DeepTomo: An Explainable Physics-Informed Deep Learning Framework for Troposphere Tomography, Toward AI-Based GNSS Data Assimilation

Abstract

Accurate representation of atmospheric moisture is essential for reliable weather forecasting, particularly for small-scale convective systems and extreme events. However, determining high-resolution water vapor (WV) fields remains challenging. Conventional global navigation satellite system (GNSS) troposphere tomography reconstructs 4-D atmospheric wet refractivity fields but is limited by sparse and uneven ray paths, an ill-conditioned coefficient matrix, and an ill-posed inverse problem. Stabilization through constraints and regularization may introduce biases, while the low probability of ray–ray intersections in the lowest tropospheric layers reduces observational influence, causing some regions to depend more on background models than observations. To address these limitations, DeepTomo, to the best of the authors’ knowledge, the first artificial intelligence (AI)-based 4-D GNSS troposphere tomography is introduced as an explainable physics-informed deep learning approach that combines hybrid observational constraints with spatiotemporal learning. Beyond tomographic reconstruction, DeepTomo is conceived as an AI-based assimilation of GNSS observations into ERA5 fields; it integrates a 3-D convolutional neural network (CNN) with residual learning and attention mechanisms and employs a hybrid physics-informed loss function that combines GNSS-derived zenith wet delay (ZWD) with radio occultation (RO) and radiosonde refractivity profiles to correct the ERA5 background toward observational constraints. By learning spatiotemporal relationships between observations and background fields, DeepTomo refines wet refractivity estimates and enables physically consistent reconstruction even in voxels with limited observations. Trained and validated over a dense GNSS network in coastal California using a six-month dataset and evaluated against radiosonde and GNSS-derived ZWD data, DeepTomo performs strongly during the extreme weather event of Hurricane Hilary, a tropical cyclone (TC), in August 2023. Compared with conventional voxel-based tomography, it reduces the root mean square error (RMSE) by up to 64.85% during the TC and 41.62% overall, capturing large moisture variability. Explainable AI (XAI) analysis reveals dynamic spatial attention to regions of enhanced variability. A preliminary sensitivity analysis using GraphCast forecasts shows that the moisture corrections introduced by DeepTomo correspond to short-range forecast errors. This analysis provides an initial indication that DeepTomo, by producing physically consistent GNSS-constrained moisture analyses from ERA5 background fields, has the potential to improve initial conditions and forecast performance in next-generation AI weather forecasting systems, such as GraphCast, bridging GNSS observations with AI-based forecast initialization.