An Empirical Global Model for Mode-1 Internal Tides

Technical Memorandum APL-UW TM 1-15 (PDF, 19 MB) Previously published at this link:  https://apl.uw.edu/project/project.php?id=tm_1-15

Dushaw, B.D., 2015: An empirical model for mode-1 internal tides derived from satellite altimetry: Computing accurate tidal predictions at arbitrary points over the world oceans. University of Washington, Applied Physics Laboratory Tech. Memo APL-UW 1-15, 114 pp., https://doi.org/10.5281/zenodo.18726454

A global estimate for harmonic constants of mode-1 internal tides is described, enabling accurate predictions of internal tide amplitude and phase in most regions of the world’s oceans. The estimates are derived from TOPEX/POSEIDON altimetry, building on a frequency-wave number tidal analysis technique described by Dushaw et al. (2011). This technique obtains tidal harmonic constants for the six largest tidal constituents (M2, S2, N2, K2, O1, K1) and the first two internal wave modes simultaneously.

The global solution requires reasonably accurate intrinsic properties of low-mode internal waves, which depend on local inertial frequency, stratification and depth. These properties are derived using the 2009 World Ocean Atlas and Smith–Sandwell global seafloor topography. To account for regional variations in internal wave properties, the global solution for internal tides is obtained by knitting together solutions obtained in 11°×11° overlapping regions. In any area of the ocean, the internal tide field generally consists of the interference pattern formed by the superposition of several or many wavetrains. Inasmuch as accurate tidal estimates are derived from the satellite altimetry, a remarkably marginal observational approach for determining properties of these waves, it is evident that the phases of the interference patterns are stable, indicating extraordinary temporal coherence. The timescales of the interference patterns are faster than the internal tide waves themselves. Over ocean basins, wavetrains traveling in particular directions can be determined, which show spatially coherent wavetrains extending across these basins and suffering little loss in amplitude.

The global solution is tested against point-wise, along-track estimates for the internal tide, with satisfactory comparisons obtained between the two results. Along-track estimates are error prone and provide for only a weak test. From the harmonic constants derived in the global solution, time series are predicted for several existing observations of mode-1 internal tides in the Atlantic and Pacific oceans. The clearest in situ measurements are provided by ocean acoustic tomography, but point measurements provided by moored thermistor arrays or mooring crawlers provide a complementary, if error prone, observation of mode-1 tides. Good predictability for both amplitude and phase, or as good as could be expected given the vagaries of ocean observation, is obtained in all cases. Some of these predictions are obtained for time series recorded about a decade before or after the altimetry data used to derive the global solution, consistent with extraordinary temporal coherence.

The Supplements.tgz file has the global empirical solution for internal-tide SSH derived from altimetry and associated software for plotting and computing mode-1 (and mode-2) tidal predictions anywhere on the globe (where it is watery).  The archive also has various time series of mode amplitude derived from tomography and thermistors from various experiments over the past couple of decades.  And it has the global solution for mode-1 properties derived from climatology that are associated with the solution for SSH, e.g., to derive predictions for internal displacement or temperature.

References

Carrere, L., and Coauthors, 2021: Accuracy assessment of global internal-tide models using satellite altimetry. Ocean Sci., 17,
147–180, https://doi.org/10.5194/os-17-147-2021

Dushaw, B. D., P. F. Worcester, B. D. Cornuelle, B. M. Howe, and D. S. Luther, 1995. Baroclinic and barotropic tides in the central North Pacific Ocean determined from long-range reciprocal acoustic transmissions. J. Phys. Oceanogr., 25, pp. 631−647.  https://doi.org/10.1175/1520-0485(1995)025%3C0631:BABTIT%3E2.0.CO;2

Dushaw, B. D., and P. F. Worcester, 1998. Resonant diurnal internal tides in the North Atlantic, Geophys. Res. Lett., 25, 2189−2193. https://doi.org/10.1029/98GL01583

Dushaw, B. D., 2002. Mapping low-mode internal tides near Hawaii using TOPEX/POSEIDON altimeter data, Geophys. Res. Lett., 29, 91-1−91-4. https://doi.org/10.1029/2001GL013944

Dushaw, B. D., 2006: Mode-1 internal tides in the western North Atlantic Ocean. Deep-Sea Res. I, 53, 449−473. https://doi.org/10.1016/j.dsr.2005.12.009

Dushaw, B. D., P. F. Worcester, and M. A. Dzieciuch, 2011: On the predictability of mode-1 internal tides. Deep-Sea Res. I, 58, 677−698. https://doi.org/10.1016/j.dsr.2011.04.00

Dushaw, B.D., 2015: An empirical model for mode-1 internal tides derived from satellite altimetry: Computing accurate tidal predictions at arbitrary points over the world oceans. University of Washington, Applied Physics Laboratory Tech. Memo APL-UW 1-15, 114 pp. https://doi.org/10.5281/zenodo.18726454

Dushaw, B. D., F. Gaillard, and T. Terre, 2017. Acoustic tomography in the Canary Basin: Meddies and tides, J. Geophys. Res., 122, 8983−9003. https://doi.org/10.1002/2017JC013356

Dushaw, B. D., 2022: Surprises in physical oceanography: Contributions from ocean acoustic tomography. Tellus, 74A, 33−67. https://doi.org/10.16993/tellusa.39

Dushaw, B. D., and D. Menemenlis, 2023: Resonant diurnal internal tides in the North Atlantic: 2. Modeling. Geophys. Res. Lett., 50, e2022GL101193. https://doi.org/10.1029/2022GL101193

Acknowledgments

This work was supported by grant NNX13AE27G (2013–2015) from the National Aeronautics and Space Administration. The farfield component of the Hawaiian Ocean Mixing Experiment and the deployment of the associated acoustic tomography arrays was supported by grants OCE-9819527 and OCE-9819525 from the National Science Foundation. The project for the tidal analysis of the altimetry data was initially supported by grant OCE-0647743 from the National Science Foundation. ONR grants N00014-09-1-0446 and N00014-12-1-0183 supported work on acoustics and acoustic tomography in the central North Pacific and Philippine Sea. Analysis of AMODE tides, barotropic and baroclinic, was supported by NSF grants OCE-9415650 and OCE-9720680. I am grateful to Z. Zhao for providing the estimates of internal tides from the IWAP program. P. Worcester and M. Dzieciuch provided the tomography data obtained in the Philippine Sea in 2009 and 2010–2011.

Unpack Supplements.tgz with: tar xfz Supplements.tgz. This will make a directory "Supplements" with subdirectories.

DATA DOWNLOAD INTEGRITY:

ls -l Supplements.tgz
-rw-r--r-- 1 dushaw users 2436381685 Sep  8 10:50 Supplements.tgz

md5sum Supplements.tgz
a4466954ce0db1ffcdc8bf214595ee62  Supplements.tgz

Subdirectories in the Supplements tarball are:

matlab: A directory of handy/useful matlab scripts

Poster: A PDF of a poster presented at AGU Ocean Sciences

Thermistors: Thermistor data of internal tides from several experiments

Global_Solution: Harmonic constants for the six largest tidal constituents in the global solution described in the PDF Technical Memorandum.  This spectral solution (in frequency and wavenumber) is stored in matlab data files.

Animations:  Global and regional animations of mode-1 internal tides and various constituents.  Animations are of omni-directional, northward, eastward, westward, and southward wavenumbers.  Animations are for sea-surface height (SSH) or internal amplitude (AMP).  The internal amplitude is the more physical quantity, since SSH variations can be affected by the changing oceanic stratification. 

Tomography: Internal tide estimates by ocean acoustic tomography estimated from several experiments.

Global_modes: The basic properties of internal tide modes derived from climatology over the world's oceans.