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NASA NTRS1982

The tide in the seas of Titan

The parameters of the tides in the near-global ocean that may exist on Titan are assessed. A formula for the difference between the maximum heights of the oceanic and body tides is used to determine that the amplitude of the apparent, near-stationary, oceanic tide on Titan is greater than about 100 m. The effects of tidal dissipation are evaluated, showing that the amplitude of the tide will vary by nine percent over its 15.95-day period. The observed eccentricity of Titan's orbit is used to establish limits on the satellite's surface topography and oceanic depths. It is concluded that either Titan is covered by a near-global methane ocean over 400 m deep, or that there is no methane ocean at all. Reflectivity measurements can decide between these alternatives.

Sagan, C.↗
NASA NTRS1985

Middle atmosphere tides

The recent direction of theoretical and observational research in middle atmosphere tides is reviewed. The diurnal tide has received considerable emphasis, including observations of evanescent components at high latitudes, numerical simulations of nonmigrating propagating components due to longitudinally varying water vapor insolation absorption in the troposphere, and implications and origins of unsteadiness in tidal oscillations over periods of days. Recent analyses of Nimbus 7 LIMS temperatures and partial reflection drift measurements of neutral winds in the tropical mesosphere have also emphasized the diurnal propagating tide. A description of the Atmospheric Tides Middle Atmosphere Program (ATMAP) and an overview of ATMAP campaign results are also presented.

Forbes, J. M.↗
NASA NTRS1988

The self-consistent dynamic pole tide in non-global oceans

The dynamic pole tide is determined by solving Laplace tide equations which take into account the presence of continents in oceans, oceanic self-gravitation and loading, and mantle elasticity. Dynamical effects are found to be only mild. It is shown that the dynamical pole tide contributes about one day more to the Chandler period than a static pole tide would, and dissipates wobble energy at a very weak rate. It is noted that, depending on the wobble period predicted for an oceanless elastic earth, mantle anelasticity at low frequencies may nevertheless contribute negligibly to the Chandler period.

Dickman, S. R.↗
NASA NTRS1989

Nonmigrating tides

Recently an interesting advancement in the study of nonmigrating tides has occurred. There have been two distinct approaches in works on this subject. One is based on mechanistic models as considering nonuniform global distribution of water vapor or heating only on land, solving a set of linear equations. It is found that insolation absorption of the nonuniformly distributed water vapor produces only weak nonmigrating tides in the lower thermosphere; the planetary boundary layer heating on land can explain the enhanced tides on land and those with short vertical wavelengths in the stratosphere. The other approach is novel and uses simulation on the general circulation model (GCM). This realistic model can reproduce tides globally and in many details. The enhancement of two nonmigrating modes as eastward traveling modes with a wave number 3 and westward traveling modes with a wave number 5 is in surprisingly good agreement with observation at sea level, at 700 mb and even at 300 mb.

Kato, S.↗
NASA NTRS1990

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 zonal response function kappa of the solid earth-ocean system is defined 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 kappa for the monthly, fortnightly, and nine-day lunar tides are estimated from 2 1/2 years of VLBI UT1 observations, corrected for atmospheric angular momentum effects using NMC wind and pressure series. Using the dynamic ocean tide model of Dickman (1988, 1989), amplitudes and phases of kappa for an elastic earth-ocean system are predicted. The predictions confirm earlier results which found that dynamic effects of the longer-period ocean tides reduce the amplitude of kappa by about 1 percent.

Nam, Young↗
NASA NTRS1991

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.

Cartwright, D. E.↗
NASA NTRS1991

Global ocean tides through assimilation of oceanographic and altimeter satellite data in a hydrodynamic model

Ocean tides must be considered in many scientific disciplines: astronomy, oceanography, geodesy, geophysics, meteorology, and space technologies. Progress in each of these disciplines leads to the need for greater knowledge and more precise predictions of the ocean tide contribution. This is particularly true of satellite altimetry. On one side, the present and future satellite altimetry missions provide and will supply new data that will contribute to the improvement of the present ocean tide solutions. On the other side, tidal corrections included in the Geophysical Data Records must be determined with the maximum possible accuracy. The valuable results obtained with satellite altimeter data thus far have not been penalized by the insufficiencies of the present ocean tide predictions included in the geophysical data records (GDR's) because the oceanic processes investigated have shorter wavelengths than the error field of the tidal predictions, so that the residual errors of the tidal corrections are absorbed in the empirical tilt and bias corrections of the satellite orbit. For future applications to large-scale oceanic phenomena, however, it will no longer be possible to ignore these insufficiencies.

Leprovost, Christian↗
NASA NTRS1994

Comparison of TOPEX sea surface heights and tide gauge sea levels

TOPEX sea surface height data from the first 300 days of the mission are compared to sea level data from 71 tide gauges. The initial comparison uses sea surface height data processed according to standard procedures as defined in the users handbook. It is found that the median correlations for island and for coastal tide gauges are 0.53 and 0.42, respectively. The analogous root mean square (RMS) differences between the two data sets are 7.9 and 10.4 cm. The comparisons improve significantly when a 60-day harmonic is fit to the differences and removed. This period captures aliased M(sub 2) and S(sub 2) tidal energy that is not removed by the tide model. Making this correction and smoothing the sea surface height data over 25-km along-track segments results in median correlations of 0.58 and 0.46 for the islands and coastal stations, and median RMS differences of 5.8 and 7.7 cm, respectively. Removing once per revolution signals from the sea surface heights results in degraded comparisons with the sea levels. It is also found that a number of stations have poor comparisons due to propagating signals that introduce temporal lags between the altimeter and tide gauge time series. A final comparison is made by eliminating stations where this propagation effect is large, discarding two stations that are suspected to have problems with the sea level data, smoothing over 10-day intervals, and restricting attention to islands gauges. This results in a set of 552 data pairs that have a correlation of 0.66 and a RMS difference of 4.3 cm. The conclusion is that on timescales longer than about 10 days the RMS sea surface height errors are less than or of the order of several centimeters.

Mitchum, Gary T.↗
NASA NTRS1994

TOPEX/POSEIDON tides estimated using a global inverse model

Altimetric data from the TOPEX/POSEIDON mission will be used for studies of global ocean circulation and marine geophysics. However, it is first necessary to remove the ocean tides, which are aliased in the raw data. The tides are constrained by the two distinct types of information: the hydrodynamic equations which the tidal fields of elevations and velocities must satisfy, and direct observational data from tide gauges and satellite altimetry. Here we develop and apply a generalized inverse method, which allows us to combine rationally all of this information into global tidal fields best fitting both the data and the dynamics, in a least squares sense. The resulting inverse solution is a sum of the direct solution to the astronomically forced Laplace tidal equations and a linear combination of the representers for the data functionals. The representer functions (one for each datum) are determined by the dynamical equations, and by our prior estimates of the statistics or errors in these equations. Our major task is a direct numerical calculation of these representers. This task is computationally intensive, but well suited to massively parallel processing. By calculating the representers we reduce the full (infinite dimensional) problem to a relatively low-dimensional problem at the outset, allowing full control over the conditioning and hence the stability of the inverse solution. With the representers calculated we can easily update our model as additional TOPEX/POSEIDON data become available. As an initial illustration we invert harmonic constants from a set of 80 open-ocean tide gauges. We then present a practical scheme for direct inversion of TOPEX/POSEIDON crossover data. We apply this method to 38 cycles of geophysical data records (GDR) data, computing preliminary global estimates of the four principal tidal constituents, M(sub 2), S(sub 2), K(sub 1) and O(sub 1). The inverse solution yields tidal fields which are simultaneously smoother, and in better agreement with altimetric and ground truth data, than previously proposed tidal models. Relative to the 'default' tidal corrections provided with the TOPEX/POSEIDON GDR, the inverse solution reduces crossover difference variances significantly (approximately 20-30%), even though only a small number of free parameters (approximately equal to 1000) are actually fit to the crossover data.

Egbert, Gary D.↗
NASA NTRS1998

Wind Stress Forcing of the North Sea "Pole Tide"

We conducted numerical simulations of the wind-forcing of the sea level variations in the North Sea using a barotropic ocean model with realistic geography, bathymetry, and boundary conditions, to examine the forcing of the 14-month "pole tide" which is known to be strong along the Denmark- Netherlands coast. The simulation input is the monthly-mean surface wind stress field from the National Centers for Environmental Prediction (NCEP) reanalysis for the 40-year period 1958-1997. The output sea level response was then compared with 10 coastal tide gauge records from the Permanent Service for Mean Sea Level (PSMSL). Besides the strong seasonal variations, several prominent quasi-periodicities exist at around 7 years, 3 years, 14 months, 9 months, and 6.5 months. Correlation and spectral analyses show remarkable agreement between the model output and the observations, particularly in the 14-month, or Chandler period band. The latter indicates that the enhanced pole tide found in the North Sea along the Denmark-Netherlands coast is actually the coastal setup response to wind stress forcing with a periodicity of 14 months. We find no need to invoke a geophysical explanation involving resonance-enhancement of pole tide in the North Sea to explain the observations.

OConnor, William P.↗
NASA NTRS1999

A Global Ocean Tide Model From TOPEX/POSEIDON Altimetry: GOT99.2

Goddard Ocean Tide model GOT99.2 is a new solution for the amplitudes and phases of the global oceanic tides, based on over six years of sea-surface height measurements by the TOPEX/POSEIDON satellite altimeter. Comparison with deep-ocean tide-gauge measurements show that this new tidal solution is an improvement over previous global models, with accuracies for the main semidiurnal lunar constituent M2 now below 1.5 cm (deep water only). The new solution benefits from use of prior hydrodynamic models, several in shallow and inland seas as well as the global finite-element model FES94.1. This report describes some of the data processing details involved in handling the altimetry, and it provides a comprehensive set of global cotidal charts of the resulting solutions. Various derived tidal charts are also provided, including tidal loading deformation charts, tidal gravimetric charts, and tidal current velocity (or transport) charts. Finally, low-degree spherical harmonic coefficients are computed by numerical quadrature and are tabulated for the major short-period tides; these are useful for a variety of geodetic and geophysical purposes, especially in combination with similar estimates from satellite laser ranging.

Ray, Richard D.↗
NASA NTRS1998

A Study of Ion Velocities Observed by TIDE and How It Relates to Magnetospheric Circulation

The high-latitude ion velocities measured by the Thermal Ion Dynamics Experiment (TIDE) instrument on the Polar spacecraft will be examined in relation to magnetospheric circulation. TIDE derives ion velocities from moments of measured distribution functions. Hydrogen and oxygen ions are 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). At perigee 0+ is typically seen flowing down in the polar cap and outflowing from the cleft. At the transition from downflowing to upflowing there is also seen a reversal in the ion convection. The convection at perigee is consistent with standard ionospheric convection models for given Interplanetary Magnetic Field (IMF) conditions. Convection at high altitude (approximately 8.9 Re) polar regions has not been studied very much since there have not been many satellites in this region. Unlike previous missions to this region TIDE in conjunction the Plasma Source Instrument (PSI) can measure ions with as low an energy as several electron Volts. The outflowing ions observed by TIDE at apogee are believed to be important to the overall circulation of the magnetosphere. The convection of these outflowing ions at apogee will be related to the IMF. This study tries to answer the question of how the IMF response of the convection influences the overall circulation of the magnetosphere.

Elliott, H. A.↗
NASA NTRS2000

Resonant Third-Degree Diurnal Tides in the Seas Off Western Europe

Third-degree diurnal tides are estimated from long time series of sea level measurements at three North Atlantic tide gauges. Although their amplitudes are only a few mm or less, their admittances are far larger than those of second-degree diurnal tides, just as Cartwright discovered for the M(sub 1) constituent. The tides are evidently resonantly enhanced owing to high spatial correlation between the third-degree spherical harmonic of the tidal potential and a near-diurnal oceanic normal mode that is most pronounced in the North Atlantic. By estimating the ocean tidal response across the diurnal band (5 tidal constituents plus nodal modulations), the period and Q of this mode and one nearby mode are estimated.

Ray, Richard D.↗
NASA NTRS2000

Modeling the Diurnal Tides in the MLT Region with the Doppler Spread Parameterization of Gravity Waves

Special Session: SA03 The mesosphere/lower thermosphere region: Structure, dynamics, composition, and emission. Ground based and satellite observations in the upper mesosphere and lower thermosphere (MLT) reveal large seasonal variations in the horizontal wind fields of the diurnal and semidiurnal tides. To provide an understanding of the observations, we discuss results obtained with our Numerical Spectral Model (NMS) that incorporates the gravity wave Doppler Spread Parameterization (DSP) of Hines. Our model reproduces many of the salient features observed, and we discuss numerical experiments that delineate the important processes involved. Gravity wave momentum deposition and the seasonal variations in the tidal excitation contribute primarily to produce the large equinoctial amplitude maxima in the diurnal tide. Gravity wave induced variations in eddy viscosity, not accounted for in the model, have been shown by Akmaev to be important too. For the semidiurnal tide, with amplitude maximum observed during winter solstice, these processes also contribute, but filtering by the mean zonal circulation is more important. A deficiency of our model is that it cannot reproduce the observed seasonal variations in the phase of the semidiurnal tide, and numerical experiments are being carried out to diagnose the cause and to alleviate this problem. The dynamical components of the upper mesosphere are tightly coupled through non-linear processes and wave filtering, and this may constrain the model and require it to reproduce in detail the observed phenomenology.

Mayr, H. G.↗
NASA NTRS1999

Simulations of the Surface Pressure Tides on Mars Incorporating New MOLA Topography Data

Simulations of surface pressure tides on Mars have been conducted previously with the NASA Ames Mars General Circulation Model (MGCM), as well as by Wilson and Hamilton. In the case of the MGCM, annual simulations with realistic (Viking-derived) dust loading have been reasonably successful at reproducing observed tides at the Viking Lander sites. One obvious discrepancy between observed and simulated tides is the amplification found in the model's diurnal tidal amplitude around L(sub s) 90. The observations show no such amplification. We report here on recent simulations of the surface pressure tide on Mars conducted with the MGCM and with the newly acquired MOLA topography data. The data is provided at 1deg x 1deg resolution, and is used by the MGCM at 7.5deg x 9deg resolution. The vertical domain of the MGCM extends to around 80 km. In the simulations reported in, the vertical domain extended to around 50 km, and the Consortium topography dataset was used. Additional information is contained in the original extended abstract.

Bridger, A. F. C.↗
NASA NTRS2000

Mesosphere Dynamics with Gravity Wave Forcing: Diurnal and Semi-Diurnal Tides - 1

We present results from a nonlinear, 3D, time dependent numerical spectral model (NSM), which extends from the ground up into the thermosphere and incorporates Hines' Doppler Spread Parameterization for small-scale gravity waves (GW). Our focal point is the mesosphere that is dominated by wave interactions. We discuss diurnal and semi-diurnal tides ill the present paper (Part 1) and planetary waves in the companion paper (Part 2). To provide an understanding of the seasonal variations of tides, in particular with regard to gravity wave processes, numerical experiments are performed that lead to the following conclusions: 1. The large semiannual variations in tile diurnal tide (DT), with peak amplitudes observed around equinox, are produced primarily by GW interactions that involve, in part, planetary waves. 2. The DT, like planetary waves, tends to be amplified by GW momentum deposition, which reduces also the vertical wavelength. 3.Variations in eddy viscosity associated with GW interactions tend to peak in late spring and early fall and call also influence the DT. 4. The semidiurnal semidiurnal tide (SDT), and its phase in particular, is strongly influenced by the mean zonal circulation. 5. The SDT, individually, is amplified by GW's. But the DT filters out GW's such that the wave interaction effectively reduces the amplitude of the SDT, effectively producing a strong nonlinear interaction between the DT and SDT. 6.) Planetary waves generated internally by baroclinic instability and GW interaction produce large amplitude modulations of the DT and SDT.

Mayr, H. G.↗
NASA NTRS2000

Estimates of Internal Tide Energy Fluxes from Topex/Poseidon Altimetry: Central North Pacific

Energy fluxes for first-mode M(sub 2) 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 were found to emanate from several large bathymetric structures, especially the Hawaiian Ridge, where the integrated flux amounts to about six gigawatts. Internal tides are generated at the Aleutian Trench near 172 deg west and propagate southwards nearly 2000 km.

Ray, Richard D.↗
NASA NTRS2001

Modeling Tides, Planetary Waves, and Equatorial Oscillations in the MLT

Applying Hines Doppler Spread Parameterization for gravity waves (GW), our 3D model reproduces some essential features that characterize the observed seasonal variations of tides and planetary waves in the upper mesosphere. In 2D, our model also reproduces the large Semi-Annual Oscillation (SAO) and Quasi Biennial Oscillation (QBO) observed in this region at low latitudes. It is more challenging to describe these features combined in a more comprehensive self consistent model, and we give a progress report that outlines the difficulties and reports some success. In 3D, the GW's are partially absorbed by tides and planetary waves to amplify them. Thus the waves are less efficient in generating the QBO and SAO at equatorial latitudes. Some of this deficiency is compensated by the fact that the GW activity is observed to be enhanced at low latitudes. Increasing the GW source has the desired effect to boost the QBO, but the effect is confined primarily to the stratosphere. With increasing altitude, the meridional circulation becomes more important in redistributing the momentum deposited in the background flow by the GW's. Another factor involved is the altitude at which the GW's originate, which we had originally chosen to be the surface. Numerical experiments show that moving this source altitude to the top of the troposphere significantly increases the efficiency for generating the QBO without affecting much the tides and planetary waves in the model. Attention to the details in which the GW source comes into play thus appears to be of critical importance in modeling the phenomenology of the MLT. Among the suite of numerical experiments reported, we present a simulation that produced significant variations of tides and planetary waves in the upper mesosphere. The effect is related to the QBO generated in the model, and GW filtering is the likely cause.

Mengel, J. G.↗