A predictive model for regional zenith tropospheric delay correction

The conventional zenith tropospheric delay(ZTD)model(known as the Saastamoinen model)does not consider seasonal variations affecting the delay,giving it low accuracy and stability.This may be improved with adjustments to account for annual and semi-annual variations.This method uses ZTD data provided by the Global Geodetic Observing System to analyze seasonal variations in the bias of the Saastamoinen model in Asia,and then constructs a model with seasonal variation corrections,denoted as SSA.To overcome the dependence of the model on in-situ meteorological parameters,the SSA+GPT3 model is formed by combining the SSA and GPT3(global pressure-temperature)models.The results show that the introduction of annual and semi-annual variations can substantially improve the Saastamoinen model,yielding small and time-stable variations in bias and root mean square(RMS).In summer and autumn,the bias and RMS are noticeably smaller than those from the Saastamoinen model.In addition,the SSA model performs better in low-latitude and low-altitude areas,and bias and RMS decease with the increase of latitude or altitude.The prediction accuracy of the SSA model is also evaluated for external consistency.The results show that the accuracy of the SSA model(bias:-0.38 cm,RMS:4.43 cm)is better than that of the Saastamoinen model(bias:1.45 cm,RMS:5.16 cm).The proposed method has strong applicability and can therefore be used for predictive ZTD correction across Asia.

A zenith tropospheric delay correction model based on the regional CORS network

Tropospheric delay is a primary error source in earth observations and a variety of radio navigation technologies. In this paper, the relationship between zenith tropospheric delays and the elevation and longitude of stations is analyzed using the zenith tropospheric delay final products of International GNSS Service （IGS） stations from 2011. Two new models are proposed for estimating zenith tropospheric delays from regional CORS data without meteorological data. The proposed models are compared with the direct interpolation method and the remove-restore method using data from Guangxi CORS. The results show that the new models significantly improve the calculated precision. Finally, the root mean square （RMS） errors of the new models were used to estimate the surface precipitable water vapor （PWV） value at CORS station, which was determined to be less than 2 mm.

Assessment of the three representative empirical models for zenith tropospheric delay(ZTD)using the CMONOC data

The precise correction of atmospheric zenith tropospheric delay(ZTD)is significant for the Global Navigation Satellite System(GNSS)performance regarding positioning accuracy and convergence time.In the past decades,many empirical ZTD models based on whether the gridded or scattered ZTD products have been proposed and widely used in the GNSS positioning applications.But there is no comprehensive evaluation of these models for the whole China region,which features complicated topography and climate.In this study,we completely assess the typical empirical models,the IGGtropSH model(gridded,non-meteorology),the SHAtropE model(scattered,non-meteorology),and the GPT3 model(gridded,meteorology)using the Crustal Movement Observation Network of China(CMONOC)network.In general,the results show that the three models share consistent performance with RMSE/bias of 37.45/1.63,37.13/2.20,and 38.27/1.34 mm for the GPT3,SHAtropE and IGGtropSH model,respectively.However,the models had a distinct performance regarding geographical distribution,elevation,seasonal variations,and daily variation.In the southeastern region of China,RMSE values are around 50 mm,which are much higher than that in the western region,approximately 20 mm.The SHAtropE model exhibits better performance for areas with large variations in elevation.The GPT3 model and the IGGtropSH model are more stable across different months,and the SHAtropE model based on the GNSS data exhibits superior performance across various UTC epochs.

Assessment of GNSS zenith tropospheric delay responses to atmospheric variables derived from ERA5 data over Nigeria

Tropospheric delay is a major error caused by atmospheric refraction in Global Navigation Satellite System(GNSS)positioning.The study evaluates the potential of the European Centre for Medium-range Weather Forecast(ECMWF)Reanalysis 5(ERA5)atmospheric variables in estimating the Zenith Tropospheric Delay(ZTD).Linear regression models(LRM)are applied to estimate ZTD with the ERA5 atmospheric variables.The ZTD are also estimated using standard ZTD models based on ERA5 and Global Pressure and Temperature 3(GPT3)atmospheric variables.These ZTD estimates are evaluated using the data collected from the permanent GNSS continuously operating reference stations in the Nigerian region.The results reveal that the Zenith Hydrostatic Delay(ZHD)from the LRM and the Saastamoinien model using ERA5 surface pressure are of identical accuracy,having a Root Mean Square(RMS)error of 2.3 mm while the GPT3-ZHD has an RMS of 3.4 mm.For the Zenith Wet Delay(ZWD)component,the best estimates are derived using ERA5 Precipitable Water Vapour(PWV).These include the ZWD derived by the LRM having an average RMS of 20.9 mm and Bevis equation having RMS of 21.1 mm and 21.0 mm for global and local weighted mean temperatures,respectively.The evaluation of GPT3-ZWD estimates gives RMS of 45.8 mm.This study has provided a valuable insight into the application of ERA5 data for ZTD estimation.In line with the fndings of the study,the ERA5 atmospheric variables are recommended for improving the accuracy in ZTD estimation,required for GNSS positioning.

Preliminary calibration results for Jason-3 and Sentinel-3 altimeters in the Wanshan Islands

We present preliminary calibration results for Jason-3 and Sentinel-3A altimeters that we set up in the Wanshan Islands in Guandong Province,China.Two campaigns were carried out in 2018,from March 8 to April 16 and from November 3 to December 11,2018.Three GPS reference stations and tide gauges were established on the islands of Zhiwan,Dangan,and Wailingding during the campaigns.The in-situ sea surface height(SSH)of the altimeter footprint was determined using the tide gauge.The tidal and geoid connection between the tide gauge locations and the altimeter footprints were computed with the NAO.99Jb tidal prediction system and the EGM 2008 geoid,respectively.The data of the tide gauges were defi ned using the GPS buoy and GPS reference stations during the campaigns.The results show that the waveform of the altimeters was slightly contaminated by the small islands.The bias associated with Jason-3 and Sentinel-3A amounted to approximately+20.7±49.7 mm and+30.1±39.4 mm,respectively,which agreed well with the results from other in-situ calibration fi elds.This indicates that the Wanshan area was very suitable as an in-situ calibration/validation fi eld.The wet zenith delay(WZD)determined from the Microwave Radiometer(MWR)and the GPS measurements diff ered from each other for the Jason-3 and Sentinel-3A by−6.6±7.4 mm and 0±6.8 mm,respectively.

Establishment and analysis of global gridded Tm-Ts relationship model

In ground-based GPS meteorology, Tm is a key parameter to calculate the conversion factor that can convert the zenith wet delay（ZWD） to precipitable water vapor（PWV）. It is generally acknowledged that Tm is in an approximate linear relationship with surface temperature Ts, and the relationship presents regional variation. This paper employed sliding average method to calculate correlation coefficients and linear regression coefficients between Tm and Ts at every 2°× 2.5° grid point using Ts data from European Centre for Medium-Range Weather Forecasts（ECMWF） and Tm data from ＂GGOS Atmosphere＂, yielding the grid and bilinear interpolation-based Tm Grid model. Tested by Tm and Ts grid data, Constellation Observation System of Meteorology, Ionosphere, and Climate（COSMIC） data and radiosonde data, the Tm Grid model shows a higher accuracy relative to the Bevis Tm-Ts relationship which is widely used nowadays. The Tm Grid model will be of certain practical value in high-precision PWV calculation.

Empirical model for mean temperature and assessment of precipitable water vapor derived from GPS

The estimation of Precipitable Water Vapor （PWV） derived from Global Positioning System （GPS） data at the IGS site WUHN is assessed by comparing with PWV obtained from radiosonde data （No.57494） in Wuhan. The applicability of Saastamoinen （SAAS）, Hopfield and Black models used for estimating Zenith Hydrostatic Delay （ZHD） and Zenith Wet Delay （ZWD） and different models is verified in the estimation of GPS-derived PWV for the applied area. The experimental results demonstrated that ： 1 ） the precision of PWV estimated from Black model used for calculating ZHD （ ZHDs ） is lower than that of SAAS （ ZHDsAAs ） model and Hopfield model （ZHDn） with the RMS of 4. 16 ram; 2） the RMS of PWV estimated from SAAS model used for calculating ZWD （SAAS） is 3.78 ram; 3 ） the well-known Bevis model gives similar accuracy compared with the site-specific models for Tm in terms of surface temperature （ Ts ） and surface pressure （Ps）, which can reach the accuracy inside 1 mm in the GPS-derived PWV estimates.

GSTAR:an innovative software platform for processing space geodetic data at the observation level

To meet the demands for the data combination with multiple space geodetic techniques at the observation level,we developed a new software platform with high extensibility and computation efficiency,named space Geodetic SpatioTemporal data Analysis and Research software(GSTAR).Most of the modules in the GSTAR are coded in C++with object-oriented programming.The layered modular theory is adopted for the design of the software,and the antenna-based data architecture is proposed for users to construct personalized geodetic application scenarios easily.The initial performance of the GSTAR software is evaluated by processing the Global Navigation Satellite System(GNSS)data collected from 315 globally distributed stations over two and a half years.The accuracy of GNSS-based geodetic products is evaluated by comparing them with those released by International GNSS Service(IGS)Analysis Centers(AC).Taking the products released by European Space Agency(ESA)as reference,the Three-Dimension(3D)Root-Mean-Squares(RMS)of the orbit differences are 2.7/6.7/3.3/7.7/21.0 cm and the STandard Deviations(STD)of the clock differences are 19/48/16/32/25 ps for Global Positioning System(GPS),GLObal NAvigation Satellite System(GLONASS),Galileo navigation satellite system(Galileo),BeiDou Navigation Satellite System(BDS),Medium Earth Orbit(MEO),and BDS Inclined Geo-Synchronous Orbit(IGSO)satellites,respectively.The mean values of the X and Y components of the polar coordinate and the Length of Day(LOD)with respect to the International Earth Rotation and Reference Systems Service(IERS)14 C04 products are-17.6 microarc-second(μas),9.2μas,and 14.0μs/d.Compared to the IGS daily solution,the RMSs of the site position differences in the north/east/up direction are 1.6/1.5/3.9,3.8/2.4/7.6,2.5/2.4/7.9 and 2.7/2.3/7.4 mm for GPS-only,GLONASS-only,Galileo-only,and BDS-only solution,respectively.The RMSs of the differences of the tropospheric Zenith Path Delay(ZPD),the north gradients,and the east gradients are 5.8,0.9,and 0.9 mm with respect to the IGS products.The X and Y components of the geocenter motion estimated from GPS-only,Galileo-only,and BDS-only observations well agree with IGS products,while the Z component values are much nosier where anomalous harmonics in GNSS draconitic year can be found.The accuracies of the above products calculated by the GSTAR are comparable with those from different IGS ACs.Compared to the precise scientific orbit products,the 3D RMS of the orbit differences for the two Gravity Recovery and Climate Experiment Follow-on(GRACE-FO)satellites is below 1.5 cm by conducting Precise Point Positioning with Ambiguity Resolution(PPP-AR).In addition,a series of rapid data processing algorithms are developed,and the operation speed of the GSTAR software is 5.6 times faster than that of the Positioning and Navigation Data Analyst(PANDA)software for the quad-system precise orbit determination procedure.

基于最小二乘法无气象要素的PWV反演

提出了一种无需气象数据,直接用对流层天顶总延迟(zenith total delay,ZTD)推导大气可降水量(precipitable water vapor,PWV)的新方法。该方法从GPS反演大气水汽的反演方程出发,基于最小二乘法建立ZTD推算PWV的模型。结果表明,就BJFS测站而言,模型推算的PWV与GPS反演的PWV的均方根(root mean square,RMS)值为4.5 mm,两者存在一个微小的系统偏差,但相关系数高达0.982。在不研究其数值大小只研究其趋势变化时,可以用模型直接推算PWV,这可为气象学短期预报提供一定参考。

基于Matern^(5/2)核函数高斯过程回归算法的实时对流层内插模型研究

连续运行基准站(continuously operating reference station,CORS)网络是网络实时动态(real-time kinematic,RTK)必需的基础硬件设施,而网络RTK依然受站间距离增长所带来的非线性大气误差影响。而精密单点定位(precise point positioning,PPP)不需要额外的参考站,其通过对各类误差精确建模,解算用户位置信息,但由于先验对流层模型精度较差、卫星端和接收机端未校准相位延迟(uncalibrated phase delays,UPD)难以与模糊度有效分离,传统PPP收敛时间过长。结合两者的优势,基于PPP-RTK的思想,通过提取固定参考站位置处的实时天顶总延迟(zenith total delay,ZTD),并采用一种基于Matern^(5/2)核函数的非线性高斯过程回归模型,在线估计核函数超参数,从而对长间距基准站网络进行ZTD实时空域建模,为网内区域提供实时高精度的ZTD产品信息。采用中国湖北省CORS网2021年2月1日至4日共4天采样率为30 s的实时观测值数据对模型进行评估。实验结果表明,其在天顶方向收敛时间为17.5 min,定位精度为2.474 cm。与常规动态PPP解算结果相比,收敛时间提升10.26%,定位精度提升4.81%;与传统的线性插值算法相比,收敛时间提升7.89%,定位精度提升3.28%。且该模型具备较好的鲁棒性。