David Wolcott Lijuan Huang Stephen Gill. Center for Operational Oceanographic Products and Services National Ocean Service/ NOAA Silver Spring, MD

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1 Establishing Tide Control in an Area with Insufficient Observational Water Level Data: A Case Study of the Kuskokwim River, AK David Wolcott Lijuan Huang Stephen Gill Center for Operational Oceanographic Products and Services National Ocean Service/ NOAA Silver Spring, MD ABSTRACT The Center for Operational Oceanographic Products and Services (CO-OPS) provides tide support to the Office of Coast Survey (OCS) for its projects by utilizing historical and recent observational water level data. This paper explores the water level gauge assessment and data collected for a 2010 hydrographic survey in the Kuskokwim River, and area with no datum control, little historical information, and a dynamic tidal regime. Datum control is difficult because of limited historical information, as well as a gap in the National Water Level Observation Network (NWLON) coverage. A semidiurnal amphidromic point near Cape Newenham and changing tide type between the Pribilof Islands and the Kuskokwim Bay make adequate datum control from existing NWLON stations in the Aleutians or Pribilof Islands impossible. Very little historical data exists on the Kuskokwim River; three months of data was collected in Bethel in 1970 and a few neighboring stations have data from the early 1900 s. As the tide propagates from the mouth of the river upstream to Bethel, the tidal range decreases more than eight feet and the phase is offset by seven hours. The installation of the five water level stations and collection of several months of data enabled CO-OPS to enhance the accuracy of tide reduction in the Kuskokwim River. INTRODUCTION Effective reduction of bathymetric soundings to a chart datum is critically dependent upon a detailed understanding of the tides in the survey area. While the details of the propagation of tides in a particular area can be estimated through the use of numerical modeling and historical observations, only a sufficient network of direct measurement of the water levels within the survey area can offer the truest information. In many areas, historical data supplemented with hydrodynamic model output is adequate to determine the movement of tides. In such cases, tide correction is a relatively easy application of tidal zoning correctors to the data from a single station. However, in some areas of the United States shoreline, particularly in relatively remote and tidally complex areas like Alaska, an absence of information about the tides restricts the Center for Operational Oceanographic Products and Services (CO-OPS) ability to provide accurate tide corrections unless substantial amounts of additional water level observations are US Hydro

2 made. The Kuskokwim River is such an area and a 2010 survey of the river exemplified the need for additional water level measurement in order to adequately understand tide propagation. Prior to the survey, cotidal lines were drawn using a very limited amount of historical information, no datum control, and no observed data. After the survey and the installation of 5 water level stations, cotidal lines were drawn again to make a comparison. Though National Water Level Observation Network (NWLON) control for datum determination was still unavailable, the new observations dramatically improved the accuracy of the tidal zoning scheme of the river. The information collected from these installations makes it even more apparent that an adequate amount of data must be collected prior to a survey in a tidally dynamic region in order to effectively account for the tides. TIDAL CHARACTERISTICS OF BRISTOL BAY AND KUSKOKWIM BAY Tides in Bristol Bay are characterized by a mixed-semidiurnal signal with a stronger diurnal component in the upper reaches of the Kuskokwim River. As the tide moves eastward along the Alaskan Peninsula the tidal range increases from around 1.0 meter at Dutch Harbor to roughly 6.0 meters in Kvichak Bay (Huang et. al, 2011). As the tide progresses around Cape Newenham and into the Kuskokwim Bay, the tide reaches a maximum amplitude of 3.7 meters at Quinhagak. A semidiurnal amphidromic point near Cape Newenham prevents a linear progression of the tide through Bristol Bay (Pearson et. al, 1981). Figure 1: The only NWLON stations in the vicinity of the Kuskokwim River are located at Village Cove, St. Paul s Harbor and Port Moller on the Alaskan Peninsula. US Hydro

3 Figure 2: Comparison of concurrent data sets from the subordinate install at Quinhagak in the Kuskokwim Bay and the two NWLON control stations at Port Moller on the Alaskan Peninsula and Village Cove on St. Paul s Island in the middle of the Bering Sea. CONTROL STATION LIMITATIONS No adequate control stations exist for the Kuskokwim River and much of Bristol Bay is located in an NWLON gap (Gill et. al, 2001). Figure 2 shows plots from the two NWLON stations in Bristol Bay and a subordinate installation at the mouth of the Kuskokwim River. The semidiurnal amphidromic point near Cape Newenham results in a 180 phase shift in the semidiurnal component of the tide as it propagates along the Alaskan Peninsula and around Cape Newenham (Pearson et. al., 1981). Figure 3 shows the approximate location of the semidiurnal amphidromic point, as shown by cophase lines for the M 2 (lunar semidiurnal constituent) derived from harmonic analysis. A comparison of the plots of Port Moller and Quinhagak shows that the semidiurnal component, as evident by the secondary tide, appears to be flipped in sequence about the time axis while the diurnal component progresses relatively linearly. As a result, no amount of phase offset can be applied in a tidal zoning scheme to Port Moller to adequately represent the tidal characteristics of Quinhagak. The significant difference in tide type and reduced amplitude of the Village Cove signal also makes it an impossible choice as a control station in the Kuskokwim River. Between the limitations of these two stations, no tidal zoning correctors could be applied to either NWLON station to adequately represent tides in the Kuskokwim River. US Hydro

4 Figure 3: Phases of the M 2 constituent throughout Bristol Bay and the Kuskokwim River. The phases for the Kuskokwim River were derived using 29-day Fourier Transform harmonic analysis results at several locations. Notice a full period of the semidiurnal tide is present from the tip of the Alaskan Peninsula to Bethel. The complexity of the phase distribution makes tidal analysis difficult in areas such as this. INITIAL ASSESSMENT Prior to the survey, very little was known about the tides of the Kuskokwim River. No sixminute or hourly observations were available. The most recent data available was a paper copy of datums computed for Bethel in 1970, which is located roughly 85 nautical miles up the river. Nevertheless, a few stations with historical observations, mostly from the 1910 s, provided enough datum information that preliminary cotidal lines could be drawn and zones were constructed. As the area has no nearby operating control stations, preliminary tidal zoning was not provided for the survey. It was required that 5 subordinate stations be installed between Quinhagak at the mouth of the river and Bethel with the understanding that all of the preliminary zoning was likely to change after the collection of data at these five points (see Table 1). US Hydro

5 Table 1: Historical data availability prior to 2010 installations on the Kuskokwim River. Datum information that is included: HWI (Greenwich High Water Interval), LWI (Greenwich Low Water Interval), GT (Great Diurnal Range) STATION Quinhagak Warehouse Creek Kuskokwim Creek Popokamute Eek Island Bethel High Water Interval HWI (hrs) Low Water Interval LWI (hrs) Great Diurnal Range of Tide GT (m) SERIES (Length and Date) Highs Highs / Lows Highs/ Lows Highs / Lows Highs / Lows months July Sep 1970 INSTALLATIONS Five stations were installed in support of the 2010 hydrographic survey of the Kuskokwim River. Three of the stations were installed at historical locations, Quinhagak, Popokamute, and Bethel. Two other stations were installed at new locations, near Helmick Point, and Lomavik Slough. Quinhagak and Bethel were installed beginning in May and ran continuously for more than four months. Popokamute, Helmick Point, and Lomavik were installed in June and ran for more than two months. Figure 4 shows the locations of all of the installations. For reference, the distance between Quinhagak and Bethel is roughly 85 miles following the center channel of the river. US Hydro

6 Figure 4: Locations of the five installations in support of the 2010 hydrographic survey in the Kuskokwim River, AK. For reference, Bethel is located roughly 85 miles from Quinhagak, as measured in the center of the river. LIMITATIONS OF SUBORDINATE INSTALLATIONS Due to the shallow slope of the river banks and mud flats, a traditional shore-based installation of a water level station was not possible at Quinhagak. With this limitation and a tidal range of nearly 3.6 meters, the sensor did not adequately pick up on the low waters. The installation team who installed the gauge, however, additionally installed two Sea-Bird bottom-mounted pressure gauges more directly in the main channel of the river that did collect the full range of tide. Using the data from these two gauges and the leveled tide gauge on the shore, a composite tide signal was established for the full range of tide. Other areas of the Kuskokwim River have similar bathymetry and topography and presented the same challenges of installation. Another subordinate gauge was installed near Helmick Point, roughly 500m into a slough. Due to the silting issues, the gauge was unable to pick up the full range of tide limiting the signal s applicability to the slough and it is not included in this analysis. However, it should be noted that an area with difficult topography and bathymetry is likely to produce unique tide signals. This is very valuable information that helps us understand the conditions that exist outside of the center channel of the Kuskokwim River. US Hydro

7 OBSERVATIONS TIDAL CHARACTERISTICS OF THE KUSKOKWIM RIVER The tides at the mouth of the Kuskokwim River are characterized by a mixed-semidiurnal signal with an amplitude of nearly 3.7 meters at Quinhagak. As the tide propagates north the range of tide diminishes and the tide type changes from mixed-semidiurnal to mixed-diurnal as it reaches Bethel with an amplitude of about 1.1 meter. Interactions between the principle diurnal constituents (K 1 +O 1 ) and semidiurnal constituent M 2 produce a diurnal inequality mainly in the high waters, which is especially evident at times of maximum or minimum lunar declination. During other times of the month, especially when the moon is on the equator, the tides assume a semidiurnal characteristic. The tide type change occurs fairly smoothly from Quinhagak to Popokamute but the river effects have very pronounced influence on the shape of the tide curve as the tides approach Bethel (see Figure 4). The relative ratios of the higher harmonics for the four subordinate installations are listed in Table 3. The higher ratio at Bethel accounts for the saw tooth-like signal during times of maximum lunar declination (Parker, 2007). While the amplitude and phase of the overall signal, as well as the averaged tide phase differences, can be calculated (see Table 2), simple tidal zoning correctors applied to any other station would not be able to account for these unique river effects in this area. According, knowing the location of the major tide type transitions is not possible without water level observations. Table 2: The results from the accepted datums at the four subordinate locations. STATION HWI LWI MN GT Quinhagak Popokamute Lomavik Bethel US Hydro

8 Figure 5: Concurrent data series from four of the five subordinate installations on the Kuskokwim River. As well as the diminishing range of tide, the frictional effects of the changing bathymetry of the river produce a response from the higher harmonics of the semidiurnal signal, reducing it down to a saw tooth wave during times of extreme lunar declination. The tide type progresses from a mixed-semidiurnal to mixed-diurnal. Table 3: Results from the harmonic analysis showing the effects of the higher harmonics caused by friction and river bathymetry. Shown are the amplitude ratios and prominent phase effects in degrees. Harmonic analysis results were derived using29-day Fourier Transform harmonic analysis. STATION (K 1 +O 1 ) / M 4 / M 2 M 6 / M 2 2M o o 2 M 4 (M 2 +S 2 ) o Quinhagak o Popokamute o Lomavik Slough Bethel o US Hydro

9 Table 4: The amplitude and phase values of the principle harmonic constituents in the Kuskokwim River. STATION M 2 (h) M 2 K 1 (h) K 1 O 1 (h) O Quinhagak Popokamute Lomavik Bethel Table 5: Comparison of the differences between the historical tidal characteristics on record before the 2010 installations and after the installations. STATION Old HWI (hrs) New HWI (hrs) Diff HWI (hrs) Old LWI (hrs) New LWI (hrs) Diff LWI (hrs) Old GT (m) New GT (m) Diff GT (m) QUINHAGAK POPOKAMUTE * * * --- LOMAVIK BETHEL * New Installation US Hydro

10 IMPLICATIONS FOR TIDE REDUCTION Figure 6: The differences between historical and recently derived high water intervals. Note that the differences become positive when the tide transitions from mixed-semidiurnal to mixeddiurnal near Bethel. Figure 7: Differences between historical and recently derived low water intervals. US Hydro

11 Figure 8: Differences between the historical and recently derived GT values. Figures 6 8 illustrate the differences in the three datum values used in the construction of tidal zoning at four different locations in the Kuskokwim River. While the range differences seem minimal, the phase offsets are significant, considering the range of tide near the mouth of the river. The HWI and LWI differences at Quinhagak average to a difference of minutes. With a range of 3.6 m, this time offset of -76 minutes could result in a realized vertical offset of 0.73m (2.36 ft) without adjustment to the time correctors. While historical datum information is adequate for drawing cotidal lines, the resulting lines do not necessarily capture changes in tide type. This difference is apparent in the Kuskokwim River. A standard collection of HWI, LWI, and GT lines was drawn from Quinhagak to Bethel using historical datum information. Without substantial amounts of observational information at the 2010 subordinate locations, very little would be know about the tide types in the river and improper application of tidal zoning correctors could have resulted in vertical errors that could exceed the Hydrographic Specifications and Deliverables tolerance for tides. The collected data and resulting analysis show a tide type that changes dramatically from the mouth of the river to Bethel. Not only is there inadequate tide control from the two NWLON stations at Port Moller and Village Cove, but no single tide station in the Kuskokwim River can provide adequate control for the entire survey area. Only with the installation of multiple subordinate gauges can the full tide signal be considered in an area like the Kuskokwim River. Use of continuous tide reduction schemes such as TCARI or hydrodynamic models could be applied in the future, but they would also suffer from a lack of historical observations at critical locations. US Hydro

12 DISCUSSION While the subordinate installations provided a wealth of information about the tides of the River, questions still exist about where significant tide type transitions occur. For example, Figure 4 shows the plots from four gauges. While the tide type transition between Quinhagak and Lomavik obviously exists, the progression is subtle. However, the transition between Lomavik and Bethel is more acute. With no bathymetry data and limited topography data, understanding where that transition occurs is difficult. The datum information at the 2010 installation locations was used to update the cotidal lines for the river. An example of a zoning challenge is presented below. A three day period of observations was taken for Lomavik and Bethel and the zoning correctors were applied from a single zone that lies between both gauges. Figure 8 shows the six-minute data plots and figure 9 shows the tidal zoning correctors to be applied. Figure 9: Time series plot of three days of six-minute data at Lomavik and Bethel Figure 10: Comparison of zoned correctors for Lomavik and Bethel. US Hydro

13 Figure 11: Comparison of the tide curves produced by applying tidal zoning correctors to Lomavik and Bethel from the same zone. The green line represents the difference between the two signals. While it is unlikely that either curve is a perfect representation of the tides at the zone, the difference of more than 1 meter at some locations indicates a variability for which tidal zoning cannot account. The resulting curves of the correctors applied to Lomavik and Bethel differed by more than a meter in some areas (see Figure 11). The uncertainties associated with computing datums in meteorologically driven areas and drawing the resulting tidal zones are significant, but the biggest component of the difference between these two tide curves is the uncertainty in the location of the tidal transition. Adequate tide reduction and appropriate application of zoning correctors is a challenge in any tidally dynamic region, but direct water level measurement in an area with no historical information is imperative for establishing accurate a zoning scheme. As well, the collection of the 2010 data greatly improves the understanding of where additional water level measurements are needed, providing invaluable information for future assessments. In an area such as the Kuskokwim River, which had effectively no observed water level measurements prior to the 2010 survey, tide reduction was not possible. This area exemplifies the need for water level collection prior to any tide reduction, and the analysis indicates that uncertainties will still remain until the area is explored further. US Hydro

14 REFERENCES Gill, S.K. and K.M. Fisher, A Network Gaps Analysis for the National Water Level Observation Network, NOAA Technical Memorandum NOS CO-OPS 0048, p. 34 Huang, L., Wolcott, D. and Yang, H., Tidal Characteristics along the Western and Northern Coast of AK. Proceedings of 2011 U.S. Hydrographic Conference, The Hydrographic Society of America, pp. 3-5 Parker, B.P., Tidal Analysis and Prediction NOAA Special Publication, NOS CO-OPS 03, pp Pearson, C.A., H.O. Mofjeld, and R.B. Tripp, Tides of the Eastern Bering Sea Shelf, In The Eastern Bering Sea Shelf: Oceanography and Resources, D. Hood and J.A. Calder (eds.), Vol. 1, USDOC / NOAA / OMPA, pp US Hydro

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