Vertical Control and Tide Reducers in Tidal to Non-tidal Transitional Areas
Carolyn Lindley, Cristina Urizar, David Wolcott, Hua Yang, Lijuan Huang
Center for Operational Oceanographic Products and Services, National Ocean Service, NOAA
1305 East-West Highway, Silver Spring, MD 20910-3218 1-301-713-2890
ABSTRACT
This paper explores the methods and procedures that the Center for Operational Oceanographic
Products and Services (CO-OPS) uses to provide accurate vertical control and tide and water
level reducers in tidal to non-tidal transitional areas. CO-OPS supports the NOAA’s Nautical
Charting mission by providing tide and water level reducers to the NOS Office of Coast Survey
and the National Geodetic Survey. The challenges of tidal zoning in a tidal transition area
include: 1) determining if an area is non-tidal, 2) identifying the cut-off line between tidal and
non-tidal areas, 3) establishing a Low Water Datum (LWD) in lieu of MLLW for Chart Datum
and MWL datum in lieu of MHW for shoreline, and 4) ensuring the adequate coverage of
subordinate water level installations. The traditional tidal zoning using time and range correctors
is not applicable in non-tidal areas, and “spatial zoning” coverage of existing stations and
subordinate stations installed for the survey is used. Tidal Constituent and Residual Interpolation
(TCARI) as a tide and water level reduction tool needs to accommodate the lack of some
harmonic constituents at non-tidal water level stations. Two case studies in Laguna Madre, TX
and Pamlico Sound, NC are presented in this paper illustrating the challenges and additional
efforts to generate water level reducers within the 0.45 m error tolerance for hydrographic
surveys.
1. INTRODUCTION
NOAA is responsible for providing nautical charts for the “safe navigation of marine
commerce.” 33 U.S.C. 883(a). This responsibility holds whether in tidal or non-tidal coastal
waters. CO-OPS supports the NOAA’s nautical charting mission by providing vertical control
and tide reducers to the Office of Coast Survey and the National Geodetic Survey. Most coastal
areas are subject to measurable tidal influences and CO-OPS provides a standard tidal datum
through the tabulation of hourly heights and daily high and low tides and their reduction to
monthly mean values, and ultimately 19-year Epoch Tidal Datums. For NOAA nautical charts,
Mean Lower Low Water (MLLW) datum is provided for the depth reference and Mean High
Water (MHW) datum for the elevations of features and overhead obstructions. For shoreline
mapping, aerial photos are taken at MHW datum and MLLW datum with 10% (for tidal range
higher than 3ft) or 0.3ft error tolerance (for tidal range less than 3ft).
In some sounds, embayments, rivers, and upper estuary reaches, however, the periodic tide is
negligible, with a mean range of tide of only a few tenths of a foot or less, or is irregularly
prominent, frequently masked by various non-tidal water level forces. It is difficult to identify
and tabulate regular daily high and low tides at stations installed in these areas, and the tidal
signal is often masked. Monthly means, or the monthly average of tabulated tides, become
statistically meaningless for tidal datum determination when based only on a few random high
1
and low waters. Such areas are classified by CO-OPS as non-tidal for datum determination
purposes and alternate datum references are established to support user applications. CO-OPS
has identified some coastal geographical areas that transition from tidal to non-tidal, such as
portions of Pamilico Sound and Albemarle Sound, NC, the upper Florida Bay, FL, and Laguna
Madre, TX.
a. Non-tidal areas classification
CO-OPS uses the definition in the Code of Federal Regulations (CFR) as the definition of nontidal. The CFR defines tidal waters as “those waters that rise and fall in a predictable and
measurable rhythm or cycle due to the gravitational pulls of the moon and the sun. Tidal waters
end where the rise and fall of the water surface can no longer be practically measured in a
predictable rhythm due to the masking by hydrologic, wind or other effects.” 33 C.F.R. 328.3(f).
The United States Army Corps of Engineers (USACE) defines tidal waters as those that “rise and
fall in a predictable and measurable rhythm or cycle due to the gravitational pulls of the moon
and the sun.” It further provides that “[t]idal waters end where the rise and fall of the water
surface can no longer be practically measured in a predictable rhythm due to masking by other
waters, wind, or other effects.” USACE Regulatory Program, PART 330-Nationwide Permit
Program. The USACE’s main focus regarding tidal waters is whether a wetland is tidal or not
and is determined by whether those “wetlands contiguous to tidal waters are located landward of
the high tide line” or “channelward of the high tide line.”
In practice, the determination of waters as non-tidal requires considerable analyses of
observational data. Using CO-OPS standard operating procedures and tabulation algorithms, it is
determined if a regularly reoccurring tide can be tabulated, and if the expected astronomical tides
occur each tidal day. The generic tabulation rule is that each high/low tidal pair must be 0.10 feet
or greater apart in elevation and 2.0 hours or greater in time apart to be tabulated as a tidal pair of
highs and lows. If the tide cannot be routinely tabulated at a particular station, that station is
considered to be non-tidal. If the time series is longer than one year, the reduction of variance
statistics derived from the 365-day least-squares harmonic analysis are also examined to
determine if the tidal constituents make a meaningful contribution to the total variability of the
observations. Excluding the seasonal constituents and the monthly harmonic constituents, if the
remaining tidal constituents account for less than 30% of the total reduction of variance, that further
demonstrates the station is non-tidal. If only a shorter series is available, then a comparison of
harmonic constituents is made on sequential 29-day periods to determine the stability of the
amplitudes and phases of the harmonic constituents over time. Amplitudes of the major semidiurnal
and diurnal constituents should be within 0.20 meters from month to month and the phases should be
within 10 degrees of each other for areas with moderate to strong tides. A spectral analysis can also
be helpful for tidal and non-tidal classification. If the energy in the spectral peaks at the semidiurnal
and diurnal frequencies is not discernible from, or just above, the frequency “continuum” and the
spectra are dominated by energy at the non-tidal frequencies, then the station may be a candidate to
be classified as non-tidal (Gill et al, 1995).
b. Identifying the cut-off line between tidal and non-tidal areas
Although for practical application for vertical control and tidal zoning limits, a discrete cut-off
line is identified, the tidal to non-tidal transition typically takes place over a geographic region
2
where the tidal signal gradually weakens. CO-OPS uses a cut-off of range of tide of 0.3 feet
(0.09 meters) when developing discrete tidal zoning that relies on range and time correctors. In
areas with range of tide less than 0.3 feet, CO-OPS provides zoning that identifies which water
level station should be used for direct control but where no correctors can be computed. The
location of the cut-off line is estimated based on interpolation of the available tidal datum
information and historical water level observations.
Discrete tidal zoning is the practice of dividing a hydrographic survey area into discrete zones,
each one possessing similar tidal characteristics. One set of tide reducers is assigned to each
zone. Tide reducers are used to adjust the soundings in that zone to chart datum (MLLW). Tidal
zoning is necessary in order to correct for differing water level heights occurring throughout the
survey area at any given time. The tide reducers are derived from the water levels recorded at an
appropriate tide station, usually nearby. The range ratio, one of two tide reducers assigned to
each zone, is used to adjust the range of the tidal signal (CO-OPS, 2000).
The interpolation results derived from Tidal Constituent and Residual Interpolation (TCARI) are
helpful for the cut-off line determination. TCARI interpolates the harmonic constituents, tidal
datums and residuals from both tidal and non-tidal stations. Although tides are negligible at nontidal stations, tidal energy is still present and tidal amplitudes and phases can still be used for
interpolation purpose. TCARI interpolates Mean Sea Level (MSL), MLLW, etc., across the
domain, the areas showing the 0 MLLW elevation value are non-tidal areas.
c. Datums in non-tidal areas for hydrographic surveys and shoreline mapping
Low Water Datum (LWD) is established in lieu of MLLW for Chart Datum and a Mean Water Level
(MWL) datum in lieu of MHW for shoreline when a survey is in a coastal area classified as non-tidal.
LWD is determined by the standard practice of subtracting 0.5feet from the observed MWL in the
area. MWL is determined from the average of the observed hourly heights adjusted to a common 19year period like MSL. This 19-year period corresponds to the same 19-year period for which tidal
datums, including MLLW, is based and is referred to as the National Tidal Datum Epoch (NTDE).
For short-term stations, this requires a simultaneous comparison of sea level with a nearby control
tide station.
This paper presents two case studies, one in Laguna Madre, TX and the other in Pamlico Sound,
NC, illustrating the process of tidal and non-tidal areas classification, discrete tidal zoning and
TCARI grid development, zoning and TCARI results quality control.
2. LAGUNA MADRE CASE STUDY
The Laguna Madre estuary is approximately 120 miles long and extends from the Brazos
Santiago Pass, just a few miles north of the Texas/Mexico Border, northward to Corpus Christi
Bay. The southern and northern extents of Laguna Madre are delineated in red lines in Figure 1.
The width of Laguna Madre is as much as 8 miles in the south and narrows to at least 2 miles to
the north. An Intracoastal Waterway extends through the length of Laguna Madre with a
managed depth of approximately 12 feet. The rest of the estuary is generally less than 10 feet in
depth. Laguna Madre is connected to the Gulf of Mexico in three inlets (1) at the Brazos
Santiago Pass, (2) the Port Mansfield Channel, and indirectly by (3) channels cut through the
3
John F. Kennedy Causeway into Corpus Christi Bay. As a result, Laguna Madre’s tidal
characteristics are highly influenced by the incoming tide at these three entrances (Gill et al,
1995). The diurnal range of tide at or near the three entrances (see Figure 1) ranges from (1)
1.37 ft at Port Isabel, (2) 0.26 ft at Port Mansfield, and (3) 0.38 ft at Packery Channel. In this
region of the U.S. coastline, tides are mainly diurnal (one high tide and one low tide per day).
Figure 1. Extent of non-tidal region in Laguna Madre, TX.
a. Classification of Tidal and Non-tidal Areas
The regions of Laguna Madre that are classified as tidal or non-tidal are documented in Gill et al,
1995. The determination was based on tide tabulations, harmonic analyses and spectral analysis
techniques on 8 stations spread out throughout the length of the estuary. Masking of the tides by
non-tidal effects (mainly meteorological effects), low energy at the diurnal and semi-diurnal tidal
frequencies, as well as an inability to tabulate the tides throughout the month formed the basis
for tidal/non-tidal determinations in Laguna Madre. The authors conclude that in southern
Laguna Madre, the tidal/non-tidal transition occurred south of Port Mansfield and in northern
Laguna Madre, the tidal/non-tidal transition occurred between Yarborough Pass and Packery
Channel.
Since 1995, additional water level data at additional stations established by Texas Coastal Ocean
Observing Network (TCOON) has allowed CO-OPS to further refine the tidal and non-tidal
boundaries. Using the techniques described in section a of the introduction, CO-OPS has
developed the orange polygon shown in Figure 1 to delineate the non-tidal areas.
4
b. Development of Discrete Tidal Zoning
There are two operating NOAA stations that are part of the National Water Level Observation
Network (NWLON) in the Laguna Madre region (Corpus Christi and Port Isabel). Corpus Christi
is located in the Gulf of Mexico side of Padre Island, while Port Isabel is inside Laguna Madre
on the southern end. Additionally, in this region there are 6 operating TCOON stations whose
data is readily available to CO-OPS. The stations are Packery Channel, Bird Island, Baffin Bay,
Rincon Del San Jose, Port Mansfield and Realitos Peninsula. Based on CO-OPS’ non-tidal
polygon, 4 of the 8 stations are located in the non-tidal region (see Figure 2). Figure 2 also
indicates the locations of historical stations whose tropic high water and tropic low water interval
values and tidal ranges were used to develop the discrete tidal zoning.
Figure 2. Two operating CO-OPS NWLON stations and six operating TCOON stations are located in Laguna
Madre TX. Additinally historical stations are located throughout (not labeled).
Tropic tides occur semi-monthly when the effect of the Moon's maximum declination is greatest.
At these times there is a tendency for an increase in the diurnal range. The tropic higher high
water interval or tropic lower low water interval is the lunitidal interval between the Moon's
transit over the local or Greenwich meridian and the following higher high or lower low water at
the time of the tropic tides (CO-OPS, 2000).
5
Within the non-tidal region, a large zone was drawn around each of the TCOON stations. In the
non-tidal region, the boundary between zones is equidistant from each neighboring station.
Within each zone, the data will be collected relative to LWD or MWL using the observed water
level data as a guide. Figure 3 indicates the control station and extent of each non-tidal zone
where the color of each zone is the same as that of its control station.
Within the tidal region, “traditional” zoning was developed and extended through to the non-tidal
polygon border. In northern Laguna Madre, Packery Channel is located approximately 4 miles
north of the tidal/non-tidal border and just south of the John F. Kennedy Causeway. The
causeway serves as a partial dam, dampening the tidal signal from Corpus Christi Bay. As such,
it is assumed that the tides are uniform in the area located between the causeway and the
tidal/non-tidal border (an area approximately 4.1 to 5.3 miles long). Thus a single zone was
drawn using Packery Channel for control.
In southern Laguna Madre, existing zoning around Port Isabel was extended northward towards
the tidal/non-tidal border using historical data at various locations as well as from the TCOON
station at Realitos Peninsula. Data from a few of the stations within the non-tidal region was
critical in helping to place the cophase lines; these stations can be found just north of the
tidal/non-tidal border in southern Laguna Madre in Figure 2.
The difficulty in developing the zoning in southern Laguna Madre was in determining at which
zone to transition from using Port Isabel as the control station to using Realitos Peninsula as
control. A gap analysis of the CO-OPS NWLON network indicated that Port Isabel could
provide coverage up to just north of Realitos Peninsula (Gill et all, 2008). A review of the range
corrector values indicated subjectively that transition from Port Isabel to Realitos Peninsula
could occur at the zone centered at 26.112° N 97.204°W, approximately 3.2 mi north of Port
Isabel and 11.6 miles south of Realitos Peninsula, where the range correctors were at a
minimum. At this zone, the Port Isabel range ratio is 0.51 and the Realitos Peninsula range ratio
is 1.52.
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Figure 3. Four non-tidal zones, each with its own TCOON operating control station.
Instead of the subjective interpolation described above, a TCARI grid was developed for Laguna
Madre to determine where to make the transition from one control station to another. The
differences between the TCARI output and the discrete tidal zoning were calculated for most of
the zones between Realitos Peninsula and Port Isabel for the data in November and December
2012. Starting at Port Isabel, the root mean square error (RMSE) of the differences at the 95%
confidence interval (CI) between the zoning controlled by Port Isabel and TCARI were less than
those between zoning controlled by Realitos Peninsula and TCARI. At a zone centered at
26.102°N 97.200°W (the boundary between red and purple zones in Figure 4), however, the
RMSE value for zoning controlled by Realitos Peninsula and TCARI (0.237 m) was less than
that of Port Isabel (.247 m). As a result, in the discrete tidal zoning, the transition between
control stations occurs at this location (2.4 mi from Port Isabel and 12.6 mi from Realitos
Peninsula). As indicated in Figure 4, the purple zones are controlled by Port Isabel and the red
zones are controlled by Realitos Peninsula.
c. Quality Control of the Zoning Results
Figure 4 summarizes the results of the error analysis of the discrete tidal zoning in Laguna Madre
(and using Figure 3 for location reference). Beginning with Packery Channel, the RMSE of the
7
difference between the water level at Packery Channel and Bird Island at the 95% CI is 0.16
meters. This means that 95% of the time, the water levels in the transition area between the tidal
Packery Channel-controlled zone and the non-tidal Bird Island-controlled zone to the south will
be within 0.16 meters of each other. This error is significant compared to the target error budget
of 0.09 meters for applying tidal information in the shoreline mapping process in areas of small
range of tide.
The RMSE of the difference between Bird Island and Baffin Bay water levels is 0.08 meters.
This indicates that water levels are fairly similar throughout the northern half of Laguna Madre.
The RMSE between Baffin Bay and Rincon Del Sal Jose, however, is 0.29 meters indicating that
water levels in the southern half of Laguna Madre are distinct from those in the northern half.
The RMSE between Rincon Del San Jose and Port Mansfield is 0.24 meters. This may be due to
Port Mansfield’s connection to the Gulf of Mexico and the variability introduced at that location.
Figure 4. Discrete tidal zoning root mean square error and total propagated error analysis.
8
The RMSE of the difference between the observed water level data at Port Mansfield, a non-tidal
station, and the corrected Realitos Peninsula water level data based on correctors from the first
zone in the tidal region is 0.18 meters. The total propagated error, which includes the datum,
processing, measurement and interpolation errors between Realitos Peninsula and Port Isabel is
0.28 meters.
d. TCARI Grid in Laguna Madre
A TCARI grid was created in Laguna Madre by interpolating harmonic constituents, tidal datum
and residuals at 8 operating stations, and several historical stations. Although periodic tides are
negligible at non-tidal stations, tidal energy still exists and tidal amplitudes and phases from
harmonic analyses are loaded into TCARI for interpolation purposes. The TCARI tide error
model was calculated by turning off tidal constituents or residuals at a station and computing the
RMSE of the difference between the predicted or observation data and the interpolated data at
the station. Figure 5 shows the error model output from TCARI grid where the error is
represented by a color scale. Most errors range from 0.0 to 0.15 meters. The yellow and red areas
(0.2 to 0.34 meters) in Laguna Madre are probably overestimated because historical or operating
stations are not available in these areas and TCARI extrapolates the error from nearby stations.
Figure 5. TCARI tide interpolation error in Laguna Madre and outer coast in meters.
A comparison of the tide reducers from two zoning schemes in November and December 2012 is
shown in Figure 6 where RMSE of the differences is represented by a color scale. Most of the
9
RMSEs (at the 95% CI) range from 0.0 to 0.15 meters. The relatively high RMSE at the 95% CI
(green and red areas in Figure 6 are ~0.10 to ~0.27 meters) are located at the transitional area
from using Port Isabel as the control station to using Realitos Peninsula, the area from using Port
Mansfield as the control station to using Ricon Del San Jose and the area from using Ricon Del
San Jose as the control station to using Baffin Bay.
Figure 6. RMSE at the 95% CI in the differences between TCARI and discrete tidal zoning tide reducers in
meters. The project is distorted by the TCARI program.
d. Conclusion
In order to meet specified error budgets, even for the non-tidal regions, additional subordinate
stations may need to be installed in order to reduce the uncertainties in data as the surveyor
transitions between zones of coverage for each operating station. TCARI generated much
smoother tide reducers across the region by interpolating water level data. However, the
accuracy of both zoning schemes depends on the observed data availability between Port Isable
and Realitos Peninsula, Port Mansfield and Ricon Del San Jose, and Ricon Del San Jose and
Baffin Bay.
3. PAMLICO SOUND CASE STUDY
a. Introduction
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The tides of Pamlico Sound and Albemarle Sound in North Carolina are not well understood and
the water levels at any given location are significantly influenced by local meteorological events.
Consequently, mapping the tides and developing a tide reduction system for hydrographic survey
purposes is challenging. In 2012, nine additional water level gauges were installed in Pamlico
Sound and Albemarle Sound. The additional data provided much more detailed information
about the propagation of tides and water levels within these two basins, identifying the regions
where tidally driven signals are overwhelmed by local meteorology and routine tidal tabulation is
no longer possible. A more rigorous scientific paper examining the details of tides and water
levels within these locations is forthcoming. This case study focuses on the operational
considerations and examines the use of TCARI as a tide reduction methodology in these tidal
transition areas, outlines some potential difficulties, and offers solutions.
The majority of the area experiences some tidal influence and the water levels at many locations
are clearly dominated by tidal forces. However, even at tidally driven locations, the range of tide
is minimal. Excluding the coastal stations, the largest ranges of tide within the sounds are found
near the inlets with the coast; the mean range of tide at Oregon Inlet is 0.28 meters, the range of
tide at Beaufort is 0.95 meters, and the mean range of tide at USCG Hatteras is only 0.13 meters
(see Figure 7). Water levels are greatly influenced by local meteorological forces and given the
small range of tide, a repeating cycle of the tides is often masked and difficult to tabulate. The
effectiveness of traditional tidal zoning is limited in areas like this because the tide transitions
prevent one control station from effectively representing the tide characteristics in other areas.
These two sounds provide a great workspace for testing the usability of a TCARI grid developed
around these transition areas.
Figure 7 shows the locations of the accepted tidal datums in the area, as well as the locations of
the nine recent additional gauges. Three of the stations, Frog Island, River Dunes, and
Portsmouth, were classified as non-tidal after the data tabulation and analyses. As noted earlier
in the paper, the classification of a station as non-tidal does not mean a tidal signal does not exist,
but rather that the water levels are not cyclic enough to be consistently tabulated. Tidal datums
are averaged from tabulations so non-tidal simply means that there were insufficient tide picks to
derive an average datum value. Even though tides cannot be tabulated, harmonic analyses if the
hourly heights can still be performed to derive harmonic constants of the major harmonic
constituents. Due to the short series length, a set of 29-day harmonic analyses were performed
for the 2012 stations to obtain a set of harmonic constants to be used for TCARI input.
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Figure 7. Pamlico and Albemarle Sound TCARI grid boundary and input stations. Note the additional 2012
installations are the maroon dots. The blue dots are stations with previously accepted tidal datums and the
yellow stars represent NWLON stations.
b. The TCARI model solutions
A preliminary TCARI grid was developed that included 12 locations with tidal datums and
harmonic constituents that met requirements for NOS acceptance. This preliminary grid
included three stations that were on the coast, specifically Duck, Cape Hatteras, and Atlantic
Beach. The preliminary grid served as a benchmark for understanding the tide ranges in the area.
A second TCARI grid was developed from the first grid’s outline. Following the data processing,
the harmonic constituent analysis, and tidal datum computation of the nine additional stations,
the additional information was integrated into the preliminary grid.
Tidal datum values are interpolated from the input data, resulting in an undulating datum surface.
Figures 8 and 9 show the MLLW surfaces from the preliminary grid and the second grid that
incorporates the additional stations. The MLLW surface is depicted numerically as the difference
in elevation relative to local MSL. A value of zero (0) indicated a non-tidal area with no range of
tide. Fortunately both grids show the same general trend but the second grid obviously improves
the resolution and more clearly shows the transitions from tidal to non-tidal. Interestingly, the
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preliminary grid has Albemarle Sound as nearly non-tidal, even with no data incorporated in the
sound. With the consistency between the two grids, there is more confidence that the transition
from tidal to non-tidal occurs in the northern parts of Croatian Sound, identified as the green
polygon in Figure 7.
Figure 8. MLLW surface relative to MSL from the preliminary grid using the original 12 stations with
accepted datums. The scale is in meters. Areas of red represent a very low range of tide, areas of blue
represent a larger tidal range.
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Figure 9. MLLW surface relative to MSL from the grid updated with nine additional stations (21 accepted
datums in total). The scale is in meters. Areas in red are non-tidal, areas in dark blue have the largest tidal
range.
c. The error model
A comprehensive uncertainty analysis was performed to help with interpretation and application
of the TCARI model output. As with typical TCARI solutions, the gridded “error model” is split
into three components, the datum error, the harmonic constituent error, and the residual error.
Each station that contributes one or more of these data types has an error associated with each
component and the gridded error model is a composite interpolation of these values.
The datum errors for a station that has less than 19 years of data are computed by using a
weighting formula that takes into account distance from the control station, ratio of the range of
tide with the control station, and the difference in time of the Greenwich Low Water Interval
values to the control station. The error for each station is computed independent of the TCARI
grid and are inherent to the datum computation, itself. For the 3-month stations installed in
2012, the largest datum errors computed was approximately 0.03 meters. To be conservative and
focus the attention on the interpolation of the tidal signal, all datum error values were set to
0.03m.
The harmonic constituent errors are specific to the TCARI grid. These errors are not inherent to
the harmonics, themselves, but the uncertainty in the TCARI grid’s ability to use surrounding
data to replicate the predicted tide at a given station. In determining these harmonic interpolation
errors, a constituent set for one of the stations included in the grid is removed from the list of
data inputs, a new solution is computed without it, and the interpolated prediction is generated at
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the location of the removed constituent set. The 95% confidence interval of the differences
between this synthesized prediction and the accepted prediction is the “error” value supplied to
the error model. Figure 10 shows the results from the error model.
Figure 10. Model of harmonic constituent error. The scale is in meters, maximum 1.650 meters, minimum
0.038 meters. The majority of Albemarle and Pamlico sounds are below 0.30 meters.
Residuals are defined as the time-varying difference between observed and predicted tides at
each station and each TCARI grid-cell. The residual error values are determined in a way that is
very similar to the harmonic constituent error. A station that would otherwise be contributing
observed data to the grid is removed, a new solution using the remaining residual stations is
determined, and an interpolated water level curve is generated at the location of the absent
station. The 95% confidence interval of the differences between the interpolated curve and the
set of true observations is the residual interpolation error.
For this TCARI application, two residual error models were developed. In one model the residual
errors are computed excluding both the residual inputs and the harmonic constituent inputs. In
the other model, the harmonics are included, but the residuals are not. By keeping the harmonic
information in the interpolation, the general tidal characteristics are maintained and the
uncertainty in the generated water level curve is limited to the contrast of the residual
information at the location in question and the neighboring stations. Accordingly, removing both
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types of input dramatically increases the uncertainty in the produced water level signal. In
locations near the boundary of the grid or isolated up a river, the tide characteristics of the closest
neighbor are applied without interpolation from multiple inputs, and the error values are
extrapolated to the boundary. This difference in the residual error model generation is illustrated
in Figures 11 and 12. For the majority of the areas, the difference in the error models is
negligible. However, in the coastal areas and boundary areas, the extrapolated values are larger.
The individual error values illuminate the significance of the effect that the tidal cycles play in
determining the water level values, despite the very low range of tide. Table 1 shows the results
of the different error model development procedures and for the non-tidal stations (bold),
eliminating the harmonic constituents increases the water level error by nearly 50%.
It should be noted that the error images, Figures 10, 11, and 12, represent error surfaces that are
dependent upon data density. The error model takes an error value for each data type at each
location in Table 1, divides that value by the distances to the nearest station with the same data
type and interpolates the divided values across the grid domain. The values in the table represent
the RMSE at the 95% CI of the difference between the real harmonic constituents/residuals and
the interpolated harmonic constituents/residuals.
Figure 11. Model of residual error, harmonics OFF for each test point. The scale is in meters, maximum
1.680, minimum 0.045m. The majority of Albemarle and Pamlico Sounds are below 0.28m.
16
Figure 12. Model of residual error, harmonics ON for each test point. The scale is in meters, maximum
1.661m, minimum 0.045m. The majority of Albemarle and Pamlico Sounds falls below 0.28m.
Table 1: List of stations included in the second TCARI solution with the harmonic
constituent error and the two residual errors.
Station
8651538
Frog Island
8651817
Edenhouse Pt
8653951
Peters Ditch
8654572
Ocracoke
8655353
Portsmouth
8654875
River Dunes
8653365
Washington
Tidal
(Y/N)
NO
Harmonic
Constituent Error
0.09
Residual Error
(HCs On)
0.11
Residual Error
(HCs Off)
0.18
YES
0.09
0.14
0.15
YES
0.11
0.14
0.16
YES
0.15
0.10
0.17
NO
0.22
0.14
0.24
NO
0.16
0.17
0.22
YES
0.22
0.22
0.29
17
Notes
8656201
Core Sound
8656467
Spooners Crk
8651370
Duck
8652587
Oregon Inlet
8656483
Beaufort
8654467
USCG Hatt.
8652247
Manns Hrbr
8652437
Oyster Creek
8652547
Roanoke Msh
8652905
Lake Worth
8654400
Cape Hatteras
8654792
Ocracoke Isl
8655875
SeaLevel Core
8656590
Atlantic Beach
YES
0.13
0.22
0.22
YES
0.58
0.12
0.16
YES
0.57
0.28
0.62
YES
0.23
0.21
0.28
YES
0.35
0.13
0.37
YES
0.18
0.10
0.14
YES
0.10
n/a
n/a
YES
0.09
n/a
n/a
YES
0.09
n/a
n/a
YES
0.11
n/a
n/a
YES
0.62
n/a
n/a
YES
0.24
n/a
n/a
YES
0.12
n/a
n/a
YES
0.84
n/a
n/a
Outer coast
Outer coast
Outer coast
d. The results
From an operational standpoint, TCARI did a reasonable job of interpolating data across
tidal/non-tidal transition areas. It is apparent that the inclusion of harmonic constituents greatly
improves the results, even in areas classified as non-tidal. Ultimately, however, the accuracy of
an interpolation model is only as good as the data being interpolated. If insufficient data in
incorporated into the grid, then the accuracy is correspondingly limited and thus it useful
application is limited. The traditional method of discrete zones, however, is also limited in that
the tide characteristics of the control station are applied to all zones that it controls. With even a
limited number of stations with harmonic constituents, TCARI should overcome this particular
weakness of what has been the standard method of dealing with non-tidal areas.
4. DISCUSSION
Each year more and more hydrographic surveys and shoreline mapping surveys are conducted in
tidal to non-tidal transitional areas. Additional efforts are needed to provide accurate vertical
control and tide and water level reducers in these areas. Although there are some criteria to
follow, the process requires an extensive analysis of the water level observations. Water levels
variations are meteorologically dominated and generally very localized in transition areas and
non-tidal areas. In the case of Laguna Madre, although there are 8 operating stations, the residual
patterns between Baffin Bay, Rincon Del San Jose and Port Mansfield are not consistent and
additional observed data are needed to fully determine the areas of coverage of switching for
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each control station. In the case of Pamlico Sound, recent observations have helped understand
the transition areas, however there still are many areas of unknown characteristics. Tidal
propagation is slow and phase changes are rapid in tidal to non-tidal transition areas. Tidal
constituents derived from harmonic analysis may not be accurate because of small tidal ranges.
More observations especially in mid-sound or mid-bay areas, would be helpful to improve the
accuracy of the location of the tidal/non-tidal cut off line used for final discrete tidal zoning and
TCARI grid boundaries. Deploying bottom mounted pressure gauges and GPS tide buoys to
collect water level observation in the middle of survey area are recommended in this type of
region.
The known shortfalls of discrete tidal zoning are obvious in tidal to non-tidal transitional areas.
As shown in the Laguna Madre case, the steps are expected when switching control stations and
datum control. The assumption of uniform tides in a large zones also cause large errors
especially when water levels are so different between two adjacent stations. A discrete zones
(polygons) need to be developed to break up the large range and time of tide changes requiring
subjectivity in their placement.
TCARI provides more accurate tide reducers than simple discrete zoning by interpolating
harmonic constituents, tidal datum and observed minus predicted residuals from both tidal and
non-tidal stations across the region. However, the accuracy of TCARI depends on the available
data and the assumption of smooth changes between two operating stations may not be the case
especially in these transitional areas. The accuracy of harmonic constituents at non-tidal stations
needs further verification using tidal hydrodynamic models and longer time periods of
observation.
5. CONCLUSION
In order to provide accurate vertical control and tide and water level reducers for tidal to nontidal transition areas, detailed analyses of observations are needed for tidal and non-tidal
identification, the cut-off line between tidal and non-tidal areas and for quality control of zoning
products. To perform a higher resolution placement of these features, more operating stations
and tidal hydrodynamic models are generally needed in the tidal to non-tidal transitional areas
due to complex tide/water level characteristics. TCARI is recommended to provide tide and
water level reducers in these transitional areas over the use of discrete zoning as it provides for a
smoother water level reducer function.
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References
CO-OPS. 2000. Tides and Currents Glossary. U.S. Department of Commerce, National Ocean
and Atmospheric Administration, National Ocean Service, Center for Operational
Oceanographic Products and Services, 28 pp.
Gill, S. K., J.R. Hubbard, and G. Dingle. 1995. Tidal Characteristics and Datums of Laguna
Madre, Texas, NOAA Technical Memorandum NOS OES 008. U.S. Department of Commerce,
National Ocean and Atmospheric Administration, National Ocean Service, 116 pp.
Gill, S. K., and K. M. Fisher. 2008. A Network Gaps Analysis For the National Water Level
Observations Network, NOAA Technical Memorandum NOS CO-OPS 0048. U.S. Department
of Commerce, National Ocean and Atmospheric Administration, National Ocean Service, 59 pp.
Hess, K.R., R. Schmalz, C. Zervas, and W. Collier, 2004. Tidal Constiuent and Residual
Interpolation (TCARI): A new method for the Tidal Correction of Bathymetry Data, NOAA
Technical Report NOS CS 4, Silver Spring, 112 pp.
Hess, K. W., E. A. Spargo, A. Wong, S. A. White and S. K. Gill, 2005. VDatum for Central
Coastal North Carolina: Tidal Datums, marine Grids, and Sea Surface Topography, NOAA
Techncial Report NOS CS 21, NOAA/NOS, Silver Spring, MD, December 2005, 46pp.
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