NOAA Technical Memorandum OAR PMEL-126

Background tides and sea level variations at Seaside,

Oregon

Harold O. Mofjeld1, Angie J. Venturato2, Frank I. Gonz ́alez1, and Vasily V. Titov2

1Pacific Marine Environmental Laboratory

7600 Sand Point Way NE

Seattle, WA 98115-6349

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

University of Washington

Box 354235

Seattle, WA 98195-4235

September 2004

Contribution 2736 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. 2736 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. Tidal Datums . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3. Tidal Harmonic Constants . . . . . . . . . . . . . . . . . . . . 6

4. Water Level Probability Distributions ............ 6

4.1 Observed Background Water Levels Near Seaside . . . . . . . 6

4.2 Predicted Background Water Levels at Seaside . . . . . . . . 10

5. Sea Level Trends . . . . . . . . . . . . . . . . . . . . . . . . . 12

6. Joint Probability Methods Versus Direct Calculations . . . 12

7. Summary and Conclusions . . . . . . . . . . . . . . . . . . . . 13

8. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . 14

List of Figures

1 Map showing Seaside and relevant tide stations ............ 2

2 Sample time series of observed water levels near Seaside ....... 3

3 Probability density functions from observed water levels ....... 8

4 Exceedance probabilities from observed water levels ......... 9

5 Same as Fig. 4 but with logarithm of exceedance probability .... 9

6 Probability density functions at South Beach and Seaside . . . . . . 11

7 Same as Fig. 7 but with logarithm of exceedance probability . . . . 11

List of Tables

1 Type of tide = (O1 + K1)/(M2 + S2) and sequence of tide =

M2◦−K1◦−O1◦ .............................. 5

2 M2 and K1 tidal harmonic constants in the Cascadia region ..... 5

3 Tidal datums relative to MLLW .................... 5

4 Tidal harmonic constants at Seaside, Toke Point, and South Beach . 7

5 Percentage heights and ranges from observed water levels . . . . . . 10

6 Observed sea level trends in the Cascadia region . . . . . . . . . . . 13

Background tides and sea level variations at Seaside, Oregon

Harold O. Mofjeld1, Angie J. Venturato2, Frank I. Gonz ́alez1, and Vasily V. Titov2

1. Introduction

The purpose of this technical memorandum is to provide a summary of the

tides and other sea level variations at Seaside, Oregon, the site for the FEMA

FIRM Tsunami Pilot Study. Because the tidal range is so large along the

U.S. West Coast, the tides and other sea level variations have a significant

effect on tsunami runup heights and inundation. For this reason, Houston

and Garcia (1978) used predicted tides when computing the 100- and 500-

year tsunami runup heights for the previous tsunami Flood Insurance Rate

Maps (FIRMs).

Since Seaside is not served by a long-term tide station, many tidal quantities that are relevant to tsunami mapping must be estimated by other means.

The results presented here are based on inferences from NOAA tide stations

in the region and from the Eastern North Pacific ENPAC 2003 tide model

of Spargo (2003) and Spargo et al. (in press). Tidal datums are available inside the mouth of the Necanicum River from water level observations taken

during Nov 1971–Sept 1972; as we will see, there are substantial differences

between these and the inferred coastal datums. The locations of the tide

stations are shown in Fig. 1.

NOAA has designated the 19-year period 1983–2001 as the official U.S.

National Tide Datum Epoch, and we have used observations from this NTDE

when these were available. It is fortunate that the time series of water

levels observed during this NTDE contain the largest El Ni ̃no events of the

Twentieth Century (1982–1983 and 1997–1998), as well as representative

distributions of other water level variations. This allows a useful comparison

between observed and predicted tides in the region.

This technical memorandum is organized into examples of tidal time series to give a general characterization of the tides in the region (this section),

tidal datums to provide information to develop digital elevation models and

compare with tsunami amplitudes (Section 2), tidal harmonic constants that

can be used for tidal prediction (Section 3), probability distributions including the average time the water level is at or above various heights (Section

4), interseismic sea level trends (Section 5), next steps to include background

water levels in the estimation of 100- and 500-yr tsunami heights at Seaside

area (Section 6), and conclusions on estimates of tides and other background

water levels at Seaside (Section 7).

The examples of observed water levels in Fig. 2 show that within the

central Cascadia region containing Seaside, the tides have very similar temporal patterns with some variation in amplitude between the tide stations.

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

WA 98115-6349 2Joint Institute for the Study of the Atmosphere and Ocean (JISAO), University of

Washington, Box 354235, Seattle, WA 98195-4235
2 Mofjeld et al.

Figure 1: Map of the Central Cascadia region showing the locations of Seaside and relevant tide stations.
Background tides and sea level variations 3

Figure 2: Sample time series of observed water levels at the three nearest long-term

tide stations to Seaside.

These tides are mixed semidiurnal (Table 1). Substantial differences (Fig. 2)

occur between successive low waters; lesser differences occur between successive high waters; and low and high waters follow the sequence LLW, LHW,

HLW, HHW. Both the amplitude and shape of the daily tidal curve are

modulated (Fig. 2) over fortnightly (two-week) and monthly time scales.

The northward increase (Table 2) of the harmonic constant amplitudes and

phase lags is consistent with northward propagating tidal waves that turn

northwestward in the Cascadia region. Descriptions of the tidal modeling

and dynamics in this region, as well as references to previous work, are given

by Mofjeld et al. (1995), Foreman et al. (2000), Myers and Baptista (2001),

Spargo (2003), and Spargo et al. (in press).

Observations and tidal theory show that the amplitudes and shapes of

the daily tidal curve vary throughout the month due to variations in the

lunar phase (new moon, first quarter...), declination (meridional angle off the

equator), and parallax (distance from the earth). Significant modulations of

the tides also occur on seasonal (solstitial-equinoctal and solar parallax) and

interannual (18.6-year lunar nodal) time scales. For the latter reason, tidal

datums (like those in the next section) are ideally computed from 19 years

of observations (e.g., NTDE 1983–2001).
4 Mofjeld et al.

2. Tidal Datums

For the Tsunami Pilot Study, tidal datums are relevant in two ways. The

first is in developing the digital elevation model (DEM) for the tsunami

inundation model. The second is in providing a succinct summary of height

scales for background water levels to compare with tsunami wave heights.

Tidal datums are for the NTDE 1983–2001, computed from observations

during this period or adjusted vertically to be consistent with it (details

documented at NOAA’s www.co-ops.nos.noaa.gov website).

Table 3 gives the official tidal datums for stations in the region surrounding Seaside as reported by NOAA/NOS/CO-OPS (National Ocean

Service/Center for Operational Oceanographic Products and Services) and

NOAA/NGS (National Geodetic Survey). For Seaside itself, three sets of datums are shown. The first set of coastal datums at Seaside were obtained by

the harmonic constant datum method (Mofjeld et al., 2004) using harmonic

constants from the ENPAC 2003 tide model. The other set of coastal datums

at Seaside were linearly interpolated in latitude from the observed datums

at Hammond and Garibaldi (Fig. 1), the closest stations to Seaside. The

third set of Seaside datums are based on 11 months (Nov 1971–Sept 1972)

of water level observations at the 12th Avenue Bridge over the Necanicum

River.

The coastal datums obtained by the two different methods are in relatively good agreement. For instance, the values of MHW relative to MLLW

(important when merging water depth and land elevation data) agree within

0.2 m. However, there is a significant difference (Table 3) between the coastal

datums and those inside the shallow river mouth. Of particular interest is the

0.76–0.96 m difference for MHW which is relevant to merging water depth

and land elevation data to form the digital elevation model for tsunami modeling. It is worth noting that reduced tidal ranges often occur in bays with

restrictive inlets (e.g., Kjerfve and Knoppers, 1991).

The larger difference (Table 3) between MLLW and the geodetic datum

NAVD 88 observed inside the river mouth is also consistent with restricted

tidal exchange through the inlet, especially near low tide when more water is retained in the estuary than would occur with free exchange. This

hypothesis is corroborated by a personal communication from Maria Little (NOAA/NOS/CO-OPS) in which she reports that a water level station

at the Seaside Sewage Plant (46◦ 0.4

N, 123◦ 55.1W), just inside the river

mouth, showed “...damping of the high waters and flat low waters, caused

by a distortion of the tide signal. There are no Accepted Values [of tidal datums] for this station.” The tidal exchange may additionally be affected by

the changing nature of the river mouth as observed over the past 30 years.

The variations in the river mouth will be discussed in a technical memorandum by Angie Venturato (in preparation). A high-resolution non-linear

tide model would be needed to fully understand the relationship between

the tides on the open coast at Seaside and those inside the Necanicum River

mouth.
Background tides and sea level variations 5

Table 1: Type of tide = (O1 + K1)/(M2 + S2) and sequence of tide = M2◦−K1◦−O1◦ at the nearest long-term

tide stations to Seaside and inferred values for the open

coast at Seaside. The Type of Tide is mixed semidiurnal

when the amplitude ratio is between 0.25 and 1.5.

Station Type Sequence

(deg)

Toke Point 0.563 127.2

Astoria 0.549 126.4

Coastal Seaside 0.611 130.7

South Beach 0.621 132.4

Table 2: M2 and K1 tidal harmonic constants observed at coastal and estuarine tide stations

in the Cascadia region. These are the largest semidiurnal and diurnal constituents, respectively.

M2 K1

Station Latitude Longitude Amp Lag Amp Lag

(deg) (deg) H (m) G (deg) H (m) G (deg)

Neah Bay 48.3683 124.6167 0.787 246.3 0.497 248.3

Toke Point 46.7083 123.9650 0.981 253.7 0.435 251.1

South Bend 46.6633 123.7983 1.124 259.7 0.428 254.8

Astoria 46.2083 123.7667 0.945 264.2 0.403 256.2

Coastal Seaside 46.0017 123.9300 0.960 229.1 0.463 238.2

Depoe Bay 44.8100 124.0583 0.890 225.0 0.438 235.0

South Beach 44.6250 124.0433 0.902 231.1 0.443 237.7

Charleston 43.3450 124.3217 0.818 225.3 0.401 235.2

Port Orford 42.7400 124.4967 0.750 216.5 0.428 231.2

Crescent City 41.7450 124.1833 0.714 212.2 0.390 228.2

North Spit 40.7667 124.2167 0.710 220.0 0.411 236.1

Table 3: Tidal datums relative to MLLW at tide stations in the region surrounding Seaside. The

coastal Seaside datums were linearly interpolated in latitude using the datums at Hammond and

Garibaldi. Also shown are the maximum and minimum observed heights at the tide station (where

available) and the geodetic datums NGVD 29 and NAVD 88.

Coastal Coastal Estuarine South

Station Hammond Seaside Seaside Seaside Garibaldi Beach

Source: Observed Model Interpolated Observed* Observed Observed

Latitude 46.2017 46.0017 46.0017 46.0017 45.5550 44.6250

Longitude 123.9450 123.9300 123.9300 123.9200 123.9117 123.0433

To Entrance 7 km 0 km 0 km 2 km 2 km 4 km

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

Max Obs 3.45 3.60 3.73

MHHW 2.54 2.74 2.52 1.77 2.48 2.54

MHW 2.33 2.51 2.31 1.55 2.26 2.33

MTL 1.36 1.47 1.35 0.84 1.35 1.38

MSL 1.34 1.46 1.34 0.83 1.33 1.36

MLW 0.39 0.44 0.39 0.12 0.40 0.42

NGVD29 0.23 1.16 1.26

NAVD 88 −0.01 −0.03 to 0.02 −0.88 0.10 0.23

MLLW 0.00 0.00 0.00 0.00 0.00 0.00

Min Obs −0.90 −0.88 −1.07

*Maria Little, NOAA/NOS/CO-OPS, personal communication
6 Mofjeld et al.

3. Tidal Harmonic Constants

Tidal predictions rely on harmonic constants (HCs) that are specific to the

location of interest. For the open coast at Seaside (46◦ 00.1

N, 123◦ 55.8W),

the HCs for the O1, K1, N2, M2, and S2 constituents were computed from the

ENPAC 2003 tide model. The minor diurnal and semidiurnal HCs (Table 4)

were inferred from South Beach amplitude ratios and phase differences using

the method outlined by Schureman (1976). The long period HCs are based

on those at South Beach. The higher frequency tides (2SM2, ...) are set to

zero amplitude because of lack of information. However, they are likely to

be small because the continental shelf west of Seaside is narrow and deepens

relatively rapidly; this limits greatly the shallow water effects that generate

such constituents. Also shown for comparison are observed HCs at Toke

Point and South Beach (Fig. 1). The 37 constituents in Table 4 are the

same as those used by NOAA for its official tidal predictions.

4. Water Level Probability Distributions

Probability distributions serve to characterize the general behavior of background water levels in terms of the duration of time spent at various ranges

of height. To apply this method, the probability distribution functions (pdfs)

are computed from observed tide gage records when these are available, or

from predicted tides.

4.1 Observed Background Water Levels Near Seaside

Shown in Fig. 3 are the observed pdfs at Toke Point, Astoria, and South

Beach (Fig. 1). The pdfs were computed by first interpolating the verified

hourly observations to 15-minute values using cubic interpolation. The 15-

minute time interval was chosen to allow accurate estimates for the heights

of the individual high and low tides that may not be resolved with 1-hr sampling. The height values in the time series were binned using a 0.1 m height

interval for each bin to form a histogram for each station. The histograms

were then renormalized so that the total (sum) over the full range of heights

is unity (1.0), as required by probability theory.

Figure 3 shows that the pdfs at the three stations tend to be large around

the frequently occurring high and low water stands, when the height is changing slowly, but much smaller at the extreme ranges that occur only rarely

in time. The pdfs at these stations are very similar. The slight upward displacement of the upper Toke Point and Astoria curves relative to the South

Beach pdf is due to the slightly larger tidal ranges at these two stations.

The shapes of the pdf curves are somewhat different near the central peaks

(pdf > 0.3); but overall, the pdfs have very similar shapes and widths (Table 5) and similar maximum values. This is expected since the distances

between the stations are small compared with the alongshore variations in

tides in the Cascadia region (Mofjeld et al., 1995; Foreman et al., 2000; Myers

and Baptista, 2001; Spargo, 2003; Spargo et al., in press). The same should

therefore be true on the open coast of Seaside since it is located between
Background tides and sea level variations 7

Table 4: Tidal harmonic constants (37 constituents) and the mean relative to MLLW for the open

coast at Seaside and at the Toke Point and South Beach tide stations.

Station: Toke Point Coastal Seaside South Beach

Location: 46.7083, 123.9650 46.0017, 123.9300 44.6250, 124.0433

Constituent Amplitude Phase Lag Amplitude Phase Lag Amplitude Phase Lag

H (m) G (deg) H (m) G (deg) H (m) G (deg)

mean 1.458 1.441 1.358

SA 0.158 289.8 0.123 281.6 0.123 281.6

SSA 0.000 0.0 0.019 258.7 0.019 258.7

MM 0.000 0.0 0.027 174.7 0.027 174.7

MSF 0.000 0.0 0.000 0.0 0.000 0.0

MF 0.024 161.8 0.019 155.0 0.019 155.0

2Q1 0.006 221.0 0.007 202.2 0.007 204.3

Q1 0.047 230.2 0.050 216.7 0.048 213.4

RHO 0.011 208.7 0.011 212.4 0.010 213.8

O1 0.264 235.4 0.288 220.2 0.269 221.0

M1 0.016 270.3 0.016 252.2 0.015 250.7

P1 0.136 249.2 0.144 235.5 0.137 234.2

S1 0.006 40.7 0.012 20.4 0.012 20.4

K1 0.435 251.1 0.463 238.2 0.443 237.7

J1 0.023 267.6 0.029 256.8 0.027 255.0

OO1 0.016 292.6 0.016 276.4 0.015 273.1

2N2 0.022 204.6 0.022 178.2 0.021 183.2

MU2 0.008 253.2 0.016 197.2 0.015 201.1

N2 0.198 229.7 0.196 203.7 0.187 207.2

NU2 0.044 228.6 0.038 206.1 0.036 209.5

M2 0.981 253.7 0.960 229.1 0.902 231.1

LAM2 0.009 269.3 0.006 241.2 0.006 243.8

L2 0.033 266.3 0.026 243.6 0.024 246.4

T2 0.017 270.5 0.015 250.6 0.014 253.8

S2 0.261 284.4 0.269 255.2 0.244 258.6

R2 0.002 285.6 0.002 255.2 0.002 258.6

K2 0.071 279.6 0.070 247.4 0.066 250.2

2SM2 0.000 0.0 0.000 0.0 0.003 63.5

2MK3 0.005 64.3 0.000 0.0 0.000 0.0

M3 0.000 0.0 0.000 0.0 0.000 0.0

MK3 0.004 10.9 0.000 0.0 0.004 172.3

MN4 0.006 335.6 0.000 0.0 0.005 164.8

M4 0.014 352.6 0.000 0.0 0.013 189.0

MS4 0.009 30.5 0.000 0.0 0.007 229.5

S4 0.000 0.0 0.000 0.0 0.000 0.0

M6 0.009 45.3 0.000 0.0 0.008 300.7

S6 0.000 0.0 0.000 0.0 0.000 0.0

M8 0.000 0.0 0.000 0.0 0.000 0.0
8 Mofjeld et al.

Figure 3: Probability density functions computed from observed water levels at

the nearest long-term tide stations to Seaside.

these tide gage stations. Other differences in the pdfs are presumably due

in part to local tidal dynamics within the three bays where the tide gages

are located and to different inlet effects on the tides in these bays.

Integrating the pdfs (Fig. 3) downward in height gives the cumulative

exceedance probability P(η), where η is the height above MLLW. P(η) represents the fraction of the time, on average, that the water level is above the

height η. As shown in Fig. 4, the exceedance probabilities decrease approximately linearly with increasing height η from MLLW (η = 0) to P = 0.1

(10% probability of exceedance). The differences in P between the three

tide stations increases upward in height to a 0.19 m difference between Toke

Point and South Beach at P = 0.1.

The values of P at larger heights are relevant to the exceedance probabilities of observed storm surges. When plotted on a log(P) scale, the exceedance curves (Fig. 5) take an asymptotic form that can be fit to extreme

value distributions. Like the tsunami probability distributions, additional

calculations using time series of storm surges, especially their duration in

time, need to be performed before distributions like those in Fig. 5 can be

used to determine event heights for various recurrence intervals (Pugh, 1987,

2004).

The percentage heights and ranges shown in Table 5, as well as the

magnitudes of the tidal datums given in Table 3, indicate that tides are large

enough to have important effects on the height probabilities of tsunamis at

Seaside. The percentage height ranges (Table 5) for the three stations are
Background tides and sea level variations 9

Figure 4: Exceedance probabilities computed from observed hourly water levels

at the nearest long-term tide stations to Seaside.

Figure 5: Same as Fig. 4 but with the logarithm of exceedance probability plotted

against height.
10 Mofjeld et al.

Table 5: Percentage heights and ranges, based on the probability distribution functions derived from observed water levels during the National

Tidal Datum Epoch 1983–2001. For a given percentage probability, a

random background water level will occur within the height range between the upper and lower bounds.

Station Height Ranges

Bounds (%): 50% Height 50% 80% 90% 98%

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

Toke Point 1.47

Upper 2.00 2.30 2.50 2.82

Lower 0.70 0.21 −0.05 −0.46

Range 1.30 2.09 2.55 3.28

Astoria 1.35

Upper 2.00 2.40 2.60 2.94

Lower 0.70 0.21 −0.02 −0.33

Range 1.30 2.19 2.62 3.27

South Beach 1.36

Upper 2.07 2.49 2.71 3.10

Lower 0.80 0.27 −0.01 −0.45

Range 1.27 2.22 2.72 3.55

very similar, differing by less than 0.2 m for probabilities of 90% or less.

Hence, these statistics are spatially uniform within a few tenths of a meter

at Toke Point, Astoria, and South Beach. By implication, the same is true

along the open coast at Seaside.

4.2 Predicted Background Water Levels at Seaside

Houston and Garcia (1978) used predicted tides to compute the effects of

background water level fluctuations on the 100- and 500-year tsunami exceedance heights along the West Coast. Since observed water levels are

available at only a limited number of sites along the West Coast and these

are typically within embayments, there is an issue as to whether predicted

tides can be used for the next generation of tsunami flood maps.

As a measure of the differences between the observed and predicted water

levels that might occur at Seaside, a comparison between these was made for

the water levels at South Beach. These are then compared with the predicted

tides at Seaside. The pdf and exceedance probabilities were computed from

19-year (NTDE 1983–2001) time series of hourly tidal predictions (cubic

interpolated to 15-minute values to be consistent with the procedures used on

the observed time series). The South Beach and Seaside harmonic constants

used to generate the predictions are shown in Table 4. The height exceedance

probabilities in Figs. 6 and 7 provide a measure of how much error would

occur on average by using predicted rather than observed water levels for

Seaside, since both South Beach and Seaside are located within the same

meteorological and oceanographic regimes. The differences in the Seaside

curves relative to those for South Beach are primarily due to the larger tidal

range at Seaside, as seen in Figs. 3 and 5 for Astoria and Toke Point.

From the standpoint of probabilities (Figs. 6 and 7), there is very close
Background tides and sea level variations 11

Figure 6: Probability density functions (pdfs) computed from predicted water

levels at South Beach and Seaside. Also shown is the pdf computed from the

observed water levels at South Beach.

Figure 7: Same as Fig. 6 but with the logarithm of exceedance probability plotted

against height.
12 Mofjeld et al.

agreement between the observations and predictions for South Beach. The

minor differences that do exist (Figs. 6 and 7) are due primarily to the storm

surges and other non-tidal water level fluctuations that are not included in

the tidal predictions. These give rise to the greater heights at low exceedance

probabilities (Fig. 7). However, there is a very low probability that the

maximum wave in a tsunami will arrive at Seaside at the same time as a

winter storm, occurring during a major El Ni ̃no, than at lower heights where

there is a very close match between the observed and predicted tides.

5. Sea Level Trends

When presenting the broad spectrum of coastal water levels, it is appropriate to also include a discussion of sea level trends. This is true even though

they are not immediately relevant to the specific issues of computing 1-

percentage-annual-chance and 0.2-percentage-annual-chance quantities that

are FEMA’s definitions for the 100- and 500-yr exceedance values, respectively.

The sea level trends (Table 6) in the Cascadia region vary considerably

between long-term tide stations. This indicates different vertical ground

movement in the vicinity of the tide gages that are significant in magnitude

compared with the present ∼1.4 mm/yr of global sea level rise (Intergovernmental Panel on Climate Change (IPCC), 2001; Pugh, 2004). The upward

ground movement at Neah Bay and Crescent City (Fig. 1) is large enough

to overwhelm oceanic sea level rise and produce negative trends that are

significant at the 95% confidence level. In contrast, the observed trend at

South Beach indicates continuing subsidence of the land near the tide gage.

The variation in trends (Table 6) along the length of Cascadia shows

that the interseismic tectonic processes presently affecting relative sea level

also vary with location along the coast. Given this variability, it is difficult to estimate the sea level trend at Seaside based solely on the observed

trends elsewhere in the region. The observed trends at other sites serve as

placing some bounds of the Seaside trend and, taken together with other information from GPS observations and geological interpretation, may help to

further constrain estimates of the interseismic Seaside trend. There is also

the important issue of coseismic ground movement (subsidence or uplift)

during regional Cascadia Subduction Zone earthquakes.

6. Joint Probability Methods Versus Direct

Calculations

One method for including tides and other water level fluctuations in the

probability estimates of coastal flooding is via the joint probability method

(JPM) described by, e.g., Tawn and Vassie (1991) and Pugh (1987, 2004).

This method convolves (integrates their product over height) the pdf of the

background water levels at a given coastal location with the pdf of modeled

storm surges to get the total exceedance probability. The revised method

(Tawn and Vassie, 1991) adjusts the probabilities to take into account the
Background tides and sea level variations 13

Table 6: Observed sea level trends at tide stations in the Cascadia region.

Shown are trends in relative sea level, which are the sum of the separate vertical

movements of the water and the land. Note that the uncertainty in the trend

decreases with increasing series length.

Station Trend Stnd. Dev. 95% C I Start End Length

(mm/yr) (mm/yr) (mm/yr) (years)

Neah Bay −1.41 0.22 0.43 1934 1999 66

Toke Point 2.82 1.05 2.06 1973 1999 27

Astoria −0.16 0.24 0.47 1925 1999 75

South Beach 3.51 0.73 1.43 1967 1999 33

Charleston 1.74 0.87 1.71 1970 1999 30

Crescent City −0.48 0.23 0.45 1933 1999 67

non-random nature of the tides and the persistence in time (redundancy) of

both the tides and the additional flooding event (e.g., storm surge), as well

as possible non-linear interactions between tsunamis and the tides. A major

issue in applying the revised JPM method to the tsunami problem would

be finding the redundancy factors for the model tsunamis and background

water levels.

An alternative to this method is that of Houston and Garcia (1978),

in which each model tsunami is slid along the time series of background

water levels. Since the time series of the model tsunamis are relatively

short compared to the duration of significant waves in observed tsunamis,

the model time series need to be extended in time. This can be done by

assuming exponential amplitude decay, which Mofjeld et al. (2000) have

shown matches closely the observed decay of Pacific tsunamis.

7. Summary and Conclusions

For tides on the open coast at Seaside, Oregon, a comparison has been

made of predictions based on the ENPAC 2003 tide model of Spargo (2003)

and Spargo et al. (in press) with the observed and predicted water levels

at long-term tide stations in the region. This comparison shows there is

close agreement for many of the tidal quantities that are relevant to probabilistic tsunami mapping. This is fortunate, since Seaside is not served by

a long-term tide station. The tidal datums inferred from the model harmonic constants and those interpolated from observed values at Hammond

and Garibaldi (Fig. 1) are found to be within 0.05 m for MHW relative

to MLLW. Having an accurate estimate of this height difference is essential for generating the digital elevation model (DEM) for tsunami modeling.

There are substantial differences between the coastal datums at Seaside and

those observed within the Necanicum River, possibly due to restricted tidal

exchange through the river mouth.

Close agreement exists between probability distributions at the long-term

South Beach station and those at the Seaside open coast. This is due in part

to the proximity of the South Beach station to the coast and the free tidal

exchange through the inlet to Yaquina Bay. Conversely, the comparison
14 Mofjeld et al.

of tidal quantities at Toke Point, Astoria, and South Beach (Fig. 1) reveals

greater differences, probably at least partly due to local tidal dynamics in the

bays where these tide stations are located. However, the exceedance curves

from all the tide stations are very close to each other and, by implication, to

that on the outer coast at Seaside. These results also suggest that predicted

tides should be adequate when linearly combining coastal tsunami heights

with background water levels to estimate probabilities.

The goal of the Tsunami Pilot Study is to develop methods that can be

applied to probabilistic tsunami hazard assessment and mapping along the

U.S. West Coast. The analyses and comparison outlined in this technical

memorandum, together with the distribution of long-term tide stations along

the Coast, suggest that the methods used here will work effectively to characterize background water levels at other locations where direct long-term

water level observations are not available.

8. Acknowledgments

The authors wish to thank Maria Little (NOAA/NOS/Center for Operational Oceanographic Products and Services), Emily Spargo, Ed Myers

(NOAA/NOS/Coastal Survey Development Laboratory), and Mike Foreman

(Fisheries and Oceans Canada/Institute of Ocean Sciences) for providing datums, harmonic constants, and other useful tidal information.

References

Foreman, M.G.G., W.R. Crawford, J.Y. Cherniawsky, R.F. Henry, and M.R. Tarbotton (2000): A high-resolution assimilating tidal model for the northeast

Pacific Ocean. J. Geophys. Res., 105 (C12), 28,629–28,651.

Houston, J.R., and A.W. Garcia (1978): Type 16 Flood Insurance Study: Tsunami

predictions for the West Coast of the Continental United States. USACE USACE Waterways Experimental Station Tech. Rprt H-78-26.

Intergovernmental Panel on Climate Change (IPCC) (2001): Climate Change 2001:

Impacts, Adaptation and Vulnerability. Cambridge Univ. Press, 1032 pp.

Kjerfve, B., and B.A. Knoppers (1991): Tidal choking in a coastal lagoon. In Tidal

Hydrodynamics, B.B. Parker (ed.), Wiley, 169–181.

Mofjeld, H.O., F.I. Gonz ́alez, E.N. Bernard, and J.C. Newman (2000): Forecasting

the heights of later waves in Pacific-wide tsunamis. Nat. Hazards, 22 , 71–89.

Mofjeld, H.O., F.I. Gonz ́alez, M.C. Eble, and J.C. Newman (1995): Ocean tides

in the continental margin off the Pacific Northwest Shelf. J. Geophys. Res.,

100 (C6), 10,789–10,800.

Mofjeld, H.O., A.J. Venturato, F.I. Gonz ́alez, V.V. Titov, and J.C. Newman (2004):

The harmonic constant datum method: Options for overcoming datum discontinuities at mixed-diurnal tidal transitions. J. Atmos. Oceanic Tech., 21 , 95–104.

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

Pacific Ocean. Adv. Water. Resour., 24 (5), 505–519.

Pugh, D.T. (1987): Tides, Surges and Mean Sea-Level. Wiley, 472 pp.

Pugh, D.T. (2004): Changing Sea Levels: Effects of Tides, Weather and Climate.

Cambridge Univ. Press, 265 pp.

Schureman, P. (1976): Manual of Harmonic Analysis and Prediction of Tides. C&GS

Spec. Publ. No. 98, U.S. Government Printing Office, 317 pp.
Background tides and sea level variations 15

Spargo, E., J. Westerink, R. Luettich, and D. Mark (2004): Developing a tidal

constituent database for the Eastern North Pacific Ocean. In Proceedings of the

8th International Conference on Estuarine and Coastal Modeling, Monterey,

CA, 3–5 November 2003, in press.

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

to Model Tides in the Eastern North Pacific Ocean. M.S. Thesis, University of

Notre Dame, 224 pp.

Tawn, J.A., and J.M. Vassie (1991): Recent improvements in the joint probability

method for estimating extreme sea levels. In Tidal Hydrodynamics, B.B. Parker

(ed.), Wiley, 813–828.

Venturato, A.J. (in preparation): A digital elevation model for Seaside, Oregon:

Procedures, data sources, and analyses. NOAA Tech. Memo.