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## Über dieses Buch

This book series is composed of peer-reviewed proceedings of selected symposia organized by the International Association of Geodesy. It deals primarily with topics related to Geodesy Earth Sciences : terrestrial reference frame, Earth gravity field, Geodynamics and Earth rotation, Positioning and engineering applications.

## Inhaltsverzeichnis

### Generation and Assessment of VMF1-Type Grids Using North-American Numerical Weather Models

Numerical weather models (NWM) have become an important source of atmospheric data for modeling error sources in geodetic positioning. One example of this is the development of the Vienna Mapping Functions (VMF1) and ray-traced zenith delays which are derived from the European Centre for Medium-range Weather Forecasts (ECMWF) datasets. These products are provided on an operational basis through the GGOS Atmosphere project. In general, relatively little consideration has been given to the choice of NWM on the derived mapping functions and zenith delay products. In this investigation we compare the gridded-VMF1 mapping functions and ray-traced zenith delays derived from the ECMWF to equivalent products derived by ray-tracing through the National Center for Environmental Prediction (NCEP) Reanalysis model. We have chosen to compare the gridded version of these products as they are available for any location on Earth, rather than only specific stations and have been shown to be essentially equivalent in terms of accuracy. This paper also includes a discussion about a systematic production of gridded-VMF1 and ray-traced zenith delays derived from the NCEP datasets (and from the Canadian Meteorological Center GEM model) on an operational basis. The benefits of the service would include: (1) a backup in the event of the ECMWF VMF1 or zenith delays being unavailable; (2) greater compatibility with other NWM derived corrections, such as atmospheric pressure loading and; (3) the availability of tropospheric delay products derived from an independent source and ray-tracing algorithms should provide more robustness for combination products which use these models.

Landon Urquhart, Marcelo C. Santos, Felipe G. Nievinski, Johannes Böhm

### DORIS Tropospheric Estimation at IGN: Current Strategies, GPS Intercomparisons and Perspectives

We reprocessed DORIS for all of 2010, using the latest model and strategy improvements to estimate Zenith Tropospheric Delays (ZTDs), as well as tropospheric horizontal gradients for about 60 ground stations. These results were compared to recent GPS-based estimates obtained at the Jet Propulsion Laboratory (JPL). After discussing some of the data processing options and current limitations of the DORIS data, we show that the DORIS-GPS comparisons possess a high degree of correlation (average being 0.97), and that total zenith delay estimates from the two techniques agree at the 3 mm level on average with 8.6 mm total RMS, with better results being obtained when a 5° elevation cutoff angle is used for DORIS. While these DORIS results cannot be used for real-time weather prediction, they could contribute to scientific investigations for climatology, thanks to the homogenous tracking network of the DORIS system, as well as the long-term history of the observation time series.

Pascal Willis, Olivier Bock, Yoaz E. Bar-Sever

### The Australian Space Research Program Project: Platform Technologies for Space Atmosphere and Climate: Progress and Preliminary Results

This paper introduces the multi-million-dollar Australian Space Research Program (ASRP) Project—“Platform Technologies for Space Atmosphere and Climate,” recently awarded to an international consortium led by RMIT University, and reports the current progress and some results achieved so far. The project is part of the Australian Government’s recent space-related initiatives to support national strategic, economic and social objectives. Its main focus is developing new algorithms, new approaches, and software and system platforms for enhancing Australia’s capability in space-related research and promoting innovative applications of space-related cutting-edge technologies in Australia. The aim and objectives, major research tasks, anticipated outcomes and key issues related to Australian space research and space industry are outlined and the progresses recently made and some selected key results are reported.

K. Zhang, J. Sang, C. S. Wang, J. C. Bennett, B. Carter, R. Norman, S. Wu

### Simulating GPS Radio Occultation Using 3-D Ray Tracing

Numerical 3-D ray tracing techniques are commonly used for calculating the path of an electromagnetic signal in a medium specified by a refractive index that depends upon position. Numerical ray tracing is an important tool for applications of L-band frequency propagation such as GPS Radio Occultation (RO), where accurate and near real-time results are required. In this study, 3-D numerical ray tracing techniques are used to simulate GPS signals received by the Low Earth Orbit (LEO) satellites and to investigate their variability as a function of time and position due to the refractivity gradients in the ionosphere and the lower atmosphere. The GPS signal paths from the GPS to LEO satellites are simulated with an emphasis on the signal paths propagating through regions of the ionosphere where the refractive gradients are greatest. The effects of the Earth’s magnetic field on the L-band RO propagation paths are also investigated.

R. Norman, J. Le Marshall, K. Zhang, C. S. Wang, B. A. Carter, Y. Li, S. Gordon

### Near Real Time Estimation of Integrated Water Vapour from GNSS Observations in Hungary

Meteorological products derived from Global Navigation Satellite Systems (GNSS) observations have been routinely used for numerical weather prediction in several regions of the world. Hungary would like to join these activities exploiting meteorological usage of the dense GNSS CORS (Continuously Operating Reference Station) network operated by the Institute of Geodesy, Cartography and Remote Sensing for positioning applications.

This paper introduces the near real-time processing system of GNSS observations for meteorological purposes in Hungary. The hourly observations of 35 Hungarian permanent GNSS CORSs are processed. This network is extended beyond the country with about 50 stations covering Eastern and Central Europe. The data analysis is being done using the Bernese V5.0 GPS data processing software. The Hungarian CORS network has an average baseline length of 60 km, thus the precipitable water vapour (PW) can be estimated with a high spatial resolution.

The estimation of the PW from the zenith wet delay (ZWD) is carried out in near real-time. Firstly, the zenith hydrostatic delays (ZHD) are subtracted from the total delays. The wet delays are then scaled to precipitable water vapour values.

The GNSS derived PW values were validated using radiosonde observations over Central Europe using the observations of a 47-day-long period (April 14–May 31, 2011). The results showed that the estimated PW values agree with radiosonde observations at the level of ±1.5 mm in terms of standard deviation. In this comparison a bias of +1.0 mm was observed. Following the validation phase, our analysis will be connected to the continental E-GVAP project (GNSS Water Vapour Programme of the Network of European Meteorological Services, EUMETNET).

Sz. Rózsa, A. Kenyeres, T. Weidinger, A. Z. Gyöngyösi

### Determining the 4D Dynamics of Wet Refractivity Using GPS Tomography in the Australian Region

The Earth’s climate and weather is a highly dynamic and complex system. Monitoring and predicting meteorological conditions with a high accuracy and reliability is, therefore, a challenging task. Water vapour (WV) has a strong influence on the Earth’s climate and weather due to the large energy transfers in the hydrological process. However, it remains poorly understood and inadequately measured both spatially and temporally, especially in Australia and the southern hemisphere. Four dimensional (4D) WV fields may be reconstructed using a tomographic inversion method that takes advantage of the high density of ground-based GPS Continue Operating Reference Station (CORS) networks. Recent development in GNSS tomography technique based on the dense Australian national positioning infrastructure has the potential to provide near real time 4D WV solutions at a high spatial and temporal resolution for numerical weather prediction, severe weather monitoring and precise positioning. This paper presents a preliminary study using the most advanced state CORS network—GPSnet as a test bed and introduces 4D GPS tomography in Australia and evaluates different parameters for voxel and height resolution and the influence of a priori data through simulations in a controlled field. Preliminary analyses of a real data campaign using a priori information are presented. These preliminary results conclude that the most optimal setup for GNSS tomography models in Victoria is: ∼55 km horizontal resolution and 15 vertical layers with a smaller spacing in the lower troposphere and a larger spacing towards the tropopause. Further analysis will be undertaken to optimize the parameter settings for real data processing. The initial investigation into real data analysis has concluded an overall RMS error of 5.8 ppm with respect to the operational Australian Numerical Weather Prediction (NWP) model for 1 day.

Toby Manning, Witold Rohm, Kefei Zhang, Fabian Hurter, Carl Wang

### Comparing GPS Radio Occultation Observations with Radiosonde Measurements in the Australian Region

GPS Radio Occultation (RO) is a robust space-based Earth observation technique, with the demonstrated potential for atmospheric profiling and meteorological applications. The GPS RO technique uses GPS receivers onboard Low Earth Orbit (LEO) satellites to measure the received radio signals from GPS satellites to obtain atmospheric profiles such as temperature, pressure, water vapour and electron concentration in the ionosphere using complicated atmospheric retrieval processes. The Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) was launched in April 2006. GPS RO data from this constellation of six LEO micro-satellites provides an observational data type for operational meteorology, providing significant information on the thermodynamic state of the atmosphere with the potential to improve atmospheric analyses and prognoses. Thus it is important to know and understand how COSMIC RO measurements compare to conventional atmospheric and meteorological sounding devices. In this study the COSMIC GPS RO temperature and pressure profiles are compared to those measured from radiosondes (Vaisala RS-92) in the Australian region.

R. Norman, J. Le Marshall, K. Zhang, C. S. Wang, B. A. Carter, W. Rohm, T. Manning, S. Gordon, Y. Li

### Zenith Wet Delay Retrieval Using Two Different Techniques for the South American Region and Their Comparison

Retrieving atmospheric water vapor content using GNSS claimed the attention of the geodetic community ever since the beginning of the GPS deployment. The main purpose of the present work is to propose a comparison of the Zenith Wet Delay (ZWD) retrieved by GPS with the direct measurements provided by the water vapor radiometer loaded on-board the Jason-1 altimetry satellite and those obtained from SIRGAS (Geocentric Reference System for the Americas) GNSS reference stations. In this respect, the work proposes a methodology for the comparison and contributes to assess the capabilities of SIRGAS permanent network to provide water vapor informations that can be useful both for short-term weather forecasting and for long-term climate studies. For the period from June 2008 to June 2010 the tropospheric parameters of more than 100 SIRGAS stations were estimated using Bernese 5.0 software with a time interval of 15 min. Since Jason-1 returns reliable measurements only over open ocean areas, a subset of 14 stations located along the coastline was selected for the comparison. A dedicated software was developed in order to effectively manage the huge amount of Jason-1 data, mainly devoted to data selection according to site position, time interval and data filtering using quality flag indicators. The Zenith Hydrostatic Delay (ZHD) provided by the European Center for Medium Weather Forecasting (ECMWF) were first corrected up to the GPS station height and then used to derive the ZWD from the GPS estimated Zenith Total Delay (ZTD). The agreement between the techniques was evaluated in terms of bias and standard deviation of the differences (i.e. GPS

ZWD

− Jason-1

ZWD

) resulting in 7.4 mm and 15.4 mm, respectively. The average correlation coefficient is 0.93.

A. Calori, G. Colosimo, M. Crespi, F. Azpilicueta, M. Gende, C. Brunini, M. V. Mackern

### Uncertainty Considerations for the Comparison of Water Vapour Derived from Radiosondes and GNSS

The integrated water vapour (IWV) can be estimated from the tropospheric delays of GNSS signals. These estimations are usually validated by radiosonde observations. However, very limited information is available on the precision of the IWV determined by radiosondes. In this paper the methodology of the computation of IWV retrieved from radiosonde data is revised using the atmospheric profiles of pressure, relative humidity and temperature. The formulae to calculate the uncertainty of the estimated values are derived, where the correlation of the neighbouring atmospheric layers is also taken into account. The results show that the mean uncertainty of the IWV from radiosonde observations reaches the level of ±0.26 kg/m

2

in case of the Vaisala RS-92 radiosondes in Central and Eastern Europe. However, it increases to ±0.7 to 0.8 kg/m

2

in summertime.Since the zenith hydrostatic delay (ZHD) must be modeled accurately to estimate the IWV from GNSS observations, the Saastamoinen, the Hopfield and the Black tropospheric delay models have been validated with ZHD values computed from radiosonde observations in Central Europe. Moreover some local models have also been derived in order to minimize the bias in IWV caused by the existing tropospheric models. In order to take the effect of the masses above the topmost level of the radiosonde profile in consideration, the International Standard Atmosphere has been used. Since the radiosonde observations terminate at different altitudes and pressure levels, which certainly affect the accuracy of the computed ZHD values, the omission error has been modeled with a simple exponential function. The results showed that the best ZHD model fitted to the radiosonde observations with the bias and standard deviation of +0.8 and ±1.2 mm, respectively. This means that the GNSS derived IWV is biased by −0.1 kg/m

2

. This value is approximately 50 % lower than the bias caused by the Saastamoinen model.Finally, the calculation of the scale factor between the zenith wet delay (ZWD) and the IWV is studied. Various models exist to determine this scale factor. There are models that derive the scale factor as a direct function of the surface temperature, while other models use a linear regression model of the surface temperature to compute the mean temperature of water vapour in the troposphere and derive the scale parameter from physical equations. Radiosonde profiles were used to test the two approached in Central and Eastern Europe. The results showed that the prior model showed no bias, while the latter one showed a relative bias of approximately 0.3 %.

Sz. Rózsa

### Mean Dynamic Ocean Topography in the Southern Ocean from GRACE and GOCE and Multi-mission Altimeter Data

The ocean north of the Antarctic continent is one of the most dynamic ocean areas on our globe. It is also critical for the regulation of the global climate. We compute a high resolution mean dynamical ocean topography (MDT) using geodetic data and derive a detailed model of the global ocean circulation in this crucial area. The MDT is determined using multi-mission altimeter data and the GRACE/GOCE gravity model GOCO2s. The mean sea surface is observed from joint cross-over adjustment of 17 years of satellite altimetry. The two geodetic gravity missions GRACE and GOCE allow the computation of a global geoid with unprecedented accuracy and spatial resolution. While GRACE greatly improved the accuracy and global consistency of gravity models at long to medium wavelengths, GOCE is adding highly accurate geoid information in the medium wavelength range. The geoid and mean sea surface have been made consistent by a spectral filter. The MDT is represented as a spherical harmonic expansion. This allows us to analyze the oceanographic content in different wavelength bands. In order to assess properties of the MDT and of the derived geostrophic velocity field, velocities are compared with independent data from satellite tracked surface drifters in the area of the Antarctic Circumpolar Current (ACC). The RMS of the differences is less than 9 cm/s even if shortest scales (100 km) are considered. Our study shows that, with just 6 months of GOCE data, we are able to improve significantly the geodetic MDT.

Alberta Albertella, Roman Savcenko, Tijana Janjić, Reiner Rummel, Wolfgang Bosch, Jens Schröter

### A Closed-Loop Simulation on Regional Modelling of Gravity Changes from GRACE

A closed-loop simulation is set up in order to study in detail regional gravity modelling from GRACE-type observations. Thereby, potential differences between two satellites are simulated from a pre-defined mass trend signal, superimposed to a static background gravity model. These simulated observations are used for regional gravity field analysis with spherical radial basis functions. Finally, we use EOF analysis to identify the trend in gravity potential from a time series of 15-days quasi-static snapshots. Regional gravity modelling on the sphere is fairly complex and introduces approximation errors and artificial effects. In order not to mix up these errors with noise from the observations, we currently use noise-free observations. The model provides a versatile tool for detailed investigation of the data analysis method. Validation of the results is performed by comparison of input and output gravity change.

Katrin Bentel, Christian Gerlach

### Estimation of PGR Induced Absolute Gravity Changes at Greenland GNET Stations

An important subject in the climate debate is the study of the major ice sheets mass balance. Knowledge of the mass balance provides understanding of changes in the relative sea-level (RSL). Several methods are used for mass balance studies but they are associated with large uncertainties. One reason for the uncertainty is the presence of the postglacial rebound (PGR) signal in the geodetic data used for mass balance estimates. Estimates of the PGR signal can be obtained by modelling and then being subtracted from the data to eliminate its influence. In this study, the PGR gravity signal will be investigated through modelling. The modelling of seven different scenarios shows that the PGR gravity signal in Greenland is less then 1 μGal/year (1 μGal = 10 nm/s

2

). Repeated absolute gravity (AG) measurements at selected Greenland network (GNET) GPS sites were initiated in 2009. These data will in the future help constrain PGR and present-day ice mass changes. The data is collected with an A10 absolute gravimeter, which has an accuracy of 10 μGal (manufacturer specification). Here we will evaluate the modelled PGR gravity signal at selected GNET sites and conclude that the signal is significantly smaller then the gravity instruments accuracy and a long time is needed to detect it. Also, it can be expected that the elastic signal will be larger and other data like GPS is needed to separate the viscous and elastic signal.

Emil Nielsen, Gabriel Strykowski, Rene Forsberg, Finn Bo Madsen

### New Finite-Element Modelling of Subduction Processes in the Andes Using Realistic Geometries

The aim of this work is the better understanding of geophysical processes in subduction zones by Finite element modelling. Here we study the effects of various parameters on the deformation and stress field. The tested parameters are the friction coefficient, convergence obliquity, bending of the subduction zone, realistic geometry and visco-elasticity. Increasing the friction coefficient from 0.0 to 0.4 increases the compression by 28 %. For both friction coefficients obliquity leads to higher compression compared to straight convergence. Comparison of the model results with real topographic data reveals considerable analogies even if crustal structure is generalised. To obtain a more realistic structure for the lithosphere we adopted the geometry from well constrained density models. For these models we chose the region in the South American subduction zone around Iquique in North Chile. Including viscosity in the models has a large effect on stress and strain. In a pure elastic model stress and strain develops nearly linear. In contrast curves for the visco-elastic models show a stress maximum and a zone of maximum curvature for the strain. The stress pattern agrees well with the earthquake distribution.

Stefanie Zeumann, Rekha Sharma, René Gassmöller, Thomas Jahr, Gerhard Jentzsch

### Pumping Induced Pore Pressure Changes in Tilt Measurements Near a Fault Zone in Mizunami, Japan

Tilt meters are a widely used tool for monitoring long-term and small-scale deformations. Therefore, they are perfectly suited to test potential subsurface waste repositories. Since November 2005 a high sensitive tilt meter of the ASKANIA-type is recording at a distance of 300 m from Mizunami Underground Research Laboratory, where two vertical shafts are under construction. During the construction of those shafts large pumps were used to reduce the groundwater level, leading to two large- and several small-scale pore pressure induced tilt signals. Due to the fault system nearby, the tilt direction does not coincide with the direction towards the pump as would be expected in homogeneous media. In this study we analyze the main surface tilt direction caused by pore pressure induced deformation. Our results show two main directions which are both nearly perpendicular to the fault. Also, the long-term signals show a high correlation with the short-term pore pressure induced tilt signals.

Matthias Queitsch, Gerhard Jentzsch, Adelheid Weise, Hiroshi Ishii, Yashuiro Asai

### Future and Development of the European Combined Geodetic Network ECGN

The European Combined Geodetic Network ECGN aims at the unification of time series of spatial/geometric observations obtained from GNSS, physical quantities from gravity field related observations, and other parameters including precise levelling, tide gauge records, and Earth and ocean tides. The objective of ECGN is to contribute to the maintenance of a stable terrestrial reference system for Europe, including 3D geometric parameters together with the gravity related height component. We discuss future, need and structure of the ECGN and a pilot project initiated for practical demonstration of the ECGN.

Markku Poutanen, Johannes Ihde, Carine Bruyninx, Olivier Francis, Ulla Kallio, Ambrus Kenyeres, Gunter Liebsch, Jaakko Mäkinen, Steve Shipman, Jaroslav Simek, Simon Williams, Herbert Wilmes

### Geocenter Coordinates from GNSS and Combined GNSS-SLR Solutions Using Satellite Co-locations

Satellite Laser Ranging (SLR) data to LAGEOS, ETALON and to Global Navigation Satellite Systems (GNSS) were combined with GNSS microwave data for 5 years. Including SLR data to GNSS satellites and estimating common orbit parameters allows it to connect both space-geodetic techniques using satellite instead of station co-location. We show that only SLR data to the spherical satellites can improve the geocenter estimates, whereas SLR data to the GNSS satellites suffer from the same GNSS orbit modelling deficiencies as in the analysis of microwave data.

Daniela Thaller, Krzysztof Sośnica, Rolf Dach, Adrian Jäggi, Gerhard Beutler, Maria Mareyen, Bernd Richter

### Analysis of the Sea Level Change in New Zealand

We analyse the sea level change in New Zealand using tide-gauge records available for over a century. The least-squares linear regression analysis is applied to estimate the linear and acceleration trends in (annual) mean sea level (MSL) data from tide gauges (TGs) in Auckland, Wellington, Lyttelton and Dunedin. The results reveal that the linear trends in relative sea level at these four TGs are between 1.2 mm/year (TG Dunedin) and 2.1 mm/year (TG Wellington). The relative sea level trend in New Zealand over the last century is estimated to be 1.7 ± 0.1 mm/year. The relative sea level trends are further corrected for the vertical land motions in order to assess the “absolute” sea level rise in New Zealand. The vertical land motions are investigated throughout New Zealand based on the analysis of GPS time series at 101 permanent sites. The GPS solutions are aligned to the ITRF2000 reference frame. The prevailing pattern of vertical motions in New Zealand is dominated by tectonic subsidence in the lower North Island, while the largest tectonic uplift is detected across the central Southern Alps in the South Island. The estimated rates of absolute sea level rise at the four TGs (co-located with GPS) are between 0.4 mm/year (TG Wellington) and 1.8 mm/year (TG Lyttelton). Based on these estimates, the absolute sea level in New Zealand raised over the last century at an average rate of 1.1 ± 0.3 mm/year.

### High Precision Deformation Monitoring at the Geodynamic Observatory Moxa/Thuringia, Germany

The Three-Component Strainmeter Assembly

With strainmeters the observation of crustal deformation is possible with a resolution better than 10

−9

m. At the Geodynamic Observatory Moxa in Thuringia/Germany an assembly of strainmeters of different types is recording deformation. Deformation mainly results from the tidal forces of sun and moon acting on the Earth, but also comes from seismic wave propagation or regional and local sources. Here we describe the results of an analysis of five time-series, each spanning 482 days, obtained from the different instruments and areal strain. We focus on the Earth tides but also look on the resonance of the Earth’s core to tidal forcing, the Nearly Diurnal Free Wobble. Even if not all five time-series show the resonance, its finding, especially in strain data, confirms the high data quality and sensitivity of the instruments. The analysis of the strainmeter data shows the comparability of the data from the different instruments as well as the good data quality connected to the very low noise level at the Geodynamic Observatory Moxa. Comparison with ocean loading shows that strong effects from local conditions like topography or rock inhomogeneities exist.

Peter Schindler, Thomas Jahr, Gerhard Jentzsch, Nina Kukowski

### A Geodetic Study of the Otago Fault System of the South Island of New Zealand

The Otago Fault System in the southern South Island of New Zealand is an area dominated by actively growing asymmetric anticlines above buried reverse faults. Geological studies indicate that the average total shortening rate across the system is 2–3 mm/year. This region was the subject of several early geodetic studies based on terrestrial techniques, which reported high (0.5 ppm/year) strain rates that are difficult to reconcile with geological estimates of fault slip rates.

We have analysed approximately 5 years of recent satellite-based geodetic data from approximately 20 stations distributed evenly over a broad corridor extending across the full extent of the Otago Fault System. We divided the data into three sub-networks to study the variation of geodetic strain over the region. The resulting strain rate tensors show a transition, with the northern subnetwork adjacent to the Alpine Fault showing predominantly a shear strain with a small transpressional component and a rate of 30 ppb/year while in the southernmost subnetwork, the strain rate tensor is consistent with uniaxial contraction at rates of 20ppb/year. Tectonically, in the northern part of our study area, the geodetic strain data are broadly consistent with elastic strain accumulation on the Alpine Fault while in the south, the strain rate tensors are consistent with the Otago Fault System. The principal axis of contraction for the southern subnetwork is about 15 ppb/year, which is consistent with geological estimates of rates of total shortening across the Otago Fault System, but is oblique to the northeast trending ranges.

P. Denys, R. Norris, C. Pearson, M. Denham

### Towards an Integrated Model of the Interseismic Velocity Field Along the Western Margin of North America

This paper describes a block model of tectonic deformation for the western part of the contiguous United States (i.e. west of longitude 100°W and between latitudes 31°N and 49°N). NOAA’s National Geodetic Survey (NGS) uses velocities predicted by this model as the basis of the horizontal velocity grids incorporated in Horizontal Time-Dependent Positioning (HTDP) software. We model the deformation of this area using 46 rotating blocks. Along with the poles of rotation, we also solve for 38 independent horizontal strain rate tensors and the elastic coupling coefficients on faults that bound adjacent blocks. For the release of HTDP 3.1, we updated estimates of model parameters by using 6,287 GPS-derived velocity vectors, that include vectors from the 2009 Plate Boundary Observatory (PBO) solution and the NGS Multiyear CORS (MYCORS) solution, and 330 geological measurements of fault slip rates and/or fault orientation. In general, the fault slip rates and the interseismic coupling coefficients are consistent with the results of previous studies; however, because of the comprehensive nature of this model, we are able to quantitatively map deformation rates over the entire plate boundary zone within the contiguous United States. Slip rates on the faults range from over 30 mm/year for the Cascadia subduction zone and parts of the San Andreas system to near zero for faults adjacent to stable North America. Block rotations play a significant role in accommodating deformation in the Pacific Northwest but make a much smaller contribution south of Cape Mendocino. Because of the variable gradient of the velocity field, HTDP3.1 incorporates a hierarchy of 5 grids with a spacing ranging from 4 nodes per degree to 100 nodes per degree.

C. F. Pearson, R. S. Snay, R. McCaffrey

### Land Subsidence, Groundwater Extraction, and Flooding in Bandung Basin (Indonesia)

Increase in urban development activities and urbanization rate in the Bandung Basin have increased groundwater extraction from the aquifers, which has then led to land subsidence in several locations in the basin. Based on GPS (Global Positioning System) and InSAR (Interferometry Syntetic Aperture Radar) data, the estimated subsidence rates vary spatially from 2 to 20 cm/year. Maximum subsidence during the period of 1999–2010 is about 3 m and largest in industrial areas. Site visit surveys were also conducted to map and evaluate the impacts of the land subsidence.

Based on the site visit surveys, the impacts of land subsidence can be seen in several forms such as cracks in buildings, damage of infrastructure (road and bridges), tilting and damaged houses, and change in the flooding inundation area. Flooding frequently occurs in the area where the subsidence rate is high. For example, the 2010 heavy flooding covered the areas where the subsidence is about 7–10 cm/year. This suggests that land subsidence aggravates the flooding hazard in the Bandung Basin.

Irwan Gumilar, H. Z. Abidin, H. Andreas, T. P. Sidiq, M. Gamal, Y. Fukuda

### Plate Boundary Deformation Following the December 26, 2004 Andaman–Sumatra Earthquake Revealed by GPS Observations and Seismic Moment Tensors

To investigate the transient strain rate of postseismic deformation associated with the highly devastating December 26, 2004 Andaman–Sumatra earthquake (M

w

9.3), a combined analysis have been done using GPS data and Seismic Moment Tensors (SMT) acquired from Andaman–Nicobar–Sumatra regions during 2005–2007. The displacement estimated during postseismic periods 2005–2006 and 2006–2007 with respect to ITRF2008 and Indian Reference Frame, display dominating arc-normal active deformation in the southern part close to epicenter, and arc-parallel deformation towards the northern part of the Andaman–Nicobar–Sumatra Subduction Zone (ANSSZ). The principal strain rates during 2005–2006 periods indicate larger strain accumulation and decreased rate of strain during 2006–2007 with a maximum arc-normal compression on southern part of ANSSZ and a changing trend of arc-parallel extension towards the central and northern part along the ANSSZ. Stress inversion using SMT also indicate compressive horizontal stress in the southern part and extensional stress towards the central and northern part of the study area, and a remarkable agreement with GPS derived strain rate pattern.

Sanjay K. Prajapati, P. S. Sunil, C. D. Reddy

### The Construction of ICRF2 and Its Impact on the Terrestrial Reference Frame

The construction of the second realization of the International Celestial Reference Frame by VLBI (ICRF2) was undertaken to take advantage of the many improvements in geodetic and astrometric VLBI and the vast increase in data since the first ICRF. The impact the switch to ICRF2 has had on the terrestrial reference frame and EOP solutions generated by VLBI is very small, at about the mm level, and should be transparent to most users of VLBI products.

D. Gordon, K. Le Bail, C. Ma, D. MacMillan, S. Bolotin, J. Gipson

### EUREF’s Contribution to National, European and Global Geodetic Infrastructures

The EUREF key infrastructures are the EUREF Permanent GNSS Network (EPN) and the Unified European Levelling Network (UELN). The EPN runs almost 250 Global Navigation Satellite System (GNSS) stations in a well organized environment and serves as the backbone of the realization of and access to the European Terrestrial Reference System (ETRS89) and as contribution to the densification of the International Terrestrial Reference Frame (ITRF2008). The upcoming European navigation system Galileo will be a big challenge for the EPN in sense of upgrading the station network.

Almost half of the EPN stations are capable of streaming their data in real-time. To strengthen the robustness of the real-time data and product distribution two additional Ntrip broadcasters were set up at different premises in Europe.

The EVRS and the ETRS89 have been adopted by the European Community as coordinate reference systems in INSPIRE for environmental policies, or policies and activities that have an impact on the environment.

J. Ihde, H. Habrich, M. Sacher, W. Söhne, Z. Altamimi, E. Brockmann, C. Bruyninx, A. Caporali, J. Dousa, R. Fernandes, H. Hornik, A. Kenyeres, M. Lidberg, J. Mäkinen, M. Poutanen, G. Stangl, J. A. Torres, C. Völksen

### External Evaluation of the Terrestrial Reference Frame: Report of the Task Force of the IAG Sub-commission 1.2

Ideally, the origin of the Terrestrial Reference Frame (TRF) is defined as the center of mass of the whole Earth system, the time evolution of its orientation is such that no global net rotation of the whole Earth’s surface is possible and the TRF scale is specified through the adoption of some physical constants and time-scale. These parameters need to be accurately determined since their choice has an influence on many Earth’s science applications. The aim of the task force “External evaluation of the Terrestrial Reference Frame” is to review all the applications for which the TRF accuracy is of fundamental importance. As the TRF choice has an influence on the interpretation of the results in these specific applications, we investigate if some evaluation procedures could be established. We classified the methods that allow evaluation of the TRF using ground, geodetic data or models that have not been used in the TRF construction, based on their expected contributions. Some of these methods have been applied to the latest International Terrestrial Reference System realizations and the results are presented here. Although further analysis will be necessary to deliver a more precise error budget, our findings demonstrate that the most recent realizations of the ITRS are more accurate than the previous in terms of origin and scale rate definition. The current level of ITRF2008 accuracy is likely to be at the level of 0.5 mm/year along each origin component and better than 0.3 mm/year in the scale rate according to the most recent studies.

X. Collilieux, Z. Altamimi, D. F. Argus, C. Boucher, A. Dermanis, B. J. Haines, T. A. Herring, C. W. Kreemer, F. G. Lemoine, C. Ma, D. S. MacMillan, J. Mäkinen, L. Métivier, J. Ries, F. N. Teferle, X. Wu

### Atmospheric Effects on VLBI-Derived Terrestrial and Celestial Reference Frames

We introduce our new terrestrial and celestial reference frames VieTRF10a and VieCRF10a, which have been estimated by the Vienna VLBI Software VieVS using VLBI observations since 1984. Details are provided about the computation, and comparisons are made with VTRF2008 and ICRF2, respectively, in terms of transformation parameters. Furthermore, we reaffirm the essentiality of a proper handling of horizontal tropospheric gradients and point out the systematic effect on the coordinates which arises through the use of constraints. We also assess the impact of two different mapping functions (GMF vs. VMF1) on terrestrial (TRF) and celestial reference frames, showing the scale difference between the TRF of 0.08 ppb which corresponds to 0.5 mm in height change.

Hana Krásná(née Spicakova), Johannes Böhm, Lucia Plank, Tobias Nilsson, Harald Schuh

### Modelling Deformation in a Kinematic Datum

The growth of accurate global satellite based positioning (GNSS) on the one hand, and geographic information systems (GIS) managing spatial definitions of features in terms of coordinates on the other creates a conflict in the use of coordinates. Whereas GNSS positioning defines geocentric coordinates in terms of a global reference frame, in GIS systems they are used as a spatial reference for objects which are moving in response to tectonic deformation and other geophysical events. The coordinates of objects in GIS systems are fixed, whereas the objects are moving. Resolving this conflict requires using a deformation model. Ultimately GIS software will need to support deformation models in the definition of spatial reference systems to accommodate deformation. As GNSS makes global datums more accessible the traditional role of national geodetic agencies of providing a national datum may change to supporting a global datum and providing a national deformation model.

Chris Crook

### Consistent Adjustment of Combined Terrestrial and Celestial Reference Frames

Today, the realization of the International Terrestrial Reference System (ITRS) and the International Celestial Reference System (ICRS) is performed separately. Consequently, the two realizations are not fully consistent and show differences in the network geometry and the realized scale of the terrestrial reference frame (TRF) and in the simultaneously estimated Earth Orientation Parameter (EOP) series. The paper deals with the common adjustment of the Terrestrial Reference Frame (TRF), the Celestial Reference Frame (CRF) and the linking EOP. It presents a computation strategy, which is based on the combination of normal equations. The main focus of the paper is on the impact of a combination of different space geodetic techniques on the CRF, which was not in detail studied so far. The influence of the local tie handling as well as the impact of the EOP combination are studied. The results show, that the combination leads only to small but partly systematic changes of the CRF. The maximum systematic effect is about 0.5 mas for source positions derived in regional networks only.

M. Seitz, P. Steigenberger, T. Artz

### On the Alternative Approaches to ITRF Formulation

A Theoretical Comparison

The one-step approach for ITRF formulation is compared with the two-step technique where the ITRF parameters are first separately estimated for each space technique separately (stacking per technique) and are then combined into the final ITRF estimates (combination step). The comparison is achieved by splitting the one-step approach into two equivalent steps such that the first one is identical to the first step of the two-step approach. It is shown that the two approaches give equivalent results when the input covariance matrices in the combination step of the two-step approach are the normal equation coefficient matrices formulated in the corresponding stacking per technique first step. Furthermore it is shown that the model of the combination step can be significantly simplified by ignoring the parameters of reference system transformation from the per technique estimates to those of the final ITRF parameter estimates.

Athanasios Dermanis

### Spatiotemporal Signal and Noise Analysis of GPS Position Time Series of the Permanent Stations in China

This paper aims to analyze the signal and noise characteristics of the GPS position time series of the permanent stations in China. We first extract the Common Mode Components (CMC) from the position series of regional GPS stations using principal component analysis and separate the GPS station position time series into CMC and the filtered series of each station. Then we detect the Unmodeled Common Signals (UCS) and Common Noises (CN) in CMC using power spectrum analysis, and analyze the noise characteristics of CN using a MINQUE (Minimum Norm Quadratic Unbiased Estimation) method of variance component estimation. We also detect periodic signals using power spectrum analysis and analyze different noise components using MINQUE method from the filtered series. Total 7-year GPS station position time series of the 24 permanent stations in China have been processed. The results show that the CMC accounts for 38.8 %, 39.1 % and 32.7 % from the total variances in north, east and up, respectively. CMC are dominated by CN. The dominant periods of UCS are about 792 days in north and up and about 594 days in east. In CN, the flicker noise is slightly larger than the white noise, and the random walk noise is very small. The periodic signals are all significant in the filtered series of all stations, especially the annual signals in up direction. Furthermore, the flicker noise of filtered series is also slightly larger than the white noise; however random walk noise is significantly large in most stations and even larger than white or flicker noise in few stations.

Yunzhong Shen, Weiwei Li

### GPS + GLONASS CORS Processing: The Asian-Pacific APREF Case

The ongoing completion of the GLONASS system asks for a new assessment of its performance in relation to CORS network processing. The recent established Asian-Pacific Reference Frame (APREF) offered such an opportunity. Daily double-difference network solutions have been computed both for GPS-only and GPS + GLONASS processings. The formal precision of the daily solutions as well as the time series of the coordinates and reference frame parameters, derived from multi-annual combinations (2. 5 years) of the daily solutions, have been used to assess the effect of the additional GLONASS observations on the estimates of the coordinates and the stability of the reference frame. Results show that, for 24-h data batches, GLONASS adds little improvement when compared to GPS-only processing.

A. Nardo, L. Huisman, P. J. G. Teunissen

### Direct VLBI Observations of Global Navigation Satellite System Signals

We describe an experiment carried out to observe signals emitted by GLONASS (GLObal NAvigation Satellite System) satellites using the Very Long Baseline Interferometry (VLBI) technique. This test was performed on a single baseline and had as its primary goal to evaluate the capability of the VLBI system to observe GNSS (Global Navigation Satellite System) signals in terms of scheduling, tracking, acquisition, recording, correlation and processing of data. The general aim of such observations is to contribute to the connection of the reference frames for GNSS and VLBI by so-called co-location in space, or

space-ties

, as a complement to the existing so-called

local-ties

on the Earth’s surface.

In our experiment we found an interferometric response from both signals emitted by GLONASS satellites and a natural radio source that was observed as a calibrator, using the same VLBI equipment. The derived fringe phase scatters were 80 ps (2.5 cm) and 1.3 ns (39 cm) in 1 s for the GLONASS satellite and the calibrator signals, respectively. This indicates that the accuracy is not limited by GLONASS signals, but by the calibrator.

Our results show that VLBI observations of GNSS signals are possible and have the potential to derive the satellite positions on a centimetre level for observing times of just a few minutes. Future experiments should include several baselines and a larger number of calibrators in close angular distance to the satellite tracks to allow frequent switching between calibrator and satellite signals.

V. Tornatore, R. Haas, S. Casey, D. Duev, S. Pogrebenko, G. Molera Calvés

### First Geodetic Results from the AuScope VLBI Network

The new Australian geodetic VLBI network operated by the University of Tasmania (UTAS) started regular observations in June, 2011. Three 12-m “Patriot” radio telescopes (Hobart in Tasmania, Yarragadee in Western Australia and Katherine in the Northern Territory) are dedicated to the improvement of the celestial and terrestrial reference frames in the southern hemisphere. We present first results from the analysis of a 16-month set of geodetic VLBI data. The data were processed within a VLBI solution for 78 sessions in 2011–2012 by the least squares collocation method using the OCCAM software. The geodetic positions of the AuScope radio telescopes were estimated with accuracy less than 10 mm, and the first sign of their motion due to tectonic plate movement was indicated. Results of independent verification using GPS and geodetic local tie for Hobart12 showed consistency within 20 mm for all three components. Positions of Hobart12 in the ITRF2005 system are presented for the 2012.0 epoch.

O. Titov, J. M. Dickey, J. E. J. Lovell, P. M. McCulloch

### Realisation of a Geodetic Datum Using a Gridded Absolute Deformation Model (ADM)

This paper describes a schema for a gridded absolute deformation model (ADM) and non-linear deformation patch model that can be used to transform point positions captured in the International Terrestrial Reference Frame (ITRF), or other closely aligned reference frame, to a reference epoch consistently over time for practical applications. The schema described utilises existing models of rigid plate motion, plate boundary deformation and non-linear deformation (e.g. coseismic and postseismic effects or subsidence). Application of an ADM and patch model can enable consistent Precise Point Positioning (PPP) over time and seamless integration of Continuously Operating Reference Station (CORS) networks within deforming zones. The strategy described can also ensure consistency of time-tagged spatial datasets (e.g. laser scanned point clouds and digital cadastral databases) and GIS within a kinematic environment. An ADM can also be used as the basis for static epoch projections of a national or regional kinematic datum. A case study from New Zealand is described.

R. Stanaway, C. Roberts, G. Blick

### Computing Scheme of Co-seismic Change of Deflection of the Vertical and Applied in the 2010 Chile Earthquake

This paper introduces a scheme to compute co-seismic change of deflection of the vertical. To compare the theoretical deflection changes with the GRACE-observed ones, the dislocation Love numbers are truncated and the Green’s functions are computed with application of a Gaussian filter. This study further examines the problem of seawater correction to modeled geoid and deflection changes. As an application of the dislocation theory and the computing scheme, we consider the 2010 Chile earthquake (Mw8.8) using two fault slip models, to compute the co-seismic geoid and deflection changes considering seawater corrections. Results indicate that the co-seismic geoid and deflection changes can be detected clearly by GRACE observation, and the co-seismic geoid change is not sensitive to the fault slip models; whereas the co-seismic deflection changes are sensitive. These behaviors provide us a new and useful approach to invert seismic faults using GRACE-observed deflection changes as constraints.

Wenke Sun, Xin Zhou

### Satellite Gravity Models and Their Use for Estimating Mean Ocean Circulation

One of the main fields of application of static gravity field models is the determination of the (geodetic) mean dynamic ocean topography (MDT) as the difference of a mean sea surface derived from multi-year satellite altimetry, and a high-resolution static geoid model. In this study the performance of several satellite-only global gravity models is evaluated based on the MDT and derived geostrophic ocean surface currents. These are the GRACE-only model ITG-Grace2010S, the GOCE-only model GOCE_TIM_R2, and the combined gravity model GOCO02S representing a consistent combination of GRACE and GOCE. The geodetic MDT results are validated against independently measured drifter data. Compared to GRACE, the new high-resolution GOCE models improve the estimates of the mean dynamic ocean topography, filtered to degree/order 180, by reducing the differences to the drifter data by 10–12 cm/s. Therefore, they contribute significantly to an improved knowledge of mean ocean circulation.

Roland Pail, Alberta Albertella, Daniel Rieser, Jan Martin Brockmann, Wolf-Dieter Schuh, Roman Savcenko

### The Integral-Equation-Based Approaches for Modelling the Local Gravity Field in the Remove–Restore Scheme

We study the accuracy of local gravity field modelling using four different types of the integral-equation-based approaches, namely the Poisson integral, Green integral, point-mass, and radial multipole approaches. We investigate how these four discretised integral equations perform when the gravity data are corrected for the residual terrain model (RTM-correction) and for the reference gravity field (remove–restore scheme). All integral equations are discretised below data points at the chosen constant depth relative to the Bjerhammar sphere. The choice of the optimal depth of discretization is done based on minimising the RMS fit between the observed and predicted gravity data. In all four approaches the number of unknown parameters is identical to the number of input gravity data and the systems of discretised integral equations are solved using Jacobi iteration. The regularisation is not applied. The study area in New Zealand comprises a rough part of the Southern Alps in the South Island with flat coastal regions including offshore areas. The results of numerical experiments are presented and discussed. We demonstrate that the application of the RTM-correction to gravity data significantly improves the accuracy of the gravity field approximation when using the Green integral approach.

A. Abdalla, R. Tenzer

### Validation of Second-Generation GOCE Gravity Field Models by Astrogeodetic Vertical Deflections in Germany

High-precision astrogeodetic vertical deflections in Germany are utilized to validate recent satellite-only global gravity field models with emphasis on the first- and second-generation GOCE models. In order to account for the different spectral characteristics of the data sets involved, the comparisons are performed with a multistage filtering procedure. The comparisons demonstrate that the second generation of GOCE models is significantly improved (by roughly 30 %) compared to the first release, and that the GOCE models contain considerably more gravity field information than pure GRACE models.

C. Voigt, H. Denker

### On the Estimate of Accuracy and Reliability of the A10 Absolute Gravimeter free-fall gravimeter

The Institute of Geodesy and Cartography in Warsaw, Poland, operates the A10-020 absolute portable gravimeter since November 2008. Numerous gravity measurements with the A10-020 gravimeter, conducted under both laboratory and field conditions, provide a unique material for the estimation of accuracy as well as reliability of the determined gravity. Monthly measurements conducted with the A10-020 at the Borowa Gora Geodetic-Geophysical Observatory, north of Warsaw, provided a 2 year long time series at two laboratory sites and one field station. They have been analysed in terms of their internal consistency and compliance with the previous measurements performed with a few other absolute gravimeters (mainly FG5). The results of a number of calibrations of both, the rubidium oscillator and the polarization-stabilized laser of the A10-020 were considered in the analysis. The effect of applying the frequency standard as well as laser calibration data on the quality of gravity determined was investigated. In addition, the impact of weather conditions as well as variability of metrological parameters on surveyed gravity was taken into consideration when evaluating accuracy and reliability of gravity survey with the A10 gravimeter.

Jan Krynski, Przemysław Dykowski, Marcin Sękowski, Jaakko Mäkinen

### Modelling and Observing the Mw 8.8 Chile 2010 and Mw 9.0 Japan 2011 Earthquakes Using GOCE

Earthquakes change the gravity field of the area affected by the earthquake due to mass redistribution in the upper layers of the Earth. In addition, for sub-oceanic earthquakes deformation of the ocean floor causes relative sea-level changes and mass redistribution of water that has again a significant effect on the gravity field. Two such recent, large sub-oceanic earthquakes are the 27 February 2010 Chile Maule earthquake with a magnitude of Mw 8.8 and the 11 March 2011 Japan Tohoku earthquake with a magnitude of Mw 9.0. The goal of ESA’s satellite GOCE—launched in March 2009—is to map the Earth’s gravity field with unprecedented accuracy and resolution. To this end, GOCE carries a gravity gradiometer. Although the mean gravity field is to be mapped, the sheer size of both earthquakes and associated mass redistribution make them both potential candidates for detecting the co-seismic gravity changes in the GOCE gradiometer data. We assess the detectability of gravity field changes in the GOCE gravity gradients by modelling these earthquakes using a forward model. Furthermore, we analyse the GOCE data before and after the respective earthquakes and assess their quality. Based on these analyses we conclude that despite its small signal size at GOCE altitude the Japan earthquake may be visible in the gravity gradients when more post-earthquake data become available. Because of the short data period before the Chile earthquake this signal will probably not be visible.

J. Bouman, M. Fuchs, T. Broerse, B. Vermeersen, P. Visser, E. Schrama, M. Schmidt

### Multi-sensor Space Observation of Heavy Flood and Drought Conditions in the Amazon Region

Variations of continental water storage and related changes of water surface extensions are being observed by a variety of contemporary geometrical and gravimetrical space observation systems and in-situ measuring instruments. Within a regional multi-sensor study in the Amazon basin we elaborate on the potential of different systems for the quantification of variations of water mass and water surface extent caused by extreme flood and drought situations during 2002–2010. In particular we focus on a rapid change between a widespread flood and a drought situation in the year 2009. Observations of water mass from satellite gravimetry (GRACE), water stage from satellite altimetry (Envisat) and water extent from L-band radar remote sensing (PALSAR) are very consistent with respect to their spatial and temporal variability. On the basis of our findings we provide an outlook on the applicability of measurements of water levels and surface water extent for an independent assessment of water volume changes. Those might be used for a cross-comparison with estimates of water storage from GRACE.

Florian Seitz, Karin Hedman, Franz J. Meyer, Hyongki Lee

### Accurate Determination of the Earth Tidal Parameters at the BIPM to Support the Watt Balance Project

To achieve the targeted accuracy in the Bureau International des Poids et Mesures (BIPM) watt balance (WB) project, the value of g (acceleration due to gravity) must be known to an accuracy of 10

−9

(10 nm/s

2

) during the operation of balance. Gravity changes due to Earth Tides are the largest time variable signal affecting g at 10

−7

. In order to improve the tidal prediction at the BIPM site, the relative spring gravimeter gPhone#032 collected observations for 6 months on site B of the BIPM. An analysis of the tidal results is presented here. We compare them with recent Earth and oceanic loading tidal models. In addition, using the gravity data from the Superconducting Gravimeter in Walferdange we demonstrate that a precision of +/−20 nm/s

2

can be achieved on the predicted value of g using a synthetic tide and including atmospheric pressure, polar motion and hydrological effects.

O. Francis, Ch. Rothleitner, Z. Jiang

### Towards Constraining Glacial Isostatic Adjustment in Greenland Using ICESat and GPS Observations

Constraining glacial isostatic adjustment (GIA) i.e. the Earth’s viscoelastic response to past ice changes, is an important task, because GIA is a significant correction in gravity-based ice sheet mass balance estimates. Here, we investigate how temporal variations in the observed and modeled crustal displacements due to the Earth’s response to ongoing ice mass changes can contribute to the process of constraining GIA. We use mass change grids of the Greenland ice sheet (GrIS) derived from NASA’s high resolution Ice, Cloud and land Elevation Satellite (ICESat) data in three overlapping time spans covering the period 2004–2009 to estimate temporal variations in the elastic response due to present day ice mass loss. The modeled crustal displacements (elastic + GIA) are compared with GPS time series from five permanent sites (KELY, KULU, QAQ1, THU2, and SCOR). We find, that the modeled pattern of elastic crustal displacements shows pronounced variation during the observation period, where an increase in elastic displacement is found at the northwest coast of Greenland, while a decrease is found at the southeast coast. This pattern of temporal changes is supported by the GPS observations. We find, that the temporal behavior of the ICESat-based modeled elastic response agrees well with the GPS observations at the sites KELY, QAQ1, and SCOR. This suggests, that our elastic models are able to resolve the temporal changes in the observed uplift, which indicates that the elastic uplift models are reliable at these sites. Therefore, we conclude that these sites are useful for constraining GIA.

Karina Nielsen, Louise S. Sørensen, Shfaqat Abbas Khan, Giorgio Spada, Sebastian B. Simonsen, René Forsberg

### Determination of High Precision Underground Equipotential Profiles for the Alignment of a Future Linear Collider

The alignment challenge presented by the Compact Linear Collider (CLIC) project requires us to look closely at the ultra-high frequencies ( < 1 km) of the gravity field and our ability to model or determine underground equipotential profiles at a very high level of precision. This is of particular importance in the context of an alignment system based on Hydrostatic Levelling System (HLS) and other instruments dependent on gravity. In the first part of this paper, the theoretical formulation of the gravity field, Astronomical Levelling and a misalignment operator are presented. Then, the error propagation model of Astronomical Levelling is revisited and adapted to the specifications of accelerator alignment. Afterwards, numerical gravity field simulations, based on sinusoidal anomalies of varying geometry and density, give the first orders of magnitude of the signals in the equipotential and in the observation space which can be expected at ultra-high frequencies. Finally, a measurement campaign based around a tunnel, 850 m in length, at a depth of 80 m, that include deflections of the vertical and gravimetric measurements is presented.

Sébastien Guillaume, Mark Jones, Beat Bürki, Alain Geiger

### Reducing the Measurement Time of the Torsion Balance

The main problem of torsion balance measurements is the long damping time however it is possible to significantly reduce the observation time by modern technology. The damping curve can be precisely determined by CCD sensors as well as computerized data collection and evaluation. The first part of this curve makes it possible at least theoretically to estimate the final position of the arm at rest. A finite element solution of a fluid dynamics model based on Navier–Stokes equations is presented here to solve the problem.

Gy. Tóth, L. Völgyesi, S. Laky

### Topographic–Isostatic Reduction of GOCE Gravity Gradients

Gravity gradients measured by ESA’s satellite mission GOCE (Gravity field and steady-state Ocean Circulation Explorer) are highly sensitive to mass anomalies and mass transports in the Earth system. The high and mid-frequency gradient components are mainly affected by the attraction of the Earth’s topographic and isostatic masses. Due to these signal components, interpolation and prediction tasks, such as a harmonic downward continuation of the gradients, can be considered as ill-conditioned processes. One approach to mitigate the resulting instability is to smooth the observed gradients by applying topographic–isostatic reductions using a Remove–Compute–Restore technique. This paper presents a reduction concept based on the developed Rock–Water–Ice decomposition in which the topography is represented by a vertical three-layer model with variable density values. Geometry and density information is derived from the topographic data base DTM2006.0. Furthermore, the Airy–Heiskanen isostatic model is adapted to the Rock–Water–Ice approach and extended by including a depth model for the Mohorovičić discontinuity obtained from the global crust model CRUST 2.0. Since these data are provided in geographical coordinates, tesseroid bodies that are arranged on an ellipsoidal reference surface are used for mass discretization. The topographic–isostatic reduction values calculated along the orbit of the GOCE satellite reach a maximum of about 1 E (Eötvös unit, 1 E = 10

−9

s

−2

) and lead to significant smoothing effects on gradient measurements, particularly in regions with highly variable topography. Taking one week of real GOCE measurements as example, the degree of smoothing is analyzed, showing a significant reduction of the standard deviation (about 30 %) and the range (about 20–40 %).

Thomas Grombein, Kurt Seitz, Bernhard Heck

### Measurement of Underground Variations in the Deflection of the Vertical with a High Precision Interferometric Deflectometer

A new system for measuring underground variations of the deflection of the vertical is presented. Based on geodetic and interferometric tilt measurements along a profile, it is designed to finally determine variations of equipotential profiles to better than 10 μm over 200 m with respect to a straight line. This condition comes from the pre-alignment constraints for the Compact Linear Collider (CLIC; Schulte, Pre-Alignment Needs for CLIC, 2009).In the first part of this paper, the basic principle is described and a mathematical model of the system is developed in order to estimate, using Monte-Carlo simulations, theoretical precisions achievable by the system in various configurations. In the second part, the first 12 m long prototype, designed and assembled at the European Organization for Nuclear Research (CERN) in Geneva, is presented. From the first experiments, it is not yet possible to validate the concept, nevertheless they permit us to identify the weaknesses which have to be solved in order to achieve the performance anticipated.

Sébastien Guillaume, Mark Jones, Beat Bürki, Alain Geiger

### Analysis of Time Variations of the Gravity Field Over Europe Obtained from GRACE Data in Terms of Geoid Height and Mass Variation

Time variations of the gravity field obtained from the series of geopotential models developed from GRACE (Gravity Recovery and Climate Experiment) data can be interpreted in terms of geoid heights and mass time variations with unprecedented temporal resolution.

Following the results of the authors previous research, the series of filtered monthly solutions of geopotential models developed from GRACE data and GLDAS (Global Land Data Assimilation System) hydrological models were used in the analysis. Variations of hydrology and geoid heights at the continental part of Europe and selected 14 subareas were estimated with a spatial resolution of 0.5º × 0.5º for the period August 2002–June 2010. Variations in mass distribution obtained from geopotential models were compared with the respective results obtained from hydrological data.

Annual periodicity of hydrology and geoid height variations with minima in September and maxima in March is observed for the area of Europe. The linear trend is also present in the signal. Contrary to the area of Northern Europe (Norway, Sweden, Finland) where dominates the signal due to Post Glacial Rebound as a secular trend, for the subareas of Central Europe only an annual periodicity appears. Results obtained using GRACE data show high correlation with the results calculated using GLDAS hydrological models.

Models of geoid height changes (parameters of trend and seasonal variations) were developed for the area of Europe and for 14 subareas. To verify those models values of geoid height changes calculated using GRACE data over the period July 2010–October 2010 were compared with the respective ones based on the models developed.

Jan Krynski, Grazyna Kloch-Glowka, Malgorzata Szelachowska

### Accurate Gravimetry at the BIPM Watt Balance Site

Accurate gravity measurements were made to support the International Bureau of Weights and Measures (BIPM) watt balance (WB) project in association with the eighth International Comparison of Absolute Gravimeters (ICAG-2009) and the accompanying Relative Gravity Campaign (RGC-2009) at the BIPM in 2009. The goal of WB project is to determine the Planck constant

h

for the realization of a new definition of the kilogram. The accurate value of free fall acceleration

g

is crucial for the precise determination of

h

.

During the formal ICAG-2009 and the RGC-2009, four absolute and six relative gravimeters took part in the WB gravity campaign. The results can therefore be converted to the international reference of the ICAG results, i.e., they are SI-traceable.

The WB gravity network is a regular 3D grid over the site in the WB laboratory that serves to evaluate gravity acceleration at the test mass centre of the future WB setup. The local Earth tide parameters were determined by analyzing a 6 months record of a gPhone spring-type gravimeter. These parameters, together with the atmospheric and polar motion corrections, enable precise prediction of the instantaneous values of the acceleration of free fall required by the WB experiment with an accuracy reaching 5 μGal. In addition, repeated precise levelling has been carried out to monitor the stability of the WB pillar.

Z. Jiang, V. Pálinkáš, O. Francis, S. Merlet, H. Baumann, M. Becker, P. Jousset, J. Mäkinen, H. R. Schulz, K. U. Kessler-Schulz, S. Svitlov, A. Coulomb, L. Tisserand, H. Hu, Ch. Rothleitner

### Study of the Time Stability of Tides Using a Long Term (1973–2011) Gravity Record at Strasbourg, France

The Gravimetric Observatory J9 located near Strasbourg (France), has a long history of recording solid Earth tides. We present here one of the longest available gravity records (1973–2011) from three different instruments operating at the J9 station: a LaCoste–Romberg spring gravimeter (ET005) from 1973 to 1985, a GWR (TT70–T005) superconducting gravimeter from 1987 to 1996 and a GWR compact superconducting gravimeter (C026) since 1996.

We give the results of a tidal analysis performed with ETERNA on these data sets. We show the improvement in terms of noise levels from the oldest type to the newest one and check the time stability of the observed tides for every instrument. This stability is also dependent on the stability of the scale factor of the cryogenic gravimeter which is derived from a direct comparison with repeated absolute gravity measurements. The response of the three gravimeters to the atmospheric pressure changes is also checked.

With all these results we found that the improvement from a mechanical spring gravimeter to a modern cryogenic instrument is obvious. And also that the improvement from the T005 SG to the C026 SG is less impressive than from L&R to the T005 SG, but still notable.

M. Calvo, S. Rosat, J. Hinderer, H. Legros, J.-P. Boy, U. Riccardi

### Submonthly GRACE Solutions from Localizing Integral Equations and Kalman Filtering

An alternative approach for the analysis of GRACE inter-satellite range observations being processed in combination with current best knowledge GRACE orbits from improved GPS relative integer ambiguity fixing has been elaborated. The observations are first reduced by available background geophysical models and subsequently inverted as well as downward continued by a rigorous formulation in terms of reproducing kernel functions. Additionally, time-variable gravity field anomaly maps with respect to the subtracted background data have been derived. The observation equations are due to their spatial representation well suited for a Kalman-filter solution that can possibly enhance time resolution towards sub-monthly time series. The theoretical foundation of the method along with first numerical results and comparison to standard GRACE products are presented.

Christian Gruber, Yongjin Moon, Frank Flechtner, Christoph Dahle, Pavel Novák, Rolf König, Hans Neumayer

### The GOCE Estimated Moho Beneath the Tibetan Plateau and Himalaya

A better understanding of the physics of the Earth’s interior is one of the key objectives of the ESA Earth Explorer missions. This work is focused on the GOCE mission and presents a numerical experiment for the Moho estimation under the Tibet-Quinghai Plateau and the Himalayan range by exploiting the gravity data collected by this mission. The gravity observations, at satellite level, are first reduced for the topography, oceans and known sediments and then the residual field is inverted to determine the crust–mantle interface. The uniqueness of the solution is guaranteed using this simplified two-layer model by making assumptions on the density contrast. Our inversion algorithm is based on the linearization of the Newton’s gravitational law around an approximate constant Moho depth. The resulting equations are inverted by exploiting the Wiener–Kolmogorov theory in the frequency domain and treating the Moho depth as a random signal with zero mean and its own covariance function. As for the input gravity observations, we considered grids of the anomalous gravitational potential and its second radial derivative at satellite altitude, as computed by applying the so called space-wise approach to 8 months of GOCE data. Errors of these grids are available by means of Monte Carlo simulations. Taking a lateral density variations for granted, the Moho beneath the Tibetan Plateau and Himalaya is computed on a grid covering the whole area with an accuracy of few kilometers and an estimated resolution of about 250 km. Taking into account this resolution, the estimated Moho generally shows a good agreement with existing local seismic profiles. The areas where this agreement is not so good can be clearly attributed to the presence of anomalies in the crust–mantle separation, such as subduction zones. The GOCE-only solution is finally improved by using seismic profiles as additional observations, locally increasing its accuracy and resolution.

Daniele Sampietro, Mirko Reguzzoni, Carla Braitenberg

### Validation of GOCE Gravitational Gradients in Satellite Track Cross-Overs

The important issue of quality assessment of GOCE gravitational gradients is addressed. The validation approach that is investigated compares measured gravitational gradients in satellite track cross-overs (XOs). Important updates and changes of our previous XO processing are presented: XO comparison has to be performed in one and the same coordinate system, which necessitates the transformation of the gravitational gradient tensor. As two of the six independent tensor components are less accurate and the remaining four components contain long-periodic inaccuracies, filtering of the gradient time series and the use of model information is required to enable tensor rotation without loss of accuracy.

The second part of the paper focuses on the analysis of residual gradient differences in cross-overs. RMS values and the geographical distribution of the XO residuals are used to assess the GOCE gravitational gradients’ quality. The RMS values of the XO residuals are about 3.2 mE for

V

xx

and

V

yy

, and 5.3 mE for

V

zz

. Areas are identified showing an accumulation of slightly larger XO residuals for individual tensor components. These larger residuals are probably caused by solar winds and an interaction of the accelerometers with the Earth’s magnetic field. In summary, the high quality of the GOCE gravitational gradients is confirmed.

Phillip Brieden, Jürgen Müller

### Reducing Non-tidal Aliasing Effects by Future Gravity Satellite Formations

One major error source in temporal gravity recovery is temporal aliasing. The satellite mission GRACE suffers from pure along-track observations of its low–low Satellite-to-Satellite Tracking (SST) on a polar orbit. This leads to the typical North-South striped error structures in time-variable gravity fields of GRACE, which are amplified because of the inherent GRACE inverse problem and downward continuation. This study analyzes the possibilities to reduce the non-tidal aliasing effects by formations of future gravity satellite missions. It concentrates on mission options which shall be feasible in the next 10 years. These options contain so-called pendulum formations and double pairs with pairs on orbits with different inclinations. Sharifi et al. Previous studies already analyzed several such mission options and this study on the one hand leads to comparable conclusions for the mission options studied in the cited papers. On the other hand combinations of two low–low SST pairs on polar and sun-synchronous orbits, respectively, which are not studied in the cited papers in detail, and its potential to reduce temporal aliasing are analyzed here. This paper focusses on non-tidal temporal aliasing effects together with typical low–low SST noise characteristics. With semi-analytical simulations it is analyzed that a noise level of

$$\mathrm{{10}}^{\mathrm{-11}}\,\mathrm{\mathrm{m}\mathrm{/}\mathrm{{s}}^{\mathrm{2}}}/\sqrt{\mathrm{Hz}}$$

of the range acceleration observations is sufficient to get sensitivity for mass variations on the Earth. Comparing the effects of non-tidal aliasing and colored observation noise, closed-loop simulations of ten different future mission options are analyzed. Pure along-track low–low SST observations like GRACE in a so-called in-line formation are highly affected by this temporal aliasing. The double pairs containing an in-line pair on a 63

inclined orbit reduce the aliasing effect most. Both the single pendulum pairs, one on a polar and another on a sun-synchronous orbit, and their combination reach the same level of aliasing reduction as the combinations with the 63

inclined pair.

Michael Murböck, Roland Pail

### Preliminary Results from the Superconducting Gravimeter SG-060 Installed in West Africa (Djougou, Benin)

A GWR superconducting gravimeter of the new generation (OSG-60) has been installed in July 2010 in sub-humid West Africa, at the Djougou station in Benin. This station is located in the AMMA-CATCH long term hydrological observing system. We present the first results in terms of instrumental drift as well as the calibration results using FG5 absolute gravity measurements. We show that geophysical contributions due to hydrological load can bias the initial drift estimate. The noise level is compared to the Strasbourg SG as well as to the reference New Low Noise Model (NLNM) used in seismology. We also investigate the gravity response to atmospheric pressure changes and show that, because of the presence of large thermal tides, the gravity response to mass changes in the atmosphere is more complex than in the simple case of a constant barometric admittance.

J. Hinderer, S. Rosat, M. Calvo, J.-P. Boy, B. Hector, U. Riccardi, L. Séguis

### Atmospheric Corrections for Superconducting Gravimeters Using Operational Weather Models

Atmospheric pressure fluctuations are a major source of noise in precise gravimetric measurements and must be corrected carefully. A big portion of this effect can be eliminated using the local air pressure and a single admittance factor, which reduces up to 90–95 % of the atmospheric signal. However, modern superconducting gravimeters require an even better atmospheric correction if small signals are to be identified. For this task the three-dimensional modeling of atmospheric mass attraction based on operational numerical weather models has shown promising results. Similar strategies are realized and applied successfully for de-aliasing measurements of satellite gravity missions, such as GRACE (Gravity Recovery and Climate Experiment). In this study we show that such models, here called AGC (Atmospheric Gravity Coefficients), can also be used to correct atmospheric effects on superconducting gravimeter (SG). The Conrad Observatory near Vienna and the SG in Membach are taken as example stations for the SG corrections. The resulting residuals using AGC are in both cases smaller than the traditional single admittance or Green’s function approach and the performance can also be compared to the more sophisticated model used by ATMACS (Atmospheric Attraction Computation Service).

Maria Karbon, Johannes Böhm, Bruno Meurers, Harald Schuh

### Micro-Gravity Measurements in Northern Victoria-Land, Antarctica: A Feasibility Study

Within the Italian Antarctic research programme repeated GPS-measurements are being carried out at well installed points in the area of Northern-Victoria-Land (NVL), Antarctica, called VLNDEF: Victoria Land Network for Deformation Control. Although the deformations obtained over a period of 4 years are quite small we consider micro-gravity measurement a suitable complement for geodynamic research. Since the German Federal Institute for Geosciences and Natural Resources (BGR) is active in that area as well, until the year 2010 performing nine expeditions comprising geological and geophysical work, we used the offer to join expedition GANOVEX X during the season 2009/2010. With three gravimeters 13 points of the Italian network near the German station Gondwana were observed. The advantage of such measurements is that they do not require topographic corrections. Thus, the instrumental resolution and the measurement conditions, resp., are the limits for the resolution and accuracy of the measurements. In order to receive a reliable data base we used three well calibrated gravimeters in parallel and repeated the measurements several times. Local effects due to changes of the ice cover and snow fall are below the achieved measurement accuracy, because the points are so exposed that local effects are negligible. Although the elevation differences up to more than 2,700 m are quite strong, the results reveal the feasibility of these measurements in that area: The obtained standard deviations are in the order of ±10 to ±20 μGal.

G. Jentzsch, R. Ricker, A. Weise, A. Capra, M. Dubbini, A. Zanutta

### High-Resolution Measurements of Non-Linear Spatial Distribution of Gravity Gradients in Hungary

Linear changing of the gravity gradients between the adjoining network points is an important demand for different interpolation methods in geodesy (e.g. interpolation of the deflection of the vertical, geoid computations, and interpolation of the gravity values or the vertical gradients of gravity). To study the linearity of gravity gradients, torsion balance measurements were made both at the field and in a laboratory: one is at the southern part of the Csepel island, and the other in the Geodynamical Laboratory of Loránd Eötvös Geophysical Institute in the Mátyás cave. The results of our investigations show that the linearity of the gravity gradients mainly depends on the given point density and the the geological fine structure of rocks and shallow subsurface density. It seems the given point density of the earlier torsion balance stations may be not enough for some geodetic purposes, moreover the problem could not be solved even applying topographic reduction of gravity gradients.

L. Völgyesi, Z. Ultmann

### Lunar Laser Ranging: Recent Results Based on Refined Modelling

Over 41 years of Lunar Laser Ranging (LLR) provide a unique data set of distance measurements between Earth and Moon with ever increasing precision. A further step on the way to mm-accurate LLR analysis is refined modelling such as that of the gravitational effect from mass multipole moments of Earth and Moon on the lunar orbit and orientation. The previous multipole expansion used at the Institut für Erdmessung has now been extended to higher degrees. The corresponding geocenter-reflector ranges are used for the comparison of the different models. For mm-accurate analysis, the complete gravity field up to degree and order 5 for the Moon and up to degree and order 4 for the Earth should be considered. For the optimal combination of the LLR data, a variance component estimation with respect to the observatories was tested and the new estimation of two relativistic parameters (equivalence principle parameter and variation of the gravitational constant) was carried out.

Jürgen Müller, Franz Hofmann, Xing Fang, Liliane Biskupek

### Recursive Adjustment Approach for the Estimation of Physical Earth Parameters from Polar Motion

The connection between highly precise time series of Earth orientation parameters (EOP) and geophysical processes in the Earth system can be studied on the basis of analytical or numerical forward models. Such models are dependent on a variety of parameters describing geometrical, physical or rheological properties of the Earth. A sensitivity analysis showed that some weakly determined Earth parameters (e.g. Love numbers) have a large effect on the forward model results. We aim at the improvement of such parameters on the basis of observed EOP. In order to make use of the long EOP time series that cover several decades, a recursive adjustment procedure is being developed. We present the principle of the approach and compare it to a least-squares adjustment in the Gauss–Helmert model. It is shown that both approaches are comparable with respect to the results, but the recursive procedure is superior in terms of computational efficiency. Our study focuses on the pole tide Love number

k

2

, a specifically critical model parameter that is directly related to period and damping of the modelled Chandler oscillation. In order to simplify the case, the algorithm is developed and tested for an example of a two-dimensional spring mass damper system in which the simulated damped oscillation is equivalent to the Chandler oscillation.

S. Kirschner, F. Seitz

### Atmospheric and Oceanic Excitation of the Free Core Nutation Estimated from Recent Geophysical Models

We study the excitation of the observed free core nutation (FCN) signal by diurnal variation of the atmospheric and oceanic angular momenta (AAM, OAM), using AAM time series based on three different atmospheric reanalysis models, NCEP-NCAR, ERA-40 and ERA-interim, combined with OAM data from the ocean model OMCT. Comparison with the VLBI nutation data shows that the excitation based on the ERA-interim model is not reliable at the diurnal retrograde frequencies. Our spectral analysis of other excitation data sets confirms the earlier conclusion that the mass term of excitation contains sufficient power to explain the observed amplitude of the FCN oscillation. The coherence analysis of geodetic and geophysical excitations is not conclusive, presumably because the signal-to-noise ratio in AAM and OAM data is too low in vicinity of the FCN frequency.

Aleksander Brzeziński, Henryk Dobslaw, Maik Thomas

### Regional Multi-Fluid-Based Geophysical Excitation of Polar Motion

By analyzing geophysical fluids’ geographic distribution, we can isolate the regional provenance for some of the important signals in polar motion. An understanding of such will enable us to determine whether certain climate signals can have an impact on polar motion. Here we have compared regional patterns of three surficial fluids: the atmosphere, ocean and land-based hydrosphere. The oceanic excitation function of polar motion was estimated with the ECCO/JPL data-assimilating model, and the atmospheric excitation function was determined from NCEP/NCAR reanalyses. The excitation function due to land hydrology was estimated from the Gravity Recovery and Climate Experiment (GRACE) data by an indirect approach that determines water thickness. Our attention focuses on the regional distribution of atmospheric and oceanic excitation of the annual and Chandler wobbles during 1993–2010, and on hydrologic excitation of these wobbles during 2002.9–2011.5. It is found that the regions of maximum fractional covariance (those exceeding a value of 3 ⋅ 10

−3

) for the annual band are over south Asia, southeast Asia and south central Indian ocean, for hydrology, atmosphere and ocean respectively; and for the Chandler period, areas over North America, Asia, and southern South America; and scattered across the southern oceans for the atmosphere and oceans respectively.

Jolanta Nastula, David A. Salstein, Richard Gross

### Quantifying the Correlation Between the MEI and LOD Variations by Decomposing LOD with Singular Spectrum Analysis

Variations in the temporal length-of-day (LOD) contain information on phenomena related to the continuous evolution of Earth processes: tidal energy dissipation and core-mantle coupling (decadal, secular), meteorological and solar-lunar tide effects (annual, semi-annual). In this work, we studied an LOD time series obtained from VLBI measurements and extracted its principal components using the Singular Spectrum Analysis (SSA). After removing the long-term trend which explains 73. 8

%

of the signal, three remaining components explain a further 22. 0

%

of the signal: an annual and a semi-annual signals as well as a second trend. We compared the Multivariate ENSO index (MEI) with the variations in the amplitudes of the annual and semi-annual components and with the second trend. The correlations are significant: 0. 58 for the annual component, − 0. 48 for the semi-annual component and 0. 46 for the second trend.

Karine Le Bail, John M. Gipson, Daniel S. MacMillan

### Advances of Engineering Geodesy and Artificial Intelligence in Monitoring of Movements and Deformations of Natural and Man-Made Structures

Rapid developments in engineering, microelectronics and computer sciences have greatly changed both the instrumentation and the methodology in engineering geodesy. Advanced technology is needed to meet the challenges of today. In dynamic monitoring, for instance, there is an urgent need for continuous geodetic measurements to determine complex movements. The development of an early warning system is possible only when exact knowledge of the process of the object’s movement (e.g. of a landslide area) and all the other physical parameters are available. Special emphasis is laid on the following research areas: detection of potential movements on a large scale, an efficient and continuous observation of critical areas and knowledge-based derivation of real time information about actual risks in order to support an alert system. The necessary tools range from conventional terrestrial measurements and alignment technology—GNSS, InSAR, geotechnical instrumentation—to software systems such as GIS, Spatial Decision Support Systems (SDSS), and so on. For the development of alert systems, the application of Artificial Intelligence (AI) techniques in engineering geodesy is studied. AI, in general, means studying and designing intelligent agents. An intelligent agent is a system which perceives its environment and takes actions to maximize its chances of success. Methods used for uncertain reasoning are probabilistic in nature, such as Bayesian networks, which represent a general tool that can be used for a large number of problems. The achievements of the work in these fields in the past 4 years are presented and discussed in this paper.

G. Retscher, G. Mentes, A. Reiterer

### Precise Antenna Calibration for Ground-Based Pseudolite

In ground-based pseudolite positioning system, one of critical problems is to calibrate the antenna phase center (APC) of the pseudolites in the positioning system frame. In this paper, a convenient method is proposed to resolve the problem. At first, the pseudolite antenna acts as a GPS receiver antenna. Therefore, the APC in the antenna frame can be determined in field. In the positioning system frame, the reference point (ARP) and the attitude of antenna can be determined with conventional ground method. Finally, APC can be transformed to the positioning system frame. Positioning results in a calibrated system demonstrate that within a specific indoor experiment an RMS error of less than 1.0 cm was obtained for the horizontal coordinates and 1.1 cm for the vertical one.

Mingkui Wu, Jingsong Huang, Yaming Xu, Yaodong Qiu, Chao Li, Renlan Cai, Yunhe Yuan

### Collaborative Positioning in GPS-Challenged Environments

GPS augmentation in the form of multi-sensor systems is an accepted approach to positioning in GPS-challenged environments. An extension of this is the concept of collaborative or cooperative positioning, through which a network of GPS users may collectively receive any available satellite signals, augmented by inter-nodal ranging and other sensory measurements to achieve joint and potentially improved position determination. This paper presents an analysis of CP techniques for robust GPS positioning in vehicular ad-hoc networks (VANETs) based around the availability of dedicated short range communications infrastructure (DSRC). Preliminary performance assessments based on simulated and field data collected at the Ohio State University in November 2011 verify that the CP algorithm developed here offers improved accuracy compared to a CP solution that uses standalone GPS positions: 50 % improvement for the duration of the OSU test and 38 % with outages simulated to represent periods of 100 % satellite unavailability.

Allison Kealy, Nima Alam, Mahmoud Efatmaneshnik, Charles Toth, Andrew Dempster, Dorota Brzezinska

### GNSS Attitude Determination for Remote Sensing: On the Bounding of the Multivariate Ambiguity Objective Function

Global Navigation Satellite Systems (GNSS)-based attitude determination is a viable alternative for traditional methods such as gyroscopes. Precise attitude determination using multiple GNSS antennas mounted on a remote sensing platform relies on successful resolution of the integer carrier phase ambiguities. The Multivariate Constrained (MC-) LAMBDA method has been developed for the multivariate quadratically constrained GNSS attitude model that incorporates the known antenna geometry. In this contribution, it is demonstrated that the currently used easy-to-compute MC-LAMBDA bounding functions are relatively loose bounds that may result in too large integer search times. To mitigate this problem, we develop alternative bounding functions and compare their performance using simulated as well as real data. As a result we are able to identify tighter bounding functions that improve the search algorithms for instantaneous GNSS attitude determination.

Nandakumaran Nadarajah, Peter J. G. Teunissen, Gabriele Giorgi

### Monitoring Ground Subsidence Using PALSAR and ASAR in Shanghai Downtown Area

As a result of underground water extraction and huge engineering constructions such as underground structures, skyscrapers and so on, ground subsidence has become a major geological disaster in Shanghai. In this paper, L band ALOS PALSAR data and C band ENVISAT ASAR data are used to extract ground subsidence information in Shanghai downtown area. Firstly, the basic principle of the SBAS algorithm is described and the procedure of extraction of the ground subsidence velocities is elaborated. Then we focus on comparing results obtained by the two kinds of data. The consistency of LOS velocities is compared on a profile over the area with the most significant subsidence, and the temporal changes of InSAR phase at four chosen points on the profile are analyzed too. The results show that the general patterns of ground subsidence from two different bands of SAR data are similar and the velocity difference is less than 5 mm on the chosen profile. Both results show that there are a few places with significant local subsidence rates at about −10 mm/year or even more.

Jicang Wu, Lina Zhang, Tao Li, Jie Chen

### Geoid of Nepal from Airborne Gravity Survey

An airborne gravity survey of Nepal was carried out December 2010 in a cooperation between DTU-Space, Nepal Survey Department, and NGA, USA. The entire country was flown with survey lines spaced 6 nm with a Beech King Air aircraft, with a varying flight altitude from 4 to 10 km. The survey operations were a major challenge due to excessive jet streams at altitude as well as occasional excessive mountain waves. Despite the large 400 mGal + range of gravity anomaly changes from the Indian plains to the Tibetan Plateau, results appear accurate to few mGal, with proper evaluation from cross-overs complicated by the high varying flight altitudes. Using a downward continuation scheme based on blocked least-squares collocation, a new geoid of Nepal was computed by Fourier methods. The new geoid shows large changes to EGM08, illustrating the impact of the new data. The new geoid is compared to limited GPS-levelling data as well as recent GPS-heights of Mt. Everest, and the new data also provide an independent validation of GOCE gravity field models at the local ∼100 km resolution scale.

Rene Forsberg, Arne Vestergaard Olesen, Indridi Einarsson, Niraj Manandhar, Kalyan Shreshta

### GOCE and the Geoid in South America

The global geopotential models GO_CONS_GCF_2_DIR_R2, GOCO02S and EIGEN06C based on GOCE data, and EGM08, represent a new important contribution to medium and long wavelength components knowledge of the gravitational field. These models have impacts on the computation of the respective wavelength components of the geoid. They have been used as reference fields in the modified Stokes integral, generating different geoid models. The terrestrial gravity data in South America have been updated with the most recent measurements in Argentina, Brazil, Ecuador and Paraguay. The short wavelength components were estimated via FFT using Featherstone modified kernel. The complete Bouguer and Helmert gravity anomalies have been derived through the geoid modelling package SHGEO by University of New Brunswick, Canada. The GGMs and the geoid models have been evaluated using GPS observations on Bench Marks of the spirit levelling network (GPS/BM). The height anomaly derived from EGM08 (degree 2190 and order 2159) has also been checked out.

A. C. O. C. de Matos, D. Blitzkow, G. N. Guimarães, M. C. B. Lobianco

### Derivation of the Topographic Potential from Global DEM Models

Spherical harmonic expansion to ultra-high resolution can be used to transform globally available digital elevation models into the high frequency content of the Earth’s gravitational potential. It thereby amends satellite-based gravity measurements (GRACE, GOCE) and ground observations such as height anomalies from GNSS-leveling or dedicated gravity campaigns on terrain. Besides a numerically stable and efficient method for the harmonic expansion on a geocentric reference sphere, the transfer from geodetic to geographic coordinates and full data restoration to appropriate heights (3-D synthesis) has to be considered. Using a series expansion eventually transforms spherical harmonic coefficients of the topography into the topographic potential or topography-reduced gravity anomalies. The concept is discussed and results from analysis of ETOPO1 are presented.

Christian Gruber, Pavel Novák, Frank Flechtner, Franz Barthelmes

### Strategies for Connecting Imbituba and Santana Brazilian Datums Based on Satellite Gravimetry and Residual Terrain Model

Due to the challenge that the Amazon Basin imposes for traditional geodetic surveys, the Brazilian Fundamental Vertical Network (BFVN) is materialized in two independent parts: the southern segment is linked to the Imbituba tide gauge and the northern part is linked to the Santana tide gauge. The mouth of the Amazon River and its surrounding wetlands generate a large area without access for spirit levelling and conventional gravimetry. There is a minimum distance of about 330 km between the nearest bench marks of the two above mentioned vertical networks. Nowadays, satellite gravity missions such as CHAMP, GRACE and GOCE make it possible to explore new solutions based on Global Geopotential Models (GGMs) obtained from satellite data only. Digital Elevation Models (DEMs) allow an improvement in the spectral resolution of the GGMs based on Residual Terrain Modelling (RTM). Such an approach is an alternative to filling the information gaps in the GGMs by reducing omission errors. The spectral improvement of the GGMs allows us to integrate the vertical datums in a more realistic way, and with a reduction of terrestrial gravity dependency. In this study, two alternatives to the indirect connection of the BFVN are analyzed. A solution is based on a combination of GGM satellite-only data from the GOCE mission and the spectral contribution of the RTM. The other solution is based on the integration of information from GOCE GGM, EGM2008 and the RTM effect. The offset obtained shows that the Imbituba datum is located 1.32 and 1.43 m below the Santana datum for the solutions GGM

GOCE+RTM

and GGM

GOCE+EGM2008+RTM

respectively.

Henry D. Montecino, Silvio R. C. de Freitas

### Realization of WHS Based on Gravity Field Models Free of Dependencies on Local Vertical Datums

A realization of the World Height System (WHS) is usually performed on the basis of global geopotential models (GGMs). In this paper we test how reducing of a stripping noise of the satellite-only GGMs can improve their contribution to WHS. Our filtering approach is based on the nonlinear diffusion on a closed surface, namely on the Earth’s surface, using the regularized Perona–Malik model. The filtered GOCE_DIR2 is used to compute the geopotential on the DTU10 mean sea surface obtained from altimetry and at the GNSS/Levelling points in Australia. In the second numerical experiment in New Zealand we present that modelling of the high-frequency part of the gravity field is practically inevitable for precise estimations of offsets of local vertical datums (LVDs). In order to get a numerical solution to the fixed gravimetric BVP in New Zealand we apply the boundary element method (BEM). Our goal is to get a local quasigeoid model not related to LVDs. Therefore we simulate 3D positions of available terrestrial gravimetric measurements using an iterative approach. The GNSS/Levelling test of the obtained BEM solution, EGM-2008 and NZGeoid09 national quasigeoid model shows how the different gravity field models can lead to different estimates of LVD offsets.

Róbert Čunderlík, Robert Tenzer, Karol Mikula

### Study of Alternatives for Combining Satellite and Terrestrial Gravity Data in Regions with Poor Gravity Information

The satellite missions CHAMP, GRACE and GOCE are substantially contributing for the improvement of the Earth gravity field knowledge. However, the respective satellite gravity information remains still limited to around 80 km of spatial resolution. In this condition, it is necessary to use local surface data in shorter wavelengths to obtain more accurate resolutions. This paper deals with strategies to model the Earth gravity field in medium and high frequencies, based on merging Global Geopotential Models (GGMs) and Digital Elevation Models (DEMs). A test area was established in southern Brazil, between the parallels 22ºS and 27ºS and meridians 48ºW and 55°W. The presented methodology uses GOCE_DIR2, already available in the degree and order of 240; GOCE_TIM2, in the degree and order of 250; GOCO02S, in the degree and order of 250; and the combined model EIGEN-06C, in the degree and order of 1420. In order to generate the proposed model, a Residual Terrain Model (RTM) technique was applied, based on the GMRT v2.0 (Global Multi-Resolution Topography 2.0 version) model data. When applying RTM technique, the proposed model achieved better resolutions than the original contained in GGMs. In the absolute analysis, the RMS in GNSS/leveling stations has been reduced by around 17 %, 18 %, 20 % and 20.5 %, respectively for GOCE_DIR2, GOCE_TIM2, GOCO02S, and EIGEN-06C models. The absolute discrepancies were reduced by around 18 % for the satellite-only models and by 28.6 % for the EIGEN-06C. Considering baselines in the range from 55 to 550 km, the contribution of the RTM for the improvement of the original resolution in ppm was around 38 %, 54 %, 57 % and 6.5 %, respectively for GOCE_DIR2, GOCE_TIM2, GOCO02S, and EIGEN-06C models.

K. P. Jamur, S. R. C. de Freitas, H. D. Montecino

### Single-Frequency PPP-RTK: Theory and Experimental Results

Integer ambiguity resolution enabled Precise (cm-level) Point Positioning (PPP) is feasible if corrections from a GPS network of CORS stations are applied to the single-receiver phase and code data of a user. The concept of PPP-RTK requires a proper definition and quality of the PPP-user network corrections, which are satellite clocks, satellite phase biases and ionospheric delays interpolated to the approximate location of the user. The availability of the satellite phase bias corrections enables the user to carry out integer resolution of ambiguities that are double-differenced, i.e., relative to those of the pivot receiver in the network. The availability of the interpolated ionospheric corrections is not absolutely required, however PPP-RTK for single-frequency users would virtually be impossible without them. A proper handling of the network corrections implies that the PPP-user should take their uncertainty into account as well. In order to limit the amount of information to be transmitted to the user, in this contribution we provide a closed-form analytical expression for the variance matrix of the network corrections which a single-frequency user can apply in his processing. Experimental results of single-frequency PPP-RTK for both a high-grade geodetic receiver as well as a low-grade mass-market receiver demonstrate that although single-epoch integer ambiguity resolution is not possible, single-frequency ambiguity resolution enabled cm-level PPP is feasible based on an accumulation of less than 10 min of observations plus network corrections on average.

Dennis Odijk, Peter J. G. Teunissen, Amir Khodabandeh

### Single Frequency PPP Using Real-Time Regional Broadcast Corrections via NTRIP for the Australian GDA94 Datum

The possibility of Real-Time Precise Point Positioning directly in the Australian GDA94 datum has become possible through the availability of Real-Time Broadcast Corrections (BCs) provided by the IGS Real-Time Pilot-Project. Generation of BCs for the GDA94 datum has some pitfalls which are identified in this contribution. It is shown that it is impossible to obtain identical positioning results using either the BCs in ITRF or BCs in GDA94 due to scale differences between both systems. A new user-friendly RBC-approach is introduced, which deals with the scale-induced biases in the current approach. The user-friendly RBC-approach eliminates the user-need of having to apply the ITRF-to-GDA94 transformation, while still giving correct horizontal PPP positions in GDA94. For users that additionally require precise height information in GDA94 as well, a simple constant height-correction, valid for the complete Australian continent, is all that is needed to obtain the correct full 3D PPP position.

Lennard Huisman, Peter J. G. Teunissen, Congwei Hu

### Global Assessment of UNB’s Online Precise Point Positioning Software

The GPS Analysis and Positioning Software (GAPS) is a GPS precise point positioning (PPP) application developed at the University of New Brunswick (UNB). GAPS exists in two forms: a web-based positioning service, to which users can upload GPS observations to be processed, and a command-line executable version, which can be used to process large amounts of GPS data in a fast and convenient manner. The objective of this paper is to summarize the main approach used in the online version of GAPS; to present the modeling options available to the user through the online interface, and to assess the accuracy of GAPS by processing a global network of IGS stations for a period 1 year; and to assess the achievable accuracy of GAPS by comparing the results with external sources and similar evaluations encountered in the literature. Results obtained indicate that GAPS can achieve at least 1 cm level accuracy for any component at any location in the world.

Landon Urquhart, Marcelo C. Santos, Carlos A. Garcia, Richard B. Langley, Rodrigo F. Leandro

### Reliable Integer Ambiguity Resolution

Soft Constraints on the Baseline Length and Direction, and New Multi-frequency Code Carrier Linear Combinations

In this paper, a maximum a posteriori probability estimation of baselines and ambiguities is proposed for RTK and attitude determination. The estimator uses statistical a priori information about the baseline length, pitch and heading, and thereby improves the accuracy of the float solution. It is more robust than traditional attitude determination techniques with deterministic baseline constraints. The inertia of the receivers are considered in a movement model, which is integrated into an extended Kalman filter. Moreover, a new set of multi-frequency code carrier linear combinations is derived, which enables an arbitrary scaling of the geometry, an arbitrary scaling of the ionospheric delay, and any preferred wavelength.

Patrick Henkel, Patryk Jurkowski

### Array-Aided CORS Network Ambiguity Resolution

Array-aided precise point positioning (A-PPP) is a measurement concept that uses Global Navigation Satellite System (GNSS) data, from multiple antennas in an array of known geometry, to realize the improved GNSS parameter estimation. In this contribution the ambiguity resolution benefits of A-PPP for antenna-array equipped CORS stations is explored. To demonstrate the performance of array-aided ambiguity resolution between-station, an 80 km baseline experiment, equipped with a 6-antenna array at each CORS station, was conducted. We formulate the underlying model, show how the array-data to be reduced and present numerical results on the ambiguity resolution performance. The results show that the use of antenna-arrays can significantly improve the CORS network ambiguity resolution.

Bofeng Li, Peter J. G. Teunissen

### A New Newton-Type Iterative Formula for Over-Determined Distance Equations

Newton-type methods were ordinarily developed by using approximate Hessian matrices to solve the nonlinear equations. For dealing with ill-posed ranging resection problems, we propose a new Newton-type iterative formula based on the precise Hessian matrix, called closed-form Newton iterative formula. An orthogonal condition is introduced to the nonlinear least squares solution of an over-determined distance equation system. It is revealed that the solution is the barycentre of a particle system composed of unit masses at the endpoints of the ranging vectors. Then a closed-form of the Newton method is given by compactly expressing the Hessian matrix. The simulation result shows that the closed-form Newton method can improve the efficiency and the stability of the convergence, especially in the case of the ill-posed positioning configurations.

Yamin Dang, Shuqiang Xue

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