Volume 5, Issue 1

This article is a personal review of the development of physical geodesy during 1984-2014. The period is characterized by an intensive advance in both data and theory to meet the growing technical demands in GPS/GNSS applications and scientific needs in geoscience. As a result,many parts of theworld are nowmapped with a 1cmdetailed geoid model, and the global long- to mediumwavelengths of the gravity field and geoid are homogeneously determined to 1 mGal and 1 cm by satellite-only dedicated satellite gravity missions. The future can expect to see even higher demands for accuracy and reliability to satisfy the specifications for a pure geoid model based vertical datum.

Recent advancement of land-based mobile mapping enables rapid and cost-effective collection of highquality road related spatial information. Mobile Mapping Systems (MMS) can provide spatial information with subdecimeter accuracy in nominal operation environments. However, performance in challenging environments such as tunnels is not well characterized. The Norwegian Public Roads Administration (NPRA) manages the country’s public road network and its infrastructure, a large segment of which is represented by road tunnels (there are about 1 000 road tunnels in Norway with a combined length of 800 km). In order to adopt mobile mapping technology for streamlining road network and infrastructure management and maintenance tasks, it is important to ensure that the technology is mature enough to meet existing requirements for object positioning accuracy in all types of environments, and provide homogeneous accuracy over the mapping perimeter. This paper presents results of a testing campaign performed within a project funded by the NPRA as a part of SMarter road traffic with Intelligent Transport Systems (ITS) (SMITS) program. The testing campaign objective was performance evaluation of high end commercial MMSs for inventory of public areas, focusing on Global Navigation Satellite System (GNSS) signal degraded environments.

Annual absolute gravity measurements with a FG5 instrument were performed in Onsala Space Observatory by the Institute of Geodesy of the Leibniz Universität Hannover from 2003 to 2011 and have been continued with the upgraded meter FG5X in 2014. Lantmäteriet, Gävle, with their FG5 absolute gravimeter have visited Onsala since 2007. Because small systematic errors may be inherent in each absolute gravimeter, their measuring level and a resulting bias (offset) between the instruments must be controlled over time by means of inter-comparison. From 2007 to 2014, 8 direct comparisons took place well distributed over the time span. A complete re-processing of the absolute gravity observations with the Hannover instrument has been conducted to improve the reduction of unwanted gravity effects. A new tidal model is based on continuous time series recorded with the GWR superconducting gravimeter at Onsala since 2009. The loading effect of the Kattegat is described with a varying sea bottom pressure (water and air mass load) and has been validated with the continuous gravity measurements. For the land uplift,which is a result of the still ongoing glacial isostatic adjustment in Fennoscandia, a secular gravity trend of −0.22 μGal/yr was obtained with a standard deviation of 0.17 μGal/yr. That indicates a slight uplift but is still not significantly different from zero.

The Onsala Space Observatory has installed a modern digital backend for geodetic and astronomical Very Long Baseline Interferometry (VLBI). This system consists of a Digital Base-Band Converter (DBBC) and a Mark 5B+ recorder. From 2011 until late 2014 this new system was run for geodetic VLBI observations in parallel with the old system consisting of a Mark 4 rack and Mark 5A recording system. Several of these observed sessions were correlated at the correlator in Bonn including both data sets. We present results from the analysis and comparison of these sessions. Both the original observed delays and corresponding geodetic parameters are compared. No significant differences are detected, for either the raw observations or for the geodetic parameters. This shows that the digital backend can be used operationally for geodetic VLBI observations.

The paper describes the development and testing of a simulation tool, called QualiSIM. The tool estimates GNSS-based position accuracy based on a simulation of the environment surrounding the GNSS antenna, with a special focus on city-scape environments with large amounts of signal reflections from non-line-of-sight satellites. The signal reflections are implemented using the extended geometric path length of the signal path caused by reflections from the surrounding buildings. Based on real GPS satellite positions, simulated Galileo satellite positions, models of atmospheric effect on the satellite signals, designs of representative environments e.g. urban and rural scenarios, and a method to simulate reflection of satellite signals within the environment we are able to estimate the position accuracy given several prerequisites as described in the paper. The result is a modelling of the signal path from satellite to receiver, the satellite availability, the extended pseudoranges caused by signal reflection, and an estimate of the position accuracy based on a least squares adjustment of the extended pseudoranges. The paper describes the models and algorithms used and a verification test where the results of QualiSIM are compared with results from collection of real GPS data in an environment with much signal reflection.

For many developing countries such as Uganda, precise gravimetric geoid determination is hindered by the low quantity and quality of the terrestrial gravity data. With only one gravity data point per 65 km2, gravimetric geoid determination in Uganda appears an impossible task. However, recent advances in geoid modelling techniques coupled with the gravity-field anomalies from the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite mission have opened new avenues for geoid determination especially for areas with sparse terrestrial gravity. The present study therefore investigates the computation of a gravimetric geoid model overUganda (UGG2014) using the Least Squares Modification of Stokes formula with additive corrections. UGG2014 was derived from sparse terrestrial gravity data from the International Gravimetric Bureau, the 3 arc second SRTM ver4.1 Digital Elevation Model from CGIAR-CSI and the GOCE-only global geopotential model GO_CONS_GCF_2_TIM_R5. To compensate for the missing gravity data in the target area, we used the surface gravity anomalies extracted from the World Gravity Map 2012. Using 10 Global Navigation Satellite System (GNSS)/levelling data points distributed over Uganda, the RMS fit of the gravimetric geoid model before and after a 4-parameter fit is 11 cm and 7 cm respectively. These results show that UGG2014 agrees considerably better with GNSS/levelling than any other recent regional/ global gravimetric geoid model. The results also emphasize the significant contribution of the GOCE satellite mission to the gravity field recovery, especially for areas with very limited terrestrial gravity data.With an RMS of 7 cm, UGG2014 is a significant step forward in the modelling of a “1-cm geoid” over Uganda despite the poor quality and quantity of the terrestrial gravity data used for its computation.

Since the year 2000, some periodic investigations have been performed in the Lilla Edet region to monitor and possibly determine the landslide of the area with GPS measurements. The responsible consultant has conducted this project by setting up some stable stations for GPS receivers in the risky areas of Lilla Edet and measured the independent baselines amongst the stations according to their observation plan. Here, we optimise the existing surveying network and determine the optimal configuration of the observation plan based on different criteria.We aim to optimise the current network to become sensitive to detect 5 mm possible displacements in each net point. The network quality criteria of precision, reliability and cost are used as object functions to perform single-, bi- and multi-objective optimisation models. It has been shown in the results that the single-objective model of reliability, which is constrained to the precision, provides much higher precision than the defined criterion by preserving almost all of the observations. However, in this study, the multi-objective model can fulfil all the mentioned quality criteria of the network by 17% less measurements than the original observation plan, meaning 17%of saving time, cost and effort in the project.

The present study aims at the validation of global gravity field models through numerical investigation in gravity field functionals based on spherical harmonic synthesis of the geopotential models and the analysis of terrestrial data. We examine gravity models produced according to the latest approaches for gravity field recovery based on the principles of the Gravity field and steadystate Ocean Circulation Explorer (GOCE) and Gravity Recovery And Climate Experiment (GRACE) satellite missions. Furthermore, we evaluate the overall spectrum of the ultra-high degree combined gravity models EGM2008 and EIGEN-6C3stat. The terrestrial data consist of gravity and collocated GPS/levelling data in the overall Hellenic region. The software presented here implements the algorithm of spherical harmonic synthesis in a degree-wise cumulative sense. This approach may quantify the bandlimited performance of the individual models by monitoring the degree-wise computed functionals against the terrestrial data. The degree-wise analysis performed yields insight in the short-wavelengths of the Earth gravity field as these are expressed by the high degree harmonics.

Ocean loading models, Baltic Sea loading and atmospheric loading tilt models are compared with the long interferometric water level tilt meter recordings at the Lohja2 geodynamics laboratory in southern Finland. The tilt meter shows a high response to different loading phenomena, and it can be used to study earth dynamics, earth structure modeling, and 2D surface mass loading model validation. Special attention is paid on the Baltic Sea and atmospheric loading tilt oscillations. The four ocean loading models used show deviating values compared to the measured earth tide tilt parameters. The CSR4.0 ocean loading model fits best to analyzed tidal tilt observations at the site. After reductions of earth tides, ocean, the Baltic Sea and atmospheric loading tilt, the largest residual tilt signals are located in frequency bands below 0.5 cycle/day.

In this paper, we introduce the Micro-g LaCoste Turnkey Airborne Gravity System (TAGS) with Fugro’s improved gravity processing and geoid modeling software package for regional gravity field mapping and geoid determination. Three test areas with different topographic characteristics under the Gravity for the Redefinition of the AmericanVertical Datum (GRAV-D) project of theUSNOAA National Geodetic Surveys (NGS) were used for case studies and determine the available accuracy of the system. The preliminary results of all these test cases show that the system with Fugro’s improved gravity and geoid processing software package is able to achieve a comparable geoid mapping result to traditional terrestrial methods.

The variance of a purely random error - “pure error” - in measuring the relative coordinates during the calculation of the orbits of binary stars, (its "unbiased estimate"), is necessary for each test used in the orbit calculation for double stars, such as the adequacy test for the orbit model, gross-error tests and the like. Since this variance is unknown, in this paper we present the robust PEROBEPE1 method which provides an unbiased variance estimate for the pure error in the coordinate measurements concerning the orbits of double stars. This estimate is independent of the model adequacy for a double-star orbit and thus can be used in any test concerning double stars.

We present rigorous solutions for the geoid-fromquasigeoid correction (GQC) using Taylor expansions of surface gravity disturbances along the vertical from the Earth’s surface to the geoid. One solution takes advantage of the topographic potential bias at the geoid, which can be expressed by a simple formula. This implies that the accurate GQC does not need a terrain correction.

We analyzed the noise characteristics of 112 continuously operating GPS stations in eastern North America using the Spectral Analysis and the Maximum Likelihood Estimation (MLE) methods. Results of both methods show that the combination ofwhite plus flicker noise is the best model for describing the stochastic part of the position time series. We explored this further using the MLE in the time domain by testing noise models of (a) powerlaw, (b)white, (c)white plus flicker, (d)white plus randomwalk, and (e) white plus flicker plus random-walk. The results show that amplitudes of all noise models are smallest in the north direction and largest in the vertical direction. While amplitudes of white noise model in (c–e) are almost equal across the study area, they are prevailed by the flicker and Random-walk noise for all directions. Assuming flicker noise model increases uncertainties of the estimated velocities by a factor of 5–38 compared to the white noise model.

The Gravity Recovery and Climate Experiment (GRACE) monthly satellite data is used to examine the extent and magnitude of Greenland ice sheet melting for 2003-2012. We show that the well documented Greenland ice mass loss in the southern region spread to northwest Greenland in the period from2007 to 2010 and 2010 to 2012 by estimating ice mass variability over time in Greenland. The ice-mass melting is estimated to –183±11 Gt/yr. This estimation means that Greenland is still losing much more ice than gained, and continuing to contribute to global sea level rise in a warming world. Unlike other recent studies, our method employs a non-isotropic filter. A nonisotropic filter is used to decorrelate the GRACE data, since the GRACE noise structure has a non-isotropic nature.

In-land geoid models rely on several measuring techniques. The quality of those models is directly related to the spatial resolution of the measurement data. Occasionally, a local geoid model does not cover the coastal area at all and a local marine geoid simply does not exist. ShipborneGNSS measurementsmay provide away of overcoming this problem in coastal areas. However, several corrections to the raw measurements must be applied in order to account for systematic effects induced by ship dynamics and other static and dynamic impacts from tides, atmospheric pressure or wind stress. This paper presents the theoretical background for the method and the results of a case study in the estuary of the Weser River in Germany. A series of GNSS measurements were carried out aboard a ship and the approximate geoid height along the river was derived. For accuracy assessments of this method, the resultswere compared to the German Combined QuasiGeoid 2011 (GCG2011). The results are very promising and indicate the ability to extract geoid heights from shipborne GNSS measurements.

Signals from Global Navigational Satellite Systems (GNSS) when integrated with surface meteorological parameters can be used to sense atmospheric water vapour. Using gLAB software and employing precise point positioning techniques, zenith troposphere delays (ZTD) for a GPS base station at KNUST, Kumasi have been computed and used to retrieve Precipitable Water (PW). The PW values obtained were compared with products from ERA-Interim and NCEP reanalysis data. The correlation coefficients, r, determined from these comparisons were 0.839 and 0.729 for ERA-interim and NCEP respectively. This study has demonstrated that water vapour can be retrieved with high precision from GNSS signal. Furthermore, a location map have been produced to serve as a guide in adopting and installing GNSS base stations in Ghana to achieve a country wide coverage of GNSS based water vapour monitoring.

Geoid determination below the topographic surface in continental areas using analytical continuation of gravity anomaly and/or an external type of solid spherical harmonics determined by an Earth GravitationalModel (EGM) inevitably leads to a topographic bias, as the true disturbing potential at the geoid is not harmonic in contrast to its estimates. We show that this bias differs for the geoid heights represented by Stokes’ formula, an EGMand for the modified Stokes formula. The differences are due to the fact that the EGM suffers from truncation and divergence errors in addition to the topographic bias in Stokes’ original formula.

The paper presents a novel original upwindbased approach for solving the oblique derivative boundary value problem by the finite volume method. In this approach, the oblique derivative boundary condition is interpreted as a stationary advection equation for the unknown disturbing potential. Its approximation is then performed by using the first order upwind scheme taking into account information from inflow parts of the finite volume boundary only. When the numerical scheme is derived, numerical simulations in 2D and 3D domains are performed and the experimental order of convergence of the proposed algorithm is studied. Moreover a comparison with a solution by the central scheme previously used for this kind of problem is performed. Finally we present numerical experiments dealing with the global and local gravity field modelling.

Many geoscientists argue that there is a gravity low of 10-30 mGal in Fennoscandia as a remaining fingerprint of the last ice age and load, both vanished about 10 kyr ago. However, the extraction of the gravity signal related with Glacial Isostatic Adjustment (GIA) is complicated by the fact that the total gravity field is caused by many significant density distributions in the Earth. Here we recall a methodology originating with A. Bjerhammar 35 years ago, that emphasizes that the present land uplift phenomenon mainly occurs in the region thatwas covered by the ice cap, and it is highly correlated with the spectral window of degrees 10-22 of the global gravity field, whose lower limit fairly well corresponds to the wavelength that agrees with the size of the region. This implies that, although in principle the GIA is a global phenomenon, the geoid and gravity lows as well as the land upheaval in Fennoscandia are typically regional phenomena that cannot be seen in a global correlation study as it is blurred by many irrelevant gravity signals. It is suggested that a regional multi-regression analysis with a band-limited spectral gravity signal as the observable, a method tested already 2 decades ago, can absorb possible significant disturbing signals, e.g. from topographic and crustal depth variations, and thereby recover the GIA signal.

The residuals of 27 globally distributed long tide gauge recordswere scrutinized after removing the globally compounding effect of the periodic lunar node tides and almost periodic solar radiation’s sub and superharmonics from the tide gauge data. The spectral analysis of the residuals revealed additional unmodeled periodicities at decadal scales, 19 of which are within the close range of 12–14 years, at 27 tide gauge stations. The amplitudes of the periodicitieswere subsequently estimated for the spectrally detected periods and they were found to be statistically significant (p «0.05) for 18 out of 27 globally distributed tide gauge stations. It was shown that the estimated amplitudes at different localities may have biased the outcome of all the previous studies based on tide gauge or satellite altimetry data that did not account for these periodicities, within the range −0.5 – 0.5 mm/yr., acting as another confounder in detecting 21st century sea level rise.