

MAIN BASIN

5206,5207 9447427 Edmonds −0.1 −3.6 −4.1 −4.7 0.0 3 mos

5205 9445639 Kingston −1.5 −5.1 −5.1 −5.2 0.0 1 mo

39 9445683 Point Jefferson 8.6 5.2 0.9 −3.3 0.0 3 mos

5106 9447265 Meadow Point −0.4 −3.9 −4.3 −4.4 0.0 3 mos

4901,4902 9445719 Poulsbo, Liberty Bay 0.1 −3.7 −4.1 −4.5 0.0 42 mos

4806,4807 9445832 Brownsville, Port Orchard −4.3 −8.4 −7.3 −6.2 0.0 1 mo

21,4104 9445958 Bremerton, Sinclair Inlet −2.7 −7.0 −5.6 −4.2 0.0 7 mos

20 9445938 Clam Bay, Rich Passage 1.1 −2.9 −3.4 −4.0 0.0 16 mos

4701 9447130 Seattle, Elliott Bay −0.2 −4.0 −4.3 −4.7 0.0 19 yrs

37 9446025 Point Vashon −1.0 −4.7 −4.9 −5.2 0.0 1 mo

3708,3709 9446248 Des Moines, East Passage 1.0 −2.4 −3.7 −4.8 0.0 1 mo

3601 9446254 Burton, Quartermaster Harbor −4.0 −7.0 −5.9 −4.9 0.0 1 mo

3401 9446484 Tacoma, Commencement Bay 0.8 −3.4 −3.8 −4.2 0.0 19 mos

3401 9446545 Tacoma, Commencement Bay 0.3 −3.6 −4.0 −4.5 0.0 9 mos

3301,3302 9446375 Tahlequah, Dalco Passage 0.6 −3.3 −3.7 −4.3 0.0 28 days

3205 9446486 Tacoma Narrows Bridge 3.8 −0.5 −2.4 −4.0 0.0 1 mo

Average: 0.1 −3.6 −4.1 −4.6 0.0
28 H.O. Mofjeld et al.

Table 5.4: (Continued)

Model Station Model — Observed Differences

Index ID Tide Station Name MHHW MHW MTL MLW MLLW Length

(cm) (cm) (cm) (cm) (cm)

SOUTH SOUND

1501 9446281 Allyn, Case Inlet 2.7 −1.7 −3.4 −5.1 0.0 9 mos

2807,2808 9446451 Green Point, Carr Inlet 2.7 −1.3 −2.9 −4.6 0.0 1 mo

14 9446491 Arletta, Hale Passage 7.3 2.7 −0.5 −3.6 0.0 1 mo

2810 9446500 Home, Carr Inlet 4.3 0.4 −1.8 −3.9 0.0 1 mo

9,1702 9446583 Ballow, Case Inlet 5.2 1.2 −1.7 −4.6 0.0 1 mo

2602 9446705 Yoman Point, Anderson Island 3.1 −1.3 −2.5 −3.5 0.0 7 mos

2701 9446714 Steilacoom, Nisqually Reach 1.5 −3.0 −3.9 −5.0 0.0 16 days

11 9446671 Devils Head, Drayton Passage −8.0 −7.2 −7.5 −7.8 0.0 26 days

1 9446800 Dofflemyer Point 1.2 −3.7 −5.2 −6.4 0.0 66 days

2107 9446828 Dupont Wharf, Nisqually Reach 3.9 −0.1 −2.1 −3.8 0.0 35 days

305 9446807 Budd Inlet, South Of Gull Harbor −0.2 −4.3 −5.2 −6.1 0.0 6 mos

301 9446969 Olympia, Budd Inlet −1.4 −3.2 −4.4 −5.6 0.0 1 yr

Average: 1.9 −1.8 −3.4 −5.0 0.0

Table 5.5: Observed heights of tidal datums and the geodetic datums NAVD29 and NAVD88, all relative

to MLLW, in Puget Sound. The heights are averages over individual benchmark values for each tide gage

that were taken from the websites of the National Geodetic Survey (www.ngs.noaa.gov) and the CO-OPS

Program (www.co-ops.nos.noaa.gov) of the National Ocean Survey.

MHHW MHW MTL NGVD MLW NAVD MLLW

Station ID Name Latitude Longitude 29 88

(m) (m) (m) (m) (m) (m) (m)

ADMIRALTY INLET

9444900 Port Townsend 48 06.9N 122 45.0W 2.58 2.36 1.57 1.50 0.78 0.37 0.00

WHIDBEY BASIN

9447952 Crescent Harbor 48 17.1N 122 37.0W 3.55 3.28 2.07 1.87 0.85 0.73 0.00

9447725 Ebey Slough 48 02.7N 122 12.7W 3.30 3.04 1.91 2.12 0.77 0.99 0.00

9447659 Everett 47 58.8N 122 13.4W 3.39 3.12 1.99 1.82 0.85 0.70 0.00

9447814 Glendale 47 56.4N 122 21.4W 3.36 3.11 1.98 1.79 0.86 0.67 0.00

HOOD CANAL

9445246 Dabob Bay 47 45.7N 122 51.0W 3.52 3.23 2.07 1.96 0.91 0.87 0.00

9445133 Bangor Wharf 47 44.9N 122 43.6W 3.39 3.12 2.00 1.87 0.89 0.79 0.00

9445389 Ayock Point 47 30.5N 124 03.2W 3.47 3.18 2.05 1.96 0.93 0.88 0.00

9445479 Union 47 21.5N 124 05.9W 3.61 3.31 2.11 1.98 0.91 0.92 0.00

MAIN BASIN

9447427 Edmonds 47 48.8N 122 23.0W 3.33 3.07 1.96 1.79 0.85 0.70 0.00

9447130 Seattle 47 36.3N 122 20.3W 3.46 3.20 2.03 1.86 0.86 0.77 0.00

9445938 Clam Bay 47 34.5N 122 32.6W 3.49 3.23 2.05 1.87 0.86 0.81 0.00

9445958 Bremerton 47 33.7N 122 37.4W 3.58 3.31 2.09 1.89 0.87 0.82 0.00

9446254 Burton 47 23.7N 122 27.8W 3.67 3.40 2.14 1.95 0.89 0.89 0.00

9446484 Tacoma 47 16.0N 122 24.8W 3.60 3.34 2.10 1.89 0.87 0.83 0.00

9446545 Tacoma 47 15.3N 122 25.9W 3.61 3.34 2.11 1.93 0.87 0.86 0.00

SOUTH SOUND

9446281 Allyn 47 23.0N 122 49.4W 4.32 4.03 2.48 2.29 0.92 1.22 0.00

9446714 Steilacoom 47 10.4N 122 36.2W 4.11 3.83 2.37 2.17 0.91 1.12 0.00

9446828 Dupont 47 07.1N 122 40.0W 4.12 3.83 2.37 2.17 0.90 1.12 0.00

9446969 Olympia 47 03.1N 122 54.2W 4.44 4.13 2.53 2.31 0.93 1.27 0.00
Tidal Datum Distributions in Puget Sound 29

6. Discussion

The model tidal datums reported here come directly from the application

of the HCD method to the harmonic constants from the channel tide model

of Lavelle et al. (1988). As such, no improvements have been made to the

model datums, e.g., by adjusting them to match the observed values. Therefore, inherent in the model datums are any limitations that exist in the HCD

method and the channel tide model. A comparison of these with the observations then provides a quantitative assessment of their effects on the datums.

The comparison shows that the model datums relative to MLLW tend to

slightly underestimate the observed datums, with the largest deviations in

Hood Canal.

The accuracy of the model datums can be improved by adjusting them

to the observations using a GIS system. The result would be a set of datum

distributions that are consistent with both observations and linear tidal dynamics. Additional modeling is also needed to resolve local tidal variations

in points of land, where high tidal currents affect the local datums, and over

tidal flats that are not included in the channel tide channel.

Since the tidal datums represent 19-year averages, they do not reflect

shorter-term variations in water levels. These include oceanic and meteorological fluctuations over synoptic to seasonal time scales. Especially high

water events occur during strong El Ni ̃nos. Mofjeld (1992) provides a description of the subtidal water level fluctuations that occur in Puget Sound

and the Strait of Juan de Fuca, and Wood (1976) describes extreme high

and low water events that occur in response to perigean spring tides. More

commonly, there are substantial fortnightly, monthly, and seasonal variations in Puget Sound tides that are described by Mofjeld and Larsen (1984).

For specific periods of time, tidal observations and predictions are available

on-line at the NOAA/NOS website www.co-ops.nos.noaa.gov.

7. Summary

The distributions of tidal datums in Puget Sound have been estimated by applying the harmonic constant datum (HCD) method to harmonic constants

from the channel tide model of Lavelle et al. (1988). These distributions

consist of gridded alongchannel datums at high spatial resolution, relative

to mean lower low water (MLLW). Of particular interest is mean high water

(MHW), because it provides the elevation differences between the reference

levels for land elevation and water depth that are needed to construct digital

elevation models.

Focusing on the model distribution of MHW, it increases along the main

axis of Puget Sound from 2.16 m at the north end of Admiralty Inlet to a

maximum of 4.17 m at the head of Oakland Bay, a side channel in the South

Sound region. It does so in stages, with larger increases per km in Admiralty

Inlet and the Tacoma Narrows and more gradual increases through the Main

Basin and the South Sound. The MHW increases with alongchannel distance

in Hood Canal and Whidbey Basin closely follow the increase along the main
30 H.O. Mofjeld et al.

axis, except for a 3.17 m maximum in Whidbey Basin and a decrease toward

Deception Pass.

The model datums relative to MLLW are slightly less than those estimated from observations at tide gages. At Seattle, the primary reference

gage for the region, the model MHW is 4.0 cm less than the observed values.

This is close to the average (3.6 cm) for the Main Basin. Elsewhere in the

Sound, the average underestimates are 1.1 cm for Admiralty Inlet, 7.8 cm

for Whidbey Basin, 8.5 cm for Hood Canal, and 1.8 cm for the South Sound.

The detailed comparison for the individual tide stations and for the other

tidal datums is provided in Section 5. The model datums can be improved

by adjusting their distributions to match the observed values and by doing

more detailed studies near points of land and tidal flat areas. This is left to

future work.

8. Acknowledgments

This work was funded in part by the National Tsunami Hazard Mitigation Program

to develop tsunami inundation maps for U.S. coastal communities. This publication

was also supported by the Joint Institute for the Study of the Atmosphere and

Ocean (JISAO) under the NOAA Cooperative Agreement #NA67RJO155. JISAO

Contribution No. 959; PMEL Contribution No. 2533.

9. Appendix: Tidal harmonic constants in Puget

Sound

Tables A.1–A.5 give representative values of observed harmonic constants

in Puget Sound, as well as various amplitude ratios and phase differences.

The channel tide model provides high-resolution profiles of the harmonic

constants (Figs. A.1–A.2) along the main axis of Puget Sound that give

a general overview of how the harmonic constants vary within the Sound.

There are substantial increases in the semidiurnal (M2, N2, and S2) amplitudes and phase lags from the northward end of Admiralty Inlet to the

southern reaches of Puget Sound. The increases are greatest in the highcurrent channels (Admiralty Inlet and the Tacoma Narrows) separating the

major basins of Puget Sound and less within the basins themselves.

The physical reasons for the distributions of the tides in Puget Sound

are discussed by Mofjeld and Larsen (1984), Lavelle et al. (1988), and in

previous publications listed in these publications. Briefly, the semidiurnal

tides form a set of partially reflecting waves in the Sound with greatest

reflection between a given basin and the channel leading to the next landward

basin. The interaction of the flow and hydraulic head through the channel

and the landward basin’s storage capacity, as measured by its surface area,

lead to the increases in the tidal amplitude. The phase lag is increased as

well, due to friction acting on the tidal flow. Whidbey Basin and Hood Canal

act to increase the effective length of Puget Sound as seen by the tides.

In contrast, the diurnal tides (O1, P1, and K1) experience much more

modest increases (Figs. A.1–A.2 and Tables A.1–A.5) in amplitude and phase
Tidal Datum Distributions in Puget Sound 31

lag through the Sound. This is because the diurnal tides have twice the

period of oscillation, as compared with the semidiurnal tides, and therefore

have twice the time for the exchange between basins to occur as the tide

rises and falls at the entrance to Puget Sound.
32 H.O. Mofjeld et al.

Tidal Amplitudes Along Main Axis of Puget Sound

0.0

0.5

1.0

1.5

0 50 100 150 200

Distance From Entrance (km)

H (m)

M2

K1

O1

P1

S2

N2 M4

Figure A.1: Profiles of O1, K1, M2 and M4 tidal amplitudes down the main axis

of Puget Sound, from the Puget Sound channel tide model (Lavelle et al., 1988).

Tidal Phase Lags Along Main Axis of Puget Sound

9 0

180

270

360

450

0 50 100 150 200

Distance From Entrance (km)

G (deg)

S2

M2

N2

K1, P1

O1

M4

Figure A.2: Profiles of O1, K1, M2 and M4 tidal phase lags down the main axis

of Puget Sound, from the Puget Sound channel tide model (Lavelle et al., 1988).
Tidal Datum Distributions in Puget Sound 33

Table A.1: Observed tidal harmonic constants at selected tide stations in Puget

Sound. Values for Port Townsend, Seattle and Tacoma are taken from the

NOAA/NOS/CO-OPS Website (www.co-ops.nos.noaa.gov). The values for

Olympia are provided by the NOAA/National Ocean Survey (data archives).

ID 9444900 9447130 9446484 9446969

Name Port Townsend Seattle Tacoma Olympia

Lat. 48◦ 06.9

N 47◦ 36.3N 47◦ 16.0N 47◦ 03.1N

Long. 122◦ 45.0

W 122◦ 20.3W 122◦ 24.8W 122◦ 54.2W

Constit. H G H G H G H G

(m) (◦) (m) (◦) (m) (◦) (m) (◦)

O1 0.450 249.9 0.458 255.4 0.459 255.1 0.463 265.1

P1 0.239 268.4 0.252 274.5 0.255 277.2 0.248 287.6

K1 0.764 270.8 0.831 277.3 0.838 277.9 0.849 288.7

N2 0.142 321.8 0.212 340.2 0.225 341.2 0.281 4.3

M2 0.684 350.5 1.070 11.4 1.139 11.8 1.464 29.9

S2 0.168 13.0 0.258 37.9 0.282 37.8 0.348 62.4

M4 0.038 59.7 0.021 194.9 0.019 207.7 0.055 291.0

M6 0.000 0.0 0.009 301.9 0.005 292.0 0.032 142.1

Table A.2: Percentage changes in the observed amplitudes H of the major tidal

constituents and M4 at selected tide stations, relative to the corresponding values

at Port Townsend near the main entrance to Puget Sound. The amplitudes are

taken from Table A.1.

Constit. Seattle Tacoma Olympia

(%) (%) (%)

O1 1.8 2.0 2.9

P1 5.4 6.7 3.8

K1 8.8 9.7 11.1

N2 49.3 58.5 97.9

M2 56.4 66.5 114.0

S2 53.6 67.9 107.1

M4 −44.7 −50.0 44.7
34 H.O. Mofjeld et al.

Table A.3: Differences in the observed phase lags G of the major tidal constituents

and M4 at selected tide stations, relative to the corresponding values at Port

Townsend near the main entrance to Puget Sound. The phase lags are taken from

Table A.1.

Constit. Seattle Tacoma Olympia

(◦) (◦) (◦)

O1 5.5 5.2 15.2

P1 6.1 8.8 19.2

K1 6.5 7.1 17.9

N2 18.4 19.4 42.5

M2 20.9 21.3 39.4

S2 24.9 24.8 49.4

M4 135.2 148.0 231.3

Table A.4: Ratios of observed amplitudes H for the major tidal constituents at

selected tide stations in Puget Sound. The amplitudes are taken from Table A.1.

Port Townsend Seattle Tacoma Olympia

O1/K1 0.589 0.551 0.548 0.545

P1/K1 0.313 0.303 0.304 0.292

N2/M2 0.208 0.198 0.198 0.192

S2/M2 0.246 0.241 0.248 0.238

Table A.5: Differences in the observed phase lags G of the major tidal constituents

at selected tide stations, relative to the corresponding values at Port Townsend near

the main entrance to Puget Sound. The phase lags are taken from Table A.1.

Port Townsend Seattle Tacoma Olympia

(◦) (◦) (◦) (◦)

K1-O1 20.9 21.9 22.8 23.6

K1-P1 2.4 2.8 0.7 1.1

M2-N2 28.7 31.2 30.6 25.6

S2-M2 22.5 26.5 26.0 32.5
Tidal Datum Distributions in Puget Sound 35

10. References

Coast and Geodetic Survey (1952): Manual of Harmonic Constant Reductions. C.

& G.S. Spec. Publ. No. 260, U.S. Gov. Printing Office, Washington, D.C.

Harris, R.A. (1894): Some connections between harmonic and nonharmonic quantities, including applications to the reduction and prediction of tides. Manual

of Tides, Part III, Appendix No. 7.

Lavelle, J.W., H.O. Mofjeld, E. Lempriere-Doggett, G.A. Cannon, D.J. Pashinski, E.D. Cokelet, L. Lytle, and S. Gill (1988): A multiply-connected channel

model of tides and tidal currents in Puget Sound, Washington and a comparison

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