利用GRACE、GPS和绝对重力数据监测斯堪的纳维亚陆地水储量变化

重力卫星GRACE(gravity recovery and climate experiment)监测斯堪的纳维亚半岛陆地水储量变化会受到冰川均衡调整(GIA)信号的严重影响。首先根据该地区绝对重力和GPS并址观测数据计算了GIA重力和垂直位移的实测线性比值,利用该比值和GPS网观测的垂直位移速度场得到了GIA重力。然后,对GRACE观测的重力变化速率进行GIA重力改正,进而可分离陆地水储量变化趋势,避免了使用GIA模型所带来的巨大不确定性,并根据观测数据完整估计了所得结果的不确定性。最后与水文模型作对比分析。结果表明,实测的GIA重力-垂直位移线性比值为0.148±0.020μGal/mm(1Gal=10-2 m/s2),该结果检验了Wahr的理论近似值且与北美实测的结果非常接近。2003年1月至2011年3月期间,斯堪的纳维亚半岛陆地水储量存在明显的增加趋势,信号的主体位于半岛南端的维纳恩湖附近,总的水量增加速率为4.6±2.1km3/a,数据观测期间的累积增加水量为38±17km3。研究结果与WGHM水文模型的结果有较好的一致性,相关系数达到0.69,而与GLDAS水文模型的相关性略小。     

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.     

Pseudo-Stochastic Orbit Modeling Techniques for Low-Earth Orbiters

The Earth’s non-spherical mass distribution and atmospheric drag cause the strongest perturbations on very low-Earth orbiting satellites (LEOs). Models of gravitational and non-gravitational accelerations are utilized in dynamic precise orbit determination (POD) with GPS data, but it is also possible to derive LEO positions based on GPS precise point positioning without dynamical information. We use the reduced-dynamic technique for LEO POD, which combines the geometric strength of the GPS observations with the force models, and investigate the performance of different pseudo-stochastic orbit parametrizations, such as instantaneous velocity changes (pulses), piecewise constant accelerations, and continuous piecewise linear accelerations. The estimation of such empirical orbit parameters in a standard least-squares adjustment process of GPS observations, together with other relevant parameters, strives for the highest precision in the computation of LEO trajectories. We used the procedures for the CHAMP satellite and found that the orbits may be validated by means of independent SLR measurements at the level of 3.2 cm RMS. Validations with independent accelerometer data revealed correlations at the level of 95% in the along-track direction. As expected, the empirical parameters compensate to a certain extent for deficiencies in the dynamic models. We analyzed the capability of pseudo-stochastic parameters for deriving information about the mismodeled part of the force field and found evidence that the resulting orbits may be used to recover force field parameters, if the number of pseudo-stochastic parameters is large enough. Results based on simulations showed a significantly better performance of acceleration-based orbits for gravity field recovery than for pulse-based orbits, with a quality comparable to a direct estimation if unconstrained accelerations are set up every 30 s.     

A continuous velocity field for Norway

In Norway, as in the rest of Fennoscandia, the process of Glacial Isostatic Adjustment causes ongoing crustal deformation. The vertical and horizontal movements of the Earth can be measured to a high degree of precision using GNSS. The Norwegian GNSS network has gradually been established since the early 1990s and today contains approximately 140 stations. The stations are established both for navigation purposes and for studies of geophysical processes. Only a few of these stations have been analyzed previously. We present new velocity estimates for the Norwegian GNSS network using the processing package GAMIT. We examine the relation between time-series length and precision. With approximately 3.5 years of data, we are able to reproduce the secular vertical rate with a precision of 0.5 mm/year. To establish a continuous crustal velocity field in areas where we have no GNSS receivers or the observation period is too short to obtain reliable results, either interpolation or modeling is required. We experiment with both approaches in this analysis by using (i) a statistical interpolation method called Kriging and (ii) a GIA forward model. In addition, we examine how our vertical velocity field solution is affected by the inclusion of data from repeated leveling. Results from our geophysical model give better estimates on the edge of the network, but inside the network the statistical interpolation method performs better. In general, we find that if we have less than 3.5 years of data for a GNSS station, the interpolated value is better than the velocity estimate based on a single time-series.     

Secular changes in Earth’s shape and surface mass loading derived from combinations of reprocessed global GPS networks

The changing distribution of surface mass (oceans, atmospheric pressure, continental water storage, groundwater, lakes, snow and ice) causes detectable changes in the shape of the solid Earth, on time scales ranging from hours to millennia. Transient changes in the Earth’s shape can, regardless of cause, be readily separated from steady secular variation in surface mass loading, but other secular changes due to plate tectonics and glacial isostatic adjustment (GIA) cannot. We estimate secular station velocities from almost 11 years of high quality combined GPS position solutions (GPS weeks 1,000–1,570) submitted as part of the first international global navigation satellite system service reprocessing campaign. Individual station velocities are estimated as a linear fit, paying careful attention to outliers and offsets. We remove a suite of a priori GIA models, each with an associated set of plate tectonic Euler vectors estimated by us; the latter are shown to be insensitive to the a priori GIA model. From the coordinate time series residuals after removing the GIA models and corresponding plate tectonic velocities, we use mass-conserving continental basis functions to estimate surface mass loading including the secular term. The different GIA models lead to significant differences in the estimates of loading in selected regions. Although our loading estimates are broadly comparable with independent estimates from other satellite missions, their range highlights the need for better, more robust GIA models that incorporate 3D Earth structure and accurately represent 3D surface displacements.     

Determination of Postglacial Land Uplift in Fennoscandia from Leveling, Tide-gauges and Continuous GPS Stations using Least Squares Collocation

Precise leveling, tide-gauge recordings and time series from continuous GPS stations are all sources of information about the ongoing postglacial land uplift in Fennoscandia. This article describes how to gather these three sources of data together in a least-squares collocation adjustment in order to calculate uplift rates, as well as new heights for the benchmarks in the leveling network. The estimated reliability of the resulting uplift model is in general better than 0.4 mm/year, decreasing in areas of fewer data.A smoother and extended version of the land uplift model described here is used in the adjustment of the new height system in Sweden (RH 2000) under the name RH 2000 LU. Later on, the name was changed to NKG2005LU. The Finnish Geodetic Institute (FGI) has decided to use the same model when they calculate their new height system, N2000.     

天文大地网与GPS2000网联合平差的地壳形变改正研究

按照中国大陆地质构造情况，将中国大陆划分成不规则的曲线网格．利用高精度GPS网平差得到的GPS速度、地震矩张量和活断层滑动速率。采用双三次样条函数拟合的方法。求出了中国大陆现今地壳运动速度场和变形场；利用中国大陆现今地壳运动速度场和变形场模型。研究分析了天文大地网与GPS2000网联合平差中是否需要对天文大地网地面观测值进行形变改正问题。研究结果表明。天文大地网观测点坐标需要改正，但不需要在联合平差中对天文大地网地面观测数据(边长、方位角)进行改正，可以省去天文大地网约30万个观测量的地壳形变改正工作。     

Long-term vertical land motion from double-differenced tide gauge and satellite altimetry data

We present a new approach to estimate precise long-term vertical land motion (VLM) based on double-differences of long tide gauge (TG) and short altimetry data. We identify and difference rates of pairs of highly correlated sea level records providing relative VLM estimates that are less dependent on record length and benefit from reduced uncertainty and mitigated biases (e.g. altimeter drift). This approach also overcomes the key limitation of previous techniques in that it is not geographically limited to semi-enclosed seas and can thus be applied to estimate VLM at TGs along any coast, provided data of sufficient quality are available. Using this approach, we have estimated VLM at a global set of 86 TGs with a median precision of 0.7 mm/year in a conventional reference frame. These estimates were compared to previous VLM estimates at TGs in the Baltic Sea and to estimates from co-located Global Positioning System (GPS) stations and Glacial Isostatic Adjustment (GIA) predictions. Differences with respect to the GPS and VLM estimates from previous studies resulted in a scatter of around 0.6 mm/year. Differences with respect to GIA predictions had a larger scatter in excess of 1 mm/year. Until satellite altimetry records reach enough length to estimate precise VLM at each TG, this new approach constitutes a substantial advance in the geodetic monitoring of TGs with major applications in long-term sea level change and climate change studies.     

Estimates of ocean tide loading displacements and its impact on position time series in Hong Kong using a dense continuous GPS network

Three-dimensional ocean tide loading (OTL) displacements of eight diurnal and semidiurnal constituents at 12 sites in Hong Kong were estimated using 3–7 years of continuous global positioning system (GPS) observations. OTL displacements were estimated using the precise point positioning (PPP) technique on a daily basis and then combined. The OTL displacements obtained by GPS were compared with predictions using seven recent global ocean tide models. The effect of OTL displacements on GPS position time series was also investigated. The study shows that the GPS-derived OTL displacements (excluding K1 and K2 constituents) agree best with those predicted by the GOT4.7 and NAO99b models. The GPS/model agreement is generally at the sub-millimeter level, except for S2, K1, and K2 constituents with relatively large errors. After systematic biases between the GPS and model values are removed, the misfits of all sites for M2, S2, N2, O1, P1, and Q1 are less than 0.5 and 1.0 mm in the horizontal and vertical components, respectively, while larger misfits (within 2.5 mm) are observed for K1 and K2. Integer ambiguity fixing slightly improves the east component of OTL displacement estimates. The study also finds that GPS-derived OTL corrections, instead of model predicts, can be used in daily data processing with the exception of K1 and K2. Including K2 corrections, a secular vertical rate of up to 1 mm/year in position time series can be induced, which needs to be confirmed by further studies.     

Evaluation of co-location ties relating the VLBI and GPS reference frames

We have compared the VLBI and GPS terrestrial reference frames, realized using 5 years of time-series observations of station positions and polar motion, with surveyed co-location tie vectors for 25 sites. The goal was to assess the overall quality of the ties and to determine whether a subset of co-location sites might be found with VLBI–GPS ties that are self-consistent within a few millimeters. Our procedure was designed to guard against internal distortion of the two space-geodetic networks and takes advantage of the reduction in tie information needed with the time-series combination method by using the very strong contribution due to co-location of the daily pole of rotation. The general quality of the available ties is somewhat discouraging in that most have residuals, compared to the space-geodetic frames, at the level of 1–2 cm. However, by a careful selection process, we have identified a subset of nine local VLBI–GPS ties that are consistent with each other and with space geodesy to better than 4 mm (RMS) in each component. While certainly promising, it is not possible to confidently assess the reliability of this particular subset without new information to verify the absolute accuracy of at least a few of the highest-quality ties. Particular care must be taken to demonstrate that possible systematic errors within the VLBI and GPS systems have been properly accounted for. A minimum of two (preferably three or four) ties must be measured with accuracies of 1 mm or better in each component, including any potential systematic effects. If this can be done, then the VLBI and GPS frames can be globally aligned to less than 1 mm in each Helmert component using our subset of nine ties. In any case, the X and Y rotations are better determined, to about 0.5 mm, due to the contribution of co-located polar motion.     

On the significance of periodic signals in noise analysis of GPS station coordinates time series

Each of the GPS-derived time series consists of the deterministic (functional) and stochastic part. We propose that the deterministic part includes all periodicities from 1st to 9th harmonics of residual Chandler, tropical and draconitic periods and compare it with commonly used calculations of the annual and semi-annual tropical curve. Then, we address the issues of whether all residual periodicities, as proposed here, need to be taken into consideration when performing noise analysis. We use the position time series from 180 International GNSS Service stations obtained at the Jet Propulsion Laboratory using the GIPSY-OASIS software in a Precise Point Positioning mode. The longest series has 22.1 years of GPS daily solutions. The spectral indices range from –0.12 to –0.92, while the median values of “global” spectral indices are equal to: –0.41 ± 0.15, –0.38 ± 0.12 and –0.33 ± 0.18 for North, East and Up components, respectively. All non-modelled geophysical processes or non-included artificial effects in time series lead to an underestimation of errors of velocities, but also to changes in the velocity values themselves. The proposed assumption of seasonals subtraction caused the Akaike information criterion values to show a decrease in the median value of 30 %, which in fact means that all the seasonals mentioned here must be taken into account when analyzing noises. Finally, we noticed that there are some of the GPS stations that improved their velocity uncertainty even of 56 %.     

Inter-annual water mass variations from GRACE in central Siberia

Our study analyses satellite and land-based observations of the Yakutsk region centred at the Lena watershed, an area characterised mainly by continuous permafrost. Using monthly solutions of the Gravity Recovery And Climate Experiment satellite mission, we detect a mass increase over central Siberia from 2002 to 2007 which reverses into a mass decrease between 2007 and 2011. No significant mass trend is visible for the whole observation period. To further quantify this behaviour, different mass signal components are studied in detail: (1) inter-annual variation in the atmospheric mass, (2) a possible effect of glacial isostatic adjustment (GIA), and (3) hydrological mass variations. In standard processing the atmospheric mass signal is reduced based on the data from numerical weather prediction models. We use surface pressure observations in order to validate this atmospheric reduction. On inter-annual time scale the difference between the atmospheric mass signal from model prediction and from surface pressure observation is $<$ 4 mm in equivalent water height. The effect of GIA on the mass signal over Siberia is calculated using a global ice model and a spherically symmetric, compressible, Maxwell-viscoelastic earth model. The calculation shows that for the investigated area any effect of GIA can be ruled out. Hence, the main part of the signal can be attributed to hydrological mass variations. We briefly discuss potential hydrological effects such as changes in precipitation, river discharge, surface and subsurface water storage.     

Numerical simulation of troposphere-induced errors in GPS-derived geodetic time series over Japan

Troposphere-induced errors in GPS-derived geodetic time series, namely, height and zenith total delays (ZTDs), over Japan are quantitatively evaluated through the analyses of simulated GPS data using realistic cumulative tropospheric delays and observed GPS data. The numerical simulations show that the use of a priori zenith hydrostatic delays (ZHDs) derived from the European Centre for Medium-Range Weather Forecasts (ECMWF) numerical weather model data and gridded Vienna mapping function 1 (gridded VMF1) results in smaller spurious annual height errors and height repeatabilities (0.45 and 2.55 mm on average, respectively) as compared to those derived from the global pressure and temperature (GPT) model and global mapping function (GMF) (1.08 and 3.22 mm on average, respectively). On the other hand, the use of a priori ZHDs derived from the GPT and GMF would be sufficient for applications involving ZTDs, given the current discrepancies between GPS-derived ZTDs and those derived from numerical weather models. The numerical simulations reveal that the use of mapping functions constructed with fine-scale numerical weather models will potentially improve height repeatabilities as compared to the gridded VMF1 (2.09 mm against 2.55 mm on average). However, they do not presently outperform the gridded VMF1 with the observed GPS data (6.52 mm against 6.50 mm on average). Finally, the commonly observed colored components in GPS-derived height time series are not primarily the result of troposphere-induced errors, since they become white in numerical simulations with the proper choice of a priori ZHDs and mapping functions.     

GPS基准站坐标与速度场精度及随时间变化规律的探讨

应用网络工程GPS基准站每周的数据，按非基准方法求得区域解和全球解，分析研究了基准站坐标位置及速度场的变化规律，并给出了站坐标和速度场精度的统计分析结果。结果显示，坐标分量的变化趋势为线性，坐标残差的变化为随机曲线，可靠地剔除野点后，速度场信息及其精度可靠且优于点位坐标精度。     

Assessment of observing time-variable gravity from GOCE GPS and accelerometer observations

An assessment has been made of the possibility to estimate time-variable gravity from GPS-derived orbit perturbations and common-mode accelerometer observations of ESA’s GOCE Earth Explorer. A number of 20-day time series of Earth’s global long-wavelength gravity field have been derived for the period November 2009 to November 2012 using different parameter setups and estimation techniques. These techniques include a conventional approach where for each period, one set of gravity coefficients is estimated, either excluding or including empirical accelerations, and the so-called Wiese approach where higher frequency coefficients are estimated for the very long wavelengths. A principal component analysis of especially the time series of gravity field coefficients obtained by the Wiese approach and the conventional approach with empirical accelerations reveals an annual signal. When fitting this annual signal directly through the time series, the sine component (maximum in spring) displays features that are similar to well-known continental hydrological mass changes for the low latitude areas, such as mass variations in the Amazon basin, Africa and Australia for spatial scales down to 1,500 km. The cosine component (maximum in winter), however, displays large signals that can not be attributed to actual mass variations in the Earth system. The estimated gravity field changes from GOCE orbit perturbations are likely affected by missing GPS observations in case of high ionospheric perturbations during periods of increased solar activity, which is minimal in Summer and maximal towards the end of autumn.     

Plate kinematics of Nubia–Somalia using a combined DORIS and GPS solution

We have used up to 12 years of data to assess DORIS performance for geodynamics applications. We first examine the noise characteristics of the DORIS time-series of weekly station coordinates to derive realistic estimates of velocity uncertainties. We find that a combination of white and flicker noise best explains the DORIS time-series noise characteristics. Second, weekly solutions produced by the Institut Géographique National/Jet Propulsion Laboratory (IGN/JPL) DORIS Analysis Centre are combined to derive a global velocity field. This solution is combined with two independent GPS solutions, including 11 sites on Nubia and 5 on the Somalia plate. The combination indicates that DORIS horizontal velocities have an average accuracy of 3 mm/year, with best-determined sites having velocity accuracy better than 1 mm/year (one-sigma levels). Using our combined velocity field, we derive an updated plate kinematics model with a focus on the Nubia–Somalia area. Including DORIS data improves the precision of the angular velocity vector for Nubia by 15%. Our proposed model provides robust bounds on the maximum opening rates along the East African Rift (4.7–6.7 mm/year). It indicates opening rates 15 and 7% slower than values predicted by NUVEL-1A for the southern Atlantic Ocean and Indian Ocean, respectively. These differences are likely to arise from the fact that NUVEL-1A considered Africa as a single non-deforming plate, while here we use a more refined approach.     

A compendium of transformation formulas useful in GPS work

In order properly to apply transformations when using data derived from different GPS solutions, the effects of plate motion on the coordinates should be accurately taken into consideration. Only then can a rigorous comparison be established between results observed at different epochs. Equations are given to relate GPS-derived Cartesian coordinates and velocities affected by changes of their reference frames and epochs. Received: 16 June 1997 / Accepted: 22 April 1998     

GPS measurements of ocean loading and its impact on zenith tropospheric delay estimates: a case study in Brittany, France

 The results from a global positioning system (GPS) experiment carried out in Brittany, France, in October 1999, aimed at measuring crustal displacements caused by ocean loading and quantifying their effects on GPS-derived tropospheric delay estimates, are presented. The loading effect in the vertical and horizontal position time series is identified, however with significant disagreement in amplitude compared to ocean loading model predictions. It is shown that these amplitude misfits result from spatial tropospheric heterogeneities not accounted for in the data processing. The effect of ocean loading on GPS-derived zenith total delay (ZTD) estimates is investigated and a scaling factor of 4.4 between ZTD and station height for a 10° elevation cut-off angle is found (i.e. a 4.4-cm station height error would map into a 1-cm ZTD error). Consequently, unmodeled ocean loading effects map into significant errors in ZTD estimates and ocean loading modeling must be properly implemented when estimating ZTD parameters from GPS data for meteorological applications. Ocean loading effects must be known with an accuracy of better than 3 cm in order to meet the accuracy requirements of meteorological and climatological applications of GPS-derived precipitable water vapor. Received: 16 July 2001 / Accepted: 25 April 2002 Acknowledgments. The authors are grateful to H.G. Scherneck for fruitful discussions and for his help with the ocean loading calculations. They thank H. Vedel for making the HIRLAM data available; D. Jerett for helpful discussions; and the city of Rostrenen, the Laboratoire d'Océanographie of Concarneau, and the Institut de Protection et de S?reté Nucléaire (BERSSIN) for their support during the GPS measurement campaign. Reviews by C.K. Shum and two anonymous referees significantly improved this paper. This work was carried out in the framework of the MAGIC project (http://www.acri.fr/magic), funded by the European Commission, Environment and Climate Program (EC Contract ENV4-CT98–0745). Correspondence to: E. Calais, Department of Earth and Atmospheric Sciences, Purdue University, West Lafayette, IN 47907-1397, USA. e-mail: ecalais@purdue.edu Tel. : +1-765-496-2915; Fax:+1-765-496-1210     

利用GPS资料采用非连续变形分析模型确定中国大陆地壳运动速度场

利用近10年来我国先后建立的多个大规模高精度GPS地壳形变监测网资料，科学合理地计算出各GPS站点的速度值。采用球面非连续变形分析（DDA）模型，以GPS观测得到的速度值为约束，拟合出了中国大陆现今地壳运动的速度场。它不仅客观地描述了地壳运动的刚性成分，也客观地描述了块体内部的变形，并且具有物理意义。该速度场模型较地质构造速度模型，离散点速度模型，刚体转运速度模型，配置拟合速度模型等有明显的优越性。     

不等式约束最小二乘问题的解及其统计性质

对不等式约束最小二乘平差问题,借助非线性规划中的凝聚约束方法把多个不等式约束转化为一个等式约束,采用拉格朗日极值法求解,解与贝叶斯解或单纯形解一致。其优点在于该解能够表示为观测的明显表达式,由此解的统计性质与最优性可以确定。给出演示该方法的GPS单点定位算例。