GNSS and InSAR based water vapor tomography: A Compressive Sensing solution

An accurate knowledge of the three-dimensional (3D) distribution of water vapor in the atmosphere is a key element for weather forecasting and climate research. In addition, a precise determination of water vapor is also required for accurate positioning and deformation monitoring using Global Navigation Satellite Systems (GNSS) and Interferometric Synthetic Aperture Radar (InSAR). Several approaches for 3D tomographic water vapor reconstruction from GNSS-based Slant Wet Delay (SWD) estimates exist. Yet, due to the usually sparsely distributed GNSS sites and due to the limited number of visible GNSS satellites, the tomographic system usually is ill-posed and needs to be regularized, e.g. by means of geometric constraints that risk to over-smooth the tomographic refractivity estimates. Therefore, this work develops and analyzes a Compressive Sensing (CS) approach for neutrospheric water vapor tomographies benefiting of the sparsity of the refractivity estimates in an appropriate transform domain as a prior for regularization. The CS solution is developed because it does not include any geometric smoothing constraints as applied in common Least Squares (LSQ) approaches and because the sparse CS solution containing only a few non-zero coefficients may be determined, at a constant number of observations, based on less parameters than the corresponding LSQ solution. In addition to the developed CS solution, this work introduces SWDs obtained from both GNSS and InSAR into the tomographic system in order to dispose of a better spatial distribution of the observations. The novelties of this approach are 1) the use of both absolute GNSS and absolute InSAR SWDs for tomography and 2) the solution of the tomographic system by means of Compressive Sensing. In addition, 3) the quality of the CS reconstruction is compared with the quality of common LSQ approaches to water vapor tomography. The tomographic reconstruction is performed, on the one hand, based on a real data set using GNSS and InSAR SWDs and, on the other hand, based on three different synthetic SWD data sets generated using wet refractivity information from the Weather Research and Forecasting (WRF) model. Thus, the validation of the achieved results focuses, on the one hand, on radiosonde profiles and, on the other hand, on a comparison of the refractivity estimates with the input WRF refractivities. The real data set resp. the first synthetic data set compares the reconstruction quality of the developed CS approach with LSQ approaches to water vapor tomography and investigates in how far the inclusion of InSAR resp. synthetic InSAR SWDs increases the accuracy and precision of the refractivity estimates. The second synthetic data set is designed in order to analyze the general effect of the observing geometry on the quality of the refractivity estimates. The third synthetic data set places a special focus on the sensibility of the tomographic reconstruction to different numbers of GNSS sites, varying voxel discretization, and different orbit constellations. In case of the real data set, for both the GNSS only solution and a combined GNSS and InSAR solution, the refractivities estimated by means of the LSQ and CS methodologies show a consistent behavior, although the two solution strategies differ. The synthetic data sets show that CS can yield very precise and accurate results, if an appropriate tomographic setting is chosen. The reconstruction quality mainly depends on i) the accuracy of the functional model relating the SWD estimates to the refractivity parameters and to the distances passed by the rays within the voxels, ii) the number of available GNSS sites, iii) the voxel discretization, and iv) the variety of ray directions introduced into the tomographic system. The sizes of the study areas associated to the real resp. to the synthetic data sets are about 120 × 120 km2 and about 100 × 100 km2, respectively. In the real data set, a total of eight GNSS sites is available and SWD estimates of GPS and InSAR are introduced. In the synthetic data sets, different numbers of sites are defined and a variety of ray directions is tested