Zenith Tropospheric Delay Time Series Research Articles

A Novel Method for Monitoring Tropical Cyclones’ Movement Using GNSS Zenith Tropospheric Delay

Precipitable water vapor (PWV) is an important meteorological factor for predicting extreme weather events such as tropical cyclones, which can be obtained from zenith tropospheric delay (ZTD) by using a conversion. A time difference of ZTD arrival (TDOZA) model was proposed to monitor the movement of tropical cyclones, and the fifth-generation reanalysis dataset of the European Centre for Medium-range Weather Forecasting (ERA5)-derived ZTD (ERA5-ZTD) was used to estimate the movement of tropical cyclones based on the model. The global navigation satellite system-derived ZTD and radiosonde data-derived PWV (RS-PWV) were used to test the accuracy of the ERA5-ZTD and analyze the correlation between ZTD and PWV, respectively. The statistics showed that the mean Bias, RMS and STD of the ERA5-ZTD were 6.4 mm, 17.1 mm and 16.5 mm, respectively, and the mean correlation coefficient of the ERA5-ZTD and RS-PWV was 0.951, which indicates that the ZTD can be used to predict weather events instead of PWV. Then, spatiao-temporal characteristics of ZTD during the four tropical cyclone (i.e., Merbok, ROKE, Neast and Hato) periods in 2017 were analyzed, and the result showed that the moving directions of ZTD and the tropical cyclones were consistent. Thus, the ZTD time series over the ERA5 grids around the tropical cyclones’ paths were used to estimate the velocity of the tropical cyclones based on the TDOZA model, when the tropical cyclones are approaching or leaving. Compared with the result from the China Meteorological Administration, the mean absolute and relative deviations of the TDOZA model-derived velocity were 2.55 km/h and 10.0%, respectively. These results suggest that ZTD can be used as a new supplementary meteorological parameter for monitoring tropical cyclone events.

Transformer-Based Global Zenith Tropospheric Delay Forecasting Model

Zenith tropospheric delay (ZTD) plays an important role in high-precision global navigation satellite system (GNSS) positioning and meteorology. At present, commonly used ZTD forecasting models comprise empirical, meteorological parameter, and neural network models. The empirical model can only fit approximate periodic variations, and its accuracy is relatively low. The accuracy of the meteorological parameter model depends heavily on the accuracy of the meteorological parameters. The recurrent neural network (RNN) is suitable for short-term series data prediction, but for long-term series, the ZTD prediction accuracy is clearly reduced. Long short-term memory (LSTM) has superior forecasting accuracy for long-term ZTD series; however, the LSTM model is complex, cannot be parallelized, and is time-consuming. In this study, we propose a novel ZTD time-series forecasting utilizing transformer-based machine-learning methods that are popular in natural language processing (NLP) and forecasting global ZTD, the training parameters provided by the global geodetic observing system (GGOS). The proposed transformer model leverages self-attention mechanisms by encoder and decoder modules to learn complex patterns and dynamics from long ZTD time series. The numeric results showed that the root mean square error (RMSE) of the forecasting ZTD results were 1.8 cm and mean bias, STD, MAE, and R 0.0, 1.7, 1.3, and 0.95, respectively, which is superior to that of the LSTM, RNN, convolutional neural network (CNN), and GPT3 series models. We investigated the global distribution of these accuracy indicators, and the results demonstrated that the accuracy in continents was superior to maritime space transformer ZTD forecasting model accuracy at high latitudes superior to that at low latitude. In addition to the overall accuracy improvement, the proposed transformer ZTD forecast model also mitigates the accuracy variations in space and time, thereby guaranteeing high accuracy globally. This study provides a novel method to estimate the ZTD, which could potentially contribute to precise GNSS positioning and meteorology.

SHAtropE—A Regional Gridded ZTD Model for China and the Surrounding Areas

A regional zenith tropospheric delay (ZTD) empirical model, referred to as SHAtropE (SHanghai Astronomical observatory tropospheric delay model—Extended), is developed and provides tropospheric propagation delay corrections for users in China and the surrounding areas with improved accuracy. The SHAtropE model was developed based on the ZTD time series of the continuous GNSS sites from the Crustal Movement Observation Network of China (CMONOC) and GNSS sites of surrounding areas. It combines the exponential and periodical functions and is provided as regional grids with a resolution of 2.5° × 2.0° in longitude and latitude. At each grid point, the exponential function converts the ZTD from the site height to the ellipsoid, and the periodical terms, including both annual and semi-annual periods, describe ZTD’s temporal variation. Moreover, SHAtropE also provides the predicted ZTD uncertainty, which is valuable in Precise Point Positioning (PPP) with ZTD being constrained for faster convergence. The data of 310 GNSS sites over 7 years were used to validate the new model. Results show that the SHAtropE ZTD has an accuracy of 3.5 cm in root mean square (RMS) quantity, which has a mean improvement of 35.2% and 5.4% over the UNB3m (5.4 cm) and GPT3 (3.7 cm) models, respectively. The predicted uncertainty of SHAtropE ZTD shows seasonal variations, where the values are larger in summer than in winter. By applying the SHAtropE model in the static PPP, the convergence time of GPS-only and BDS-only solutions are reduced by 8.1% and 14.5% respectively compared to the UNB3m model, and the reductions are 6.9% and 11.2% respectively for the GPT3 model. As no meteorological data are required for the implementation of the model, the SHAtropE could thus be a refined tropospheric model for GNSS users in mainland China and the surrounding areas. The method of modeling the ZTD uncertainty can also be used in further global tropospheric delay modeling.

Interpretation of the Tropospheric Gradients Estimated With GPS During Hurricane Harvey

During the last decade Global Positioning System (GPS) Continuous Operating Reference Stations networks have become a new important data source for meteorology. This has dramatically improved the ability to remotely sense the atmosphere under the influence of severe mesoscale and synoptic systems. The zenith tropospheric delay (ZTD) is one of the atmospheric variables continuously observed, and its horizontal variations, the horizontal tropospheric gradients, are routinely computed nowadays within the dual‐frequency GPS processing, but their interpretation and relationship with the weather is still an open question. The purpose of this paper is to contribute in this direction by studying the effect that Hurricane Harvey had on the spatial and temporal behavior of the ZTDs and gradients, when it reached Texas coast, during 18–31 August 2017. The results show that ZTD time series present a clear and rapid increase larger than 10 cm in a few hours when the hurricane reached the area. Gradients behaviors show that the hurricane also produced significant changes on them, since the magnitude and predominant directions before and after the hurricane arrived are completely different. Noticeably, the gradient vectors before the landing are consistently related to the horizontal winds and pressure fields. In this manuscript we demonstrate that the ZTD gradients can show a consistent signature under severe weather events, strongly suggesting their potential application for short‐term weather forecasting.

Variability and accuracy of Zenith Total Delay over the East African tropical region

The Global Navigation Satellite System (GNSS) can be used to derive accurately the Zenith Tropospheric Delay (ZTD) under all-weather conditions. The derived ZTDs play a vital role in climate studies, weather forecasting and are operationally assimilated into numerical weather prediction models. In this study, variations and statistical analysis of GNSS-derived ZTD over the East African tropical region are analysed. The data is collected from 13 geodetic permanent stations for the period of 4 years from 2013 to 2016. The 13 stations consist of 5 International GNSS Service (IGS) stations plus 8 stations as follows: 4 Africa Array stations and 4 Malawi Rifting stations from Uganda, Kenya, Tanzania and Rwanda. The ZTD time series were processed using goGPS software version 1.0 beta1, a MATLAB based GNSS processing software, originally developed for kinematic applications but recently re-engineered for quasi static applications. The annual variation of the ZTD time series was investigated using Lomb Scargle periodograms. The semi-annual frequency has the dominant power in subregion 1 (latitudes 4 °S and 4 °N) and the annual frequency has the dominant power in subregion 2 (latitudes 12 °S to 4 °S). The highest ZTD estimates occur during the rainy seasons, at all stations, and the lowest estimates occur during the dry seasons. The results also show that the ZTD estimates are largest at stations located at low elevation (regions close to the Indian Ocean). The derived ZTDs are compared to the values derived from the GIPSY-OASIS via Jet Propulsion Laboratory (JPL) online Automatic Precise Positioning Service (APPS) and the Unified Environmental Modelling System (UEMS) numerical weather prediction (NWP) model. The comparison of goGPS and APPS ZTD at the 13 stations shows an overall average bias, Root Mean Square (RMS) and standard deviation (stdev) of −0.9 mm, 3.2 mm and 3.0 mm respectively, with correlation coefficients ranging from 0.974 to 0.999. The comparison of goGPS ZTD against UEMS NWP ZTD at 8 selected stations shows average bias, RMS and stdev of −12.4 mm, 22.0 mm and 17.6 mm respectively, with correlation coefficients ranging from 0.802 to 0.974. The agreement between the GPS ZTD and the NWP ZTD indicates that goGPS ZTD can be assimilated into NWP models in the East African region.

Global positioning systems meteorology over Morocco: accuracy assessment and comparison of zenith tropospheric delay from global positioning systems and radiosondes

Global positioning systems (GPSs) have become a powerful remote sensing tool to estimate the water vapour in the troposphere. This study describes the operational processing of the Moroccan ground‐based GPS meteorology stations. It presents the evaluation of the accuracy of zenith tropospheric delay (ZTD). The accuracy is evaluated first in relation to the International Global Navigation Satellite System Service (IGS) final products, and second by comparison to equivalent values derived from radiosonde profiles. The comparison of near‐real‐time ZTD with the IGS final product shows a bias of −1 mm with a standard deviation of 6 mm. The comparison with radiosondes shows a bias of −2.82 mm and a standard deviation of 14.01 mm. Also, the comparison of GPS ZTD and radiosonde ZTD time series over almost 1 year (2016) shows good agreement and a seasonal signal with higher values of ZTD in summer.

Assessment of the Impact of GNSS Processing Strategies on the Long-Term Parameters of 20 Years IWV Time Series

Advanced processing of collected global navigation satellite systems (GNSS) observations allows for the estimation of zenith tropospheric delay (ZTD), which in turn can be converted to the integrated water vapour (IWV). The proper estimation of GNSS IWV can be affected by the adopted GNSS processing strategy. To verify which of its elements cause deterioration and which improve the estimated GNSS IWV, we conducted eight reprocessings of 20 years of GPS observations (01.1996–12.2015). In each of them, we applied a different mapping function, the zenith hydrostatic delay (ZHD) a priori value, the cut-off angle, software, and the positioning method. Obtained in such a way, the ZTD time series were converted to the IWV using the meteorological parameters sourced from the ERA-Interim. Then, based on them, the long-term parameters were estimated and compared to those obtained from the IWV derived from the radio sounding (RS) observations. In this paper, we analyzed long-term parameters such as IWV mean values, linear trends, and amplitudes of annual and semiannual oscillations. A comparative analysis showed, inter alia, that in terms of the investigation of the IWV linear trend the precise point positioning (PPP) method is characterized by higher accuracy than the differential one. It was also found that using the GPT2 model and the higher elevation mask brings benefits to the GNSS IWV linear trend estimation.

Real-Time Tropospheric Delay Retrieval from Multi-GNSS PPP Ambiguity Resolution: Validation with Final Troposphere Products and a Numerical Weather Model

The multiple global navigation satellite systems (multi-GNSS) bring great opportunity for the real-time retrieval of high-quality zenith tropospheric delay (ZTD), which is a critical quality for atmospheric science and geodetic applications. In this contribution, a multi-GNSS precise point positioning (PPP) ambiguity resolution (AR) analysis approach is developed for real-time tropospheric delay retrieval. To validate the proposed multi-GNSS ZTD estimates, we collected and processed data from 30 Multi-GNSS Experiment (MGEX) stations; the resulting real-time tropospheric products are evaluated by using standard post-processed troposphere products and European Centre for Medium-Range Weather Forecasts analysis (ECMWF) data. An accuracy of 4.5 mm and 7.1 mm relative to the Center for Orbit Determination in Europe (CODE) and U.S. Naval Observatory (USNO) products is achievable for real-time tropospheric delays from multi-GNSS PPP ambiguity resolution after an initialization process of approximately 5 min. Compared to Global Positioning System (GPS) results, the accuracy of retrieved zenith tropospheric delay from multi-GNSS PPP-AR is improved by 16.7% and 31.7% with respect to USNO and CODE final products. The GNSS-derived ZTD time-series exhibits a great agreement with the ECMWF data for a long period of 30 days. The average root mean square (RMS) of the real-time zenith tropospheric delay retrieved from multi-GNSS PPP-AR is 12.5 mm with respect to ECMWF data while the accuracy of GPS-only results is 13.3 mm. Significant improvement is also achieved in terms of the initialization time of the multi-GNSS tropospheric delays, with an improvement of 50.7% compared to GPS-only fixed solutions. All these improvements demonstrate the promising prospects of the multi-GNSS PPP-AR method for time-critical meteorological applications.

Investigation of the 16-year and 18-year ZTD Time Series Derived from GPS Data Processing

The GPS system can play an important role in activities related to the monitoring of climate. Long time series, coherent strategy, and very high quality of tropospheric parameter Zenith Tropospheric Delay (ZTD) estimated on the basis of GPS data analysis allows to investigate its usefulness for climate research as a direct GPS product. This paper presents results of analysis of 16-year time series derived from EUREF Permanent Network (EPN) reprocessing performed by the Military University of Technology. For 58 stations Lomb-Scargle periodograms were performed in order to obtain information about the oscillations in ZTD time series. Seasonal components and linear trend were estimated using Least Square Estimation (LSE) and Mann—Kendall trend test was used to confirm the presence of a linear trend designated by LSE method. In order to verify the impact of the length of time series on trend value, comparison between 16 and 18 years were performed.

A comparative study of zenith tropospheric delay and precipitable water vapor estimates using scientific GPS processing software and web based automated PPP service

The zenith tropospheric delay (ZTD) is a significant error source which affects the GPS signal propagation time. ZTD time series can directly or indirectly reflect the weather variations. In geodetic studies their computation is important since it improves position accuracy. Sophisticated software packages using network data of ground-based GPS receivers are used for this purpose. During the last years, various web based precise point positioning (PPP) services can provide position solutions. Additional products, such as ZTD estimates, can be derived both from PPP as well as from network solutions. Research institutes and laboratories like JPL provide similar services. This study’s objective is twofold. In a first instance we used the Bernese and GAMIT software packages and the PPP service via the JPL webpage to estimate ZTD values every hour for a period of one month. We selected a geographical area in Greece, where seasonal weather variations are frequent and GPS permanent station infrastructure is available. The estimated ZTD values derived from GPS processing for a single station were compared with the ZTD estimates derived directly from the Saastamoinen model using meteorological data from a co-located meteorological sensor as input to this model. The results show an rms agreement of about 45 mm. The second scope of this study is to compare precipitable water (PW) values between different processing schemes. For this purpose, we used the derived zenith wet delay estimates of each processing scheme and a global formula for the computation of the weighted mean temperature of the atmosphere for our area of study. The rms differences between the web PPP solution and the Bernese derived estimates were 0.35 mm. The rms of the differences between and the web PPP solution and the GAMIT derived estimates of PW were 1.67 mm. We conclude that this difference follows from the zenith hydrostatic delay component that needs to be properly modeled when high accuracy results are required.

A new global zenith tropospheric delay model IGGtrop for GNSS applications

Tropospheric delay is one of the main sources of measurement error in global navigation satellite systems. It is usually compensated by using an empirical correction model. In this paper, temporal and spatial variations of the global zenith tropospheric delay (ZTD) are further analyzed by ZTD time series from global International GNSS Service stations and annual ZTDs derived from global National Centers for Environmental Prediction reanalysis data, respectively. A new ZTD correction model, named IGGtrop, is developed based on the characteristics of ZTD. Experimental results show that this new 3D-grid-based model that accommodates longitudinal as well as latitudinal variations of ZTD performs better than latitude-only based models (such as UNB3, EGNOS, and UNB3m). The global average bias and RMS for IGGtrop are about −0.8 cm and 4.0 cm, respectively. Bias values for UNB3, EGNOS, and UNB3m are 2.0, 2.0, and 0.7 cm, respectively, and respective RMS values 5.4, 5.4, and 5.0 cm. IGGtrop shows much more consistent prediction errors for different areas than EGNOS and UNB3m. In China, the performance of IGGtrop (bias values from −2.0 to 0.4 cm and RMS from 2.1 to 6.4 cm) is clearly superior to those of EGNOS and UNB3m. It is also demonstrated that IGGtrop biases vary little with height, and its RMS values tend to decrease with increasing height. In addition, IGGtrop generally estimates ZTD with greater accuracy than EGNOS and UNB3m in the Southern Hemisphere.

Seasonal variability of GPS‐derived zenith tropospheric delay (1994–2006) and climate implications

The total zenith tropospheric delay (ZTD) is an important parameter of the atmosphere and directly or indirectly reflects the weather and climate processes and variations. In this paper the ZTD time series with a 2‐hour resolution are derived from globally distributed 150 International GPS Service (IGS) stations (1994–2006), which are used to investigate the secular trend and seasonal variation of ZTD as well as its implications in climate. The mean secular ZTD variation trend is about 1.5 ± 0.001 mm/yr at all IGS stations. The secular variations are systematically increasing in most parts of the Northern Hemisphere and decreasing in most parts of the Southern Hemisphere. Furthermore, the ZTD trends are almost symmetrically decreasing with increasing altitude, while the summation of upward and downward trends at globally distributed GPS sites is almost zero, possibly reflecting that the secular ZTD variation is in balance at a global scale. Significant annual variations of ZTD are found over all GPS stations with the amplitude from 25 to 75 mm. The annual variation amplitudes of ZTD near oceanic coasts are generally larger than in the continental inland. Larger amplitudes of annual ZTD variation are mostly found at middle latitudes (near 20°S and 40°N) and smaller amplitudes of annual ZTD variation are located at higher latitudes (e.g., Antarctic) and the equator areas. The phase of annual ZTD variation is about 60° in the Southern Hemisphere (about February, summer) and about 240° in the Northern Hemisphere (about August, summer). The mean amplitude of semiannual ZTD variations is about 10 mm, much smaller than annual variations. The semiannual amplitudes are larger in the Northern Hemisphere than in the Southern Hemisphere, indicating that the semiannual variation amplitudes of ZTD in the Southern Hemisphere are not significant. In addition, the higher‐frequency variability (RMS of ZTD residuals) ranges from 15 to 65 mm of delay, depending on altitude of the station. Inland stations tend to have lower variability and sites at ocean and coasts have higher variability. These seasonal ZTD cycles are due mainly to the wet component variations (ZWD).