Tropospheric Delay Research Articles

Performance-Driven Design of Carrier Phase Differential Navigation Frameworks With Megaconstellation LEO Satellites

A navigation framework with carrier phase differential measurements from megaconstellation low Earth orbit (LEO) satellite signals is developed. The measurement errors due to ephemeris errors and ionospheric and tropospheric delays are derived and the statistics of the dilution of precision is characterized. Moreover, the joint probability density function of the megaconstellation LEO satellites' azimuth and elevation angles is derived to (i) enable performance characterization of navigation frameworks with LEO satellites in computationally efficient way and (ii) facilitate parameter design, namely, the differential baseline, to meet desired performance requirements. The Starlink constellation is used as a specific LEO megaconstellation example to demonstrate the developed carrier phase differential LEO (CD-LEO) navigation framework. Simulation results are presented demonstrating the efficacy of the proposed CD-LEO framework for an unmanned aerial vehicle (UAV) navigating for 15.1 km in 300 seconds, while using signals from 44 Starlink satellites, achieving a three-dimensional (3-D) position root mean squared error (RMSE) of 2.2 m and a 2-D RMSE of 32.4 cm. Experimental results are presented showing UAV navigating for 2.28 km in 2 minutes over Aliso Viejo, California, USA, using exclusively signals from only two Orbcomm LEO satellites, achieving an unprecedented position RMSE of 14.8 m.

Assessment of GNSS zenith tropospheric delay responses to atmospheric variables derived from ERA5 data over Nigeria

Tropospheric delay is a major error caused by atmospheric refraction in Global Navigation Satellite System (GNSS) positioning. The study evaluates the potential of the European Centre for Medium-range Weather Forecast (ECMWF) Reanalysis 5 (ERA5) atmospheric variables in estimating the Zenith Tropospheric Delay (ZTD). Linear regression models (LRM) are applied to estimate ZTD with the ERA5 atmospheric variables. The ZTD are also estimated using standard ZTD models based on ERA5 and Global Pressure and Temperature 3 (GPT3) atmospheric variables. These ZTD estimates are evaluated using the data collected from the permanent GNSS continuously operating reference stations in the Nigerian region. The results reveal that the Zenith Hydrostatic Delay (ZHD) from the LRM and the Saastamoinien model using ERA5 surface pressure are of identical accuracy, having a Root Mean Square (RMS) error of 2.3 mm while the GPT3-ZHD has an RMS of 3.4 mm. For the Zenith Wet Delay (ZWD) component, the best estimates are derived using ERA5 Precipitable Water Vapour (PWV). These include the ZWD derived by the LRM having an average RMS of 20.9 mm and Bevis equation having RMS of 21.1 mm and 21.0 mm for global and local weighted mean temperatures, respectively. The evaluation of GPT3-ZWD estimates gives RMS of 45.8 mm. This study has provided a valuable insight into the application of ERA5 data for ZTD estimation. In line with the findings of the study, the ERA5 atmospheric variables are recommended for improving the accuracy in ZTD estimation, required for GNSS positioning.

Comprehensive Analysis of the Global Zenith Tropospheric Delay Real-Time Correction Model Based GPT3

To obtain a higher accuracy for the real-time Zenith Tropospheric Delay (ZTD), a refined tropospheric delay correction model was constructed by combining the tropospheric delay correction model based on meteorological parameters and the GPT3 model. The meteorological parameters provided by the Global Geodetic Observing System (GGOS) Atmosphere and the zenith tropospheric delay data provided by Centre for Orbit Determination in Europe (CODE) were used as references, and the accuracy and spatial–temporal characteristics of the proposed model were compared and studied. The results show the following: (1) Compared with the UNB3m, GPT and GPT2w models, the accuracy and stability of the GPT3 model were significantly improved, especially the estimation accuracy of temperature, the deviation (Bias) of the estimated temperature was reduced by 90.60%, 32.44% and 0.30%, and the root mean square error (RMS) was reduced by 42.40%, 11.02% and 0.11%, respectively. (2) At different latitudes, the GPT3 + Saastamoinen, GPT3 + Hopfield and UNB3m models had great differences in accuracy and applicability. In the middle and high latitudes, the Biases of the GPT3 + Saastamoinen model and the GPT3 + Hopfield model were within 0.60 cm, and the RMS values were within 4 cm; the Bias of the UNB3m model was within 2 cm, and the RMS was within 5 cm; in low latitudes, the accuracy and stability of the GPT3 + Saastamoinen model were better than those of the GPT3 + Hopfield and UNB3m models; compared with the GPT3 + Hopfield model, the Bias was reduced by 22.56%, and the RMS was reduced by 5.67%. At different heights, the RMS values of the GPT3 + Saastamoinen model and GPT3 + Hopfield model were better than that of the UNB3m model. When the height was less than 500 m, the Biases of the GPT3 + Saastamoinen, GPT3 + Hopfield and UNB3m models were 3.46 cm, 3.59 cm and 4.54 cm, respectively. At more than 500 m, the Biases of the three models were within 4 cm. In different seasons, the Bias of the ZTD estimated by the UNB3m model had obvious global seasonal variation. The GPT3 + Saastamoinen model and the GPT3 + Hopfield model were more stable, and the values were within 5 cm. The research results can provide a useful reference for the ZTD correction accuracy and applicability of GNSS navigation and positioning at different latitudes, at different heights and in different seasons.

Tropospheric Delay Model Based on VMF and ERA5 Reanalysis Data

The global tropospheric zenith delay grid products of VMF1 and VMF3 (Vienna mapping functions) with different resolutions are used to calculate the tropospheric zenith delay of eight IGS (International GNSS Service) stations in China, and the accuracy of the two products under different interpolation methods is analyzed. As a result, the accuracy of utilizing different interpolation methods shows no obvious differences. The interpolation accuracy of the VMF3 grid model is slightly higher than that of the VMF1, and the interpolation accuracy of tropospheric delay is related to the elevation difference of grid points. In addition, according to ERA5 (the fifth generation of the Global Climate Information Analysis data set), the atmospheric stratification tropospheric delay is obtained, and a ZTD (the zenith tropospheric delay) height change grid model is constructed using the least squares exponential fitting method. The accuracy of the model is verified using the tropospheric delay product provided by the IGS. Finally, the constructed ZTD height change grid model is used as ZTD height reduction to solve the problem of large tropospheric delay errors in the VMF interpolation when the height change is large. The model accuracy of URUM station improve from 96.47 mm.to 32.97 mm (65.82%).

Regional Tropospheric Correction Model from GNSS–Saastamoinen–GPT2w Data for Zhejiang Province

Tropospheric delay models based on GNSS observations are essential for studying tropospheric changes. However, the uneven distribution of GNSS stations reduces the accuracy of GNSS tropospheric delay models in remote areas. Moreover, the accuracy of the tropospheric delay calculated by traditional models, which rely on meteorological parameters, is lower compared to the accuracy achieved by GNSS tropospheric models. At present, there are sufficient surface meteorological observation facilities around the world that can obtain surface meteorological parameters in real time. It is of great importance to make full use of the measured meteorological parameters to establish tropospheric correction models. Moreover, the empirical tropospheric models use free and open data, and one can obtain tropospheric parameters through the model without requiring any auxiliary information. We established a provincial real-time regional tropospheric fusion model using ground-based GNSS observations, a meteorological model, and empirical model data. Results showed that the tropospheric delay observations of the three models can be fused to establish a real-time tropospheric delay model with better accuracy and higher spatiotemporal resolution. The accuracy of Zenith Total Delay (ZTD) estimated by the fusion model reached 0.96/1.04/3.11 cm during the tropospheric quiet/active/typhoon period.

A Deep-Learning-Facilitated, Detection-First Strategy for Operationally Monitoring Localized Deformation with Large-Scale InSAR

SAR interferometry (InSAR) has emerged in the big-data era, particularly benefitting from the acquisition capability and open-data policy of ESA’s Sentinel-1 SAR mission. A large number of Sentinel-1 SAR images have been acquired and archived, allowing for the generation of thousands of interferograms, covering millions of square kilometers. In such a large-scale interferometry scenario, many applications actually aim at monitoring localized deformation sparsely distributed in the interferogram. Thus, it is not effective to apply the time-series InSAR analysis to the whole image and identify the deformed targets from the derived velocity map. Here, we present a strategy facilitated by the deep learning networks to firstly detect the localized deformation and then carry out the time-series analysis on small interferogram patches with deformation signals. Specifically, we report following-up studies of our proposed deep learning networks for masking decorrelation areas, detecting local deformation, and unwrapping high-gradient phases. In the applications of mining-induced subsidence monitoring and slow-moving landslide detection, the presented strategy not only reduces the computation time, but also avoids the influence of large-scale tropospheric delays and unwrapping errors. The presented detection-first strategy introduces deep learning to the time-series InSAR processing chain and makes the mission of operationally monitoring localized deformation feasible and efficient for the large-scale InSAR.

GNSS standard point positioning method based on spherical harmonic expansion of signal propagation path relating errors

The errors affecting standard point positioning mainly include the ionospheric delay error, tropospheric delay error, clock bias, and multipath effect. The errors are divided into two categories depending on the relation to the signal propagation path: errors related to the propagation path and errors unrelated to the propagation path. The ionospheric delay error, tropospheric delay error, and multipath effect are related to the satellite signal propagation path. Based on this characteristic, a new GPS standard point positioning algorithm based on spherical harmonic expansion (SPP-SH) is proposed, which uses spherical harmonic expansion to represent the errors related to the propagation path. We hope to continuously promote the further development of standard point positioning (SPP) by proposing this new algorithm and to further reduce the redundancy of SPP algorithms and improve the efficiency and reliability of the algorithms. The most important purpose of this manuscript is to validate the proposed SPP-SH algorithm based on GPS data provided by IGS stations. Pseudorange data of multiple continuous epochs are used to achieve a sequential sliding point positioning solution, and the truncated singular value decomposition and iteration method correcting characteristic values are used to solve the ill-conditioned equations in the SPP-SH algorithm. The SPP-SH algorithm is implemented and verified using IGS station data. The positioning accuracy of the SPP-SH algorithm for both dual-frequency data and single-frequency data is better than that of a traditional SPP algorithm. By analyzing the positioning results of the stations at different latitudes, when the spherical harmonic expansion is expanded to the same degree, the positioning accuracy in low latitude areas is poor because the station is seriously affected by factors such as the ionosphere and water vapor, while the positioning accuracy at high latitude stations is the best. The proposed SPP-SH algorithm is also realized in the kinematic scene based on the dual-frequency data collected dynamically. The kinematic data is collected by an Android phone which supports receiving dual-frequency GPS observations. To validate the reliability of the SPP-SH algorithm, two strategies are designed to validate the results, which proves that the newly proposed method can be used for positioning with low accuracy in kinematic conditions.

BDS-3 Triple-Frequency Timing Group Delay/Differential Code Bias and Its Effect on Positioning

BeiDou Global Navigation Satellite System (BDS-3) broadcasts multifrequency signals that offer more choices of frequencies and more signal combinations for positioning. This paper analyzes the effect of timing group delay (TGD) and differential code bias (DCB) of BDS-3 on the corresponding triple-frequency positioning. The triple-frequency observation models of BDS-3 are summarized and the DCB correction models are derived for the four different frequency combinations of triple-frequency ionospheric-free (IF) combination (IF123), two dual-frequency IF combinations (IF1213) and triple-frequency uncombined (UC123) positioning modes. Standard point positioning (SPP) and precise point positioning (PPP) experiments were conducted using 30 days of observations from 25 multi-GNSS experiment (MGEX) stations. The results show that the TGD/DCB correction has a significant impact on the accuracy of SPP. The positioning accuracy using IF123 and IF1213 models improved by about 73~90% after TGD correction, in comparison to a 27~30% improvement achieved using the UC123 model. In addition, the correction effect of DCB is slightly better than TGD. The DCB correction significantly improves accuracy in the initial epoch of the PPP, which helps the convergence of the filtering and reduces the convergence time. The average convergence times of IF123, IF1213 and UC123 are 26.1, 26.9 and 38.3 min, respectively, which are reduced by 6.79, 2.54 and 8.59% with DCB correction. The pseudorange residuals are closer to zero-mean random noise after DCB correction. Furthermore, the DCB affects the evaluation of the inter-frequency bias (IFB), ionospheric delay and floating ambiguity parameters. However, the tropospheric delay is almost unaffected by DCB.

A BeiDou Single-Frequency Pseudo-range Differential Positioning Algorithm Optimized for Trajectory

This paper proposes a BeiDou differential positioning algorithm for guided munitions. It builds on the traditional differential positioning algorithm, with the tropospheric delay corrected according to the trajectory altitude, which reduces the positioning error caused by the large elevation difference between the rover and base stations. Through simulation and real flight tests, it is verified that the algorithm can effectively improve the differential positioning accuracy of the missile-borne satellite receiver.

Accuracy Analysis of Real-Time Precise Point Positioning—Estimated Precipitable Water Vapor under Different Meteorological Conditions: A Case Study in Hong Kong

Precipitable water vapor (PWV) monitoring with real-time precise point positioning (PPP) is required for the improved early detection of increasingly common extreme weather occurrences. This study takes Hong Kong as the research object. The aim is to explore the accuracy of real-time global navigation satellite system (GNSS) PPP in estimating PWV at low latitudes and under different weather conditions. In this paper, real-time PPP is realized by using observation data from continuously operating reference stations (CORS) in Hong Kong and real-time products from the Centre National d’Etudes Spatiales (CNES). The Tm model calculated using numerical weather prediction (NWP) data converts the zenith tropospheric delay (ZTD) of real-time PPP inversion into PWV and evaluates its accuracy using postprocessing products. The experimental results show that compared with GPS, multi-GNSS can reduce the convergence time of PPP by 29.20% during rainfall periods and by 12.06% during nonrainfall periods. The improvement in positioning accuracy is not obvious, and the positioning accuracy of the two is equivalent. Real-time PPP ZTD experiments show that there are lower average values for bias, standard deviation (STDEV), and root mean square (RMS) during nonrainfall periods than during rainfall periods. Real-time PPP PWV experiments show that there are also lower bias, STDEV, and RMS values during nonrainfall periods than during rainfall periods. The comparative study between rainfall and nonrainfall periods is of great significance for the real-time monitoring and forecasting of water vapor changes.

Retrieving Accurate Precipitable Water Vapor Based on GNSS Multi‐Antenna PPP With an Ocean‐Based Dynamic Experiment

AbstractAs an attractive technique for measuring water vapor, the Global Navigation Satellite System (GNSS) faces additional challenges in dynamic applications such as in the open sea. We present a new method of retrieving precipitable water vapor (PWV) based on GNSS multi‐antenna precise point positioning (PPP), which uses GNSS data from multiple antennas and incorporates the constraints of known baseline vector and common tropospheric delay. The 4‐day shipborne dynamic experiment along the China coast demonstrates that the baseline vector constraint shortens the convergence time of positioning and atmospheric parameters, and also slightly improves their accuracies. The common tropospheric delay constraint helps to provide compromised, more robust, and sometimes more accurate PWV estimates. An evaluation with radiosonde‐derived PWVs shows that the combination of the two constraints achieves the best accuracy reaching 4.2 mm. This method helps to expand GNSS meteorology to the vast ocean and benefits satellite altimetry and weather forecasting.

An ERA5 tropospheric parameters-augmented approach for improving GNSS precise point positioning

Precise Point Positioning (PPP) technology has developed into a potent instrument for geodetic positioning, ionospheric modeling, tropospheric atmospheric parameter detection, and seismic monitoring. As atmospheric reanalysis data products' accuracy and spatiotemporal resolution have improved recently, it has become important to apply these products to obtain high-accuracy tropospheric delay parameters, like zenith tropospheric delay (ZTD) and tropospheric horizontal gradient. These tropospheric delay parameters can be applied to PPP to reduce the convergence time and to increase the accuracy in the vertical direction of the position. The European Centre for Medium-Range Weather Forecasts Reanalysis 5 (ERA5) atmospheric reanalysis data is the latest product with a high spatiotemporal resolution released by the European Center for Medium-Range Weather Forecasts (ECMWF). Only a few researches have evaluated the application of ERA5 data to Global Navigation Satellite System (GNSS) PPP. Therefore, this study compared and validated the ZTD products derived from ERA5 data using ZTD values provided by 290 global International GNSS Service (IGS) stations for 2016–2017. The results indicated a stable performance for ZTD, with annual average bias and RMS values of 0.23 cm and 1.09 cm, respectively. Further, GNSS observations for one week in each of the four seasons (spring: DOY 92–98; summer: DOY 199–205; autumn: DOY 275–281; and winter: DOY 22–28) from 34 multi-GNSS experiments (MGEX) stations distributed globally in 2016 were considered to evaluate the performance of ERA5-derived tropospheric delay products in GNSS PPP. The performance of ERA5-enhanced PPP was compared with that of the two standard GNSS PPP schemes (without estimated tropospheric horizontal gradient and with estimated tropospheric horizontal gradient). The results demonstrated that ERA5-enhanced GNSS PPP showed no significant improvement in the convergence times in both the Eastern (E) and Northern (N) directions, while the average convergence time over four weeks in the vertical (U) direction improved by 53.3% and 52.7%, respectively (in the case of pngm station). The average convergence times for each week in the U direction of the northern and southern hemisphere stations indicated a decrease of 16.3%, 12.6%, 9.6%, and 9.1%, and 16.9%, 9.6%, 8.9%, and 14.5%, respectively. Regarding positioning accuracy, ERA5-enhanced PPP showed an improvement of 13.3% and 16.2% over the two standard PPP schemes in the U direction, respectively. No significant improvement in the positioning performance was observed in both the E and N directions. Thus, this study demonstrated the potential application of the ERA5 tropospheric parameters-augmented approach to Beidou navigation and positioning.

Coseismic Deformation Field and Fault Slip Distribution Inversion of the 2020 Jiashi Ms 6.4 Earthquake: Considering the Atmospheric Effect with Sentinel-1 Data Interferometry

Due to some limitations associated with the atmospheric residual phase in Sentinel-1 data interferometry during the Jiashi earthquake, the detailed spatial distribution of the line-of-sight (LOS) surface deformation field is still not fully understood. This study, therefore, proposes an inversion method of coseismic deformation field and fault slip distribution, taking atmospheric effect into account to address this issue. First, an improved inverse distance weighted (IDW) interpolation tropospheric decomposition model is utilised to accurately estimate the turbulence component in tropospheric delay. Using the joint constraints of the corrected deformation fields, the geometric parameters of the seismogenic fault and the distribution of coseismic slip are then inverted. The findings show that the coseismic deformation field (long axis strike was nearly east-west) was distributed along the Kalpingtag fault and the Ozgertaou fault, and the earthquake was found to occur in the low dip thrust nappe structural belt at the subduction interface of the block. Correspondingly, the slip model further revealed that the slips were concentrated at depths between 10 and 20 km, with a maximum slip of 0.34 m. Accordingly, the seismic magnitude of the earthquake was estimated to be Ms 6.06. Considering the geological structure in the earthquake region and the fault source parameters, we infer that the Kepingtag reverse fault is responsible for the earthquake, and the improved IDW interpolation tropospheric decomposition model can perform atmospheric correction more effectively, which is also beneficial for the source parameter inversion of the Jiashi earthquake.

Global Navigation Satellite System-Based Retrieval of Precipitable Water Vapor and Its Relationship with Rainfall and Drought in Qinghai, China

Qinghai Province is situated deep in inland China, on the Qinghai-Tibet plateau, and it has unique climate change characteristics. Therefore, understanding the temporal and spatial distributions of water vapor in this region can be of great significance. The present study applied global navigation satellite system (GNSS) technology to retrieve precipitable water vapor (PWV) in Qinghai and analyzed its relationship with rainfall and drought. Firstly, radiosonde (RS) data is used to verify the precision of the surface pressure (P) and temperature (T) from the fifth-generation atmosphere reanalysis data set (ERA5) of the European Centre for Medium-Range Weather Forecasts (ECMWF), as well as the zenith troposphere delay (ZTD), calculated based on the data from continuously operating reference stations (CORS) in Qinghai. Secondly, a regional atmospheric weighted mean temperature (Tm) (QH-Tm) model was developed for Qinghai based on P, T, and relative humidity, as well as the consideration of the influence of seasonal changes in Tm. Finally, the PWV of each CORS in Qinghai was calculated using the GNSS-derived ZTD and ERA5-derived meteorological data, and its relationship with rainfall and drought was evaluated. The results show that the ERA5-derived P and T have high precision, and their average root mean square (RMS), mean absolute error (MAE) and bias were 1.06/0.85/0.01 hPa and 2.98/2.42/0.03 K, respectively. The RMS, MAE and bias of GNSS-derived ZTD were 13.2 mm, 10.3 mm and −1.8 mm, respectively. The theoretical error for PWV was 1.98 mm; compared with that of RS- and ERA5-derived PWV, the actual error was 2.69 mm and 2.16 mm, respectively. In addition, the changing trend of GNSS-derived PWV was consistent with that of rainfall events, and it closely and negatively correlated with the standardized precipitation evapotranspiration index. Therefore, the PWV retrieved from GNSS data in this study offers high precision and good feasibility for practical applications; thus, it can serve as a crucial tool for investigating water vapor distribution and climate change in Qinghai.

A tropospheric delay model to integrate ERA5 and GNSS reference network for mountainous areas: application to precise point positioning

A tropospheric delay model to integrate ERA5 and GNSS reference network for mountainous areas: application to precise point positioning

Analysis of systematic biases in tropospheric hydrostatic delay models and construction of a correction model

Abstract. In the field of space geodetic techniques, such as global navigation satellite systems (GNSSs), tropospheric zenith hydrostatic delay (ZHD) is chosen as the a priori value of tropospheric total delay. Therefore, the inaccuracy of ZHD will definitely affect parameters like the wet delay and the horizontal gradient of tropospheric delay, accompanied by an indirect influence on the accuracy of geodetic parameters, if not dealt with well at low elevation angles. In fact, however, the most widely used ZHD model currently seems to contain millimeter-level biases from the precise integral method. We explored the bias of traditional ZHD models and analyzed the characteristics in different aspects on a global annual scale. It was found that biases differ significantly with season and geographical location, and the difference between the maximum and minimum values exceeds 30 mm, which should be fully considered in the field of high-precision measurement. Then, we constructed a global grid correction model, which is named ZHD_crct, based on the meteorological data of the year 2020 from the ECMWF (European Centre for Medium-Range Weather Forecasts), and it turned out that the bias of traditional models in the current year could be reduced by ∼ 50 % when the ZHD_crct was added. When we verified the effect of ZHD_crct on the biases in the next year, it worked almost the same as the former year. The mean absolute biases (MABs) of ZHD will be narrowed within ∼ 0.5 mm for most regions, and the SDs (standard deviations) will be within ∼ 0.7 mm. This improvement will be helpful for research on meteorological phenomena as well.

Overbounding residual zenith tropospheric delays to enhance GNSS integrity monitoring

Overbounding residual zenith tropospheric delays to enhance GNSS integrity monitoring

Evaluation of InSAR Tropospheric Delay Correction Methods in a Low-Latitude Alpine Canyon Region

Tropospheric delay error must be reduced during interferometric synthetic aperture radar (InSAR) measurement. Depending on different geographical environments, an appropriate correction method should be selected to improve the accuracy of InSAR deformation monitoring. In this study, surface deformation monitoring was conducted in a high mountain gorge region in Yunnan Province, China, using Sentinel-1A images of ascending and descending tracks. The tropospheric delay in the InSAR interferogram was corrected using the Linear, Generic Atmospheric Correction Online Service for InSAR (GACOS) and ERA-5 meteorological reanalysis data (ERA5) methods. The correction effect was evaluated by combining phase standard deviation, semi-variance function, elevation correlation, and global navigation satellite system (GNSS) deformation monitoring results. The mean value of the phase standard deviation (Aver) of the linear correction interferogram and the threshold value (sill) of the semi-variogram were reduced by –20.98% and –41%, respectively, while the accuracy of the InSAR deformation points near the GNSS site was increased by 58%. The results showed that the three methods reduced the tropospheric delay error of InSAR deformation monitoring by different degrees in low-latitude mountains and valleys. Linear correction was the best at alleviating the tropospheric delay, followed by GACOS, while ERA5 had poor correction stability.

Regional/Single Station Zenith Tropospheric Delay Combination Prediction Model Based on Radial Basis Function Neural Network and Improved Long Short-Term Memory

Atmospheric water vapor is an essential source of information that predicts global climate change, rainfall, and disaster-natured weather. It is also a vital source of error for Earth observation systems, such as the global navigation satellite system (GNSS). The Zenith Tropospheric Delay (ZTD) plays a crucial role in applications, such as atmospheric water vapor inversion and GNSS precision positioning. ZTD has specific temporal and spatial variation characteristics. Real-time ZTD modeling is widely used in modern society. The conventional back propagation (BP) neural network model has issues, such as local, optimal, and long short-term memory (LSTM) model needs, which help by relying on long historical data. A regional/single station ZTD combination prediction model with high precision, efficiency, and suitability for online modeling was proposed. The model, called K-RBF, is based on the machine learning algorithms of radial basis function (RBF) neural network, assisted by the K-means cluster algorithm (K-RBF) and LSTM of real-time parameter updating (R-LSTM). An online updating mechanism is adopted to improve the modeling efficiency of the traditional LSTM. Taking the ZTD data (5 min sampling interval) of 13 international GNSS service stations in southern California in the United States for 90 consecutive days, K-RBF, R-LSTM, and K-RBF were used for regions, single stations, and a combination of ZTD prediction models regarding research, respectively. Real-time/near real-time prediction results show that the root-mean-square error (RMSE), mean absolute error (MAE), coefficient of determination (R2), and training time consumption (TTC) of the K-RBF model with 13 station data are 8.35 mm, 6.89 mm, 0.61, and 4.78 s, respectively. The accuracy and efficiency of the K-RBF model are improved compared with those of the conventional BP model. The RMSE, MAE, R2, and TTC of the R-LSTM model with WHC1 station data are 6.74 mm, 5.92 mm, 0.98, and 0.18 s, which improved by 67.43%, 66.42%, 63.33%, and 97.70% compared with those of the LSTM model. The comparison experiments of different historical observation data in 24 groups show that the real-time update model has strong applicability and accuracy for the time prediction of small sample data. The RMSE and MAE of K-RBF with 13 station data are 4.37 mm and 3.64 mm, which improved by 47.70% and 47.20% compared to K-RBF and by 28.48% and 31.29% compared to R-LSTM, respectively. The changes in the temporospatial features of ZTD are considered, as well, in the combination model.

Comparison of tropospheric delay correction methods for InSAR analysis using a mesoscale meteorological model: a case study from Japan

A major source of error in interferometric synthetic aperture radar (InSAR), used for mapping ground deformation, is the delay caused by changes in the propagation velocity of radar microwaves in the troposphere. Correcting this tropospheric delay noise using numerical weather models is common because of their global availability. Various correction methods and tools exist; selecting the most appropriate one by considering weather models, delay models, and delay calculation algorithms is essential for specific applications. We compared the performance of two tropospheric delay correction methods applied to Advanced Land Observing Satellite-2 (ALOS-2) data acquired over Japan, where the atmospheric field is complex with significant seasonal variation. We tested: (1) a method of delay integration along the slant radar line-of-sight (LOS) path using the mesoscale model (MSM) provided by the Japan Meteorological Agency and (2) the Generic Atmospheric Correction Online Service (GACOS) for InSAR, which estimates delay using the high-resolution forecast (HRES)-European Centre for Medium-Range Weather Forecasts (ECMWF) products along with an iterative decomposition approach. The results showed that the tropospheric delay correction using the slant-delay integration approach with MSM, which has a finer temporal and spatial resolution, performed slightly better than GACOS. We further found that the differences in the refractivity models would have limited significance, suggesting that the difference in performance mainly originates from differences in the numerical weather models being used. This study highlights the importance of using the best-available numerical weather model data for tropospheric delay calculations.Graphical