VLBI terrestrial reference frame contributions to ITRF2008

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.     

地球参考标架和动态地球

本文首先对天球参考标架和地球参考标架作了一般叙述。其次较详细地说明地球参考标架究竟是什么,它是如何形成的,直到现在它的发展情况。最后说明了地球参考标架在有关学科中的应用。     

Future global SLR network evolution and its impact on the terrestrial reference frame

Satellite laser ranging (SLR) is an important technique that contributes to the determination of terrestrial geodetic reference frames, especially to the realization of the origin and the scale of global networks. One of the major limiting factors of SLR-derived reference frame realizations is the datum accuracy which significantly suffers from the current global SLR station distribution. In this paper, the impact of a potential future development of the SLR network on the estimated datum parameters is investigated. The current status of the SLR network is compared to a simulated potential future network featuring additional stations improving the global network geometry. In addition, possible technical advancements resulting in a higher amount of observations are taken into account as well. As a result, we find that the network improvement causes a decrease in the scatter of the network translation parameters of up to 24%, and up to 20% for the scale, whereas the technological improvement causes a reduction in the scatter of up to 27% for the translations and up to 49% for the scale. The Earth orientation parameters benefit by up to 15% from both effects.     

多普勒系统对历元地球参考框架的影响研究

针对历元地球参考框架在确定站点高频非线性运动和季节性变化方面具有国际地球参考框架不具备的优势问题,该文通过比较两种技术间组合策略建立的多源融合历元地球参考框架的精度,研究DORIS对于多源融合历元地球参考框架的影响。通过基于坐标的法方程叠加方法进行技术内法方程叠加和技术间组合,并利用并置站条件联系不同技术的法方程,从而建立多源融合历元地球参考框架。结果表明,DORIS的引入并不会对多源融合历元地球参考框架的基准定义或其他3种技术站点的点位精度产生较大的影响,同时能够体现4种技术中精度较差的DORIS对于ETRF的精度及稳定性的影响。     

地球参考框架联合解算方法

地球参考框架是地球坐标系统的实现,本文系统介绍了地球参考框架的确定方法,结合ITRF2005参考框架,详细介绍了地球参考框架联合解算的方法,并对地球参考框架的质量分析方法进行了探讨。     

顾及时变的参考框架转换研究

在传统的大地坐标参考框架转换中,参考点都被固定在同一个历元。由于各种地球动力学现象的存在,以大地测量为目的的静态参考系统已不存在,同时随着高精度参考框架的连续观测和测定,参考框架的转化必须顾及时变性。本文讨论了时变参考框架转换中2个互逆的过程,采纳了相似转换中参考点之间的内在约束来克服转换中人为的公式简化和秩亏问题。通过数值计算分析,该方法成功实现了坐标框架之间的转换,并保持了尺度、旋转和平移参数及其变化率精度的独立性。     

Quality assessment of GPS reprocessed terrestrial reference frame

The International GNSS Service (IGS) contributes to the construction of the International Terrestrial Reference Frame (ITRF) by submitting time series of station positions and Earth Rotation Parameters (ERP). For the first time, its submission to the ITRF2008 construction is based on a combination of entirely reprocessed GPS solutions delivered by 11 Analysis Centers (ACs). We analyze the IGS submission and four of the individual AC contributions in terms of the GNSS frame origin and scale, station position repeatability and time series seasonal variations. We show here that the GPS Terrestrial Reference Frame (TRF) origin is consistent with Satellite laser Ranging (SLR) at the centimeter level with a drift lower than 1 mm/year. Although the scale drift compared to Very Long baseline Interferometry (VLBI) and SLR mean scale is smaller than 0.4 mm/year, we think that it would be premature to use that information in the ITRF scale definition due to its strong dependence on the GPS satellite and ground antenna phase center variations. The new position time series also show a better repeatability compared to past IGS combined products and their annual variations are shown to be more consistent with loading models. The comparison of GPS station positions and velocities to those of VLBI via local ties in co-located sites demonstrates that the IGS reprocessed solution submitted to the ITRF2008 is more reliable and precise than any of the past submissions. However, we show that some of the remaining inconsistencies between GPS and VLBI positioning may be caused by uncalibrated GNSS radomes.     

The terrestrial and lunar reference frame in lunar laser ranging

The initial value problem and the stability of solution in the determination of the coordinates of three observing stations and four retro-reflectors by lunar laser ranging are discussed. Practical iterative computations show that the station coordinates can be converged to about 1 cm, but there will be a slight discrepancy of the longitudinal components computed by various analysis centers or in different years. There are several factors, one of which is the shift of the right ascension of the Moon, caused by the orientation deviation of the adopted lunar ephemeris, which can make the longitudinal components of all observing stations rotate together along the longitudinal direction with same angle. Additionally, the frame of selenocentric coordinates is stable, but a variation or adjustment of lunar third-degree gravitational coefficients will cause a simultaneous shift along the reflectors' longitudes or rotation around the Y axis. Received: 21 August 1996 / Accepted: 17 November 1998     

测站坐标时间序列跳变探测研究及对TRF的影响

针对地球参考架测站坐标残差数据中仍存在一些较大的未被标注的跳变,这会引起该测站坐标和速度因未标注的跳变而估计有误的问题,该文利用广义离群检测(GESD)算法的粗差和野值探测及基于t-检验序贯格局转换分析(STARS)法的跳变探测,更好地剔除了野值、标志出了未被标注的跳变.由于测站坐标时间序列的复杂性,跳变检测的误报率和漏检时有发生,故该文采用了与STARS方法相结合的差值法和人眼观察法综合检测跳变;然后基于上海天文台建立的中国地球自转与地球参考系服务地球参考架和地球定向参数确定软件包,重新进行地球参考框架建立和维持,消除未标注跳变对地球参考框架的不利影响.结果 表明,重新解算的测站坐标残差明显减小,对测站非连续性也有了很好修复,不仅提高了地球参考架精度和稳定性,而且有助于后续周期性信号的拟合和提取.     

ITRF2008: an improved solution of the international terrestrial reference frame

ITRF2008 is a refined version of the International Terrestrial Reference Frame based on reprocessed solutions of the four space geodetic techniques: VLBI, SLR, GPS and DORIS, spanning 29, 26, 12.5 and 16?years of observations, respectively. The input data used in its elaboration are time series (weekly from satellite techniques and 24-h session-wise from VLBI) of station positions and daily Earth Orientation Parameters (EOPs). The ITRF2008 origin is defined in such a way that it has zero translations and translation rates with respect to the mean Earth center of mass, averaged by the SLR time series. Its scale is defined by nullifying the scale factor and its rate with respect to the mean of VLBI and SLR long-term solutions as obtained by stacking their respective time series. The scale agreement between these two technique solutions is estimated to be 1.05 ± 0.13 ppb at epoch 2005.0 and 0.049 ± 0.010?ppb/yr. The ITRF2008 orientation (at epoch 2005.0) and its rate are aligned to the ITRF2005 using 179 stations of high geodetic quality. An estimate of the origin components from ITRF2008 to ITRF2005 (both origins are defined by SLR) indicates differences at epoch 2005.0, namely: ?0.5, ?0.9 and ?4.7?mm along X, Y and Z-axis, respectively. The translation rate differences between the two frames are zero for Y and Z, while we observe an X-translation rate of 0.3?mm/yr. The estimated formal errors of these parameters are 0.2?mm and 0.2?mm/yr, respectively. The high level of origin agreement between ITRF2008 and ITRF2005 is an indication of an imprecise ITRF2000 origin that exhibits a Z-translation drift of 1.8?mm/yr with respect to ITRF2005. An evaluation of the ITRF2008 origin accuracy based on the level of its agreement with ITRF2005 is believed to be at the level of 1?cm over the time-span of the SLR observations. Considering the level of scale consistency between VLBI and SLR, the ITRF2008 scale accuracy is evaluated to be at the level of 1.2?ppb (8?mm at the equator) over the common time-span of the observations of both techniques. Although the performance of the ITRF2008 is demonstrated to be higher than ITRF2005, future ITRF improvement resides in improving the consistency between local ties in co-location sites and space geodesy estimates.     

Assessment of the possible contribution of space ties on-board GNSS satellites to the terrestrial reference frame

The realization of the international terrestrial reference frame (ITRF) is currently based on the data provided by four space geodetic techniques. The accuracy of the different technique-dependent materializations of the frame physical parameters (origin and scale) varies according to the nature of the relevant observables and to the impact of technique-specific errors. A reliable computation of the ITRF requires combining the different inputs, so that the strengths of each technique can compensate for the weaknesses of the others. This combination, however, can only be performed providing some additional information which allows tying together the independent technique networks. At present, the links used for that purpose are topometric surveys (local/terrestrial ties) available at ITRF sites hosting instruments of different techniques. In principle, a possible alternative could be offered by spacecrafts accommodating the positioning payloads of multiple geodetic techniques realizing their co-location in orbit (space ties). In this paper, the GNSS–SLR space ties on-board GPS and GLONASS satellites are thoroughly examined in the framework of global reference frame computations. The investigation focuses on the quality of the realized physical frame parameters. According to the achieved results, the space ties on-board GNSS satellites cannot, at present, substitute terrestrial ties in the computation of the ITRF. The study is completed by a series of synthetic simulations investigating the impact that substantial improvements in the volume and quality of SLR observations to GNSS satellites would have on the precision of the GNSS frame parameters.     

A review of algebraic constraints in terrestrial reference frame datum definition

 Station coordinates are combined with velocities estimated by space geodesy techniques to produce the International Terrestrial Reference System. The input is sets of coordinates and velocities calculated by International Earth Rotation Service analysis centers using space geodesy techniques. The working reference system of individual analysis centers is generally conventionally defined. However, the implications of such processing can have an effect on the resulting combined set. The problem of datum definition as a function of coordinate combinations is reviewed. In particular, the problem of minimum constraints is clearly emphasized and the reference system effect is defined. The goal is to build a process that could be used generally to remove uncertainties in the underlying coordinate system without disturbing the underlying information with additional unnecessary information. Received: 25 January 1999 / Accepted: 20 September 2000     

On the long-term stability of terrestrial reference frame solutions based on Kalman filtering

The Global Geodetic Observing System requirement for the long-term stability of the International Terrestrial Reference Frame is 0.1 mm/year, motivated by rigorous sea level studies. Furthermore, high-quality station velocities are of great importance for the prediction of future station coordinates, which are fundamental for several geodetic applications. In this study, we investigate the performance of predictions from very long baseline interferometry (VLBI) terrestrial reference frames (TRFs) based on Kalman filtering. The predictions are computed by extrapolating the deterministic part of the coordinate model. As observational data, we used over 4000 VLBI sessions between 1980 and the middle of 2016. In order to study the predictions, we computed VLBI TRF solutions only from the data until the end of 2013. The period of 2014 until 2016.5 was used to validate the predictions of the TRF solutions against the measured VLBI station coordinates. To assess the quality, we computed average WRMS values from the coordinate differences as well as from estimated Helmert transformation parameters, in particular, the scale. We found that the results significantly depend on the level of process noise used in the filter. While larger values of process noise allow the TRF station coordinates to more closely follow the input data (decrease in WRMS of about 45%), the TRF predictions exhibit larger deviations from the VLBI station coordinates after 2014 (WRMS increase of about 15%). On the other hand, lower levels of process noise improve the predictions, making them more similar to those of solutions without process noise. Furthermore, our investigations show that additionally estimating annual signals in the coordinates does not significantly impact the results. Finally, we computed TRF solutions mimicking a potential real-time TRF and found significant improvements over the other investigated solutions, all of which rely on extrapolating the coordinate model for their predictions, with WRMS reductions of almost 50%.     

Effects of adopting new precession,nutation and equinox corrections on the terrestrial reference frame

First, the paper is devoted to the effects of adopting new definitive precession and equinox corrections on the terrestrial reference frame: The effect on polar motion is a diurnal periodic term with an amplitude increasing linearly in time; on UT1 it is a linear term. Second, general principles are given the use of which can determine the effects of small rotations (such as precession, nutation or equinox corrections) of the frame of a Conventional Inertial Reference System (CIS) on the frame of the Conventional Terrestrial Reference System (CTS). Next, seven CTS options are presented, one of which is necessary to accommodate such rotations (corrections). The last of these options requiring no changes in the origin of terrestrial longitudes and in UT1 is advocated; this option would be maintained by eventually referencing the Greenwich Mean Sidereal Time to a fixed point on the equator, instead of to the mean equinox of date, the current practice. Accommodating possible future changes in the astronomical nutation is discussed in the last section. The Appendix deals with the effects of differences which may exist between the various CTS's and CIS's (inherent in the various observational techniques) on earth rotation parameters (ERP) and how these differences can be determined. It is shown that the CTS differences can be determined from observations made at the same site, while the CIS differences by comparing the ERP's determined by the different techniques during the same time period. Presented at XVIII General Assembly of the International Astronomical Union Patras, Greece, August 17–26, 1982.     

On calculating the Earth's C21 and S21 gravity coefficients in the IERS terrestrial reference frame

Modern models of the Earth's gravity field are developed in the IERS (International Earth Rotation Service) terrestrial reference frame. In this frame the mean values for gravity coefficients of the second degree and first order, C ₂₁(IERS) and S ₂₁(IERS), by the current IERS Conventions are recommended to be calculated by using the observed polar motion parameters. Here, it is proved that the formulae presently employed by the IERS Conventions to obtain these coefficients are insufficient to ensure their values as given by the same source. The relevant error of the normalized mean values for C ₂₁(IERS) and S ₂₁(IERS) is 3×10⁻¹², far above the adopted cutoff (10⁻¹³) for variations of these coefficients. Such an error in C ₂₁ and S ₂₁ can produce non-modeled perturbations in motion prediction of certain artificial Earth satellites of a magnitude comparable to the accuracy of current tracking measurements. Received: 14 September 1998 / Accepted: 20 May 1999     

Spatiotemporal variation in the terrestrial vegetation phenology of Iraq and its relation with elevation

Iraq contains the Great Mesopotamian alluvial plain of the Euphrates and Tigris rivers. Its regional vegetation phenological patterns are worthy of investigation because relatively little is known about the phenology of semi-arid environments, and because their inter-annual variation is expected to be driven by uncertain rainfall and varied topography. The aim of this research was to assess and map the spatial variation in key land surface phenology (LSP) parameters over the last decade and their relation with elevation. It is the first study mapping land surface phenology during last decade over the whole of Iraq, and one of only a few studies on vegetation phenology in a semi-arid environment. Time-series of Moderate Resolution Imaging Spectroradiometer (MODIS) normalised difference vegetation index (NDVI) data at 250 m spatial resolution and 8 day temporal resolution, were employed to map the spatial variation in three LSP parameters for the major vegetation types in Iraq during 2001–2012. LSP parameters were defined by inflection points after smoothing the vegetation phenological signals using the Fourier technique. The estimated key LSP parameters indicated that the relatively shorter length of season (LOS) in the north of Iraq resulted from a delayed start of season (SOS). Greater spatial variation occurred in the SOS than end of season (EOS), which may be due to the spatial distribution of rainfall and temperature as a function of elevation. A positive correlation was observed for SOS and EOS with elevation for all major land cover types with EOS producing the largest positive correlation (R² = 0.685, R² = 0.638 and R² = 0.588, p < 0.05 in shrubland, cropland and grassland, respectively). The magnitude of delay in SOS and EOS increased in all land cover types along a rising elevation gradient where for each 500 m increase, SOS was delayed by around 25 or more days and EOS delayed by around 22 or more days, except for grassland. The SOS and EOS also varied temporally during the last decade, particularly the SOS in the lowland, north of the country where the standard deviation was around 80 to 120 days, due mainly to the practice of crop rotation and the traditional biennial cropping system. Thus, the results of this research emphasize the effect of elevation on key LSP parameters over Iraq, for all major vegetation types.     

Basic equations for constructing geopotential models from the gravitational potential derivatives of the first and second orders in the terrestrial reference frame

This research represents a continuation of the investigation carried out in the paper of Petrovskaya and Vershkov (J Geod 84(3):165–178, 2010) where conventional spherical harmonic series are constructed for arbitrary order derivatives of the Earth gravitational potential in the terrestrial reference frame. The problem of converting the potential derivatives of the first and second orders into geopotential models is studied. Two kinds of basic equations for solving this problem are derived. The equations of the first kind represent new non-singular non-orthogonal series for the geopotential derivatives, which are constructed by means of transforming the intermediate expressions for these derivatives from the above-mentioned paper. In contrast to the spherical harmonic expansions, these alternative series directly depend on the geopotential coefficients ${\bar{{C}}_{n,m}}$ and ${\bar{{S}}_{n,m}}$ . Each term of the series for the first-order derivatives is represented by a sum of these coefficients, which are multiplied by linear combinations of at most two spherical harmonics. For the second-order derivatives, the geopotential coefficients are multiplied by linear combinations of at most three spherical harmonics. As compared to existing non-singular expressions for the geopotential derivatives, the new expressions have a more simple structure. They depend only on the conventional spherical harmonics and do not depend on the first- and second-order derivatives of the associated Legendre functions. The basic equations of the second kind are inferred from the linear equations, constructed in the cited paper, which express the coefficients of the spherical harmonic series for the first- and second-order derivatives in terms of the geopotential coefficients. These equations are converted into recurrent relations from which the coefficients ${\bar{{C}}_{n,m}}$ and ${\bar{{S}}_{n,m}}$ are determined on the basis of the spherical harmonic coefficients of each derivative. The latter coefficients can be estimated from the values of the geopotential derivatives by the quadrature formulas or the least-squares approach. The new expressions of two kinds can be applied for spherical harmonic synthesis and analysis. In particular, they might be incorporated in geopotential modeling on the basis of the orbit data from the CHAMP, GRACE and GOCE missions, and the gradiometry data from the GOCE mission.