Cross–Spectrum–Based Shallow Water Retrieval Using High–Resolution C–Band Miniaturized SAR Satellites

Topographic and geomorphic information provides an essential basis for human development and utilization of natural resources, disaster prevention and mitigation, ecological environment protection, and scientific research. Among spaceborne remote sensing approaches, Synthetic Aperture Radar (SAR) stands out due to its ability to actively transmit and receive microwave signals, enabling high spatial coverage, all–weather, and all–day observation. With the rapid development of miniaturized satellite constellations, high–revisit and high–resolution SAR data have become more accessible, offering unprecedented opportunities for dynamic ocean observation. However, existing SAR–based bathymetry methods based on power–spectrum analysis are susceptible to sea–spike noise and 180° directional ambiguity, limiting their accuracy in shallow coastal waters. To address these limitations, a Cross–Spectrum–based Wave Ray Tracking bathymetry retrieval algorithm (CS–WRT) is developed using high–resolution imagery from mini–SAR constellations including HiSea–1 and Chaohu–1. The method incorporates cross–spectrum analysis into a localized wave ray tracking framework to effectively suppress sea–spike noise and accurately extract shallow–water wave vectors. Applied to six SAR images over the Taiwan Strait, CS–WRT consistently outperformed the power–spectrum approach in coastal environments. In the Jinjiang coastal region, comparison with Electronic Navigational Chart (ENC) data yielded a root mean square error of 2.22 m, a mean absolute percentage error of 7.06%, and a Pearson correlation coefficient of 0.84. Analysis of the shoaling slope parameter k further revealed that stronger wave shoaling effects correlate with improved retrieval accuracy, suggesting its potential as a diagnostic indicator of retrieval reliability.