Tropospheric wet delay, the main source of which is water vapor, is one of the major factors affecting the accuracy of positioning techniques using microwave. Tropospheric tomography is a powerful method to reconstruct the water vapor content in four-dimensional (4D) space. This paper studies the effect of using function-based and voxel-based tropospheric tomography methods on the positioning accuracy. This examination is performed on the static and kinematic positioning modes using Global Navigation Satellite Systems (GNSS) stations under different weather conditions. After validating the results of tomography methods using radiosonde observations, the tomography-based positioning solutions, including function-based and voxel-based approaches, are compared with the positions obtained using tropospheric models. The results of two GPS stations show that the accuracy increases when applying tomography approaches. The function-based tomography is able to increase the accuracy of the up component of the static and kinematic modes by about 0.42 and 0.79 cm, respectively, compared to the voxel-based method. In addition, the use of the function-based tropospheric tomography can decrease the convergence time of the kinematic Precise Point Positioning (PPP) solution.

Tropospheric signals are considered as one of the most important performance limitations to compute the deformations caused by earthquake, subsidence, volcano, and so on using interferometric synthetic aperture radar (InSAR) technique. Various correction methods have been proposed to reduce the effect of these signals in displacement fields in previous research works. Different types of correction methods are used to estimate the tropospheric signal on InSAR observations. For this purpose, meteorological data derived from ERA-Interim (ERA-I) data, Weather Research and Forecasting (WRF) model, and Advanced Synthetic Aperture Radar/ENVISAT acquisitions are used. ERA-I reanalysis data and a locally run WRF model are also used to compute the tropospheric corrections with integral of the air refractivity method, which is called integration method. Also, the ability of ray tracing techniques to reduce the effect of the tropospheric signal in unwrapped interferogram is compared with integration method. To carry out a comprehensive study, the effects of correction methods are studied in two different areas. The results of the ray tracing methods have a significant difference with the results obtained from integration method and are more efficient when the weather condition between two satellite acquisitions is more different. The results show that the three-dimensional ray tracing method can reduce the root-mean-square error of the results up to 4.8 cm compared to the integration methods.

Tropospheric tomography is one of the most important techniques to reconstruct three-dimensional (3D) images of the tropospheric water vapor fields using a local GNSS network. In the conventional tropospheric tomography method, called voxel-based tropospheric tomography, the 3D space is divided into many voxels and the amount of water vapor is estimated for each voxel. This method suffers from three disadvantages. First, it needs empirical constraints in order to fix the rank deficiency of the coefficient matrix. Second, the amount of water vapor is assumed to be constant in the 3D space of a voxel despite the large spatial variations of this parameter. Third, the number of unknown parameters is high compared to the number of observations. Therefore, an approach based on mathematical functions, called function-based tropospheric tomography, is presented to overcome these problems. The tropospheric tomography using the voxel-based and function-based approaches is performed using 17 GPS stations. Radiosonde observations and precise point positioning results are used to validate the obtained results. A comparison of the results with the radiosonde data indicates that using the function-based method reduces the mean RMSE by about 0.3 gr/m³. Validation using positioning under different wet conditions shows that in wet weather conditions the difference between the RMSE of the two tropospheric tomography approaches is significant. All the validations show the ability and applicability of the function-based tropospheric tomography approach.

Atmospheric phase screen (APS) is one of the main error sources of interferometric synthetic aperture radar (InSAR) measurements. In order to accurately retrieve displacement fields, it is necessary to use advanced methods to eliminate the tropospheric effect of interferograms. In this paper, the land subsidence in Kurdistan province of Iran is investigated using Sentinel-1A acquisitions on a single track for the period 2014–2018. The accurate and applicable 3D ray tracing technique is used to accurately estimate the APS. The ERA-I reanalysis data generated by European Centre for Medium Range Weather Forecasts (ECMWF) are used to implement the 3D ray tracing technique. In order to determine the effect of using the 3D ray tracing technique, the APSs are also determined using a traditional approach called, spatiotemporal filters method. To evaluate the capability of the two methods, the results are compared with the weather research and forecasting model (WRF) model. Finally, the interferograms are corrected using APSs from 3D ray tracing technique and traditional method and the subsidence rate in the study area is computed. Comparing the subsidence rates obtained from two APS estimation methods with piezometric data, GPS and precise levelling observations shows that the 3D ray tracing technique is significantly more accurate than traditional method in computing InSAR displacement fields.