Nuclear norm minimization for gap-filling GNSS precipitable water vapor

Abstract

Abstract

Abstract Continuous precipitable water vapor (PWV) time series derived from Global Navigation Satellite System (GNSS) observations are essential for climate monitoring, numerical weather prediction, and tropospheric modeling, yet data gaps from equipment failures and quality-control filtering remain prevalent. This study investigates Nuclear Norm Minimization (NNM), a convex matrix completion method that recovers missing entries by exploiting the low-rank structure inherent in spatiotemporal PWV fields. Singular value decomposition of PWV matrices constructed from 200 California GNSS stations shows that only 4-6 components explain over 95 % of the total variance, indicating that the low-rank assumption central to NNM is well satisfied in dense networks. NNM reconstructs missing PWV values by jointly exploiting temporal continuity and spatial coherence among neighboring stations through an alternating direction method of multipliers (ADMM) solver. Cross-validation over 174 stations during 2011-2020 yields a mean root-mean-square error (RMSE) of 1.05 mm (median 0.98 mm, bootstrap standard deviation 0.15 mm), compared with 1.53 mm for ERA5 reanalysis. Independent validation against radiosonde observations at four co-located stations shows that the RMSE between radiosonde and NNM-filled values (0.95-1.47 mm) is consistent with the baseline GNSS-radiosonde RMSE, indicating that gap-filling preserves the original data consistency. A station-spacing degradation experiment shows that NNM effectiveness depends critically on interstation distance: networks with spacing below approximately 100 km maintain high accuracy even for gaps exceeding 180 days, whereas ERA5 becomes competitive when spacing exceeds 200 km.