Resonant Platform Response and Vertical Velocity Biases in ADCP Measurements from Quasi-Lagrangian Platforms

Andrey Y. Shcherbina , Eric A. D'Asaro

Autonomous surface and subsurface platforms equipped with acoustic Doppler current profilers (ADCPs) are increasingly used to observe ocean velocities, but in the presence of surface waves these measurements can be biased by orbital motion and wave-induced platform tilting. Previous work quantified such biases for idealized platform responses that were in phase with the wave forcing. Here we extend this framework to the general case of a partially resonant platform response, in which the tilt amplitude is enhanced and phase-lagged relative to the waves, as expected for real-world platforms. We derive analytical expressions for wave-induced ADCP biases under arbitrary linear tilt response and show that phase-lagged platform motion generates biases in vertical velocity in addition to previously reported horizontal biases. These vertical biases scale with the imaginary part of the platform tilt transfer function and depend on wave properties, platform depth, and measurement distance. Biases also depend on ADCP beam geometry, alignment with wave propagation, and instrument orientation (upward or downward). Under certain conditions, a five-beam vertical velocity reconstruction can be formed that is unbiased on average and generally outperforms standard four-beam and vertical-beam estimates. The theory is applied to a Lagrangian float whose empirical tilt response suggests partial resonance at short wave periods. Using realistic wind–wave spectra, we quantify the resulting biases and find typical magnitudes of several centimeters per second for horizontal velocities and several millimeters per second for vertical velocities under open-ocean conditions. Because wave-induced biases depend strongly on platform configuration, we provide an analytical framework and numerical tools to assess biases for individual platforms and deployments.