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  • 1
    Publication Date: 2023-07-03
    Description: XGM2019e is a combined global gravity field model represented by spheroidal harmonics up to degree and order (d/o) 5399, corresponding to a spatial resolution of 2′ (~ 4 km). As data sources, it includes the satellite model GOCO06s in the longer wavelength range up to d/o 300 combined with a ground gravity grid which also covers the shorter wavelengths. The ground data consist over land and ocean of gravity anomalies provided by courtesy of NGA (15′ resolution, identical to XGM2016) augmented with topographically derived gravity information over land (EARTH2014). Over the oceans, gravity anomalies derived from satellite altimetry are used (DTU13 with a resolution of 1′). The combination of the satellite data with the ground gravity observations is performed by using full normal equations up to d/o 719 (15′). Beyond d/o 719, a block-diagonal least squares solution is calculated for the high-resolution ground gravity data (from topography and altimetry). All calculations are performed in the spheroidal harmonic domain. In the spectral band up to d/o 719, the new model shows a slightly improved behaviour in the magnitude of a few mm RMS over land as compared to preceding models such as XGM2016, EIGEN6c4 or EGM2008 when validated with independent geoid information derived from GNSS/levelling. Over land and in the spectral range above d/o 719, the accuracy of XGM2019e marginally suffers from the sole use of topographic forward modelling, and geoid differences at GNSS/levelling stations are increased in the order of several mm RMS in well-surveyed areas, such as the US and Europe, compared to models containing real gravity data over their entire spectrum, e.g. EIGEN6c4 or EGM2008. However, GNSS/levelling validation also indicates that the performance of XGM2019e can be considered as globally more consistent and independent of existing high-resolution global models. Over the oceans, the model exhibits an enhanced performance (equal or better than preceding models), which is confirmed by comparison of the MDT’s computed from CNES/CLS 2015 mean sea surface and the high-resolution geoid models. The MDT based on XGM2019e shows fewer artefacts, particularly in the coastal regions, and fits globally better to DTU17MDT which is considered as an independent reference MDT.
    Description: European Space Agency http://dx.doi.org/10.13039/501100000844
    Keywords: ddc:526 ; Gravity ; Combined gravity field model ; Spherical harmonics ; Spheroidal harmonics ; Full normal equation systems ; High-performance computing
    Language: English
    Type: doc-type:article
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  • 2
    Publication Date: 2023-06-22
    Description: We present a partition-enhanced least-squares collocation (PE-LSC) which comprises several modifications to the classical LSC method. It is our goal to circumvent various problems of the practical application of LSC. While these investigations are focused on the modeling of the exterior gravity field the elaborated methods can also be used in other applications. One of the main drawbacks and current limitations of LSC is its high computational cost which grows cubically with the number of observation points. A common way to mitigate this problem is to tile the target area into sub-regions and solve each tile individually. This procedure assumes a certain locality of the LSC kernel functions which is generally not given and, therefore, results in fringe effects. To avoid this, it is proposed to localize the LSC kernels such that locality is preserved, and the estimated variances are not notably increased in comparison with the classical LSC method. Using global covariance models involves the calculation of a large number of Legendre polynomials which is usually a time-consuming task. Hence, to accelerate the creation of the covariance matrices, as an intermediate step we pre-calculate the covariance function on a two-dimensional grid of isotropic coordinates. Based on this grid, and under the assumption that the covariances are sufficiently smooth, the final covariance matrices are then obtained by a simple and fast interpolation algorithm. Applying the generalized multi-variate chain rule, also cross-covariance matrices among arbitrary linear spherical harmonic functionals can be obtained by this technique. Together with some further minor alterations these modifications are implemented in the PE-LSC method. The new PE-LSC is tested using selected data sets in Antarctica where altogether more than 800,000 observations are available for processing. In this case, PE-LSC yields a speed-up of computation time by a factor of about 55 (i.e., the computation needs only hours instead of weeks) in comparison with the classical unpartitioned LSC. Likewise, the memory requirement is reduced by a factor of about 360 (i.e., allocating memory in the order of GB instead of TB).
    Description: Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659
    Description: Technische Universität München (1025)
    Keywords: ddc:526 ; Gravity field ; Least squares collocation (LSC) ; Covariance function ; Data combination ; Prediction ; Antarctica
    Language: English
    Type: doc-type:article
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