Slant Delays Research Articles

A rapid ray tracing method to evaluate the performances of ERA5 and MERRA2 in retrieving global tropospheric delay

Atmospheric reanalysis plays an important role in retrieving the atmospheric tropospheric delays with ray tracing for space geodetic techniques. In order to represent the complex weather and climate conditions better, the spatiotemporal resolutions of the newly developed atmospheric reanalysis products are improved significantly. The increased spatiotemporal resolution provides a great opportunity to improve the accuracy of the tropospheric delays derived from ray tracing, but it remains a challenge due to the highly increased computation costs. In this paper, we develop a rapid ray tracing method with refined height interval determination to accommodate the increased spatiotemporal resolution of the atmospheric reanalysis products. The accuracy of this method was validated by the 2010 International Association of Geodesy Working Group 4.3.3 ray tracing Comparison Campaign reference results. Zenith and slant delays were obtained by tracing 342 global International Global Navigation Satellite System Service (IGS) stations. Compared to the traditional method, this reduced memory footprint by 16.1%, global refractivity field construction time by 13.6%, and per ray trace time by 22.5% while maintaining accuracy. Based on this methodology, ray tracing using state-of-the-art fifth-generation European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA5) and second Modern-Era Retrospective Analysis for Research and Applications (MERRA2) at 342 IGS stations assessed tropospheric delay performance in 2021. Results showed significant ERA5 and MERRA2 slant delay and mapping factor differences up to the decimeter level, especially for the wet component. Additionally, using IGS zenith total delay (ZTD) as a reference, ERA5 ZTD bias and root mean square error (RMSE) were 2.3 and 11.9 mm, versus that of 1.8 and 16.2 mm for MERRA2 ZTD. At extreme weather-affected AIRA stations over August 5–9, 2021, ERA5 ZTD mean and RMSE differences were −3.0 and 19.8 mm, and −5.3 and 21.7 mm for MERRA2 ZTD. Tropospheric delays and models derived from ERA5 can support space geodetic applications given improved performance and temporal resolution.

On the Impact of GPS Multipath Correction Maps and Post-Fit Residuals on Slant Wet Delays for Tracking Severe Weather Events

Climate change has increased the frequency and intensity of weather events with heavy precipitation, making communities worldwide more vulnerable to flash flooding. As a result, accurate fore- and nowcasting of impending excessive rainfall is crucial for warning and mitigating these hydro-meteorological hazards. The measurement of integrated water vapour along slant paths is made possible by ground-based global positioning system (GPS) receiver networks, delivering three-dimensional (3D) water vapour distributions at low cost and in real-time. As a result, these data are an invaluable supplementary source of knowledge for monitoring storm events and determining their paths. However, it is generally known that multipath effects at GPS stations have an influence on incoming signals, particularly at low elevations. Although estimates of zenith total delay and horizontal linear gradients make up the majority of the GPS products for meteorology to date, these products are not sufficient for understanding the full 3D distribution of water vapour above a station. Direct utilization of slant delays can address this lack of azimuthal information, although, at low elevations it is more prone to multipath (MP) errors. This study uses the convective storm event that happened on 27 July 2017 over Bulgaria, Greece, and Turkey, which caused flash floods and severe damage, to examine the effects of multipath-corrected slant wet delay (SWD) estimations on monitoring severe weather events. First, we reconstructed the one-way SWD by adding GPS post-fit phase residuals, describing the anisotropic component of the SWD. Because MP errors in the GPS phase observables can considerably impact SWD from individual satellites, we used an averaging technique to build station-specific MP correction maps by stacking the post-fit phase residuals acquired from a precise point positioning (PPP) processing strategy. The stacking was created by spatially organizing the residuals into congruent cells with an optimal resolution in terms of the elevation and azimuth at the local horizon.This enables approximately equal numbers of post-fit residuals to be distributed across each congruent cell. Finally, using these MP correction maps, the one-way SWD was improved for use in the weather event analysis. We found that the anisotropic component of the one-way SWD accounts for up to 20% of the overall SWD estimates. For a station that is strongly influenced by site-specific multipath error, the anisotropic component of SWD can reach up to 4.3 mm in equivalent precipitable water vapour. The result also showed that the spatio-temporal changes in the SWD as measured by GPS closely reflected the moisture field estimated from a numerical weather prediction model (ERA5 reanalysis) associated with this weather event.

Improving the performance of tropospheric mapping function in low elevation angle using artificial neural network

Tropospheric delay is one of the major error sources in global navigation satellite systems (GNSS). The position accuracy determined using GNSS depends on the satellite’s geometry factor. However, in low elevation angle GNSS signals have a high tropospheric slant delay error and need a good mapping function model to cover this error. In this paper, two new tropospheric mapping functions (hydrostatic and non-hydrostatic) were developed based on an artificial neural network (ANN). The first model (Model A) was based on the day of the year (DOY), latitude and longitude. The second model (Model B) added real-time surface pressure to the parameters of Model “A.” The two developed models showed a strong correlation with the ray tracing mapping function, with a significant t-test value.The applicability of these mapping functions was tested over the Egypt region. The comparison was done with ray tracing of 5220 traces for 145 days from 2014 to 2017 as well as by assessing it (Mohamed et al., Vienna and Niell). This evaluation showed that the new model “B” agrees very well with the ray trace value. Model “B” and ray traces are on par with each other for a very low elevation angle 2⁰ the hydrostatic and non-hydrostatic mapping functions. Models “B” and “A” gave hydrostatic mean biases of 32 and 39 mm, respectively, and for non-hydrostatic, 4.5 and 4.9 mm, respectively. Vienna, Niell, and Mohamed et al. gave 46, 45, and 94 mm in hydrostatic, respectively, and 5.4, 5.2 and 9.2 mm in non-hydrostatic, respectively.

PPP-RTK considering the ionosphere uncertainty with cross-validation

With the high-precision products of satellite orbit and clock, uncalibrated phase delay, and the atmosphere delay corrections, Precise Point Positioning (PPP) based on a Real-Time Kinematic (RTK) network is possible to rapidly achieve centimeter-level positioning accuracy. In the ionosphere-weighted PPP–RTK model, not only the a priori value of ionosphere but also its precision affect the convergence and accuracy of positioning. This study proposes a method to determine the precision of the interpolated slant ionospheric delay by cross-validation. The new method takes the high temporal and spatial variation into consideration. A distance-dependent function is built to represent the stochastic model of the slant ionospheric delay derived from each reference station, and an error model is built for each reference station on a five-minute piecewise basis. The user can interpolate ionospheric delay correction and the corresponding precision with an error function related to the distance and time of each reference station. With the European Reference Frame (EUREF) Permanent GNSS (Global Navigation Satellite Systems) network (EPN), and SONEL (Système d'Observation du Niveau des Eaux Littorales) GNSS stations covering most of Europe, the effectiveness of our wide-area ionosphere constraint method for PPP-RTK is validated, compared with the method with a fixed ionosphere precision threshold. It is shown that although the Root Mean Square (RMS) of the interpolated ionosphere error is within 5 cm in most of the areas, it exceeds 10 cm for some areas with sparse reference stations during some periods of time. The convergence time of the 90th percentile is 4.0 and 20.5 min for horizontal and vertical directions using Global Positioning System (GPS) kinematic solution, respectively, with the proposed method. This convergence is faster than those with the fixed ionosphere precision values of 1, 8, and 30 cm. The improvement with respect to the latter three solutions ranges from 10 to 60%. After integrating the Galileo navigation satellite system (Galileo), the convergence time of the 90th percentile for combined kinematic solutions is 2.0 and 9.0 min, with an improvement of 50.0% and 56.1% for horizontal and vertical directions, respectively, compared with the GPS-only solution. The average convergence time of GPS PPP-RTK for horizontal and vertical directions are 2.0 and 5.0 min, and those of GPS + Galileo PPP-RTK are 1.4 and 3.0 min, respectively.

Coupling a weather model directly to GNSS orbit determination – case studies with OpenIFS

Abstract. Neutral gas atmosphere bends and delays propagation of microwave signals in satellite-based navigation. Weather prediction models can be used to estimate these effects by providing three-dimensional refraction fields to ray-trace the signal delays. In this study, a global numerical weather prediction model (Open Integrated Forecasting System (OpenIFS) licensed for Academic use by the European Centre for Medium-Range Weather Forecast) is used to generate the refraction fields. The ray-traced slant delays are supplied as such – in contrast to mapping – for an orbit solver (GROOPS (Gravity Recovery Object Oriented Programming System) software toolkit of Graz University of Technology) which applies the raw observation method. Here we show that such a close coupling is possible without need for major additional modifications in the solver codes. The main finding here is that the adopted approach provides a very good a priori model for the atmospheric effects on navigation signals. We suspect that removal of the intermediate mapping step allows us to take advantage of the local refraction field asymmetries in the GNSS signal processing. Moreover, the direct coupling helps in identifying deficiencies in the slant delay computation because the modeling errors are not convoluted in the mapping procedures. These conclusions appear robust, despite the relatively small data set of raw code and phase observations covering the core network of 66 ground-based stations of the International GNSS Service over 1-month periods in December 2016 and June 2017. More generally, the new configuration enhances our control of geodetic and meteorological aspects of the orbit problem. This is pleasant because we can, for instance, regulate at will the weather model output frequency and increase coverage of spatiotemporal aspects of weather variations. The direct coupling of a weather model in precise GNSS orbit determination presented in this paper provides a unique framework for benefiting even more widely than previously the apparent synergies in space geodesy and meteorology.

TMF: A GNSS Tropospheric Mapping Function for the Asymmetrical Neutral Atmosphere

Tropospheric mapping function plays a vital role in the high precision Global Navigation Satellites Systems (GNSS) data processing for positioning. However, most mapping functions are derived under the assumption that atmospheric refractivity is spherically symmetric. In this paper, the pressure, temperature, and humidity fields of ERA5 data with the highest spatio-temporal resolution available from the European Centre for Medium-range Weather Forecast (ECMWF) were utilized to compute ray-traced delays by the software WHURT. Results reveal the universal asymmetry of the hydrostatic and wet tropospheric delays. To accurately represent these highly variable delays, a new mapping function that depends on elevation and azimuth angles—Tilting Mapping Function (TMF)—was applied. The basic idea is to assume an angle between the tropospheric zenith direction and the geometric zenith direction. Ray-traced delays served as the reference values. TMF coefficients were fitted by Levenberg–Marquardt nonlinear least-squares method. Comparisons demonstrate that the TMF can improve the MF-derived slant delay’s accuracy by 73%, 54% and 29% at the 5° elevation angle, against mapping functions based on the VMF3 concept, without, with a total and separate estimation of gradients, respectively. If all coefficients of a symmetric mapping function are determined together with gradients by a least-square fit at sufficient elevation angles, the accuracy is only 6% lower than TMF. By adopting the b and c coefficients of VMF3, TMF can keep its high accuracy with less computational cost, which could be meaningful for large-scale computing.

Water Vapor Tomography of the Lower Atmosphere from Multiparametric Inversion: the Mt. Etna Volcano Test Case

Space techniques based on GPS and SAR interferometry allow measuring millimetric ground deformations. Achieving such accuracy means removing atmospheric anomalies that frequently affect volcanic areas by modeling the tropospheric delays. Due to the prominent orography and the high spatial and temporal variability of weather conditions, the active volcano Mt. Etna (Italy) is particularly suitable to carry out research aimed at estimating and filtering atmospheric effects on GPS and DInSAR ground deformation measurements. The aim of this work is to improve the accuracy of the ground deformation measurements by modeling the tropospheric delays at Mt. Etna volcano. To this end, data from the monitoring network of 29 GPS permanent stations and MODIS multispectral satellite data series are used to reproduce the tropospheric delays affecting interferograms. A tomography algorithm has been developed to reproduce the wet refractivity field over Mt. Etna in 3D, starting from the slant tropospheric delays calculated by GPS in all the stations of the network. The developed algorithm has been tested on a synthetic atmospheric anomaly. The test confirms the capability of the software to faithfully reconstruct the simulated anomaly. With the aim of applying this algorithm to real cases, we introduce the water vapor content measured by the MODIS instrument on board Terra and Aqua satellites. The use of such data, although limited by cloud cover, provides a two-fold benefit: it improves the tomographic resolution and adds feedback for the GPS wet delay measurements. A cross-comparison between GPS and MODIS water vapor measurements for the first time shows a fair agreement between those indirect measurements on an entire year of data (2015). The tomography algorithm was applied on selected real cases to correct the Sentinel-1 DInSAR interferograms acquired over Mt. Etna during 2015. Indeed, the corrected interferograms show that the differential path delay reaches 0.1 m (i.e. 3 C-band fringes) in ground deformation, demonstrating how the atmospheric anomaly affects precision and reliability of DInSAR space-based techniques. The real cases show that the tomography is often able to capture the atmospheric effect at the large scale and correct interferograms, although in limited areas. Furthermore, the introduction of MODIS data significantly improves by ∼80% voxel resolution at the critical layer (1,000 m). Further improvements will be suitable for monitoring active volcanoes worldwide.

Influence of the inhomogeneous troposphere on GNSS positioning and integer ambiguity resolution

The tropospheric delay is one of many error sources that affect the Global Navigation Satellite System (GNSS) positioning solutions. The widely used troposphere models assume a homogeneous atmosphere so that only the zenith delay needs to be determined and is mapped through an elevation-dependent mapping function. This procedure is to reduce the computational burden and keep the positioning model full-rank. However, this assumption fails for a realistic description of the troposphere, which is always asymmetrical at a certain elevation angle, especially during a weather event when the weather conditions are very complex. These imperfectly modelled tropospheric delays may influence the positioning accuracy and integer ambiguity resolution performance. In this case, this contribution aims to investigate the effects of the model errors due to the asymmetrical troposphere on GNSS estimations. The Numerical Weather Prediction (NWP) model is applied to generate the actual ray-tracing tropospheric delay in Western Europe, and the tropospheric model errors are calculated in a normal weather condition and a weather event condition by comparing the slant delay calculated from the NWP model and the mapping function. Case studies on the same GNSS station are conducted in two weather conditions: a normal troposphere condition and a weather event with heavy rainfall. The results based on the case studies show that the troposphere in the normal weather condition is nearly homogeneous that the azimuthal-dependent discrepancies of the tropospheric delay are less than 1cm at a very low elevation angle; meanwhile, the discrepancies between different azimuthal angles can reach to more than 25cm in the weather event. A single-frequency Single Point Positioning (SPP) model and a Precise Point Positioning (PPP) model that preserves the integer property of ambiguity are chosen for studying the estimation biases caused by the troposphere model errors. It turns out that almost all horizontal positioning biases of SPP and PPP are less than 1cm in the normal weather condition; however, the scales of the horizontal and 3D biases are concentrated in 1 to 10cm in the weather event for these two models. This contribution also contains the study of the actual integer ambiguity resolution success rate in the presence of the tropospheric model errors by applying the Monte Carlo simulation, and the success rates of PPP in the normal weather condition are consistent with the theoretical values calculated with the ideal troposphere which is totally symmetrical. However, the actual success rates in the weather event are extremely low at some epochs due to the tropospheric model errors, which means that wrong fixing may occur since the theoretical values cannot take into account these model errors. Note that the horizontal tropospheric gradients are not involved in the processing, which means that an optimistic performance might be expected if the gradients are considered.

Martian Lander Radio Science Data Calibration for Mars Troposphere

AbstractThe tropospheric propagation effect is one of several sources of error in radio science measurements. Systematically calibrated for the Earth troposphere disturbances, the ranging and Doppler data provided by the Martian landers have not been corrected so far for Mars troposphere effects. These effects were considered negligible because the Mars atmosphere is a hundred times less dense than that of the Earth. The constantly improving lander data accuracy and the challenging science objectives of the InSight‐Rotation and Interior Structure Experiment (RISE) and ExoMars‐2022‐LaRa radio science experiments motivated this work. We propose here a simple model to compute the Mars troposphere errors affecting a radio wave transponded from the surface of Mars. The troposphere zenithal delay is first derived from the surface pressure at the lander location. We use a mapping function to infer the slant delay (range errors) induced by the troposphere of Mars. Being proportional to range rates, the contribution of Mars troposphere to the Doppler measurements is derived from the slant delays. Using our model, an elevation threshold of 15° above the lander is identified, below which the Doppler data should be calibrated for Mars troposphere. When applied to the X‐band Doppler data from Mars surface missions, the model predicts significant Mars troposphere contribution for less than 1% of RISE data, 2% of Opportunity data, and 2.5% of Pathfinder data. Among these tracking passes, some are strongly affected by the troposphere of Mars, with Doppler errors reaching sometimes more than 3 times the nominal noise level (>10 mHz at 60 s integration time).

VMF3o: the Vienna Mapping Functions for optical frequencies

The troposphere is considered as one of the major error sources in space geodetic techniques. Thus, accurate troposphere delay models are essential to provide high-quality products, such as reference frames, satellite orbits, or Earth rotation parameters. In this paper, a new troposphere delay model for satellite laser ranging, the Vienna Mapping Functions 3 for optical frequencies (VMF3o), is introduced. The model parameters are derived from ray-traced delays generated by an in-house ray-tracing software. VMF3o comprises not only zenith delays and mapping functions, but also linear horizontal gradients, which are not part of the standard SLR analysis yet. The model parameters are dedicated to a signal wavelength of 532 nm. Since some SLR stations operate also with other wavelengths, VMF3o provides a correction formula to transform the model parameters to any requested wavelength between 350 and 1064 nm. A test demonstrates that the correction formula approximates slant delays calculated at different wavelengths very accurately. The remaining error for slant delays at a wavelength of 1064 nm adds up to only a few millimetres at 10^{circ } elevation angle. A comparison study of the modelled delays that are derived from VMF3o and ray-traced delays was carried out to examine the quality of the model approach. The remaining differences of modelled and ray-traced delays are expressed as mean absolute error. At 5^{circ } elevation angle, the mean absolute error is only a few millimetres. At 10^{circ } elevation angle, it is at the 1 mm level. The results of the comparison also reveal that introducing linear horizontal gradients reduces the mean absolute error by more than 80% for low elevation angles.

Observing geometry effects on a Global Navigation Satellite System (GNSS)-based water vapor tomography solved by least squares and by compressive sensing

Abstract. In this work, the effect of the observing geometry on the tomographic reconstruction quality of both a regularized least squares (LSQ) approach and a compressive sensing (CS) approach for water vapor tomography is compared based on synthetic Global Navigation Satellite System (GNSS) slant wet delay (SWD) estimates. In this context, the term “observing geometry” mainly refers to the number of GNSS sites situated within a specific study area subdivided into a certain number of volumetric pixels (voxels) and to the number of signal directions available at each GNSS site. The novelties of this research are (1) the comparison of the observing geometry's effects on the tomographic reconstruction accuracy when using LSQ or CS for the solution of the tomographic system and (2) the investigation of the effect of the signal directions' variability on the tomographic reconstruction. The tomographic reconstruction is performed based on synthetic SWD data sets generated, for many samples of various observing geometry settings, based on wet refractivity information from the Weather Research and Forecasting (WRF) model. The validation of the achieved results focuses on a comparison of the refractivity estimates with the input WRF refractivities. The results show that the recommendation of Champollion et al. (2004) to discretize the analyzed study area into voxels with horizontal sizes comparable to the mean GNSS intersite distance represents a good rule of thumb for both LSQ- and CS-based tomography solutions. In addition, this research shows that CS needs a variety of at least 15 signal directions per site in order to estimate the refractivity field more accurately and more precisely than LSQ. Therefore, the use of CS is particularly recommended for water vapor tomography applications for which a high number of multi-GNSS SWD estimates are available.

Performance Evaluation of Troposphere Estimated from Galileo-Only Multi-Frequency Observations

The tropospheric delays estimated from the Global Navigation Satellite System (GNSS) have been proven to be an efficient product for monitoring variations of water vapor, which plays an important role in meteorology applications. The operational GNSS water vapor monitoring system is currently based on the Global Positioning System (GPS) and GLObal NAvigation Satellite System(GLONASS) dual-frequency observations. The Galileo satellite navigation system has been evolving continuously, and on 11 February 2019, the constellation reached 22 active satellites, achieving a capability of standalone Precise Point Positioning (PPP) and tropospheric estimation that is global in scope. This enhancement shows a 37% improvement if the precision of the Galileo-only zenith tropospheric delay, while we may anticipate further benefits in terms of tropospheric gradients and slant delays in the future if an optimal multi-constellation and multi-frequency processing strategy is used. First, we analyze the performance of the multi-frequency troposphere estimates based on the PPP raw observation model by comparing it with the standard ionosphere-free model. The performance of the Galileo-only tropospheric solution is then validated with respect to GPS-only solution using 48 globally distributed Multi-GNSS Experiment (MGEX) stations. The averaged bias and standard deviations are −0.3 and 5.8 mm when only using GPS satellites, respectively, and 0.0 and 6.2 mm for Galileo, respectively, when compared to the International GNSS Service (IGS) final Zenith Troposphere Delay(ZTD) products. Using receiver antenna phase center corrections from the corresponding GPS dual-frequency observations does not affect the Galileo PPP ambiguity float troposphere solutions. These results demonstrate a comparable precision achieved for both Galileo-only and GPS-only ZTD solutions, however, horizontal tropospheric gradients, estimated from standalone GPS and Galileo solutions, still show larger discrepancies, mainly due to their being less Galileo satellites than GPS satellites. Including Galileo E1, E5a, E5b, and E5 signals, along with their proper observation weighting, show the benefit of multi-frequency observations, further improving the ZTD precision by 4% when compared to the dual-frequency raw observation model. Overall, the presented results demonstrate good prospects for the application of multi-frequency Galileo observations for the tropospheric parameter estimates.

On the Study of Influences of Different Factors on the Rapid Tropospheric Tomography

A rapid tropospheric tomography system was developed by using algebraicreconstruction technique. Influences of different factors on the tomographic results, including theground meteorological data, the multi-Global Navigation Satellite System (GNSS) observations, theground station distribution and the tomographic horizontal resolution, were systematicallyinvestigated. In order to exclude the impacts from discrepancies of water vapor informationbetween input observations and references on the tomographic results, the latest reanalysisproducts, ERA5, which were taken as references for result evaluations, were used to simulate slantwet delay (SWD) observations at GNSS stations. Besides, the slant delays derived from GNSSprocessing were also used to evaluate the reliability of simulated observations. Tomography resultsshow that the input both SWD and ground meteorological data could improve the tomographicresults where SWD mainly improve the results at middle layers (500 to 5000m, namely 2 to 16 layer)and ground meteorological data could improve the humidity fields at bottom layers further (0 to500m, namely 0 to 2 layer). Compared to the usage of Global Positioning System (GPS) only SWD,the inclusion of multi-GNSS SWD does not significantly improve the tomographic results at alllayers due to the almost unchanged dispersion of puncture points of GNSS signals. However,increases in the ground GNSS stations can benefit the tomography, with improvements of morethan 10% at bottom and middle layers. Higher tomographic horizontal resolution can furtherslightly improve the tomographic results (about 3-6% from 0.5 to 0.25 degrees), which, however,will also increase the computational burden at the same time.

Corrections of BDS Code Multipath Error in Geostationary Orbit Satellite and Their Application in Precise Data Processing.

Multipath error is a main error source in Global Navigation Satellite System (GNSS) data processing, which cannot be removed by a differential technique because of the strong relationship with the environment around the station. The multipath effect of the code observables is more complex than that of the carrier-phase observables, especially for BeiDou Navigation Satellite System (BDS) geostationary orbit (GEO) satellites. In this contribution, we deeply analyzed the characteristic and effect on the precise data processing of GEO satellite multipath errors based on a large number of permanent GNSS stations. A linear combination of code and carrier-phase observables was used to analyze the characteristics of repeatability for BDS GEO’s multipath. Then, a correction method was proposed to eliminate the multipath error of the GEO code observables, based on wavelet transform. The experiment data were collected at 83 globally distributed stations, from multi-GNSS experiments and national BDS augmentation systems, from days 32 to 66 in 2017. The results show that the systematic multipath variation component of the GEO code observables can be obtained with wavelet transform, which can significantly contribute to correcting the multipath error of GEO satellites. The average root mean square error (RMSE) of the multipath series is decreased by approximately 19.5%, 20.2%, and 7.5% for B1, B2, and B3, respectively. In addition, some experiments, including ionospheric delay extraction and satellite clock estimation, were conducted in simulated real-time mode in order to validate the effect of the correction methods. For the ionospheric delay estimation, the average RMSE of the slant ionospheric delay is reduced by approximately 15.5%. Moreover, the multipath correction can contribute greatly to shortening the convergence time of the satellite clock estimation of the BDS GEO satellites.

A New Method for converting Slant Ionospheric Delays to Vertical for SBAS Ionospheric corrections

SBAS gives ionospheric correction data to GNSS users for more accurate positioning. SBAS uses obliquity factor of thin shell model to convert slant ionospheric delays to vertical delays which is not precise especially at lower elevation angle. This paper suggests a new method for estimating the vertical delays which are needed for generating the ionospheric corrections. The new method uses Chapman profile assumption by which the vertical electron density distribution can be modeled. It is also assumed that Chapman profile’s parameters are given and the vertical ionospheric delay can be linearly modeled. We divided ionosphere into multi-layer and mapped ionospheric vertical delays with a linear function. Converting vertical delays of each layer to slant delays, we can set a linear equation for the vertical ionospheric delay at IPP. We used IRI model to get information about ionosphere for simulation to verify our new method. Estimation error of vertical ionospheric delay at IPP was decreased about 40% in average when using our new method.

Assessment of ionospheric corrections for PPP-RTK using regional ionosphere modelling

This paper presents an analysis of the ionospheric corrections required to get a significant improvement in PPP-RTK performance. The main aim was to determine the improvement in the position precision and time-to-first-fix in the PPP-RTK user side using ionospheric corrections computed from a network. The study consists of two main steps. The first one includes an empirical investigation of the ionosphere model precision necessary to greatly improve the PPP-RTK performance in a simulated environment in terms of precision and convergence time. In the second one, an optimal ionosphere representation was developed to provide precise ionospheric corrections by parameterizing the ionospheric slant delays after the PPP-RTK network processing in terms of ionosphere model coefficients and differential code biases using real GNSS measurements. Experimental results demonstrate that the proposed methodology can be used for reliable regional ionosphere modeling and satellite code bias estimation, due to the consistency of the satellite code bias estimates with those provided from the International GNSS Service Analysis Centres, the high stability of the estimated receiver and satellite code biases and the low least-squares residuals of the network-based ionosphere modeling solution. Finally, it has been shown that the precision of ionospheric corrections at zenith needs to be better than 5 cm to enable faster PPP-RTK solutions.

The Effects of Higher-Order Ionospheric Terms on GPS Tropospheric Delay and Gradient Estimates

Atmospheric delays, e.g., ionospheric delay and tropospheric delay, are the dominant error sources for the Global Navigation Satellite System (GNSS), especially for Precise Point Positioning (PPP). The common method for eliminating ionospheric delay is to form an ionosphere-free (IF) observable, which is a linear combination of observables on two frequencies such as GPS L1 and L2. As for the tropospheric delay, the dry component can be precisely corrected by empirical models, while the wet component is usually estimated as unknowns. However, the higher-order ionospheric (HOI) terms are not totally cancelled out in the (first-order) IF observable and as such, when not accounted for, they degrade the accuracy of other parameters. The impact of HOI corrections is well documented in the literature. This paper investigates the temporal effects of HOI terms on estimated tropospheric parameters, i.e., zenith tropospheric wet delay (ZWD) and north and east gradients. For this purpose, observations from over 100 stations with good global coverage were used considering various geographic and geophysical conditions. The results of numerical experiments show that HOI effects have a significant impact on the estimated tropospheric parameters, and the influence is dependent on location and time. The maximum differences of ZWD estimates reach over 20 mm during periods of activity such as solar storms and geomagnetic storms. Additionally, the north gradients are more likely to be affected by HOI effects compared with east gradients. In particular, the tropospheric gradient component is most affected for low latitude station during daytime. Additionally, the effects of bending errors and HOI terms on slant tropospheric delay at low elevation angles are much larger than those at high elevation angles.

An improved atmospheric correction method in repeat-pass InSAR measurements

ABSTRACTAs is well known, the problem of atmospheric phase delays is currently one of the major limitations to high precision repeat-pass interferometric synthetic aperture radar (InSAR) applications. Therefore, accurately mitigating atmospheric phase delays is a key but unresolved problem. In recent decades, many researchers have attempted to mitigate the atmospheric phase delays. A typical method is to calculate the atmospheric phase along radar line of sight direction using precipitable water vapour products. However, this method completely neglects the atmospheric turbulence and heterogeneity in the horizontal direction when the zenith wet delays are converted to slant wet delays, reducing the accuracy of the approach. In this article, we systematically analysed the atmospheric turbulence and heterogeneity in the horizontal direction as well as the vertical stratification of water vapour in the troposphere. From this analysis, we found that the atmospheric turbulence and heterogeneity in the horizontal direction cannot be neglected in estimating atmospheric phase delays. Moreover, the vertical stratification of water vapour and the satellite orbit azimuth can be integrated into the calculation of slant phase delays. We therefore propose an improved atmospheric correction method in repeat-pass InSAR measurements, weighted-sampling radiometer correction. The proposed method was applied to the investigation of ground subsidence in an area of Beijing, China to validate its feasibility and accuracy. The results illustrate that atmospheric phase delays and ground subsidence information can be retrieved more accurately using the proposed method than was obtained using the conventional method.

New Adaptable All-in-One Strategy for Estimating Advanced Tropospheric Parameters and Using Real-Time Orbits and Clocks

We developed a new strategy for a synchronous generation of real-time (RT) and near real-time (NRT) tropospheric products. It exploits the precise point positioning method with Kalman filtering and backward smoothing, both supported by real-time orbit and clock products. The strategy can be optimized for the latency or the accuracy of NRT production. In terms of precision, it is comparable to the traditional NRT network solution using deterministic models in the least-square adjustment. Both RT and NRT solutions provide a consistent set of tropospheric parameters such as zenith total delays, horizontal tropospheric gradients and slant delays, all with a high resolution and optimally exploiting all observations from available GNSS multi-constellations. As the new strategy exploits RT processing, we assessed publicly precise RT products and results of RT troposphere monitoring. The backward smoothing applied for NRT solution, when using an optimal latency of 30 min, reached an improvement of 20% when compared to RT products. Additionally, multi-GNSS solutions provided more accurate (by 25%) tropospheric parameters, and the impact will further increase when constellations are complete and supported with precise models and products. The new strategy is ready to replace our NRT contribution to the EUMETNET EIG GNSS Water Vapour Programme (E-GVAP) and effectively support all modern multi-GNSS tropospheric products.

Study the Effect of New Egypt Wet Mapping Function on Space Geodetic Measurements

Atmospheric water vapour degrades the accuracy of the results of space geodetic observations due to permanent electric dipole moments. It creates excess path lengths by retarding (slowing and bending) the propagation of the electromagnetic waves that are used in global positioning system (GPS) and very long baseline interferometry (VLBI) observations. It is known that the excess path lengths are less than 30~40 cm at the most, and are the primary obstacles of space geodesy because of the highly variable distribution of water vapour in the atmosphere. In this study, we compared modern five wet mapping functions by evaluating their effects on the tropospheric signal delay and position estimates in GPS data processing, and precise Egypt wet mapping function model is derived based on eight stations of radiosonde data well-distributed over and around Egypt (five stations used to estimate new model and other three as check points). To derive the new Egypt wet mapping function, the troposphere is divided into regular small layers. Ray tracing technique of actual signal path traveled in the troposphere is used to estimate tropospheric slant delay. Real GPS data of five stations (RTK-Network methods) were used for the assessment of new model against the available international models. These international models include Niell (NMF), Black & Eisner (B&EMF), Ifidas (IFMF), Hearing (HMF), and UNBabc MF. The data were processed using Bernese software version 5.0. The results indicate that the new Egypt wet MF model is the best model at Egypt region and has improved the wet tropospheric delay estimation up to 23.3 percent at five degree elevation angles.