Hawaiian Barotropic Tides
(Predictions for HOME PIs)

• Introduction
• TPXO.3 Model Predictions of Tidal Sea Heights & Currents Offshore
• Coastal Tide Heights Predictions
• Currents in Mamala Bay (Diamond Head to Barber's Pt., Oahu)

Last Update: 22 August 2000

Preface

The material presented here is intended as an aid to planning the HOME field work, especially the Survey program beginning at the end of August, 2000. If HOME PIs have any questions or would like to see tidal predictions at locations not supplied on these web pages, please contact Doug Luther (email: dluther@soest.hawaii.edu; phone: 808-956-5875). Direct contributors to this web page include E. Firing and D. Luther. Indirect contributors are referenced throughout. This work is supported by the National Science Foundation Ocean Sciences Division under Grant Number OCE98-19517. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the principal investigators and do not necessarily reflect the views of the National Science Foundation.

N.B., this web page and all its plots & data can be downloaded onto your computer for ease of access. Download this single 11.4 MB file: WWWBaroTide.tar.gz. Then, "gunzip" it, un-"tar" it, and open the file barotide.htm with your web browser. The total disk space you'll need is about 23 MB.

Introduction

It is assumed that low frequency variations (e.g., the bi-weekly spring-neap beat due to M2 & S2 constituents) of the strength of the barotropic tide are relevant factors in designing experiments to locate and identify internal wave or turbulence phenomena generated by the barotropic tide (hereafter, just `tide' or `tides'). The tides in sea level at Hawaii have diurnal and semi-diurnal constituents with very similar amplitudes. In total, the diurnal part of the tide reaches slightly larger amplitudes than the semi-diurnal part, resulting in an often confused and weak spring-neap cycle in Hawaiian sea level.

However, it's not the tidal sea level fluctuations that are of greatest concern to HOME, but rather the strengths of the tidal currents. In the neighborhood of Hawaii, despite the near equivalence of diurnal and semi-diurnal contributions to sea level tides, the semi-diurnal currents are stronger than the diurnal currents, which is well known to those of you who have been playing with the output from Egbert's TPXO.3 tide model (see Egbert, 1997 , for a description of the model). As an example, Figure SO22158.gif shows the sea level height, zonal current, meridional current, and speed of the tides at HOT site ALOHA for Sep.-Oct., 2000, based on TPXO.3. The dominance of the diurnal components in sea level is clear in the figure, as is the irregularity of the spring-neap cycle in sea level. But, in the currents, the semi-diurnal tide dominates, providing a much clearer spring-neap cycle in tidal current amplitudes, which cycle is not necessarily in phase with the spring-neap cycle of the sea level tides. The spring-neap cycles do not vary much from the Big Island to French Frigate Shoals (FFS), but, while the sea level tide amplitude decreases from the Big Island to FFS, the tidal current amplitudes increase (see additional plots below; especially, see the comparison plots at the bottom of the plot/data table).

Despite the dominance of the semi-diurnal constituents in the currents, the diurnal currents can provide a non-trivial increase to the amplitude of the currents during a `spring' tide cycle (e.g., days 287-290 and 300-303 in Fig. SO22158.gif ). The diurnal contribution to the currents becomes more pronounced toward the end of CY2000 (see the plots below). Insofar as the processes of interest to HOME investigators depend non-linearly on the tidal currents, then the diurnal constituents may still play a role in this study.

Based on the TPXO.3 tidal current predictions for Sept.-Dec., 2000, the following calendar indicates the days when the strongest and weakest tidal currents will occur. The strongest tidal currents will occur on the days surrounding the dates indicated with an `S'. The weakest tidal currents will occur on the days surrounding the dates indicated with a `W'.

Below you will find plots and the hourly values of predictions of the following:

• tidal sea level and currents for 7 locations offshore of the Hawaiian Ridge, from the island of Hawaii to French Frigate Shoals, derived from Egbert's (1997) TPXO.3 model that is based on an assimilation of TOPEX/Poseidon altimeter-measured sea surface heights; and,
• tidal sea level for 7 coastal sites from the island of Hawaii to French Frigate Shoals, which are based on a harmonic analysis of observed sea level.

This map shows the locations of the sites for which tide predictions are included in this web site.

Click to enlarge.

The 7 TPXO.3 sites were chosen to provide good coverage along the Ridge, to show the slight to moderate spatial variability of the tides, while still being at a distance far enough from the Ridge so that inaccuracies in the tide predictions that might arise from inaccuracies of the representation of the Ridge bathymetry in the model could be expected to be small. Upon request, tidal predictions can be provided at other locations, even right at the Ridge (caveat emptor).

The coastal sites were also chosen to demonstrate the slight to moderate variability of tidal sea level along the Ridge, while keeping the number of stations modest. Even though the variation of tidal sea level as a function of time does not vary greatly along the Ridge, any Captain relying on Honolulu tide predictions, for instance, to maneuver his sailboat out of Kaneohe Bay (across Oahu Is. from Honolulu) could easily wind up on a sandbar. Even cross-island tidal sea level differences can be as much as a foot in maximum or minimum height and two hours of delay in the time of high or low water. Upon request, tidal predictions can be provided for the following additional sites.

Island	Station	Latitude	Longitude	Click to enlarge.
Kauai	Nawiliwili	21.96N	159.37W
	Pt. Allen	21.90N	159.60W
Oahu	Waianae	21.44N	158.17W
	Honolulu	21.31N	157.87W
	Mokuoloe	21.44N	157.79W
Molokai	Kaunakakai	21.09N	157.03W
Maui	Lahaina	20.88N	156.69W
	Kihei	20.78N	156.47W
Island of Hawaii	Honokohau	19.67N	156.03W
	Kapoho	19.50N	154.82W

TPXO.3 Model Predictions of Tidal Sea Heights & Currents Offshore

A brief description of the TPXO.3 tide prediction method, taken from the README file accompanying the tide model available via anonymous ftp at oce.orst.edu/dist/tides/Global, can be found here. The model incorporates 17 diurnal and semi-diurnal constituents. Especially note the comparison plots provided at the bottom of the table below.

The plots are provided in both `.eps' and `.gif' formats. The `.gif' files are usually smaller, but the `.eps' plots have better resolution. The abscissae of the plots are in units of days after 1/1/2000 00h UT. Therefore, day 245 is Sept. 1, day 275 is Oct. 1, day 306 is Nov.1, and day 336 is Dec. 1.

Coastal Tide Height Predictions

One to sixteen years of sea level data from each of the coastal tide gauge stations in the table below have been analyzed for 20 tidal constituents (2Q1, SIG1, Q1, RO1, O1, M1 sub-group, PI1, P1, K1, J1, OO1, 2N2, MU2, N2, NU2, M2, L2, T2, S2 and K2 ). Where the harmonic analysis produced inaccurate estimates, as for the weaker constituents in the shorter records, the weaker constituents were inferred using a modified admittance method. The estimated and inferred constituents for each station are listed below. All nodal factor corrections have been applied. Especially note the comparison plots provided at the bottom of the table.

Currents in Mamala Bay (Diamond Head to Barber's Pt., Oahu)

During 1994-1995, Science Applications International Corp., under contract from the City and County of Honolulu, conducted an 18-month-long study of the current and temperature variability in Mamala Bay, the bay off Honolulu between Diamond Head and Barber's Pt. on the south shore of Oahu. Very good vertical coverage was obtained at 13 mooring locations, via ADCP or distributed current meters, permitting the estimation of both barotropic and baroclinic tide components. The two figures below, taken from the SAIC technical report written by Hamilton et al. (1995), illustrate the barotropic tidal current ellipses for the principal semi-diurnal (M2) and diurnal (K1) constituents. Note that the isobaths shown are 20 m, 75 m, 250 m and 500 m.

Click to enlarge M2 plot.

Click to enlarge K1 plot.

The figures show that the semi-diurnal currents are generally quite a bit stronger than the diurnal currents, as expected from the TPXO.3 predictions above. Notably for HOME field work planning, there is substantial variation in current amplitudes over short horizontal distances in this shallow, geometrically complex region, both alongshore and offshore; although, there is a consistent tendency toward along-isobath orientation of the tidal current ellipses. Depending on alongshore location, the tidal currents are stronger near the coast, or not.

The phases of the M2 currents indicate a convergence-divergence of the tidal flow at a location halfway between Barber's Pt. and the entrance to Pearl Harbor. Hamilton (1996) argues convincingly that this convergence-divergence drives a strong internal tide with a westward propagation tendency, possibly dominated by a Kelvin Wave. No such convergence-divergence pattern is indicated in the K1 current field.

• Hamilton, P., J. Singer and E. Waddell, 1995: Mamala Bay Study: Ocean Current Measurements. SAIC Project MB-6 Tech. Rep.
• Hamilton, P., 1996: Observations of tidal circulation in Mamala Bay, Hawaii. Unpublished ms.