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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of geodesy 69 (1995), S. 244-251 
    ISSN: 1432-1394
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Summary The global power of the differences of altimetric sea heights at collocated points in the first 44 cycles of the Topex/Poseidon (T/P) mission, apparently shows the influence of errors in the major tides and long period ocean signals. Results show the principal semidiurnal tides (M2/S2 lumped together) in the Cartwright and Ray (1991) model are probably in error globally by 3–4 cm (rms). The dominant fluctuation in the differences over the 44 cycles (14 months total) arises from an annual signal of 4–6 cm (rms), significantly greater than long term climate data suggests (but with considerable uncertainty due to unresolved semiannual effects).
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    [s.l.] : Nature Publishing Group
    Nature 188 (1960), S. 638-641 
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] IN 1952, Schumann1,2 published a detailed description of the resonant modes to be expected for the concentric spherical cavity bounded by the Earth and the lower region of the ionosphere. For such a cavity with perfectly conducting walls, the resonant frequencies should obey the relation : fn(» + ...
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of geodesy 71 (1997), S. 603-616 
    ISSN: 1432-1394
    Keywords: Key words. Crossover satellite altimetry ; Latitude-lumped coefficients ; Coordinate systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract. Latitude-lumped coefficients (LLC) are defined, representing geopotential-orbit variations for dual-satellite crossovers (DSC). Formulae are derived for their standard errors from the covariances of geopotential field models. Numerical examples are presented for pairs of the altimeter-bearing satellites TOPEX/Poseidon, ERS 1, and Geosat, using the error matrices of recent gravity models. The DSC, connecting separate missions, will play an increasingly important role in oceanography spanning decades only when its nonoceanographic signals are thoroughly understood. In general, the content of even the long-term averaged DSC is more complex then their single satellite crossover (SSC) counterpart. The LLC, as the spatial spectra for the geopotential-caused crossover effects, discriminate these source-differences sharply. Thus, the zero-order LLC in DSC data contains zonal gravity information not present in SSC data. In addition, zero- and first-order LLC of DSC data can reveal a geocenter discrepancy between the orbit tracking of the separate satellite missions. For example, DSC analysis from orbits computed with JGM 2 show that the y-axis of the geocenter for Geosat in 1986–1988 is shifted with respect to T/P by 6–9 cm towards the eastern Pacific. Also, where the time-gap is necessarily large (as between, say, Geosat and T/P missions) oceanographic (sea-level) differences in DSC may corrupt the geopotential interpretation of the data. Most importantly, 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 LLC of zero order best shows this contrast. Using the higher-order LLC of DSC for both Geosat-T/P and ERS 1-T/P as likely representation of geopotential-only error, we show by comparison with the predicted standard errors of JGM 2 that the latter's previously calibrated covariance matrix is generally valid.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of geodesy 73 (2000), S. 671-683 
    ISSN: 1432-1394
    Keywords: Key words: Satellite altimetry – Single and dual crossovers – Student-t statistics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract.  The single- and dual-satellite crossover (SSC and DSC) residuals between and among Geosat, TOPEX/Poseidon (T/P), and ERS 1 or 2 have been used for various purposes, applied in geodesy for gravity field accuracy assessments and determination as well as in oceanography. The theory is presented and various examples are given of certain combinations of SSC and DSC that test for residual altimetry data errors, mostly of non-gravitational origin, of the order of a few centimeters. There are four types of basic DSCs and 12 independent combinations of them in pairs which have been found useful in the present work. These are defined in terms of the `mean' and `variable' components of a satellite's geopotential orbit error from Rosborough's 1st-order analytical theory. The remaining small errors, after all altimeter data corrections are applied and the relative offset of coordinate frames between altimetry missions removed, are statistically evaluated by means of the Student distribution. The remaining signal of `non-gravitational' origin can in some cases be attributed to the main ocean currents which were not accounted for among the media or sea-surface corrections. In future, they may be resolved by a long-term global circulation model. Experience with two current models, neither of which are found either to cover the most critical missions (Geosat & TOPEX/Poseidon) or to have the accuracy and resolution necessary to account for the strongest anomalies found across them, is described. In other cases, the residual signal is due to errors in tides, altimeter delay corrections or El Niño. (Various examples of these are also presented.) Tests of the combinations of the JGM 3-based DSC residuals show that overall the long-term data now available are well suited for a gravity field inversion refining JGM 3 for low- and resonant-order geopotential harmonics whose signatures are clearly seen in the basic DSC and SSC sets.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of geodesy 73 (1999), S. 138-146 
    ISSN: 1432-1394
    Keywords: Key words. Dynamics of artificial satellites ; Satellite altimetry ; Dual-satellite crossover altimetry ; Gravity-field models ; Accuracy assessments ; Reference systems ; Coordinate system offset
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract. A detailed accuracy assessment of the geopotential model Jgm3 is made based on independent single- and dual-satellite sea-height differences at crossovers from altimetry with Jgm3-based orbits. These differences, averaged over long time spans and in latitude bands, are converted to spectra (latitude-lumped coefficients) by least-squares estimation. The observed error spectra so obtained are then compared directly to error projections for them from the Jgm3 variance–covariance matrix. It is found from these comparisons that Jgm3 is generally well calibrated with respect to the crossover altimetry of and between Geosat, TOPEX/Poseidon (T/P), and Ers 1. Some significant discrepancies at a few lower orders (namely m=1 and 3) indicate a need for further improvement of Jgm3. A companion calibration (by order) of the geopotential model Jgm2 shows its variance–covariance matrix also to be generally well calibrated for the same single- and dual-satellite altimeter data sets (but based on Jgm2 orbits), except that the error projections for Geosat are too pessimistic. The analysis of the dual-satellite crossovers reveals possible relative coordinate system offsets (particularly for Geosat with respect to T/P) which have been discussed previously. The long-term detailed seasonally averaged Geosat sea level with respect to T/P (covering 1985–1996) should be useful in gauging the relative change in sea level between different parts of the ocean over the single 4-year gap between these missions (1988–1992).
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Celestial mechanics and dynamical astronomy 2 (1970), S. 228-236 
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The non-linear differential equation $$\ddot x + p(t)x^3 = 0$$ , wherep(t) is a periodic square wave function of time with period τ, has been integrated by using a table of Jacobian elliptic functions. In the neighborhood of a typical elliptic fixed point, namely that for 11τ, 12-decimal accuracy has been used to determine a region which is stable.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Celestial mechanics and dynamical astronomy 16 (1977), S. 143-163 
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Until very recently, there has been no identification of the significant gravitational constraints on the many common artificial earth satellite orbits in shallow resonance. Without them it is difficult to compare results derived for different sets of harmonics from different orbits. With them it is possible to extend these results to any degree without reintegration of the orbits. All such constraints are shown to be harmonic in the argument of perigee with constants determinable from tracking data: $$(C*,S*) = (C_0 ,S_0 ) + \sum\limits_{i = 1}^\infty {(C_{Ci} ,S_{Ci} )\cos i\omega + (C_{Si} ,S_{Si} )\sin i\omega .} $$ The constants are simple linear combinations of geopotential harmonics. Five such constants (lumped harmonics) have been derived for the GEOS-2 orbit (order 13, to 30th degree) whose principal resonant period is 6 days. These five lumped harmonics are shown to account for almost all (〉98%) of the resonant information in the tracking. They agree well with recent gravitational models which include substantial amounts of GEOS-2 data.
    Type of Medium: Electronic Resource
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  • 8
  • 9
  • 10
    Publication Date: 2004-02-17
    Print ISSN: 0027-8424
    Electronic ISSN: 1091-6490
    Topics: Biology , Medicine , Natural Sciences in General
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