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NASA NTRS1993

Dynamic ocean-tide effects on Earth's rotation

This article develops 'broad-band' Liouville equations which are capable of determining the effects on the rotation of the Earth of a periodic excitation even at frequencies as high as semi-diurnal; these equations are then used to predict the rotational effects of altimetric, numerical and 32-constituent spherical harmonic ocean-tide models. The rotational model includes a frequency-dependent decoupled core, the effects of which are especially marked near retrograde diurnal frequencies; and a fully dynamic oceanic response, whose effects appear to be minor despite significant frequency dependence. The model also includes solid-earth effects which are frequency dependent as the result of both anelasticity at long periods and the fluid-core resonance at nearly diurnal periods. The effects of both tidal inertia and relative angular momentum on Earth rotation (polar motion, length of day, 'nutation' and Universal Time) are presented for 32 long- and short-period ocean tides determined as solutions to the author's spherical harmonic tide theory. The lengthening of the Chandler wobble period by the pole tide is also re-computed using the author's full theory. Additionally, using the spherical harmonic theory, tidal currents and their effects on rotation are determined for available numerical and altimetric tide height models. For all models, we find that the effects of tidal currents are at least as important as those of tide height for diurnal and semi-diurnal constituents.

Dickman, S. R.↗
NASA NTRS1998

Lunar and Solar Torques on the Oceanic Tides

A general framework for calculating lunar and solar torques on the oceanic tides is developed in terms of harmonic constituents. Axial torques and their associated angular momentum and earth-rotation variations are deduced from recent satellite-altimeter and satellite-tracking tide solutions. Torques on the prograde components of the tide produce the familiar secular braking of the rotation rate. The estimated secular acceleration is approximately -1300 sec/century(sup 2) (less 4% after including atmospheric tides); the implied rate of change in the length of day is 2.28 milliseconds/century. Torques on the retrograde components of the tide produce periodic rotation variations at twice the tidal frequency. Interaction torques, e.g. solar torques on lunar tides, generate a large suite of rotation-rate variations at sums and differences of the original tidal frequencies. These are estimated for periods from 18.6 years to quarter-diurnal. At subdaily periods the angular momentum variations are 5 to 6 orders of magnitude smaller than the variations caused by ocean tidal currents.

Ray, Richard D.↗
NASA NTRS1999

Geodynamic Effects of Ocean Tides: Progress and Problems

Satellite altimetry, particularly Topex/Poseidon, has markedly improved our knowledge of global tides, thereby allowing significant progress on some longstanding problems in geodynamics. This paper reviews some of that progress. Emphasis is given to global-scale problems, particularly those falling within the mandate of the new IERS Special Bureau for Tides: angular momentum, gravitational field, geocenter motion. For this discussion I use primarily the new ocean tide solutions GOT99.2, CSR4.0, and TPXO.4 (for which G. Egbert has computed inverse-theoretic error estimates), and I concentrate on new results in angular momentum and gravity and their solid-earth implications. One example is a new estimate of the effective tidal Q at the M_2 frequency, based on combining these ocean models with tidal estimates from satellite laser ranging. Three especially intractable problems are also addressed: (1) determining long-period tides in the Arctic [large unknown effect on the inertia tensor, particularly for Mf]; (2) determining the global psi_l tide [large unknown effect on interpretations of gravimetry for the near-diurnal free wobble]; and (3) determining radiational tides [large unknown temporal variations at important frequencies]. Problems (2) and (3) are related.

Richard, Ray↗
NASA NTRS1992

Constraints on Energy Dissipation in the Earth's Body Tide From Satellite Tracking and Altimetry

The phase lag by which the earth's body tide follows the tidal potential is estimated for the principal lunar semidiurnal tide M(sub 2). The estimate results from combining recent tidal solutions from satellite tracking data and from Topex/Poseidon satellite altimeter data. Each data type is sensitive to the body-tide lag: gravitationally for the tracking data, geometrically for the altimetry. Allowance is made for the lunar atmospheric tide. For the tidal potential Love number kappa(sub 2) we obtain a lag epsilon of 0.20 deg +/- 0.05 deg, implying an effective body-tide Q of 280 and body-tide energy dissipation of 110 +/- 25 gigawatts.

Ray, Richard D.↗
NASA NTRS2011

The Contribution of Io-Raised Tides to Europa's Diurnally-Varying Surface Stresses

Europa's icy surface records a rich history of geologic activity, Several features appear to be tectonic in origin and may have formed in response to Europa's daily-varying tidal stress [I]. Strike-slip faults and arcuate features called cycloids have both been linked to the patterns of stress change caused by eccentricity and obliquity [2J[3]. In fact, as Europa's obliquity has not been directly measured, observed tectonic patterns arc currently the best indicators of a theoretically supported [4] non-negligible obliquity. The diurnal tidal stress due to eccentricity is calculated by subtracting the average (or static) tidal shape of Europa generated by Jupiter's gravitational field from the instantaneous shape, which varies as Europa moves through its eccentric orbit [5]. In other words, it is the change of shape away from average that generates tidal stress. One might expect tidal contributions from the other large moons of Jupiter to be negligible given their size and the height of the tides they raise on Europa versus Jupiter's mass and the height of the tide it raises on Europa, However, what matters for tidally-induced stress is not how large the lo-raised bulge is compared to the Jupiter-raised bulge but rather the differences bet\Veen the instantaneous and static bulges in each case. For example, when Europa is at apocenter, Jupiter raises a tide 30m lower than its static tide. At the same time, 10 raises a tide about 0.5m higher than its static tide. Hence, the change in Io's tidal distortion is about 2% of the change in the Jovian distortion when Europa is at apocenter

Rhoden, Alyssa Rose↗
NASA NTRS2011

Fortnightly Earth Rotation, Ocean Tides, and Mantle Anelasticity

Sustained accurate measurements of earth rotation are one of the prime goals of Global Geodetic Observing System (GGOS). We here concentrate on the fortnightly (Mf) tidal component of earth-rotation data to obtain new results concerning anelasticity of the mantle at this period. The study comprises three parts: (1) a new determination of the Mf component of polar motion and length-of-day from a multi-decade time series of space-geodetic data; (2) the use of the polar-motion determination as one constraint in the development of a hydrodynamic ocean model of the Mf tide; and (3) the use of these results to place new constraints on mantle anelasticity. Our model of the Mf ocean tide assimilates more than fourteen years of altimeter data from the Topex/Poseidon and Jason-1 satellites. The polar motion data, plus tide-gauge data and independent altimeter data, give useful additional information, with only the polar motion putting constraints on tidal current velocities. The resulting ocean-tide model, plus the dominant elastic body tide, leaves a small residual in observed length-of-day caused by mantle anelasticity. The inferred effective tidal 0 of the anelastic body tide is 90 and is in line with a omega-alpha frequency dependence with alpha in the range 0.2--0.3.

Ray, Richard D.↗
NASA NTRS2012

Fortnightly Ocean Tides, Earth Rotation, and Mantle Anelasticity

The fortnightly Mf ocean tide is the largest of the long-period tides (periods between 1 week and 18.6 years), but Mf is still very small, generally 2 cm or less. All long-period tides are thought to be near equilibrium with the astronomical tidal potential, with an almost pure zonal structure. However, several lines of evidence point to Mf having a significant dynamic response to forcing. We use a combination of numerical modeling, satellite altimetry, and observations of polar motion to determine the Mf ocean tide and to place constraints on certain global properties, such as angular momentum. Polar motion provides the only constraints on Mf tidal currents. With a model of the Mf ocean tide in hand, we use it to remove the effects of the ocean from estimates of fortnightly variations in length-of-day. The latter is dominated by the earth's body tide, but a small residual allows us to place new constraints on the anelasticity of the earth's mantle. The result gives the first experimental confirmation of theoretical predictions made by Wahr and Bergen in 1986.

Ray, Richard↗
NASA NTRS2014

Thermal Tides During the 2001 Martian Global-Scale Dust Storm

The 2001 (Mars Year 25) global dust storm radically altered the dynamics of the Martian atmosphere. Using observations from the Thermal Emission Spectrometer onboard the Mars Global Surveyor spacecraft and Mars WRF general circulation model simulations, we examine the changes to thermal tides and planetary waves caused by the storm. We find that the extratropical diurnal migrating tide is dramatically enhanced during the storm, particularly in the southern hemisphere, reaching amplitudes of more than 20 K. The tropical diurnal migrating tide is weakened to almost undetectable levels. The diurnal Kelvin waves are also significantly weakened, particularly during the period of global expansion at Ls=200deg-210deg. In contrast, the westward propagating diurnal wavenumber 2 tide strengthens to 4-8 K at altitudes above 30km. The wavenumber 1 stationary wave reaches amplitudes of 10-12 K at 50deg-70degN, far larger than is typically seen during this time of year. The phase of this stationary wave and the enhancement of the diurnal wavenumber 2 tide appear to be responses to the high-altitude westward propagating equatorial wavenumber 1 structure in dust mixing ratio observed during the storm in previous works. This work provides a global picture of dust storm wave dynamics that reveals the coupling between the tropics and high-latitude wave responses. We conclude that the zonal distribution of thermotidal forcing from atmospheric aerosol concentration is as important to understanding the atmospheric wave response as the total global mean aerosol optical depth.

Thermal tides↗
NASA NTRS1978

Lunar tidal acceleration obtained from satellite-derived ocean tide parameters

Observation equations for the M2 ocean tide are computed from Geos 3 data for the long periodic variations of the inclination and node of the orbit. M2 ocean tide parameter values C22+ = 3.23 + or - 0.25 cm, epsilon 22+ = 331 + or - 6 deg, and epsilon 42+ = 113 + or - 6 deg are determined. With the assumption of zero solid tide phase lag, the lunar tidal acceleration is mostly (85%) due to the C22+ term in the expansion of the M2 tide with additional small contributions from the O1 and N2 tides. The calculated value for the tidal acceleration in lunar longitude is -27.4 + or - 3 arc sec/sq (100 yr) which is similar to values determined from astronomical data. The mean elements of Geos 3 are presented in tabular form.

Goad, C. C.↗
NASA NTRS1979

M2, S2, K1 models of the global ocean tide

Ocean tidal signals appear in many geophysical measurements. Geophysicists need realistic tidal models to aid in interpretation of their data. Because of the closeness to resonance of dissipationless ocean tides, it is difficult for numerical models to correctly represent the actual open ocean tide. As an approximate solution to this problem, test functions derived by solving Laplace's Tidal Equations with ocean loading and self gravitation are used as a basis for least squares dynamic interpolation of coastal and island tidal data for the constituents M2, S2, and Kl. The resulting representations of the global tide are stable over at least a ?5% variation in the mean depth of the model basin, and they conserve mass. Maps of the geocentric tide, the induced free space potential, the induced vertical component of the solid earth tide, and the induced vertical component of the gravitational field for each contituent are presented.

Parke, M. E.↗
NASA NTRS1986

Modelling the pole tide and its effect on the earth's rotation

The pole tide is the response of the ocean to incremental centrifugal forces associated with the Chandler wobble. The tide has a potentially important effect on the period and damping of the wobble, but it is at present not well constrained by observations. Here, both analytical and numerical models for the pole tide are constructed. The analytical models consider the tide first in a global ocean and then in an enclosed basin on a beta-plane. The results are found to approach equilibrium linearly with decreasing frequency and inversely with increasing basin depth. The numerical models solve Laplace's tidal equations over the world's oceans using realistic continental boundaries and bottom topography. The results indicate that the effects of non-equilibrium portion of the deep ocean tide on the Chandler wobble period and damping are negligible.

Carton, J. A.↗
NASA NTRS1991

Ocean tide models for satellite geodesy and Earth rotation

A theory is presented which predicts tides in turbulent, self-gravitating, and loading oceans possessing linearized bottom friction, realistic bathymetry, and continents (at coastal boundaries no-flow conditions are imposed). The theory is phrased in terms of spherical harmonics, which allows the tide equations to be reduced to linear matrix equations. This approach also allows an ocean-wide mass conservation constraint to be applied. Solutions were obtained for 32 long and short period luni-solar tidal constituents (and the pole tide), including the tidal velocities in addition to the tide height. Calibrating the intensity of bottom friction produces reasonable phase lags for all constituents; however, tidal amplitudes compare well with those from observation and other theories only for long-period constituents. In the most recent stage of grant research, traditional theory (Liouville equations) for determining the effects of angular momentum exchange on Earth's rotation were extended to encompass high-frequency excitations (such as short-period tides).

Dickman, Steven R.↗
NASA NTRS1990

Orthogonal stack of global tide gauge sea level data

Yearly and monthly tide gauge sea level data from around the globe are fitted to numerically generated equilibrium tidal data to search for the 18.6 year lunar tide and 14 month pole tide. Both tides are clearly evident in the results, and their amplitudes and phases are found to be consistent with a global equilibrium response. Global, monthly sea level data from outside the Baltic sea and Gulf of Bothnia are fitted to global atmospheric pressure data to study the response of the ocean to pressure fluctuations. The response is found to be inverted barometer at periods greater than two months. Global averages of tide gauge data, after correcting for the effects of post glacial rebound on individual station records, reveal an increase in sea level over the last 80 years of between 1.1 mm/yr and 1.9 mm/yr.

Trupin, A.↗
NASA NTRS1993

Global ocean tide models on the eve of Topex/Poseidon

Some existing global ocean tide models that can provide tide corrections to Topex/Poseidon altimeter data are described. Emphasis is given to the Schwiderski and Cartwright-Ray models, as these are the most comprehensive, highest resolution models, but other models that will soon appear are mentioned. Differences between models for M2 often exceed 10 cm over vast stretches of the ocean. Comparisons to 80 selected pelagic and island gauge measurements indicate the Schwiderski model is more accurate for the major solar tides, Cartwright-Ray for the major lunar tides. The adequacy of available tide models for studying basin-scale motions is probably marginal at best.

Ray, Richard D.↗
NASA NTRS1990

Ocean tides for satellite geodesy

Spherical harmonic tidal solutions have been obtained at the frequencies of the 32 largest luni-solar tides using prior theory of the author. That theory was developed for turbulent, nonglobal, self-gravitating, and loading oceans possessing realistic bathymetry and linearized bottom friction; the oceans satisfy no-flow boundary conditions at coastlines. In this theory the eddy viscosity and bottom drag coefficients are treated as spatially uniform. Comparison of the predicted degree-2 components of the Mf, P1, and M2 tides with those from numerical and satellite-based tide models allows the ocean friction parameters to be estimated at long and short periods. Using the 32 tide solutions, the frequency dependence of tidal admittance is investigated, and the validity of sideband tide models used in satellite orbit analysis is examined. The implications of admittance variability for oceanic resonances are also explored.

Dickman, S. R.↗
NASA NTRS1998

Wind Forcing of the North Sea Pole Tide

The Chandler wobble of the earth's rotation has a period near 14 months and sets up the 0.5 cm amplitude pole tide in the deep oceans, However, the pole tide is anomalously large in the North Sea, where the amplitude increases sharply up to 3 cm along the continental coast. It is shown here that the sea levels are well correlated with winds at the pole tide frequency. The Princeton Ocean Model is used to investigate the response of the North Sea to wind forcing. The barotropic numerical ocean model depicts realistic coastlines and bathymetry at 5 ft x 5 ft resolution, with 97 x 73 grid points. The monthly mean wind fields for the 40-year period (1958-1997) from the National Centers for Atmospheric Prediction (NCEP) reanalysis were used to force the model. The winds were converted to stress with a neutral drag coefficient that varied linearly with windspeed (instead of using the NCEP windstress). A 5-day simulation was made for each month until the resulting flow regime came into equilibrium, and model water levels at various station locations were saved for comparison with tidal-gauge observed sea levels from the Permanent Service for Mean Sea Level (PSMSL). The comparison is made for 10 North Sea stations with high quality tide gauge data. We find: (1) good agreement in annual and semi-annual phases and in the trend of amplitude w.r.t. latitude; (2) more importantly for this study, the model-predicted and observed non-seasonal sea level variations show a very significant temporal correlation as well as spectral coherence. However, a large amplitude difference exists between the two sets -- the overall amplitude variability of the observed is generally a factor of 2-3 larger than the model prediction (this same phenomenon has been reported in ocean circulation studies, although the cause is not yet clear.) Our results indicate that the wind forcing is the main cause of the observed large pole tide in the North Sea.

OConnor, W.↗
NASA NTRS1998

Lunar and Solar Torques on the Oceanic Tides

Brosche and Seiler recently suggested that direct lunar and solar tidal torques on the oceanic tides play a significant role in the earth's short-period angular momentum balance ("short-period" here meaning daily and sub-daily). We reexamine that suggestion here, concentrating on axial torques and hence on variations in rotation rate. Only those spherical harmonic components of the ocean tide having the same degree and order as the tidal potential induce nonzero torques. Prograde components (those moving in the same direction as the tide-generating body) produce the familiar secular braking of the earth's rotation. Retrograde components, however, produce rapid variations in UTI at twice the tidal frequency. There also exist interaction torques between tidal constituents, e.g. solar torques on lunar tides. They generate UTI variations at frequencies equal to the sums and differences of the original tidal frequencies. We give estimates of the torques and angular momentum variations for each of the important regimes, secular to quarter-diurnal. For the M(sub 2) potential acting on the M(sub 2) ocean tide, we find an associated angular momentum variation of amplitude 3 x 10(exp 19) N m. This is 5 to 6 orders of magnitude smaller than the angular momentum variations associated with tidal currents. We conclude that these torques do not play a significant role in the short-period angular momentum balance.

Ray, Richard D.↗
NASA NTRS1999

Waves: Internal Tides

Oceanic internal tides are internal waves with tidal periodicities. They are ubiquitous throughout the ocean, although generally more pronounced near large bathymetric features such as mid-ocean ridges and continental slopes. The internal vertical displacements associated with these waves can be extraordinarily large. Near some shelf breaks where the surface tides are strong, internal displacements (e.g., of an isothermal surface) can exceed 200 meters. Displacements of 10 meters in the open ocean are not uncommon. The associated current velocities are usually comparable to or larger than the currents of the surface tide. On continental shelves internal tides can occasionally generate packets of internal solitons, which are detectable in remote sensing imagery. Other common nonlinear features are generation of higher harmonics (e.g., 6-hr waves) and wave breaking. Internal tides are known to be an important energy source for mixing of shelf waters. Recent research suggests that they may also be a significant energy source for deep-ocean mixing.

Ray, Richard D.↗