Zenith Total Delay Time Series Research Articles

A Cloud-native Approach for Processing of Crowdsourced GNSS Observations and Machine Learning at Scale: A Case Study from the CAMALIOT Project

The era of modern smartphones, running on Android version 7.0 and higher, facilitates nowadays acquisition of raw dual-frequency multi-constellation GNSS observations. This paves the way for GNSS community data to be potentially exploited for precise positioning, GNSS reflectometry or geoscience applications at large. The continuously expanding global GNSS infrastructure along with the enormous volume of prospective GNSS community data bring, however, major challenges related to data acquisition, its storage, and subsequent processing for deriving various parameters of interest. In addition, such large datasets cannot be managed manually anymore, leading thus to the need for fully automated and sophisticated data processing pipelines. Application of Machine Learning Technology for GNSS IoT data fusion (CAMALIOT) was an ESA NAVISP Element 1 project (NAVISP-EL1-038.2) with activities aiming to address the aforementioned points related to GNSS community data and their exploitation for scientific applications with the use of Machine Learning (ML). This contribution provides an overview of the CAMALIOT project with information on the designed and implemented cloud-native software for GNSS processing and ML at scale, developed Android application for retrieving GNSS observations from the modern generation of smartphones through dedicated crowdsourcing campaigns, related data ingestion and processing, and GNSS analysis concerning both conventional and smartphone GNSS observations. With the use of the developed GNSS engine employing an Extended Kalman Filter, example processing results related to the Zenith Total Delay (ZTD) and Slant Total Electron Content (STEC) are provided based on the analysis of observations collected with geodetic-grade GNSS receivers and from local measurement sessions involving Xiaomi Mi 8 that collected GNSS observations using the developed Android application. For smartphone observations, ZTD is derived in a differential manner based on a single-frequency double-difference approach employing GPS and Galileo observations, whereas satellite-specific STEC time series are obtained through carrier-to-code leveling based on the geometry-free linear combination of observations from both GPS and Galileo constellations. Although the ZTD and STEC time series from smartphones were derived on a demonstration basis, a rather good level of consistency of such estimates with respect to the reference time series was found. For the considered periods, the RMS of differences between the derived smartphone-based time series of differential zenith wet delay and reference values were below 3.1 mm. In terms of satellite-specific STEC time series expressed with respect to the reference STEC time series, RMS of the offset-reduced differences below 1.2 TECU was found. Smartphone-based observations require special attention including additional processing steps and a dedicated parameterization in order to be able to acquire reliable atmospheric estimates. Although with lower measurement quality compared to traditional sources of GNSS data, an augmentation of ground-based networks of fixed high-end GNSS receivers with GNSS-capable smartphones would however, form an interesting source of complementary information for various studies relying on GNSS observations.

Estimation and Evaluation of Zenith Tropospheric Delay from Single and Multiple GNSS Observations

Multi-Global Navigation Satellite Systems (multi-GNSS) (including GPS, BDS, Galileo, and GLONASS) provide a significant opportunity for high-quality zenith tropospheric delay estimation and its applications in meteorology. However, the performance of zenith total delay (ZTD) retrieval from single- or multi-GNSS observations is not clear, particularly from the new, fully operating BDS-3. In this paper, zenith tropospheric delay is estimated using the single-, dual-, triple-, or four-GNSS Precise Point Positioning (PPP) technique from 55 Multi-GNSS Experiment (MGEX) stations over one year. The performance of GNSS ZTD estimation is evaluated using the International GNSS Service (IGS) standard tropospheric products, radiosonde, and the fifth-generation European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis (ERA5). The results show that the GPS-derived ZTD time series is more consistent and reliable than those derived from BDS-only, Galileo-only, and GLONASS-only solutions. The performance of the single-GNSS ZTD solution can be enhanced with better accuracy and stability by combining multi-GNSS observations. The accuracy of the ZTD from multi-GNSS observations is improved by 13.8%, 43.8%, 27.6%, and 22.9% with respect to IGS products for the single-system solution (GPS, BDS, Galileo, and GLONASS), respectively. The ZTD from multi-GNSS observations presents higher accuracy and a significant improvement with respect to radiosonde and ERA5 data when compared to the single-system solution.

Investigating temporal and spatial patterns in the stochastic component of ZTD time series over Europe

The EUREF Permanent GNSS Network (EPN) provides a unique atmospheric dataset over Europe in the form of Zenith Total Delay (ZTD) time series. These ZTD time series are estimated independently by different analysis centers, but a combined solution is also provided. Previous studies showed that changes in the processing strategy do not affect trends and seasonal amplitudes. However, its effect on the temporal and spatial variations of the stochastic component of ZTD time series has not yet been investigated. This study analyses the temporal and spatial correlations of the ZTD residuals obtained from four different datasets: one solution provided by ASI (Agenzia Spaziale Italiana Centro di Geodesia Spaziale, Italy), two solutions provided by GOP (Geodetic Observatory Pecny, Czech Republic), and one combined solution resulting from the EPN’s second reprocessing campaign. We find that the ZTD residuals obtained from the three individual solutions can be modeled using a first-order autoregressive stochastic process, which is less significant and must be completed by an additional white noise process in the combined solution. Although the combination procedure changes the temporal correlation in the ZTD residuals, it neither affects its spatial correlation structure nor its time-variability, for which an annual modulation is observed for stations up to 1,000 km apart. The main spatial patterns in the ZTD residuals also remain identical. Finally, we compare two GOP solutions, one of which only differs in the modeling of non-tidal atmospheric loading at the observation level, and conclude that its modeling has a negligible effect on ZTD values.

An Improved Model for Detecting Heavy Precipitation Using GNSS-Derived Zenith Total Delay Measurements

In recent years, precipitable water vapor has been widely used in heavy precipitation prediction, which is obtained from a conversion of the zenith total delay (ZTD) of the GNSS signal. Since the parameter directly estimated for the tropospheric delay from Global Navigation Satellite Systems (GNSS) data processing is the ZTD, this study investigated the feasibility of directly using ZTD to predict heavy precipitation. Based on the finding that, prior to a heavy precipitation events, ZTD was likely to start with a duration of continuous rise followed by a sharp drop, a new heavy precipitation detection model containing seven predictors derived from ZTD was established. The seven predictors reflect not only the ascending and descending trends but also long-term and short-term variations in the ZTD time series. Three criteria, representing different situations for the formation of heavy precipitation, were also constructed using the predictors to detect heavy precipitation. The optimal set of thresholds for the seven predictors for each summer month were determined based on hourly ZTD and precipitation records at a pair of co-located GNSS/weather station−HKSC-KP in Hong Kong over the period 2010−2017. The model was evaluated using the predictions in 2018 and 2019 to compare against the corresponding precipitation records. Results showed that the new model correctly predicted 98.8% of the heavy precipitation events, with a mean lead time of 4.37 h. Compared with the existing models, the new model also reduced the false alarms by 32.3%. Similar results were also obtained from the other three pairs of co-located stations. These results suggest that it is rational and effective to use the new ZTD-based model for improving the performance of heavy precipitation detection.

Trend estimation of zenith total delays at IGS stations by using nonparametric methods

Global Navigation Satellite System (GNSS) observations play an important role in climate studies because of the advantages they provide. An analysis of the GNSS observations can be used to obtain the zenith total delay (ZTD) parameter, which represents the effect of weather conditions. In this study, the trends of the time series of IGS (International GNSS Service) Repro1 ZTD data recorded between 1995 and 2010 at 19 GNSS stations throughout Turkey and Europe reprocessed in the framework of COST Action ES1206 were investigated. The trends of the time series were estimated by using the Mann–Kendall rank correlation test in addition to Spearman’s rho test and Sen’s slope method. In addition, the Run (Swed–Eisenhart) test was performed to test for homogeneity. The aim of this study was to evaluate the advantages and disadvantages of the applications of different methods to the estimation of trends in the ZTD time series. According to the Mann–Kendall rank correlation test, the ANKR, GRAS, HERS and MAS1 stations exhibited an increasing trend. Using the Spearman rho test, increasing trends were observed at the ANKR, EBRE and MAS1 stations, while decreasing trends were observed at the BRUS and GRAS stations. Finally, negative slope values were obtained at the BRUS, GRAS, GRAZ, HERS, JOZE, PENC and WTZR stations by using the Sen slope method.

Comparison of GPS tropospheric delays derived from two consecutive EPN reprocessing campaigns from the point of view of climate monitoring

Abstract. The main purpose of this research was to acquire information about consistency of ZTD (zenith total delay) linear trends and seasonal components between two consecutive GPS reprocessing campaigns. The analysis concerned two sets of the ZTD time series which were estimated during EUREF (Reference Frame Sub-Commission for Europe) EPN (Permanent Network) reprocessing campaigns according to 2008 and 2015 MUT AC (Military University of Technology Analysis Centre) scenarios. Firstly, Lomb–Scargle periodograms were generated for 57 EPN stations to obtain a characterisation of oscillations occurring in the ZTD time series. Then, the values of seasonal components and linear trends were estimated using the LSE (least squares estimation) approach. The Mann–Kendall trend test was also carried out to verify the presence of linear long-term ZTD changes. Finally, differences in seasonal signals and linear trends between these two data sets were investigated. All these analyses were conducted for the ZTD time series of two lengths: a shortened 16-year series and a full 18-year one. In the case of spectral analysis, amplitudes of the annual and semi-annual periods were almost exactly the same for both reprocessing campaigns. Exceptions were found for only a few stations and they did not exceed 1 mm. The estimated trends were also similar. However, for the reprocessing performed in 2008, the trends values were usually higher. In general, shortening of the analysed time period by 2 years resulted in a decrease of the linear trends values of about 0.07 mm yr−1. This was confirmed by analyses based on two data sets.

14 years of GPS tropospheric delays in the French–Italian border region: comparisons and first application in a case study

Global Positioning System (GPS) data from 181 permanent stations extracted from different networks covering France and the Italian part of the Alps are used to estimate a homogeneous set of tropospheric parameters over 14 years (from January 1998 to May 2012). The tropospheric Zenith Total Delay (ZTD) quantified in the GPS data analysis is closely related to the value of integrated water vapor above each GPS station. GPS ZTD is already successfully used for operational weather prediction and meteorological analyses, providing valuable data to improve our comprehension of the tropospheric water cycle and in particular to improve the prediction of precipitations. Moreover, GPS tropospheric measurements are intrinsically stable, so that long-term observations represent a signi``ficant contribution to climatological studies. The results of a homogeneous reanalysis of up to 14 years of data with MIT’s GAMIT/GLOBK software are presented. The estimated tropospheric parameters are one ZTD every 2 h and one couple of horizontal tropospheric gradients, seven times a day for each station, simultaneously with a daily positioning solution. A quality check of the tropospheric parameter time series identifies offsets, for example, due to instrument changes at individual sites. Our analysis strategy using the empirical GMF is validated by a comparison with the new GPT2 model. Moreover, a comparison with the IGS analysis of 1 year is provided for common stations. The resulting verified time series can be used for meteorological and climatological studies. As first examples, we present a convergence test for the ZTD change in time and a regional climatological approach that could permit identifying specific patterns of ZTD variation that are related to severe weather events. The 181 ZTD and gradient time series are made available in the Reseau National GPS permanent (RENAG) database.

GPS derived Zenith Total Delay (ZTD) observed at tropical locations in South India during atmospheric storms and depressions

Global Positioning System (GPS) monitoring of Zenith Total Delay (ZTD) of the troposphere which is related to water vapor is important as it may help us in weather forecasting. The atmospheric water vapor varies according to the season and it also varies quickly on short temporal and spatial scales during stormy periods. Thus it plays a crucial role in meteorology. GPS is one of the relatively inexpensive tools available to monitor the water vapor content in the atmosphere. In the present study, the efficacy of GPS data to monitor perturbations in tropospheric water content (GPS meteorology) associated with atmospheric storms and depressions is investigated utilizing the data from a tropical region of India, recorded between 15th October, 2010 and 27th December, 2010 during which Southern India was affected by a few significant atmospheric events. The ZTD was estimated for this period at the NGRI operated GPS stations at Hyderabad (HYDE) and MS University, Tirunelveli (MSUN). The accuracy of GPS derived ZTD was validated from the close match seen with ZTD values estimated from numerical weather modeling data. During the stormy periods there were strong variations of the ZTD. Corresponding changes in precipitable water vapor were estimated for the International GNSS Service station HYDE. The average ZTD was found to be higher near the coastal station at MSUN and less at the inland station HYDE. Most of the observed peaks in the ZTD time series were well correlated to the atmospheric events that influenced the region. The study extended to two more locations in the equatorial Indian Ocean region showed spatial variations in the ZTD values, which suggest the weakening of ZTD towards the coast. Our observations are yet another illustration for the application of GPS observations to monitor tropospheric water content variations associated with severe atmospheric events.

Assessment of ECMWF-derived tropospheric delay models within the EUREF Permanent Network

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

Precipitable Water Vapour and Zenith Total Delay time series and models over Slovakia and vicinity

More than 50 permanent GNSS (Global Navigation Satellite Systems) stationsare processed continually within the Central European Permanent Network. ZenithTotal Delay (ZTD), one of the processing outputs, reflects a delay of the GNSS signalcaused by troposphere. Precipitable Water Vapour (PWV ) is calculated when groundmeteorological observations are available. Model of PWV over Slovakia and its vicinity isproduced using digital elevation model data for height correction. Real variation of PWVover the area shows a model of normalized PWV (nPWV ), which is created from PWVvalues reduced by theoretical PWV values corresponding to altitude and latitude of thestation. Time series of ZTD and PWV since 1996 and models of PWV and nPWV arepublished on the web page, using Web Map Service and other web technologies. Data arecontinually updated and can be downloaded for free.

Diurnal and semidiurnal atmospheric tides observed by co-located GPS and VLBI measurements

The tropospheric zenith total delay (ZTD) derived from very long baseline interferometry (VLBI) is an important parameter of the atmosphere, reflecting various atmosphere-related processes and variations. In this paper, ZTD time series of the IVS rapid combined tropospheric product (2002–2006) with a 1-h resolution are used for the first time to investigate the diurnal and semidiurnal oscillations. Significant diurnal and semidiurnal variations of ZTD are found at all VLBI stations. The amplitude of the diurnal cycle S 1 is 0.6–1.2 mm at most of the VLBI stations, and the amplitude of the semidiurnal cycle S 2 is 0.2–1.9 mm, which nearly accord with the surface pressure tides S 1/ S 2 and co-located GPS estimated S 1/ S 2. The results indicate that the S 1 and S 2 behaviors are mainly dominated by the hydrostatic component, namely pressure tides. In general, the semidiurnal S 2 amplitudes are slightly larger than the diurnal S 1. While S 1 shows no clear dependency on site altitude, S 2 has a regular distribution with VLBI site altitude. The results are in accordance with predictions of the classic tidal theory [Chapman, S., Lindzen, R.S., 1970. Atmospheric Tides, Gordon and Breach, New York].

Characterization of Atmospheric Parameters using a Ground Based GPS Network in North Europe

We characterize the temporal and spatial variation of the Zenith Wet Delay (ZWD) and the Zenith Total Delay (ZTD), estimated using a network of Global Positioning System (GPS) receivers. This characterization is important for the improvement and validation of atmospheric water vapor models, applicable in GPS meteorology, as well as in the navigation. We treat the estimates of Zenith Hydrostatic Delay (ZHD) and ZWD as realizations of random walk stochastic processes and we derive the corresponding parameters for different locations and measurement techniques for data acquired at intervals of 1 to 3 hours. The monthly standard deviation (StD) of the ZTD is less than 50 mm and does not exhibit a strong seasonal signature over the period 1997-1998 for any of the studied GPS sites. However, the StDs of the pairwise-differenced ZTD time series show a seasonal dependence, mainly due to the spatial variations of the ZWD, which should be considered when GPS data are assimilated in weather prediction models. We show the differences in typical spatial characteristics of ZHD and ZWD for the winter and summer seasons in North Europe. Finally, we describe the use of temporal structure functions for detection of rapid changes in ZTD.

Real time GPS data processing for regional atmospheric delay derivation

We have developed a GPS data processing software and demonstrate that by using receivers in an area of approximately 800 × 400 km we can produce estimates of the atmospheric zenith total delay (ZTD) with a latency of a few seconds. It is based on a Kalman filter which simultaneously estimates clock offsets and satellite coordinates. The ZTD quality is typically 15 mm in terms of rms difference to post‐processed ZTD time series. This level of uncertainty is useful in many navigation applications and if an additional reduction in the uncertainty can be obtained the usefulness for short term weather forecasting could be significant.