Optimizing GNSS Tomographic Node Distribution Using Signal Geometry for Enhanced Tropospheric Sensing

Global Navigation Satellite Systems (GNSS) are a powerful tool for high-resolution tropospheric sensing, offering valuable data for weather forecasting and climate monitoring. One of the key techniques for estimating three-dimensional fields of humidity-related parameters in the troposphere using GNSS data is tomography. Recent studies revealed its potential for application in data assimilation into numerical weather prediction models. However, the accuracy of the tomographic models depends heavily on the approach to the distribution of the tomographic nodes. Traditionally, the nodes are placed on a regular grid, without accounting for the uneven distribution of GNSS signal information in the troposphere, which often leads to suboptimal results.

 

In this study, we propose a novel approach to optimize the spatial arrangement of tomographic nodes, based on the geometry of the GNSS signals and the non-uniformity of the information they provide. The proposed algorithm is based on four steps to define the optimal arrangement of the tomographic nodes: 1) selecting the most valuable GNSS signals in terms of geometry (those that cross with other signals), 2) identification of the intersection spots, 3) cluster analysis of the defined intersections using DBSCAN algorithm, 4) introducing regularly-distributed nodes in the locations with lower-density of the GNSS signals to increase stability of the model. The final solution is performed using a node-based parameterization approach with interpolation of wet refractivity based on natural cubic splines. To evaluate the effectiveness of the optimized node distribution, we compare the performance of our approach with that of three conventional parameterization methods (both voxel-based and node-based with trilinear and spline-based interpolation), using cross-validation based on outputs from the Weather Research and Forecasting (WRF) model and radiosonde observations. The methodology was tested in an urban area, using zenith tropospheric delay estimates from a dense network of 16 low-cost multi-GNSS receivers located in Wrocław, Poland, with an average inter-receiver distance of 3 km.

 

The results show that the optimized node placement improves the accuracy of wet refractivity estimation, with a reduction in RMSE of 0.5–2 ppm, especially in the altitude range of 0.5–2.0 km. The proposed solution gave the best results compared to the other parameterization approaches (both voxel-based and node-based). The largest impact was noticed in the areas where the highest number of the GNSS signals’ intersections occurred. This study highlights the importance of considering the geometry of GNSS signals when designing tomographic networks and suggests that optimizing node distribution is a promising avenue for future research in GNSS-based tropospheric sensing.