External atmospheric corrections in geodetic very-long-baseline interferometry

Three methods to correct for the atmospheric propagation delay in very-long-baseline interferometry (VLBI) measurements were investigated. In the analysis, the NASA R&D experiments from January 1993 to June 1995 were used. The methods were compared in correcting for the excess propagation delay due to water vapour, the “wet” delay, at one of the sites, the Onsala Space Observatory on the west coast of Sweden. The three methods were: (1) estimating the wet delay using the VLBI data themselves; (2) inferring the wet delay from water vapour radiometer (WVR) data, and (3) using independent estimates based on data from the global positioning system (GPS). Optimum elevation cutoff angles were 22^∘ and 26^∘ when using WVR and GPS data, respectively. The results were found to be similar in terms of reproducibility of the estimated baseline lengths. The shortest baselines tend to benefit from external measurements, whereas the lack of improvement in the longer baselines may be partly due to the large amount of data thrown away when removing observations at low elevation angles. Over a 2 week period of intensive measurements, the two methods using external data showed an overall improvement, for all baseline lengths, compared to the first method. This indicates that there are long-term systematic errors in the wet delay data estimated using WVR and GPS data. Received: 27 October 1998 / Accepted: 20 May 1999     

A case study of using Raman lidar measurements in high-accuracy GPS applications

This paper investigates the impact of rapid small-scale water vapor fluctuations on GPS height determination. Water vapor measurements from a Raman lidar are used for documenting the water vapor heterogeneities and correcting GPS signal propagation delays in clear sky conditions. We use data from four short observing sessions (6 h) during the VAPIC experiment (15 May–15 June 2004). The retrieval of wet delays from our Raman lidar is shown to agree well with radiosonde retrievals (bias and standard deviation (SD) were smaller than 1 and 2.8 mm, respectively) and microwave radiometers (from two different instruments, bias was 6.0/−6.6 mm and SD 1.3/3.8 mm). A standard GPS data analysis is shown to fail in accurately reproducing fast zenith wet delay (ZWD) variations. The ZWD estimates could be improved when mean post-fit phase residuals were removed. Several methodologies for integrating zenith lidar observations into the GPS data processing are also presented. The final method consists in using lidar wet delays for correcting a priori the GPS phase observations and estimating a scale factor for the lidar wet delays jointly with the GPS station position. The estimation of this scale factor allows correcting for a mis-calibration in the lidar data and provides in the same way an estimate of the Raman lidar instrument constant. The agreement of this constant with an independent determination using radiosonde data is at the level of 1–4%. The lidar wet delays were derived by ray-tracing from zenith pointing measurements: further improvement in GPS positioning is expected from slant path lidar measurements that would properly account for water vapor anisotropy.     

Tropospheric delay gradients from numerical weather prediction models: effects on GPS estimated parameters

Several numerical weather prediction (NWP) models provide information on the 3D state of the neutral atmosphere which has enabled GNSS researchers to have improved a priori information of the delay induced in the GNSS signals. However, the quality of weather models on the one hand and computational difficulties on the other, are motivations to develop an algorithm based partly on NWP models, while still estimating the remaining residual delay through GNSS processing strategies. An algorithm has been developed to estimate horizontal delay gradients from Meteorological Service of Canada NWP models. The GNSS software “Bernese” has also been modified to handle these gradients, as well as zenith delay and mapping functions based on NWP models in phase and code observation equations. Month-long precise point positioning results show strong correlation between north–south hydrostatic gradients and latitude differences, with significant but less strong correlation with the height and zenith total delay parameters. The longitude components were not sensitive to the implementation of gradients. High precision GNSS applications such as long term geodynamics studies, realization of terrestrial reference frames and climatology and consequential interpretations may be affected by ignoring the asymmetry of the neutral atmosphere. In addition to estimating the gradients, implementing a priori information on gradients in the processing software may have an impact on estimated results and consequential interpretations.     

Improvement in PWV estimation from GPS due to the absolute calibration of antenna phase center variations

Climatology of column-integrated atmospheric water vapor over Spain has been carried out by means of three techniques: soundings, sun photometers and GPS receivers. Comparing data from stations equipped with more than one of these instruments, we found that a large discontinuity occurred on November 6, 2006, in the differences between the data series from GPS receivers and those from the other two techniques. Prior to that date, the GPS data indicate a wet bias of 2–3 mm for all stations when compared with sounding or photometer data, whereas after that date this bias practically reduces to zero. The root mean square error also decreases about half of its value. On November 6, 2006, the International GNSS Service adopted an absolute calibration model for the antennas of the GPS satellites and receivers instead of the relative one. This change is expected to be an improvement, increasing the accuracy of station position determination and consequently benefiting post-processing products such as zenith total delay from which the atmospheric water vapor content is calculated.     

GPS-PWV estimation and validation with radiosonde data and numerical weather prediction model in Antarctica

Three permanent GPS tracking stations in the trans Antarctic mountain deformation (TAMDEF) network were used to estimate precipitable water vapor (PWV) using measurement series covering the period of 2002–2005. TAMDEF is a National Science Foundation funded joint project between The Ohio State University and the United States Geological Survey. The TAMDEF sites with the longest GPS data spans considered in this research are Franklin Island East (FIE0), the International GNSS Service site McMurdo (MCM4), and Cape Roberts (ROB1). For the experiment, PWV was extracted from the ionosphere-free double-difference carrier phase observations, processed using the adjustment of GPS ephemerides (PAGES) software. The GPS data were processed with a 30 s sampling rate, 15-degree cutoff angle, and precise GPS orbits disseminated by IGS. The time-varying part of the zenith wet delay is estimated using the Marini mapping function, while the constant part is evaluated using the corresponding Marini tropospheric model. Previous studies using TAMDEF data for PWV estimation show that the Marini mapping function performs the best among the models offered by PAGES. The data reduction to compute the zenith wet delay follows the step piecewise linear strategy, which is subsequently transformed to PWV. The resulting GPS-based PWV is compared to the radiosonde observations and to values obtained from the Antarctic mesoscale prediction system (AMPS). This comparison revealed a consistent bias of 1.7 mm between the GPS solution and the radiosonde and AMPS reference values.     

Geodetic measurement of horizontal strain across the Red River fault near Thac Ba, Vietnam, 1963–1994

Geodetic measurements from 1963 through 1994 are used to estimate horizontal strain rates across the Red River fault near Thac Ba, Vietnam. Whether or not this fault system is currently active is a subject of some debate. By combining: (1) triangulation from 1963, (2) triangulation in 1983, and (3) Global Positioning System (GPS) observations in 1994, horizontal shear strain rates are estimated without imposing any prior information on fixed stations. The estimated rates of shear strain in ten triangular subnetworks surrounding the fault trace are not significantly different from zero at 95% confidence. The maximum rate of dextral shear is less than 0.3 μrad/year in all but one of the triangles. The estimates help bound the slip rate in a simple elastic dislocation model for a locked, vertical strike-slip fault. By assuming a locking depth of 5–20 km, the most likely values for the deep slip rate are between 1 and 5 mm/year of right-lateral motion. These values delimit the 23% confidence interval. At 95% confidence, the slip rate estimate falls between 7 mm/year of left-lateral motion and 15 mm/year of right-lateral motion. Received: 18 November 1997 / Accepted: 28 January 1999     

Wet tropospheric effects on precise relative GPS height determination

Summary Considerable interest has been generated recently in the use of the Global Positioning System (GPS) for precise height determination. A major error source in these measurements is the propagation delay due to atmospheric water vapour. In order to achieve the high precisions required for such applications as absolute sea-level monitoring improvement of wet delay modelling is necessary. Results from a GPS campaign show a significant correlation (0.91) between the variability of the wet delay measured using a water vapour radiometer (WVR) at the Onsala site and the absolute value of the residual error in the height determination of a 134 km baseline from Onsala to Jönköping. This correlation indicates that the atmosphericvariability as inferred from the WVR data includes information on the quality of the GPS height estimate. During periods of high atmospheric activity, e.g., during the passage of a weather front, the use of a six-parameter gradient model reduces the spread for the vertical coordinate from 40 mm to 20 mm (with standard deviations of 17 mm and 9 mm respectively) over the 134 km baseline (less than 1 × 10^–7) using 8 hour data spans on 11 different days over a six month period.     

利用地基GPS资料分析成都地区大气可降水量

利用成都地区GPS地震监测网的观测资料,通过Bernese软件求解获得CHDU、JYAN、PIXI、QLAI、RENS、ZHJI测站的天顶总延迟和湿延迟,运用湿延迟与大气可降水量之间的转换关系得到各测站大气可降水量,与站点地面实际降雨量及SONDE大气可降水量进行了比较分析。结果表明：地基GPS监测大气可降水量变化与地面实际降雨量有很强的相关性,与SONDE大气可降水量的平均差值为0．43mm,均方偏差为2．56mm。多站点GPS监测大气可降水量联合分析,对于研究区域大气可降水量的变化有一定的意义。     

无气象要素的GPS对流层延迟推算可降水量的研究

本文针对武汉地区GPS气象网资料,进行了GPS对流层延迟直接推算可降水量的研究。在武汉东湖站GPS对流层延迟与无线电探空可降水量的比较中,两者具有很好的相关性,相关系数达到了0.93;推导了对流层延迟直接推算可降水量的模型,对模型结果进行了检验,在武汉东湖站的对流层延迟转换的可降水量与无线电探空可降水量的比较中,均方根为7.8mm,相关性为0.91,这说明了在没有气象数据的地区对流层延迟直接推算的可降水量可以作为气象短期预报的参考。     

GPS sensitivity analysis applied to non-permanent deformation control networks

This paper illustrates the surveys and the results obtained in an experiment whose goal is to evaluate the Global Positioning System (GPS) sensitivity and accuracy for deformation control on non-permanent network of different extensions. To this aim a high-precision device was properly built to set up known displacements along three orthogonal axes of a GPS antenna. One of the antennas in the considered GPS networks was moved according to centimeter and sub-centimeter displacements; after careful GPS data processing, it was evaluated whether these simulated deformations were correctly a posteriori detected and at which probability level. This experiment was carried out both on a local (baselines ranging between 3 and 30 km) and on a regional (baselines ranging between 300 and 600 km) GPS network. The results show that in the local network it is possible to identify the displacements at a level of 10 mm in height and at a level of 5 mm in horizontal position. The analysis of the regional network showed that it is fundamental to investigate new strategies to model the troposphere; in fact, it is necessary to improve the precision of the height in order to correctly identify displacements lower than 60–80 mm; on the contrary, horizontal displacements can be evidenced at the level of 20 mm. Received: 27 April 1998 / Accepted: 14 December 1998     

DETERMINATION OF WEIGHTED MEAN TROPOSPHERIC TEMPERATURE USING GROUND METEOROLOGICAL MEASUREMENTS

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Determination of weighted mean tropospheric temperature using ground meteorological measurements

The weighted mean tropospheric temperature is a critical parameter in the conversion of wet zenith delay to precipitable water vapor in GPS Meteorology. This parameter can not be calculated from the radiosonde data in real time through the conventional methods. In this study, we first discuss the admissible error of weighted mean temperature to enable the accuracy of the conversion better than 1 mm, then summarize the performance of some of the existing methods. An empirical formula is established that satisfies the real-time requirement in GPS meteorology using Sequential Regression Analysis method. It is shown that this real-time formula as compared with other empirical methods is more accurate for local applications.     

成都地区大气平均温度建模及其在GPS/PWV计算中的应用研究

地基GPS气象学的关键技术是在于通过垂直方向上GPS信号的湿分量延迟值来确定大气可降水量-PWV,而这两个物理量间进行转换时需要用到一个关键性的参数——大气加权平均温度。本文首先讨论了估算加权平均温度的几种方法,然后利用成都地区2005年全年的大气探空数据,采用回归分析方法,建立了适合成都地区的大气加权平均温度模型,精度为±2.21K。最后将该公式应用到成都地区PWV的计算中,得到了非常理想的效果。     

Multi-technique comparisons of 10?years of wet delay estimates on the west coast of Sweden

We present comparisons of 10-year-long time series of the atmospheric zenith wet delay (ZWD), estimated using the global positioning system (GPS), geodetic very long baseline interferometry (VLBI), a water vapour radiometer (WVR), radiosonde (RS) observations, and the reanalysis product of the European Centre for Medium-Range Weather Forecasts (ECMWF). To compare the data sets with each other, a Gaussian filter is applied. The results from 10 GPS–RS comparisons using sites in Sweden and Finland show that the full width at half maximum at which the standard deviation (SD) is a minimum increases with the distance between each pair. Comparisons between three co-located techniques (GPS, VLBI, and WVR) result in mean values of the ZWD differences at a level of a few millimetres and SD of less than 7?mm. The best agreement is seen in the GPS–VLBI comparison with a mean difference of ?3.4?mm and an SD of 5.1?mm over the 10-year period. With respect to the ZWD derived from other techniques, a positive bias of up to ~7?mm is obtained for the ECMWF reanalysis product. Performing the comparisons on a monthly basis, we find that the SD including RS or ECMWF varies with the season, between 3 and 15?mm. The monthly SD between GPS and WVR does not have a seasonal signature and varies from 3 to 7?mm.     

利用地面气象观测资料确定对流层加权平均温度

地基GPS气象学的核心思想是通过垂直方向上GPS信号的湿分量延时确定出可降水分 ,而这两个物理量之间的转换必须使用对流层加权平均温度。本文首先讨论了上述转换估计中加权平均温度的几种逼近方式及其容许误差 ,然后利用香港地区的地面和高空气象资料 ,采用逐步回归分析方法 ,建立了适合香港地区的对流层加权平均温度计算公式 ,通过数据分析表明 ,这个公式有效地消除了在香港地区使用Bevis经验公式引起的系统误差 ,较好地满足了地基GPS气象应用中实时性和高精度的要求。本研究也充分表明 ,在地基GPS气象研究中 ,应该利用本地区的气象资料来确定适合本地区的估计对流层加权平均温度的经验公式。     

Interpolating atmospheric water vapor delay by incorporating terrain elevation information

In radio signal-based observing systems, such as Global Positioning System (GPS) and Interferometric Synthetic Aperture Radar (InSAR), the water vapor in the atmosphere will cause delays during the signal transmission. Such delays vary significantly with terrain elevation. In the case when atmospheric delays are to be eliminated from the measured raw signals, spatial interpolators may be needed. By taking advantage of available terrain elevation information during spatial interpolation process, the accuracy of the atmospheric delay mapping can be considerably improved. This paper first reviews three elevation-dependent water vapor interpolation models, i.e., the Best Linear Unbiased Estimator in combination with the water vapor Height Scaling Model (BLUE + HSM), the Best Linear Unbiased Estimator coupled with the Elevation-dependent Covariance Model (BLUE + ECM), and the Simple Kriging with varying local means based on the Baby semi-empirical model (SKlm + Baby for short). A revision to the SKlm + Baby model is then presented, where the Onn water vapor delay model is adopted to substitute the inaccurate Baby semi-empirical model (SKlm + Onn for short). Experiments with the zenith wet delays obtained through the GPS observations from the Southern California Integrated GPS Network (SCIGN) demonstrate that the SKlm + Onn model outperforms the other three. The RMS of SKlm + Onn is only 0.55 cm, while those of BLUE + HSM, BLUE + ECM and SKlm + Baby amount to 1.11, 1.49 and 0.77 cm, respectively. The proposed SKlm + Onn model therefore represents an improvement of 29–63% over the other known models.     

Ray-traced slant factors for mitigating the tropospheric delay at the observation level

Three-dimensional ray tracing through a numerical weather model has been applied to a global precise point positioning (PPP) campaign for modeling both the elevation angle- and azimuth-dependence of the tropospheric delay. Rather than applying the ray-traced slant delays directly, the delay has been parameterized in terms of slant factors, which are applied in a similar manner to traditional mapping functions, but which can account for the azimuthal asymmetry of the delay. Five strategies are considered: (1) Vienna Mapping Functions 1 (VMF1) and estimation of a residual zenith delay parameter; (2) VMF1, estimation of a residual zenith delay and estimation of two tropospheric gradient parameters; (3) three-dimensional ray-traced slant factors and estimation of a residual zenith delay; (4) using only ray-traced slant factors and no estimation of any tropospheric parameters and; (5) using both ray-traced slant factors and estimating a residual zenith delay and two tropospheric gradient parameters. The use of the ray-traced slant factors (solution 3) showed a 3.8% improvement in the repeatability of the up component when compared to the assumption of a symmetric atmosphere (solution 1), while the estimation of two tropospheric gradient parameters gave the best results showing an 7.6% improvement over solution 1 in the up component. Solution 4 performed well in the horizontal domain, allowing for sub-centimeter repeatability but the up component was degraded due to deficiencies in the modeling of the zenith delay, particularly for stations located at equatorial latitudes. The magnitude of the differences in the mean coordinates between solution 2 and solution 3, and the strong correlation with the differences between the north component and the ray-traced gradients (coefficient of correlation of 0.83), as well as the impact of observation geometry on the gradient solution indicate that the use of the ray-traced slant factors could have an implication on the realization of reference frames. The estimated tropospheric products from the PPP solutions were compared to those derived from ray tracing. For the zenith delay, a root mean square (RMS) of 5.4 mm was found, while for the gradient terms, a correlation coefficient of 0.46 for the N–S and 0.42 for the E–W was found for the north–south and east–west components, suggesting that there are still important differences in the gradient parameters which could be due to either errors in the NWM or to non-tropospheric error sources leaking into the PPP-estimated gradients.     

基于北斗的精密单点定位估计对流层天顶延迟精度分析

通过全球导航卫星（GNSS）系统获取对流层天顶延迟对于气象和电波折射修正具有重要应用价值。利用自主研发的静态精密单点定位软件CRPPP,基于国际GNSS地球动力学服务局（IGS）发布的北斗系统（BDS）精密星历和精密钟差,给出了BDS估算天顶延迟结果。以IGS发布的全球定位系统（GPS）结果为参考对比,BDS估算天顶延迟结果平均偏差优于5mm,均方根误差（rms）优于2．3cm．同时,给出了西沙地区GPS与BDS估计结果,结果表明：利用北斗系统估计的对流层天顶延迟精度与GPS相当。     

地基GPS遥感大气水汽含量的误差分析

讨论并分析了利用地基ＧＰＳ遥感大气水汽含量时的误差源及其数值评估。其误差来自三个方面：一是计算ＧＰＳ讯号传输时间中湿延迟的误差;二是将该湿延迟转换为大气水汽含量公式中测定转换因子的误差;三是转换模型的误差。     

GPS对流层延迟改正UNB3模型及其精度分析

就GPS对流层延迟改正UNB3模型的天顶延迟模型和Niell映射函数模型进行了详细的探讨,采用C 语言编程,建立了相应的程序模块;在GPS普通单点定位中,比较分析了UNB3模型的修正精度;通过IGS跟踪站的大量数据分析计算表明,UNB3天顶延迟模型的修正精度在平面x、y方向上与Saastamoinen天顶延迟模型相当,在高程H方向上优于Saastamoinen天顶延迟模型.