Data from: The motion and tilts of subsurface floats due to surface waves

Subsurface and nearly neutrally-buoyant floats can be stable, well-behaved
platforms for measuring ocean dynamics in the near-surface wave zone. In
this work, we measure and model the wave-induced tilt of one such platform
with the goal of understanding how to best optimize velocity measurements
in the upper ocean from floats. We use data from Lagrangian floats built
at APL/UW (Applied Physics Laboratory) and carrying a Nortek Signature1000
acoustic Doppler current profiler with an AHRS (Attitude and Heading
Reference System). We analyze carefully chosen data segments where the
wave-induced tilts are measurable yet small, and the float does not rotate
significantly. We adopt a two-dimensional, depth-downwave coordinate
system and assume small tilts and linear surface wave dynamics. By
combining the constraints due to geometry, a wave-following float, and
wave dynamics, we link measurements of both linear and angular
acceleration to measure the tilts to an accuracy of a few tenths of a
degree and simultaneously show that the data is consistent with the
analysis assumptions. This analysis is further vetted by swinging the AHRS
on pendulums in the laboratory. The same tests disturbingly indicate that
the AHRS attitude readings can have large errors for tilts larger than a
few degrees. The wave-induced tilt of the floats is predicted to an
accuracy of about 10\% from the wave properties by a 3-parameter linear
semi-empirical model calibrated with field data. The waves force tilt
through their horizontal acceleration and through their strain exerting
torques on the float. These floats are a somewhat underdamped oscillator
(Quality Factor=3, resonance at 3 second period) and will exhibit a
decaying oscillation of a few cycles when perturbed. This archive contains
the data and programs necessary to reproduce the analysis described above.