Multi-technique comparison of troposphere zenith delays and gradients during CONT08

CONT08 was a 15 days campaign of continuous Very Long Baseline Interferometry (VLBI) sessions during the second half of August 2008 carried out by the International VLBI Service for Geodesy and Astrometry (IVS). In this study, VLBI estimates of troposphere zenith total delays (ZTD) and gradients during CONT08 were compared with those derived from observations with the Global Positioning System (GPS), Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), and water vapor radiometers (WVR) co-located with the VLBI radio telescopes. Similar geophysical models were used for the analysis of the space geodetic data, whereas the parameterization for the least-squares adjustment of the space geodetic techniques was optimized for each technique. In addition to space geodetic techniques and WVR, ZTD and gradients from numerical weather models (NWM) were used from the European Centre for Medium-Range Weather Forecasts (ECMWF) (all sites), the Japan Meteorological Agency (JMA) and Cloud Resolving Storm Simulator (CReSS) (Tsukuba), and the High Resolution Limited Area Model (HIRLAM) (European sites). Biases, standard deviations, and correlation coefficients were computed between the troposphere estimates of the various techniques for all eleven CONT08 co-located sites. ZTD from space geodetic techniques generally agree at the sub-centimetre level during CONT08, and??as expected??the best agreement is found for intra-technique comparisons: between the Vienna VLBI Software and the combined IVS solutions as well as between the Center for Orbit Determination (CODE) solution and an IGS PPP time series; both intra-technique comparisons are with standard deviations of about 3?C6?mm. The best inter space geodetic technique agreement of ZTD during CONT08 is found between the combined IVS and the IGS solutions with a mean standard deviation of about 6?mm over all sites, whereas the agreement with numerical weather models is between 6 and 20?mm. The standard deviations are generally larger at low latitude sites because of higher humidity, and the latter is also the reason why the standard deviations are larger at northern hemisphere stations during CONT08 in comparison to CONT02 which was observed in October 2002. The assessment of the troposphere gradients from the different techniques is not as clear because of different time intervals, different estimation properties, or different observables. However, the best inter-technique agreement is found between the IVS combined gradients and the GPS solutions with standard deviations between 0.2 and 0.7?mm.     

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).     

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.     

Systematic differences between VTEC obtained by different space-geodetic techniques during CONT08

The ionosphere is a dispersive medium for microwaves, and most space-geodetic techniques using two or more signal frequencies can be applied to extract information on ionospheric parameters, including terrestrial as well as satellite-based GNSS, DORIS, altimetry, and VLBI. Because of their different sensitivity regarding ionization, their different spatial and temporal data distribution, and their different signal paths, a joint analysis of all observation types seems reasonable and promises the best results for ionosphere modeling. However, it has turned out that there exist offsets between ionospheric observations of the diverse techniques mainly caused by calibration uncertainties or model errors. Direct comparisons of the information from different data types are difficult because of the inhomogeneous measurement epochs and locations. In the approach presented here, all measurements are combined into one ionosphere model of vertical total electron content (VTEC). A variance component estimation is applied to take into account the different accuracy levels of the observations. In order to consider systematic offsets, a constant bias term is allowed for each observation group. The investigations have been performed for the time interval of the CONT08 campaign (2 weeks in August 2008) in a region around the Hawaiian Islands. Almost all analyzed observation techniques show good data sensitivity and are suitable for VTEC modeling in case the systematic offsets which can reach up to 5 TECU are taken into account. Only the Envisat DORIS data cannot provide reliable results.     

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.     

Earth orientation parameters estimated from VLBI during the CONT11 campaign

In this paper we investigate the accuracy of the earth orientation parameters (EOP) estimated from the continuous VLBI campaign CONT11. We first estimated EOP with daily resolution and compared these to EOP estimated from GNSS data. We find that the WRMS differences are about 31  $\upmu $ as for polar motion and 7  $\upmu $ s for length of day. This is about the precision we could expect, based on Monte Carlo simulations and the results of the previous CONT campaigns. We also estimated EOP with hourly resolution to study the sub-diurnal variations. The results confirm the results of previous studies, showing that the current IERS model for high-frequency EOP variations does not explain all the sub-diurnal variations seen in the estimated time series. We then compared our results to various empirical high-frequency EOP models. However, we did not find that any of these gave any unambiguous improvement. Several simulations testing the impact of various aspects of, e.g. the observing network were also made. For example, we made simulations assuming that all CONT11 stations were equipped with fast VLBI2010 antennas. We found that the WRMS error decreased by about a factor five compared to the current VLBI system. Furthermore, the simulations showed that it is very important to have a homogenous global distribution of the stations for achieving the highest precision for the EOP.     

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.     

Use of atmospheric angular momentum forecasts for UT1 predictions: analyses over CONT08

Real-time orbit determination and interplanetary navigation require accurate predictions of the orientation of the Earth in the celestial reference frame and in particular that for Universal Time UT1. Much of the UT1 variations over periods ranging from hours to a couple of years are due to the global atmospheric circulation. Therefore, the axial atmospheric angular momentum (AAM) forecast series may be used as a proxy index to predict UT1. Our approach taking advantage of this fact is based on an adaptive procedure. It involves incorporating integrations of AAM estimates into UT1 series. The procedure runs on a routine basis using AAM forecasts that are based on the two meteorological series, from the US National Centers for Environmental Prediction and the Japan Meteorological Agency. It is pertinent to test the prediction method for the period that includes the special CONT08 campaign over which we expect a significant improvement in UT1 accuracy. The studies we carried out were aimed both to compare atmospheric forecasts and analyses, as well as to compare the skills of the UT1 forecasts based on the method with atmospheric forecasts and that using current statistical processes, as applied to the C04 Earth orientation parameters series derived by the International Earth rotation and Reference Systems service (IERS). Here we neglect the oceanic sub-diurnal and diurnal variations, as these signals are expected to be smaller than the UT1-equivalent of 100 μs, when averaged over a few days. The prediction performances for a 2-day forecast are similar, but at a forecast horizon of a week, the AAM-based forecast is roughly twice as skillful as the statistically based one.     

精密单点定位中对流层延迟参数的相关性研究

为了确定对流层延迟参数的自相关性及其与坐标参数的互相关性,本文研究采用随机卡尔曼滤波进行精密单点定位解算。根据自相关原理计算出对流层天顶延迟误差的自相关函数,采用4种经验函数模型分别对自相关函数进行拟合,结果表明exponential-cos为最佳拟合模型;对对流层天顶延迟误差与坐标垂直分量误差的互相关性进行了分析,结果表明二者显著负线性相关;坐标垂直分量误差波动幅度是对流层天顶延迟误差波动幅度的4倍左右;卫星截止高度角越低,参数相关性越强。     

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.     

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.     

GPS定位中的对流层模型分析

系统地分析对流层延迟特性在GPS导航中造成的定位误差,并主要介绍目前卫星定位领域主要应用的一些对流层折射修正模型。基于霍普尔德模型和萨斯塔莫宁模型,提出一种在缺少实测气象参数条件下,使用的简单对流层延迟修正模型。利用Matlab仿真软件对静态和动态接收机实测数据进行分析。结果表明,无气象参数的简单修正模型可以消除70％左右的对流层影响,有效地提高GPS的定位精度。     

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.     

Assessment of troposphere mapping functions using three-dimensional ray-tracing

The troposphere delay is an important source of error for precise GNSS positioning due to its high correlation with the station height parameter. It has been demonstrated that errors in mapping functions can cause sub-annual biases as well as affect the repeatability of GNSS solutions, which is a particular concern for geophysical studies. Three-dimensional ray-tracing through numerical weather models (NWM) is an excellent approach for capturing the directional and daily variation of the tropospheric delay. Due to computational complexity, its use for positioning purposes is limited, but it is an excellent tool for evaluating current state-of-the-art mapping functions used for geodetic positioning. Many mapping functions have been recommended in the past such as the Niell Mapping Function (NMF), Vienna Mapping Function 1 (VMF1), and the Global Mapping Function (GMF), which have been adopted by most IGS analysis centers. A new Global Pressure Temperature model (GPT2) has also been developed, which has been shown to improve upon the original atmospheric model used for the GMF. Although the mapping functions mentioned above use the same functional formulation, they vary in terms of their atmospheric source and calibration approach. A homogeneous data set of three-dimensional ray-traced delays is used to evaluate all components of the mapping functions, including their underlying functional formulation, calibration, and compression method. Additionally, an alternative representation of the VMF1 is generated using the same atmospheric source as the truth data set to evaluate the differences in ray-tracing methods and their effect on the end mapping function. The results of this investigation continue to support the use of the VMF1 as the mapping function of choice when geodetic parameters are of interest. Further support for the GPT2 and GMF as reliable back-ups when the VMF1 is not available was found due to their high consistency with the NWM-derived mapping function. Additionally, a small latitude-dependent bias in station height was found in the current mapping functions. This bias was identified to be due to the assumption of a constant radius of the earth and was largest at the poles and at the equator. Finally, an alternative version of the VMF1 is introduced, namely the UNB-VMF1 which provides users with an independent NWM-derived mapping function to support geodetic positioning.     

高精度GNSS服务中对流层映射函数的影响性分析

针对GNSS服务中如何获取高精度的大地高以及GNSS气象中对流层湿延迟项,文中采用3种试验方案,利用对流层变化复杂的香港区域CORS,分析不同映射函数存不同高度角时对精密服务的影响。结果表明：存高度角为15°时VMFl、GMF、NMF映射函数获取基线重复性相当,天顶延迟变化规律一致;在低高度角为10°时,基于VMFl映射函数的基线重复率更好,对大气变化的敏感性更强,GMF映射函数获取的天顶延迟精度较好,NMF映射函数获取的精度较弱。     

不同对流层改正方法对 PPP 定位效果影响的对比分析

对流层延迟是影响精密单点定位效果的一项重要误差源,不同的对流层改正方法直接影响PPP的定位结果。对比分析采用UNB3模型、Saastamoinen模型、ZTD参数估计3种方法对PPP定位精度和收敛时间的影响。实验结果表明:3种模型平面改正精度和收敛时间基本一致。天顶方向改正精度UNB3模型与ZTD参数估计法基本相当,但两者优于Saastamoinen模型;收敛速度UNB3模型与Saastamoinen模型基本一致,ZTD参数估计法收敛速度较慢。     

长距离网络实时动态对流层延迟误差改正

针对长距离网络RTK的范围较大,造成区域观测误差的相关性降低,影响对流层延迟误差的内插计算和改正这一情况,该文提出了一种改进的对流层延迟误差计算和改正方法。首先利用确定的参考站网整周模糊度和载波相位观测值计算各参考站的天顶对流层延迟,然后将各参考站天顶对流层延迟误差播发给流动站用户,用户根据内插模型内插计算出流动站处的天顶对流层延迟误差,并进行流动站各卫星的对流层延迟误差计算和改正。通过长距离CORS网实测数据的实验证明,该文方法可以取得理想的长距离网络RTK误差改正效果和流动站定位结果。     

高精度对流层天顶湿延迟模型研究

对流层湿延迟是GPS误差源中最难确定的量,鉴于目前的对流层湿延迟模型较少考虑相对湿度随高度变化对湿延迟估计的影响,文章根据对流层湿延迟折射率的变化特征,提出新的分段湿延迟模型TTZWD.通过实验证明TTZWD湿延迟精度较Saastamoinen模型有不同程度的提高,与IGS后处理结果吻合精度好,基本可以达到半波长以内.实验还证明在相对湿度未知的情况下,将相对湿度设置为1,TTZWD模型依然可以使用,与相对湿度已知时的精度相当.     

Combination of long time-series of troposphere zenith delays observed by VLBI

Within the International Very Long Baseline Interferometry (VLBI) Service for Geodesy and Astrometry (IVS), long time-series of zenith wet and total troposphere delays have been combined at the level of parameter estimates. The data sets were submitted by eight IVS Analysis Centers (ACs) and cover January 1984 to December 2004. In this paper, the combination method is presented and the time-series submitted by the eight IVS ACs are compared with each other. The combined zenith delays are compared with time-series provided by the International Global Navigation Satellite System (GNSS) Service (IGS), and with zenith delays derived from the European Centre for Medium-Range Weather Forecasts (ECMWF). Before the combination, outliers are eliminated from the individual time-series using the robust BIBER (bounded influence by standardized residuals) estimator. For each station and AC, relative weight factors are obtained by variance component estimation. The mean bias of the IVS ACs’ time-series with respect to the IVS combined time-series is 0.89 mm and the mean root mean square is 7.67 mm. Small differences between stations and ACs can be found, which are due to the inhomogeneous analysis options, different parameterizations, and different treatment of missing in-situ pressure records. Compared to the IGS zenith total delays, the combined IVS series show small positive mean biases and different long-term trends. Zenith wet delays from the ECMWF are used to validate the IVS combined series. Inconsistencies, e.g., long-term inhomogeneity of the in-situ pressure data used for the determination of VLBI zenith delays, are identified.