Richard D. Ray

Recent Greenland ice mass loss by drainage system from satellite gravity observations.

Mass changes of the Greenland Ice Sheet resolved by drainage system regions were derived from a local mass concentration analysis of NASA–Deutsches Zentrum für Luftund Raumfahrt Gravity Recovery and Climate Experiment (GRACE mission) observations. From 2003 to 2005, the ice sheet lost 101 ± 16 gigaton/year, with a gain of 54 gigaton/year above 2000 meters and a loss of 155 gigaton/year at lower elevations. The lower elevations show a large seasonal cycle, with mass losses during summer melting followed by gains from fall through spring. The overall rate of loss reflects a considerable change in trend (–113 ± 17 gigaton/year) from a near balance during the 1990s but is smaller than some other recent estimates.

Estimates of M2 Tidal Energy Dissipation from TOPEX/Poseidon Altimeter Data

Most of the tidal energy dissipation in the ocean occurs in shallow seas, as has long been recognized. However, recent work has suggested that a significant fraction of the dissipation, perhaps 1 TW or more, occurs in the deep ocean. This paper builds further evidence for that conclusion. More than 6 years of data from the TOPEX/Poseidon satellite altimeter are used to map the tidal dissipation rate throughout the world ocean. The dissipation rate is estimated as a balance between the rate of working by tidal forces and the energy flux divergence, computed using currents derived by least squares fitting of the altimeter data and the shallow water equations. Such calculations require dynamical assumptions, in particular about the nature of dissipation. To assess sensitivity of dissipation estimates to input assumptions, a large suite of tidal inversions based on a wide range of drag parameterizations and employing both real and synthetic altimeter data are compared. These experiments and Monte Carlo error fields from a generalized inverse model are used to establish error uncertainties for the dissipation estimates. Owing to the tight constraints on tidal elevation fields provided by the altimeter, area integrals of the energy balance are remarkably insensitive to required dynamical assumptions. Tidal energy dissipation is estimated for all major shallow seas (excluding individual polar seas) and compared with previous model and data-based estimates. Dissipation in the open ocean is significantly enhanced around major bathymetric features, in a manner consistent with simple theories for the generation of baroclinic tides.

Accuracy assessment of recent ocean tide models

Over 20 global ocean tide models have been developed since 1994, primarily as a consequence of analysis of the precise altimetric measurements from TOPEX/POSEIDON and as a result of parallel developments in numerical tidal modeling and data assimilation. This paper provides an accuracy assessment of 10 such tide models and discusses their benefits in many fields including geodesy, oceanography, and geophysics. A variety of tests indicate that all these tide models agree within 2-3 cm in the deep ocean, and they represent a significant improvement over the classical Schwiderski 1980 model by approximately 5 cm rms. As a result, two tide models were selected for the reprocessing of TOPEX/POSEIDON Geophysical Data Records in late 1995. Current ocean tide models allow an improved observation of deep ocean surface dynamic topography using satellite altimetry. Other significant contributions include theft applications in an improved orbit computation for TOPEX/POSEIDON and other geodetic satellites, to yield accurate predictions of Earth rotation excitations and improved estimates of ocean loading corrections for geodetic observatories, and to allow better separation of astronomical tides from phenomena with meteorological and geophysical origins. The largest differences between these tide models occur in shallow waters, indicating that the current models are still problematic in these areas. Future improvement of global tide models is anticipated with additional high-quality altimeter data and with advances in numerical techniques to assimilate data into high-resolution hydrodynamic models.

Surface manifestation of internal tides generated near Hawaii

Analysis of Topex/Poseidon satellite altimetry reveals short-wavelength fluctuations in the ocean surface tide that are attributable to internal tides. A significant fraction of the semidiurnal internal tide generated at the Hawaiian Ridge is evidently phase-locked to the astronomical potential and can modulate the amplitude of the surface tide by ∼5 cm. The internal tide is thus easily mapped along satellite groundtracks, and it is found to be spatially coherent over great distances, with waves propagating well over 1000 km from the Hawaiian Ridge before decaying below noise level. Both first and second baroclinic modes are observed in both the M 2 (lunar) and S 2 (solar) tides. The high space-time coherence is in sharp contrast to what is often inferred from current-meter observations, but it confirms recent speculations from an acoustic experiment north of Hawaii.

Surface manifestation of internal tides in the deep ocean : observations from altimetry and island gauges

The sea-surface height signatures of internal tides in the deep ocean, amounting to a few centimeters or less, are studied using two complementary measurement types: satellite altimetry and island tide gauges. Altimetry can detect internal tides that maintain coherence with the astronomical forcing; island gauges can monitor temporal variability which, in some circumstances, is due to internal tides varying in response to changes in the oceanic medium. This latter mechanism is at work at Hilo and other stations on the northern coasts of the Hawaiian Islands. By detecting spatially coherent low-frequency internal-tide modulations, the tide gauges, along with inverted echo sounders at sea, suggest that the mean internal tide is also spatially coherent; satellite altimetry confirms this. At Hawaii and in many other places, Topex/Poseidon altimetry detects mean surface waves, spatially coherent and propagating great distances (> 1000 km) before decaying below background noise. When temporal variability is small, the altimetry (plus information on ocean density) sets useful constraints on energy fluxes into internal tides. At the Hawaiian Ridge, 15 GW of tidal power is being converted from barotropic to first-mode baroclinic motion. Examples elsewhere warn that a simplistic interpretation of the altimetry, without regard to variability, noise, or in situ information, may be highly misleading. With such uncertainties, extension of the Hawaiian results into a usefully realistic estimate of the global internal-tide energy balance appears premature at this time.

Accuracy assessment of global barotropic ocean tide models

The accuracy of state-of-the-art global barotropic tide models is assessed using bottom pressure data, coastal tide gauges, satellite altimetry, various geodetic data on Antarctic ice shelves, and independent tracked satellite orbit perturbations. Tide models under review include empirical, purely hydrodynamic (“forward”), and assimilative dynamical, i.e., constrained by observations. Ten dominant tidal constituents in the diurnal, semidiurnal, and quarter-diurnal bands are considered. Since the last major model comparison project in 1997, models have improved markedly, especially in shallow-water regions and also in the deep ocean. The root-sum-square differences between tide observations and the best models for eight major constituents are approximately 0.9, 5.0, and 6.5 cm for pelagic, shelf, and coastal conditions, respectively. Large intermodel discrepancies occur in high latitudes, but testing in those regions is impeded by the paucity of high-quality in situ tide records. Long-wavelength components of models tested by analyzing satellite laser ranging measurements suggest that several models are comparably accurate for use in precise orbit determination, but analyses of GRACE intersatellite ranging data show that all models are still imperfect on basin and subbasin scales, especially near Antarctica. For the M2 constituent, errors in purely hydrodynamic models are now almost comparable to the 1980-era Schwiderski empirical solution, indicating marked advancement in dynamical modeling. Assessing model accuracy using tidal currents remains problematic owing to uncertainties in in situ current meter estimates and the inability to isolate the barotropic mode. Velocity tests against both acoustic tomography and current meters do confirm that assimilative models perform better than purely hydrodynamic models.

Ocean self‐attraction and loading in numerical tidal models

The formalism for handling ocean tidal self‐attraction and loading in numerical tide models is reviewed. These forcing terms require global integrations of the tidal elevations, turning the dynamical differential equations into integro‐differential equations. Following Accad and Pekeris, many authors approximate the self‐attraction/loading terms by a simple scalar multiplier of the local tidal elevation, but the choice of multiplier is not obvious and is often confused. The one recommended by Accad and Pekeris generates large errors in the open ocean. Other scaling factors are examined here; none is recommended in general, and most serious applications should use the full integral formulation. New estimates of the self‐attraction/loading fields, based on global tidal measurements from recent satellite altimeters, are now readily available.

Estimates of internal tide energy fluxes from Topex/Poseidon altimetry: central North Pacific

Energy fluxes for first-mode M2 internal tides are deduced throughout the central North Pacific Ocean from Topex/Poseidon satellite altimeter data. Temporally coherent internal tide signals in the altimetry, combined with climatological hydrographic data, determine the tidal displacements, pressures, and currents at depth, which yield power transmission rates. For a variety of reasons the deduced rates should be considered lower bounds. Internal tides are found to emanate from several large bathymetric structures, especially the Hawaiian Ridge, where the integrated flux amounts to about 6 gigawatts. Internal tides are generated at the Aleutian Trench near 172°W and propagate southwards nearly 2000 km.

Diurnal/semidiurnal polar motion excited by oceanic tidal angular momentum

The axial component of the oceanic tidal angular momentum (OTAM) has been demonstrated to be responsible for most of the diurnal and semidiurnal variations in Earths rotational rate. In this paper we study the equatorial components of OTAM and their corresponding effects on the orientation of Earths rotational axis, or polar motion. Three ocean tide models derived from TOPEX/Poseidon satellite altimetry are employed to predict the polar motion excited by eight major diurnal/semidiurnal tides (Q1,O1,P1, K1, N2, M2, S2, K2). The predictions are compared with geodetic measurements of polar motion from both long-term observations and during the intensive campaign Cont94. The prograde diurnal and prograde and retrograde semidiurnal periods are treated, whereas the retrograde diurnal polar motion is not treated (because it cannot be observed directly and uniquely.) The comparison shows generally good agreement, with discrepancies typically within 10–30 micro-arc- seconds for the largest tides. The eight tides collectively explain nearly 60% of the total variance in subdaily polar motion during Cont94. This establishes the dominant role of OTAM in exciting the diurnal/semidiurnal polar motion and paves the way for detailed studies of short-period nontidal polar motion. The present accuracy, however, is inadequate to shed light on the prograde diurnal polar libration.

Diurnal and Semidiurnal Variations in the Earth's Rotation Rate Induced by Oceanic Tides

Recent space-geodetic observations have revealed daily and subdaily variations in the Earths rotation rate. Although spectral analysis suggests that the variations are primarily of tidal origin, comparisons to previous theoretical predictions based on various ocean models have been less than satisfactory. This disagreement is partly caused by deficiencies in physical modeling. Rotation predictions based on a reliable tidal-height model, with corresponding tidal currents inferred from a modified form of Laplaces momentum equations, yield predictions of tidal variations in Universal Time that agree with very long baseline interferometer observations to 2 microseconds. This agreement resolves a major discrepancy between theory and observation and establishes the dominant role of oceanic tides for inducing variation in the Earths rotation at these frequencies.