GNSS Storm Nowcasting Demonstrator for Bulgaria

Global Navigation Satellite System (GNSS) is an established atmospheric monitoring technique delivering water vapour data in near-real time with a latency of 90 min for operational Numerical Weather Prediction in Europe within the GNSS water vapour service (E-GVAP). The advancement of GNSS processing made the quality of real-time GNSS tropospheric products comparable to near-real-time solutions. In addition, they can be provided with a temporal resolution of 5 min and latency of 10 min, suitable for severe weather nowcasting. This paper exploits the added value of sub-hourly real-time GNSS tropospheric products for the nowcasting of convective storms in Bulgaria. A convective Storm Demonstrator (Storm Demo) is build using real-time GNSS tropospheric products and Instability Indices to derive site-specific threshold values in support of public weather and hail suppression services. The Storm Demo targets the development of service featuring GNSS products for two regions with hail suppression operations in Bulgaria, where thunderstorms and hail events occur between May and September, with a peak in July. The Storm Demo real-time Precise Point Positioning processing is conducted with the G-Nut software with a temporal resolution of 15 min for 12 ground-based GNSS stations in Bulgaria. Real-time data evaluation is done using reprocessed products and the achieved precision is below 9 mm, which is within the nowcasting requirements of the World Meteorologic Organisation. For the period May–September 2021, the seasonal classification function for thunderstorm nowcasting is computed and evaluated. The probability of thunderstorm detection is 83%, with a false alarm ration of 38%. The added value of the high temporal resolution of the GNSS tropospheric gradients is investigated for a storm case on 24–30 August 2021. Real-time tropospheric products and classification functions are integrated and updated in real-time on a publicly accessible geoportal.

Multi-GNSS-Weighted Interpolated Tropospheric Delay to Improve Long-Baseline RTK Positioning

Until now, RTK (real-time kinematic) and NRTK (Network-based RTK) have been the most popular cm-level accurate positioning approaches based on Global Navigation Satellite System (GNSS) signals in real-time. The tropospheric delay is a major source of RTK errors, especially for medium and long baselines. This source of error is difficult to quantify due to its reliance on highly variable atmospheric humidity. In this paper, we use the NRTK approach to estimate double-differenced zenith tropospheric delays alongside ambiguities and positions based on a complete set of multi-GNSS data in a sample 6-station network in Europe. The ZTD files published by IGS were used to validate the estimated ZTDs. The results confirmed a good agreement, with an average Root Mean Squares Error (RMSE) of about 12 mm. Although multiplying the unknowns makes the mathematical model less reliable in correctly fixing integer ambiguities, adding a priori interpolated ZTD as quasi-observations can improve positioning accuracy and Integer Ambiguity Resolution (IAR) performance. In this work, weighted least-squares (WLS) were performed using the interpolation of ZTD values of near reference stations of the IGS network. When using a well-known Kriging interpolation, the weights depend on the semivariogram, and a higher network density is required to obtain the correct covariance function. Hence, we used a simple interpolation strategy, which minimized the impact of altitude variability within the network. Compared to standard RTK where ZTD is assumed to be unknown, this technique improves the positioning accuracy by about 50%. It also increased the success rate for IAR by nearly 1.

Comprehensive Study on the Tropospheric Wet Delay and Horizontal Gradients during a Severe Weather Event

GNSS meteorology is today one of the most growing technologies to monitor severe weather events. In this paper, we present the usage of 160 GPS reference stations over the period of 14 days to monitor and track Hurricane Harvey, which struck Texas in August 2017. We estimate the Zenith Wet Delay (ZWD) and the tropospheric gradients with 30 s interval using TOMION v2 software and carry out the processing in Precise Point Positioning (PPP) mode. We study the relationship of these parameters with atmospheric variables extracted from Tropical Rainfall Measuring Mission (TRMM) satellite mission and climate reanalysis model ERA5. This research finds that the ZWD shows patterns related to the rainfall rate and to the location of the hurricane. We also find that the tropospheric gradients are correlated with water vapor gradients before and after the hurricane, and with the wind and the pressure gradients only after the hurricane. This study also shows a new finding regarding the spectral distribution of the gradients, with a clear diurnal period present, which is also found on the ZWD itself. This kind of study approaches the GNSS meteorology to the increasing requirements of meteorologist in terms of monitoring severe weather events.

Understanding the Present-Day Spatiotemporal Variability of Precipitable Water Vapor over Ethiopia: A Comparative Study between ERA5 and GPS

Atmospheric water vapor plays a crucial role in atmospheric, climate change, meteorological, and hydrological processes. In a country like Ethiopia, with its complex topography and synoptic-scale spatiotemporal circulation patterns, the analysis of the spatiotemporal variability of precipitable water vapor (PWV) is very challenging, and is hampered by the lack of long observational datasets. In this study, we process the PWV over eight Ethiopian global positioning system (GPS) sites and one close to the Ethiopian eastern border, for the available common period 2013–2020, and compare with the PWV retrieved from the state-of-the-art ERA5 reanalysis. Both PWV datasets agree very well at our sample, with correlation coefficients between 0.96 and 0.99, GPS-PWV show a moderate wet bias compared to ERA5-PWV for the majority of the sites, and an overall root mean square error of 3.4 mm. Seasonal and diurnal cycles are also well captured by these datasets. The seasonal variations of PWV and precipitation at the sites agree very well. Maximum diurnal PWV amplitudes are observed for stations near water bodies or dense vegetation, such as Arbaminch (ARMI) and Bahir Dar (BDMT). At those stations, the PWV behavior at heavy rainfall events has been investigated and an average 25% increase (resp. decrease) from 12 h before (resp. 12 h after) the start of the rainfall event, when the PWV peaks, has been observed.

Interannual Variability of the GNSS Precipitable Water Vapor in the Global Tropics

This paper addresses the subject of inter-annual variability of the tropical precipitable water vapor (PWV) derived from 18 years of global navigation satellite system (GNSS) observations. Non-linear trends of retrieved GNSS PWV were investigated using the singular spectrum analysis (SSA) along with various climate indices. For most of the analyzed stations (~49%) the GNSS PWV anomaly was related to the El Niño Southern Oscillation (ENSO), although its influence on the PWV variability was not homogeneous. The cross-correlations coefficient values estimated between the Multivariate ENSO Index (MEI) and PWV were up to 0.78. A strong cross-correlation was also found for regional climate pattern expressed through CAR, DMI, HAW, NPGO, TNA and TSA indices. A distinct agreement was also found when instead of climate indices, the local sea surface temperature was examined (average correlation 0.60). The SSA method made it also possible to distinguish small-scale phenomena that affect PWV, such as local droughts or wetter rainy seasons. The overall nature of the investigated changes was also verified through linear trend analysis. In general, not a single station was characterized by a negative trend and its weighted mean value, calculated for all stations was equal to 0.08 ± 0.01 mm/year.

VLBI measurement of the vector baseline between geodetic antennas at Kokee Park Geophysical Observatory, Hawaii

We measured the components of the 31-m-long vector between the two very-long-baseline interferometry (VLBI) antennas at the Kokee Park Geophysical Observatory (KPGO), Hawaii, with approximately 1 mm precision using phase delay observables from dedicated VLBI observations in 2016 and 2018. The two KPGO antennas are the 20 m legacy VLBI antenna and the 12 m VLBI Global Observing System (VGOS) antenna. Independent estimates of the vector between the two antennas were obtained by the National Geodetic Survey (NGS) using standard optical surveys in 2015 and 2018. The uncertainties of the latter survey were 0.3 and 0.7 mm in the horizontal and vertical components of the baseline, respectively. We applied corrections to the measured positions for the varying thermal deformation of the antennas on the different days of the VLBI and survey measurements, which can amount to 1 mm, bringing all results to a common reference temperature. The difference between the VLBI and survey results are 0.2 ± 0.4 mm, -1.3 ± 0.4 mm, and 0.8 ± 0.8 mm in the East, North, and Up topocentric components, respectively. We also estimate that the Up component of the baseline may suffer from systematic errors due to gravitational deformation and uncalibrated instrumental delay variations at the 20 m antenna that may reach ± 10 and -2 mm, respectively, resulting in an accuracy uncertainty on the order of 10 mm for the relative heights of the antennas. Furthermore, possible tilting of the 12 m antenna increases the uncertainties in the differences in the horizontal components to 1.0 mm. These results bring into focus the importance of (1) correcting to a common reference temperature the measurements of the reference points of all geodetic instruments within a site, (2) obtaining measurements of the gravitational deformation of all antennas, and (3) monitoring local motions of the geodetic instruments. These results have significant implications for the accuracy of global reference frames that require accurate local ties between geodetic instruments, such as the International Terrestrial Reference Frame (ITRF).

GNSS-Based Machine Learning Storm Nowcasting

Nowcasting of severe weather events and summer storms, in particular, are intensively studied as they have great potential for large economic and societal losses. Use of Global Navigation Satellite Systems (GNSS) observations for weather nowcasting has been investigated in various regions. However, combining the vertically integrated water vapour (IWV) with vertical profiles of wet refractivity derived from GNSS tomography has not been exploited for short-range forecasts of storms. In this study, we introduce a methodology to use the synergy of IWV and tomography-based vertical profiles to predict 0–2 h of storms using a machine learning approach for Poland. Moreover, we present an analysis of the importance of features that take part in the prediction process. The accuracy of the model reached over 87%, and the precision of prediction was about 30%. The results show that wet refractivity below 6 km and IWV on the west of the storm are among the significant parameters with potential for predicting storm location. The analysis of IWV demonstrated a correlation between IWV changes and storm occurrence.

Precipitable Water Vapor Retrieval from Shipborne GNSS Observations on the Korean Research Vessel ISABU

We estimate precipitable water vapor (PWV) from data collected by the low-cost Global Navigation Satellite System (GNSS) receiver at a vessel. The dual-frequency GNSS receiver that the vessel ISABU is equipped with that is operated by the Korea Institute of Ocean Science and Technology. The ISABU served in the Pacific Ocean for scientific research during a period from August 30 to September 21, 2018. It also performs radiosonde observations to obtain a vertical profile of troposphere on the vessel’s path. The GNSS-derived PWV is compared to radiosonde observations and the Atmospheric Infrared Sounder (AIRS) on NASA’s Aqua satellite output. A bias and root-mean-square (RMS) error between shipborne GNSS-PWV and radiosonde-PWV were −1.48 and 5.22 mm, respectively. When compared to the ground GNSS-PWV, shipborne GNSS-PWV has a relatively large RMS error in comparison with radiosonde-PWV. However, the GNSS observations on the vessel are still in good agreement with radiosonde observations. On the other hand, the GNSS-PWV is not well linearly correlated with AIRS-PWV. The RMS error between the two observations was approximately 8.97 mm. In addition, we showed that the vessel on the sea surface has significantly larger carrier phase multipath error compared to the ground-based GNSS observations. This also can result in reducing the accuracy of shipborne GNSS-PWV. However, we suggest that the shipborne GNSS has sufficient potential to derive PWV with the kinematic precise point positioning (PPP) solution on the vessel.

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 ∘ 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 ∘ elevation angle, the mean absolute error is only a few millimetres. At 10 ∘ 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.

A Tropospheric Tomography Method with a Novel Height Factor Model Including Two Parts: Isotropic and Anisotropic Height Factors

Global Navigation Satellite System (GNSS) tomography has developed into an efficient tool for sensing the high spatiotemporal variability of atmospheric water vapor. The integration of GNSS top signals and side rays for tropospheric tomography systems using a novel height factor model (HFM) is proposed and discussed in this paper. Within the HFM, the sectional slant wet delay (SWD) of inside signals (the part of the side signal inside the tomography area), which is considered a key factor for modeling side rays, is separated into isotropic and anisotropic components. Correspondingly, two height factors are defined to calculate the isotropic and anisotropic part of tropospheric delays in the HFM. In addition, the dynamic tomography top boundary is first analyzed and determined based on 30-year radiosonde data to reasonably divide signals into top and side rays. Four special experimental schemes based on different tomography regions of Hong Kong are performed to assess the proposed HFM method, the results of which show increases of 33.42% in the mean utilization of rays, as well as decreases of 0.46 g/m3 in the average root mean square error (RMSE), compared to the traditional approach, revealing the improvement of tomography solutions when the side signals are included in the modeling. Furthermore, compared with the existing correction model for modeling side rays, the water vapor profiles retrieved from the proposed improved model are closer to the radiosonde data, which highlights the advantages of the proposed HFM for optimizing the GNSS tomography model.

Precise Point Positioning on the Reliable Detection of Tropospheric Model Errors

Precise point positioning (PPP) is one of the well-known applications of Global Navigation Satellite System (GNSS) and provides precise positioning solutions using accurate satellite orbit and clock products. The tropospheric delay due to the neutral atmosphere for microwave signals is one of the main sources of measurement error in PPP. As one component of this delay, the hydrostatic delay is usually compensated by using an empirical correction model. However, how to eliminate the effects of the wet delay during a weather event is a challenge because current troposphere models are not capable of considering the complex atmosphere around the receiver during situations such as typhoons, storms, heavy rainfall, et cetera. Thus, how positioning results can be improved if the residual wet delays are taken into account needs to be investigated . In this contribution, a real-time procedure of recursive detection, identification and adaptation (DIA) is applied to detect the model errors which have the same effects on both phase and code observables; e.g., the model error caused by the tropospheric delay. Once the model errors are identified, additional parameters are added to the functional model to account for the measurement residuals. This approach is evaluated with Global Positioning System (GPS) data during two rainfall events in Darwin, Australia, proving the usefulness of compensated residual slant wet delay for positioning results. Comparisons with the standard approach show that the precision of the up component is improved significantly during the periods of the weather events; for the two case studies, 72.46% and 64.41% improvements of root mean squared error (RMS) resulted, and the precision of the horizontal component obtained by the proposed approach is also improved more than 30% compared to the standard approach. The results also show that the identified model errors are concentrated at the beginning of both heavy rainfall processes when the front causes significant spatial and temporal gradients of the integrated water vapor above the receiver.

The Performance of Different Mapping Functions and Gradient Models in the Determination of Slant Tropospheric Delay

Global navigation satellite systems (GNSSs) have become an important tool for remotely sensing water vapor in the atmosphere. In GNSS data processing, mapping functions and gradient models are needed to map the zenith tropospheric delay (ZTD) to the slant total tropospheric delay (STD) along a signal path. Therefore, it is essential to investigate the spatial–temporal performance of various mapping functions and gradient models in the determination of STD. In this study, the STDs at nine elevations were first calculated by applying the ray-tracing method to the atmospheric European Reanalysis-Interim (ERA—Interim) dataset. These STDs were then used as the reference to study the accuracy of the STDs that determined the ZTD together with mapping functions and gradient models. The performance of three mapping functions (i.e., Niell mapping function (NMF), global mapping function (GMF), and Vienna mapping function (VMF1)) and three gradient models (i.e., Chen, MacMillan, and Meindl) in six regions (the temperate zone, Qinghai–Tibet Plateau, Equator, Sahara Desert, Amazon Rainforest, and North Pole) in determining slant tropospheric delay was investigated in this study. The results indicate that the three mapping functions have relatively similar performance above a 15° elevation, but below a 15° elevation, VMF1 clearly performed better than the GMF and NMF. The results also show that, if no gradient model is included, the root-mean-square (RMS) of the STD is smaller than 2 mm above the 30° elevation and smaller than 9 mm above the 15° elevation but shows a significant increase below the 15° elevation. For example, in the temperate zone, the RMS increases from approximately 35 mm at the 10° elevation to approximately 160 mm at the 3° elevation. The inclusion of gradient models can significantly improve the accuracy of STDs by 50%. All three gradient models performed similarly at all elevations and in all regions. The bending effect was also investigated, and the results indicate that the tropospheric delay caused by the bending effect is normally below 13 mm above a 15° elevation, but this delay increases dramatically from approximately 40 mm at a 10° elevation to approximately 200 mm at a 5° elevation, and even reaches 500–700 mm at a 3° elevation in most studied regions.

Cross-Comparison and Methodological Improvement in GPS Tomography

GPS tomography has been investigated since 2000 as an attractive tool for retrieving the 3D field of water vapour and wet refractivity. However, this observational technique still remains a challenging task that requires improvement of its methodology. This was the purpose of this study, and for this, GPS data from the Australian Continuously Operating Research Station (CORS) network during a severe weather event were used. Sensitivity tests and statistical cross-comparisons of tomography retrievals with independent observations from radiosonde and radio-occultation profiles showed improved results using the presented methodology. The initial conditions, which were associated with different time-convergence of tomography inversion, play a critical role in GPS tomography. The best strategy can reduce the normalised root mean square (RMS) of the tomography solution by more than 3 with respect to radiosonde estimates. Data stacking and pseudo-slant observations can also significantly improve tomography retrievals with respect to non-stacked solutions. A normalised RMS improvement up to 17% in the 0–8 km layer was found by using 30 min data stacking, and RMS values were divided by 5 for all the layers by using pseudo-observations. This result was due to a better geometrical distribution of mid- and low-tropospheric parts (a 30% coverage improvement). Our study of the impact of the uncertainty of GPS observations shows that there is an interest in evaluating tomography retrievals in comparison to independent external measurements and in estimating simultaneously the quality of weather forecasts. Finally, a comparison of multi-model tomography with numerical weather prediction shows the relevant use of tomography retrievals to improving the understanding of such severe weather conditions.

Impact of ECOM Solar Radiation Pressure Models on Multi-GNSS Ultra-Rapid Orbit Determination

The Global Navigation Satellite System (GNSS) ultra-rapid precise orbits are crucial for global and wide-area real-time high-precision applications. The solar radiation pressure (SRP) model is an important factor in precise orbit determination. The real-time orbit determination is generally less accurate than the post-processed one and may amplify the instability and mismodeling of SRP models. Also, the impact of different SRP models on multi-GNSS real-time predicted orbits demands investigations. We analyzed the impact of the ECOM 1 and ECOM 2 models on multi-GNSS ultra-rapid orbit determination in terms of ambiguity resolution performance, real-time predicted orbit overlap precision, and satellite laser ranging (SLR) validation. The multi-GNSS observed orbital arc and predicted orbital arcs of 1, 3, 6, and 24 h are compared. The simulated real-time experiment shows that for GLONASS and Galileo ultra-rapid orbits, compared to ECOM 1, ECOM 2 increased the ambiguity fixing rate to 89.3% and 83.1%, respectively, and improves the predicted orbit accuracy by 9.2% and 27.7%, respectively. For GPS ultra-rapid orbits, ECOM 2 obtains a similar ambiguity fixing rate as ECOM 1 but slightly better orbit overlap precision. For BDS GEO ultra-rapid orbits, ECOM 2 obtains better overlap precision and SLR residuals, while for BDS IGSO and MEO ultra-rapid orbits, ECOM 1 obtains better orbit overlap precision and SLR residuals.

PPP and PPP-AR Kinematic Post-Processed Performance of GPS-Only, Galileo-Only and Multi-GNSS

Precise point positioning (PPP) has been used for decades not only for general positioning needs but also for geodetic and other scientific applications. The CNES-CLS Analysis Centre (AC) of the International GNSS Service (IGS) is performing PPP with phase ambiguity resolution (PPP-AR) using the zero-difference ambiguity fixing approach also known as “Integer PPP” (IPPP). In this paper we examine the postprocessed kinematic PPP and PPP-AR using Galileo-only, GPS-only and Multi-GNSS (GPS + Galileo) constellations. The interest is to examine the accuracy for each GNSS system individually but also of their combination to measure the current benefits of using Galileo within a Multi-GNSS PPP and PPP-AR. Results show that Galileo-only positioning is nearly at the same level as GPS-only; around 2–4 mm horizontal and aound 10 mm vertical repeatability (example station of BRUX). In addition, the use of Galileo system—even uncompleted—improves the performance of the positioning when combined with GPS giving mm level repeatability (improvement of around 30% in East, North and Up components). Repeatabilities observed for Multi-GNSS (GPS + GAL) PPP-AR, taking into account the global network statistics, are a little larger, with 8 mm in horizontal and 17 mm in vertical directions. This result shows that including Galileo ameliorates the best positioning accuracy achieved until today with GPS PPP-AR.

Accurate and Rapid Broadcast Ephemerides for Beidou-Maneuvered Satellites

The geostationary earth orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites of the Beidou navigation satellite system are maneuvered frequently. The broadcast ephemeris can be interrupted for several hours after the maneuver. The orbit-only signal-in-space ranging errors (SISREs) of broadcast ephemerides available after the interruption are over two times larger than the errors during normal periods. To shorten the interruption period and improve the ephemeris accuracy, we propose a two-step orbit recovery strategy based on a piecewise linear thrust model. The turning points of the thrust model are firstly determined by comparison of the kinematic orbit with an integrated orbit free from maneuver; afterward, precise orbit determination (POD) is conducted for the maneuvered satellite by estimating satellite orbital and thrust parameters simultaneously. The observations from the IGS Multi-Global Navigation Satellite System (GNSS) Experiment (MGEX) network and ultra-rapid products of the German Research Center for Geosciences (GFZ) are used for orbit determination of maneuvered satellites from Sep to Nov 2017. The results show that for the rapidly recovered ephemerides, the average orbit-only SISREs are 1.15 and 1.0 m 1 h after maneuvering for GEO and IGSO respectively, which is comparable to the accuracy of Beidou broadcast ephemerides in normal cases.

Improving GNSS Zenith Wet Delay Interpolation by Utilizing Tropospheric Gradients: Experiments with a Dense Station Network in Central Europe in the Warm Season

The Benchmark data set collected within the European COST Action ES1206 has aimed to support the development and validation of advanced Global Navigation Satellite System (GNSS) tropospheric products, in particular high-resolution zenith delays and tropospheric gradients. In this work we utilize this unique data set to show that the interpolation of GNSS Zenith Wet Delays (ZWDs) can be improved by utilizing tropospheric gradients. To do this we first prove the concept with simulated observations, that is, zenith delays and tropospheric gradients derived from a Numerical Weather Model. We show how tropospheric gradients can be converted to ZWD gradients. Then the ZWD gradients together with the ZWDs at selected reference stations are used in an inverse distance weighting interpolation scheme to estimate the ZWD at some target station. For a station configuration with an average station distance of 50 km in Germany and a period of two months (May and June 2013), we find an improvement of 20% in interpolated ZWDs when tropospheric gradients are taken into account. Next, we replace the simulated by real observations, that is, zenith delays and tropospheric gradients from a Precise Point Positioning (PPP) solution provided with the G-Nut/Tefnut analysis software. Here we find an improvement of 10% in interpolated ZWDs when tropospheric gradients are taken into account.

Estimating the Impact of Global Navigation Satellite System Horizontal Delay Gradients in Variational Data Assimilation

We developed operators to assimilate Global Navigation Satellite System (GNSS) Zenith Total Delays (ZTDs) and horizontal delay gradients into a numerical weather model. In this study we experiment with refractivity fields derived from the Global Forecast System (GFS) available with a horizontal resolution of 0.5°. We begin our investigations with simulated observations. In essence, we extract the tropospheric parameters from the GFS analysis, add noise to mimic observation errors and assimilate the simulated observations into the GFS 24h forecast valid at the same time. We consider three scenarios: (1) the assimilation of ZTDs (2) the assimilation of horizontal delay gradients and (3) the assimilation of both ZTDs and horizontal delay gradients. The impact is measured by utilizing the refractivity fields. We find that the assimilation of the horizontal delay gradients in addition to the ZTDs improves the refractivity field around 800 hPa. When we consider a single station there is a clear improvement when horizontal delay gradients are assimilated in addition to the ZTDs because the horizontal delay gradients contain information that is not contained in the ZTDs. On the other hand, when we consider a dense station network there is not a significant improvement when horizontal delay gradients are assimilated in addition to the ZTDs because the horizontal delay gradients do not contain information that is not already contained in the ZTDs. Finally, we replace simulated by real observations, that is, tropospheric parameters from a Precise Point Positioning solution provided with the G-Nut/Tefnut software, in order to show that the GFS 24h forecast is indeed improved when GNSS horizontal delay gradients are assimilated in addition to GNSS ZTDs; for the considered station (Potsdam, Germany) and period (June and July, 2017) we find an improvement in the retrieved refractivity of up to 4%.

Residuals of Tropospheric Delays from GNSS Data and Ray-Tracing as a Potential Indicator of Rain and Clouds

The Global Navigation Satellite System (GNSS) is commonly recognized by its all-weather capability. However, observations depend on atmospheric conditions which requires the induced tropospheric delay to be estimated as an unknown parameter. In the following study, we investigate the impact of intense weather events on GNSS estimates. GNSS slant total delays (STD) in Precise Point Positioning technique (PPP) strategy were calculated for stations in southwest Poland in a 56 days period covering several heavy precipitation cases. The corresponding delays retrieved from Weather Research and Forecasting (WRF) model by a ray-tracing technique considered only gaseous parts of the atmosphere. The discrepancies are correlated with rain rates and cloud type products from remote sensing platforms. Positive correlation is found as well as GNSS estimates tend to be systematically larger than modeled delays. Mean differences mapped to the zenith direction are showed to vary between 10 mm and 30 mm. The magnitude of discrepancies follows the intensity of phenomena, especially for severe weather events. Results suggest that effects induced by commonly neglected liquid and solid water terms in the troposphere modeling should be considered in precise GNSS applications for the atmosphere monitoring. The state-of-art functional model applied in GNSS processing strategies shows certain deficits. Estimated tropospheric delays with gradients and post-fit residuals could be replaced by a loosely constrained solution without loss of quality.

Real-time tropospheric delay retrieval with GPS, GLONASS, Galileo and BDS data

The precise point positioning (PPP) is a promising technology for the real-time retrieval of atmospheric parameters with a single receiver in anywhere, all-weather and any time. The real-time atmospheric parameters can be applied to the time-critical meteorology, such as the severe weather nowcasting. The PPP is a satellite-based technology. Multi-constellation integration can enhance satellite geometry and increase measurement redundancy so that the solutions of atmospheric parameters are expected to be improved. Currently, the Global Navigation Satellite System (GNSS) family includes recovered GLONASS and modernized GPS as well as the emerging Galileo and BDS. A week of GNSS observations from 160 stations are processed to retrieve the tropospheric zenith total delay (ZTD) in real time. The four-constellation mixed real-time precise products including satellite orbit and clock corrections are adopted, and their quality is evaluated. The performance of ZTD estimates is assessed in terms of accuracy and convergence time by comparing with final tropospheric ZTD products provided by two analysis centers. The ZTDs retrieved from different constellation combinations (i.e., GPS/GLONASS/Galileo/BDS, GPS/GLONASS, and GPS-only), different processing models for ionospheric delays (i.e., ionospheric-free (IF) combined PPP, and uncombined (UC) PPP), and different modes (i.e., real-time mode, and post-processing mode) are compared.

GPS/BDS Medium/Long-Range RTK Constrained with Tropospheric Delay Parameters from NWP Model

Tropospheric delay is a major error source that affects the performance of the Global Navigation Satellite Systems (GNSS) Real Time Kinematic (RTK) positioning especially for the medium/long-range baseline. Although high precision tropospheric delay can be estimated by GNSS carrier phase measurement, together with position and ambiguity, a relatively long period of convergence time is necessary. In this study, we develop a new GPS/BDS RTK algorithm constrained with a tropospheric delay parameters from Numerical weather prediction (NWP) model for medium/long-range baselines. The accuracy of the tropospheric delays derived from NWP is assessed through comparisons with the results of GAMIT (GNSS at MIT). The positioning performance with standard GPS RTK, standard GPS/BDS RTK, the developed NWP-constrained GPS RTK and NWP-constrained GPS/BDS RTK over medium/long-range baselines are compared in terms of the initialization time and the positioning accuracy. Experiment results show that the mean differences between the NWP and GAMIT zenith tropospheric delay (ZTD) are between −5.50 mm and 5.60 mm, and the RMS values of the NWP ZTD residuals are from 24.02 mm to 32.62 mm. A reduction in the initialization time of over 41% and 58% for medium- and long-range baselines can be achieved with the NWP-constrained RTK (both GPS alone and GPS/BDS RTK solutions) compared to the standard RTK solution, respectively. An improvement of over 30% can be found with the GPS/BDS RTK compared with that of the GPS alone RTK for both standard and the NWP-constrained modes. The positioning precision of NWP-constrained GPS/BDS RTK is better than 3 cm in the horizontal direction and better than 5 cm in the vertical direction, which satisfies the requirement of the precise positioning service.

Combined orbits and clocks from IGS second reprocessing

The Analysis Centers (ACs) of the International GNSS Service (IGS) have reprocessed a large global network of GPS tracking data from 1994.0 until 2014.0 or later. Each AC product time series was extended uniformly till early 2015 using their weekly operational IGS contributions so that the complete combined product set covers GPS weeks 730 through 1831. Three ACs also included GLONASS data from as early as 2002 but that was insufficient to permit combined GLONASS products. The reprocessed terrestrial frame combination procedures and results have been reported already, and those were incorporated into the ITRF2014 multi-technique global frame released in 2016. This paper describes the orbit and clock submissions and their multi-AC combinations and assessments. These were released to users in early 2017 in time for the adoption of IGS14 for generating the operational IGS products. While the reprocessing goal was to enable homogeneous modeling, consistent with the current operational procedures, to be applied retrospectively to the full history of observation data in order to achieve a more suitable reference for geophysical studies, that objective has only been partially achieved. Ongoing AC analysis changes and a lack of full participation limit the consistency and precision of the finished IG2 products. Quantitative internal measures indicate that the reprocessed orbits are somewhat less precise than current operational orbits or even the later orbits from the first IGS reprocessing campaign. That is even more apparent for the clocks where a lack of robust AC participation means that it was only possible to form combined 5-min clocks but not the 30-s satellite clocks published operationally. Therefore, retrospective precise point positioning solutions by users are not recommended using the orbits and clocks. Nevertheless, the orbits do support long-term stable user solutions when used with network processing with either double differencing or explicit clock estimation. Among the main benefits of the reprocessing effort is a more consistent long product set to analyze for sources of systematic error and accuracy. Work to do that is underway but the reprocessing experience already points to a number of ways future IGS performance and reprocessing campaigns can be improved.

Refined discrete and empirical horizontal gradients in VLBI analysis

Missing or incorrect consideration of azimuthal asymmetry of troposphere delays is a considerable error source in space geodetic techniques such as Global Navigation Satellite Systems (GNSS) or Very Long Baseline Interferometry (VLBI). So-called horizontal troposphere gradients are generally utilized for modeling such azimuthal variations and are particularly required for observations at low elevation angles. Apart from estimating the gradients within the data analysis, which has become common practice in space geodetic techniques, there is also the possibility to determine the gradients beforehand from different data sources than the actual observations. Using ray-tracing through Numerical Weather Models (NWMs), we determined discrete gradient values referred to as GRAD for VLBI observations, based on the standard gradient model by Chen and Herring (J Geophys Res 102(B9):20489-20502, 1997. 10.1029/97JB01739) and also for new, higher-order gradient models. These gradients are produced on the same data basis as the Vienna Mapping Functions 3 (VMF3) (Landskron and Böhm in J Geod, 2017. 10.1007/s00190-017-1066-2), so they can also be regarded as the VMF3 gradients as they are fully consistent with each other. From VLBI analyses of the Vienna VLBI and Satellite Software (VieVS), it becomes evident that baseline length repeatabilities (BLRs) are improved on average by 5% when using a priori gradients GRAD instead of estimating the gradients. The reason for this improvement is that the gradient estimation yields poor results for VLBI sessions with a small number of observations, while the GRAD a priori gradients are unaffected from this. We also developed a new empirical gradient model applicable for any time and location on Earth, which is included in the Global Pressure and Temperature 3 (GPT3) model. Although being able to describe only the systematic component of azimuthal asymmetry and no short-term variations at all, even these empirical a priori gradients slightly reduce (improve) the BLRs with respect to the estimation of gradients. In general, this paper addresses that a priori horizontal gradients are actually more important for VLBI analysis than previously assumed, as particularly the discrete model GRAD as well as the empirical model GPT3 are indeed able to refine and improve the results.

The Impact of Estimating High-Resolution Tropospheric Gradients on Multi-GNSS Precise Positioning

Benefits from the modernized US Global Positioning System (GPS), the revitalized Russian GLObal NAvigation Satellite System (GLONASS), and the newly-developed Chinese BeiDou Navigation Satellite System (BDS) and European Galileo, multi-constellation Global Navigation Satellite System (GNSS) has emerged as a powerful tool not only in positioning, navigation, and timing (PNT), but also in remote sensing of the atmosphere and ionosphere. Both precise positioning and the derivation of atmospheric parameters can benefit from multi-GNSS observations. In this contribution, extensive evaluations are conducted with multi-GNSS datasets collected from 134 globally-distributed ground stations of the International GNSS Service (IGS) Multi-GNSS Experiment (MGEX) network in July 2016. The datasets are processed in six different constellation combinations, i.e., GPS-, GLONASS-, BDS-only, GPS + GLONASS, GPS + BDS, and GPS + GLONASS + BDS + Galileo precise point positioning (PPP). Tropospheric gradients are estimated with eight different temporal resolutions, from 1 h to 24 h, to investigate the impact of estimating high-resolution gradients on position estimates. The standard deviation (STD) is used as an indicator of positioning repeatability. The results show that estimating tropospheric gradients with high temporal resolution can achieve better positioning performance than the traditional strategy in which tropospheric gradients are estimated on a daily basis. Moreover, the impact of estimating tropospheric gradients with different temporal resolutions at various elevation cutoff angles (from 3° to 20°) is investigated. It can be observed that with increasing elevation cutoff angles, the improvement in positioning repeatability is decreased.

Application of ray-traced tropospheric slant delays to geodetic VLBI analysis

The correction of tropospheric influences via so-called path delays is critical for the analysis of observations from space geodetic techniques like the very long baseline interferometry (VLBI). In standard VLBI analysis, the a priori slant path delays are determined using the concept of zenith delays, mapping functions and gradients. The a priori use of ray-traced delays, i.e., tropospheric slant path delays determined with the technique of ray-tracing through the meteorological data of numerical weather models (NWM), serves as an alternative way of correcting the influences of the troposphere on the VLBI observations within the analysis. In the presented research, the application of ray-traced delays to the VLBI analysis of sessions in a time span of 16.5 years is investigated. Ray-traced delays have been determined with program RADIATE (see Hofmeister in Ph.D. thesis, Department of Geodesy and Geophysics, Faculty of Mathematics and Geoinformation, Technische Universität Wien. http://resolver.obvsg.at/urn:nbn:at:at-ubtuw:1-3444, 2016) utilizing meteorological data provided by NWM of the European Centre for Medium-Range Weather Forecasts (ECMWF). In comparison with a standard VLBI analysis, which includes the tropospheric gradient estimation, the application of the ray-traced delays to an analysis, which uses the same parameterization except for the a priori slant path delay handling and the used wet mapping factors for the zenith wet delay (ZWD) estimation, improves the baseline length repeatability (BLR) at 55.9% of the baselines at sub-mm level. If no tropospheric gradients are estimated within the compared analyses, 90.6% of all baselines benefit from the application of the ray-traced delays, which leads to an average improvement of the BLR of 1 mm. The effects of the ray-traced delays on the terrestrial reference frame are also investigated. A separate assessment of the RADIATE ray-traced delays is carried out by comparison to the ray-traced delays from the National Aeronautics and Space Administration Goddard Space Flight Center (NASA GSFC) (Eriksson and MacMillan in http://lacerta.gsfc.nasa.gov/tropodelays, 2016) with respect to the analysis performances in terms of BLR results. If tropospheric gradient estimation is included in the analysis, 51.3% of the baselines benefit from the RADIATE ray-traced delays at sub-mm difference level. If no tropospheric gradients are estimated within the analysis, the RADIATE ray-traced delays deliver a better BLR at 63% of the baselines compared to the NASA GSFC ray-traced delays.

Physical applications of GPS geodesy: a review

Geodesy, the oldest science, has become an important discipline in the geosciences, in large part by enhancing Global Positioning System (GPS) capabilities over the last 35 years well beyond the satellite constellation's original design. The ability of GPS geodesy to estimate 3D positions with millimeter-level precision with respect to a global terrestrial reference frame has contributed to significant advances in geophysics, seismology, atmospheric science, hydrology, and natural hazard science. Monitoring the changes in the positions or trajectories of GPS instruments on the Earth's land and water surfaces, in the atmosphere, or in space, is important for both theory and applications, from an improved understanding of tectonic and magmatic processes to developing systems for mitigating the impact of natural hazards on society and the environment. Besides accurate positioning, all disturbances in the propagation of the transmitted GPS radio signals from satellite to receiver are mined for information, from troposphere and ionosphere delays for weather, climate, and natural hazard applications, to disturbances in the signals due to multipath reflections from the solid ground, water, and ice for environmental applications. We review the relevant concepts of geodetic theory, data analysis, and physical modeling for a myriad of processes at multiple spatial and temporal scales, and discuss the extensive global infrastructure that has been built to support GPS geodesy consisting of thousands of continuously operating stations. We also discuss the integration of heterogeneous and complementary data sets from geodesy, seismology, and geology, focusing on crustal deformation applications and early warning systems for natural hazards.

Improving GLONASS Precise Orbit Determination through Data Connection

In order to improve the precision of GLONASS orbits, this paper presents a method to connect the data segments of a single station-satellite pair to increase the observation continuity and, consequently, the strength of the precise orbit determination (POD) solution. In this method, for each GLONASS station-satellite pair, the wide-lane ambiguities derived from the Melbourne–Wübbena combination are statistically tested and corrected for phase integer offsets and then the same is carried out for the narrow-lane ambiguities calculated from the POD solution. An experimental validation was carried out using one-month GNSS data of a global network with 175 IGS stations. The result shows that, on average, 27.1% of the GLONASS station-satellite pairs with multiple data segments could be connected to a single long observation arc and, thus, only one ambiguity parameter was estimated. Using the connected data, the GLONASS orbit overlapping RMS at the day boundaries could be reduced by 19.2% in ideal cases with an averaged reduction of about 6.3%.

Study of Alternative GPS Network Meteorological Sensors in Taiwan: Case Studies of the Plum Rains and Typhoon Sinlaku

Plum rains and typhoons are important weather systems in the Taiwan region. They can cause huge economic losses, but they are also considered as important water resources as they strike Taiwan annually and fill the reservoirs around the island. There are many meteorological sensors available for investigating the characteristics of weather and climate systems. Recently, the use of GPS as an alternative meteorological sensor has become popular due to the catastrophic impact of global climate change. GPS provides meteorological parameters mainly from the atmosphere. Precise Point Positioning (PPP) is a proven algorithm that has attracted attention in GPS related studies. This study uses GPS measurements collected at more than fifty reference stations of the e-GPS network in Taiwan. The first data set was collected from June 1st 2008 to June 7th 2008, which corresponds to the middle of the plum rain season in Taiwan. The second data set was collected from September 11th to September 17th 2008 during the landfall of typhoon Sinlaku. The data processing strategy is to process the measurements collected at the reference stations of the e-GPS network using the PPP technique to estimate the zenith tropospheric delay (ZTD) values of the sites; thus, the correlations between the ZTD values and the variation of rainfall during the plum rains and typhoon are analyzed. In addition, several characteristics of the meteorological events are identified using spatial and temporal analyses of the ZTD values estimated with the GPS network PPP technique.

Low-Frequency Gravitational Wave Searches Using Spacecraft Doppler Tracking

This paper discusses spacecraft Doppler tracking, the current-generation detector technology used in the low-frequency (∼millihertz) gravitational wave band. In the Doppler method the earth and a distant spacecraft act as free test masses with a ground-based precision Doppler tracking system continuously monitoring the earth-spacecraft relative dimensionless velocity 2Δv/c = Δν/ν0, where Δν is the Doppler shift and ν0 is the radio link carrier frequency. A gravitational wave having strain amplitude h incident on the earth-spacecraft system causes perturbations of order h in the time series of Δν/ν0. Unlike other detectors, the ∼ 1-10 AU earth-spacecraft separation makes the detector large compared with millihertz-band gravitational wavelengths, and thus times-of-flight of signals and radio waves through the apparatus are important. A burst signal, for example, is time-resolved into a characteristic signature: three discrete events in the Doppler time series. I discuss here the principles of operation of this detector (emphasizing transfer functions of gravitational wave signals and the principal noises to the Doppler time series), some data analysis techniques, experiments to date, and illustrations of sensitivity and current detector performance. I conclude with a discussion of how gravitational wave sensitivity can be improved in the low-frequency band.