Outlier Correction in Remote Sensing Retrieval of Ocean Wave Wavelength and Application to Bathymetry

The extraction of ocean wave wavelengths from optical imagery via Fast Fourier Transform (FFT) exhibits significant potential for Wave-Derived Bathymetry (WDB). However, in practical applications, this method frequently produces anomalously large wavelength estimates. To date, there has been insufficient exploration into the mechanisms underlying image spectral leakage to low wavenumbers and its suppression strategies. This study investigates three plausible mechanisms contributing to spectral leakage in optical images and proposes a subimage-based preprocessing framework: prior to executing two-dimensional FFT, the remote sensing subimages employed for wavelength inversion undergo three sequential steps: (1) truncation of distorted pixel values using a Gaussian mixture model; (2) application of a polynomial detrending surface; (3) incorporation of a two-dimensional Hann window. Subsequently, the dominant wavenumber peak is localized in the power spectrum and converted to wavelength values. Water depth is then inverted using the linear dispersion equation, combined with wave periods derived from ERA5. Taking 2 m-resolution WorldView-2 imagery of Sanya Bay, China as a case study, 1024 m subimages are utilized, with validation conducted against chart-sounding data. Results demonstrate that the proportion of subimages with anomalous wavelengths is reduced from 18.9% to 3.3% (in contrast to 14.0%, 7.8%, and 16.6% when the three preprocessing steps are applied individually). Within the 0–20 m depth range, the water depth retrieval accuracy achieves a Mean Absolute Error (MAE) of 1.79 m; for the 20–40 m range, the MAE is 6.38 m. A sensitivity analysis of subimage sizes (512/1024/2048 m) reveals that the 1024 m subimage offers an optimal balance between accuracy and coverage. However, residual anomalous wavelengths persist in near-shore subimages, and errors still increase with increasing water depth. This method is both concise and effective, rendering it suitable for application in shallow-water WDB scenarios.