Tropospheric Delay Research Articles

Analysis of GNSS-ZTD retrieval using dual-frequency raw observations

The Global Navigation Satellite System (GNSS) is promising technology for zenith tropospheric delay (ZTD) retrieval. With the emergence of new multi-GNSS frequencies and maturity of precise point positioning ambiguity resolution (PPP-AR) technology, opportunities and challenges have arisen in high-precision GNSS-ZTD retrieval. However, certain strategies have usually been adopted, such as the traditional dual-frequency combination of American global positioning system (GPS) technology, for ZTD retrieval, but the influence of AR on ZTD retrieval has been ignored. To address this issue, in this study, the GNSS-ZTD retrieval performance of all existing dual-frequency combinations was first comprehensively evaluated by raw observations. Then, the influences of AR and system combinations were analysed with popular dual-frequency combinations. Finally, La Niña occurred during the GNSS data period considered in this article, and the effect on GNSS-ZTD retrieval was examined. The results of this study could not only provide a reference for GNSS-ZTD retrieval but also provide insight into the relationship between La Niña occurrence and GNSS-ZTD retrieval performance.

Quantitative analysis of the tropospheric delay differences for 1–300 GHz microwave signals with ground-based microwave radiometric profiles

Tropospheric delay is a significant source of error in various microwave measurement technologies. As the tropospheric delay differences associated with the signal frequency can be neglected for signals near the L band, the Global Navigation Satellite System (GNSS) is frequently used to assist other microwave measurements on tropospheric delay correction for its high precision and all-weather capabilities. However, when the signal frequency differences are significant, further analysis of tropospheric delay related to signal frequency is required for higher accuracy in long-distance propagation. This study quantitatively analyzed the tropospheric delay differences from L-band to millimeter band (1–300 GHz) affected by dry air, water vapor, and liquid water, based on Microwave Radiometer (MWR) measurement profiles and the Millimeter-wave Propagation Model93 (MPM93) at Shanghai. Relative to the GNSS L-band signal of 1.2 GHz, the RMS of tropospheric delay differences over 1–300 GHz varies from 0.033 mm to 9.436 mm, with the maximum tropospheric delay differences up to 18.03 mm at 300 GHz. Tropospheric delay differences strongly correlate with surface temperature and surface pressure, except for some of the atmosphere absorption bands. These quantitative analyses are helpful for the comprehensive application of GNSS to assist other microwave measurement techniques.

Mitigation of tropospheric delay induced errors in TS-InSAR ground deformation monitoring

ABSTRACT Interferometric Synthetic Aperture Radar (InSAR) is capable of detecting crust deformation. However, the accuracy is limited by spatiotemporal changes in the lower troposphere. In this paper, we constructed a periodic zenith total delay negative exponential function (PZTD-NEF) model of atmospheric spatiotemporal variation characteristics based on ERA-5 data to alleviate the temporal oscillation bias introduced by tropospheric delay and improve the accuracy of time series InSAR (TS-InSAR) inversion of surface deformation. We evaluated the model’s performance using the phase standard deviation (STD), atmospheric delay correlation coefficient with topography and the spatial structure function. The results were compared with a linear topography-dependent empirical model, generic atmospheric correction online service (GACOS) and ERA-5 methods. Our method reduces the STD of the phase of 83% of the interferograms by 12.8%. For vertical stratification delay correction, the correlation between the proposed method and the Linear, GACOS, and ERA-5 reached 0.734, 0.708, and 0.729, respectively. We found that accounting for spatiotemporal variation characteristics of tropospheric delay can alleviate the seasonal oscillations of vertical stratification delay and improve the accuracy of the deformation time series solution by 40.04%. We also used the Kunming continuous operation reference station system (KMCORS) to verify the displacement results of our method.

Clock-modeling-constrained Epoch Relative Positioning for GPS coseismic displacement estimation

High-rate GNSS technology is invaluable for capturing surface displacements. However, vertical displacement is strongly linked to zenith tropospheric delay (ZTD) and receiver clock bias, compromising accuracy and impeding the detection of weak seismic waves. Some GNSS stations, fortunately, feature high-stability oscillators, enabling receiver clock modeling instead of epoch-wise estimation. This paper introduces an epoch relative positioning approach (ERP)with receiver clock modeling (CMC-ERP) to enhance coseismic displacement accuracy. Applied to earthquakes in Japan and the United States, the method improves vertical displacement accuracy by 24% to 61%. Furthermore, P-wave arrival times are determined by processing displacement sequences extracted through both CMC-ERP and ERP methods using STA/LTA. Compared to theoretical arrival times calculated by TauP software, CMC-ERP accuracy is enhanced by 74%–99%, further confirming its effectiveness.

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

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

THE EFFECT OF SEASONAL VARIATION ON GNSS ZENITH TROPOSPHERIC DELAY

Abstract. The Global Navigation Satellite System (GNSS) signal experiences delays caused by the atmosphere, leading to the lengthening of the geometric path of the ray, commonly referred to as tropospheric delay. This delay is a significant source of error in GNSS positioning, contributing to a bias in the height component of several centimeters, even when meteorological data are simultaneously recorded and used in tropospheric models. In this study, considering seasonal variations, we investigated the impact of tropospheric delay on the GNSS height component. GNSS stations, part of the Turkish RTK CORS Network known as TUSAGA-Active (Turkish National Permanent GNSS Network Active), covered different heights over the 2014–2019 period. Daily coordinates of GNSS stations and tropospheric zenith delay were obtained through the GAMIT/GLOBK software solution.In the study, temperature, pressure, and relative humidity data of meteorological stations at different heights were converted to mean sea level. By using these values, interpolation estimates were made for the continuous GNSS stations in the same region with the IDW method. The most significant delay in GNSS signals occurs in July and August. This effect, which causes periodic changes in the zenith delay, varies inversely with the station's height. With the increase in the amount of water vapor in the atmosphere in parallel with the rise in the temperature in the summer months, it is seen that the stations at a low height are more exposed to the tropospheric effect than the stations at higher heights. In addition, GNSS stations' reduced meteorological values (temperature, pressure and relative humidity) show that the zenith delay values changed directly proportional to the temperature and inversely proportional to the pressure and relative humidity.

Troposphere delay modeling in SLR based on PMF, VMF3o, and meteorological data

Satellite laser ranging (SLR) requires accurate troposphere delay models to properly correct the observed distances to satellites and derive fundamental geodetic and geodynamic parameters. The currently used models for the tropospheric delay employ in situ meteorological data collected simultaneously with laser measurements. However, the standard models assume full symmetry of the atmosphere above the SLR stations because all meteorological data come from one sensor. In this study, we evaluate various methods of troposphere delay modeling based on numerical weather models, such as the Potsdam Mapping Function (PMF) and Vienna Mapping Function for optical frequencies (VMF3o), in situ measurements, the Wrocław gradient model (WGM) and the combination of different models. We found large discrepancies between pressure, temperature, and humidity records between in situ measurements and numerical models. The best results for the zenith delays are obtained when using in situ meteorological data with the estimation of tropospheric biases. For stations with some deficiencies in proper humidity measurements, e.g., Zimmerwald in Switzerland, the best results are obtained when using hydrostatic zenith delays based on in situ data and wet delays based on numerical weather models. Finally, we found that using horizontal gradients of the tropospheric delay is indispensable to avoid biases in the SLR-based Earth rotation parameters of approximately 20 μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu$$\\end{document}as for polar motion. The horizontal gradients successfully account for the asymmetry of the troposphere above SLR stations and can be derived from PMF, VMF3o, or a parameterized WGM model with similar accuracies.

Validation and Calibration of Tropospheric Wet Delay Models over Nigeria Using GPS Data

Validation and Calibration of Tropospheric Wet Delay Models over Nigeria Using GPS Data

Enhancing InSAR accuracy: Unveiling more accurate displacement fields through 3-D troposphere tomography

Interferometric Synthetic Aperture Radar (InSAR) measurements are susceptible to tropospheric delay induced by changes in tropospheric temperature, pressure, and water vapor. While pressure and temperature temporal variations have a limited impact on phase gradients, variations in water vapor, which contribute to the wet component of tropospheric delay, play a significant role. Therefore, obtaining a more accurate estimation of the wet refractivity of the tropospheric layer is crucial for improving InSAR displacement field accuracy. This paper presents the utilization of Global Navigation Satellite Systems (GNSS) tropospheric tomography for reconstructing three-dimensional (3-D) wet refractivity. Various data sources are employed, including GNSS measurements, ERA5 reanalysis data, radiosonde observations, and Sentinel-1A radar acquisitions. ERA5 reanalysis data and radiosonde observations are used to calculate tropospheric hydrostatic delay and to evaluate the wet refractivity obtained from tomography, respectively. The effectiveness of tomography techniques in mitigating the tropospheric signal in unwrapped interferograms is compared with the total tropospheric delay obtained from Generic Atmospheric Correction Online Service (GACOS) products, which is one of the most common approach for tropospheric correction of InSAR measurements. To ensure a comprehensive analysis, the effects of the correction methods are investigated in two different weather conditions. Based on the results, GNSS tropospheric tomography reduces the mean Root Mean Square Error (RMSE) by about 1.2 cm compared to GACOS products. This technique proves to be highly effective in improving the accuracy of InSAR displacement field estimation, particularly under challenging weather conditions.

Real‐Time Water Levels Using GNSS‐IR: A Potential Tool for Flood Monitoring

AbstractGlobal Navigation Satellite System Interferometric Reflectometry (GNSS‐IR) using low‐cost antennas is a practical solution for monitoring water levels from rivers, lakes and seas that does not require submerging any instruments in water. Here we present a novel method for obtaining real‐time water levels using multiple low‐cost antennas that we validate by comparing with measurements from a co‐located pressure gauge at two sites with variable tides. Additionally, we use survey measurements to show that there is a site‐dependant mean bias in GNSS‐IR measurements up to a few centimeters, but this mean bias can be effectively removed by using a correction for the effect of tropospheric delay. We conclude that GNSS‐IR water level sensors could be a powerful tool for real‐time applications such as flood or storm surge monitoring and water resource management, as well as for improving the spatial coverage of sensors in remote regions.

Refined troposphere delay models by NWM ray-tracing for pseudolite positioning system and their performance assessment

Pseudolite positioning system can enhance GNSS (Global Navigation Satellite System) by improving satellite geometry and providing services independently in the GNSS unavailable environment. Many error items of pseudolite positioning system, e.g., tropospheric delay error, need to be corrected by an accurate model. While several tropospheric delay models suitable for pseudolite positioning systems have been proposed, the key parameters indicating the upper boundaries for tropospheric refraction are fixed to an experimental value in these models. In this paper, we studied the spatiotemporal characteristics of the upper boundary heights for hydrostatic and wet tropospheric delay based on the ERA5 global meteorological reanalysis data. With the refined height boundary term, we refine four existing tropospheric delay models for pseudolite positioning systems, including RTCA, MRTCA, Bouska and Hopfield models. To evaluate the performance of the refined models, we selected 12 airports distributed globally as experimental areas and analyzed the error characteristics of the four refined tropospheric models and the LTC model (independent of height). The experimental results show that when the slant distance between the pseudolite base station and the receiver is constant at 5 km, the MRTCA model has the best performance, with an RMSE (root mean square error) of about 0.15 m. When the elevation angle between the pseudolite base station and the receiver is constant, the RMSE of the LTC model is the smallest at the low elevation angle, and the RMSE of the MRTCA model is the smallest at the high elevation. The RMSE of pseudolite tropospheric delay models show seasonal variation.

Improving GNSS PPP-RTK through global forecast system zenith wet delay augmentation

The precise point positioning real-time kinematic (PPP-RTK) is a high-precision global navigation satellite system (GNSS) positioning technique that combines the advantages of wide-area coverage in precise point positioning (PPP) and of rapid convergence in real-time kinematic (RTK). However, the PPP-RTK convergence is still limited by the precision of slant ionospheric delays and tropospheric zenith wet delay (ZWD), which affects the PPP-RTK network parameters estimation and user positioning performance. The present study aims to construct a PPP-RTK model augmented with a priori ZWD values derived from the global forecast system (GFS) product (a global numerical weather prediction (NWP) model) to improve the PPP-RTK performance. This study gives a priori ZWD values and conversion based on the GFS products, and the full-rank GFS-augmented undifferenced and uncombined (UDUC) PPP-RTK network model is derived. To verify the performance of GFS-augmented UDUC PPP-RTK, a comprehensive evaluation using 10-day GNSS observation data from three different GNSS station networks in the United States (US), Australia, and Europe is conducted. The results show that with the GFS ZWD a priori information, PPP-RTK performance significantly improves at the initial filtering stage, but this advantage gradually decays over time. Based on 10-day positioning results for all user stations, the GFS ZWD-augmented PPP-RTK approach reduces the average convergence time by 46% from 10.0 to 5.4 min, the three-dimensional root-mean-square (3D-RMS) error by 5.7% from 3.5 to 3.3 cm, and the time to first fix (TTFF) value by 35.8% from 6.7 to 4.3 min, all when compared to the traditional PPP-RTK without GFS ZWD constraints.

A Hybrid Deep Learning Algorithm for Tropospheric Zenith Wet Delay Modeling with the Spatiotemporal Variation Considered

The tropospheric Zenith Wet Delay (ZWD) is one of the primary sources of error in Global Navigation Satellite Systems (GNSS). Precise ZWD modeling is essential for GNSS positioning and Precipitable Water Vapor (PWV) retrieval. However, the ZWD modeling is challenged due to the high spatiotemporal variability of water vapor, especially in low latitudes and specific climatic regions. Traditional ZWD models make it difficult to accurately fit the nonlinear variations in ZWD in these areas. A hybrid deep learning algorithm is developed for high-precision ZWD modeling, which considers the spatiotemporal characteristics and influencing factors of ZWD. The Convolutional Neural Network (CNN) and Long Short-Term Memory (LSTM) are combined in the proposed algorithm to make a novel architecture, namely, the hybrid CNN-LSTM (CL) algorithm, combining CNN for local spatial feature extracting and LSTM for complex sequence dependency training. Data from 46 radiosonde sites in South America spanning from 2015 to 2021 are used to develop models of ZWD under three strategies, i.e., model CL-A without surface parameters, model CL-B with surface temperature, and model CL-C introducing surface temperature and water vapor pressure. The modeling accuracy of the proposed models is validated using the data from 46 radiosonde sites in 2022. The results indicate that CL-A demonstrates slightly better accuracy compared to the Global Pressure and Temperature 3 (GPT3) model; CL-B shows a precision increase of 14% compared to the Saastamoinen model, and CL-C exhibits accuracy improvements of 30% and 12% compared to the Saastamoinen and Askne and Nordius (AN) model, respectively. Evaluating the models’ generalization capabilities at non-modeled sites in South America, data from six sites in 2022 were used. CL-A shows overall better performance compared to the GPT3 model; CL-B’s accuracy is 19% better than the Saastamoinen model, and CL-C’s accuracy is enhanced by 33% and 10% compared to the Saastamoinen and AN model, respectively. Additionally, the proposed hybrid algorithm demonstrates a certain degree of improvement in both modeling accuracy and generalization accuracy for the South American region compared to individual CNN and LSTM algorithm.

An initial investigation of the non-isotropic feature of GNSS tropospheric delay

Tropospheric delay is a significant error source in Global Navigation Satellite Systems (GNSS) positioning. Slant Path Delay (SPD) is commonly derived by multiplying Zenith Tropospheric Delay (ZTD) with a mapping function. However, mapping functions, assuming atmospheric isotropy, restrict the accuracy of derived SPDs. To improve the accuracy, a horizontal gradient correction is introduced to account for azimuth-dependent SPD variations, treating the atmosphere as anisotropic. This study uncovers that, amidst atmospheric dynamics and spatiotemporal changes in moisture content, the SPD deviates from that based on traditional isotropy or anisotropy assumption. It innovatively introduces the concept that SPD exhibits non-isotropy with respect to azimuth angles. Hypothesis validation involves assessing SPD accuracy using three mapping functions at five International GNSS Service (IGS) stations, referencing the SPD with the ray-tracing method. It subsequently evaluates the SPD accuracy with horizontal gradient correction based on Vienna Mapping Function 3 (VMF3) estimation. Lastly, the non-isotropic of SPD is analyzed through the ray-tracing method. The results indicate the smallest residual (1.1–82.7 mm) between the SPDs with VMF3 and those with the ray-tracing. However, introducing horizontal gradient correction yields no significant improvement of SPD accuracy. Considering potential decimeter-level differences in SPD due to non-isotropic tropospheric delay across azimuth angles, a precise grasp and summary of these variations is pivotal for accurate tropospheric delay modeling. This finding provides vital support for future high-precision tropospheric delay modeling.

A method for calculating real-time ZTD grid data in Chinese regions based on GNSS ZTD modified ERA5 grid products

The low spatial and temporal resolution and poor accuracy of real-time zenith tropospheric delay (ZTD) have always been one of the main constraints during the development of real-time GNSS applications. This paper presents a method to obtain real-time ZTD grid data in Chinese regions utilizing the ZTD-modified ERA5 grid products from GNSS stations. Initially, the original ZTD fitting function for vertical variation is improved. Then, the real-time ZTD grid data for the Chinese region (RZTDG) could be obtained by correcting the 7-day earlier ERA5 data through the real-time ZTD data from the GNSS stations. In this paper, we analyze the performance of the model under various weather conditions, and the results show that it still keeps a high accuracy even under variable weather conditions. ZTD data from 66 radiosonde stations in China in 2022 are used as reference values to evaluate the accuracy of the RZTDG. Experimental results show that the RMSE (2.3 cm) and MAE (1.8 cm) of the RZTDG are comparable to the ERA5 data of the day (RMSE: 2.4 cm, MAE: 1.8 cm) and significantly better than the accuracy of the HGPT2 (RMSE: 5.1 cm, MAE: 4.1 cm). Meanwhile, the Bias of RZTDG (0.1 cm) is much smaller than the Bias of HGPT2 (−0.9 cm) and the Bias of ERA5 (−0.8 cm), proving that the method in this paper has less deviation from the radiosonde ZTD data. Finally, the convergence times of the float PPP with and without tropospheric constraints are counted for 120 GNSS stations for DOY 11–13, DOY 101–103, and DOY 192–194 in 2022. The results show that the convergence time of the float PPP is reduced by 30% after constraining the ZTD using RZTDG.

Global zenith wet delay modeling with surface meteorological data and machine learning

The tropospheric delay is a major error source for space geodetic techniques, and the performance of its modeling is significantly limited due to the high spatiotemporal variability of the moisture in the lower atmosphere. In this study, global modeling of the tropospheric zenith wet delay (ZWD) was realized based on surface meteorological data obtained from radiosondes and Global Positioning System (GPS) radio occultation (RO) measurements through the random forest (RF) and backpropagation neural network (BPNN) regression analysis. The modeling performance was further validated based on two kinds of global atmospheric profiles for the year 2020. Our results show that the ZWD modeling accuracy gained by two machine learning regression approaches is significantly improved by taking into account surface meteorological parameters, especially the surface water vapor pressure when compared to the Global Pressure and Temperature 3 (GPT3) model. When surface meteorological data are available, the RF-B model yields ZWD estimations with an overall agreement of 3.1 cm in comparison with the sounding profiles and 2.4 cm in contrast to the GPS RO atmospheric profiles. The RF-B is superior to other models based on surface meteorological parameters for ZWD calculation, e.g., the accuracy improves by 21.8–23.8% against the approach by Saastamoinen and 7–12.2% against the formula by Askne and Nordius.

Enhancing Tropospheric Zenith Wet Delay Interpolation with Gaussian Process Regression

Enhancing Tropospheric Zenith Wet Delay Interpolation with Gaussian Process Regression

Показатель пожарной опасности для лесной среды с использованием метеорологических и GPS-данных на территории Забайкальского национального парка

The main indicators of potential fire hazards are temperature, relative humidity, precipitation, and wind speed readings. Prompt detection of fire risk should be an integral part of forest protection systems. For this purpose, it is essential to use automatic instruments based on comprehensive meteorological observations. In recent years, most forest fires in the Republic of Buryatia have started due to natural rather than anthropogenic causes. To assess the risk of forest fire based on current weather conditions, the Nesterov index is used. Continuous GPS measurements, combined with highprecision geodetic techniques, allow us to regularly obtain data on tropospheric signal delays, which provide information about the total water vapor content in the atmosphere (IWV). The possibility of using the IWV values obtained to assess the fire risk of forest areas is demonstrated, taking into account data from the Ust-Barguzin weather station located on the territory of the Trans-Baikal National Park. Creating an online resource based on Nesterov's complex indicator using GPS measurements and meteorological data would allow for real-time monitoring of fire risk in forests.

A predictive model for regional zenith tropospheric delay correction

A predictive model for regional zenith tropospheric delay correction

Advanced Tropospheric Delay Mitigation Method Using InSAR-Based Iterative Decomposition by Considering the Statistical Characteristics of Atmospheric Turbulence

Advanced Tropospheric Delay Mitigation Method Using InSAR-Based Iterative Decomposition by Considering the Statistical Characteristics of Atmospheric Turbulence