Brian Dushaw


Acoustics Department




An Empirical Model for Mode-1 Internal Tides

APL-UW Technical Memorandum 1-15

Sea Surface Height

Mode Amplitude



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) [B. D. Dushaw, P. F. Worcester, and M. A. Dzieciuch, 2011. On the predictability of mode-1 internal tides, Deep-Sea Res. I, 58, 677−698]. 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.

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.

Questions concerning this report may be addressed to:

Brian D. Dushaw

Applied Physics Laboratory

University of Washington

1013 N.E. 40th Street, Seattle, WA 98105-6698


(206) 543-1300

After 1 September 2015:

Brian D. Dushaw

The Nansen Environmental and Remote Sensing Center

Thormøhlens gate 47

Bergen, Norway N-5006