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A high-degree spherical harmonic series is used to compute the radial deformation of the Earth by oceanic tidal loading. By exploiting fast numerical transforms, this approach is found to be much more efficient, but no less accurate, than the traditional Green's function approach. The method is used to derive an atlas of load tide maps for 10 constitutents of the NSWC ocean tide model.
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Mathematical and programming techniques to numerically calculate Earth response to global semidiurnal and diurnal ocean tide models were developed. Global vertical crustal deformations were evaluated for M sub 2, S sub 2, N sub 2, K sub 2, K sub 1, O sub 1, and P sub 1 ocean tide loading, while horizontal deformations were evaluated for the M sub 2 tidal load. Tidal gravity calculations were performed for M sub 2 tidal loads, and strain tensor elements were evaluated for M sub 2 loads. The M sub 2 solution used for the ocean tide included the effects of self-gravitation and crustal loading.
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.
The earth's imperfectly elastic response to body and loading tidal forces is discussed using complex Love numbers and complex mass loading coefficients. Exact analytical expressions were derived relating the energy dissipation within an inhomogeneous, compressible solid earth to the surface values of these complex characteristic numbers, thus relating the global dissipation function Q to the phase shifts in the potential, gravity, tilt, strain and displacement tides. Integration of a global ocean tidal model shows that energy dissipated in the solid earth due to ocean loading is at least 10% of that dissipated in the body tides.
The observed triaxial ellipsoid shape of Mimas, in conjunction with a mean density of 1137 kg/cu cm, is presently used as the basis of hydrostatic equilibrium and nonhydrostatic models of internal structure whose outer layers are sufficiently strong to support part of the tidal load. Such plausible internal structures are consistent with the shape and density constraints as (1) a two-layer model in hydrostatic equilibrium, (2) a hydrostatic model with four layers of equal depth, and (3) a nonhydrostatic constant-density model with an elastic lithosphere; these models admit either homogeneous or heterogeneous accretion, as well as either a cold thermal history or melting and differentiation.
The VLBI data set spanning Aug. 1919 to the present is a major constituent of ITRF2000 because of the time span, the geometric strength and the accuracy of the modeling. Formal velocity errors for the best stations are less than 0.3 mm/yr while the probable frame definition error for station velocities is approximately 0.4 mm/yr. The primary systematic errors are the troposphere and tidal loading (solid Earth and ocean). However, the scale of the VLBI TRF is probably only weakly affected because of continued improvements in the tropospheric mapping function and gradient estimation. There are some weaknesses in the spatial distribution of data, particularly in the southern hemisphere, and the quality of the mobile VLBI results is now suboptimal. The deployment of the TIGO system to Chile will improve the geometric coverage. The current state of the art of VLBI analysis will be discussed.
Two papers on tidal dissipation were completed and published. The first of these extended our earlier work, which focused on the dominant M2 constituent, to include 7 additional constituents. In addition to confirming a total deep water dissipation total very close to 1 TW, this study demonstrated significant differences in the distribution of dissipation between diurnal and semi-diurnal constituents. The second paper involved an extensive modeling study of tides in the present day and the last glacial maximum. In this study we showed that accuracy of tidal solutions for the present day Ocean were significantly improved by including a parameterization of internal tide drag over rough topography in the deep ocean. It was also demonstrated that a complete self-consistent treatment of Ocean self attraction and tidal loading was required for accurate solutions.
The current cache of S/X-band geodetic/astrometric VLBI data accumulated since 1979 is approx. 5 million observations and is increasing by approx. 300,000 observations per year. The long time interval and access to all such VLBI data for re-analysis have contributed to their usefulness for the terrestrial and celestial reference frames, Earth orientation parameters, tidal and non-tidal loading, and troposphere. While data access and integrity have been maintained through the Mark III data base system as storage devices and media have evolved, past transitions have been major projects. A new format and retention concept to ensure eternal archiving and access should make use of self-documentation, generalized media, network connectivity and multiple redundancy. Similarly permanent organizations or sequences of organizations are also necessary.
The gravity fields of celestial bodies that possess an atmosphere are periodically perturbed by the redistribution of fluid mass associated with the atmospheric dynamics. A component of this perturbation is due to the gravitational response of the body to the deformation of its surface induced by the atmospheric pressure loading. The magnitude of this effect depends on the relation between the loading and the response in terms of geopotential variations measured by the load Love numbers. In this work, we simulate and analyze the gravity field generated by the atmospheres of Venus and Mars by accounting for different models of their internal structure. By precisely characterizing the phenomena that drive the mass transportation in the atmosphere through general circulation models, we determine the effect of the interior structure on the response to the atmospheric loading. An accurate estimation of the time-varying gravity field, which measures the atmospheric contribution, may provide significant constraints on the interior structure through the measurement of the load Love numbers. A combined determination of tidal and load Love numbers would enhance our knowledge of the interior of planetary bodies, providing further geophysical constraints in the inversion of internal structure models.The gravity fields of celestial bodies that possess an atmosphere are periodically perturbed by the redistribution of fluid mass associated with the atmospheric dynamics. A component of this perturbation is due to the gravitational response of the body to the deformation of its surface induced by the atmospheric pressure loading. The magnitude of this effect depends on the relation between the loading and the response in terms of geopotential variations measured by the load Love numbers. In this work, we simulate and analyze the gravity field generated by the atmospheres of Venus and Mars by accounting for different models of their internal structure. By precisely characterizing the phenomena that drive the mass transportation in the atmosphere through general circulation models, we determine the effect of the interior structure on the response to the atmospheric loading. An accurate estimation of the time-varying gravity field, which measures the atmospheric contribution, may provide significant constraints on the interior structure through the measurement of the load Love numbers. A combined determination of tidal and load Love numbers would enhance our knowledge of the interior of planetary bodies, providing further geophysical constraints in the inversion of internal structure models.
Forward modeling of non-tidal atmospheric loading displacements at geodetic tracking stations have not routinely been included in Doppler Orbitography and Radiopositionning Integrated by Satellite (DORIS) or Satellite Laser Ranging (SLR) station analyses for either POD applications or reference frame determination. The displacements which are computed from 6-hourly models such as the ECMWF and can amount to 3-10 mm in the east, north and up components depending on the tracking station locations. We evaluate the application of atmospheric loading in a number ways using the NASA GSFC GEODYN software: First we assess the impact on SLR & DORIS-determined orbits such as Jason-2, where we evaluate the impact on the tracking data RMS of fit and how the total orbits are changed with the application of this correction. Preliminary results show an RMS radial change of 0.5 mm for Jason-2 over 54 cycles and a total change in the Z-centering of the orbit of 3 mm peak-to-peak over one year. We also evaluate the effects on other DORIS-satellites such as Cryosat-2, Envisat and the SPOT satellites. In the second step, we produce two SINEX time series based on data from available DORIS satellites and assess the differences in WRMS, scale and Helmert translation parameters. Troposphere refraction is obviously an important correction for radiometric data types such as DORIS. We evaluate recent improvements in DORIS processing at GSFC including the application of the Vienna Mapping Function (VMF1) grids with a-priori hydrostatic (VZHDs) and wet (VZWDs) zenith delays. We reduce the gridded VZHD at the stations height using pressure and temperature derived from GPT (strategy 1) and Saastamoinen. We discuss the validation of the VMF1 implementation and its application to the Jason-2 POD processing, compared to corrections using the Niell mapping function and the GMF. Using one year of data, we also assess the impact of the new troposphere corrections on the DORIS-only solutions, most importantly on the scale of the weekly solutions.
The effects of long-wavelength (> 100 km), seasonal variability in continental water storage on vertical crustal motions are assessed. The modeled vertical displacements (delta-r(sub M)) have root-mean-square (RMS) values for 1994-1998 as large as 8 mm with ranges up to 30 mm, and are predominantly annual in character. Regional strains are on the order of 20 nanostrain for tilt and 5 nanostrain for horizontal deformation. We compare delta-r(sub M) with observed Global Positioning System (GPS) heights (delta-r(sub O)) (which include adjustments to remove estimated effects of atmospheric pressure and annual tidal and non-tidal ocean loading) for 147 globally distributed sites. When the delta-r(sub O) time series are adjusted by delta-r(sub M), their variances are reduced, on average, by an amount equal to the variance of the delta-r(sub M). Of the delta-r(sub O) time series exhibiting a strong annual signal, more than half are found to have an annual harmonic that is in phase and of comparable amplitude with the annual harmonic in the delta-r(sub M). The delta-r(sub M) time series exhibit long-period variations that could be mistaken for secular tectonic trends or post-glacial rebound when observed over a time span of a few years.
In recent years, Kalman filtering has emerged as a suitable technique to determine terrestrial reference frames (TRFs), a prime example being JTRF2014. The time series approach allows variations of station coordinates that are neither reduced by observational corrections nor considered in the functional model to be taken into account. These variations are primarily due to non-tidal geophysical loading effects that are not reduced according to the current IERS Conventions (2010). It is standard practice that the process noise models applied in Kalman filter TRF solutions are derived from time series of loading displacements and account for station dependent differences. So far, it has been assumed that the parameters of these process noise models are constant over time. However, due to the presence of seasonal and irregular variations, this assumption does not truly reflect reality. In this study, we derive a station coordinate process noise model allowing for such temporal variations. This process noise model and one that is a parameterized version of the former are applied in the computation of TRF solutions based on very long baseline interferometry data. In comparison with a solution based on a constant process noise model, we find that the station coordinates are affected at the millimeter level.
I will provide an overview of advances in VLBI data analysis implemented at NASA GSFC. That include the use of B-splines for modeling non-linear station position evolution, the use of all non-tidal mass loadings in data reduction, the use of slant a priori path delays from the output of numerical weather models, the use of B-splines for evaluation of the Earth orientation parameters as a continuous function, the use of elevation-dependent weighting, processing both 24 hr and 1 hr experiments in a single least square solutions and other innovations. I will show how this changes in data analysis affect space geodesy results, such as estimation of station positions, Earth orientation parameters, and source coordinates.
The current cache of S/X-band geodetic/astrometric VLBI data accumulated since 1979 is approx.4.2 million observations and is increasing by approx.300,000 observations per year. The long time interval and access to all such VLBI data for re-analysis have contributed to their usefulness for the terrestrial and celestial reference frames, Earth orientation parameters, tidal and nontidal loading, and troposphere. While data access and integrity have been maintained through the Mark III data base system as storage devices and media have evolved, past transitions have been major projects. A new format and retention concept to ensure eternal archiving and access should make use of self-documentation, generalized media, network connectivity and multiple redundancy. Similarly permanent organizations or sequences of organizations are also necessary.
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.
A computer software system is described which computes global numerical solutions of the integro-differential Laplace tidal equations, including dissipation terms and ocean loading and self-gravitation effects, for arbitrary diurnal and semidiurnal tidal constituents. The integration algorithm features a successive approximation scheme for the integro-differential system, with time stepping forward differences in the time variable and central differences in spatial variables. Solutions for M2, S2, N2, K2, K1, O1, P1 tidal constituents neglecting the effects of ocean loading and self-gravitation and a converged M2, solution including ocean loading and self-gravitation effects are presented in the form of cotidal and corange maps.
The Jason-2 satellite, launched in June 2008, is the latest follow-on to the successful Jason-1 altimetry satellite mission launched in December 7, 2001. Both, Jason-2 and Jason-1 are equipped with a GPS dual-frequency receiver, a laser retroreflector array, and a DORIS receiver for precise orbit determination (POD). A series of dynamic and reduced-dynamic Jason-2 orbits computed at NASA GSFC, based on GPS-only data and the std0905 standards, have been completed till cy74through cycle 74 using the IGS05 framework. These orbits, now publicly available, have been shown to agree radially at 1 cm RMS with the GSFC std0905 SLR/DORIS orbits and in comparison with orbits produced by JPL, ESA and CNES. In this paper, we describe the implementation of the IGS08 and repro1 framework for the Jason-2 and Jason-1 GPS POD processing with the NASA GSFC GEODYN software. . In our updated GPS POD, ambiguity fixing and updated time variable and static gravity fields. We also evaluate the implementation of non-tidal and degree-1 loading displacement as forward modeling to the tracking stations. Reduced-dynamic versus dynamic orbit differences are used to characterize the remaining force model errors and TRF instability. In particular, we assess their consistency radially and the stability of the altimeter satellite reference frame in the North/South direction as a proxy to assess the consistency of the reference frame.