Copula, a new approach for optimum design of Voxel-based GNSS tropospheric tomography based on the atmospheric dynamics

Global Navigation Satellite System (GNSS) signals scan the earth’s atmosphere with a high spatiotemporal resolution. They have promoted the application of the GNSS networks as an imaging system for the tomographic reconstruction of wet refractivity ( N_w) .To come up with a unique solution of this inverse problem and to preserve the atmospheric dynamics intact by solution, the resolution of reconstructed images of wet refractivityis usually increased. We propose a Copula-based approach as a geometry-free technique to develop a tomography network over southwest Germany and a part of France. Here, we apply the estimated N_w time series from Weather Research and Forecasting model from April to October 2016 and evaluate the pixel-wise dependence structure and dissimilarity measures of the N_w time series at seven pressure levels from 949.2 to 263.8 hPa. At each level, the most appropriate dissimilarity measure to give an optimal resolution is identified based on the percentage of pair pixels with asymmetric Copulas. Then, the optimum resolution is identified by evaluating the distance-based variations of dissimilarity values. The investigations propose a non-uniform tomography network for this region. Furthermore, we assess the geometry of the problem by investigating the resolution matrix of the tomography model in all hourly time epochs of Day of Year (DoY) 279. According to the results, using uniform voxel size for tomography reconstruction in the area leads to missing information in the lower parts of the troposphere. Moreover, we show that combining our method and resolution matrix provides a mathematical tool for deciding on the required compromise between the geometry and dynamics in Global Positioning System (GPS) tomography.