Journal of Geodesy (J GEODESY)

Publications in this journal

• Article: Separation of global time-variable gravity signals into maximally independent components

  Ehsan Forootan, Jürgen Kusche
  [show abstract] [hide abstract]
  ABSTRACT: The Gravity Recovery and Climate Experiment (GRACE) products provide valuable information about total water storage variations over the whole globe. Since GRACE detects mass variations integrated over vertical columns, it is desirable to separate its total water storage anomalies into their original sources. Among the statistical approaches, the principal component analysis (PCA) method and its extensions have been frequently proposed to decompose the GRACE products into space and time components. However, these methods only search for decorrelated components that on the one hand are not always interpretable and on the other hand often contain a superposition of independent source signals. In contrast, independent component analysis (ICA) represents a technique that separates components based on assumed statistical independence using higher-order statistical information. If one assumes that independent physical processes generate statistically independent signal components added up in the GRACE observations, separating them by ICA is a reliable strategy to identify these processes. In this paper, the performance of the conventional PCA, its rotated extension and ICA are investigated when applied to the GRACE-derived total water storage variations. These analyses have been tested on both a synthetic example and on the real GRACE level-2 monthly solutions derived from GeoForschungsZentrum Potsdam (GFZ RL04) and Bonn University (ITG2010). Within the synthetic example, we can show how imposing statistical independence in the framework of ICA improves the extraction of the ‘original’ signals from a GRACE-type super-position. We are therefore confident that also for the real case the ICA algorithm, without making prior assumptions about the long-term behaviour or on the frequencies contained in the signal, improves over the performance of PCA and its rotated extension in the separation of periodical and long-term components.
  Journal of Geodesy 07/2012; 86(7):477 - 497.
• Article: Monitoring ground deformation in Beijing, China with persistent scatterer SAR interferometry

  Alex Hay-Man Ng, Linlin Ge, Xiaojing Li, Kui Zhang
  [show abstract] [hide abstract]
  ABSTRACT: This paper investigated the long term ground deformation in Beijing, China, using persistent/permanent scatterer interferometry (PSI) techniques. GEOS-PSI (Geodesy and Earth Observing Systems-PSI), an in-house software developed at UNSW for PSI, has been applied to 41 ENVISAT ASAR images acquired over the metropolitan area of Beijing City between June 2003 and March 2009 and 24 ALOS PALSAR images (two Paths: 10 acquisitions from January 2007 to October 2008 and 14 acquisitions from February 2007 to September 2009). The results generated using these datasets from the two satellites were cross-validated. Correlations between the results of ENVISAT ASAR and ALOS PALSAR agreed very well. The horizontal and vertical displacement rate maps over Beijing City were obtained from the results generated with data acquired by both satellites over the period from 1st February 2007 to 1st November 2008. The results indicate that the displacements in Beijing City were mainly in the vertical direction. The majority of the easting displacement rates were in the range of -10 mm/year to 10 mm/year, while the vertical rates were in the range of -115 mm/year to 6 mm/year. The possible cause for the ground deformation is groundwater extraction based on our research as well as earlier published studies.
  Journal of Geodesy 06/2012; 86(6):375-392.
• Article: On the combination of high-resolution and satellite-only global gravity models

  Mirko Reguzzoni, Fernando Sansò
  [show abstract] [hide abstract]
  ABSTRACT: The issue of combining high-resolution gravity models, based on observations taken on the Earth surface, with those derived from satellite-only observations is of increasing importance, due to the new data provided by gravity satellite missions, CHAMP, GRACE and GOCE. The paper addresses this issue with a twofold purpose. On the one hand, it is an attempt to discuss and assess general concepts, well known in literature, such as achievable resolution, regularization in the least-squares sense or in an infinite dimensional setup, combination criteria, symmetry and block diagonal structures. In particular, as for the symmetry question, a well-defined result, generalizing known facts, is derived. On the other hand, the outcomes of the general discussion are specifically applied to the combination of a high-resolution model (e.g. EGM08) with a GOCE gravity model estimated by the so-called space-wise approach. Small numerical examples are developed to clarify the property of the proposed solution. KeywordsData combination–GOCE mission–Collocation–Space-wise approach–Block diagonal structures
  Journal of Geodesy 05/2012;
• Article: Impact of network geometry, observation schemes and telescope structure deformations on local ties: simulations applied to Sardinia Radio Telescope

  Claudio Abbondanza, Pierguido Sarti
  [show abstract] [hide abstract]
  ABSTRACT: The 64-m Sardinia Radio Telescope (SRT) is currently under construction in Sardinia (Italy). To ensure future surveying and monitoring operations at an utmost level of accuracy, we aim at selecting the optimal design and the most cost-effective solution for the establishment of the local ground control network (LGCN). We simulate and test 45 data sets corresponding to 5 different network configurations. We investigate the influence of 2 LGCN geometries (14 or 8 ground markers) and 3 terrestrial observation schemes (based on redundant forward intersections or side shots) on the precision and accuracy of the conventional reference point (CRP) of SRT and the simulated tie vector with a global navigation satellite system (GNSS) station. In addition, thermal and gravitational deformations of the radio telescope structure are simulated as systematic errors introduced into the observations and their effects on the CRP estimates are quantified. The state-of-the-art of CRP surveying and computation, based on terrestrial indirect methods, is applied. We show how terrestrial indirect methods can estimate the position of the radio telescope CRP to the millimeter precision level. With our simulations, we prove that limiting the LGCN to a 8-point configuration ensures the same precision on the CRP obtained with a 14-point network. Furthermore, we demonstrate that in the absence of telescope deformations, side shots, despite the lower redundancy, preserve a precision similar to that of redundant forward intersections. We show that the deformations due to gravitational flexure and thermal expansion of the radio telescope cannot be neglected in the tie vector computation, since they may bias the CRP estimate by several millimeters degrading its accuracy but not impacting on its formal precision. We highlight the dependency of the correlation matrices of the solutions on the geometry of the network and the observation schemes. Similarly, varying the extent of telescope deformations, we show that the CRP estimate again depends on the combination of the network geometry and the observation schemes. KeywordsVLBI–Tie vector–Local tie–Geodetic network design–Indirect methods–Gravitational and thermal deformations
  Journal of Geodesy 05/2012; 86(3):181-192.
• Article: Height bias and scale effect induced by antenna gravitational deformations in geodetic VLBI data analysis

  Pierguido Sarti, Claudio Abbondanza, Leonid Petrov, Monia Negusini
  [show abstract] [hide abstract]
  ABSTRACT: The impact of signal path variations (SPVs) caused by antenna gravitational deformations on geodetic very long baseline interferometry (VLBI) results is evaluated for the first time. Elevation-dependent models of SPV for Medicina and Noto (Italy) telescopes were derived from a combination of terrestrial surveying methods to account for gravitational deformations. After applying these models in geodetic VLBI data analysis, estimates of the antenna reference point positions are shifted upward by 8.9 and 6.7mm, respectively. The impact on other parameters is negligible. To simulate the impact of antenna gravitational deformations on the entire VLBI network, lacking measurements for other telescopes, we rescaled the SPV models of Medicina and Noto for other antennas according to their size. The effects of the simulations are changes in VLBI heights in the range [−3, 73] mm and a net scale increase of 0.3–0.8ppb. The height bias is larger than random errors of VLBI position estimates, implying the possibility of significant scale distortions related to antenna gravitational deformations. This demonstrates the need to precisely measure gravitational deformations of other VLBI telescopes, to derive their precise SPV models and to apply them in routine geodetic data analysis. KeywordsVLBI–ITRF–Reference frames–Signal path variation–Antenna gravitational deformation
  Journal of Geodesy 05/2012; 85(1):1-8.
• Article: Global optimization of the Gauss conformal mappings of an ellipsoid to a sphere

  Mercedes Bermejo-Solera, Jesús Otero
  [show abstract] [hide abstract]
  ABSTRACT: The Gauss conformal mappings (GCMs) of an oblate ellipsoid of revolution to a sphere are those that transform the meridians into meridians, and the parallels into parallels of the sphere. The infinitesimal-scale function associated with these mappings depends on the geodetic latitude and contains three parameters, including the radius of the sphere. Gauss derived these constants by imposing local optimum conditions on certain parallel. We deal with the problem of finding the constants to minimize the Chebyshev or maximum norm of the logarithm of the infinitesimal-scale function on a given ellipsoidal segment (the region contained between two parallels). We show how to solve this minimax problem using the intrinsic function fminsearch of Matlab. For a particular ellipsoidal segment, we get the solution and show the alternation property characteristic of best Chebyshev approximations. For a pair of points relatively close in the ellipsoid at different latitudes, the best minimax GCM on the segment defined by these points is used to approximate the geodesic distance between them by the spherical distance between their projections on the corresponding sphere. This approach, combined with the best locally GCM if the points are on the same parallel, is illustrated by applying it to some case studies but specially to a 10°× 10° region contained between portions of two parallels and two meridians. In this case, the maximum absolute error of this spherical approximation is equal to 2.9mm occurring at a distance about 1,360km. This error decreases up to 0.94mm on an 8°× 8° region of this type. So, the spherical approximation to the solution of the inverse geodesic problem by best GCM can be acceptable in many practical geodetic activities. KeywordsGeometrical geodesy-Conformal mapping-Distortion analysis-Inverse geodesic problem
  Journal of Geodesy 05/2012; 84(8):481-489.
• Article: The convergence problem of collocation solutions in the framework of the stochastic interpretation

  F. Sansò, G. Venuti
  [show abstract] [hide abstract]
  ABSTRACT: The problem of the convergence of the collocation solution to the true gravity field was defined long ago (Tscherning in Boll Geod Sci Affini 39:221–252, 1978) and some results were derived, in particular by Krarup (Boll Geod Sci Affini 40:225–240, 1981). The problem is taken up again in the context of the stochastic interpretation of collocation theory and some new results are derived, showing that, when the potential T can be really continued down to a Bjerhammar sphere, we have a quite general convergence property in the noiseless case. When noise is present in data, still reasonable convergence results hold true. “Democrito che ’l mondo a caso pone” “Democritus who made the world stochastic” Dante Alighieri, La Divina Commedia, Inferno, IV – 136 KeywordsLeast squares collocation–Functional analysis
  Journal of Geodesy 05/2012; 85(1):51-63.
• Article: The effect of using inconsistent ocean tidal loading models on GPS coordinate solutions

  Yuning Fu, Jeffrey T. Freymueller, Tonie van Dam
  [show abstract] [hide abstract]
  ABSTRACT: We use up to a 6-year span of GPS data from 85 globally distributed stations to compare solutions using ocean tidal loading (OTL) corrections computed in different reference frames: center of mass of the solid Earth (CE), and center of mass of the Earth system (CM). We compare solution sets that differ only in the frame used for the OTL model computations, for three types of GPS solutions. In global solutions with all parameters including orbits estimated simultaneously, we find coordinate differences of ~0.3mm between solutions using OTL computed in CM and OTL computed in CE. When orbits or orbits and clocks are fixed, larger biases appear if the user applies an OTL model inconsistent with that used to derive the orbit and clock products. Network solutions (orbits fixed, satellite clocks estimated) show differences smaller than 0.5 mm due to model inconsistency, but PPP solutions show distortions at the ~1.3mm level. The much larger effect on PPP solutions indicates that satellite clock estimates are sensitive to the OTL model applied. The time series of coordinate differences shows a strong spectral peak at a period of ~14 days when inconsistent OTL models are applied and smaller peaks at ~annual and ~semi-annual periods, for both ambiguity-free and ambiguity-fixed solutions. These spurious coordinate variations disappear in solutions using consistent OTL models. Users of orbit and clock products must ensure that they use OTL coefficients computed in the same reference frame as the OTL coefficients used by the analysis centers that produced the products they use; otherwise, systematic errors will be introduced into position solutions. All modern products should use loading models computed in the CM frame, but legacy products may require loading models computed in the CE frame. Analysts and authors need to document the frame used for all loading computations in product descriptions and papers. KeywordsOcean tide loading (OTL)–Reference frame–Geocenter–Global Positioning System (GPS)–Center of mass correction (CMC)–Power spectrum
  Journal of Geodesy 05/2012;
• Article: A global mean dynamic topography and ocean circulation estimation using a preliminary GOCE gravity model

  P. Knudsen, R. Bingham, O. Andersen, Marie-Helene Rio
  [show abstract] [hide abstract]
  ABSTRACT: The Gravity and steady-state Ocean Circulation Explorer (GOCE) satellite mission measures Earth’s gravity field with an unprecedented accuracy at short spatial scales. In doing so, it promises to significantly advance our ability to determine the ocean’s general circulation. In this study, an initial gravity model from GOCE, based on just 2months of data, is combined with the recent DTU10MSS mean sea surface to construct a global mean dynamic topography (MDT) model. The GOCE MDT clearly displays the gross features of the ocean’s steady-state circulation. More significantly, the improved gravity model provided by the GOCE mission has enhanced the resolution and sharpened the boundaries of those features compared with earlier satellite only solutions. Calculation of the geostrophic surface currents from the MDT reveals improvements for all of the ocean’s major current systems. In the North Atlantic, the Gulf Stream is stronger and more clearly defined, as are the Labrador and the Greenland currents. Furthermore, the finer scale features, such as eddies, meanders and branches of the Gulf Stream and North Atlantic Current system are visible. Similar improvements are seen also in the North Pacific Ocean, where the Kuroshio and its extension are well represented. In the Southern hemisphere, both the Agulhas and the Brazil-Malvinas Confluence current systems are well defined, and in the Southern ocean the Antarctic Circumpolar Current appears enhanced. The results of this preliminary analysis, using an initial GOCE gravity model, clearly demonstrate the potential of the GOCE mission. Already, at this early stage of the mission, the resolution of the MDT has been improved and the estimated surface current speeds have been increased compared with a GRACE satellite-only MDT. Future GOCE gravity models are expected to build further upon this early success. KeywordsGOCE–Dynamic ocean topography–Ocean circulation–Altimetry
  Journal of Geodesy 05/2012; 85(11):861-879.
• Article: Monument-antenna effects on GPS coordinate time series with application to vertical rates in Antarctica

  Matt A. King, Michael Bevis, Terry Wilson, Bjorn Johns, Frederick Blume
  [show abstract] [hide abstract]
  ABSTRACT: We examine the electromagnetic coupling of a GPS antenna–monument pair in terms of its simulated affect on long GPS coordinate time series. We focus on the Earth and Polar Observing System (POLENET) monument design widely deployed in Antarctica and Greenland in projects interested particularly in vertical velocities. We base our tests on an absolute robot calibration that included the top ~0.15 m of the monument and use simulations to assess its effect on site coordinate time series at eight representative POLENET sites in Antarctica over the period 2000.0–2011.0. We show that the neglect of this calibration would introduce mean coordinate bias, and most importantly for velocity estimation, coordinate noise which is highly sensitive to observation geometry and hence site location and observation period. Considering only sub-periods longer than 2.5 years, we show vertical site velocities may be biased by up to ±0.4mm/year, and biases up to 0.2mm/year may persist for observation spans of 8 years. Changing between uniform and elevation-dependent observation weighting alters the time series but does not remove the velocity biases, nor does ambiguity fixing. The effect on the horizontal coordinates is negligible. The ambiguities fixed series spectra show noise between flicker and random walk with near-white noise at the highest frequencies, with mean spectral indices (frequencies <20 cycles per year) of approximately −1.3 (uniform weighting) and −1.4 (elevation-dependent weighting). While the results are likely highly monument specific, they highlight the importance of accounting for monument effects when analysing vertical coordinate time series and velocities for the highest precision and accuracy geophysical studies. KeywordsGPS–Monumentation effect–Phase centre variation–Velocity accuracy
  Journal of Geodesy 05/2012; 86(1):53-63.
• Article: Ray-traced slant factors for mitigating the tropospheric delay at the observation level

  Landon Urquhart, Felipe G. Nievinski, Marcelo C. Santos
  [show abstract] [hide abstract]
  ABSTRACT: Three-dimensional ray tracing through a numerical weather model has been applied to a global precise point positioning (PPP) campaign for modeling both the elevation angle- and azimuth-dependence of the tropospheric delay. Rather than applying the ray-traced slant delays directly, the delay has been parameterized in terms of slant factors, which are applied in a similar manner to traditional mapping functions, but which can account for the azimuthal asymmetry of the delay. Five strategies are considered: (1) Vienna Mapping Functions 1 (VMF1) and estimation of a residual zenith delay parameter; (2) VMF1, estimation of a residual zenith delay and estimation of two tropospheric gradient parameters; (3) three-dimensional ray-traced slant factors and estimation of a residual zenith delay; (4) using only ray-traced slant factors and no estimation of any tropospheric parameters and; (5) using both ray-traced slant factors and estimating a residual zenith delay and two tropospheric gradient parameters. The use of the ray-traced slant factors (solution 3) showed a 3.8% improvement in the repeatability of the up component when compared to the assumption of a symmetric atmosphere (solution 1), while the estimation of two tropospheric gradient parameters gave the best results showing an 7.6% improvement over solution 1 in the up component. Solution 4 performed well in the horizontal domain, allowing for sub-centimeter repeatability but the up component was degraded due to deficiencies in the modeling of the zenith delay, particularly for stations located at equatorial latitudes. The magnitude of the differences in the mean coordinates between solution 2 and solution 3, and the strong correlation with the differences between the north component and the ray-traced gradients (coefficient of correlation of 0.83), as well as the impact of observation geometry on the gradient solution indicate that the use of the ray-traced slant factors could have an implication on the realization of reference frames. The estimated tropospheric products from the PPP solutions were compared to those derived from ray tracing. For the zenith delay, a root mean square (RMS) of 5.4mm was found, while for the gradient terms, a correlation coefficient of 0.46 for the N–S and 0.42 for the E–W was found for the north–south and east–west components, suggesting that there are still important differences in the gradient parameters which could be due to either errors in the NWM or to non-tropospheric error sources leaking into the PPP-estimated gradients. KeywordsGlobal positioning system–Numerical weather models–Troposphere gradients–Troposphere zenith delay–Precise point positioning
  Journal of Geodesy 05/2012; 86(2):149-160.
• Article: An analytical method to transform geocentric into geodetic coordinates

  Hugues Vermeille
  [show abstract] [hide abstract]
  ABSTRACT: A closed-form analytical method needing no approximation and deduced from a single quartic equation is offered to transform geocentric into geodetic coordinates. It is valid at any point inside and outside the Earth including the polar axis, the equatorial plane and the Earth’s center. Comparison with the method of extrema with constraints to obtain this quartic equation is made. KeywordsAnalytical coordinates transformation–Coordinates transformation–Geocentric coordinates–Geodetic coordinates
  Journal of Geodesy 05/2012; 85(2):105-117.
• Article: An iterative solution of weighted total least-squares adjustment

  Yunzhong Shen, Bofeng Li, Yi Chen
  [show abstract] [hide abstract]
  ABSTRACT: Total least-squares (TLS) adjustment is used to estimate the parameters in the errors-in-variables (EIV) model. However, its exact solution is rather complicated, and the accuracies of estimated parameters are too difficult to analytically compute. Since the EIV model is essentially a non-linear model, it can be solved according to the theory of non-linear least-squares adjustment. In this contribution, we will propose an iterative method of weighted TLS (WTLS) adjustment to solve EIV model based on Newton–Gauss approach of non-linear weighted least-squares (WLS) adjustment. Then the WLS solution to linearly approximated EIV model is derived and its discrepancy is investigated by comparing with WTLS solution. In addition, a numerical method is developed to compute the unbiased variance component estimate and the covariance matrix of the WTLS estimates. Finally, the real and simulation experiments are implemented to demonstrate the performance and efficiency of the presented iterative method and its linearly approximated version as well as the numerical method. The results show that the proposed iterative method can obtain such good solution as WTLS solution of Schaffrin and Wieser (J Geod 82:415–421, 2008) and the presented numerical method can be reasonably applied to evaluate the accuracy of WTLS solution. KeywordsErrors-in-variables model–Total least-squares adjustment–Iterative least-squares adjustment–Unbiased variance component estimate
  Journal of Geodesy 05/2012; 85(4):229-238.
• Article: CPLat: first operational experimental processing center for SIRGAS in Argentina

  María Paula Natali, M. Müller, L. Fernández, C. Brunini
  [show abstract] [hide abstract]
  ABSTRACT: The SIRGAS permanent GPS network which is in fact the IGS network densification for the American continent, consists today of more than 200 stations covering the continent and islands. It is currently processed by the IGS RNAAC SIR centre at Deutsches Geodätisches Forschungsinstitut producing weekly free solutions relying on IGS final orbits and EOP that contribute to the ITRF through IGS. By August 2006, the SIRGAS Working Group I had accepted five proposals for experimental processing centers within the region that would collaborate with IGS RNAAC SIR. One of them, Centro de Procesamiento La Plata (CPLat) in Argentina, began processing 60 stations on October 2006. By January 2007 CPLat reached operational capability, delivering weekly free solution SINEX files, with an internal consistency of 1.5mm average for the horizontal components, and 3mm in the vertical. Comparisons with IGS global and IGS RNAAC SIR weekly solutions were taken as external consistency indications, showing average RMS residuals of 1.8, 2.4 and 5mm for the north, east, and vertical component, respectively. Analysis and comparison of adjusted solution time series from CPLat and other processing centers has proved to be highly valuable for solution QC, namely detection and identification of station anomalous behavior or modelling problems. These procedures will ensure the maintenance of the performance specifications for CPLat solutions. Action is being taken in order to guarantee the continuity of this effort beyond the experimental phase.
  Journal of Geodesy 05/2012; 83(3):219-226.
• Article: On the topographic bias in geoid determination by the external gravity field

  Lars E. Sjöberg
  [show abstract] [hide abstract]
  ABSTRACT: The topographic bias is defined as the error/bias committed by continuing the external gravity field inside the topographic masses by a harmonic function. We study the topographic bias given by a digital terrain model defined by a spherical template, and we show that the topographic bias is given only by the potential of an inner-zone cap, and it equals the bias of the Bouguer shell, independent of the size of the cap. Then we study the effect on the real Earth by decomposing its topography into a template, and we show also in this case that the topographic bias is that of the Bouguer shell, independent of the shape of the terrain. Finally, we show that the topographic potential of the terrain at the geoid can be determined to any precision by a Taylor expansion outside the Earth’s surface. The last statement is demonstrated by a Taylor expansion to fourth order.
  Journal of Geodesy 05/2012; 83(10):967-972.