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All sourcesNASA NTRSDOE OSTI
NASA NTRS2017

Using an Altimeter-Derived Internal Tide Model to Remove Tides from in Situ Data

Internal waves at tidal frequencies, i.e., the internal tides, are a prominent source of variability in the ocean associated with significant vertical isopycnal displacements and currents. Because the isopycnal displacements are caused by ageostrophic dynamics, they contribute uncertainty to geostrophic transport inferred from vertical profiles in the ocean. Here it is demonstrated that a newly developed model of the main semidiurnal (M2) internal tide derived from satellite altimetry may be used to partially remove the tide from vertical profile data, as measured by the reduction of steric height variance inferred from the profiles. It is further demonstrated that the internal tide model can account for a component of the near-surface velocity as measured by drogued drifters. These comparisons represent a validation of the internal tide model using independent data and highlight its potential use in removing internal tide signals from in situ observations.

Zaron, Edward D.↗
NASA NTRS1978

The inverse problem: Ocean tides derived from earth tide observations

Indirect mapping ocean tides by means of land and island-based tidal gravity measurements is presented. The inverse scheme of linear programming is used for indirect mapping of ocean tides. Open ocean tides were measured by the numerical integration of Laplace's tidal equations.

Kuo, J. T.↗
NASA NTRS1978

What can earth tide measurements tell us about ocean tides or earth structure?

Current experimental problems in Earth tides are reviewed using comparisons of tidal gravity and tilt measurements in Europe with loading calculations are examples. The limitations of present day instrumentation and installation techniques are shown as well as some of the ways in which they can be improved. Many of the geophysical and oceanographic investigations that are possible with Earth tide measurements are discussed with emphasis on the percentage accuracies required in the measurements in order to obtain new information about Earth or its oceans.

Baker, T. F.↗
NASA NTRS1993

The effect of ocean tides on the earth's rotation as predicted by the results of an ocean tide model

The published ocean tidal angular momentum results of Seiler (1991) are used to predict the effects of the most important semidiurnal, diurnal, and long period ocean tides on the earth's rotation. The separate, as well as combined, effects of ocean tidal currents and sea level height changes on the length-of-day, UT1, and polar motion are computed. The predicted polar motion results reported here account for the presence of the free core nutation and are given in terms of the motion of the celestial ephemeris pole so that they can be compared directly to the results of observations. Outside the retrograde diurnal tidal band, the summed effect of the semidiurnal and diurnal ocean tides studied here predict peak-to-peak polar motion amplitudes as large as 2 mas. Within the retrograde diurnal tidal band, the resonant enhancement caused by the free core nutation leads to predicted polar motion amplitudes as large as 9 mas.

Gross, Richard S.↗
DOE OSTI2025

DS-TIDE: Harnessing Dynamical Systems for Efficient Time-Independent Differential Equation Solving

Time-Independent Differential Equations (TIDEs) are central to modeling equilibrium behavior across a wide range of scientific and engineering domains, from electrostatics to porous media flow. Conventional numerical solvers offer reliable solutions but incur significant computational costs due to fine-grained discretization and iterative procedures. Machine learning-based approaches address this by replacing iterative solving processes with one-time inference; however, their sophisticated models require extensive training resources that often exceed those of traditional solvers. Consequently, designing a TIDE solver that achieves high accuracy, broad applicability, and exceptional computational efficiency remains a fundamental challenge. In this paper, we propose DS-TIDE, a novel hardware solver that is inspired by, and subsequently leverages, the intrinsic connection between Dynamical Systems (DS) and Differential Equations (DEs) to efficiently and accurately solve TIDEs. DS-TIDE employs a CMOS-compatible DS-based processor, whose physical states evolve under carefully designed DE-driven dynamics and naturally converge to equilibrium -- the solution of the target TIDE -- within ~1µs on a ~1-watt DS-TIDE processor. To enhance expressivity, DS-TIDE incorporates Heterogeneous Dynamics with Temporal Layering (HDTL), which solves TIDEs through a three-stage DS evolution -- conditioning, solving, and decoding -- each governed by specialized dynamics. The entire evolution process is analogous to an infinitely deep neural network temporally unrolled, offering the system the capability of representing complex equations. Furthermore, DS-TIDE is equipped with an on-device DS-DE Auto-Alignment mechanism that dynamically adapts intrinsic hardware dynamics within milliseconds, effectively aligning the system’s dynamics to diverse target DEs. Experimental results across TIDEs from a wide range of scientific and engineering domains demonstrate that DS-TIDE achieves ~10^3× speedup, ~10^5× energy savings, and competitive or superior accuracy compared to state-of-the-art numerical and ML-based solvers.

Liu, Chuan↗
NASA NTRS2006

Application of the Convolution Formalism to the Ocean Tide Potential: Results from the Gravity and Recovery and Climate Experiment (GRACE)

A computationally efficient approach to reducing omission errors in ocean tide potential models is derived and evaluated using data from the Gravity Recovery and Climate Experiment (GRACE) mission. Ocean tide height models are usually explicitly available at a few frequencies, and a smooth unit response is assumed to infer the response across the tidal spectrum. The convolution formalism of Munk and Cartwright (1966) models this response function with a Fourier series. This allows the total ocean tide height, and therefore the total ocean tide potential, to be modeled as a weighted sum of past, present, and future values of the tide-generating potential. Previous applications of the convolution formalism have usually been limited to tide height models, but we extend it to ocean tide potential models. We use luni-solar ephemerides to derive the required tide-generating potential so that the complete spectrum of the ocean tide potential is efficiently represented. In contrast, the traditionally adopted harmonic model of the ocean tide potential requires the explicit sum of the contributions from individual tidal frequencies. It is therefore subject to omission errors from neglected frequencies and is computationally more intensive. Intersatellite range rate data from the GRACE mission are used to compare convolution and harmonic models of the ocean tide potential. The monthly range rate residual variance is smaller by 4-5%, and the daily residual variance is smaller by as much as 15% when using the convolution model than when using a harmonic model that is defined by twice the number of parameters.

models↗
NASA NTRS2023

Terdiurnal Radiational Tides

Terdiurnal atmospheric tides induce an S 3 radiational ocean tide, similar to radiational tides S 1 and S 2 in the diurnal and semidiurnal bands. Although of small amplitude, the terdiurnal tide has some intriguing properties. The tide has an unusually pronounced seasonal variation, manifested by annual sidelines here denoted R 3 and T 3 , which causes the tide to nearly vanish during times near an equinox. Forcing is generally largest in the winter hemisphere. Complicating matters, the two sideline frequencies coincide with those of nonlinear compound tides SK 3 and SP 3 . Whether radiational tides or nonlinear tides (or both) are appearing at any given tide gauge can usually be determined by the relative amplitudes and phase differences of the two sidelines. The amplitudes of R 3 and T 3 are generally comparable; the amplitudes of SK 3 and SP 3 are not. Proper identification can lead to a small improvement in tidal prediction, but more importantly can lead to improved physical interpretation. An example from recent measurements under the Ross Ice Shelf bears on the role of nonlinearity in interactions between the ocean tide and the floating ice shelf.

Atmospheric waves↗
NASA NTRS2003

Non-Migrating Tides, with Zonally Symmetric Component, Generated in the Mesosphere

For comparison with measurements from the TIMED satellite and coordinated ground based observations, we discuss results from our Numerical Spectral Model (NSM) that incorporates the Doppler Spread Parameterization (Hines, 1997) for small-scale gravity waves (GWs). The NSM extends from the ground into the thermosphere and describes the major dynamical features of the atmosphere including the wave driven equatorial oscillations (QBO and SAO), and the seasonal variations of tides and planetary waves. With emphasis on the non-migrating tides, having periods of 24 and 12 hours, we discuss our modeling results that account for the classical migrating solar excitation sources only. As reported earlier, the NSM reproduces the observed seasonal variations and in particular the large equinoctial maxima in the amplitude of the migrating diurnal tide at altitudes around 90 km. Filtering of the tide by the zonal circulation and GW momentum deposition was identified as the cause. The GWs were also shown to produce a strong non-linear interaction between the diurnal and semi-diurnal tides. Confined largely to the mesosphere, the NSM produces through dynamical interactions a relatively large contribution of non-migrating tides. A striking feature is seen in the diurnal and semi-diurnal oscillations of the zonal mean (m = 0). Eastward propagating tides are also generated for zonal wave numbers m = 1 to 4. When the NSM is run without GWs, the amplitudes for the non-migrating tides, including m = 0, are generally small. Planetary wave interaction and non-linear coupling that involves the filtering of GWs and related height integration of dynamical features are discussed as possible mechanisms for generating these non-migrating tides in the NSM. As is the case for the solar migrating tides, the non-migrating tides reveal persistent seasonal variations. Under the influence of the QBO and SAO, interannual variations are produced.

Mayr, H. G.↗
NASA NTRS2003

Tides and Decadal Variability

This paper reviews the mechanisms by which oceanic tides and decadal variability in the oceans are connected. We distinguish between variability caused by tides and variability observed in the tides themselves. Both effects have been detected at some level. The most obvious connection with decadal timescales is through the 18.6-year precession of the moon's orbit plane. This precession gives rise to a small tide of the same period and to 18.6-year modulations in the phase and amplitudes of short-period tides. The 18.6-year "node tide" is very small, no more than 2 cm anywhere, and in sea level data it is dominated by the ocean's natural Variability. Some authors have naively attributed climate variations with periods near 19 years directly to the node tide, but the amplitude of the tide is too small for this mechanism to be operative. The more likely explanation (Loder and Garrett, JGR, 83, 1967-70, 1978) is that the 18.6-y modulations in short-period tides, especially h e principal tide M2, cause variations in ocean mixing, which is then observed in temperature and other climatic indicators. Tidally forced variability has also been proposed by some authors, either in response to occasional (and highly predictable) tidal extremes or as a nonlinear low-frequency oscillation caused by interactions between short-period tides. The former mechanism can produce only short-duration events hardly more significant than normal tidal ranges, but the latter mechanism can in principle induce low-frequency oscillations. The most recent proposal of this type is by Keeling and Whorf, who highlight the 1800-year spectral peak discovered by Bond et al. (1997). But the proposal appears contrived and should be considered, in the words of Munk et al. (2002), "as the most likely among unlikely candidates."

Ray, Richard D.↗
NASA NTRS2021

Accuracy Assessment of Global Internal-Tide Models Using Satellite Altimetry Models Using Satellite Altimetry

Altimeter measurements are corrected for several geophysical parameters in order to access ocean signals of interest, like mesoscale or sub-mesoscale variability. The ocean tide is one of the most critical corrections due to the amplitude of the tidal elevations and to the aliasing phenomena of high-frequency signals into the lower-frequency band, but the internal-tide signatures at the ocean surface are not yet corrected globally. Internal tides can have a signature of several centimeters at the surface with wavelengths of about 50–250 km for the first mode and even smaller scales for higher-order modes. The goals of the upcoming Surface Water Ocean Topography (SWOT) mission and other high-resolution ocean measurements make the correction of these small-scale signals a challenge, as the correction of all tidal variability becomes mandatory to access accurate measurements of other oceanic signals. In this context, several scientific teams are working on the development of new internal-tide models, taking advantage of the very long altimeter time series now available, which represent an unprecedented and valuable global ocean database. The internal-tide models presented here focus on the coherent internal-tide signal and they are of three types: empirical models based upon analysis of existing altimeter missions, an assimilative model and a three-dimensional hydrodynamic model. A detailed comparison and validation of these internal-tide models is proposed using existing satellite altimeter databases. The analysis focuses on the four main tidal constituents: M2, K1, O1 and S2. The validation process is based on a statistical analysis of multi-mission altimetry including Jason-2 and Cryosphere Satellite-2 data. The results show a significant altimeter variance reduction when using internal-tide corrections in all ocean regions where internal tides are generating or propagating. A complementary spectral analysis also gives some estimation of the performance of each model as a function of wavelength and some insight into the residual non-stationary part of internal tides in the different regions of interest. This work led to the implementation of a new internal-tide correction (ZARON'one) in the next geophysical data records version-F (GDR-F) standards.

Loren Carrere↗
NASA NTRS2015

Atmospheric Tides in Gale Crater, Mars

Atmospheric tides are the primary source of daily air pressure variation at the surface of Mars. These tides are forced by solar heating of the atmosphere and modulated by the presence of atmospheric dust, topography, and surface albedo and thermal inertia. This results in a complex mix of sun-synchronous and nonsun- synchronous tides propagating both eastward and westward around the planet in periods that are integer fractions of a solar day. The Rover Environmental Monitoring Station on board the Mars Science Laboratory has observed air pressure at a regular cadence for over 1 Mars year and here we analyze and diagnose atmospheric tides in this pressure record. The diurnal tide amplitude varies from 26 to 63 Pa with an average phase of 0424 local true solar time, while the semidiurnal tide amplitude varies from 5 to 20 Pa with an average phase of 0929. We find that both the diurnal and semidiurnal tides in Gale Crater are highly correlated to atmospheric opacity variations at a value of 0.9 and to each other at a value of 0.77, with some key exceptions occurring during regional and local dust storms. We supplement our analysis with MarsWRF general circulation modeling to examine how a local dust storm impacts the diurnal tide in its vicinity. We find that both the diurnal tide amplitude enhancement and regional coverage of notable amplitude enhancement linearly scales with the size of the local dust storm. Our results provide the first long-term record of surface pressure tides near the martian equator.

Guzewich, Scott D,↗
NASA NTRS2013

Precise Comparisons of Bottom-Pressure and Altimetric Ocean Tides

A new set of pelagic tide determinations is constructed from seafloor pressure measurements obtained at 151 sites in the deep ocean. To maximize precision of estimated tides, only stations with long time series are used; median time series length is 567 days. Geographical coverage is considerably improved by use of the international tsunami network, but coverage in the Indian Ocean and South Pacific is still weak. As a tool for assessing global ocean tide models, the data set is considerably more reliable than older data sets : the root-mean-square difference with a recent altimetric tide model is approximately 5 mm for the M2 constituent. Precision is sufficiently high to allow secondary effects in altimetric and bottom-pressure tide differences to be studied. The atmospheric tide in bottom pressure is clearly detected at the S1, S2, and T2 frequencies. The altimetric tide model is improved if satellite altimetry is corrected for crustal loading by the atmospheric tide. Models of the solid body tide can also be constrained. The free corenutation effect in the K1 Love number is easily detected, but the overall estimates are not as accurate as a recent determination with very long baseline interferometry.

tides↗
NASA NTRS1986

New aspects of the equilibrium pole tide

A new spherical harmonic algorithm is developed for the calculation of the loading and self-gravitating equilibrium pole tide. Based on a suggestion of Dahlen (1976), this approach minimizes the distortions in tide height caused by an incomplete representation of the ocean function. With slight modification this approach easily could be used to compute self-gravitating and loading lunisolar tides as well. Using the algorithm, the static pole tide is compared with tide observations at a variety of locations around the world, and statistically significant evidence for pole tide enhancements is found in midocean as well as the shallow seas. Also included is a reinvestigation of the effect of the static tide on the Chandler-wobble period. The difference between the wobble period of an oceanless elastic earth with a fluid core (Smith and Dahlen, 1981) and the period of an earth minus static oceans yields a 7.4-day discrepancy. It is concluded from tide observations that much of the discrepancy can probably be accounted for by nonequilibrium pole-tide behavior in the deep oceans.

Dickman, S. R.↗
NASA NTRS1995

A numerical model of nonmigrating diurnal tides between the surface and 65 km

Observations of surface pressure and middle atmosphere temperatures and winds indicate that a substantial nonmigrating component is present in the diurnal tide. The nonmigrating tides, which propagate with a zonal phase speed that is different from the earth's rotation, are attributed to the diurnal heating of geographically fixed sources. In this study we utilize a classical tidal model to examine the propagation characteristics of diurnal tides. The global fields of tropospheric sensible, radiative, and latent heating used to drive the model are supplied from summer and winter diurnal climatologies of the National Center for Atmospheric Research (NCAR) Community Climate Model (CCM2). A novel aspect of this study is the focus on the relative importance of the nonmigrating components. The classical model successfully reproduces many observed features of the low-latitude diurnal surface pressure tides. In the middle atmosphere, the simulated migrating (or sun-synchronous) tide shows qualitative agreement with November-March Limb Infrared Monitor of the Stratosphere (LIMS) observations. Tropospheric solar heating is clearly the dominant driving force for the migrating tide, with secondary contributions from boundary-layer sensible heating and tropospheric latent heat release. The leading modes of the zonal mean tide are also driven chiefly by tropospheric solar heating. The higher-order modes of the zonal mean and eastward propagating tides may be attributed to the joint effects of tropospheric solar heating, sensible heating, and latent heat release. The LIMS and other data reveal features that cannot be explained or examined within the context of the classical model used in the present study. These include upward phase propagation, vertical attenuation, and temporal variations in the migrating diurnal tide.

Lieberman, Ruth S.↗
NASA NTRS1994

Geographical representation of radial orbit perturbations due to ocean tides: Implications for satellite altimetry

In analogy to the geographical representation of the zeroth-order radial orbit perturbations due to the static geopotential, similar relationships have been derived for radial orbit perturbations due to the ocean tides. At each location these perturbations are seen to be coherent with the tide height variations. The study of this singularity is of obvious importance to the estimation of ocean tides from satellite altimeter data. We derive analytical expressions for the sensitivity of altimeter derived ocean tide models to the ocean tide force model induced errors in the orbits of the altimeter satellite. In particular, we focus on characterizing and quantifying the nonresonant tidal orbit perturbations, which cannot be adjusted into the empirical accelerations or radial perturbation adjustments commonly used during orbit determination and in altimeter data processing. As an illustration of the utility of this technique, we study the differences between a TOPEX/POSEIDON-derived ocean tide model and the Cartwright and Ray 1991 Geosat model. This analysis shows that nearly 60% of the variance of this difference for M(sub 2) can be explained by the Geosat radial orbit eror due to the omission of coefficients from the GEM-T2 background ocean tide model. For O(sub 1), K(sub 1), S(sub 2), and K(sub 2) the orbital effects account for approximately 10 to 40% of the variances of these differences. The utility of this technique to assessment of the ocean tide induced errors in the TOPEX/POSEIDON-derived tide models is also discussed.

Bettadpur, Srinivas V.↗