Ultra-rapid earth rotation determination with VLBI during CONT11 and CONT14

We present earth rotation results from the ultra-rapid operations during the continuous VLBI campaigns CONT11 and CONT14. The baseline Onsala–Tsukuba, i.e., using two out of the 13 and 17 stations contributing to CONT11 and CONT14, respectively, was used to derive UT1-UTC in ultra-rapid mode during the ongoing campaigns. The latency between a new observation and a new UT1-UTC result was less than 10 min for more than 95% of the observations. The accuracy of the derived ultra-rapid UT1-UTC results is approximately a factor of three worse than results from optimized one-baseline sessions and/or complete analysis of large VLBI networks. This is, however, due to that the one-baseline picked from the CONT campaigns is not optimized for earth rotation determination. Our results prove that the 24/7 operation mode planned for VGOS, the next-generation VLBI system, is possible already today. However, further improvements in data connectivity of stations and correlators as well in the automated analysis are necessary to realize the ambitious VGOS plans.     

Universal time from VLBI single-baseline observations during CONT08

The IVS Intensive sessions are single-baseline, 1-h VLBI sessions carried out everyday in order to determine Universal Time (UT1). We investigate different possibilities to improve the results of such sessions. We do this investigation by extracting 2-h single-baseline sessions from the CONT08 data set. These are analysed like normal Intensives, and the results are compared to the results of the analysis of the full CONT08 data set. We find that tropospheric asymmetry is the major error source for the single-baseline sessions. It is possible to improve the accuracy of the estimated UT1 either by using accurate a priori tropospheric gradients or by estimating gradients in the data analysis.     

Achievements of the Earth orientation parameters prediction comparison campaign

Precise transformations between the international celestial and terrestrial reference frames are needed for many advanced geodetic and astronomical tasks including positioning and navigation on Earth and in space. To perform this transformation at the time of observation, that is for real-time applications, accurate predictions of the Earth orientation parameters (EOP) are needed. The Earth orientation parameters prediction comparison campaign (EOP PCC) that started in October 2005 was organized for the purpose of assessing the accuracy of EOP predictions. This paper summarizes the results of the EOP PCC after nearly two and a half years of operational activity. The ultra short-term (predictions to 10 days into the future), short-term (30 days), and medium-term (500 days) EOP predictions submitted by the participants were evaluated by the same statistical technique based on the mean absolute prediction error using the IERS EOP 05 C04 series as a reference. A combined series of EOP predictions computed as a weighted mean of all submissions available at a given prediction epoch was also evaluated. The combined series is shown to perform very well, as do some of the individual series, especially those using atmospheric angular momentum forecasts. A main conclusion of the EOP PCC is that no single prediction technique performs the best for all EOP components and all prediction intervals.     

On comparison of the Earth orientation parameters obtained from different VLBI networks and observing programs

In this paper, a new geometry index of very long baseline interferometry (VLBI) observing networks, the volume of network V, is examined as an indicator of the errors in the Earth orientation parameters (EOP) obtained from VLBI observations. It has been shown that both EOP precision and accuracy can be well described by the power law σ = aV ^c in a wide range of the network size from domestic to global VLBI networks. In other words, as the network volume grows, the EOP errors become smaller following a power law. This should be taken into account for a proper comparison of EOP estimates obtained from different VLBI networks. Thus, performing correct EOP comparison allows us to investigate accurately finer factors affecting the EOP errors. In particular, it was found that the dependence of the EOP precision and accuracy on the recording data rate can also be described by a power law. One important conclusion is that the EOP accuracy depends primarily on the network geometry and to lesser extent on other factors, such as recording mode and data rate and scheduling parameters, whereas these factors have a stronger impact on the EOP precision.     

Combined Earth orientation parameters based on homogeneous and continuous VLBI and GPS data

The CONT02 campaign is of great interest for studies combining very long baseline interferometry (VLBI) with other space-geodetic techniques, because of the continuously available VLBI observations over 2 weeks in October 2002 from a homogeneous network. Especially, the combination with the Global Positioning System (GPS) offers a broad spectrum of common parameters. We combined station coordinates, Earth orientation parameters (EOPs) and troposphere parameters consistently in one solution using technique- specific datum-free normal equation systems. In this paper, we focus on the analyses concerning the EOPs, whereas the comparison and combination of the troposphere parameters and station coordinates are covered in a companion paper in Journal of Geodesy. In order to demonstrate the potential of the VLBI and GPS space-geodetic techniques, we chose a sub-daily resolution for polar motion (PM) and universal time (UT). A consequence of this solution set-up is the presence of a one-to-one correlation between the nutation angles and a retrograde diurnal signal in PM. The Bernese GPS Software used for the combination provides a constraining approach to handle this singularity. Simulation studies involving both nutation offsets and rates helped to get a deeper understanding of this singularity. With a rigorous combination of UT1–UTC and length of day (LOD) from VLBI and GPS, we showed that such a combination works very well and does not suffer from the systematic effects present in the GPS-derived LOD values. By means of wavelet analyses and the formal errors of the estimates, we explain this important result. The same holds for the combination of nutation offsets and rates. The local geodetic ties between GPS and VLBI antennas play an essential role within the inter-technique combination. Several studies already revealed non-negligible discrepancies between the terrestrial measurements and the space-geodetic solutions. We demonstrate to what extent these discrepancies propagate into the combined EOP solution.     

VLBI技术CONT观测的高频ERP解算

国际VLBI测天测地服务机构(IVS)已组织了多次VLBI连续加密观测(CONT),提供了高精度连续的原始观测数据,在地球自转参数(ERP)的连续高频解算中起到积极的作用,揭示了地球自转高频变化的观测资料和理论模型之间的差异,有助于进一步解析其激发机制改进模型.这里使用VLBI资料处理软件系统OCCAM处理了CONT02,CONT05和CONT08数据,并进行ERP高频解算及频谱分析.从各次CONT观测的残差频谱中发现较强周期信号,反映了地球自转的特性.特别是CONT08残差频谱中存在明显的周日项信患,揭示了北半球夏季月份大气激发对地球自转的作用.     

High-resolution atmospheric angular momentum functions related to Earth rotation parameters during CONT08

Due to the temporal resolution of available numerical weather analyses, the effect of the atmosphere on Earth rotation at daily and sub-daily periods is usually investigated using 6-hourly atmospheric angular momentum (AAM) functions. During the period of CONT08, however, atmospheric analysis data were provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) also on an hourly basis. In this paper, we, therefore, determine two sets of AAM functions from ECMWF data—one for CONT08 with hourly resolution and one for the year 2008 with 6-hourly resolution. The comparisons of the AAM functions to high-resolution Earth rotation parameters (ERP) from VLBI and GPS observations are carried out in the frequency domain. Special attention is paid to the preparation of the high-resolution data sets for the geodetic purposes, as there are jump discontinuities at 12 h intervals. Hence, the hourly AAM functions need to be concatenated. The revised functions yield much smaller amplitudes than their 6-hourly counterparts, as can be seen from the equatorial and the axial frequency spectra of atmospheric excitation in Earth rotation. This decrease of spectral power in the hourly AAM functions is found to be associated with a strong counteraction of pressure and wind terms, which originates from atmospheric circulation on short time scales. The results are compared to previous findings published by Brzeziński and Petrov (IERS Tech Note 28:53–60, 2000) based on the data from the U.S. National Centers for Environmental Prediction (NCEP).     

Earth orientation determinations by short duration VLBI observations

Summary In May 1989 and April 1990 the radio telescopes of the Wettzell Geodetic Fundamental Station in Germany and of the Shanghai Observatory near Seshan in China observed two series of daily VLBI experiments of short duration for precise determination of UT1. In 1990 a few experiments were complemented by the Hartebeesthoek Radio Astronomy Observatory in South Africa and the Medicina telescope of the Bologna Istituto di Radioastronomia in Italy. Employing the South African station together with the east-west baseline formed by the observatories of Seshan and Medicina permitted simultaneous determinations of UT1 and polar motion. Here we report on the results of these observations. Comparing the UT1 results with those of the IRIS Intensive series gives a clear indication of the absolute accuracy of such short duration VLBI measurements which is estimated to be of the order of ±60µs.     

Is there utility in rigorous combinations of VLBI and GPS Earth orientation parameters?

Combinations of station coordinates and velocities from independent space-geodetic techniques have long been the standard method to realize robust global terrestrial reference frames (TRFs). In principle, the particular strengths of one observing method can compensate for weaknesses in others if the combination is properly constructed, suitable weights are found, and accurate co-location ties are available. More recently, the methodology has been extended to combine time-series of results at the normal equation level. This allows Earth orientation parameters (EOPs) to be included and aligned in a fully consistent way with the TRF. While the utility of such multi-technique combinations is generally recognized for the reference frame, the benefits for the EOPs are yet to be quantitatively assessed. In this contribution, which is a sequel to a recent paper on co-location ties (Ray and Altamimi in J Geod 79(4–5): 189–195, 2005), we have studied test combinations of very long baseline interferometry (VLBI) and Global Positioning System (GPS) time-series solutions to evaluate the effects on combined EOP measurements compared with geophysical excitations. One expects any effect to be small, considering that GPS dominates the polar motion estimates due to its relatively dense and uniform global network coverage, high precision, continuous daily sampling, and homogeneity, while VLBI alone observes UT1-UTC. Presently, although clearly desirable, we see no practical method to rigorously include the GPS estimates of length-of-day variations due to significant time-varying biases. Nevertheless, our results, which are the first of this type, indicate that more accurate polar motion from GPS contributes to improved UT1-UTC results from VLBI. The situation with combined polar motion is more complex. The VLBI data contribute directly only very slightly, if at all, with an impact that is probably affected by the weakness of the current VLBI networks (small size and sparseness) and the quality of local ties relating the VLBI and GPS frames. Instead, the VLBI polar motion information is used primarily in rotationally aligning the VLBI and GPS frames, thereby reducing the dependence on co-location tie information. Further research is needed to determine an optimal VLBI-GPS combination strategy that yields the highest quality EOP estimates. Improved local ties (including internal systematic effects within the techniques) will be critically important in such an effort.     

VLBI-derived troposphere parameters during CONT08

Time-series of zenith wet and total troposphere delays as well as north and east gradients are compared, and zenith total delays (ZTD) are combined on the level of parameter estimates. Input data sets are provided by ten Analysis Centers (ACs) of the International VLBI Service for Geodesy and Astrometry (IVS) for the CONT08 campaign (12?C26 August 2008). The inconsistent usage of meteorological data and models, such as mapping functions, causes systematics among the ACs, and differing parameterizations and constraints add noise to the troposphere parameter estimates. The empirical standard deviation of ZTD among the ACs with regard to an unweighted mean is 4.6?mm. The ratio of the analysis noise to the observation noise assessed by the operator/software impact (OSI) model is about 2.5. These and other effects have to be accounted for to improve the intra-technique combination of VLBI-derived troposphere parameters. While the largest systematics caused by inconsistent usage of meteorological data can be avoided and the application of different mapping functions can be considered by applying empirical corrections, the noise has to be modeled in the stochastic model of intra-technique combination. The application of different stochastic models shows no significant effects on the combined parameters but results in different mean formal errors: the mean formal errors of the combined ZTD are 2.3?mm (unweighted), 4.4?mm (diagonal), 8.6?mm [variance component (VC) estimation], and 8.6?mm (operator/software impact, OSI). On the one hand, the OSI model, i.e. the inclusion of off-diagonal elements in the cofactor-matrix, considers the reapplication of observations yielding a factor of about two for mean formal errors as compared to the diagonal approach. On the other hand, the combination based on VC estimation shows large differences among the VCs and exhibits a comparable scaling of formal errors. Thus, for the combination of troposphere parameters a combination of the two extensions of the stochastic model is recommended.     

Multi-technique comparison of tropospheric zenith delays derived during the CONT02 campaign

In October 2002, 15 continuous days of Very Long Baseline Interferometry (VLBI) data were observed in the Continuous VLBI 2002 (CONT02) campaign. All eight radio telescopes involved in CONT02 were co-located with at least one other space-geodetic technique, and three of them also with a Water Vapor Radiometer (WVR). The goal of this paper is to compare the tropospheric zenith delays observed during CONT02 by VLBI, Global Positioning System (GPS), Doppler Orbitography Radiopositioning Integrated by Satellite (DORIS) and WVR and to compare them also with operational pressure level data from the European Centre for Medium-Range Weather Forecasts (ECMWF). We show that the tropospheric zenith delays from VLBI and GPS are in good agreement at the 3–7 mm level. However, while only small biases can be found for most of the stations, at Kokee Park (Hawaii, USA) and Westford (Massachusetts, USA) the zenith delays derived by GPS are larger by more than 5 mm than those from VLBI. At three of the four DORIS stations, there is also a fairly good agreement with GPS and VLBI (about 10 mm), but at Kokee Park the agreement is only at about 30 mm standard deviation, probably due to the much older installation and type of DORIS equipment. This comparison also allows testing of different DORIS analysis strategies with respect to their real impact on the precision of the derived tropospheric parameters. Ground truth information about the zenith delays can also be obtained from the ECMWF numerical weather model and at three sites using WVR measurements, allowing for comparisons with results from the space-geodetic techniques. While there is a good agreement (with some problems mentioned above about DORIS) among the space-geodetic techniques, the comparison with WVR and ECMWF is at a lower accuracy level. The complete CONT02 data set is sufficient to derive a good estimate of the actual precision and accuracy of each geodetic technique for applications in meteorology.     

Comparison of individual and combined zenith tropospheric delay estimations during CONT08 campaign

CONT campaigns are 2-week campaigns of continuous VLBI observations. The IERS working group on combination at the observation level uses these campaigns to study such combinations. In this work, combinations of DORIS, GPS, SLR, and VLBI technique measurements are studied during CONT08. We present different results concerning the use of common zenith tropospheric delay (ZTD) during the combination. We compare the ZTD obtained separately using each individual technique data processing, the combined ZTD, and the ZTD derived from a meteorological model. This resulted in a high level of consistency between each of these ZTD at a sub-centimeter level, a consistency which especially depends on the number of observations per estimated ZTD and the humidity level in the troposphere. We noted that GPS provides the main information about the combined ZTD, the other techniques providing complementary information when a lack of GPS observations occurs.     

EOP and scale from continuous VLBI observing: CONT campaigns to future VGOS networks

Continuous (CONT) VLBI campaigns have been carried out about every 3 years since 2002. The basic idea of these campaigns is to acquire state-of-the-art VLBI data over a continuous time period of about 2 weeks to demonstrate the highest accuracy of which the current VLBI system is capable. In addition, these campaigns support scientific studies such as investigations of high-resolution Earth rotation, reference frame stability, and daily to sub-daily site motions. The size of the CONT networks and the observing data rate have increased steadily since 1994. Performance of these networks based on reference frame scale precision and polar motion/LOD comparison with global navigation satellite system (GNSS) earth orientation parameters (EOP) has been substantially better than the weekly operational R1 and R4 series. The precisions of CONT EOP and scale have improved by more than a factor of two since 2002. Polar motion precision based on the WRMS difference between VLBI and GNSS for the most recent CONT campaigns is at the 30 \(\upmu \)as level, which is comparable to that of GNSS. The CONT campaigns are a natural precursor to the planned future VLBI observing networks, which are expected to observe continuously. We compare the performance of the most recent CONT campaigns in 2011 and 2014 with the expected performance of the future VLBI global observing system network using simulations. These simulations indicate that the expected future precision of scale and EOP will be at least 3 times better than the current CONT precision.     

Prediction of Earth orientation parameters by artificial neural networks

 Earth orientation parameters (EOPs) [polar motion and length of day (LOD), or UT1–UTC] were predicted by artificial neural networks. EOP series from various sources, e.g. the C04 series from the International Earth Rotation Service and the re-analysis optical astrometry series based on the HIPPARCOS frame, served for training the neural network for both short-term and long-term predictions. At first, all effects which can be described by functional models, e.g. effects of the solid Earth tides and the ocean tides or seasonal atmospheric variations of the EOPs, were removed. Only the differences between the modeled and the observed EOPs, i.e. the quasi-periodic and irregular variations, were used for training and prediction. The Stuttgart neural network simulator, which is a very powerful software tool developed at the University of Stuttgart, was applied to construct and to validate different types of neural networks in order to find the optimal topology of the net, the most economical learning algorithm and the best procedure to feed the net with data patterns. The results of the prediction were analyzed and compared with those obtained by other methods. The accuracy of the prediction is equal to or even better than that by other prediction methods. Received: 6 February 2001 / Accepted: 23 October 2001     

Methodology for the combination of sub-daily Earth rotation from GPS and VLBI observations

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.     

Stability of the determination of earth rotation parameters (ERP) from VLBI

The observations of theIRIS network are used to study the stability of the determination ofERP fromVLBI. It is concluded that the uncertainties in the initial values ofERP, the errors of other parameters and analyst noise are at the same level as the formal errors in the determination ofERP. The geometric effect on the determination ofERP is important and gives rise to systematic errors. The geometric effect on polar motion is greate than onUT1, and much greater for the continental network. The stability of the determination ofERP fromVLBI can be improved either by creating new stations at reasonable locations in a network or by creating new networks. At last a comparison is provided between the determinations ofERP from theIRIS andTEMPO networks.     

Effect of different tropospheric mapping functions on the TRF, CRF and position time-series estimated from VLBI

This paper compares estimated terrestrial reference frames (TRF) and celestial reference frames (CRF) as well as position time-series in terms of systematic differences, scale, annual signals and station position repeatabilities using four different tropospheric mapping functions (MF): The NMF (Niell Mapping Function) and the recently developed GMF (Global Mapping Function) consist of easy-to-handle stand-alone formulae, whereas the IMF (Isobaric Mapping Function) and the VMF1 (Vienna Mapping Function 1) are determined from numerical weather models. All computations were performed at the Deutsches Geodätisches Forschungsinstitut (DGFI) using the OCCAM 6.1 and DOGS-CS software packages for Very Long Baseline Interferometry (VLBI) data from 1984 until 2005. While it turned out that CRF estimates only slightly depend on the MF used, showing small systematic effects up to 0.025 mas, some station heights of the computed TRF change by up to 13 mm. The best agreement was achieved for the VMF1 and GMF results concerning the TRFs, and for the VMF1 and IMF results concerning scale variations and position time-series. The amplitudes of the annual periodical signals in the time-series of estimated heights differ by up to 5 mm. The best precision in terms of station height repeatability is found for the VMF1, which is 5–7% better than for the other MFs.