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1.
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.  相似文献   

2.
The Global Positioning System (GPS) observations from the EUREF Permanent Network (EPN) are routinely analyzed by the EPN analysis centers using a tropospheric delay modeling based on standard pressure values, the Niell Mapping Functions (NMF), a cutoff angle of 3° and down-weighting of low elevation observations. We investigate the impact on EPN station heights and Zenith Total Delay (ZTD) estimates when changing to improved models recommended in the updated 2003 International Earth Rotation and Reference Systems Service (IERS) Conventions, which are the Vienna Mapping Functions 1 (VMF1) and zenith hydrostatic delays derived from numerical weather models, or the empirical Global Mapping Functions (GMF) and the empirical Global Pressure and Temperature (GPT) model. A 1-year Global Positioning System (GPS) data set of 50 regionally distributed EPN/IGS (International GNSS Service) stations is processed. The GPS analysis with cutoff elevation angles of 3, 5, and 10° revealed that changing to the new recommended models introduces biases in station heights in the northern part of Europe by 2–3 mm if the cutoff is lower than 5°. However, since large weather changes at synoptic time scales are not accounted for in the empirical models, repeatability of height and ZTD time series are improved with the use of a priori Zenith Hydrostatic Delays (ZHDs) derived from numerical weather models and VMF1. With a cutoff angle of 3°, the repeatability of station heights in the northern part of Europe is improved by 3–4 mm.  相似文献   

3.
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.  相似文献   

4.
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.  相似文献   

5.
Troposphere zenith path delays derived from the Global Data Assimilation System (GDAS) numerical weather model (NWM) are compared with those of the International GNSS Service (IGS) solutions over a 1.5-year period at 18 globally distributed IGS stations. Meteorological parameters can be interpolated from the NWM model at any location and at any time after December 2004. The meteorological parameters extracted from the NWM model agree with in situ direct measurements at some IGS stations within 1 mbar for pressure, 3° for temperature and 13% for relative humidity. The hydrostatic and wet components of the zenith path delay (ZPD) are computed using the meteorological parameters extracted from the NWM model. The total ZPDs derived from the GDAS NWM agree with the IGS ZPD solutions at 3.0 cm RMS level with biases of up to 4.5 cm, which can be attributed to the wet ZPDs estimates from the NWM model, considering the less accurate interpolated relative humidity parameter. Based on this study, it is suggested that the availability and the precision of the GDAS NWM ZPD should be sufficient for nearly all GPS navigation solutions.
Constantin-Octavian AndreiEmail:
  相似文献   

6.
Implementation and testing of the gridded Vienna Mapping Function 1 (VMF1)   总被引:6,自引:5,他引:1  
J. Kouba 《Journal of Geodesy》2008,82(4-5):193-205
The new gridded Vienna Mapping Function (VMF1) was implemented and compared to the well-established site-dependent VMF1, directly and by using precise point positioning (PPP) with International GNSS Service (IGS) Final orbits/clocks for a 1.5-year GPS data set of 11 globally distributed IGS stations. The gridded VMF1 data can be interpolated for any location and for any time after 1994, whereas the site-dependent VMF1 data are only available at selected IGS stations and only after 2004. Both gridded and site-dependent VMF1 PPP solutions agree within 1 and 2 mm for the horizontal and vertical position components, respectively, provided that respective VMF1 hydrostatic zenith path delays (ZPD) are used for hydrostatic ZPD mapping to slant delays. The total ZPD of the gridded and site-dependent VMF1 data agree with PPP ZPD solutions with RMS of 1.5 and 1.8 cm, respectively. Such precise total ZPDs could provide useful initial a priori ZPD estimates for kinematic PPP and regional static GPS solutions. The hydrostatic ZPDs of the gridded VMF1 compare with the site-dependent VMF1 ZPDs with RMS of 0.3 cm, subject to some biases and discontinuities of up to 4 cm, which are likely due to different strategies used in the generation of the site-dependent VMF1 data. The precision of gridded hydrostatic ZPD should be sufficient for accurate a priori hydrostatic ZPD mapping in all precise GPS and very long baseline interferometry (VLBI) solutions. Conversely, precise and globally distributed geodetic solutions of total ZPDs, which need to be linked to VLBI to control biases and stability, should also provide a consistent and stable reference frame for long-term and state-of-the-art numerical weather modeling.  相似文献   

7.
The troposphere delay is an important source of error for precise GNSS positioning due to its high correlation with the station height parameter. It has been demonstrated that errors in mapping functions can cause sub-annual biases as well as affect the repeatability of GNSS solutions, which is a particular concern for geophysical studies. Three-dimensional ray-tracing through numerical weather models (NWM) is an excellent approach for capturing the directional and daily variation of the tropospheric delay. Due to computational complexity, its use for positioning purposes is limited, but it is an excellent tool for evaluating current state-of-the-art mapping functions used for geodetic positioning. Many mapping functions have been recommended in the past such as the Niell Mapping Function (NMF), Vienna Mapping Function 1 (VMF1), and the Global Mapping Function (GMF), which have been adopted by most IGS analysis centers. A new Global Pressure Temperature model (GPT2) has also been developed, which has been shown to improve upon the original atmospheric model used for the GMF. Although the mapping functions mentioned above use the same functional formulation, they vary in terms of their atmospheric source and calibration approach. A homogeneous data set of three-dimensional ray-traced delays is used to evaluate all components of the mapping functions, including their underlying functional formulation, calibration, and compression method. Additionally, an alternative representation of the VMF1 is generated using the same atmospheric source as the truth data set to evaluate the differences in ray-tracing methods and their effect on the end mapping function. The results of this investigation continue to support the use of the VMF1 as the mapping function of choice when geodetic parameters are of interest. Further support for the GPT2 and GMF as reliable back-ups when the VMF1 is not available was found due to their high consistency with the NWM-derived mapping function. Additionally, a small latitude-dependent bias in station height was found in the current mapping functions. This bias was identified to be due to the assumption of a constant radius of the earth and was largest at the poles and at the equator. Finally, an alternative version of the VMF1 is introduced, namely the UNB-VMF1 which provides users with an independent NWM-derived mapping function to support geodetic positioning.  相似文献   

8.
This paper focuses on the precise point positioning (PPP) ambiguity resolution (AR) using the observations acquired from four systems: GPS, BDS, GLONASS, and Galileo (GCRE). A GCRE four-system uncalibrated phase delay (UPD) estimation model and multi-GNSS undifferenced PPP AR method were developed in order to utilize the observations from all systems. For UPD estimation, the GCRE-combined PPP solutions of the globally distributed MGEX and IGS stations are performed to obtain four-system float ambiguities and then UPDs of GCRE satellites can be precisely estimated from these ambiguities. The quality of UPD products in terms of temporal stability and residual distributions is investigated for GPS, BDS, GLONASS, and Galileo satellites, respectively. The BDS satellite-induced code biases were corrected for GEO, IGSO, and MEO satellites before the UPD estimation. The UPD results of global and regional networks were also evaluated for Galileo and BDS, respectively. As a result of the frequency-division multiple-access strategy of GLONASS, the UPD estimation was performed using a network of homogeneous receivers including three commonly used GNSS receivers (TRIMBLE NETR9, JAVAD TRE_G3TH DELTA, and LEICA). Data recorded from 140 MGEX and IGS stations for a 30-day period in January in 2017 were used to validate the proposed GCRE UPD estimation and multi-GNSS dual-frequency PPP AR. Our results show that GCRE four-system PPP AR enables the fastest time to first fix (TTFF) solutions and the highest accuracy for all three coordinate components compared to the single and dual system. An average TTFF of 9.21 min with \(7{^{\circ }}\) cutoff elevation angle can be achieved for GCRE PPP AR, which is much shorter than that of GPS (18.07 min), GR (12.10 min), GE (15.36 min) and GC (13.21 min). With observations length of 10 min, the positioning accuracy of the GCRE fixed solution is 1.84, 1.11, and 1.53 cm, while the GPS-only result is 2.25, 1.29, and 9.73 cm for the east, north, and vertical components, respectively. When the cutoff elevation angle is increased to \(30{^{\circ }}\), the GPS-only PPP AR results are very unreliable, while 13.44 min of TTFF is still achievable for GCRE four-system solutions.  相似文献   

9.
In GPS meteorology, the weighted mean temperature is usually obtained by using a linear function of the surface temperature T s. However, not every GPS station can measure the surface temperature. The current study explores the characteristics of surface temperature and weighted mean temperature based on the global pressure and temperature model (GPT) and the Bevis T mT s relationship (T m =?a?+?bT s). A new global weighted mean temperature (GWMT) model has been built which directly uses three-dimensional coordinates and day of the year to calculate the weighted mean temperature. The data of year 2005–2009 from 135 radiosonde stations provided by the Integrated Global Radiosonde Archive were used to calculate the model coefficients, which have been validated through examples. The result shows that the GWMT model is generally better than the existing liner models in most areas according to the statistic indexes (namely, mean absolute error and root mean square). Then we calculated precipitable water vapor, and the result shows that GWMT model can also yield high precision PWV.  相似文献   

10.
非差非组合精密单点定位需要估计电离层延迟参数,采用电离层先验改正模型约束可以辅助电离层参数解算。针对先验电离层改正量与实际观测量之间权比关系难以确定的问题,本文提出一种电离层约束权因子搜索算法,采用权因子对先验电离层改正量的方差进行调整,根据验后残差加权平方和最小原则通过搜索找出较优的权因子,利用验后残差动态调整先验电离层改正量的方差从而达到改善定位结果的目的。采用8个MGEX跟踪站的GPS/BDS观测数据对该算法进行验证。静态结果表明:对比传统约束方法,采用搜索算法后平均三维定位精度由3.96 cm提高到3.40 cm,平均收敛时间由76.3 min缩短为59.9 min。  相似文献   

11.
《测量评论》2013,45(48):57-58
Abstract

When a beacon B h stands on a mountain of height h, the bearing of B h as seen from another station A is in general affected by its elevation. The correction never exceeds one second of arc, but in primary triangulation it is not always negligible.  相似文献   

12.
对流层映射函数是将对流层天顶延迟转化为信号传播路径上总延迟的重要模型,选择合适的映射函数对反演大气可降水量(PWV)精度的提高具有十分重要的意义.本文研究了对流层映射函数对反演PWV精度的影响,选取VMF1、GMF、NMF 3种映射函数,利用GAMIT解算比较3种映射函数在不同季节、不同高度角对网基线解算以及反演PWV的精度影响.结果表明,在进行PWV反演时,选择10°高度角作为解算截止高度角的GMF函数模型反演精度最佳,为进一步提高GNSS水汽反演的实时精度提供了参考.   相似文献   

13.
During past decades, precise point positioning (PPP) has been proven to be a well-known positioning technique for centimeter or decimeter level accuracy. However, it needs long convergence time to get high-accuracy positioning, which limits the prospects of PPP, especially in real-time applications. It is expected that the PPP convergence time can be reduced by introducing high-quality external information, such as ionospheric or tropospheric corrections. In this study, several methods for tropospheric wet delays modeling over wide areas are investigated. A new, improved model is developed, applicable in real-time applications in China. Based on the GPT2w model, a modified parameter of zenith wet delay exponential decay wrt. height is introduced in the modeling of the real-time tropospheric delay. The accuracy of this tropospheric model and GPT2w model in different seasons is evaluated with cross-validation, the root mean square of the zenith troposphere delay (ZTD) is 1.2 and 3.6 cm on average, respectively. On the other hand, this new model proves to be better than the tropospheric modeling based on water-vapor scale height; it can accurately express tropospheric delays up to 10 km altitude, which potentially has benefits in many real-time applications. With the high-accuracy ZTD model, the augmented PPP convergence performance for BeiDou navigation satellite system (BDS) and GPS is evaluated. It shows that the contribution of the high-quality ZTD model on PPP convergence performance has relation with the constellation geometry. As BDS constellation geometry is poorer than GPS, the improvement for BDS PPP is more significant than that for GPS PPP. Compared with standard real-time PPP, the convergence time is reduced by 2–7 and 20–50% for the augmented BDS PPP, while GPS PPP only improves about 6 and 18% (on average), in horizontal and vertical directions, respectively. When GPS and BDS are combined, the geometry is greatly improved, which is good enough to get a reliable PPP solution, the augmentation PPP improves insignificantly comparing with standard PPP.  相似文献   

14.
G. T. M. 《测量评论》2013,45(21):428-429
Abstract

It is frequently required to find whether a feature A of height h 0 will interrupt the view between two other features A1 and A2, of heights h 1 and h 2 respectively. Suppose that the right line from A1 to A2, whose zenith distance is ζ at A1, has a height h at A; it is then obvious that no more is necessary than to compute h and compare it with the known height h 0 of the feature A.  相似文献   

15.
Multi-GNSS precise point positioning (MGPPP) using raw observations   总被引:5,自引:2,他引:3  
A joint-processing model for multi-GNSS (GPS, GLONASS, BDS and GALILEO) precise point positioning (PPP) is proposed, in which raw code and phase observations are used. In the proposed model, inter-system biases (ISBs) and GLONASS code inter-frequency biases (IFBs) are carefully considered, among which GLONASS code IFBs are modeled as a linear function of frequency numbers. To get the full rank function model, the unknowns are re-parameterized and the estimable slant ionospheric delays and ISBs/IFBs are derived and estimated simultaneously. One month of data in April, 2015 from 32 stations of the International GNSS Service (IGS) Multi-GNSS Experiment (MGEX) tracking network have been used to validate the proposed model. Preliminary results show that RMS values of the positioning errors (with respect to external double-difference solutions) for static/kinematic solutions (four systems) are 6.2 mm/2.1 cm (north), 6.0 mm/2.2 cm (east) and 9.3 mm/4.9 cm (up). One-day stabilities of the estimated ISBs described by STD values are 0.36 and 0.38 ns, for GLONASS and BDS, respectively. Significant ISB jumps are identified between adjacent days for all stations, which are caused by the different satellite clock datums in different days and for different systems. Unlike ISBs, the estimated GLONASS code IFBs are quite stable for all stations, with an average STD of 0.04 ns over a month. Single-difference experiment of short baseline shows that PPP ionospheric delays are more precise than traditional leveling ionospheric delays.  相似文献   

16.
Ambiguity resolution (AR) for a single receiver has been a popular topic in Global Positioning System (GPS) recently. Ambiguity-resolution methods for precise point positioning (PPP) have been well documented in recent years, demonstrating that it can improve the accuracy of PPP. However, users are often concerned about the reliability of ambiguity-fixed PPP solution in practical applications. If ambiguities are fixed to wrong integers, large errors would be introduced into position estimates. In this paper, we aim to assess the correct fixing rate (CFR), i.e., number of ambiguities correctly fixing to the total number of ambiguities correctly and incorrectly fixing, for PPP user ambiguity resolution on a global scale. A practical procedure is presented to evaluate the CFR of PPP user ambiguity resolution. GPS data of the first 3 days in each month of 2010 from about 390 IGS stations are used for experiments. Firstly, we use GPS data collected from about 320 IGS stations to estimate global single-differenced (SD) wide-lane and narrow-lane satellite uncalibrated phase delays (UPDs). The quality of UPDs is evaluated. We found that wide-lane UPD estimates have a rather small standard deviation (Std) between 0.003 and 0.004 cycles while most of Std of narrow-lane estimates are from 0.01 to 0.02 cycles. Secondly, many experiments have been conducted to investigate the CFR of integer ambiguity resolution we can achieve under different conditions, including reference station density, observation session length and the ionospheric activity. The results show that the CFR of PPP can exceed 98.0 % with only 1 h of observations for most user stations. No obvious correlation between the CFR and the reference station density is found. Therefore, nearly homogeneous CFR can be achieved in PPP AR for global users. At user end, higher CFR could be achieved with longer observations. The average CFR for 30-min, 1-h, 2-h and 4-h observation is 92.3, 98.2, 99.5 and 99.7 %, respectively. In order to get acceptable CFR, 1 h is a recommended minimum observation time. Furthermore, the CFR of PPP can be affected by diurnal variation and geomagnetic latitude variation in the ionosphere. During one day at the hours when rapid ionospheric variations occur or in low geomagnetic latitude regions where equatorial electron density irregularities are produced relatively frequently, a significant degradation of the CFR is demonstrated.  相似文献   

17.
Estimating forest structural attributes using multispectral remote sensing is challenging because of the saturation of multispectral indices at high canopy cover. The objective of this study was to assess the utility of hyperspectral data in estimating and mapping forest structural parameters including mean diameter-at-breast height (DBH), mean tree height and tree density of a closed canopy beech forest (Fagus sylvatica L.). Airborne HyMap images and data on forest structural attributes were collected from the Majella National Park, Italy in July 2004. The predictive performances of vegetation indices (VI) derived from all possible two-band combinations (VI(i,j) = (Ri − Rj)/(Ri + Rj), where Ri and Rj = reflectance in any two bands) were evaluated using calibration (n = 33) and test (n = 20) data sets. The potential of partial least squares (PLS) regression, a multivariate technique involving several bands was also assessed. New VIs based on the contrast between reflectance in the red-edge shoulder (756–820 nm) and the water absorption feature centred at 1200 nm (1172–1320 nm) were found to show higher correlations with the forest structural parameters than standard VIs derived from NIR and visible reflectance (i.e. the normalised difference vegetation index, NDVI). PLS regression showed a slight improvement in estimating the beech forest structural attributes (prediction errors of 27.6%, 32.6% and 46.4% for mean DBH, height and tree density, respectively) compared to VIs using linear regression models (prediction errors of 27.8%, 35.8% and 48.3% for mean DBH, height and tree density, respectively). Mean DBH was the best predicted variable among the stand parameters (calibration R2 = 0.62 for an exponential model fit and standard error of prediction = 5.12 cm, i.e. 25% of the mean). The predicted map of mean DBH revealed high heterogeneity in the beech forest structure in the study area. The spatial variability of mean DBH occurs at less than 450 m. The DBH map could be useful to forest management in many ways, e.g. thinning of coppice to promote diameter growth, to assess the effects of management on forest structure or to detect changes in the forest structure caused by anthropogenic and natural factors.  相似文献   

18.
An approach for estimating soil moisture is presented and tested by using surface-temperature-based soil evaporation transfer coefficient (ha), a coefficient recently proposed through the equation ha = (Ts − Ta)/(Tsd − Ta), where Ts, Tsd, and Ta are land surface temperature (LST), reference soil (dry soil without evaporation) surface temperature, and air temperature respectively. Our analysis and controllable experiment indicated that ha closely related to soil moisture, and therefore, a relationship between field soil moisture and ha could be developed for soil moisture estimation. Field experiments were carried out to test the relationship between ha and soil moisture. Time series Aqua-MODIS images were acquired between 11 Sep. 2006 and 1 Nov. 2007. Then, MODIS derived ha and simultaneous measured soil moisture for different soil depths were used to establish the relations between the two variables. Results showed that there was a logarithmic relationship between soil moisture and ha (P < 0.01). These logarithmic models were further validated by introducing another ground-truth data gathered from 46 meteorological stations in Hebei Province. Good agreement was observed between the measured and estimated soil moisture with RMSE of 0.0374 cm3/cm3 and 0.0503 cm3/cm3 for surface energy balance method at two soil depths (10 cm and 20 cm), with RMSE of 0.0467 cm3/cm3 and 0.0581 cm3/cm3 for maximum temperature method at two soil depths. For vegetated surfaces, the ratio of ha and NDVI suggested to be considered. The proposed approach has a great potential for soil moisture and drought evaluation by remote sensing.  相似文献   

19.
GPT2w模型在南极地区精度分析   总被引:1,自引:0,他引:1  
孔建  姚宜斌  单路路  王泽民 《测绘学报》2018,47(10):1316-1325
GPT2w(global pressure and temperature 2 wet)是目前应用较为广泛的对流层延迟经验模型之一,可提供气压、温度、水汽压等气象参数。为验证和分析GPT2w模型在南极地区的精度,本文利用分布在南极区域的探空站数据和中国第33次南极科考期间的实测探空气球数据对模型气压、温度、水汽压参数进行分层精度检验。与探空站数据比较发现,在南极地区地面高度上,GPT2w模型精度较高,与全球其他区域精度较为一致;进一步通过对比1月和7月统计结果,发现Bias和RMS呈现出季节特性;同时发现模型在垂直方向存在较大误差,表现为随着高度的增加,精度随之下降并逐步趋于稳定。实测数据对比方面,首先利用ECMWF(European Centre for Medium-range Weather Forecasts)气压分层数据对实测数据的可靠性进行验证,结果显示,实测数据与ECMWF分层数据符合得较好;同时通过比对发现,GPT2w天内精度在地面高度上仍与月平均精度相当,但垂直方向随着高度的增加精度相比于暖季精度会有所下滑,说明未考虑日周期项变化对模型精度存在一定影响。用探空数据计算的对流层延迟(zenith tropospheric delay,ZTD)来分析GPT2w的计算精度,结果表明GPT2w在南极区域ZTD计算精度在厘米级,与全球其他位置计算精度相当。  相似文献   

20.
VMF3/GPT3: refined discrete and empirical troposphere mapping functions   总被引:1,自引:0,他引:1  
Incorrect modeling of troposphere delays is one of the major error sources for space geodetic techniques such as Global Navigation Satellite Systems (GNSS) or Very Long Baseline Interferometry (VLBI). Over the years, many approaches have been devised which aim at mapping the delay of radio waves from zenith direction down to the observed elevation angle, so-called mapping functions. This paper contains a new approach intended to refine the currently most important discrete mapping function, the Vienna Mapping Functions 1 (VMF1), which is successively referred to as Vienna Mapping Functions 3 (VMF3). It is designed in such a way as to eliminate shortcomings in the empirical coefficients b and c and in the tuning for the specific elevation angle of \(3^{\circ }\). Ray-traced delays of the ray-tracer RADIATE serve as the basis for the calculation of new mapping function coefficients. Comparisons of modeled slant delays demonstrate the ability of VMF3 to approximate the underlying ray-traced delays more accurately than VMF1 does, in particular at low elevation angles. In other words, when requiring highest precision, VMF3 is to be preferable to VMF1. Aside from revising the discrete form of mapping functions, we also present a new empirical model named Global Pressure and Temperature 3 (GPT3) on a \(5^{\circ }\times 5^{\circ }\) as well as a \(1^{\circ }\times 1^{\circ }\) global grid, which is generally based on the same data. Its main components are hydrostatic and wet empirical mapping function coefficients derived from special averaging techniques of the respective (discrete) VMF3 data. In addition, GPT3 also contains a set of meteorological quantities which are adopted as they stand from their predecessor, Global Pressure and Temperature 2 wet. Thus, GPT3 represents a very comprehensive troposphere model which can be used for a series of geodetic as well as meteorological and climatological purposes and is fully consistent with VMF3.  相似文献   

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