(1) Astronom. Inst. Acad. Sci. Czech Rep., CZ-251 65 Ondrejov Obs.
(2) J. Kostelecky, Research Inst. Geodesy, Topogr. Cartogr., CZ-250 66 Zdiby 98
A dual-satellite crossover difference is a difference between the radial distance (or height above a reference body) of two distinct orbits at the same geographic location. Altimeter heights at crossovers of a single orbit (SSC) have been used for many years for various goals, the dual-satellite crossovers (DSC) have been studied recently and they were found to be useful for precise orbit determination, accuracy tests of the Earth's gravity field models, and for a gravitational modelling. Most importantly, oceanographers have recognized that altimetry with DSCs provides the only link to connect ocean variability maps between ephemeral satellite missions, eventually over decades. Very recently, a coordinate system offset of GEOSAT with respect to that of TOPEX/Poseidon (T/P) has been discovered from DSC residua of this pair of satellites.
There are 4 types of the DSC (between Ascending track of the first satellite and Descending track of the second satellite, AD, and DA, AA, and DD. Formulae for mapping the variance-covariance matrix of the harmonic geopotential coefficients of gravity field models to the DSC standard deviations (''errors'') of the 4 types (AD, DA, AA, and DD) were derived, based on analytical Rosborough's theory, They revealed that the projections for the individual types of the DSCs differ. Numerical examples for various orbits and recent gravity model covariances are presented.
In an analogy to the single Latitude Lumped Coefficients, already known and used for gravity field accuracy assessments and various intercomparisons, the dual-LLC are defined, representing geopotential-orbit variations for the DSC. Formulae are derived for their standard errors from the covariances of geopotential field models. Numerical examples are presented for GEOSAT, ERS-1(2), and T/P for a comparison of the individual missions accuracy and sensitivity to the gravity field errors with those for the pairs of the altimeter missions, using recent models (like JGM 2, 3 or GRIM 4S4).
The DSC, connecting separate missions, will play an increasingly important role in oceanography spanning decades only when its non-oceanographic signals are thoroughly understood. In general, the content of even the long term averaged DSC is more complex then their SSC counterpart. The dual-LLC, as the spatial spectra for the geopotential-caused crossover effects, discriminate these source-differences sharply. Thus, the order zero dual-LLC (m=0) in DSC data contains zonal gravity information not present in the SSC (and single-LLC) data. In addition, order m=0 and 1 LLC of DSC data can reveal a geocenter discrepancy between the orbit tracking of the separate satellite missions. Also, where the time gap is necessarily large (as between say, GEOSAT and T/P missions), oceanographic (sea level) differences in the DSC may corrupt the geopotential interpretation of the data. Most important, as we illustrate, media delays for the altimeter (from the ionosphere, wet troposphere and sea state bias) are more likely sources of contamination across two missions than in SSC analyses. Again, the dual-LLC at m=0 best shows this contrast. Using the higher order dual-LLC errors (m&#gt;1) for both GEOSAT-T/P and ERS1-T/P pairs as likely representation of geopotential-only error, we show by comparison with the predicted standard errors of JGM~2 that the latters previously calibrated covariance matrix is generally valid. (Thus, we confirm similar older results obtained with the single-LLC using SSC residua of GEOSAT, ERS 1 and T/P, separately).
We present a geometrical and dynamical approach to the evaluation of the coordinate system shift between GEOSAT and T/P, using their DSC residua (after all known corrections are applied), and we provide numerical results, i.e. the values of dx, dy, and dz (Geosat' system relative to that of T/P taken as errorless) or of (relative values of) the so-called 'forbidden' harmonic geopotential coefficeints C'_{11}, S'_{11}, and C'_{10}. We present sea-height surfaces before and after elimination of this effect.
The DSC residua, especially of pass-pairs close in time, are uniquely sensitive to the geopotential through its effects on the satellite's orbit; thus, it may be useful to include various types of crossover data in gravity field recovery from diverse sources. The corrected crossover data from one satellite (the SSC residua) and from a pair of satellites (the DSC residua) -- always after all known error sources removed -- are used in a common inversion for harmonic geopotential coefficients C_{lm}, S_{lm} (of pre-selected degrees l and orders m ) as the solved-for parameters, by a standard least-squares adjustment. The partial derivatives of the design matrix of the problem are derived analytically from the definitions of the single- and dual-LLC, relevant to the SSC and DSC, respectively. The analytical approach is based again on the Rosborough's theory. Long term averages of SSC and DSC residuals of sea height (based on JGM 2 orbits) have been used for GEOSAT, ERS 1, and T/P (corrected for media, sea level, 1 cycle per revolution orbit, geocenter and time-tag errors). Results show that gravity field improvement in lower degree and resonant geopotential terms is possible utilizing this data.