131433522
Dynamic ocean-tide effects on Earth's rotation
SUMMARY 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.
129727296
Limits on lateral pressure gradients in the outer core from geodetic observations
Abstract Lateral variations in pressure associated with flow at the core-mantle boundary will produce deformations of the mantle. It is shown here that geostrophically plausible pressure gradients are sufficient to produce measurable changes in the length-of-day, polar motion, J2, sea-level, tilt, gravity and strain. Of these, polar motion is the most discriminating and limits intra-annual variations in the lateral pressure field, at planetary wavelength, to less than − 104 Pa. Satellite observations of changes in J2 are potentially even more useful. However, at present the time span of observations is short and the separation of a residual, which might be due to a change in the distribution of pressure at the core-mantle boundary, from other causes, such as post-glacial rebound, is ambiguous. It is suggested that not more than 10% of the decade variations in the length-of-day may be caused by pressure fluctuations at the core mantle boundary.
129641128
Effects of dynamic long-period ocean tides on changes in Earth's rotation rate
As a generalization of the zonal response coefficient first introduced by Agnew and Farrell (1978), the authors define the zonal response function k of the solid earth-ocean system as the ratio, in the frequency domain, of the tidal change in Earth's rotation rate to the tide-generating potential. Amplitudes and phases of k for the monthly, fortnightly, and 9-day lunar tides are estimated from 2 1/2 years of very long baseline interferometry UTI observations (both 5-day and daily time series), corrected for atmospheric angular momentum effects using NMC wind and pressure series. Using the dynamic ocean tide model of Dickman (1988a, 1989a), the authors predict amplitudes and phases of k for an elastic earth-ocean system. The predictions confirm earlier results which found that dynamic effects of the longer-period ocean tides reduce the amplitude of k by about 1%. However, agreement with the observed k is best achieved for all three tides if the predicted tide amplitudes are combined with the much larger satellite-observed ocean tide phases; in these cases the dynamic tidal effects reduce k by up to 8%. Finally, comparison between the observed and predicted amplitudes of k implies that anelastic effects on Earth's rotation at periods less than fortnightlymore » cannot exceed 2%.« less
128607751
Tidal variations of earth rotation
We have rederived the periodic variations of the earth's rotation due to the tidal deformation of the earth by the sun and moon and included all terms with amplitudes ≥0.002 milliseconds (1 mm). This series applies to the mantle (plus crust) and oceans, which rotate together for characteristic tidal periods. The parameter which scales the rotational series is k/C, where k is that fraction of the Love number which causes the tidal variation in the moment of inertia of the coupled mantle and oceans while C is the dimensionless polar moment of inertia of the coupled units. If the whole earth (minus oceans) were coupled rotationally, then k = 0.30 and C = 0.33. Ocean tides increase k by 0.04. Decoupling of the fluid core from the mantle decreases k by 0.06 while C = Cmantle = 0.29, since neither pressure, viscous, nor hydromagnetic coupling locks the fluid to the mantle for periods less than 5 to 25 years. From the analysis of lunar laser ranging data we find that k/C at monthly and fortnightly frequencies equals 0.99 ±0.15 and 0.99 ± 0.20 as compared with a theoretical value of 0.94 ± 0.04. In addition, we have estimated theoretically the effects of ocean tides on earth rotation, nutation and polar motion using models based on the Laplace tidal equations.
128101187
Oceanic tide maps and spherical harmonic coefficients from Geosat altimetry
Maps and tables for the global ocean tides, 69 degree N to 68 degree S, derived from two years of Geosat altimetry are presented. Global maps of local and Greenwich admittance of the (altimetric) ocean tide, and maps of amplitude and Greenwich phase lag of the ocean tide are shown for M(sub 2), S(sub 2), N(sub 2), O(sub 1), and K(sub 1). Larger scale maps of amplitude and phases are also shown for regional areas of special interest. Spherical harmonic coefficients of the ocean tide through degree and order 8 are tabulated for the six major constituents.
129796972
Normal Modes of the World Ocean. Part IV: Synthesis of Diurnal and Semidiurnal Tides
Abstract Diurnal and semidiurnal tides of second and third degree are synthesized from 60 normal modes with period in the range 8 to 96 h. Diurnal tides, especially those of second degree, can be represented by remarkably few modes. The principal lunar diurnal constituent, for example, consists almost entirely of a single forced mode excited mainly in the Pacific and Indian Oceans. Semidiurnals are spectrally more heterogeneous, and more resonant, than diurnals, but some specific features can be attributed to individual modes. Several of the most energetic modes in the principal lunar semidiurnal constituent are prominent in the Atlantic Ocean. Together with the fact that diurnally excited modes are relatively weak in that region, this presumably accounts for the observed tendency for the total tide to be predominantly semidiurnal in the Atlantic but mixed diurnal and semidiurnal in many parts of the Pacific and Indian Oceans.
121185009
Ocean tides for satellite geodesy
Abstract 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, PI, 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. By extending the theory to include a second constraint derived from tide observa...
130614413
The self-consistent dynamic pole tide in non-global oceans
Summary 
 
Fluid dynamic theories of the pole tide are in conflict with pole tide observations. The former predict that the oceanic response to the Chandler wobble should be nearly static; while the latter reveal the tide to possess significant non-equilibrium characteristics. Resolution of the conflict would determine whether mantle anelasticity or non-equilibrium oceans is responsible for a measurable contribution to the Chandler period. 
 
 
 
It is possible that resolution might be achieved through a more exact mathematical investigation of pole tide fluid dynamics than theories have carried out to date. The theories have also neglected to consider a unique property of the pole tide, its ability to lengthen the period of its own forcing function; this property implies that the pole tide characteristics and effects on wobble cannot be correctly determined unless the tide and wobble equations are jointly solved. 
 
 
 
This work constitutes a first attempt to determine, accurately and self-consistently, the nature of the pole tide and its effects on the Chandler wobble. The Laplace tidal equations, modified by the addition of bottom friction but with no simplifying approximations, are employed together with the Liouville equations to elucidate pole tide characteristics. This work is a first attempt because the earth model chosen is a crude one, consisting of global oceans of uniform depth overlying a rigid mantle with a fluid core. Results for this model suggest that departures of the pole tide from equilibrium may indeed be minimal. The relevance of these results to the actual pole tide, however, must await the application of our self-consistent and more exact dynamical theory to the situation of realistic oceans.
130614413
The self-consistent dynamic pole tide in non-global oceans
Summary 
 
Fluid dynamic theories of the pole tide are in conflict with pole tide observations. The former predict that the oceanic response to the Chandler wobble should be nearly static; while the latter reveal the tide to possess significant non-equilibrium characteristics. Resolution of the conflict would determine whether mantle anelasticity or non-equilibrium oceans is responsible for a measurable contribution to the Chandler period. 
 
 
 
It is possible that resolution might be achieved through a more exact mathematical investigation of pole tide fluid dynamics than theories have carried out to date. The theories have also neglected to consider a unique property of the pole tide, its ability to lengthen the period of its own forcing function; this property implies that the pole tide characteristics and effects on wobble cannot be correctly determined unless the tide and wobble equations are jointly solved. 
 
 
 
This work constitutes a first attempt to determine, accurately and self-consistently, the nature of the pole tide and its effects on the Chandler wobble. The Laplace tidal equations, modified by the addition of bottom friction but with no simplifying approximations, are employed together with the Liouville equations to elucidate pole tide characteristics. This work is a first attempt because the earth model chosen is a crude one, consisting of global oceans of uniform depth overlying a rigid mantle with a fluid core. Results for this model suggest that departures of the pole tide from equilibrium may indeed be minimal. The relevance of these results to the actual pole tide, however, must await the application of our self-consistent and more exact dynamical theory to the situation of realistic oceans.
129555022
A complete spherical harmonic approach to luni-solar tides
SUMMARY 
 
In this work a spherical harmonic theory of ocean tides is presented. The theory is based on Laplace tide equations modified to include turbulence with constant eddy viscosity, linearized bottom friction, and oceanic loading and self-gravitation. Variable bathymetry is also treated in harmonic terms, and no-flow boundary conditions are applied at continental coastlines. The tide and boundary constraint equations are reduced to matrix form and solved by a weighted least-squares procedure. Five zonal luni–solar tides, ranging in period from 14 days to 18.6 yr, are investigated using the theory; such tides have typically been difficult to compute using traditional numerical approaches. The polar motion and changes in the length of day induced by these long-period tides are calculated. Tidal solutions are compared extensively with results from other tidal theories and from recent satellite and sea-level observations. The greatest limitation to accurate prediction of zonal tides—for any theory—appears to be the marginal failure of all tide theories to conserve mass globally; the use of additional mass constraints may be warranted.
129046869
Experiments in tidal mass conservation
SUMMARY 
A common feature of theoretical ocean tide models is their failure to conserve mass over the oceans. This failure distorts the tidal solution and imparts ambiguity to the calculation of tidal effects on gravity, crustal loading, and Earth rotation; for example, predicted effects of long-period tides on rotation could be uncertain by up to 50 per cent in magnitude and 100 per cent in phase. Using the spherical harmonic tide theory developed by Dickman (1989), the influence of various global conservation constraints on the tidal solution is explored. an ocean-wide mass conservation constraint, implemented using Lagrange multipliers, produces a realistic and significantly more accurate and unambiguous tidal solution.
140545494
O1, P1, N2 models of the global ocean tide on an elastic earth plus surface potential and spherical harmonic decompositions for M2, S2, and K1
Abstract Because of the growing utility of having models of additional tidal constituents, this paper supplements models of M2, S2, and K1 presented previously in this journal with models of O1, P1, and N2 produced in exactly the same way. As before, the models satisfy specified elevation boundary conditions and are generated by fitting a small number of test functions to island data. Having models of three constituents in each band allows for estimates of cross‐band variations. Model admittances vary smoothly from place to place throughout the deep oceans, although significant variations can occur over distances as short as a few thousand kilometers; the most significant variations occur in the South Atlantic and Pacific oceans. As before, this paper presents 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 new component based on Farrell's 1972 Green's functions. In...
129047276
Effect of the fluid core on changes in the length of day due to long period tides.
The long period luni-solar tidal potential is known to cause periodic changes in the earth's rotation rate. It is found that the effect of a dissipationless fluid outer core is to reduce the amplitudes of these tidal perturbations by about 11 percent. When the fluid core effect is added to Agnew and Farrell's (1978) estimate of the effect of an equilibrium ocean, the result is in accord with observation. The effects of dissipative processes within the fluid core are also examined. Out-of-phase perturbations are found which could be as large as about 10 ms at 18.6 yr. It is concluded, however, that the poorly understood decade fluctuations in the earth's rotation rate will prohibit observation of this effect.
120007490
A Search for the Earth's ‘Nearly Diurnal Free Wobble’
Summary 
 
The existence of the Earth's liquid core, besides affecting the period of the Chandler wobble, gives rise to a second free wobble mode, with period short of a sidereal day by a factor of the order of the ellipticity of the coremantle boundary. Seen from space this nearly diurnal geographic motion of the pole should appear as a nutation of the Earth's rotation axis, with a period theoretically calculated to be about 460 days, and (as pointed out by Toomre) an amplitude correspondingly 460 times larger than that of the associated wobble. The curious history of the ‘nearly diurnal wobble’ problem is reviewed, and the relevant dynamics derived and described in terms of Poinsot's scheme. A special method developed for harmonic analysis of non-equispaced data, applied to a 20-year record of observations with Loomis Polar Telescope of Yale University Observatory, sets an upper limit of 0"·12–0"·26 on the amplitude of any free nutation in obliquity in the frequency range 0–4 cpy, i.e. an upper limit of 0"·0003–0"·0006 on the amplitude of the nearly diurnal free wobbble. This supports Toomre's contention that earlier reports of observations of this wobble, with amplitudes in the range 0"·01–0"·02, cannot be correct.
128385124
The period and Q of the Chandler wobble
Summary. We have extended our calculation of the theoretical period of the Chandler wobble to account for the non-hydrostatic portion of the Earth’s equatorial bulge and the effect of the fluid core upon the lengthening of the period due to the pole tide. We find the theoretical period of a realistic perfectly elastic Earth with an equilibrium pole tide to be 426.7 sidereal days, which is 8.5 day shorter than the observed period of 435.2 day. Using Rayleigh’s principle for a rotating Earth, we exploit this discrepancy together with the observed Chandler Q to place constraints on the frequency dependence of mantle anelasticity. If Q, in the mantle varies with frequency u as u” between 30 s and 14 months and if Q, in the lower mantle is of order 225 at 30 s, we find that 0.04 5 a 5 0.1 1 ; if instead Q, in the lower mantle is of order 350 near 200 s, we find that 0.11 5 a 0.19. In all cases these limits arise from exceeding the 68 per cent confidence limits of ? 2.6 day in the observed period. Since slight departures from an equilibrium pole tide affect the Q much more strongly than the period we believe these limits to be robust.
129173071
Body tides on an elliptical, rotating, elastic and oceanless earth
Summary. The Earth's deformation caused by the luni-solar tidal force is defined as the 'body tide'. We compute the effects of the Earth's rotation and elliptical stratification on the body tide for a number of modern elastic structural models. Rotation and ellipticity within the mantle are found to affect tidal observations by about 1 per cent. A consequence is an improved estimate for the fluid core resonance in the diurnal tidal band. Agreement between results for the different structural models is very good. As a result, the results computed here can be used to model the tidal effects of a globally averaged, oceanless, rotating, elliptical and elastic earth to an accuracy of at least one part in 300. The combined gravitational force of the Sun and Moon on the Earth consists of a dominant portion which affects the Earth's orbit in space, plus a smaller remainder: the luni-solar tidal force. Although the tidal force exerts no net force on the Earth, it induces a response consisting of deformation (the body tide), changes in the Earth's angular orientation in space (forced precession and nutation), and changes in the Earth's rotation rate. We will describe, below, a simultaneous computation of the Earth's deformational and rotational tidal response which systematically includes the effects of the Earth's rotation and elliptical material stratification. Since the deformation is observed primarily by geodesists and the Earth's rotation by astronomers, it is conventional (and useful) to separate the solution into deformational and rotational components and to consider these terms separately. We will primarily be concerned in this paper with the body tide. The motivation for the present work is the hope that accurate observations of the body tide can improve our knowledge of the Earth's structure and dynamical behaviour. This question is likely to become increasingly important in light of the recent, rapid development of precise geodetic techniques. Seismological and astrometric observations indicate that the
128666828
THE DAMPING OF THE CHANDLER WOBBLE AND THE POLE TIDE
The damping of the Chandler wobble is an old yet actively researched problem still awaiting resolution in a number of respects. Due to both observational and theoretical limitations the actual damping rate is uncertain even now; a decay time of 45–70 years or more seems probable. The two most likely candidates for dissipating wobble energy are mantle anelasticity and a dynamic response of the oceans to wobble. Because of the frequency dependence of anelastic mechanisms, study of the oceanic response may be useful for constraining low-frequency anelasticity.
123155861
The Passive Influence of the Oceans upon the Rotation of the Earth
A general theory is developed which allows the exact numerical computation of the static equilibrium response of a non-rotating spherically symmetric Earth model covered by thin oceans with geometrically irregular coastlines to the action of an imposed static tidal or centrifugal potential. The theory is self-consistent, and takes into account the gravitational self-attraction of the oceans and the elastic-gravitational response of the Earth model to both the applied potential and the equilibrium oceanic tidal load on the surface. The results are used to determine the influence of an equilibrium pole tide on the free period and the associated rotational eigenfunction of the Chandler wobble. If the pole is globally well represented by this equilibrium approximation, its effect is to increase the Chandler wobble period by 27·6 days. It is shown that a fully self-consistent theory of the rotation of an Earth model with oceans predicts that changes in spin and wobble will be coupled, and that the Chandler wobble should, as a result, be accompanied by an associated periodic change in the length of day. The consequences of spin-wobble coupling are explored quantitatively, and found to be slight.
130369665
The effects of mantle anelasticity on nutations, earth tides, and tidal variations in rotation rate
Summary. We model the effects of mantle anelasticity on luni-solar nutations, on tidal deformation, on tidal variations in rotation rate, and on the eigenfrequency of the free core nutation. Our results can be used to invert observations to solve for the anelastic contributions to the shear and bulk moduli of the upper and lower mantle. We use specific anelastic models to numerically estimate the effects of anelasticity on these geodetic observables. We compare our nutation estimates with observational results. Among our conclusions: (1) mantle anelasticity is likely to be the most important source of damping for the free core nutation; (2) present VLBI nutation results are, in principle, accurate enough to usefully bound anelasticity at diurnal periods. But, the discrepancy between the VLBI observed nutations and the 1984 IAU nutation model cannot be explained by anelasticity, and is not yet well enough understood to allow anelasticity to be determined from the data.
129309600
Zonal tides and changes in the length of day
Summary 
 
The theory of changes in the length of day produced by the long period zonal tides is examined in an attempt to resolve the discrepancy between theoretical and observational results. It is argued here that as a result of the lack of coupling between core and mantle each conserves angular momentum separately with the result that only the changes in mantle moment of inertia influence the changes in rotation rate. 
 
 
 
The difference between theory and observation is reduced to 2 per cent, well within the error bars of observation. The zonal response coefficient is κ= 0.315.
140725611
Atlas of ocean tidal charts and maps, Part I: The semidiurnal principal lunar tide M2
Abstract In this paper the author presents the NSWC ocean tide model of the semidiurnal principal lunar (M2) tide in an atlas of ocean tidal charts and maps. The model is the computer result of a unique combination of mathematical and empirical techniques, which was introduced, extensively tested, and evaluated by Schwiderski (1978a, 1980a, b, 1983e). The computed M2 amplitudes and phases are tabulated along with all specially labeled empirical input data on a 1° × 1 ° grid system in 42° × 71° overlapping charts covering the whole oceanic globe. Corresponding global and arctic corange and cotidal maps are included to provide a quick overview of the major tidal phenomena. Significant qualitative and quantitative features are explained and discussed for proper application. In particular, the charted harmonic constants may be used to compute instantaneous M2 ocean tides with an accuracy of better than 5 cm any time and anywhere in the open oceans. Limitations of this accuracy in coastal waters and border sea...
130322521
An Analysis of Tidal Variations In the Length of Day
Observations of the length of day (LOD), corrected for the effects of variations in the angular momentum due to changes in wind velocity and atmospheric pressure, ocean tide heights and currents, and solid Earth zonal tides, were analyzed. The apparent effect of atmospheric angular momentum (AAM) on the astronomically determined LOD is found to be much less at the highest frequencies than at lower frequencies. For periods shorter than ten days there appears to be essentially no correlation between AAM and LOD. The International Earth Rotation Service (IERS) Standards (1992) model for the effects of zonal tides on the Earth’s rotation, which includes ocean tidal effects, adequately accounts for the observations of the variations in the length of day with periods between five and 180 days at the present level of accuracy. A currently unexplained semi-annual variation in the length of day remains, but this may be due to the unmodeled effects of stratospheric winds. The power spectrum of the remaining variations with periods less than twenty days is essentially that of a white-noise process. The amplitudes of the remaining unexplained variations in length of day are less than thirty microseconds. This paper has been accepted by Geophysical Journal International for publication.