Gap-free GNSS-R Wind Field Reconstruction Using a Physics-Informed 4DVarNet Scheme

Spaceborne Global Navigation Satellite System Reflectometry (GNSS-R) has emerged as a new technique for ocean wind speed retrieval, offering unprecedented temporal resolution and all-weather capacity. However, the track-wise sampling of current GNSS-R missions leads to substantial spatial and temporal gaps in gridded wind fields. In this study, we apply a physics-informed 4DVarNet scheme to reconstruct gap-free ocean surface wind fields from Cyclone GNSS (CYGNSS) observations. This end-to-end scheme operates by following the four-dimensional variational (4DVar) data assimilation principle, where a dynamic prior model provides state forecasts, and a gradient solver minimizes the 4DVar loss function. Both parts are implemented through physics-informed neural networks, i.e., a bilinear autoencoder, and a convolutional Long-Short-Term Memory (LSTM) network, respectively, which are trained using European Center for Medium-Range Weather (ECMWF) ERA5 hourly 10-meter ocean wind products as reference. NOAA CYGNSS Version 1.2 level 2 (L2) wind speed retrieval products from 2018-2022 were gridded at 0.25° spatial resolution and 1-hour, 3-hour, and 6-hour temporal resolutions over the western North Pacific (0-37°N, 100°-160°E). Validation using independent 2021 data shows that the reconstructed wind fields achieve RMSEs of 1.13 m/s, 1.16 m/s, and 1.24 m/s relative to ERA5 winds, and 1.40 m/s, 1.41 m/s, and 1.48 m/s relative to Advanced Microwave Scanning Radiometer-2 all-weather winds, for the 1-hour, 3-hour, and 6-hour gridded products, respectively. Furthermore, 3-hour results show a better performance for wind speeds larger than 20 m/s, indicating a better tradeoff between the number of grids with available GNSS-R observables in each map (coverage rate) and a enough data frequency to capture the temporal variations. The interpolation error of the developed 4DVarNet model shows a strong dependence on coverage rate, with a correlation coefficient of -0.849 after applying a 7-day rolling average. Error discrepancies between GNSS-R and ERA5 reconstructed winds could contribute to recalibrating GNSS-R observables or improving the ECMWF forecasting model. Case studies demonstrate the capability of the reconstructed fields to capture tropical cyclone coverage and evolution. For Super Typhoon Surigae in 2021, the peak intensity derived from GNSS-R reconstructions is temporally consistent with International Best Track Archive for Climate Stewardship (IBTrACS) records, while ERA5 data exhibit a two-day delay. For Tropical Storm Kompasu in 2021, pronounced wind asymmetries and a well-defined eye structure were detected. In the storm-centric coordinate, the maximum wind occurs in the northeast quadrant with a radius of 587.5 km, approximately 38% larger than that in the northwest quadrant on 2021-10-09 06:00 UTC. Despite these encouraging results, the reconstructed products still exhibit track-wise artifacts, high-wind underestimation, and limited uncertainty characterization. However, these results demonstrate the great potential of 4DVarNet in gap filling and data assimilation. Future work will integrate additional GNSS-R missions, including Fengyun-3, Tianmu-1, and recently launched ESA HydroGNSS, and develop tropical cyclone specific models using complementary high-wind reference datasets to further improve coverage and accuracy.