Retrieval of Vertical Doppler Frequency and Deflection of the Vertical from SAR Altimetry via Deep Learning

SDeriving deflection of the vertical (DOV) from satellite altimetry data via the difference quotient method often leads to severe noise amplification as spatial resolution increases, limiting the inversion of high-frequency signals in the marine gravity field. To address this bottleneck, this study proposes a novel algorithm for extracting the Vertical Doppler (V-Doppler) frequency from radar altimetry signals. First, the Fast Fourier Transform (FFT) is employed to transform signals from the time domain to the frequency domain, generating a Delay/Doppler Map (DDM). Second, to mitigate noise interference within the DDM, a Hybrid Deep Learning Edge Extraction (HDLEE) architecture is constructed by leveraging the Segment Anything Model 2 (SAM 2) deep neural network, which significantly improves the accuracy and robustness of V-Doppler extraction. Third, a weighted multi-window calibration algorithm is designed to correct low-frequency systematic bias of V-Doppler frequency by exploiting the stability of the difference quotient method in suppressing low-frequency noise. Finally, using the South Sandwich Trench as a validation area, V-Doppler frequencies are extracted from CryoSat-2, Sentinel-3, and Sentinel-6 observational data on a burst-by-burst basis, and then the along-track DOVs are computed. Compared with the difference quotient method, the proposed V-Doppler algorithm for DOV achieves a remarkable improvement in precision at high spatial resolutions. At a 2 km spatial scale, defined in this study as the along-track averaging scale of the final DOV estimates, the measurement precision of the DOV derived via V-Doppler for CryoSat-2, Sentinel-3, and Sentinel-6 improves by factors of 4.39, 5.27, and 6.57, respectively. Notably, the absolute precision for Sentinel-6 reaches 3.23 μrad. Furthermore, comparisons between the calculated DOV and corresponding values from the EGM2008 model demonstrate good consistency, indicating the potential of the proposed V-Doppler extraction algorithm.