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NASA NTRS1986

Calibrating an altimeter - How many tide gauges is enough?

The dominant contributor to the random error of an altimetric satellite system is the long wavelength uncertainty in the orbital radius. It is shown that calibration by a comparatively modest tide gauge system can drastically reduce the overall error in global estimates of large-scale oceanic variability. The procedure used is a form of optimal estimation. Absolute (time average) altimetric calibration is much more difficult because it requires absolute calibration of the tide gauge positions (in three dimensions) but the error reduction process would be the same.

Wunsch, Carl↗

NASA NTRS1987

On the choice of orbits for an altimetric satellite to study ocean circulation and tides

The choice of an orbit for satellite altimetric studies of the ocean's circulation and tides requires an understanding of the orbital characteristics that influence the accuracy of the satellite's measurements of sea level and the temporal and spatial distribution of the measurements. The orbital characteristics that influence accurate calculations of the satellite's position as a function of time are examined, and the pattern of ground tracks laid down on the ocean's surface as a function of the satellite's altitude and inclination is studied. The results are used to examine the aliases in the measurements of surface geostrophic currents and tides. Finally, these considerations are used to specify possible orbits that may be useful for the upcoming Topex/Poseidon mission.

Parke, Michael E.↗

NASA NTRS1989

Global behavior of the height/seasonal structure of tides between 40 deg and 60 deg latitude

The radars utilized are meteor (2), medium frequency (2) and the new low frequency (1) systems: analysis techniques were exhaustively studied internally and comparatively and are not thought to affect the results. Emphasis is placed upon the new height-time contours of 24-, 12-h tidal amplitudes and phases, which best display height and seasonal structures; where possible high resolution (10 d) is used (Saskatoon), but all stations provide monthly mean resolution. At these latitudes the diurnal tide is generally smaller than the semidiurnal, and displays more variability. However, there is a tendency for vertical wavelengths and amplitudes to be larger during summer months. On occasions in winter and fall, wavelengths may be less than 50 km. The dominant semidiurnal tide shows significant regular season structure; wavelengths are generally small (about 50 km) in winter, large in summer (equal to or greater than 100 km), and these states are separated by rapid equinoctial transitions. There is some evidence for less regularity toward 40 deg. Coupling with mean winds is apparent. Data from earlier ATMAP campaigns are mentioned, and reasons for their inadequacies presented.

Manson, A. H.↗

NASA NTRS1989

Nonlinear interaction between the diurnal and semidiurnal tides: Terdiurnal and diurnal secondary waves

Many years of measurements obtained using French meteor radars at Garchy (latitude 47 N) and Montpazier (latitude 44 N) are used to show the existence of an 8 hour oscillation. Some examples of the structure of this wave are displayed and compared with measurements performed at Saskatoon (latitude 52 N) and Budrio (latitude 45 N). This wave can be interpreted as the solar driven terdiurnal tide, or as the result of the nonlinear interaction between the diurnal and semidiurnal tides. Both hypotheses are tested with numerical models. Incidentally, the possible existence of a 24 hour wave resulting from this interaction is also studied.

Teitelbaum, H.↗

NASA NTRS1990

Observations of the Mf ocean tide from Geosat altimetry

Zonal averages of the 13.66-day Mf tide are derived from one year of Geosat altimetry records. The orbit errors are reduced by 1/revolution corrections taken over long (several day) arcs. The short-period tides are removed using a model previously derived from the same data. The Mf zonal averages indicate definite nonequilibrium character at nearly all latitudes. The imaginary admittances indicate a Q of at least 8; such a value is consistent with a simplified theory of coupled gravitational and vorticity modes and suggests a value for Proudman's 'friction period' about 123 days.

Cartwright, David E.↗

NASA NTRS1991

Nonmigrating diurnal tides in the equatorial middle atmosphere

Data from the Nimbus-7 Limb Infrared Monitor of the Stratosphere (LIMS) are used to extend the analysis of diurnal tides in the middle atmosphere to include the zonally symmetric and eastward propagating components. These modes show vertical and meridional structures that are generally consistent with the predictions of linear tidal theory. The zonal and meridional wind fields are calculated from the tidal temperatures. Diurnal perturbations in LIMS temperature and derived winds agree well with equinoctial model calculations. Comparisons with day-night differences of radiosonde temperature and rocket winds show qualitative agreement in vertical structure and amplitude. The zonally symmetric and eastward migrating tidal components show a higher degree of temporal variability than the sun-synchronous component. These modes at times contribute substantially to the diurnal signal in wind and temperature, with combined amplitudes equal to or in excess of the amplitude of the main migrating diurnal tide. The observed vertical phase variations suggest that their forcing may originate below the stratosphere.

Lieberman, Ruth S.↗

NASA NTRS1991

The effects of the solid inner core and nonhydrostatic structure on the earth's forced nutations and earth tides

This paper computes the effects of the solid inner core (IC) on the forced nutations and earth tides, and on certain of the earth's rotational normal modes. The theoretical results are extended to include the effects of a solid IC and of nonhydrostatic structure. The presence of the IC is responsible for a new, almost diurnal, prograde normal mode which involves a relative rotation between the IC and fluid outer core about an equatorial axis. It is shown that the small size of the IC's effects on both nutations and tides is a consequence of the fact that the IC's moments of inertia are less than 1/1000 of the entire earth's.

De Vries, Dan↗

NASA NTRS1991

Global-scale sea surface variability from combined altimetric and tide gauge measurements

By correcting Geosat altimetric data for a set of line frequencies, and then doing a heavy average in space and time, a set of global maps of sea surface variability is produced over time intervals ranging from three months to two years. These maps are demonstrated to be consistent with the global network of tide gauges and sets of maps incorporating those data into the altimetric estimates are also produced. Tide gauge records too fragmentary for computation of a two-year mean are employed by time-differencing them. An estimate of the global difference of sea level change over one year, on very large space scales, shows the effects of the 1987 El Nino. The spherical harmonic coefficients employed in the computations are then used to estimate the full three-dimensional frequency/wavenumber spectrum of surface circulation variability.

Wunsch, Carl↗

NASA NTRS1991

Global ocean tide mapping using TOPEX/Poseidon altimetry

The investigation's main goals are to produce accurate tidal maps of the main diurnal, semidiurnal, and long-period tidal components in the world's deep oceans. This will be done by the application of statistical estimation techniques to long time series of altimeter data provided by the TOPEX/POSEIDON mission, with additional information provided by satellite tracking data. In the prelaunch phase, we will use in our simulations and preliminary work data supplied by previous oceanographic missions, such as Seasat and Geosat. These results will be of scientific interest in themselves. The investigation will also be concerned with the estimation of new values, and their uncertainties, for tidal currents and for the physical parameters appearing in the Laplace tidal equations, such as bottom friction coefficients and eddy viscosity coefficients. This will be done by incorporating the altimetry-derived charts of vertical tides as boundary conditions in the integration of those equations. The methodology of the tidal representation will include the use of appropriate series expansions such as ocean-basin normal modes and spherical harmonics. The results of the investigation will be space-determined tidal models of coverage and accuracy superior to that of the present numerical models of the ocean tides, with the concomitant benefits to oceanography and associated disciplinary fields.

Sanchez, Braulio V.↗

NASA NTRS1993

Gravitational tides in the outer planets. I - Implications of classical tidal theory. II - Interior calculations and estimation of the tidal dissipation factor

Classical tidal theory is applied to the atmospheres of the outer planets. The tidal geopotential due to satellites of the outer planets is discussed, and the solution of Laplace's tidal equation for Hough modes appropriate to tides on the outer planets is examined. The vertical structure of tidal modes is described, noting that only relatively high-order meridional mode numbers can propagate vertically with growing amplitude. Expected magnitudes for tides in the visible atmosphere of Jupiter are discussed. The classical theory is extended to planetary interiors taking the effects of spherically and self-gravity into account. The thermodynamic structure of Jupiter is described and the WKB theory of the vertical structure equation is presented. The regions for which inertial, gravity, and acoustic oscillations are possible are delineated. The case of a planet with a neutral interior is treated, discussing the various atmospheric boundary conditions and showing that the tidal response is small.

Ioannou, Petros J.↗

NASA NTRS1993

Mars dust-driven tides and their impact on the thermosphere

It has been known since the early Mariner 6, 7, and 9 missions that dust loading of the lower atmosphere and the subsequent aerosol heating during dusty periods impacts the martian middle and upper atmospheres. A quantitative measure of this lower atmosphere forcing was obtained by the Viking 1 and 2 landers, from which observed amplitudes of semidiurnal surface-pressure oscillations were correlated with normal-incidence dust optical depths. It appears that the dominant semidiurnal mode is a good indicator of global dust content or mean dust optical depth, especially during dust storm events. A classical tidal model that reproduces the surface pressure oscillations measured by these Viking landers in 1977 was used to calculate tidal amplitudes and phases up to approximately 43 km. These tidal characteristics were calculated for various dust optical depth conditions ranging from typical dusty periods to global dust storm times. Reasonable extrapolations can be made to higher altitudes if one assumes that the vertically propagating tidal modes continue to grow without dissipation or breaking. It is very likely that gravity waves also play an important role in the structure and dynamics of the middle atmosphere of Mars, since the large topographical relief should produce vigorous gravity wave fluxes. Semidiurnal tidal modes, significantly enhanced by lower atmosphere dust-induced heating, may indeed propagate to the Mars thermosphere (approximately less than 100 km) before breaking and generating turbulence. The preferential enhancement of the semidiurnal tides during dust storm onset is primarily due to the elevation of the tidal heating source in a very dusty atmosphere. The (2,2) semidiurnal tidal tidal mode was shown to have the largest variation with dust optical depth, as measured by Viking lander instruments. Also, the (2,2) mode has the largest vertical wavelength of all the semidiurnal tidal modes, and thus is most likely to penetrate into the thermosphere before breaking and to modify the largely in situ solar-driven behavior otherwise expected. The tides may also be partially responsible for determining the height of the martian homopause (approximately 125 km).

Bougher, Stephen W.↗

NASA NTRS1995

Minutes of TOPEX/POSEIDON Science Working Team Meeting and Ocean Tides Workshop

This third TOPEX/POSEIDON Science Working Team meeting was held on December 4, 1994 to review progress in defining ocean tide models, precision Earth orbits, and various science algorithms. A related workshop on ocean tides convened to select the best models to be used by scientists in the Geophysical Data Records.

Fu, Lee-Lueng↗

NASA NTRS1998

Observation of the middle atmospheric thermal tides using lidar measurements over Mauna Loa Observatory (19.5 deg N, 155.6 deg W)

Temperature measurements in the middle atmosphere using Rayleigh lidars have been performed for several decades now. The high accuracy and vertical resolution provided by lidars allow to study the temperature variability at various scales with high confidence levels. One of the numerous applications is the study of the middle atmospheric thermal tides. Although Rayleigh lidar measurements are basically possible only at nighttime, diurnal and semidiurnal components can often be extracted if the results are taken with care and correctly interpreted. Using results from more than 200 hours of nighttime measurements obtained by lidar in October 1996 and 1997 at Mauna Loa Observatory, Hawaii, a study of the middle atmospheric (25-90 km) thermal tides is presented in this paper. The amplitudes and phases of the diurnal and semidiurnal components were calculated for some altitudes where the fits converged significantly, and compared to that of the Global Scale Wave Model (GSWM).

Leblanc, Thierry↗

NASA NTRS1999

Stratospheric Tides and Data Assimilation

In the upper stratosphere, the atmosphere exhibits significant diurnal and semi-diurnal tidal variations, with typical amplitude of about 2K in mid-latitudes. In this paper we examine how well the tidal variations in temperature are represented by the Goddard Geodesic Earth Orbiting Satellite (GEOS-2) data assimilation system. We show that the GEOS-2 atmospheric model is quite successful at simulating the tidal temperature variations. However, the assimilation of satellite temperature soundings significantly damps the simulated tides. The reason is because the tides are not well represented by the satellite retrievals used by the assimilation system (which have a typical tidal amplitude of around 1K). As a result of this study, we suggest improvements that should be made to the treatment of satellite soundings by the assimilation system.

Swinbank, R.↗

NASA NTRS1997

Ion Outflow and Convection in the Polar Cap and Cleft as Measured by Tide, EFI, MFE and Timas

This study examines high-latitude ion outflows and velocities perpendicular to the magnetic field derived from moments of ion distributions measured by the TIDE (Thermal Ion Dynamics Experiment) instrument on the Polar satellite. Hydrogen and oxygen ions are shown to be E X B drifting in the polar cap and cleft regions with a speed of about 5-20 km/s at apogee (approximately 9 Re) and a speed of 1-2 km/s at perigee (approximately 1. 8 Re). E X B drifts are calculated from electric fields measured by EFI (Electric Field Instrument) and magnetic fields measured by MFE (Magnetic Field Experiment) both of which are also on Polar. How convection at Polar's perigee relates to potential patterns of the ionosphere will be discussed. In the cusp/cleft the distribution of hydrogen extends over a large enough range of energy to be measured by both TIDE and the Toroidal Imaging Mass-Angle Spectrograph (TIMAS). Such comparisons will be also be presented.

Elliott, H. A.↗

NASA NTRS2002

The Role of Tides in Known Multi-Planet Systems

The first known extrasolar planet system, upsilon Andromedae, was discovered in 1999. The number of stars known to possess more than one planet has been growing rapidly since then. The dynamical interactions among such planets can be quite strong. These interactions can excite the orbital eccentricities of planets, even planets orbiting very close to their stars. Stellar tides can damp the eccentricities of such close-in planets, removing dynamical energy from the system and ultimately affecting the motions of all of the planets. These and other effects of tides in extrasolar multi-planet systems will be discussed.

Lissauer, Jack J.↗

NASA NTRS2002

The IERS Special Bureau for Tides

The Global Geophysical Fluids Center of the International Earth Rotation Service (IERS) comprises 8 special bureaus, one of which is the Special Bureau for Tides. Its purpose is to facilitate studies related to tidal effects in earth rotation. To that end it collects various relevant datasets and distributes them, primarily through its website at bowie.gsfc.nasa.gov/ggfc/tides. Example datasets include tabulations of tidal variations in angular momentum and in earth rotation as estimated from numerical ocean tide models and from meteorological reanalysis products. The web site also features an interactive tidal prediction "machine" which generates tidal predictions (e.g., of UT1) from lists of harmonic constants. The Special Bureau relies on the tidal and earth-rotation communities to build and enlarge its datasets; further contributions from this community are most welcome.

Ray, Richard D.↗

NASA NTRS2005

Ocean Tide Loading Computation

September 15,2003 through May 15,2005 This grant funds the maintenance, updating, and distribution of programs for computing ocean tide loading, to enable the corrections for such loading to be more widely applied in space- geodetic and gravity measurements. These programs, developed under funding from the CDP and DOSE programs, incorporate the most recent global tidal models developed from Topex/Poscidon data, and also local tide models for regions around North America; the design of the algorithm and software makes it straightforward to combine local and global models.

Agnew, Duncan Carr↗