Water vapor is one of the most variable components in the earth's atmosphere and has a significant role in forming clouds, rain and snow, air pollution, and acid rain. Therefore, increasing the accuracy of estimated water vapor can lead to more accurate predictions of severe weather, upcoming storms, and natural hazards. In recent years, GNSS has turned out to be a valuable tool for remotely sensing the atmosphere. In this context, GNSS tomography evolved to an extremely promising technique to reconstruct the spatiotemporal structure of the troposphere. However, locating dual-frequency (DF) receivers with a spatial resolution of a few tens of kilometers sufficient for GNSS tomography is not economically feasible. Therefore, in this research, the feasibility of using single-frequency (SF) observations in GNSS tomography as an alternative approach has been investigated. The algebraic reconstruction technique (ART) and the total variation (TV) method are examined to reconstruct a regularized solution. The accuracy of the reconstructed water vapor distribution model using low-cost receivers is verified by radiosonde measurements in the area of the EPOSA (Echtzeit Positionierung Austria) GNSS network, which is mostly located in the east part of Austria for the period DoY 232–245, 2019. The results indicate that irrespective of the investigated ART and TV techniques, the quality of the reconstructed wet refractivity field is comparable for both SF and DF schemes. However, in the SF scheme the MAE with respect to the radiosonde measurements for ART + NWM and ART + TV can reach up to 10 ppm during noontime. Despite that, all statistical results demonstrate the degradation of the retrieved wet refractivity field of only 10–40% when applying the SF scheme in the presence of the initial guess.

Water vapour plays a key role in long-term climate studies and short-term weather forecasting. Therefore, to understand atmospheric variations, it is crucial to observe water vapour and its spatial distribution. In the current era, Global Navigation Satellite Systems (GNSS) are widely used to monitor this critical atmospheric component because GNSS signals pass through the atmosphere, allowing us to estimate water vapour at various locations and times. The amount of precipitable water vapour ($PWV$) is one of the most fascinating quantities, which provides meteorologists and climate scientists with valuable information. However, calculating $PWV$ accurately from processing GNSS observations usually requires the input of further observed meteorological parameters with adequate quality and latency. To bypass this problem, hourly $PWV$s without meteorological parameters are computed using the Random Forest and Artificial Neural Network algorithms in this research. The first step towards this objective is establishing a regional weighted mean temperature model for Austria. To achieve this, measurements of radiosondes launched from different locations in Austria are employed. The results indicate that Random Forest is the most accurate method compared to regression (linear and polynomial), Artificial Neural Network, and empirical methods. $PWV$ models are then developed using data from 39 GNSS stations that cover Austria’s entire territory. The models are afterwards tested under different atmospheric conditions with four radiosonde stations. Based on the obtained results, the Artificial Neural Network model with a single hidden layer slightly outperforms other investigated models, with only a 5% difference in mean absolute error. As a result, the hourly $PWV$ can be estimated without relying on measured meteorological parameters with an average mean absolute error of less than 2.5 mm in Austria.

GNSS tomography is an emerging remote sensing technique in the field of meteorology that is gaining increased attention in recent years. This method is used as a tool for atmospheric (particularly tropospheric) sensing and then applied in nowcasting and forecasting research. The tomographic approach can be used to determine the distribution of water vapour (WV), the most active component of the atmosphere. WV is one of the most important drivers of convection and precipitation. In this method, numerous line-of-sight integral observations at different locations and directions are used to derive a 3D distribution of a water vapor structure. One of the challenges in GNSS tomography is that different parameterisation methods are used for computing the design matrix. Here, the effect of the straight-line method versus the ray-tracing method is investigated for computing the length of a ray which passes through the model element. In addition, the effect of considering the topography of the area in the tomography model is analysed.The accuracy of the developed model is verified using radiosonde measurements in the COST benchmark dataset. Results show that the Eikonal ray-tracing method is superior to other schemes whether used with topography or not. The mean values of RMSE of estimated wet refractivity with respect to the radiosonde profiles for these schemes are about 1.313 ppm and 1.766 ppm, respectively. This work is conducted within COST Action ES1206 on Advanced global navigation satellite systems tropospheric products for monitoring severe weather events and climate (GNSS4SWEC) (2013 2017) and IAG Working Group GNSS tomography'

One of the most promising methods of GNSS meteorology is GNSS Tomography. This method can be used for the determination of water vapor distribution, which contributes to the reliability of weather forecasting and early warning of severe weather. Therefore, GNSS Tomography is a valuable source of information for meteorological and weather forecast. The system of equations of this problem is mixed-determined because propagated signals do not pass through some of the model elements within the area of interest. Consequently, the normal matrix is close to singular without any unique solution. To avoid singularity and achieve a unique solution, additional sources or horizontal and/or vertical constraints are usually applied. Here, three schemes have been considered for remedying the rank deficiency of the problem. In the first scheme, minimum horizontal and vertical constraints were imposed on the system of observation equations. Then, we have defined three schemes to evaluate the impact of Virtual Reference Stations (VRS) in comparison to horizontal and vertical constraints in the sparse GNSS network. Within a network of Austrian GNSS reference stations these schemes have been analyzed and validated with available radiosonde profiles for the period DoY 245–256 in 2017. According to our results, the consistency of the estimated refractivity field with radiosonde profiles in the dense GNSS network was generally better (RMSE 2.80 ppm) than for the two other schemes in the period of interest. Moreover, in the sparse GNSS network, the average of RMSE for schemes with VRS stations and constraints equation was about 3.02 and 3.27 ppm, respectively. Hence, the obtained results illustrate that applying VRS stations in the sparse GNSS network can lead to a better solution in comparison to applying horizontal and vertical constraints.

GNSS tropospheric tomography is one of the applications of the Global Navigation Satellite Systems (GNSS) signals which attracts more and more interest in the field of meteorology. This method can reconstruct the water vapour of the atmosphere, which has a considerable effect on weather forecasting and early warning systems of severe weather. In GNSS tomography, traditionally, a regular spaced 3D grid stretches from the GNSS network to the effective height of the troposphere in the area of interest. Therefore, this method can offer a permanent monitoring service for water vapour and wet refractivity fields at a low cost and a reasonable spatial resolution compared to conventional observations, like radiosonde and radio occultation profiles. Nevertheless, the quality of the reconstructed field is still one of the challenges in the GNSS tomography. In this research, we propose the concept of spread as a mathematical tool to provide a quality measure without using the reference field and calculating statistical measures likeRMSEandBias. Thereby, two synthetic and one real datasets (part of Germany and Czechia) covering overlapping periods between 29 May and 14 Jun of the year 2013 (DoY 149–165; DoY 160–165; DoY 160–165, 2013) have been tested to investigate the proposed method. According to the obtained results, the proposed tool shows a strong correlation (up to 0.81 for synthetic and 0.72 for real observations) with the standard deviation of the reconstructed wet refractivity with respect to the radiosonde profile reference. The correlation between spread and theBiasof the retrieved wet refractivity field is also significant. However, there is no clear picture depending on the applied spread computation models. Therefore, the spread of the resolution matrix can be used as a proxy for the accuracy of the tomography reconstruction field based on the quality of the observations, the initial field, and the design matrix.

GNSS tomography is an all-weather remote sensing technique to capture the spatiotemporal behavior of the atmospheric water vapor using the standing infrastructure of GNSS satellites and networks. In this method, the troposphere is discretized to a finite number of 3D elements (voxel) in horizontal and vertical directions. Then, the wet refractivity in these voxels is reconstructed using the Slant Wet Delay (SWD) observations in the desired tomography domain by means of the discrete inverse concept. Due to the insufficient spatial coverage of GNSS signals in the voxels within the given time window, some of the voxels are intersected by a few signals or plenty of signals, and others are not passed by any signals at all. Therefore, the design matrix is sparse, and the observation equation system of the tomography model is mixed-determined. Some constraints have to be applied or external data sources should be added to the tomography problem in order to reconstruct the wet refractivity field. Moreover, the GNSS tomography is a kind of discrete ill-posed problem, as all singular values of the structure matrix (A) in the tomography problem decay gradually to zero without any noticeable gap in the spectrum. Hence, slight changes in the measurements can lead to extremely unstable parameter solutions. In consequence, the regularization method should be applied to the inversion process and ensure a stable and unique solution for the tomography problem. In this research, the Total Variation (TV) method is suggested to retrieve a regularized solution. TV is a nonlinear technique, which resists noise and efficiently preserves discontinuities in the model. This method can also reconstruct the wet refractivity field without any initial field in a shorter time span. For this purpose, observation data from the EPOSA (Echtzeit Positionierung Austria) GNSS network located in the eastern part of Austria is processed within the period DoYs 232-245 in 2019. Then, the TV method is performed in six different tomography windows (10–60 min) with a time step of 10 min by focusing on near-real-time applications. Finally, radiosonde measurements in the area of interest are utilized to compare the estimated wet refractivity field in order to obtain the accuracy of the proposed method.