Accuracy of bathymetry and current retrievals from airborne optical time-series imaging of shoaling waves

A sequence of visual images of shoaling ocean waves collected from an aircraft can be used to retrieve maps of water depth and/or currents. The data are mapped to rectilinear coordinates on the mean ocean surface, and three-dimensional (3D) cubes of these data (typically 2-min dwell and 256 m × 256 m square area) are Fourier transformed to provide the 3D frequency-wavenumber spectrum of the modulations. The spectrum is fitted by the theoretical two-dimensional dispersion surface for linear gravity waves, with the depth and current vector as free parameters, and the errors determined by comparison with simultaneously collected in situ data. Very little attention has been focused on the limitations and inherent errors in this approach for retrieving these parameters in the past. This paper examines the dependence of these errors upon various instrumental and collection geometry parameters in order to estimate the achievable retrieval accuracy and provide collection guidelines. Significant errors occur when the mapping is inaccurate and when the data cubes are too small either spatially or temporally. Data cubes of the size given above, or larger, are required to contain the relative errors within 5% to 10% of the ground truth values. The spatial resolution and temporal sampling rate are less critical, and pixel sizes of ∼3-4 m and framing rates of ∼0.5 Hz for depth and 1-2 Hz for currents are sufficient for providing adequate results with the data examined here. Finally, we show that the covariance matrix from the functional fit provides a quantitative measure of the retrieval accuracy, independent of in situ data.