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A two-dimensional time-dependent hybrid Fourier-Chebyshev method of collocation is developed and used for the study of tidal effects in accretion discs, under the assumption of a polytropic equation of state and a standard alpha viscosity prescription.
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.
Fabry-Perot interferometer observations of the mesospheric hydroxyl emission and the lower thermospheric OI (5577A) emission have been conducted from an airglow observatory at a dark field site in southeastern Michigan for the past several years. The primary functions of the observatory are to provide a database for correlative observations with the UARS satellite and to provide a synoptic measurement program for the coupling energetics and dynamics of atmospheric regions effort, An intensive operational effort between May 1993 and July 1994 has resulted in a substantial data set from which neutral winds have been determined from the bifilter acquisition sequence. A 'best fit' analysis in the least squares sense of the simultaneous measurements of the neutral winds to a 12-hour periodicity has provided amplitude and phase parameters for the semidiurnal tide as well as a measure of the mean wind. The measured tidal amplitude is greater at the higher altitude, though the seasonal behavior at both altitudes is similar with greater amplitudes during August/September and April/May. Both meridional and zonal wind components are consistent with a semidiurnal tidal description during the entire observational sequence except for the May to July 1993 period. The mean winds show annual variation in the meridional flow, being equatorward from May to October and poleward during the winter. The zonal flow is primarily eastward during the entire observational window with higher speed flows during May/June at the higher attitude and June/July at the lower altitude. A comparison with a semidiurnal tidal model indicates that the measured tidal amplitudes are a factor of 2 times greater, while the phases show similar equinoctial transitions.
Three measurements of ionospheric electric field were made during the 24-h ALADDIN rocket program at Wallops Island on June 29-30, 1974. The first of these used a double probe instrument, flown at 1500 Local Solar Time, and the second and third measurements were made by barium cloud releases at evening and morning twilight. These three electric field vectors have been compared with the predictions of a number of models of electric field due to the dynamo effects of various atmospheric tides, and also of a possible magnetospheric origin. On the assumption that the measurements were made at a location equatorward of the afternoon convergence and poleward of the morning divergence in the electric field patterns related to the Sq current system, Stening's (1973) model of the diurnal variation of the electric field induced by the (1, -2) tidal model at the time of the summer solstice correctly predicts the directions of the observed electric field. Forbes and Lindzen's (1976, 1977) model, incorporating the three major propagating tidal modes as well as the evanescent (1, -2) mode, also bears an acceptable relationship to the ALADDIN electric field directions. The ALADDIN E-field magnitudes are comparable with those obtained by ground-based observations from Millstone Hill and from Saint Santin but are about half of Stening's model values, and three times those of Forbes and Lindzen. Saint Santin E-field directions, at the same latitude but 75 deg difference in longitude, are distinctly different from ALADDIN, implying that longitudinal differences are significant.
Major new computations of terrestrial gravitational field models were performed by the Geodynamics Branch of Goddard Space Flight Center (GSFC). This development has incorporated the present state of the art results in satellite geodesy and have relied upon a more consistent set of reference constants than was heretofore utilized in GSFC's GEM models. The solutions are complete in spherical harmonic coefficients out to degree 50 for the gravity field parameters. These models include adjustment for a subset of 66 ocean tidal coefficients for the long wavelength components of 12 major ocean tides. This tidal adjustment was made in the presence of 550 other fixed ocean tidal terms representing 32 major and minor ocean tides and the Wahr frequency dependent solid earth tidal model. In addition 5-day averaged values for Earth rotation and polar motion were derived for the time period of 1980 onward. Two types of models were computed. These are satellite only models relying exclusively on tracking data and combination models which have incorporated satellite altimetry and surface gravity data. The satellite observational data base consists of over 1100 orbital arcs of data on 31 satellites. A large percentage of these observations were provided by third generation laser stations (less than 5 cm). A calibration of the model accuracy of the GEM-T2 satellite only solution indicated that it was a significant improvement over previous models based solely upon tracking data. The rms geoid error for this field is 110 cm to degree and order 36. This is a major advancement over GEM-T1 whose errors were estimated to be 160 cm. An error propagation using the covariances of the GEM-T2 model for the TOPEX radial orbit component indicates that the rms radial errors are expected to be 12 cm. The combination solution, PGS-3337, is a preliminary effort leading to the development of GEM-T3. PGS-3337 has incorporated global sets of surface gravity data and the Seasat altimetry to produce a model complete to (50,50). A solution for the dynamic ocean topography to degree and order 10 was included as part of this adjustment.
Knowledge of global oceanic tides has markedly advanced over the last two decades, in no small part because of the near-global measurements provided by satellite altimeters, and especially the long and precise Topex/Poseidon time series e.g. [2]. Satellite altimetry in turn places very severe demands on the accuracy of tidal models. The reason is clear: tides are by far the largest contributor to the variance of sea-surface elevation, so any study of non-tidal ocean signals requires removal of this dominant tidal component. Efforts toward improving models for altimetric tide corrections have understandably focused on deep-water, open-ocean regions. These efforts have produced models thought to be generally accurate to about 2 cm rms. Corresponding tide predictions in shelf and near-coastal regions, however, are far less accurate. This paper discusses the status of our current abilities to provide near-global tidal predictions in shelf and near-coastal waters, highlights some of the difficulties that must be overcome, and attempts to divine a path toward some degree of progress. There are, of course, many groups worldwide who model tides over fairly localized shallow-water regions, and such work is extremely valuable for any altimeter study limited to those regions, but this paper considers the more global models necessary for the general user. There have indeed been efforts to patch local and global models together, but such work is difficult to maintain over many updates and can often encounter problems of proprietary or political nature. Such a path, however, might yet prove the most fruitful, and there are now new plans afoot to try again. As is well known, tides in shallow waters tend to be large, possibly nonlinear, and high wavenumber. The short spatial scales mean that current mapping capabilities with (multiple) nadir-oriented altimeters often yield inadequate coverage. This necessitates added reliance on numerical hydrodynamic models and data assimilation, which in turn necessitates very accurate bathymetry with high spatial resolution. Nonlinearity means that many additional compound tides and overtides must be accounted for in our predictions, which increases the degree of modeling effort and increases the amounts of data required to disentangle closely aliased tides.
Evidence for the coupling of diurnal and semidiurnal thermal tides, observed as surface pressure oscillations at the Viking Lander 1 and 2 landing sites, to Martian global dust storms is presented and the implications for models of dust storm generation are discussed. Local atmospheric opacity increases and jumps in atmospheric pressure ranges were found to be essentially simultaneous, and diurnal and semidiurnal components of the pressure and wind oscillations were observed to increase markedly after the onset of a dust storm. The semidiurnal wind component can be related to the observed surface pressure variations by means of a model of a semidiurnally forced Ekman boundary layer. However, a classical atmospheric tidal model shows that the preferential enhancement of the semidiurnal surface pressure oscillation observed at the Lander 1 site can be produced by a tidal heating distribution in which most of the heating is done at an altitude above 10 km. Observations suggest that various mechanisms are important for the generation and decay of global Martian dust storms.
BM Camelopardalis (=12 Cam) is a chromospherically active binary star with a relatively large orbital eccentricity. Systems with large eccentricities usually rotate pseudosynchronously. However, BM Cam has been a puzzle since its observed rotation rate is virtually equal to its orbital period indicating synchronization. All available photometry data for BM Cam have been collected and analyzed. Two models of modulated ellipticity effect are proposed, one based on equilibrium tidal deformation of the primary star and the other on a dynamical tidal effect. When the starspot variability is removed from the data, the dynamical tidal model was the better approximation to the real physical situation. The analysis indicates that BM Cam is not rotating pseudosynchronously but rotating in virtual synchronism after all.
The paper presents a steady state, zonally symmetric response of an atmospheric circulation to the combined effects of the very large zonal-mean diabatic heating and thermotidal forcing thought to exist in the dusty Martian atmosphere during one of its episodic global dust storms. The zonal-mean components of the tidal flux-convergences of momentum and heat are computed using an existing classical atmospheric tidal model constrained by the surface pressure observations at the two Viking Lander sites on Mars. A nearly inviscid two-dimensional model is used to compute the zonally symmetric response to the computed tidal flux-convergences and to the zonal-mean heating of the airborne dust. The results are compared with data from the Viking missions.
Goddard Earth Model T1 (GEM-T1), which was developed from an analysis of direct satellite tracking observations, is the first in a new series of such models. GEM-T1 is complete to degree and order 36. It was developed using consistent reference parameters and extensive earth and ocean tidal models. It was simultaneously solved for gravitational and tidal terms, earth orientation parameters, and the orbital parameters of 580 individual satellite arcs. The solution used only satellite tracking data acquired on 17 different satellites and is predominantly based upon the precise laser data taken by third generation systems. In all, 800,000 observations were used. A major improvement in field accuracy was obtained. For marine geodetic applications, long wavelength geoidal modeling is twice as good as in earlier satellite-only GEM models. Orbit determination accuracy has also been substantially advanced over a wide range of satellites that have been tested.
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).
Pluto and its largest satellite, Charon, currently orbit in a mutually synchronous state; both bodies continuously show the same face to one another. This orbital configuration is a natural end-state for bodies that have undergone tidal dissipation. In order to achieve this state, both bodies would have experienced tidal heating and stress, with the extent of tidal activity controlled by the orbital evolution of Pluto and Charon and by the interior structure and rheology of each body. As the secondary, Charon would have experienced a larger tidal response than Pluto, which may have manifested as observable tectonism. Unfortunately, there are few constraints on the interiors of Pluto and Charon. In addition, the pathway by which Charon came to occupy its present orbital state is uncertain. If Charon's orbit experienced a high-eccentricity phase, as suggested by some orbital evolution models, tidal effects would have likely been more significant. Therefore, we determine the conditions under which Charon could have experienced tidally-driven geologic activity and the extent to which upcoming New Horizons spacecraft observations could be used to constrain Charon's internal structure and orbital evolution. Using plausible interior structure models that include an ocean layer, we find that tidally-driven tensile fractures would likely have formed on Charon if its eccentricity were on the order of 0.01, especially if Charon were orbiting closer to Pluto than at present. Such fractures could display a variety of azimuths near the equator and near the poles, with the range of azimuths in a given region dependent on longitude; east-west-trending fractures should dominate at mid-latitudes. The fracture patterns we predict indicate that Charon's surface geology could provide constraints on the thickness and viscosity of Charon's ice shell at the time of fracture formation.
The tidal heating components for the dusty Martian atmosphere are computed based on dust optical parameters estimated from Viking Lander imaging data, and used to compute the variation of the tidal surface pressure components at the Viking Lander sites as a function of season and the total vertical extinction optical depth of the atmosphere. An atmospheric tidal model is used which is based on the inviscid, hydrostatic primitive equations linearized about a motionless basic state the temperature of which varies only with height, and the profiles of the tidal forcing components are computed using a delta-Eddington approximation to the radiative transfer equations. Comparison of the model results with the observed variations of surface pressure and overhead dust opacity at the Viking Lander 1 site reveal that the dust opacities and optical parameters derived from imaging data are roughly representative of the global dust haze necessary to reproduce the observed surface pressure amplitudes, with the exception of the model-inferred asymmetry parameter, which is smaller during the onset of a great storm. The observed preferential enhancement of the semidiurnal tide with respect to the diurnal tide during dust storm onset is shown to be due primarily to the elevation of the tidal heating source in a very dusty atmosphere.
The solar tide in an ancient Venusian ocean is simulated using a dedicated numerical tidal model. Simulations with varying ocean depth and rotational periods ranging from −243 to 64 sidereal Earth days are used to calculate the tidal dissipation rates and associated tidal torque. The results show that the tidal dissipation could have varied by more than 5 orders of magnitude, from 0.001 to 780 GW, depending on rotational period and ocean depth. The associated tidal torque is about 2 orders of magnitude below the present day Venusian atmospheric torque, and could change the Venusian daylength by up to 72 days per million years depending on rotation rate. Consequently, an ocean tide on ancient Venus could have had significant effects on the rotational history of the planet. These calculations have implications for the rotational periods of similarly close-in exoplanetary worlds and the location of the inner edge of the liquid water habitable zone.
Solid body tides provide key information on the interior structure, evolution, and origin of the planetary bodies. Our Solar system harbours a very diverse population of planetary bodies, including those composed of rock, ice, gas, or a mixture of all. While a rich arsenal of geophysical methods has been developed over several years to infer knowledge about the interior of the Earth, the inventory of tools to investigate the interiors of other Solar-system bodies remains limited. With seismic data only available for the Earth, the Moon, and Mars, geodetic measurements, including the observation of the tidal response, have become especially valuable and therefore, has played an important role in understanding the interior and history of several Solar system bodies. To use tidal response measurements as a means to obtain constraints on the interior structure of planetary bodies, appropriate understanding of the viscoelastic reaction of the materials from which the planets are formed is needed. Here, we review the fundamental aspects of the tidal modeling and the information on the present-day interior properties and evolution of several planets and moons based on studying their tidal response. We begin with an outline of the theory of viscoelasticity and tidal response. Next, we proceed by discussing the information on the tidal response and the inferred structure of Mercury, Venus, Mars and its moons, the Moon, and the largest satellites of giant planets, obtained from the analysis of the data that has been provided by space missions. We also summarise the upcoming possibilities offered by the currently planned missions.
The solar tide in an ancient Venusian ocean is simulated using a dedicated numerical tidal model. Simulations with varying ocean depth and rotational periods ranging from minus 243 to 64 sidereal Earth days are used to calculate the tidal dissipation rates and associated tidal torque. The results show that the tidal dissipation could have varied by more than 5 orders of magnitude, from 0.001 to 780 gigawatts (GW), depending on rotational period and ocean depth. The associated tidal torque is about 2 orders of magnitude below the present day Venusian atmospheric torque, and could change the Venusian daylength by up to 72 days per million years depending on rotation rate. Consequently, an ocean tide on ancient Venus could have had significant effects on the rotational history of the planet. These calculations have implications for the rotational periods of similarly close-in exoplanetary worlds and the location of the inner edge of the liquid water habitable zone.
This report summarizes the activities of NASA grant NAG5-11068, "Dynamicai Studies of the Middle Atmosphere Using High Resolution Doppler Imager Observations." The High Resolution Doppler Imager (HRDI) on the Upper Atmosphere Research Satellite (UARS) has been providing direct measurements of the Earth's horizontal wind field in the stratosphere, mesosphere and lower thermosphere. Mesospheric temperatures, ozone, and O((sup 1) D) densities, and stratospheric aerosol extinctions coefficients, are also retrieved. The goal of HRDI is to measure the vector winds in the stratosphere (10-40 km), mesosphere, and lower thermosphere (approximately 50-120 km) during the day, and the lower thermosphere at night (approximately 95 km) to an accuracy of 5 m/s. The horizontal wind vector is measured by observing the Doppler shift of rotational lines of molecular oxygen along two lines of sight. In addition to winds, temperatures and volume emission rates are determined in the mesosphere and lower thermosphere, from which ozone and O((sup 1) D) concentrations can be derived, and aerosol scattering coefficients are determined in the stratosphere. UARS was launched on September 12, 1991, into a 585-km circular orbit inclined 57 degrees to the equator HRDI was activated September 28, 1991 and following a period of checkout and adjustment of the instrument parameters, scientific observations began November 2, 199 1. HRDI operated nearly continuously from launch until April 1995. At that time the UARS solar array drive failed, forcing the instruments to time-share the available power. From July 1995 to July 1996 HRDI operated approximately 50% of the time. At that point, one of the three spacecraft batteries failed and from then until September 1998 the duty cycle was less than 20% per month, At that time it was determined that HRDI could operate during each daytime pass, which increased the daytime duty cycle to close to l00%, while nighttime operations were limited to about a week per month. In the fall of 1999, the second tape recorder failed requiring a real time contact with a TRDSS satellite to retrieve that data. This resulted in about 60% data collection efficiency. Finally, in the summer of 2000, the second star sensor failed requiring the spacecraft attitude to be controlled by a three axis magnetometer and sun sensor. This resulted in a loss of attitude knowledge but operations continue with the anticipation of correcting the attitude. A new method for determining the tide and mean structure from satellite data in conjunction with a new tidal model has been devised. For brevity, it shall be referred to as the TMAT or Tide-Mean Assimilation Technique. Most previous methods of tidal analysis are based on various ways of slicing the data set.
Wind measurements from the Michelson Interferometer for Global High-resolution Ther-23mospheric Imaging (MIGHTI) instrument on the Ionospheric CONnections (ICON) mis-24sion provide new insights into the semidiurnal tidal spectrum in the thermosphere, cov-25ering latitudes 9◦S-39◦N and altitudes 100-280 km altitude throughout 2020. Latitude26versus day of year (DOY) variability of solar semidiurnal tides SE2, S0, SW1, SW2, SW327and SW4 at 250 km are presented for the first time, and evaluated relative to similar re-28sults at 106 km. Using daytime-only data, height versus latitude and height versus DOY29variability of SE2, S0, SW1. SW3 and SW4 amplitudes and phases are depicted for the30first time, revealing the effects of a dissipative thermosphere on the vertical evolutions31of these tidal structures. SW2 is absent from these depictions due to potential aliasing32by zonal mean winds. The above results are considered in light of the Climatological Tidal33Model of the Thermosphere (CTMT), which is based on fits to tidal winds and temper-34atures from the Thermosphere-Ionosphere-Mesosphere Energetics and Dynamics (TIMED)35mission between 80 and 120 km during 2002-2008, and extrapolated to an altitude of 40036km based on modeled tidal structures propagating in a dissipative thermosphere, but with-37out in-situ sources of excitation due to tide-tide or tide-ion drag nonlinear interactions.38On the basis of comparisons with the CTMT and other characteristics revealed in the39MIGHTI tidal structures, it is concluded that in-situ sources exist for S0, SW1, SW2 and40SW3 in the thermosphere above about 200 km.