Prediction of troposphere wet delay

The study of climate change is an important field of research. Monitoring of atmospheric variability especially the tropospheric precipitable water vapor (PWV) is a powerful way to investigate climate change. Global navigation satellite systems (GNSS) provide a good tool for studying atmospheric parameters as GNSS signals along its path from the satellites to the ground based receivers suffer a significant delay due to the refractivity of earth’s atmosphere. GNSS signals are not only delayed but also refracted in the neutral atmosphere. The zenith wet delays (ZWD) caused by the troposphere can be estimated during the geodetic processing of GNSS signals. Since the ZWD is tightly correlated to the PWV, GNSS observations can be used to study the changes of PWV. In this study GNSS data from the Egyptian permanent GNSS network (EPGN), International GNSS Service (IGS), EUREF Permanent Network (EPN) and Scripps Orbit and Permanent Array Center (SOPAC), for the years 2013 and 2014, were used. These GNSS stations provided a good geometrical coverage over the respective region. All GNSS data were processed using Bernese V 5.2 software. The needed product from GNSS data processing is the tropospheric zenith total delay (ZTD) over each GNSS site. The ZTD is divided based on physical parameters into zenith hydrostatic delay (ZHD) and zenith wet delay (ZWD). The ZWD is the basic observable used to calculate PWV. The values of the PWV were calculated and its variation over the study area was investigated. The quality of calculated PWV values from GNSS data evaluated against traditional Radiosonde (RS) measurements. The results of GNSS PWV showed good agreement with RS PWV when the PWV values were low, but this agreement became worse at high PWV values as the differences between the two techniques increased. The correlation coefficient between RS PWV and GNSS PWV varied from 0.31 to 0.84. Standard deviation of the differences between RS PWV and GNSS PWV ranged from 2.369 to 5.973 mm. The PWV estimated from GNSS observations had annual cycle, and its cycle in 2013 was different from that in 2014. The PWV differences between the 2 years clarified that the water vapor content over the east Mediterranean in most of 2014 days was higher than that in 2013. Furthermore, PWV variations were noted on both temporal and spatial scales. The highest temporal variation value was 25.41 mm whereas the maximum value of the spatial variation was 19.67 mm. The present study illustrated the importance of using geodetic networks to provide atmospheric information.

The tropospheric wet delay is a significant systematic error of GNSS positioning, nevertheless it carries important information to meteorologists. It is closely related to the integrated water vapour that is the upper limit of precipitable water. The zenith wet delay can be converted to the integrated water vapour using a simple conversion factor. This conversion factor can be determined with the empirical formulae derived from radiosonde observations. In the past decades, numerous models were derived for this purpose, but all of these models rely on radiosonde observations stemming from a limited area of the globe. Although these models are valid for the area, where the underlying radiosonde observations were measured, there are several examples that these empirical formulae are used to validate GNSS based integrated water vapour estimations all over the globe. Our aim is to create a global model for the conversion of the zenith tropospheric delay to the integrated water vapour for realtime and nearrealtime applications using globally available Numerical Weather Models (NWM). Thus our model takes into consideration the fact that the model parameters strongly depend on the geographical location. 10 years of monthly mean ECMWF (European Center for Medium-Range Weather Forecast) dataset were used for the derivation of the model parameters in a grid with the resolution of 1° × 1°. The empirical coefficients of the developed models depend on two input parameters, namely the geographical location and the surface temperature measured at the station. Thus, the new models can be used for both realtime and near-realtime GNSS meteorological applications. The developed models were validated using 6 years of independent global ECMWF monthly mean analysis datasets (2011–2016). The results showed, that the application of the original models outside the area of the underlying radiosonde data sets can result in a relative systematic error of 7–8% in the estimation of the conversion factor as well as the estimated IWV values.

The accurate modeling of tropospheric path delay is significant for data processing of radio space-geodetic techniques such as Global Navigation Satellite System (GNSS) and Very-Long-Baseline Interferometry (VLBI). The Vienna Mapping Function 1 (VMF1) model, based on continuous update of Numerical Weather Prediction (NWP) data from the European Centre for Medium-Range Weather Forecasts (ECMWF), is recommended for this purpose in post-processing. The VMF1 coefficients determined from forecast data of the ECMWF are now readily and freely available. However, little or no implementation of this forecast VMF1 (VMF1-FC) model in real-time GNSS or VLBI applications has occurred. This study investigates the performance of the VMF1-FC model in terms of its three components which are critical for the modeling of tropospheric path delay: the Zenith Hydrostatic Delay (ZHD), the Zenith Wet Delay (ZWD) and mapping functions. All three components are assessed in the context of GNSS Precise Point Positioning (PPP) using 28 global stations over a 70-day period. The Zenith Total Delays (ZTD) derived with the VMF1-FC (implemented in real-time PPP) are shown to agree well with the tropospheric delay product from the Center for Orbit Determination Europe (CODE). Root mean square (RMS) errors associated with these ZTD estimates are < 10 mm at all 28 stations. The results also show that the VMF1-FC model performs better than empirical models such as the widely used Global Pressure and Temperature 2 (GPT2) and GPT2 wet (GPT2w), with smaller RMS errors associated with the ZTD estimates. It is recommended that VMF1-FC be applied for future tropospheric delay modeling in real-time GNSS and VLBI applications.

Observations performed with ground-based space geodetic and remote sensing techniques are sensitive to the amount of water vapour in the neutral atmosphere. Corresponding parameters that describe the signal delay in the troposphere can be derived for example from the analysis of data collected from geodetic Very Long Baseline Interferometry (VLBI), Global Navigation Satellite System (GNSS), as well as microwave radiometers. The latter instruments are often referred to as water vapour radiometers (WVR). The Onsala Space Observatory (OSO) operates a number of such instruments for VLBI, GNSS and WVR measurements, all co-located within about 600 m. Among these are the Onsala twin telescopes (OTT), two modern 13.2~m diameter radio telescopes performing observations in the VLBI Global Observing System (VGOS) of the International VLBI Service for Geodesy and Astrometry (IVS). The OTT are the first operational VGOS twin telescopes worldwide and are contributing with observations to the IVS since 2019. OSO also operates eight permanently installed GNSS stations, of which two are official stations in the International GNSS Service (IGS) network. Furthermore, OSO operates ground-based microwave radiometers, which are used for atmospheric research and perform continuous observations of the water vapour content in the neutral atmosphere. Data analysis of all three techniques, VLBI, GNSS and WVR, allows to derive information on the temporal and spatial variations of water vapour in the neutral atmosphere. Using co-located instrumentation within a few hundred metres distance thus offers a perfect opportunity for comparisons and assessments of the results. We focus on data recorded at OSO during 2022 and compare the parameters describing the signal delay in the neutral atmosphere, i.e. the so-called equivalent zenith total delays and the linear horizontal delay gradients. The temporal resolution of the derived parameters is 15 min or less. Out of more than 40 VGOS experiments in 2022, each of a duration of 24 h, we have WVR data covering at least half of the session in all except one. &amp;#160;We have examples where the equivalent zenith wet delay only varies by 2--3 cm over an experiment during rather stable atmospheres. &amp;#160;When the atmosphere is more variable the zenith wet delay can vary by more than 10 cm over 24 h.

&amp;lt;p&amp;gt;Radio signals transmitted by Global Navigation Satellite System (GNSS) satellites propagate through the atmosphere before being received on Earth. Thereby, the signal is delayed and tropospheric parameters can be estimated. The good global coverage of GNSS receivers, combined with the high temporal resolution and the high accuracy, make GNSS a suitable tool for studies on the atmosphere.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;Atmospheric delays are differentiated into a zenith hydrostatic (ZHD) and a non-hydrostatic, or zenith wet delay (ZWD). The hydrostatic part has a larger contribution (causing a delay of roughly 2.4 meters in the zenith direction) but can be modeled with sufficient accuracy using analytical methods. The ZWD has a smaller contribution (causing a delay between 0 to 40 centimeters) and depends mainly on the water vapour content in the atmosphere. However, due to the variable nature of water vapour, the ZWD is difficult to model and is therefore typically estimated. Its quantification is essential since it drives weather systems and climate change to a great extent. For many applications, such as weather forecasting or positioning using low-cost GNSS receivers such as smartphones, global real-time monitoring or even predictions of ZWD would be required and be beneficial.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;In the last decade, machine learning (ML) algorithms have gained a lot of interest and are successfully utilized in many different fields. Thereby, ML algorithms have proven to be able to efficiently process and combine large amounts of data and solve problems of various kinds.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;This motivated us to investigate the feasibility of ML algorithms for the prediction of tropospheric parameters, in particular ZWD, with the help of meteorological data such as the water vapour content. The work aims to develop a global model capable of predicting ZWD in space and time. Therefore, different ML algorithms are used to train a model based on meteorological features. The performance of the utilized algorithms is evaluated based on commonly used performance metrics, such as Root Mean Squared Error (RMSE) and R&amp;amp;#178;.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;Preliminary investigations are carried out utilizing 3000 GNSS stations distributed over Europe. The performance of various ML methods, such as Linear Regression methods, Random Forest, (Extreme) Gradient Boosting, and Multilayer Perceptron is compared. Furthermore, different feature combinations, as well as training sample sizes are investigated. It is revealed that linear methods are not able to properly reflect the observations. Instead, our Random Forest approach provides, so far, the highest model accuracy with an RMSE of 1.7 centimeters and an R&amp;amp;#178; value of 0.88.&amp;lt;/p&amp;gt;

Global Navigation Satellite System (GNSS) signals arrive at the Earth in a nonlinear and slightly curved way due to the refraction effect caused by the troposphere. The troposphere delay of the GNSS signal consists of hydrostatic and wet parts. In particular, tropospheric wet delay prediction and interpolation are more difficult than those of the dry component due to the rapid temporal and spatial variation of the water vapor content. Wet delay estimation and interpolation with a sufficient accuracy is an important issue for all parameters obtained by GNSS positioning techniques. In particular, in real-time positioning applications, errors caused by interpolation of the wet troposphere delay are reflected in the height component of about 1 to 2 cm. Furthermore, the amount of water vapor in the troposphere is very important information in weather forecast applications obtained as a function of wet delay. Therefore, real-time monitoring of the troposphere can be achieved with a higher resolution and accuracy by utilizing neural network models for interpolation of the wet tropospheric delay. In addition, in the absence of the GNSS station, wet delays can be interpolated by means of the surrounding stations to the desired location. In this study, a back propagation artificial neural network (BPNN) model based on meteorological parameters obtained from The New Austrian Meteorological Measuring Network (TAWES) was used to interpolate wet troposphere delay. Analysis was carried out at 40 reference stations of the Echtzeit Positionierung Austria (EPOSA) GNSS Network covering the whole of Austria. The interpolation of zenith wet delays based on the artificial neural network was performed by using latitude, longitude, altitude and meteorological parameters (temperature, pressure, weighted mean temperature, and water vapor pressure). These parameters were then subtracted from the artificial neural network model one by one and six different artificial neural networks were designed. In addition, the linear interpolation method (LIN) and inverse distance weighted interpolation method (IDW) were used as conventional interpolation methods. In order to investigate the effect of the network density on interpolation methods, three networks, including 40, 30, and 20 reference stations, were formed and the increased distance effect on interpolation methods was evaluated. In addition, analyses were conducted in winter, spring, and summer to evaluate the seasonal effects on interpolation methods. According to the statistical analysis, the root mean square error (RMSE) values of the IDW, LIN, and BPNN methods were found to be 12.6, 13.4, and 5.9 mm, respectively.

One of the challenges in the innovative application of global navigation satellite systems (GNSS) lies in real-time single-frequency precise point positioning (RT-SFPPP). The well-known problems associated with SFPPP are its slow convergence and lower positioning accuracy due to the effects of various errors inherited by the GNSS positioning, including the atmospheric error. In order to mitigate the two above-mentioned problems, several scenarios for the reduction of the atmospheric delays in RT-SFPPP, including the ionospheric constraint and tropospheric constraint, were investigated in this research. The performance of the RT-SFPPP utilizing the above-mentioned methods was evaluated using one-week observations from multi-GNSS experiment stations in a simulated kinematic mode. Results showed that the convergence time of the RT-SFPPP was significantly shortened when the slant ionospheric delays derived from the real-time ionospheric products provided by Centre National d’Études Spatiales were applied as the pseudo-observations. Results also showed that the convergence time of GPS + GLONASS RT-SFPPP can be reduced by modeling the frequency-dependent part of the GLONASS receiver uncalibrated code delay as a quadratic polynomial function of GLONASS frequency number. The a priori zenith wet delays (ZWDs) derived from forecast Vienna Mapping Functions 3 (VMF3_FC) were compared to the reference ZWDs from globally distributed radiosonde stations. The mean root mean square error of the a priori ZWDs resulting from VMF3_FC at 381 radiosonde stations in 2020 was 1.53 cm compared to the radiosonde-based ZWDs. When the ZWDs derived from VMF3_FC were used as pseudo-observations in the position estimation system, the convergence time for the vertical positioning reaching a 0.3 m accuracy was considerably shortened.

Accurate tropospheric delays are of great importance for both Global Navigation Satellite System (GNSS)-based positioning and precipitable water vapor monitoring. The gridded tropospheric delay products, including zenith hydrostatic delays (ZHD) and zenith wet delays (ZWD), are the most ideal method for accessing accurate tropospheric delays. The vertical adjustment method is critical for implementing the gridded tropospheric products. In this work, we consider the different models used for grid products and assess their performance over Yunnan mountains with complex topography. We summarize the main results as follows: (1) The products can provide accurate ZHD with mean biases of −2.6 mm and mean Standard Deviation (STD) of 1.5 mm while the ZWD results from grid products show a performance with biases of −0.4 mm and STD of 1.3 cm over the Yunnan area. (2) The Tv-based model shows a better performance than the T0-based model and IGPZWD in rugged areas with large height differences. The grid products can provide hourly ZHD with biases of 3 mm and wet delay with mean biases of within 2 cm and mean STD of below 3 cm in the Yunnan mountains, which exhibit a large height difference of around 1.5 km. (3) The radiosondes results confirm that the Tv-based model has an obvious advantage in calculating ZHD height corrections for differences within 2 km while the T0-model suffers from a loss in accuracy in the case of large height differences. If the site is located more than 1 km below the reference height, the IGPZWD model can provide a better ZWD with a mean bias of 1.5 cm and a mean STD of 1.7 cm. With vertical reduction models, the grid products can provide accurate ZHD and ZWD in real time, even if in complex area.

Developing a new combined model of zenith wet delay by using neural network

The BDS-3 provides signals at six different frequency bands, which are expected to improve the precision and convergence speed of Precise Point Positioning (PPP). To fully utilize the full-frequency data from BDS-3, three PPP function models were constructed: the six-frequency undifferenced and non-combined model (UC6), the single-layer six-frequency ionosphere-free model (IF6-1), and the six-frequency ionosphere-free dual-combination model (IF6-2).For the six-frequency undifferenced and non-combined model (UC6), the IFB (Inter-frequency Bias) processing strategy was studied, and the impact of three commonly used processing strategies on IFB estimation was analyzed. The results showed that when using constant models and random walk models, the estimated IFB values were similar, while the white noise model, despite slight fluctuations in the estimated IFB, exhibited a trend consistent with the other two models.The positioning experimental results indicated that the positioning accuracy after static convergence for the UC6, IF6-1, and IF6-2 models was similar. The horizontal mean accuracy was 1.36, 1.35, and 1.39 cm, respectively, and the vertical accuracy was 1.42, 1.45, and 1.63 cm. In dynamic mode, the horizontal accuracy was 4.04, 4.10, and 4.12 cm, and the vertical accuracy was 5.52 cm, 5.19 cm, and 5.02 cm.In terms of convergence time, the IF6-1 model showed superior static and dynamic convergence performance compared to the UC6 and IF6-2 models. Further analysis compared the receiver clock offsets, inter-frequency biases, and zenith wet delays between the different models. The receiver clock offset time series from all three models were consistent, and the inter-frequency bias for the same receiver model remained stable throughout the day. Additionally, the zenith wet delay estimates from all three models tended to converge after the process reached steady-state.

Atmospheric wet delay caused by Precipitable Water Vapor (PWV) significantly impacts the performance of many geodetic surveying systems such as Global Navigation Satellite System (GNSS). In this study, we use wet delay corrections forecast by the Weather Research and Forecasting (WRF) model to enhance GNSS Precise Point Positioning (PPP) during two observation periods with two different weather conditions, that is, period 1: March 01 to 14, 2020 (average PWV: 23.5 kg/m2) and period 2: June 02 to 15, 2020 (flooding weather with average PWV: 55.6 kg/m2), over the South China. PWV data from 277 to 263 GNSS stations are assimilated into WRF model to enhance the WRF water vapor forecasting capability for period 1 and period 2, respectively. Wet delay corrections from two different WRF configurations, that is, WRF no data assimilation and WRF with assimilation of GNSS PWV, are used to augment the PPP. Totally, eight WRF‐enhanced PPP schemes are tested. The results show that WRF‐enhanced PPP schemes generally have a better positioning performance in the up component than traditional PPP. After using WRF wet delay corrections, for static mode, the vertical positioning accuracy is improved by 14.6% and 33.7% for period 1 and period 2, respectively. The corresponding convergence time are reduced by 41.8% and 25.0% for period 1 and period 2, respectively. For kinematic mode, the positioning accuracy improvements in the up component reach 13.8% and 19.0% for period 1 and period 2, respectively. The kinematic PPP convergence time is reduced by up to 8.2% for period 1.

Atmospheric water vapor estimates from static ground-based Global Navigation Satellite System (GNSS) receivers are now operationally assimilated into numerical weather prediction models, either as total precipitable water vapor (PWV) or zenith total delay. To extend this concept, the estimation of water vapor using kinematic GNSS has been investigated for over a decade. Previous kinematic GNSS PWV studies suggest a 2–3-mm PWV measurement agreement with radiosondes, almost commensurate with static GNSS PWV measurement accuracy, but the only comprehensive experiments undertaken have been shipborne. As a first step toward extending sea level–based studies to airborne experiments that obtain atmospheric profiles, the authors considered the kinematic GNSS estimation of atmospheric water vapor along a repeatable trajectory spanning substantial topographic relief, namely, the Snowdon Mountain Railway, United Kingdom. The atmospheric water vapor was indirectly quantified through the GNSS estimation of zenith wet delay (ZWD). Static GNSS [GPS+ Globalnaya Navigatsionnaya Sputnikovaya Sistema (GLONASS)] reference receivers were installed at the 950-m-altitude profile’s extremities, providing ZWD reference values that were interpolated to the train’s altitude, together with profiles from 100-m-resolution runs of the Met Office Unified Model. Similar GNSS ZWD accuracies to those from shipborne studies are demonstrated, namely, 12.1 mm (RMS) using double-difference relative kinematic GPS and 16.2 mm using kinematic GPS precise point positioning (PPP), but which is improved to 11.6 mm when using kinematic GPS+GLONASS PPP, commensurate with the relative kinematic GPS. The PPP solution represents a more typical airborne estimation scenario, that is, without relying on nearby GNSS reference stations.

Atmospheric precipitable water vapor (PWV) is a key variable for weather forecast and climate research. Various techniques (e.g., radiosondes, global navigation satellite system, satellite remote sensing and reanalysis products by data assimilation) can be used to measure (or retrieve) PWV. However, gathering PWV data with high spatial and temporal resolutions remains a challenge. In this study, we propose a new empirical PWV grid model (called ASV-PWV) using the zenith wet delay from the Askne model and improved by the spherical harmonic function and vertical correction. Our method is convenient and enables the user to gain PWV data with only four input parameters (e.g., the longitude and latitude, time, and atmospheric pressure of the desired position). Profiles of 20 radiosonde stations in Qinghai Tibet Plateau, China, along with the latest publicly available C-PWVC2 model are used to validate the local performance. The PWV data from ASV-PWV and C-PWVC2 is generally consistent with radiosonde (the average annual bias is −0.44 mm for ASV-PWV and −1.36 mm for C-PWVC2, the root mean square error (RMSE) is 3.44 mm for ASV-PWV and 2.51 mm for C-PWVC2, respectively). Our ASV-PWV performs better than C-PWVC2 in terms of seasonal characteristics. In general, a sound consistency exists between PWV values of ASV-PWV and the fifth generation of European Centre for Medium-Range Weather Forecasts Atmospheric Reanalysis (ERA5) (total 7381 grid points in 2020). The average annual bias and RMSE are −0.73 mm and 4.28 mm, respectively. ASV-PWV has a similar performance as ERA5 reanalysis products, indicating that ASV-PWV is a potentially alternative option for rapidly gaining PWV.

The vertical structure of the atmospheric water vapor induces phase errors in interferometric synthetic aperture radar (SAR) data. This paper presents a simulation study to investigate whether spaceborne submillimeter radiometric observations, which can be realized with fairly high spatial resolution, are able to derive the vertical structure of the atmospheric wet delay. The accuracy of the retrieved zenith wet delay (ZWD) trend as a function of surface height is assessed in order to correct the associated height dependence of the interferometric phase error in a SAR interferogram. Using a simulated benchmark, we evaluate the errors associated with the use of both a linear and an exponential model of the behavior of ZWD as a function of the surface height. This paper shows a fairly accurate reconstruction of the trend parameters estimated from radiometer brightness temperature images, with respect to realistic atmospheric profiles provided by radiosounding observations (RAOBs). The trend parameters that we consider in this paper are the slope K for the linear model and scale height H for the exponential one. An overall better accuracy is found for the exponential model, which is more representative of the actual behavior of ZWD with height, resulting in a residual uncertainty in the path delay due to the atmospheric stratification of approximately 0.2-0.3 cm and nearly zero bias, as compared to RAOBs.

Tropospheric delay is an important error source in Global Navigation Satellite System (GNSS) positioning and can also be used in water vapor monitoring. Many models have been built to correct tropospheric delays or to convert zenith wet delays to precipitable water vapor. However, these models suffer from limited resolutions (spatial resolution lower than 1° and temporal resolution lower than 6 hr), which affects their performance. The release of European Centre for Medium‐Range Weather Forecasts ReAnalysis 5 (ERA5) provides the opportunity to lift this limit. In this study, we use the ERA5 hourly 0.5° × 0.5° data to build a new model over China, which integrates tropospheric delay correction for GNSS positioning and weighted mean temperature calculation for GNSS meteorology. By modeling the diurnal variations of zenith hydrostatic delay, zenith wet delay, and weighted mean temperature and the seasonal variations in their lapse rates, this model has the state‐of‐the‐art spatial resolution of 0.5° × 0.5° and temporal resolution of 1 hr. We validate this new model by the ERA5 data, the radiosonde data, and the GNSS data in comparison with the canonical GPT2w model. The results show that the new model has better accuracies in terms of root‐mean‐square than the GPT2w model in all parameters. Especially, the new model well captures the diurnal variations in tropospheric delay and weighted mean temperature. This new model provides accurate tropospheric delays and weighted mean temperature simultaneously, which enables GNSS receivers to measure precipitable water vapor directly and also benefits GNSS positioning.