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Knowledge of the static and morphodynamic components of the river bed is important for the maintenance of waterways. Under the action of a current, parts of the river bed sediments can move in the form of dunes. Recordings of the river bed by multibeam echosounding are used as input data within a morphological analysis in order to compute the bedload transport rate using detected dune shape and migration. Before the morphological analysis, a suitable processing of the measurement data is essential to minimize inherent uncertainties. This paper presents a simulation-based evaluation of suitable data processing concepts for vertical sections of bed forms based on a case study at the river Rhine. For the presented spatial approaches, suitable parameter sets are found, which allow the reproduction of nominal dune parameters in the range of a few centimetres. However, if parameter sets are chosen inadequately, the subsequently derived dune parameters can deviate by several decimetres from the simulated truth. A simulation-based workflow is presented, to find the optimal hydrographic data processing strategy for a given dune geometry.

The absolute and relative accuracy of sea surface heights derived from six altimeter missions (Jason-1/2/3, Envisat, Saral, Sentinel-3A) is evaluated at five GNSS-controlled tide gauge stations in the German Bight (SE North Sea). The precision of the total water level envelope (TWLE) is assessed for the period 2000 to 2019 based on RMS errors and explained variances. The comparison is based on TWLE instead of dealiased sea level data since the tidal and barotropic dynamic is not known with sufficient accuracy in this area. The tide gauges are partly located at the open sea, partly at the coast close to mudflats. The tide gauge data is available every minute, the 20 Hz level 2 altimetry data is interpolated to virtual stations at distances between 2 and 15 km to the tide gauges. The altimeter data is based on standard retrackers, the correction models are adjusted to coastal applications and exclude the corrections for ocean tides and dynamic atmosphere to allow a direct comparison to the tide gauge data. To account for slight differences of the tidal dynamics between gauge and altimetry an optimal time shift and scale between each pair of locations is estimated and applied. This tidal correction improves the RMS errors by 15-75%. The explained variances are excellent at all stations (> 96%). The resultant RMS errors are mainly between 2-5 cm depending on location and mission. The RMS errors rise up to 10 cm where coastal dynamics play a dominant role or the altimeter approaches the land very closely (

The International VLBI Service for Geodesy and Astrometry (IVS) regularly produces high-quality Earth orientation parameters from observing sessions employing extensive networks or individual baselines. The master schedule is designed according to the telescope days committed by the stations and by the need for dense sampling of the Earth orientation parameters (EOP). In the pre-2011 era, the network constellations with their number of telescopes participating were limited by the playback and baseline capabilities of the hardware (Mark4) correlators. This limitation was overcome by the advent of software correlators, which can now accommodate many more playback units in a flexible configuration. In this paper, we describe the current operations of the IVS with special emphasis on the quality of the polar motion results since these are the only EOP components which can be validated against independent benchmarks. The polar motion results provided by the IVS have improved continuously over the years, now providing an agreement with IGS results at the level of 20–25 $$\upmu $$ as in a WRMS sense. At the end of the paper, an outlook is given for the realization of the VLBI Global Observing System.

Daily Very Long Baseline Interferometry (VLBI) intensive measurements make an important contribution to the regular monitoring of Earth rotation variations. Since these variations are quite rapid, their knowledge is important for navigation with global navigation satellite system and for investigations in Earth sciences. Unfortunately, the precision of VLBI intensive observations is 2–3 times worse than the precision of regular 24h-VLBI measurements with networks of 5–10 radio telescopes. The major advancement of research in this paper is the improvement of VLBI intensive results by (a) using twin telescopes instead of single telescopes and (b) applying an entirely new scheduling concept for the individual observations. Preparatory investigations of standardintensive sessions suggest that the impact factors of the observations are well suited for the identification of the most influential observations which are needed for the determination of certain parameters within the entire design of a VLBI session. Based on this experience, the scheduling method is designed for optimizing the observations’ geometry for a given network of radio telescopes and a predefined set of parameters to be estimated. The configuration of at least two twin telescopes, or one twin and two single telescopes, offers the possibility of building pairwise sub-nets that observe two different sources simultaneously. In addition to an optimized observing plan, a special parametrization for twin telescopes leads to an improved determination of Earth rotation variations, as it is shown by simulated observations. In general, an improvement of about 50 % in the formal errors can be realized using twin radio telescopes. This result is only due to geometric improvements as higher slew rates of the twin telescopes are not taken into account.

Deformations of radio telescopes used in geodetic and astrometric very long baseline interferometry (VLBI) observations belong to the class of systematic error sources which require correction in data analysis. In this paper we present a model for all path length variations in the geometrical optics of radio telescopes which are due to gravitational deformation. The Effelsberg 100 m radio telescope of the Max Planck Institute for Radio Astronomy, Bonn, Germany, has been surveyed by various terrestrial methods. Thus, all necessary information that is needed to model the path length variations is available. Additionally, a ray tracing program has been developed which uses as input the parameters of the measured deformations to produce an independent check of the theoretical model. In this program as well as in the theoretical model, the illumination function plays an important role because it serves as the weighting function for the individual path lengths depending on the distance from the optical axis. For the Effelsberg telescope, the biggest contribution to the total path length variations is the bending of the main beam located along the elevation axis which partly carries the weight of the paraboloid at its vertex. The difference in total path length is almost $$-$$ 100 mm when comparing observations at 90 $$^\circ $$ and at 0 $$^\circ $$ elevation angle. The impact of the path length corrections is validated in a global VLBI analysis. The application of the correction model leads to a change in the vertical position of $$+120$$ mm. This is more than the maximum path length, but the effect can be explained by the shape of the correction function.

We describe a VLBI experiment in which, for the first time, the clock reference is delivered from a National Metrology Institute to a radio telescope using a coherent fibre link 550 km long. The experiment consisted of a 24-hours long geodetic campaign, performed by a network of European telescopes; in one of those (Medicina, Italy) the local clock was alternated with a signal generated from an optical comb slaved to a fibre-disseminated optical signal. The quality of the results obtained with this facility and with the local clock is similar: interferometric fringes were detected throughout the whole 24-hours period and it was possible to obtain a solution whose residuals are comparable to those obtained with the local clock. These results encourage further investigation of the ultimate VLBI performances achievable using fibre dissemination at the highest precision of state-of-the-art atomic clocks.

Space-geodetic techniques at radio wavelength, such as global navigation satellite systems and very long baseline interferometry (VLBI), suffer from refractivity of the Earth’s atmosphere. These highly dynamic processes, particularly refractivity variations in the neutral atmosphere, contribute considerably to the error budget of these space-geodetic techniques. Here, microscale fluctuations in refractivity lead to elevation-dependent uncertainties and induce physical correlations between the observations. However, up to now such correlations are not considered routinely in the stochastic model of space-geodetic observations, which leads to very optimistic standard deviations of the derived target parameters, such as Earth orientation parameters and station positions. In this study, the standard stochastic model of VLBI observations, which only includes, almost exclusively, the uncertainties from the VLBI correlation process, is now augmented by a variance–covariance matrix derived from an atmospheric turbulence model. Thus, atmospheric refractivity fluctuations in space and time can be quantified. One of the main objectives is to realize a suitable stochastic model of VLBI observations in an operational way. In order to validate the new approach, the turbulence model is applied to several VLBI observation campaigns consisting of different network geometries leading the path for the next-generation VLBI campaigns. It is shown that the stochastic model of VLBI observations can be improved by using high-frequency atmospheric variations and, thus, refining the stochastic model leads to far more realistic standard deviations of the target parameters. The baseline length repeatabilities as a general measure of accuracy of baseline length determinations improve for the turbulence-based solution. Further, this method is well suited for routine VLBI data analysis with limited computational costs.

A combination procedure of Earth orientation parameters from Global Positioning System (GPS) and Very Long Baseline Interferometry (VLBI) observations was developed on the basis of homogeneous normal equation systems. The emphasis and purpose of the combination was the determination of sub-daily polar motion (PM) and universal time (UT1) for a long time-span of 13 years. Time series with an hourly resolution and a model for tidal variations of PM and UT1-TAI (dUT1) were estimated. In both cases, 14-day nutation corrections were estimated simultaneously with the ERPs. Due to the combination procedure, it was warranted that the strengths of both techniques were preserved. At the same time, only a minimum of de-correlating or stabilizing constraints were necessary. Hereby, a PM time series was determined, whose precision is mainly dominated by GPS observations. However, this setup benefits from the fact that VLBI delivered nutation and dUT1 estimates at the same time. An even bigger enhancement can be seen for the dUT1 estimation, where the high-frequency variations are provided by GPS, while the long term trend is defined by VLBI. The estimated combined tidal PM and dUT1 model was predominantly determined from the GPS observations. Overall, the combined tidal model for the first time completely comprises the geometrical benefits of VLBI and GPS observations. In terms of root mean squared (RMS) differences, the tidal amplitudes agree with other empirical single-technique tidal models below 4 μas in PM and 0.25 μs in dUT1. The noise floor of the tidal ERP model was investigated in three ways resulting in about 1 μas for diurnal PM and 0.07 μs for diurnal dUT1 while the semi-diurnal components have a slightly better accuracy.

In preparation of activities planned for the realization of the Global Geodetic Observing System (GGOS), a group of German scientists has carried out a study under the acronym GGOS-D which closely resembles the ideas behind the GGOS initiative. The objective of the GGOS-D project was the investigation of the methodological and information-technological realization of a global geodetic-geophysical observing system and especially the integration and combination of the space geodetic observations. In the course of this project, highly consistent time series of GPS, VLBI, and SLR results were generated based on common state-of-the-art standards for modeling and parameterization. These series were then combined to consistently and accurately compute a Terrestrial Reference Frame (TRF). This TRF was subsequently used as the basis to produce time series of station coordinates, Earth orientation, and troposphere parameters. In this publication, we present results of processing algorithms and strategies for the integration of the space-geodetic observations which had been developed in the project GGOS-D serving as a prototype or a small and limited version of the data handling and processing part of a global geodetic observing system. From a comparison of the GGOS-D terrestrial reference frame results and the ITRF2005, the accuracy of the datum parameters is about 5–7 mm for the positions and 1.0–1.5 mm/year for the rates. The residuals of the station positions are about 3 mm and between 0.5 and 1.0 mm/year for the station velocities. Applying the GGOS-D TRF, the offset of the polar motion time series from GPS and VLBI is reduced to 50 μas (equivalent to 1.5 mm at the Earth’s surface). With respect to troposphere parameter time series, the offset of the estimates of total zenith delays from co-located VLBI and GPS observations for most stations in this study is smaller than 1.5 mm. The combined polar motion components show a significantly better WRMS agreement with the IERS 05C04 series (96.0/96.0 μas) than VLBI (109.0/100.7 μas) or GPS (98.0/99.5 μas) alone. The time series of the estimated parameters have not yet been combined and exploited to the extent that would be possible. However, the results presented here demonstrate that the experiences made by the GGOS-D project are very valuable for similar developments on an international level as part of the GGOS development.

We present an empirical model for periodic variations of diurnal and sub-diurnal Earth rotation parameters (ERPs) that was derived based on the transformation of normal equation (NEQ) systems of Very Long Baseline Interferometry (VLBI) observing sessions. NEQ systems that contain highly resolved polar motion and UT1-TAI with a temporal resolution of 15 min were generated and then transformed to the coefficients of the tidal ERP model to be solved for. To investigate the quality of this model, comparisons with empirical models from the Global Positioning System (GPS), another VLBI model and the model adopted by the conventions of the International Earth Rotation and Reference Systems Service (IERS) were performed. The absolute coefficients of these models agree almost completely within 7.5 μ as in polar motion and 0.5 μs in UT1-TAI. Several bigger differences exist, which are discussed in this paper. To be able to compare the model estimates with results of the continuous VLBI campaigns, where signals with periods of 8 and 6 h were detected, terms in the ter- and quarter-diurnal band were included in the tidal ERP model. Unfortunately, almost no common features with the results of continuous VLBI campaigns or ERP predictions in these tidal bands can be seen.

In late 2008, the Product Center for the International Terrestrial Reference Frame (ITRF) of the International Earth Rotation and Reference Systems Service (IERS) issued a call for contributions to the next realization of the International Terrestrial Reference System, ITRF2008. The official contribution of the International VLBI Service for Geodesy and Astrometry (IVS) to ITRF2008 consists of session-wise datum-free normal equations of altogether 4,539 daily Very Long Baseline Interferometry (VLBI) sessions from 1979.7 to 2009.0 including data of 115 different VLBI sites. It is the result of a combination of individual series of session-wise datum-free normal equations provided by seven analysis centers (ACs) of the IVS. All series are completely reprocessed following homogeneous analysis options according to the IERS Conventions 2003 and IVS Analysis Conventions. Altogether, nine IVS ACs analyzed the full history of VLBI observations with four different software packages. Unfortunately, the contributions of two ACs, Institute of Applied Astronomy (IAA) and Geoscience Australia (AUS), had to be excluded from the combination process. This was mostly done because the IAA series exhibits a clear scale offset while the solution computed from normal equations contained in the AUS SINEX files yielded unreliable results. Based on the experience gathered since the combination efforts for ITRF2005, some discrepancies between the individual series were discovered and overcome. Thus, the consistency of the individual VLBI solutions has improved considerably. The agreement in terms of WRMS of the Terrestrial Reference Frame (TRF) horizontal components is 1 mm, of the height component 2 mm. Comparisons between ITRF2005 and the combined TRF solution for ITRF2008 yielded systematic height differences of up to 5 mm with a zonal signature. These differences can be related to a pole tide correction referenced to a zero mean pole used by four of five IVS ACs in the ITRF2005 contribution instead of a linear mean pole path as recommended in the IERS Conventions. Furthermore, these systematics are the reason for an offset in the scale of 0.4 ppb between the IVS’ contribution to ITRF2008 and ITRF2005. The Earth orientation parameters of seven series used as input for the IVS combined series are consistent to a huge amount with about 50 μas WRMS in polar motion and 3 μs in dUT1.

Space-Geodetic techniques are used to provide fundamental scientific products like the terrestrial and celestial reference frame or the Earth orientation parameters (EOPs). These parameters are typically determined in a least squares adjustment of redundant observations. Within this process, numerical issues materializing in the condition of the equation system as well as in insufficient stability of the solution play an important role. While bad condition numbers are an indicator of numerical problems having no connection to the solution strategy i.e., the algorithms used for solving the equation system, numerical stability refers to the algorithms which are used. This paper focuses on the impact of numerical conditioning on EOPs.

In 2017, the astronomical and geodetic communities will celebrate the 50-year anniversary of the first Very Long Baseline Interferometry (VLBI) experiments. The Journal of Geodesy Special Issue titled “VLBI contribution to reference frames and Earth’s rotation studies” is dedicated to this great jubilee. VLBI plays a key role in astronomy and geodesy. It provides unprecedented spatial resolution and position measurements on the sky with an accuracy superior to other techniques. VLBI is a key space geodetic technique since the 1970s, which fundamentally contributes to the maintenance of terrestrial (TRF) and celestial (CRF) reference frames, including the International Terrestrial (ITRF) and Celestial (ICRF) Reference Frames, and monitoring of the Earth’s rotation with respect to the ITRF and ICRF through determination of highly accurate Earth orientation parameters (EOP). Furthermore, the VLBI technique is unique in determining the Universal Time and the precession–nutation of the Earth’s rotation axis in space. Consequently, it is the only technique capable to provide a consistent TRF–EOP–CRF solution. VLBI also essentially contributes to Solar System dynamics and space and terrestrial navigation, atmospheric studies and refining geophysical models, crustal movements and plate tectonics, time and frequency transfer, and testing physical theories. The most accurate and valuable VLBI results are obtained from global VLBI station networks involving radio telescopes located in different countries on different continents. Therefore, a successful realization of the VLBI observing programs requires both inter-institutional and international cooperation. Since 1999, this cooperation is realized through the International VLBI Service for Geodesy and Astrometry (IVS). Moreover, the IVS provides the combined IVS products, such as EOP and VLBI TRF realization (VTRF). The latter essentially contributes to the multi-technique ITRF solution providing the longest station position time series and defining, together with Satellite Laser Ranging (SLR), the ITRF scale and scale rate. Including the radio source positions in the combination is under investigation. A dedicated paper in this issue describes the current state and perspectives of the IVS operations. The previous Special Issue of Journal of Geodesy devoted to VLBI and published in June 2007 (volume 81, issue 6–8) was highly successful. Since that time, many important changes and impressive improvements in the VLBI technique and analysis happened, such as VLBI2010 technical design, the start of the next-generation global VLBI network VLBI Global Observing System (VGOS), publishing ICRF2 and preparing ICRF3, and implementing new IVS combined EOP–TRF products based on combination of datum-free normal equations. All these researches and developments aim at achieving the 1 mm accuracy in TRF and EOP. To reach this goal, the development of technology should be accompanied by improvement in the geophysical and astronomical modelling as well as in the analysis strategy. This Special Issue of Journal of Geodesy is intended to put together papers describing the latest developments in geodetic and astrometric VLBI. Taking into account the scope of the Journal and the limited size of the volume, only the papers devoted to the geodetic and astrometric data analysis were called for. After the Call for papers was sent to the community, we received many responses from our colleagues expressing their interest to contribute to the volume. We believe that the papers published here comprise a representative collection reflecting the main topics of geodetic and astrometric data analysis, which will provide a good reference source for future research in the field. It is a pleasure to express our gratitude to all the authors presenting their results in this issue. All the papers submitted to this volume have passed a peer-review process following the standard procedure of the Journal of Geodesy. We are much indebted to many reviewers whose valuable comments and suggestions helped to prepare the final papers of high quality included in this volume. Finally, we would like to acknowledge the hard and continuous work of all the IVS components over many years—stations, correlators, technology development, operational and analysis centers that regularly deliver data and products of highest quality for scientific analysis and practical applications.

In this paper, a methodology for automatic scheduling of Very Long Baseline Interferometry (VLBI) observations of satellites is presented and first scheduling approaches are investigated. For this investigation the orbit of a geostationary satellite has been chosen, but, the methodology has also been successfully applied to an orbit of a Global Navigation Satellite Systems satellite. A scheduling procedure based on covariance optimization is developed and observations are simulated. In contrast to other simulation studies for a dedicated VLBI satellite mission, we are performing a scheduling process where observations of quasars and satellites are considered being equally important. Thus, the satellites are consistently included into a VLBI experiment. To validate the individual schedules, simplistic daily constant orbit shifts are estimated and analyzed. In this way, the necessary time between two subsequent satellite observations and the geometry of the observing network are investigated. Taking into account all circumstances, large global networks are the best option for estimating orbit shifts. Such a configuration leads to a large number of observations and a good observing geometry for the orbit. For a geostationary satellite, it is sufficient to carry out only one observation per hour or even longer. However, the presented results are only valid for the estimation of orbit shifts. Various improvements of these initial investigations are imaginable, e.g., considering orbit parameters within the scheduling process or estimating realistic orbit parameters.

The path of signals from space geodetic techniques, such as Very Long Baseline Interferometry (VLBI) or Global Navigation Satellite Systems (GNSS), is affected by refractivity variations in the neutral atmosphere. This tropospheric delay, which represents a major contribution to the error budget of space geodetic observations, is generally considered by applying an adequate model (hydrostatic component) and by additionally estimating tropospheric parameters (wet component). Sometimes, the standard approach may lead to negative tropospheric parameters. Due to the fact, that there is nothing like negative water vapour, these negative estimates do not reflect the meteorological conditions in a plausible way.In this paper, we introduce an Inequality Constrained Least Squares (ICLS) method from the field of convex optimization to constrain the tropospheric parameters to non-negative values. We applied this new methodology to 17 years of VLBI sessions. For about 20% of these sessions the method automatically applied inequality constraints. For many sessions the procedure is successful. However, deficiencies in the hydrostatic modeling also lead to worse results for a few sessions. Thus, the methodology is applicable to VLBI data analyses if the a priori modeling is correct which is not always the case for the data set available at the moment.

The currently existing realizations of the International Celestial Reference System (ICRS), the International Celestial Reference Frame 1 (ICRF1) and ICRF2, are based on solutions estimated by one VLBI group. In contrast, the International Terrestrial Reference Frame (ITRF) is based on a multi-technique combination with contributions from different geodetic space techniques. Furthermore, these individual technique-specific solutions are generated in an intra-technique combination. To overcome the shortcomings of the past ICRF determination, one of the main goals for the upcoming realizations of the ICRS and ITRS is an entirely consistent and simultaneous computation of both frames. This includes inter- as well as intra-technique combinations.

The estimates based on laser scans of surfaces with unknown deformations are biased and not reproducible when changing the scanning geometry. While the existence of a bias is only disadvantageous at some applications, non-reproducible estimates are never desired. Hence, this varying bias and its origin need to be investigated - since this situation has not been examined sufficiently in the literature. Analyzing this situation, the dependence of the estimation on the network configuration is highlighted: the network configuration - studied similarly to geodetic networks - rules about the impact of the deformation.As pointed out, this impact can be altered by manipulating the network configuration. Therefore, several strategies are proposed. These include manipulations of the leastsquares adjustment as well as robust estimation. It is revealed that the reproducibility of the estimates can indeed be significantly increased by some of the proposed leastsquares manipulations. However, the bias can only be significantly reduced by robust estimation.

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.

[1] Subdiurnal periodic effects in the Earth's rotation as seen by Very Long Baseline Interferometry (VLBI) are investigated on the basis of continuous VLBI observing campaigns (CONT) observed by the International VLBI Service for Geodesy and Astrometry (IVS). In 2008, the latest campaign (CONT08) was observed adding another valuable data set of 15 consecutive days to the series of CONT sessions. Among other things, CONT08 as well as CONT02 and CONT05 had been scheduled with the aim of observing short-period variations of the Earth orientation parameters. In this publication, we describe an analysis, which is based on hourly estimates of polar motion and UT1-TAI and a subsequent spectral analysis. The generation of the time series is performed with a modified analysis approach. We add the normal equations of each individual 24 hour session to one big equation system for the whole campaign where observations of adjacent sessions contribute to parameters at session borders simultaneously. Over the years, the experience in operating and analyzing the CONT sessions has improved and the procedures have been adapted for improvement of the results. However, at the same time, the observing network has suffered considerable changes. Thus, a comparative overview over the three CONT campaigns is given in this paper. The intermittent detection of periodicities as reported by Haas and Wunsch (2006) applies in this analysis for CONT02 as well. For CONT05 and CONT08 minute signals at periods of around 6 hours are contained in the amplitude spectra. The origin of these signals is still questionable.

[1] The analysis coordinator of the International VLBI Service for Geodesy and Astrometry (IVS) regularly disseminates the official IVS products of Earth orientation parameters (EOPs). For 2 years now, these parameters have been produced by combining datum-free normal equations of up to six IVS analysis centers. In this paper we document the combination methodology, discuss critical issues, and report on the quality of the products. The agreement of the very long baseline interferometry results with the International Global Navigation Satellite Systems (GNSS) Service GPS EOPs is of the order of 18 μs for length of day and 100 μas (microarc seconds) and 300 μas/d for the polar motion components and their rates, respectively.

Consistent and homogeneous long-time series of the space geodetic techniquesGlobal Positioning System (GPS), Satellite Laser Ranging (SLR), andVery Long Baseline Interferometry (VLBI) provide the basis for thecombination efforts of GGOS-D. For a consistent combination, thedefinition of common standards for parameterization and modeling isessential. These standards and the technique-specific processingoptions of all individual GPS, SLR, and VLBI solutions as well asthe combined SLR and VLBI solutions are discussed.

The generation of the GGOS-D global terrestrial reference frame is based on VLBI, SLR, and GPS observations. The respective observation blocks, analysed as individual units, depend on the technique and cover either full weeks, full days (GPS and SLR) or observing sessions of 24 h duration (VLBI). From these observation units, time series of parameters have been inferred and studies of the quality of the results have been carried out for the identification of deficits in the analyses. In this paper, we describe examples of time series of site coordinates, Earth orientation, and atmosphere parameters as well as peculiarities in the behaviour of these parameters.