Impact of loading displacements on SLR-derived parameters and on the consistency between GNSS and SLR results

Displacements of the Earth’s surface caused by tidal and non-tidal loading forces are relevant in high-precision space geodesy. Some of the corrections are recommended by the international scientific community to be applied at the observation level, e.g., ocean tidal loading (OTL) and atmospheric tidal loading (ATL). Non-tidal displacement corrections are in general recommended not to be applied in the products of the International Earth Rotation and Reference Systems Service, in particular atmospheric non-tidal loading (ANTL), oceanic and hydrological non-tidal corrections. We assess and compare the impact of OTL, ATL and ANTL on SLR-derived parameters by reprocessing 12 years of SLR data considering and ignoring individual corrections. We show that loading displacements have an influence not only on station long-term stability, but also on geocenter coordinates, Earth Rotation Parameters, and satellite orbits. Applying the loading corrections reduces the amplitudes of annual signals in the time series of geocenter and station coordinates. The general improvement of the SLR station 3D coordinate repeatability when applying OTL, ATL and ANTL corrections are 19.5 %, 0.2 % and 3.3 % respectively, w.r.t. the solutions without loading corrections. ANTL corrections play a crucial role in the combination of optical (SLR) and microwave (GNSS, VLBI, DORIS) space geodetic observation techniques, because of the so-called Blue-Sky effect: SLR measurements can be carried out only under cloudless sky conditions—typically during high air pressure conditions, when the Earth’s crust is deformed, whereas microwave observations are weather-independent. Thus, applying the loading corrections at the observation level improves SLR-derived products as well as the consistency with microwave-based results. We assess the Blue-Sky effect on SLR stations and the consistency improvement between GNSS and SLR solutions when ANTL corrections are included. The omission of ANTL corrections may lead to inconsistencies between SLR and GNSS solutions of up to 2.5 mm for inland stations. As a result, the estimated GNSS–SLR coordinate differences correspond better to the local ties at the co-located stations when applying ANTL corrections.     

Seasonal and secular positional variations at eight co-located GPS and VLBI stations

Time series of daily position solutions at eight co-located GPS and VLBI stations are used to assess the frequency features in the solutions over various time-scales. This study shows that there are seasonal and inter-annual signals in all three coordinate components of the GPS and VLBI solutions. The power and frequency of the signals vary with time, the station considered and the coordinate components, and between the GPS and VLBI solutions. In general, the magnitudes of the signals in the horizontal coordinate components (latitude and longitude) are weaker than those in the height component. The weighted means of the estimated annual amplitudes from the eight GPS stations are, respectively, 1.0, 0.8 and 3.6 mm for the latitude, longitude and height components, and are, respectively, 1.5, 0.7 and 2.2 mm for the VLBI solutions. The phases of the annual signals estimated from the GPS and VLBI solutions are consistent for most of the co-located stations. The seasonal signals estimated from the VLBI solutions are, in general, more stable than those estimated from the GPS solutions. Fluctuations at inter-annual time-scales are also found in the series. The inter-annual fluctuations are up to ∼5 mm for the latitude and longitude components, and up to ∼10 mm for the height component. The effects of the seasonal and inter-annual variations on the estimated linear rates of movement of the stations are also evaluated.     

Evaluation of the impact of atmospheric pressure loading modeling on GNSS data analysis

In recent years, several studies have demonstrated the sensitivity of Global Navigation Satellite System (GNSS) station time series to displacements caused by atmospheric pressure loading (APL). Different methods to take the APL effect into account are used in these studies: applying the corrections from a geophysical model on weekly mean estimates of station coordinates, using observation-level corrections during data analysis, or solving for regression factors between the station displacement and the local pressure. The Center for Orbit Determination in Europe (CODE) is one of the global analysis centers of the International GNSS Service (IGS). The current quality of the IGS products urgently asks to consider this effect in the regular processing scheme. However, the resulting requirements for an APL model are demanding with respect to quality, latency, and—regarding the reprocessing activities—availability over a long time interval (at least from 1994 onward). The APL model of Petrov and Boy (J Geophys Res 109:B03405, 2004) is widely used within the VLBI community and is evaluated in this study with respect to these criteria. The reprocessing effort of CODE provides the basis for validating the APL model. The data set is used to solve for scaling factors for each station to evaluate the geophysical atmospheric non-tidal loading model. A consistent long-term validation of the model over 15 years, from 1994 to 2008, is thus possible. The time series of 15 years allows to study seasonal variations of the scaling factors using the dense GNSS tracking network of the IGS. By interpreting the scaling factors for the stations of the IGS network, the model by (2004) is shown to meet the expectations concerning the order of magnitude of the effect at individual stations within the uncertainty given by the GNSS data processing and within the limitations due to the model itself. The repeatability of station coordinates improves by 20% when applying the effect directly on the data analysis and by 10% when applying a post-processing correction to the resulting weekly coordinates compared with a solution without taking APL into account.     

Effect of the selection of reference radio sources on geodetic estimates from VLBI observations

This paper evaluates the effect of the accuracy of reference radio sources on the daily estimates of station positions, nutation angle offsets, and the estimated site coordinates determined by very long baseline interferometry (VLBI), which are used for the realization of the international terrestrial reference frame (ITRF). Five global VLBI solutions, based on VLBI data collected between 1979 and 2006, are compared. The reference solution comprises all observed radio sources, which are treated as global parameters. Four other solutions, comprising different sub-sets of radio sources, were computed. The daily station positions for all VLBI sites and the corrections to the nutation offset angles were estimated for these five solutions. The solution statistics are mainly affected by the positional instabilities of reference radio sources, whereas the instabilities of geodetic and astrometric time-series are caused by an insufficient number of observed reference radio sources. A mean offset of the three positional components (Up, North, East) between any two solutions was calculated for each VLBI site. From a comparison of the geodetic results, no significant discrepancies between the respective geodetic solutions for all VLBI sites in the Northern Hemisphere were found. In contrast, the Southern Hemisphere sites were more sensitive to the selected set of reference radio sources. The largest estimated mean offset of the vertical component between two solutions for the Australian VLBI site at Hobart was 4 mm. In the worst case (if a weak VLBI network observed a limited number of reference radio sources) the daily offsets of the estimated height component at Hobart exceeded 100 mm. The exclusion of the extended radio sources from the list of reference sources improved the solution statistics and made the geodetic and astrometric time-series more consistent. The problem with the large Hobart height component offset is magnified by a comparatively small number of observations due to the low slewing rate of the VLBI dish (1°/ s). Unless a minimum of 200 scans are performed per 24-h VLBI experiment, the daily vertical positions at Hobart do not achieve 10 mm accuracy. Improving the slew rate at Hobart and/or having an increased number of new sites in the Southern Hemisphere is essential for further improvement of geodetic VLBI results for Southern Hemisphere sites.     

Comparison of GMF/GPT with VMF1/ECMWF and implications for atmospheric loading

This paper compares estimates of station coordinates from global GPS solutions obtained by applying different troposphere models: the Global Mapping Function (GMF) and the Vienna Mapping Function 1 (VMF1) as well as a priori hydrostatic zenith delays derived from the Global Pressure and Temperature (GPT) model and from the European Centre for Medium-Range Weather Forecasts (ECMWF) numerical weather model data. The station height differences between terrestrial reference frames computed with GMF/GPT and with VMF1/ECMWF are in general below 1 mm, and the horizontal differences are even smaller. The differences of annual amplitudes in the station height can also reach up to 1 mm. Modeling hydrostatic zenith delays with mean (or slowly varying empirical) pressure values instead of the true pressure values results in a partial compensation of atmospheric loading. Therefore, station height time series based on the simple GPT model have a better repeatability than those based on more realistic ECMWF troposphere a priori delays if atmospheric loading corrections are not included. On the other hand, a priori delays from numerical weather models are essential to reveal the full atmospheric loading signal.     

长距离GPS/BDS双系统网络RTK方法

基于区域参考站网的网络实时动态定位(real-time kinematic,RTK)方法是实现全球定位系统(global positioning system,GPS)、北斗卫星导航系统(BeiDou satellite navigation system,BDS)高精度定位的主要手段.研究了一种长距离GPS/BDS双...     

大气负荷对我国GNSS站地壳垂向形变影响分析

为了研究近年来我国GNSS基准站地壳大气负荷垂向形变细部特征,使用格林函数积分及简化方法对中国大陆构造环境监测网络中的6个基准站共计36个月的大气负荷效应进行了计算和分析,结果表明,大气负荷是造成地壳非构造垂向形变的重要因素,大气负荷效应引起的地壳垂向形变量的区域性差异及垂向形变量在我国东北部和西部新疆地区为最大,大气负荷效应改正可使GPS垂向精度进一步提高。      

Estimating atmospheric pressure loading regression coefficients from GPS observations

The loading exerted by atmospheric pressure on the surface of the Earth causes deformations, mainly in vertical direction. Consequently, these deformations are also subject to pressure variations. At present this effect is only modeled by a few research groups in the post-processing of very long baseline interferometry (VLBI) and global positioning system (GPS) observations. As the displacements may clearly exceed the accuracy goals, we implement vertical pressure loading regression coefficients as a new estimable parameter type in the Bernese GPS software. This development is applied to a network of 60 European permanent GPS stations extending from 35 to 79° northern latitude. The analysis comprises 1,055 days of observations between January 2001 and February 2004. During that period pressure variations as large as 80 hPa occurred at high latitude sites. A least squares solution including all observations and all relevant parameters yields significant regression coefficients for all stations but reveals also some critical issues with regard to the capability of this geodetic approach to verify results based on the geophysical convolution method.An erratum to this article can be found at     

Strategies to mitigate aliasing of loading signals while estimating GPS frame parameters

Although GNSS techniques are theoretically sensitive to the Earth center of mass, it is often preferable to remove intrinsic origin and scale information from the estimated station positions since they are known to be affected by systematic errors. This is usually done by estimating the parameters of a linearized similarity transformation which relates the quasi-instantaneous frames to a long-term frame such as the International Terrestrial Reference Frame (ITRF). It is well known that non-linear station motions can partially alias into these parameters. We discuss in this paper some procedures that may allow reducing these aliasing effects in the case of the GPS techniques. The options include the use of well-distributed sub-networks for the frame transformation estimation, the use of site loading corrections, a modification of the stochastic model by downweighting heights, or the joint estimation of the low degrees of the deformation field. We confirm that the standard approach consisting of estimating the transformation over the whole network is particularly harmful for the loading signals if the network is not well distributed. Downweighting the height component, using a uniform sub-network, or estimating the deformation field perform similarly in drastically reducing the amplitude of the aliasing effect. The application of these methods to reprocessed GPS terrestrial frames permits an assessment of the level of agreement between GPS and our loading model, which is found to be about 1.5 mm WRMS in height and 0.8 mm WRMS in the horizontal at the annual frequency. Aliased loading signals are not the main source of discrepancies between loading displacement models and GPS position time series.     

A first look at the effects of ionospheric signal bending on a globally processed GPS network

This study provides a first attempt at quantifying potential signal bending effects on the GPS reference frame, coordinates and zenith tropospheric delays (ZTDs). To do this, we homogeneously reanalysed data from a global network of GPS sites spanning 14 years (1995.0–2009.0). Satellite, Earth orientation, tropospheric and ground station coordinate parameters were all estimated. We tested the effect of geometric bending and dTEC bending corrections, which were modelled at the observation level based, in part, on parameters from the International Reference Ionosphere 2007 model. Combined, the two bending corrections appear to have a minimal effect on site coordinates and ZTDs except for low latitude sites. Considering five days (DOY 301–305, 28 October–1 November 2001) near ionospheric maximum in detail, they affect mean ZTDs by up to ~1.7 mm at low latitudes, reducing to negligible levels at high latitudes. Examining the effect on coordinates in terms of power-spectra revealed the difference to be almost entirely white noise, with noise amplitude ranging from 0.3 mm (high latitudes) to 2.4 mm (low latitudes). The limited effect on station coordinates is probably due to the similarity in the elevation dependence of the bending term with that of tropospheric mapping functions. The smoothed z-translation from the GPS reference frame to ITRF2005 changes by less than 2 mm, though the effect combines positively with that from the second order ionospheric refractive index term. We conclude that, at the present time, and for most practical purposes, the geometric and dTEC bending corrections are probably negligible at current GPS/reference frame precisions.     

大气压力变化对武汉台站重力场观测的影响

利用全球2°×2.5°、中国及邻区域30′×30′ 气压资料和Farrell弹性地球模型负荷理论,采用数值积分方法,计算了大气压力变化对武汉台站重力场观测的影响。对1990年1月1日至12月31日的数值结果分析表明,全球大气压力变化对武汉台站重力的影响峰对峰达12微伽,大气重力导纳的年平均值为-0.260 μGal/mba(1 mba=1 hPa),这一结果同潮汐分析中由回归分析方法获得的导纳值相近。说明在利用超导重力仪观测资料应用于地球动力学研究之前,有必要作精细的全球气压变化改正。     

The mobile VLBI campaigns in Norway (1989–1993)

Summary Since 1989 several mobile VLBI campaigns have been carried out in Europe with a total of 14 sites occupied. The Norwegian stations at Tromsø and Trysil are the only mobile VLBI stations in Europe observed in more than one epoch, so they have produced the most interesting data from these campaigns. Tromsø is the only station observed in the two summer campaigns (1989 and 1992), while Trysil has been the winter site for MV-2 since late 1991 until the spring of 1993. In this paper we describe the mobile VLBI campaigns in Norway including the observational work and the detailed geodetic analysis performed with OCCAM V3.3. We have also analyzed a series of GPS data sets from Tromsø in order to check the reliability of the VLBI results for that station. The results reveal the need for a very careful design of mobile VLBI experiments, in particular regarding the consistency of the network and of the observation schedules, and the special care that is required in the analysis of the mobile VLBI data in order to achieve significant conclusions.     

Short Note: A global model of pressure and temperature for geodetic applications

The empirical model GPT (Global Pressure and Temperature), which is based on spherical harmonics up to degree and order nine, provides pressure and temperature at any site in the vicinity of the Earth’s surface. It can be used for geodetic applications such as the determination of a priori hydrostatic zenith delays, reference pressure values for atmospheric loading, or thermal deformation of Very Long Baseline Interferometry (VLBI) radio telescopes. Input parameters of GPT are the station coordinates and the day of the year, thus also allowing one to model the annual variations of the parameters. As an improvement compared with previous models, it reproduces the large pressure anomaly over Antarctica, which can cause station height errors in the analysis of space-geodetic data of up to 1 cm if not considered properly in troposphere modelling. First tests at selected geodetic observing stations show that the pressure biases considerably decrease when using GPT instead of the very simple approaches applied to various Global Navigation Satellite Systems (GNSS) software packages so far. GPT also provides an appropriate model for the annual variability of global temperature. Electronic supplementary material The online version of this article (doi: contains supplementary material, which is available to authorized users.     

IGS contribution to the ITRF

We examine the contribution of the International GNSS Service (IGS) to the International Terrestrial Reference Frame (ITRF) by evaluating the quality of the incorporated solutions as well as their major role in the ITRF formation. Starting with the ITRF2005, the ITRF is constructed with input data in the form of time series of station positions (weekly for satellite techniques and daily for VLBI) and daily Earth Orientation Parameters. Analysis of time series of station positions is a fundamental first step in the ITRF elaboration, allowing to assess not only the stations behavior, but also the frame parameters and in particular the physical ones, namely the origin and the scale. As it will be seen, given the poor number and distribution of SLR and VLBI co-location sites, the IGS GPS network plays a major role by connecting these two techniques together, given their relevance for the definition of the origin and the scale of the ITRF. Time series analysis of the IGS weekly combined and other individual Analysis Center solutions indicates an internal precision (or repeatability) <2 mm in the horizontal component and <5 mm in the vertical component. Analysis of three AC weekly solutions shows generally poor agreement in origin and scale, with some indication of better agreement when the IGS started to use the absolute model of antenna phase center variations after the GPS week 1400 (November 2006).     

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.     

Continental hydrology loading observed by VLBI measurements

Variations in continental water storage lead to loading deformation of the crust with typical peak-to-peak variations at very long baseline interferometry (VLBI) sites of 3–15 mm in the vertical component and 1–2 mm in the horizontal component. The hydrology signal at VLBI sites has annual and semi-annual components and clear interannual variations. We have calculated the hydrology loading series using mass loading distributions derived from the global land data assimilation system (GLDAS) hydrology model and alternatively from a global grid of equal-area gravity recovery and climate experiment (GRACE) mascons. In the analysis of the two weekly VLBI 24-h R1 and R4 network sessions from 2003 to 2010 the baseline length repeatabilities are reduced in 79 % (80 %) of baselines when GLDAS (GRACE) loading corrections are applied. Site vertical coordinate repeatabilities are reduced in about 80 % of the sites when either GLDAS or GRACE loading is used. In the horizontal components, reduction occurs in 70–80 % of the sites. Estimates of the annual site vertical amplitudes were reduced for 16 out of 18 sites if either loading series was applied. We estimated loading admittance factors for each site and found that the average admittances were 1.01 \(\pm \) 0.05 for GRACE and 1.39 \(\pm \) 0.07 for GLDAS. The standard deviations of the GRACE admittances and GLDAS admittances were 0.31 and 0.68, respectively. For sites that have been observed in a set of sufficiently temporally dense daily sessions, the average correlation between VLBI vertical monthly averaged series and GLDAS or GRACE loading series was 0.47 and 0.43, respectively.     

Modeling thermal deformation of VLBI antennas with a new temperature model

Temperature variations at very long baseline interferometry (VLBI) sites cause thermal deformations of the VLBI antennas and corresponding displacements of the VLBI reference points. The thermal deformation effects typically contain seasonal and daily signatures. The amplitudes of the annual vertical motion of the antenna reference point can reach several millimeters, depending on the design of the antenna structure, on the material, and on the environmental effects such as global station position, station height and climatology effects. Simple methods to correct this effect use the difference of the environmental temperature with respect to a defined reference temperature, the antenna dimensions, the elevation of the antenna, the material of antenna structure. Applying these simple models for thermal deformation in the VLBI data analysis improves the baseline length repeatability by 3.5%. A comparison of these simple models with local thermal deformation measurements at the antennas in Onsala and Wettzell show that the local measurements and the modeled corrections agree well when the temperature of the antenna structure is used, but agree less good when the surrounding air temperatures are used. To overcome this problem we present a method to model temperature penetration into the antenna structures, that allows to model thermal deformation effects that agree with the observed vertical deformation of the Onsala and Wettzell radio telescopes with a root mean square deviation of 0.07 and 0.13 mm, respectively. Possible implementations in the VLBI analysis are presented, and the definition of an adequate reference temperature is discussed.     

GPS精密定位中的海潮位移改正

根据海洋负荷潮理论，利用NAO99b全球海潮模型，计算了中国部分IGS站的海潮位移改正，并将海潮位移改正应用到GPS数据处理当中。在GAMIT软件的解算过程中，分别按加入和不加入海潮位移改正，对GPS基线分量和测站坐标分别进行了计算和比较分析。结果表明，海潮位移改正无论是对GPS基线分量还是对测站坐标，都有一定的影响。     

Impact of seasonal station motions on VLBI UT1 intensives results

UT1 estimates obtained from the very long baseline interferometry (VLBI) Intensives data depend on the station displacement model used during processing. In particular, because of seasonal variations, the instantaneous station position during the specific intensive session differs from the position predicted by the linear model generally used. This can cause systematic errors in UT1 Intensives results. In this paper, we first investigated the seasonal signal in the station displacements for the 5 VLBI antennas participating in UT1 Intensives observing programs, along with the 8 collocated GPS stations. It was found that a significant annual term is present in the time series for most stations, and its amplitude can reach 8 mm in the height component, and 2 mm in horizontal components. However, the annual signals found in the displacements of the collocated VLBI and GPS stations at some sites differ substantially in amplitude and phase. The semiannual harmonics are relatively small and unstable, and for most stations no prevailing signal was found in the corresponding frequency band. Then two UT1 Intensives series were computed with and without including the seasonal term found in the previous step in the station movement model. Comparison of these series has shown that neglecting the seasonal station position variations can cause a systematic error in UT1 estimates, which can exceed 1  $\upmu $ s, depending on the observing program.     

华北区域GNSS基准站高程时间序列的非线性变化分析

基于陆态网络全球卫星导航系统（GNSS）观测成果,采用功率谱分析法和最小二乘方法,以华北地区为例,研究了区域基准站高程时间序列的非线性变化特征,并分析了不同环境负载的影响.结果表明,GNSS基准站高程方向存在显著的周年和半年周期特征,且周年特征要显著于半周年特征.位于不同地区的基准站的振幅和相位存在差异,华北平原南部地区的周年振幅要大于北部地区,整体上华北地区周年变化在秋季时节振幅达到最大.不同环境负载效应对华北GNSS高程位移的影响不一致,利用三种环境负载修正GNSS序列后,水文负载的修正效果最好,非潮汐大气负载次之,非潮汐海洋负载修正结果不理想.