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Kusche J.,University of Bonn | Klemann V.,German Research Center for Geosciences | Bosch W.,Deutsches Geodatisches Forschungsinstitut
Journal of Geodynamics | Year: 2012

Melting of continental ice sheets and glaciers, changes in ocean circulation pattern and in sea level, variations of surface and ground water levels and river discharge, glacial-isostatic adjustment, mantle convection and tectonics, all this causes transport and (re-) distribution of mass inside the Earth and at its surface. Equipped with precise sensor systems, gravity field and altimeter satellites observe these mass-transport processes. During 2006-2012, the German Research Association DFG had established the SPP 1257, 'Mass distribution and Mass Transport in the Earth System' as a coordinated research programme to facilitate integrated analysis of these data, to improve our knowledge about several transport processes within the Earth system and to investigate their interactions. This special issue reports about the findings of the first 4. years within the programme. © 2012 Elsevier Ltd.

Sebera J.,Czech Technical University | Sebera J.,Academy of Sciences of the Czech Republic | Bouman J.,Deutsches Geodatisches Forschungsinstitut | Bosch W.,Deutsches Geodatisches Forschungsinstitut
Journal of Geodesy | Year: 2012

Gravity data observed on or reduced to the ellipsoid are preferably represented using ellipsoidal harmonics instead of spherical harmonics. Ellipsoidal harmonics, however, are difficult to use in practice because the computation of the associated Legendre functions of the second kind that occur in the ellipsoidal harmonic expansions is not straightforward. Jekeli's renormalization simplifies the computation of the associated Legendre functions. We extended the direct computation of these functions-as well as that of their ratio-up to the second derivatives and minimized the number of required recurrences by a suitable hypergeometric transformation. Compared with the original Jekeli's renormalization the associated Legendre differential equation is fulfilled up to much higher degrees and orders for our optimized recurrences. The derived functions were tested by comparing functionals of the gravitational potential computed with both ellipsoidal and spherical harmonic syntheses. As an input, the high resolution global gravity field model EGM2008 was used. The relative agreement we found between the results of ellipsoidal and spherical syntheses is 10 -14, 10 -12 and 10 -8 for the potential and its first and second derivatives, respectively. Using the original renormalization, this agreement is 10 -12, 10 -8 and 10 -5, respectively. In addition, our optimized recurrences require less computation time as the number of required terms for the hypergeometric functions is less. © 2012 Springer-Verlag.

Seitz M.,Deutsches Geodatisches Forschungsinstitut
International Association of Geodesy Symposia | Year: 2015

The combination of space geodetic techniques is today and becomes in future more and more important for the computation of Earth system parameters as well as for the realization of reference systems. Precision, accuracy, long-term stability and reliability of the products can be improved by the combination of different observation techniques, which provide an individual sensitivity with respect to several parameters. The estimation of geodetic parameters from observations is mostly done by least squares adjustment within a Gauß-Markov model. The combination of different techniques can be done on three different levels: on the level of observations, on the level of normal equations and on the level of parameters. The paper discusses the differences between the approaches from a theoretical point of view. The combination on observation level is the most rigorous approach since all observations are processed together ab initio, including all pre-processing steps, like e.g. outlier detection. The combination on normal equation level is an approximation of the combination on observation level. The only difference is that pre-processing steps including an editing of the observations are done techniquewise. The combination on the parameter level is more different: Technique-individual solutions are computed and the solved parameters are combined within a second least squares adjustment process. Reliable pseudo-observations (constraints) have to be applied to generate the input solutions. In order to realize the geodetic datum of the combined solution independently from the datum of the input solutions, parameters of a similarity transformation have to be set up for each input solution within the combination. Due to imperfect network geometries, the transformation parameters can absorb also nondatum effects. The multiple parameter solution of the combination process leads to a stronger dependency of the combined solution on operator decisions and on numerical aspects. © Springer International Publishing Switzerland 2015.

Fuchs M.J.,Deutsches Geodatisches Forschungsinstitut | Bouman J.,Deutsches Geodatisches Forschungsinstitut | Broerse T.,Technical University of Delft | Visser P.,Technical University of Delft | Vermeersen B.,Technical University of Delft
Journal of Geophysical Research: Solid Earth | Year: 2013

The Japan Tohoku-Oki earthquake (9.0 Mw) of 11 March 2011 has left signatures in the Earth's gravity field that are detectable by data of the Gravity field Recovery and Climate Experiment (GRACE) mission. Because the European Space Agency's (ESA) satellite gravity mission Gravity field and steady-state Ocean Circulation Explorer (GOCE) - launched in 2009 - aims at high spatial resolution, its measurements could complement the GRACE information on coseismic gravity changes, although time-variable gravity was not foreseen as goal of the GOCE mission. We modeled the coseismic earthquake geoid signal and converted this signal to vertical gravity gradients at GOCE satellite altitude. We combined the single gradient observations in a novel way reducing the noise level, required to detect the coseismic gravity change, subtracted a global gravity model, and applied tailored outlier detection to the resulting gradient residuals. Furthermore, the measured gradients were along-track filtered using different gradient bandwidths where in the space domain Gaussian smoothing has been applied. One-year periods before and after earthquake occurrence have been compared with the modeled gradients. The comparison reveals that the earthquake signal is well above the accuracy of the vertical gravity gradients at orbital height. Moreover, the obtained signal from GOCE shows a 1.3 times higher amplitude compared with the modeled signal. Besides the statistical significance of the obtained signal, it has a high spatial correlation of ~0.7 with the forward modeled signal. We conclude therefore that the coseismic gravity change of the Japan Tohoku-Oki earthquake left a statistically significant signal in the GOCE measured gravity gradients. Key Points GOCE observes Tohoku-Oki 2011 coseismic gravity change ©2013. American Geophysical Union. All Rights Reserved.

Drewes H.,Deutsches Geodatisches Forschungsinstitut
International Association of Geodesy Symposia | Year: 2012

Geodetic parameters always correspond to a reference system defined by conventions and realized by a reference frame through materialized points with given coordinates. For the coordinate estimation one has to fix the geodetic datum, i.e. the origin and directions of the coordinate axes, and the scale unit. In geosciences applications, e.g. for geodynamics and global change research, the datum has to be fixed over a very long time period in order to refer time-dependent parameters to one and the same reference frame. The paper focuses on the methodology how to fix the datum by parameters independent of the measurements and deformations of the reference frame, and to hold it over a long time span. It is shown that transformations between reference frames at different epochs are not suited to realize the datum parameters because systematic network deformations may affect it. Independent parameters are in particular the first degree and order harmonic coefficients of the gravity field for fixing the origin, and external calibration for fixing the scale. The long-term stability is achieved by the permanent fixing of the datum parameters. Regional reference frames must refer to the global datum by using epoch station coordinates as fiducial values. © Springer-Verlag Berlin Heidelberg 2012.

Singh A.,TU Munich | Seitz F.,TU Munich | Schwatke C.,Deutsches Geodatisches Forschungsinstitut
Remote Sensing of Environment | Year: 2012

The estimation of water storage variations in lakes is essential for water resource management activities in a region. In areas of ungauged or poorly gauged water bodies, satellite altimetry acts as a powerful tool to measure changes in surface water level. Remote sensing provides images of temporal coastline variations, and a combination of both measurement techniques can indicate a change in water volume. In this study variations of the water level of the Aral Sea were computed for the period 2002-2011 from the combination of radar and laser satellite altimetry data sets over the lake. The estimated water levels were analyzed in combination with coastline changes from Landsat images in order to obtain a comprehensive picture of the lake water changes. In addition to these geometrical observations temporal changes of water storage in the lake and its surrounding were computed from GRACE satellite gravimetry. With respect to its temporal evolution the GRACE results agree very well with the geometrical changes determined from altimetry and Landsat. The advancing desiccation until the beginning of 2009 and a subsequent abrupt gain of water in 2009-2010 due to exceptional discharge from Amu Darya can clearly be identified in all data sets. © 2011 Elsevier Inc.

Bouman J.,Deutsches Geodatisches Forschungsinstitut
Journal of Geodesy | Year: 2012

The vertical gradients of gravity anomaly and gravity disturbance can be related to horizontal first derivatives of deflection of the vertical or second derivatives of geoidal undulations. These are simplified relations of which different variations have found application in satellite altimetry with the implicit assumption that the neglected terms-using remove-restore-are sufficiently small. In this paper, the different simplified relations are rigorously connected and the neglected terms are made explicit. The main neglected terms are a curvilinear term that accounts for the difference between second derivatives in a Cartesian system and on a spherical surface, and a small circle term that stems from the difference between second derivatives on a great and small circle. The neglected terms were compared with the dynamic ocean topography (DOT) and the requirements on the GOCE gravity gradients. In addition, the signal root-mean-square (RMS) of the neglected terms and vertical gravity gradient were compared, and the effect of a remove-restore procedure was studied. These analyses show that both neglected terms have the same order of magnitude as the DOT gradient signal and may be above the GOCE requirements, and should be accounted for when combining altimetry derived and GOCE measured gradients. The signal RMS of both neglected terms is in general small when compared with the signal RMS of the vertical gravity gradient, but they may introduce gradient errors above the spherical approximation error. Remove-restore with gravity field models reduces the errors in the vertical gravity gradient, but it appears that errors above the spherical approximation error cannot be avoided at individual locations. When computing the vertical gradient of gravity anomaly from satellite altimeter data using deflections of the vertical, the small circle term is readily available and can be included. The direct computation of the vertical gradient of gravity disturbance from satellite altimeter data is more difficult than the computation of the vertical gradient of gravity anomaly because in the former case the curvilinear term is needed, which is not readily available. © 2011 Springer-Verlag.

Drewes H.,Deutsches Geodatisches Forschungsinstitut
ZFV - Zeitschrift fur Geodasie, Geoinformation und Landmanagement | Year: 2012

The International Association of Geodesy (IAG) is a constituent Association of the International Union of Geodesy and Geophysics (IUGG) since 1922, and the successor organization of the Mitteleuropäische Gradmessung. Its activities have changed dramatically from its beginning in 1862 till today. While it started with the aim of determining the regional anomalies of the Earth's curvature in Europe by connecting astronomical observatories through triangulation networks, it concentrates now on the observation and modelling of the phenomena and effects of physical processes in the System Earth employing mainly space techniques. The structural and scientific developments over time are summarised, and the present structure and activities are described in detail.

Seitz M.,Deutsches Geodatisches Forschungsinstitut | Angermann D.,Deutsches Geodatisches Forschungsinstitut | Blossfeld M.,Deutsches Geodatisches Forschungsinstitut | Drewes H.,Deutsches Geodatisches Forschungsinstitut | Gerstl M.,Deutsches Geodatisches Forschungsinstitut
Journal of Geodesy | Year: 2012

A new realization of the International Terrestrial System was computed at the ITRS Combination Centre at DGFI as a contribution to ITRF2008. The solution is labelled DTRF2008. In the same way as in the DGFI computation for ITRF2005 it is based on either normal equation systems or estimated parameters derived from VLBI, SLR, GPS and DORIS observations by weekly or session-wise processing. The parameter space of the ITRS realization comprises station positions and velocities and daily resolved Earth Orientation Parameters (EOP), whereby for the first time also nutation parameters are included. The advantage of starting from time series of input data is that the temporal behaviour of geophysical parameters can be investigated to decide whether the parameters can contribute to the datum realization of the ITRF. In the same way, a standardized analysis of station position time series can be performed to detect and remove discontinuities. The advantage of including EOP in the ITRS realization is twofold: (1) the combination of the coordinates of the terrestrial pole-estimated from all contributing techniques-links the technique networks in two components of the orientation, leading to an improvement of consistency of the Terrestrial Reference Frame (TRF) and (2) in their capacity as parameters common to all techniques, the terrestrial pole coordinates enhance the selection of local ties as they provide a measure for the consistency of the combined frame. The computation strategy of DGFI is based on the combination of normal equation systems while at the ITRS Combination Centre at IGN solutions are combined. The two independent ITRS realizations provide the possibility to assess the accuracy of ITRF by comparison of the two frames. The accuracy evaluation was done separately for the datum parameters (origin, orientation and scale) and the network geometry. The accuracy of the datum parameters, assessed from the comparison of DTRF2008 and ITRF2008, is between 2-5 mm and 0.1-0.8 mm/year depending on the technique. The network geometry (station positions and velocities) agrees within 3.2 mm and 1.0 mm/year. A comparison of DTRF2008 and ITRF2005 provides similar results for the datum parameters, but there are larger differences for the network geometry. The internal accuracy of DTRF2008-that means the level of conservation of datum information and network geometry within the combination-was derived from comparisons with the technique-only multi-year solutions. From this an internal accuracy of 0.32 mm for the VLBI up to 3.3 mm for the DORIS part of the network is found. The internal accuracy of velocities ranges from 0.05 mm/year for VLBI to 0.83 mm/year for DORIS. The internal consistency of DTRF2008 for orientation can be derived from the analysis of the terrestrial pole coordinates. It is estimated at 1.5-2.5 mm for the GPS, VLBI and SLR parts of the network. The consistency of these three and the DORIS network part is within 6.5 mm. © 2012 Springer-Verlag.

Rodriguez-Solano C.J.,TU Munich | Hugentobler U.,TU Munich | Steigenberger P.,TU Munich | Blossfeld M.,Deutsches Geodatisches Forschungsinstitut | Fritsche M.,TU Dresden
Journal of Geodesy | Year: 2014

Systematic errors at harmonics of the GPS draconitic year have been found in diverse GPS-derived geodetic products like the geocenter Z-component, station coordinates, Y-pole rate and orbits (i.e. orbit overlaps). The GPS draconitic year is the repeat period of the GPS constellation w.r.t. the Sun which is about 351 days. Different error sources have been proposed which could generate these spurious signals at the draconitic harmonics. In this study, we focus on one of these error sources, namely the radiation pressure orbit modeling deficiencies. For this purpose, three GPS+GLONASS solutions of 8 years (2004-2011) were computed which differ only in the solar radiation pressure (SRP) and satellite attitude models. The models employed in the solutions are: (1) the CODE (5-parameter) radiation pressure model widely used within the International GNSS Service community, (2) the adjustable box-wing model for SRP impacting GPS (and GLONASS) satellites, and (3) the adjustable box-wing model upgraded to use non-nominal yaw attitude, specially for satellites in eclipse seasons. When comparing the first solution with the third one we achieved the following in the GNSS geodetic products. Orbits: the draconitic errors in the orbit overlaps are reduced for the GPS satellites in all the harmonics on average 46, 38 and 57 % for the radial, along-track and cross-track components, while for GLONASS satellites they are mainly reduced in the cross-track component by 39 %. Geocenter Z-component: all the odd draconitic harmonics found when the CODE model is used show a very important reduction (almost disappearing with a 92 % average reduction) with the new radiation pressure models. Earth orientation parameters: the draconitic errors are reduced for the X-pole rate and especially for the Y-pole rate by 24 and 50 % respectively. Station coordinates: all the draconitic harmonics (except the 2nd harmonic in the North component) are reduced in the North, East and Height components, with average reductions of 41, 39 and 35 % respectively. This shows, that part of the draconitic errors currently found in GNSS geodetic products are definitely induced by the CODE radiation pressure orbit modeling deficiencies. © 2014 Springer-Verlag Berlin Heidelberg.

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